TSTP Solution File: SWW626_2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW626_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.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 : Fri Sep 1 00:50:56 EDT 2023
% Result : Theorem 23.02s 4.06s
% Output : Proof 33.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWW626_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.09/0.35 % Computer : n032.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8042.1875MB
% 0.09/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Aug 27 22:24:15 EDT 2023
% 0.09/0.35 % CPUTime :
% 0.15/0.63 ________ _____
% 0.15/0.63 ___ __ \_________(_)________________________________
% 0.15/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.15/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.15/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.15/0.63
% 0.15/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.15/0.63 (2023-06-19)
% 0.15/0.63
% 0.15/0.63 (c) Philipp Rümmer, 2009-2023
% 0.15/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.15/0.63 Amanda Stjerna.
% 0.15/0.63 Free software under BSD-3-Clause.
% 0.15/0.63
% 0.15/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.15/0.63
% 0.15/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.15/0.65 Running up to 7 provers in parallel.
% 0.15/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.15/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.15/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.15/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.15/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.15/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.15/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 6.30/1.73 Prover 1: Preprocessing ...
% 6.30/1.73 Prover 4: Preprocessing ...
% 6.30/1.74 Prover 5: Preprocessing ...
% 6.30/1.74 Prover 3: Preprocessing ...
% 6.30/1.74 Prover 0: Preprocessing ...
% 6.30/1.75 Prover 6: Preprocessing ...
% 6.30/1.75 Prover 2: Preprocessing ...
% 15.73/3.03 Prover 1: Warning: ignoring some quantifiers
% 16.39/3.14 Prover 4: Warning: ignoring some quantifiers
% 17.00/3.24 Prover 1: Constructing countermodel ...
% 17.00/3.25 Prover 6: Proving ...
% 17.00/3.26 Prover 3: Warning: ignoring some quantifiers
% 17.00/3.27 Prover 4: Constructing countermodel ...
% 17.77/3.29 Prover 5: Proving ...
% 17.77/3.31 Prover 0: Proving ...
% 17.99/3.34 Prover 3: Constructing countermodel ...
% 17.99/3.57 Prover 2: Proving ...
% 23.02/4.05 Prover 3: proved (3367ms)
% 23.02/4.05
% 23.02/4.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.02/4.06
% 23.02/4.06 Prover 0: stopped
% 23.02/4.06 Prover 6: stopped
% 23.02/4.07 Prover 5: stopped
% 23.02/4.11 Prover 2: stopped
% 23.60/4.13 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 23.60/4.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 23.60/4.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 23.60/4.13 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 23.60/4.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.68/4.44 Prover 13: Preprocessing ...
% 25.15/4.50 Prover 7: Preprocessing ...
% 26.60/4.53 Prover 8: Preprocessing ...
% 26.60/4.55 Prover 11: Preprocessing ...
% 26.83/4.56 Prover 10: Preprocessing ...
% 29.04/4.92 Prover 10: Warning: ignoring some quantifiers
% 29.95/5.00 Prover 8: Warning: ignoring some quantifiers
% 29.95/5.03 Prover 10: Constructing countermodel ...
% 29.95/5.06 Prover 7: Warning: ignoring some quantifiers
% 29.95/5.09 Prover 8: Constructing countermodel ...
% 29.95/5.14 Prover 7: Constructing countermodel ...
% 29.95/5.19 Prover 13: Warning: ignoring some quantifiers
% 29.95/5.26 Prover 11: Warning: ignoring some quantifiers
% 30.89/5.30 Prover 13: Constructing countermodel ...
% 30.89/5.30 Prover 1: Found proof (size 96)
% 30.89/5.30 Prover 1: proved (4644ms)
% 30.89/5.31 Prover 4: stopped
% 32.29/5.31 Prover 8: stopped
% 32.29/5.31 Prover 7: stopped
% 32.29/5.31 Prover 11: Constructing countermodel ...
% 32.29/5.31 Prover 10: stopped
% 32.29/5.33 Prover 11: stopped
% 32.29/5.34 Prover 13: stopped
% 32.29/5.34
% 32.29/5.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.29/5.34
% 32.59/5.36 % SZS output start Proof for theBenchmark
% 32.59/5.37 Assumptions after simplification:
% 32.59/5.37 ---------------------------------
% 32.59/5.37
% 32.59/5.37 (append_assoc)
% 32.59/5.39 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : !
% 32.59/5.39 [v5: uni] : ( ~ (infix_plpl(v0, v4, v3) = v5) | ~ (infix_plpl(v0, v1, v2) =
% 32.59/5.39 v4) | ~ ty(v0) | ~ uni(v3) | ~ uni(v2) | ~ uni(v1) | ? [v6: uni] :
% 32.59/5.39 (infix_plpl(v0, v2, v3) = v6 & infix_plpl(v0, v1, v6) = v5 & uni(v6) &
% 32.59/5.39 uni(v5)))
% 32.59/5.39
% 32.59/5.39 (bridgeR)
% 32.59/5.39 ! [v0: uni] : ! [v1: list_elt] : ( ~ (tb2t(v0) = v1) | ~ uni(v0) | t2tb(v1)
% 32.59/5.39 = v0)
% 32.59/5.39
% 32.59/5.39 (infix_plpl_def)
% 32.59/5.39 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : !
% 32.59/5.39 [v5: uni] : ( ~ (infix_plpl(v0, v4, v1) = v5) | ~ (cons(v0, v2, v3) = v4) |
% 32.59/5.39 ~ ty(v0) | ~ uni(v3) | ~ uni(v2) | ~ uni(v1) | ? [v6: uni] :
% 32.59/5.39 (infix_plpl(v0, v3, v1) = v6 & cons(v0, v2, v6) = v5 & uni(v6) & uni(v5))) &
% 32.59/5.39 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : (v3 = v1 | ~
% 32.59/5.39 (infix_plpl(v0, v2, v1) = v3) | ~ (nil(v0) = v2) | ~ ty(v0) | ~ uni(v1))
% 32.59/5.39
% 32.59/5.39 (length_nil)
% 32.59/5.40 ! [v0: ty] : ! [v1: uni] : ! [v2: int] : (v2 = 0 | ~ (length(v0, v1) = v2)
% 32.59/5.40 | ~ ty(v0) | ~ uni(v1) | ? [v3: uni] : ( ~ (v3 = v1) & nil(v0) = v3 &
% 32.59/5.40 uni(v3))) & ! [v0: ty] : ! [v1: uni] : ( ~ (length(v0, v1) = 0) | ~
% 32.59/5.40 ty(v0) | ~ uni(v1) | nil(v0) = v1)
% 32.59/5.40
% 32.59/5.40 (permut_append)
% 32.59/5.40 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : !
% 32.59/5.40 [v5: uni] : ! [v6: uni] : ! [v7: int] : (v7 = 0 | ~ (permut(v0, v5, v6) =
% 32.59/5.40 v7) | ~ (infix_plpl(v0, v3, v4) = v6) | ~ (infix_plpl(v0, v1, v2) = v5)
% 32.59/5.40 | ~ ty(v0) | ~ uni(v4) | ~ uni(v3) | ~ uni(v2) | ~ uni(v1) | ? [v8:
% 32.59/5.40 any] : ? [v9: any] : (permut(v0, v2, v4) = v9 & permut(v0, v1, v3) = v8 &
% 32.59/5.40 ( ~ (v9 = 0) | ~ (v8 = 0))))
% 32.59/5.40
% 32.59/5.40 (permut_length)
% 32.59/5.40 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ( ~ (permut(v0, v1, v2) = 0) | ~
% 32.59/5.40 ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v3: int] : (length(v0, v2) = v3 &
% 32.59/5.40 length(v0, v1) = v3))
% 32.59/5.40
% 32.59/5.40 (permut_trans)
% 32.59/5.40 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: int] : (v4
% 32.59/5.40 = 0 | ~ (permut(v0, v1, v3) = v4) | ~ (permut(v0, v1, v2) = 0) | ~ ty(v0)
% 32.59/5.40 | ~ uni(v3) | ~ uni(v2) | ~ uni(v1) | ? [v5: int] : ( ~ (v5 = 0) &
% 32.59/5.40 permut(v0, v2, v3) = v5))
% 32.59/5.40
% 32.59/5.40 (prefix_length)
% 32.59/5.40 ! [v0: ty] : ! [v1: int] : ! [v2: uni] : ! [v3: uni] : ! [v4: int] : (v4
% 32.59/5.40 = v1 | ~ ($lesseq(0, v1)) | ~ (prefix(v0, v1, v2) = v3) | ~ (length(v0,
% 32.59/5.40 v3) = v4) | ~ ty(v0) | ~ uni(v2) | ? [v5: int] : ($lesseq(1,
% 32.59/5.40 $difference(v1, v5)) & length(v0, v2) = v5))
% 32.59/5.40
% 32.59/5.40 (sorted_Nil)
% 32.59/5.41 ty(elt1) & ? [v0: uni] : ? [v1: list_elt] : (sorted(v1) = 0 & tb2t(v0) = v1
% 32.59/5.41 & nil(elt1) = v0 & list_elt(v1) & uni(v0))
% 32.59/5.41
% 32.59/5.41 (sorted_One)
% 32.59/5.41 ty(elt1) & ? [v0: uni] : (nil(elt1) = v0 & uni(v0) & ! [v1: elt] : ! [v2:
% 32.59/5.41 uni] : ( ~ (t2tb1(v1) = v2) | ~ elt(v1) | ? [v3: uni] : ? [v4:
% 32.59/5.41 list_elt] : (sorted(v4) = 0 & tb2t(v3) = v4 & cons(elt1, v2, v0) = v3 &
% 32.59/5.41 list_elt(v4) & uni(v3))))
% 32.59/5.41
% 32.59/5.41 (sorted_inversion)
% 32.59/5.41 ty(elt1) & ? [v0: uni] : ? [v1: list_elt] : (tb2t(v0) = v1 & nil(elt1) = v0
% 32.59/5.41 & list_elt(v1) & uni(v0) & ! [v2: list_elt] : (v2 = v1 | ~ (sorted(v2) =
% 32.59/5.41 0) | ~ list_elt(v2) | ? [v3: elt] : ? [v4: elt] : ? [v5: list_elt] :
% 32.59/5.41 ? [v6: uni] : ? [v7: uni] : ? [v8: uni] : ? [v9: list_elt] : ? [v10:
% 32.59/5.41 uni] : ? [v11: uni] : (t2tb1(v4) = v6 & t2tb1(v3) = v10 & sorted(v9) =
% 32.59/5.41 0 & tb2t(v11) = v2 & tb2t(v8) = v9 & t2tb(v5) = v7 & le(v3, v4) = 0 &
% 32.59/5.41 cons(elt1, v10, v8) = v11 & cons(elt1, v6, v7) = v8 & list_elt(v9) &
% 32.59/5.41 list_elt(v5) & elt(v4) & elt(v3) & uni(v11) & uni(v10) & uni(v8) &
% 32.59/5.41 uni(v7) & uni(v6)) | ? [v3: elt] : ? [v4: uni] : ? [v5: uni] :
% 32.59/5.41 (t2tb1(v3) = v4 & tb2t(v5) = v2 & cons(elt1, v4, v0) = v5 & elt(v3) &
% 32.59/5.41 uni(v5) & uni(v4))))
% 32.59/5.41
% 32.59/5.41 (wP_parameter_rev_sort)
% 32.59/5.42 ty(elt1) & ? [v0: uni] : ? [v1: uni] : ? [v2: list_elt] : ? [v3: any] :
% 32.59/5.42 (sorted(v2) = v3 & tb2t(v1) = v2 & reverse(elt1, v0) = v1 & nil(elt1) = v0 &
% 32.59/5.42 list_elt(v2) & uni(v1) & uni(v0) & ? [v4: int] : ? [v5: list_elt] : ?
% 32.59/5.42 [v6: uni] : ? [v7: int] : ? [v8: int] : ? [v9: uni] : ? [v10: uni] : ?
% 32.59/5.42 [v11: list_elt] : ($lesseq(v8, v7) & $lesseq(0, v8) & $lesseq(v4, v7) &
% 32.59/5.42 $lesseq(4, v4) & div(v4, 2) = v8 & prefix(elt1, v8, v6) = v9 &
% 32.59/5.42 prefix(elt1, v4, v6) = v10 & tb2t(v10) = v11 & t2tb(v5) = v6 &
% 32.59/5.42 length(elt1, v6) = v7 & list_elt(v11) & list_elt(v5) & uni(v10) & uni(v9)
% 32.59/5.42 & uni(v6) & ? [v12: list_elt] : ? [v13: uni] : ? [v14: uni] : ? [v15:
% 32.59/5.42 uni] : ? [v16: uni] : ? [v17: int] : ($lesseq(2, v8) & prefix(elt1,
% 32.59/5.42 $difference(v4, v8), v13) = v15 & tb2t(v16) = v11 & tb2t(v14) = v5 &
% 32.59/5.42 t2tb(v12) = v13 & infix_plpl(elt1, v9, v15) = v16 & infix_plpl(elt1, v9,
% 32.59/5.42 v13) = v14 & length(elt1, v13) = v17 & list_elt(v12) & uni(v16) &
% 32.59/5.42 uni(v15) & uni(v14) & uni(v13) & ? [v18: list_elt] : ? [v19: uni] : ?
% 32.59/5.42 [v20: uni] : ($lesseq(v4, $sum(v17, v8)) & $lesseq(2, $difference(v4,
% 32.59/5.42 v8)) & sorted(v18) = 0 & t2tb(v18) = v19 & permut(elt1, v19, v9) =
% 32.59/5.42 0 & infix_plpl(elt1, v0, v19) = v20 & list_elt(v18) & uni(v20) &
% 32.59/5.42 uni(v19) & ? [v21: list_elt] : ? [v22: uni] : ? [v23: uni] : (v3 =
% 32.59/5.42 0 & sorted(v21) = 0 & t2tb(v21) = v22 & permut(elt1, v22, v15) = 0 &
% 32.59/5.42 infix_plpl(elt1, v20, v22) = v23 & list_elt(v21) & uni(v23) &
% 32.59/5.42 uni(v22) & ! [v24: elt] : ! [v25: elt] : ! [v26: uni] : ! [v27:
% 32.59/5.42 uni] : ( ~ (t2tb1(v25) = v27) | ~ (t2tb1(v24) = v26) | ~
% 32.59/5.42 (mem(elt1, v27, v22) = 0) | ~ elt(v25) | ~ elt(v24) | ? [v28:
% 32.59/5.42 any] : ? [v29: any] : (le(v24, v25) = v29 & mem(elt1, v26, v0)
% 32.59/5.42 = v28 & ( ~ (v28 = 0) | v29 = 0))) & ! [v24: elt] : ! [v25:
% 32.59/5.42 elt] : ! [v26: uni] : ! [v27: uni] : ( ~ (t2tb1(v25) = v27) | ~
% 32.59/5.42 (t2tb1(v24) = v26) | ~ (mem(elt1, v27, v19) = 0) | ~ elt(v25) |
% 32.59/5.42 ~ elt(v24) | ? [v28: any] : ? [v29: any] : (le(v24, v25) = v29 &
% 32.59/5.42 mem(elt1, v26, v0) = v28 & ( ~ (v28 = 0) | v29 = 0))) & ? [v24:
% 32.59/5.42 list_elt] : ? [v25: uni] : ? [v26: uni] : ? [v27: list_elt] :
% 32.59/5.42 ? [v28: int] : ( ~ (v28 = 0) & sorted(v27) = 0 & tb2t(v26) = v27 &
% 32.59/5.42 t2tb(v24) = v25 & permut(elt1, v25, v23) = 0 & permut(elt1, v25,
% 32.59/5.42 v10) = v28 & reverse(elt1, v25) = v26 & list_elt(v27) &
% 32.59/5.42 list_elt(v24) & uni(v26) & uni(v25)))))))
% 32.59/5.42
% 32.59/5.42 (function-axioms)
% 32.59/5.43 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : !
% 32.59/5.43 [v5: ty] : ! [v6: ty] : (v1 = v0 | ~ (match_list(v6, v5, v4, v3, v2) = v1) |
% 32.59/5.43 ~ (match_list(v6, v5, v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : !
% 32.59/5.43 [v2: uni] : ! [v3: uni] : ! [v4: bool] : ! [v5: ty] : (v1 = v0 | ~
% 32.59/5.43 (match_bool(v5, v4, v3, v2) = v1) | ~ (match_bool(v5, v4, v3, v2) = v0)) &
% 32.59/5.43 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: ty] : (v1 =
% 32.59/5.43 v0 | ~ (prefix(v4, v3, v2) = v1) | ~ (prefix(v4, v3, v2) = v0)) & ! [v0:
% 32.59/5.43 uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : (v1 = v0 |
% 32.59/5.43 ~ (rev_append(v4, v3, v2) = v1) | ~ (rev_append(v4, v3, v2) = v0)) & !
% 32.59/5.43 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: uni] : ! [v3:
% 32.59/5.43 uni] : ! [v4: ty] : (v1 = v0 | ~ (permut(v4, v3, v2) = v1) | ~
% 32.59/5.43 (permut(v4, v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: uni] : !
% 32.59/5.43 [v3: uni] : ! [v4: ty] : (v1 = v0 | ~ (num_occ(v4, v3, v2) = v1) | ~
% 32.59/5.43 (num_occ(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 32.59/5.43 MultipleValueBool] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : (v1 = v0 |
% 32.59/5.43 ~ (mem(v4, v3, v2) = v1) | ~ (mem(v4, v3, v2) = v0)) & ! [v0: uni] : !
% 32.59/5.43 [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : (v1 = v0 | ~
% 32.59/5.43 (infix_plpl(v4, v3, v2) = v1) | ~ (infix_plpl(v4, v3, v2) = v0)) & ! [v0:
% 32.59/5.43 uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : (v1 = v0 |
% 32.59/5.43 ~ (cons(v4, v3, v2) = v1) | ~ (cons(v4, v3, v2) = v0)) & ! [v0: int] : !
% 32.59/5.43 [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~ (mod(v3, v2) = v1) |
% 32.59/5.43 ~ (mod(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3:
% 32.59/5.43 int] : (v1 = v0 | ~ (div(v3, v2) = v1) | ~ (div(v3, v2) = v0)) & ! [v0:
% 32.59/5.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: elt] : ! [v3:
% 32.59/5.43 elt] : (v1 = v0 | ~ (le(v3, v2) = v1) | ~ (le(v3, v2) = v0)) & ! [v0:
% 32.59/5.43 uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~
% 32.59/5.43 (reverse(v3, v2) = v1) | ~ (reverse(v3, v2) = v0)) & ! [v0: int] : ! [v1:
% 32.59/5.43 int] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (length(v3, v2) = v1) | ~
% 32.59/5.43 (length(v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : !
% 32.59/5.43 [v3: ty] : (v1 = v0 | ~ (cons_proj_2(v3, v2) = v1) | ~ (cons_proj_2(v3, v2)
% 32.59/5.43 = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 =
% 32.59/5.43 v0 | ~ (cons_proj_1(v3, v2) = v1) | ~ (cons_proj_1(v3, v2) = v0)) & !
% 32.59/5.43 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: uni] : ! [v3:
% 32.59/5.43 ty] : (v1 = v0 | ~ (sort(v3, v2) = v1) | ~ (sort(v3, v2) = v0)) & ! [v0:
% 32.59/5.43 int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (abs(v2) = v1) | ~
% 32.59/5.43 (abs(v2) = v0)) & ! [v0: elt] : ! [v1: elt] : ! [v2: uni] : (v1 = v0 | ~
% 32.59/5.43 (tb2t1(v2) = v1) | ~ (tb2t1(v2) = v0)) & ! [v0: uni] : ! [v1: uni] : !
% 32.59/5.43 [v2: elt] : (v1 = v0 | ~ (t2tb1(v2) = v1) | ~ (t2tb1(v2) = v0)) & ! [v0:
% 32.59/5.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: list_elt] : (v1 =
% 32.59/5.43 v0 | ~ (sorted(v2) = v1) | ~ (sorted(v2) = v0)) & ! [v0: list_elt] : !
% 32.59/5.43 [v1: list_elt] : ! [v2: uni] : (v1 = v0 | ~ (tb2t(v2) = v1) | ~ (tb2t(v2) =
% 32.59/5.43 v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: list_elt] : (v1 = v0 | ~
% 32.59/5.43 (t2tb(v2) = v1) | ~ (t2tb(v2) = v0)) & ! [v0: ty] : ! [v1: ty] : ! [v2:
% 32.59/5.43 ty] : (v1 = v0 | ~ (list(v2) = v1) | ~ (list(v2) = v0)) & ! [v0: uni] :
% 32.59/5.43 ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~ (nil(v2) = v1) | ~ (nil(v2) = v0))
% 32.59/5.43 & ! [v0: uni] : ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~ (witness(v2) = v1)
% 32.59/5.43 | ~ (witness(v2) = v0))
% 32.59/5.43
% 32.59/5.43 Further assumptions not needed in the proof:
% 32.59/5.43 --------------------------------------------
% 32.59/5.43 abs_def, abs_le, abs_pos, append_Num_Occ, append_l_nil, append_length,
% 32.59/5.43 bool_inversion, bridgeL, bridgeL1, bridgeR1, compatOrderMult, cons_proj_1_def,
% 32.59/5.43 cons_proj_1_sort, cons_proj_2_def, cons_proj_2_sort, cons_sort, div_1,
% 32.59/5.43 div_bound, div_inf, div_mod, div_mult, div_sign_neg, div_sign_pos,
% 32.59/5.43 infix_plpl_sort, length_def, length_nonnegative, list_inversion,
% 32.59/5.43 match_bool_False, match_bool_True, match_bool_sort, match_list_Cons,
% 32.59/5.43 match_list_Nil, match_list_sort, mem_Num_Occ, mem_append, mem_decomp, mem_def,
% 32.59/5.43 mod_1, mod_bound, mod_inf, mod_mult, mod_sign_neg, mod_sign_pos, nil_Cons,
% 32.59/5.43 nil_sort, num_occ_def, permut_append_swap, permut_assoc, permut_cons,
% 32.59/5.43 permut_cons_append, permut_def, permut_mem, permut_refl, permut_swap,
% 32.59/5.43 permut_sym, prefix_append, prefix_def1, prefix_def2, prefix_sort, refl,
% 32.59/5.43 rev_append_append_l, rev_append_append_r, rev_append_def, rev_append_def1,
% 32.59/5.43 rev_append_length, rev_append_sort, reverse_append, reverse_cons, reverse_def,
% 32.59/5.43 reverse_length, reverse_mem, reverse_num_occ, reverse_reverse, reverse_sort,
% 32.59/5.43 rounds_toward_zero, sorted_Two, sorted_append, sorted_mem, sorted_rev_append,
% 32.59/5.43 sorted_reverse_cons, sorted_reverse_cons2, sorted_reverse_mem, t2tb_sort,
% 32.59/5.43 t2tb_sort1, total, trans, true_False, tuple0_inversion, witness_sort
% 32.59/5.43
% 32.59/5.43 Those formulas are unsatisfiable:
% 32.59/5.43 ---------------------------------
% 32.59/5.43
% 32.59/5.43 Begin of proof
% 32.59/5.43 |
% 32.59/5.43 | ALPHA: (length_nil) implies:
% 32.59/5.44 | (1) ! [v0: ty] : ! [v1: uni] : ! [v2: int] : (v2 = 0 | ~ (length(v0,
% 32.59/5.44 | v1) = v2) | ~ ty(v0) | ~ uni(v1) | ? [v3: uni] : ( ~ (v3 = v1)
% 32.59/5.44 | & nil(v0) = v3 & uni(v3)))
% 32.59/5.44 |
% 32.59/5.44 | ALPHA: (infix_plpl_def) implies:
% 32.59/5.44 | (2) ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : (v3 = v1 |
% 32.59/5.44 | ~ (infix_plpl(v0, v2, v1) = v3) | ~ (nil(v0) = v2) | ~ ty(v0) | ~
% 32.59/5.44 | uni(v1))
% 32.59/5.44 |
% 32.59/5.44 | ALPHA: (sorted_Nil) implies:
% 32.59/5.44 | (3) ? [v0: uni] : ? [v1: list_elt] : (sorted(v1) = 0 & tb2t(v0) = v1 &
% 32.59/5.44 | nil(elt1) = v0 & list_elt(v1) & uni(v0))
% 32.59/5.44 |
% 32.59/5.44 | ALPHA: (sorted_One) implies:
% 32.59/5.44 | (4) ? [v0: uni] : (nil(elt1) = v0 & uni(v0) & ! [v1: elt] : ! [v2: uni]
% 32.59/5.44 | : ( ~ (t2tb1(v1) = v2) | ~ elt(v1) | ? [v3: uni] : ? [v4:
% 32.59/5.44 | list_elt] : (sorted(v4) = 0 & tb2t(v3) = v4 & cons(elt1, v2, v0)
% 32.59/5.44 | = v3 & list_elt(v4) & uni(v3))))
% 32.59/5.44 |
% 32.59/5.44 | ALPHA: (sorted_inversion) implies:
% 32.59/5.44 | (5) ? [v0: uni] : ? [v1: list_elt] : (tb2t(v0) = v1 & nil(elt1) = v0 &
% 32.59/5.44 | list_elt(v1) & uni(v0) & ! [v2: list_elt] : (v2 = v1 | ~
% 32.59/5.44 | (sorted(v2) = 0) | ~ list_elt(v2) | ? [v3: elt] : ? [v4: elt] :
% 32.59/5.44 | ? [v5: list_elt] : ? [v6: uni] : ? [v7: uni] : ? [v8: uni] : ?
% 32.59/5.44 | [v9: list_elt] : ? [v10: uni] : ? [v11: uni] : (t2tb1(v4) = v6 &
% 32.59/5.44 | t2tb1(v3) = v10 & sorted(v9) = 0 & tb2t(v11) = v2 & tb2t(v8) = v9
% 32.59/5.44 | & t2tb(v5) = v7 & le(v3, v4) = 0 & cons(elt1, v10, v8) = v11 &
% 32.59/5.44 | cons(elt1, v6, v7) = v8 & list_elt(v9) & list_elt(v5) & elt(v4) &
% 32.59/5.44 | elt(v3) & uni(v11) & uni(v10) & uni(v8) & uni(v7) & uni(v6)) | ?
% 32.59/5.44 | [v3: elt] : ? [v4: uni] : ? [v5: uni] : (t2tb1(v3) = v4 &
% 32.59/5.44 | tb2t(v5) = v2 & cons(elt1, v4, v0) = v5 & elt(v3) & uni(v5) &
% 32.59/5.44 | uni(v4))))
% 32.59/5.44 |
% 32.59/5.44 | ALPHA: (wP_parameter_rev_sort) implies:
% 32.59/5.45 | (6) ty(elt1)
% 33.04/5.45 | (7) ? [v0: uni] : ? [v1: uni] : ? [v2: list_elt] : ? [v3: any] :
% 33.04/5.45 | (sorted(v2) = v3 & tb2t(v1) = v2 & reverse(elt1, v0) = v1 & nil(elt1) =
% 33.04/5.46 | v0 & list_elt(v2) & uni(v1) & uni(v0) & ? [v4: int] : ? [v5:
% 33.04/5.46 | list_elt] : ? [v6: uni] : ? [v7: int] : ? [v8: int] : ? [v9:
% 33.04/5.46 | uni] : ? [v10: uni] : ? [v11: list_elt] : ($lesseq(v8, v7) &
% 33.04/5.46 | $lesseq(0, v8) & $lesseq(v4, v7) & $lesseq(4, v4) & div(v4, 2) = v8
% 33.04/5.46 | & prefix(elt1, v8, v6) = v9 & prefix(elt1, v4, v6) = v10 &
% 33.04/5.46 | tb2t(v10) = v11 & t2tb(v5) = v6 & length(elt1, v6) = v7 &
% 33.04/5.46 | list_elt(v11) & list_elt(v5) & uni(v10) & uni(v9) & uni(v6) & ?
% 33.04/5.46 | [v12: list_elt] : ? [v13: uni] : ? [v14: uni] : ? [v15: uni] :
% 33.04/5.46 | ? [v16: uni] : ? [v17: int] : ($lesseq(2, v8) & prefix(elt1,
% 33.04/5.46 | $difference(v4, v8), v13) = v15 & tb2t(v16) = v11 & tb2t(v14) =
% 33.04/5.46 | v5 & t2tb(v12) = v13 & infix_plpl(elt1, v9, v15) = v16 &
% 33.04/5.46 | infix_plpl(elt1, v9, v13) = v14 & length(elt1, v13) = v17 &
% 33.04/5.46 | list_elt(v12) & uni(v16) & uni(v15) & uni(v14) & uni(v13) & ?
% 33.04/5.46 | [v18: list_elt] : ? [v19: uni] : ? [v20: uni] : ($lesseq(v4,
% 33.04/5.46 | $sum(v17, v8)) & $lesseq(2, $difference(v4, v8)) &
% 33.04/5.46 | sorted(v18) = 0 & t2tb(v18) = v19 & permut(elt1, v19, v9) = 0 &
% 33.04/5.46 | infix_plpl(elt1, v0, v19) = v20 & list_elt(v18) & uni(v20) &
% 33.04/5.46 | uni(v19) & ? [v21: list_elt] : ? [v22: uni] : ? [v23: uni] :
% 33.04/5.46 | (v3 = 0 & sorted(v21) = 0 & t2tb(v21) = v22 & permut(elt1, v22,
% 33.04/5.46 | v15) = 0 & infix_plpl(elt1, v20, v22) = v23 & list_elt(v21)
% 33.04/5.46 | & uni(v23) & uni(v22) & ! [v24: elt] : ! [v25: elt] : !
% 33.04/5.46 | [v26: uni] : ! [v27: uni] : ( ~ (t2tb1(v25) = v27) | ~
% 33.04/5.46 | (t2tb1(v24) = v26) | ~ (mem(elt1, v27, v22) = 0) | ~
% 33.04/5.46 | elt(v25) | ~ elt(v24) | ? [v28: any] : ? [v29: any] :
% 33.04/5.46 | (le(v24, v25) = v29 & mem(elt1, v26, v0) = v28 & ( ~ (v28 =
% 33.04/5.46 | 0) | v29 = 0))) & ! [v24: elt] : ! [v25: elt] : !
% 33.04/5.46 | [v26: uni] : ! [v27: uni] : ( ~ (t2tb1(v25) = v27) | ~
% 33.04/5.46 | (t2tb1(v24) = v26) | ~ (mem(elt1, v27, v19) = 0) | ~
% 33.04/5.46 | elt(v25) | ~ elt(v24) | ? [v28: any] : ? [v29: any] :
% 33.04/5.46 | (le(v24, v25) = v29 & mem(elt1, v26, v0) = v28 & ( ~ (v28 =
% 33.04/5.46 | 0) | v29 = 0))) & ? [v24: list_elt] : ? [v25: uni]
% 33.04/5.46 | : ? [v26: uni] : ? [v27: list_elt] : ? [v28: int] : ( ~
% 33.04/5.46 | (v28 = 0) & sorted(v27) = 0 & tb2t(v26) = v27 & t2tb(v24) =
% 33.04/5.46 | v25 & permut(elt1, v25, v23) = 0 & permut(elt1, v25, v10) =
% 33.04/5.46 | v28 & reverse(elt1, v25) = v26 & list_elt(v27) &
% 33.04/5.46 | list_elt(v24) & uni(v26) & uni(v25)))))))
% 33.04/5.46 |
% 33.04/5.46 | ALPHA: (function-axioms) implies:
% 33.04/5.46 | (8) ! [v0: uni] : ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~ (nil(v2) =
% 33.04/5.46 | v1) | ~ (nil(v2) = v0))
% 33.04/5.46 | (9) ! [v0: uni] : ! [v1: uni] : ! [v2: list_elt] : (v1 = v0 | ~
% 33.04/5.46 | (t2tb(v2) = v1) | ~ (t2tb(v2) = v0))
% 33.04/5.46 | (10) ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4:
% 33.04/5.46 | ty] : (v1 = v0 | ~ (infix_plpl(v4, v3, v2) = v1) | ~
% 33.04/5.46 | (infix_plpl(v4, v3, v2) = v0))
% 33.04/5.46 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: uni]
% 33.04/5.46 | : ! [v3: uni] : ! [v4: ty] : (v1 = v0 | ~ (permut(v4, v3, v2) = v1)
% 33.04/5.46 | | ~ (permut(v4, v3, v2) = v0))
% 33.04/5.46 |
% 33.04/5.46 | DELTA: instantiating (3) with fresh symbols all_110_0, all_110_1 gives:
% 33.04/5.47 | (12) sorted(all_110_0) = 0 & tb2t(all_110_1) = all_110_0 & nil(elt1) =
% 33.04/5.47 | all_110_1 & list_elt(all_110_0) & uni(all_110_1)
% 33.04/5.47 |
% 33.04/5.47 | ALPHA: (12) implies:
% 33.04/5.47 | (13) nil(elt1) = all_110_1
% 33.04/5.47 |
% 33.04/5.47 | DELTA: instantiating (4) with fresh symbol all_120_0 gives:
% 33.04/5.47 | (14) nil(elt1) = all_120_0 & uni(all_120_0) & ! [v0: elt] : ! [v1: uni] :
% 33.04/5.47 | ( ~ (t2tb1(v0) = v1) | ~ elt(v0) | ? [v2: uni] : ? [v3: list_elt] :
% 33.04/5.47 | (sorted(v3) = 0 & tb2t(v2) = v3 & cons(elt1, v1, all_120_0) = v2 &
% 33.04/5.47 | list_elt(v3) & uni(v2)))
% 33.04/5.47 |
% 33.04/5.47 | ALPHA: (14) implies:
% 33.04/5.47 | (15) uni(all_120_0)
% 33.04/5.47 | (16) nil(elt1) = all_120_0
% 33.04/5.47 |
% 33.04/5.47 | DELTA: instantiating (5) with fresh symbols all_123_0, all_123_1 gives:
% 33.04/5.47 | (17) tb2t(all_123_1) = all_123_0 & nil(elt1) = all_123_1 &
% 33.04/5.47 | list_elt(all_123_0) & uni(all_123_1) & ! [v0: any] : (v0 = all_123_0
% 33.04/5.47 | | ~ (sorted(v0) = 0) | ~ list_elt(v0) | ? [v1: elt] : ? [v2:
% 33.04/5.47 | elt] : ? [v3: list_elt] : ? [v4: uni] : ? [v5: uni] : ? [v6:
% 33.04/5.47 | uni] : ? [v7: list_elt] : ? [v8: uni] : ? [v9: uni] :
% 33.04/5.47 | (t2tb1(v2) = v4 & t2tb1(v1) = v8 & sorted(v7) = 0 & tb2t(v9) = v0 &
% 33.04/5.47 | tb2t(v6) = v7 & t2tb(v3) = v5 & le(v1, v2) = 0 & cons(elt1, v8,
% 33.04/5.47 | v6) = v9 & cons(elt1, v4, v5) = v6 & list_elt(v7) & list_elt(v3)
% 33.04/5.47 | & elt(v2) & elt(v1) & uni(v9) & uni(v8) & uni(v6) & uni(v5) &
% 33.04/5.47 | uni(v4)) | ? [v1: elt] : ? [v2: uni] : ? [v3: uni] : (t2tb1(v1)
% 33.04/5.47 | = v2 & tb2t(v3) = v0 & cons(elt1, v2, all_123_1) = v3 & elt(v1) &
% 33.04/5.47 | uni(v3) & uni(v2)))
% 33.04/5.47 |
% 33.04/5.47 | ALPHA: (17) implies:
% 33.04/5.47 | (18) nil(elt1) = all_123_1
% 33.04/5.47 |
% 33.04/5.47 | DELTA: instantiating (7) with fresh symbols all_126_0, all_126_1, all_126_2,
% 33.04/5.47 | all_126_3 gives:
% 33.04/5.48 | (19) sorted(all_126_1) = all_126_0 & tb2t(all_126_2) = all_126_1 &
% 33.04/5.48 | reverse(elt1, all_126_3) = all_126_2 & nil(elt1) = all_126_3 &
% 33.04/5.48 | list_elt(all_126_1) & uni(all_126_2) & uni(all_126_3) & ? [v0: int] :
% 33.04/5.48 | ? [v1: list_elt] : ? [v2: uni] : ? [v3: int] : ? [v4: int] : ?
% 33.04/5.48 | [v5: uni] : ? [v6: uni] : ? [v7: list_elt] : ($lesseq(v4, v3) &
% 33.04/5.48 | $lesseq(0, v4) & $lesseq(v0, v3) & $lesseq(4, v0) & div(v0, 2) = v4
% 33.04/5.48 | & prefix(elt1, v4, v2) = v5 & prefix(elt1, v0, v2) = v6 & tb2t(v6) =
% 33.04/5.48 | v7 & t2tb(v1) = v2 & length(elt1, v2) = v3 & list_elt(v7) &
% 33.04/5.48 | list_elt(v1) & uni(v6) & uni(v5) & uni(v2) & ? [v8: list_elt] : ?
% 33.04/5.48 | [v9: uni] : ? [v10: uni] : ? [v11: uni] : ? [v12: uni] : ? [v13:
% 33.04/5.48 | int] : ($lesseq(2, v4) & prefix(elt1, $difference(v0, v4), v9) =
% 33.04/5.48 | v11 & tb2t(v12) = v7 & tb2t(v10) = v1 & t2tb(v8) = v9 &
% 33.04/5.48 | infix_plpl(elt1, v5, v11) = v12 & infix_plpl(elt1, v5, v9) = v10 &
% 33.04/5.48 | length(elt1, v9) = v13 & list_elt(v8) & uni(v12) & uni(v11) &
% 33.04/5.48 | uni(v10) & uni(v9) & ? [v14: list_elt] : ? [v15: uni] : ? [v16:
% 33.04/5.48 | uni] : ($lesseq(v0, $sum(v13, v4)) & $lesseq(2, $difference(v0,
% 33.04/5.48 | v4)) & sorted(v14) = 0 & t2tb(v14) = v15 & permut(elt1, v15,
% 33.04/5.48 | v5) = 0 & infix_plpl(elt1, all_126_3, v15) = v16 &
% 33.04/5.48 | list_elt(v14) & uni(v16) & uni(v15) & ? [v17: list_elt] : ?
% 33.04/5.48 | [v18: uni] : ? [v19: uni] : (all_126_0 = 0 & sorted(v17) = 0 &
% 33.04/5.48 | t2tb(v17) = v18 & permut(elt1, v18, v11) = 0 &
% 33.04/5.48 | infix_plpl(elt1, v16, v18) = v19 & list_elt(v17) & uni(v19) &
% 33.04/5.48 | uni(v18) & ! [v20: elt] : ! [v21: elt] : ! [v22: uni] : !
% 33.04/5.48 | [v23: uni] : ( ~ (t2tb1(v21) = v23) | ~ (t2tb1(v20) = v22) |
% 33.04/5.48 | ~ (mem(elt1, v23, v18) = 0) | ~ elt(v21) | ~ elt(v20) | ?
% 33.04/5.49 | [v24: any] : ? [v25: any] : (le(v20, v21) = v25 & mem(elt1,
% 33.04/5.49 | v22, all_126_3) = v24 & ( ~ (v24 = 0) | v25 = 0))) & !
% 33.04/5.49 | [v20: elt] : ! [v21: elt] : ! [v22: uni] : ! [v23: uni] : (
% 33.04/5.49 | ~ (t2tb1(v21) = v23) | ~ (t2tb1(v20) = v22) | ~ (mem(elt1,
% 33.04/5.49 | v23, v15) = 0) | ~ elt(v21) | ~ elt(v20) | ? [v24:
% 33.04/5.49 | any] : ? [v25: any] : (le(v20, v21) = v25 & mem(elt1,
% 33.04/5.49 | v22, all_126_3) = v24 & ( ~ (v24 = 0) | v25 = 0))) & ?
% 33.04/5.49 | [v20: list_elt] : ? [v21: uni] : ? [v22: uni] : ? [v23:
% 33.04/5.49 | list_elt] : ? [v24: int] : ( ~ (v24 = 0) & sorted(v23) = 0
% 33.04/5.49 | & tb2t(v22) = v23 & t2tb(v20) = v21 & permut(elt1, v21, v19)
% 33.04/5.49 | = 0 & permut(elt1, v21, v6) = v24 & reverse(elt1, v21) = v22
% 33.04/5.49 | & list_elt(v23) & list_elt(v20) & uni(v22) & uni(v21))))))
% 33.04/5.49 |
% 33.04/5.49 | ALPHA: (19) implies:
% 33.04/5.49 | (20) nil(elt1) = all_126_3
% 33.22/5.50 | (21) ? [v0: int] : ? [v1: list_elt] : ? [v2: uni] : ? [v3: int] : ?
% 33.22/5.50 | [v4: int] : ? [v5: uni] : ? [v6: uni] : ? [v7: list_elt] :
% 33.22/5.50 | ($lesseq(v4, v3) & $lesseq(0, v4) & $lesseq(v0, v3) & $lesseq(4, v0) &
% 33.22/5.50 | div(v0, 2) = v4 & prefix(elt1, v4, v2) = v5 & prefix(elt1, v0, v2) =
% 33.22/5.50 | v6 & tb2t(v6) = v7 & t2tb(v1) = v2 & length(elt1, v2) = v3 &
% 33.22/5.50 | list_elt(v7) & list_elt(v1) & uni(v6) & uni(v5) & uni(v2) & ? [v8:
% 33.22/5.50 | list_elt] : ? [v9: uni] : ? [v10: uni] : ? [v11: uni] : ?
% 33.22/5.50 | [v12: uni] : ? [v13: int] : ($lesseq(2, v4) & prefix(elt1,
% 33.22/5.50 | $difference(v0, v4), v9) = v11 & tb2t(v12) = v7 & tb2t(v10) = v1
% 33.22/5.50 | & t2tb(v8) = v9 & infix_plpl(elt1, v5, v11) = v12 &
% 33.22/5.50 | infix_plpl(elt1, v5, v9) = v10 & length(elt1, v9) = v13 &
% 33.22/5.50 | list_elt(v8) & uni(v12) & uni(v11) & uni(v10) & uni(v9) & ? [v14:
% 33.22/5.50 | list_elt] : ? [v15: uni] : ? [v16: uni] : ($lesseq(v0,
% 33.22/5.50 | $sum(v13, v4)) & $lesseq(2, $difference(v0, v4)) & sorted(v14)
% 33.22/5.50 | = 0 & t2tb(v14) = v15 & permut(elt1, v15, v5) = 0 &
% 33.22/5.50 | infix_plpl(elt1, all_126_3, v15) = v16 & list_elt(v14) &
% 33.22/5.50 | uni(v16) & uni(v15) & ? [v17: list_elt] : ? [v18: uni] : ?
% 33.22/5.50 | [v19: uni] : (all_126_0 = 0 & sorted(v17) = 0 & t2tb(v17) = v18
% 33.22/5.50 | & permut(elt1, v18, v11) = 0 & infix_plpl(elt1, v16, v18) =
% 33.22/5.50 | v19 & list_elt(v17) & uni(v19) & uni(v18) & ! [v20: elt] : !
% 33.22/5.50 | [v21: elt] : ! [v22: uni] : ! [v23: uni] : ( ~ (t2tb1(v21) =
% 33.22/5.50 | v23) | ~ (t2tb1(v20) = v22) | ~ (mem(elt1, v23, v18) =
% 33.22/5.50 | 0) | ~ elt(v21) | ~ elt(v20) | ? [v24: any] : ? [v25:
% 33.22/5.50 | any] : (le(v20, v21) = v25 & mem(elt1, v22, all_126_3) =
% 33.22/5.50 | v24 & ( ~ (v24 = 0) | v25 = 0))) & ! [v20: elt] : !
% 33.22/5.50 | [v21: elt] : ! [v22: uni] : ! [v23: uni] : ( ~ (t2tb1(v21) =
% 33.22/5.50 | v23) | ~ (t2tb1(v20) = v22) | ~ (mem(elt1, v23, v15) =
% 33.22/5.50 | 0) | ~ elt(v21) | ~ elt(v20) | ? [v24: any] : ? [v25:
% 33.22/5.50 | any] : (le(v20, v21) = v25 & mem(elt1, v22, all_126_3) =
% 33.22/5.50 | v24 & ( ~ (v24 = 0) | v25 = 0))) & ? [v20: list_elt] : ?
% 33.22/5.50 | [v21: uni] : ? [v22: uni] : ? [v23: list_elt] : ? [v24:
% 33.22/5.50 | int] : ( ~ (v24 = 0) & sorted(v23) = 0 & tb2t(v22) = v23 &
% 33.22/5.50 | t2tb(v20) = v21 & permut(elt1, v21, v19) = 0 & permut(elt1,
% 33.22/5.50 | v21, v6) = v24 & reverse(elt1, v21) = v22 & list_elt(v23)
% 33.22/5.50 | & list_elt(v20) & uni(v22) & uni(v21))))))
% 33.22/5.50 |
% 33.22/5.50 | DELTA: instantiating (21) with fresh symbols all_128_0, all_128_1, all_128_2,
% 33.22/5.50 | all_128_3, all_128_4, all_128_5, all_128_6, all_128_7 gives:
% 33.22/5.50 | (22) $lesseq(all_128_3, all_128_4) & $lesseq(0, all_128_3) &
% 33.22/5.50 | $lesseq(all_128_7, all_128_4) & $lesseq(4, all_128_7) & div(all_128_7,
% 33.22/5.50 | 2) = all_128_3 & prefix(elt1, all_128_3, all_128_5) = all_128_2 &
% 33.22/5.50 | prefix(elt1, all_128_7, all_128_5) = all_128_1 & tb2t(all_128_1) =
% 33.22/5.50 | all_128_0 & t2tb(all_128_6) = all_128_5 & length(elt1, all_128_5) =
% 33.22/5.50 | all_128_4 & list_elt(all_128_0) & list_elt(all_128_6) & uni(all_128_1)
% 33.22/5.50 | & uni(all_128_2) & uni(all_128_5) & ? [v0: list_elt] : ? [v1: uni] :
% 33.22/5.50 | ? [v2: uni] : ? [v3: uni] : ? [v4: uni] : ? [v5: int] :
% 33.22/5.50 | ($lesseq(2, all_128_3) & prefix(elt1, $difference(all_128_7,
% 33.22/5.50 | all_128_3), v1) = v3 & tb2t(v4) = all_128_0 & tb2t(v2) =
% 33.22/5.50 | all_128_6 & t2tb(v0) = v1 & infix_plpl(elt1, all_128_2, v3) = v4 &
% 33.22/5.50 | infix_plpl(elt1, all_128_2, v1) = v2 & length(elt1, v1) = v5 &
% 33.22/5.51 | list_elt(v0) & uni(v4) & uni(v3) & uni(v2) & uni(v1) & ? [v6:
% 33.22/5.51 | list_elt] : ? [v7: uni] : ? [v8: uni] : ($lesseq(all_128_7,
% 33.22/5.51 | $sum(v5, all_128_3)) & $lesseq(2, $difference(all_128_7,
% 33.22/5.51 | all_128_3)) & sorted(v6) = 0 & t2tb(v6) = v7 & permut(elt1,
% 33.22/5.51 | v7, all_128_2) = 0 & infix_plpl(elt1, all_126_3, v7) = v8 &
% 33.22/5.51 | list_elt(v6) & uni(v8) & uni(v7) & ? [v9: list_elt] : ? [v10:
% 33.22/5.51 | uni] : ? [v11: uni] : (all_126_0 = 0 & sorted(v9) = 0 &
% 33.22/5.51 | t2tb(v9) = v10 & permut(elt1, v10, v3) = 0 & infix_plpl(elt1,
% 33.22/5.51 | v8, v10) = v11 & list_elt(v9) & uni(v11) & uni(v10) & ! [v12:
% 33.22/5.51 | elt] : ! [v13: elt] : ! [v14: uni] : ! [v15: uni] : ( ~
% 33.22/5.51 | (t2tb1(v13) = v15) | ~ (t2tb1(v12) = v14) | ~ (mem(elt1,
% 33.22/5.51 | v15, v10) = 0) | ~ elt(v13) | ~ elt(v12) | ? [v16: any]
% 33.22/5.51 | : ? [v17: any] : (le(v12, v13) = v17 & mem(elt1, v14,
% 33.22/5.51 | all_126_3) = v16 & ( ~ (v16 = 0) | v17 = 0))) & ! [v12:
% 33.22/5.51 | elt] : ! [v13: elt] : ! [v14: uni] : ! [v15: uni] : ( ~
% 33.22/5.51 | (t2tb1(v13) = v15) | ~ (t2tb1(v12) = v14) | ~ (mem(elt1,
% 33.22/5.51 | v15, v7) = 0) | ~ elt(v13) | ~ elt(v12) | ? [v16: any]
% 33.22/5.51 | : ? [v17: any] : (le(v12, v13) = v17 & mem(elt1, v14,
% 33.22/5.51 | all_126_3) = v16 & ( ~ (v16 = 0) | v17 = 0))) & ? [v12:
% 33.22/5.51 | list_elt] : ? [v13: uni] : ? [v14: uni] : ? [v15: list_elt]
% 33.22/5.51 | : ? [v16: int] : ( ~ (v16 = 0) & sorted(v15) = 0 & tb2t(v14) =
% 33.22/5.51 | v15 & t2tb(v12) = v13 & permut(elt1, v13, v11) = 0 &
% 33.22/5.51 | permut(elt1, v13, all_128_1) = v16 & reverse(elt1, v13) = v14
% 33.22/5.51 | & list_elt(v15) & list_elt(v12) & uni(v14) & uni(v13)))))
% 33.22/5.51 |
% 33.22/5.51 | ALPHA: (22) implies:
% 33.22/5.51 | (23) uni(all_128_2)
% 33.22/5.51 | (24) uni(all_128_1)
% 33.22/5.51 | (25) t2tb(all_128_6) = all_128_5
% 33.22/5.51 | (26) tb2t(all_128_1) = all_128_0
% 33.22/5.51 | (27) prefix(elt1, all_128_3, all_128_5) = all_128_2
% 33.22/5.51 | (28) ? [v0: list_elt] : ? [v1: uni] : ? [v2: uni] : ? [v3: uni] : ?
% 33.22/5.51 | [v4: uni] : ? [v5: int] : ($lesseq(2, all_128_3) & prefix(elt1,
% 33.22/5.51 | $difference(all_128_7, all_128_3), v1) = v3 & tb2t(v4) = all_128_0
% 33.22/5.51 | & tb2t(v2) = all_128_6 & t2tb(v0) = v1 & infix_plpl(elt1, all_128_2,
% 33.22/5.51 | v3) = v4 & infix_plpl(elt1, all_128_2, v1) = v2 & length(elt1, v1)
% 33.22/5.51 | = v5 & list_elt(v0) & uni(v4) & uni(v3) & uni(v2) & uni(v1) & ?
% 33.22/5.51 | [v6: list_elt] : ? [v7: uni] : ? [v8: uni] : ($lesseq(all_128_7,
% 33.22/5.51 | $sum(v5, all_128_3)) & $lesseq(2, $difference(all_128_7,
% 33.22/5.51 | all_128_3)) & sorted(v6) = 0 & t2tb(v6) = v7 & permut(elt1,
% 33.22/5.51 | v7, all_128_2) = 0 & infix_plpl(elt1, all_126_3, v7) = v8 &
% 33.22/5.51 | list_elt(v6) & uni(v8) & uni(v7) & ? [v9: list_elt] : ? [v10:
% 33.22/5.51 | uni] : ? [v11: uni] : (all_126_0 = 0 & sorted(v9) = 0 &
% 33.22/5.51 | t2tb(v9) = v10 & permut(elt1, v10, v3) = 0 & infix_plpl(elt1,
% 33.22/5.51 | v8, v10) = v11 & list_elt(v9) & uni(v11) & uni(v10) & ! [v12:
% 33.22/5.51 | elt] : ! [v13: elt] : ! [v14: uni] : ! [v15: uni] : ( ~
% 33.22/5.51 | (t2tb1(v13) = v15) | ~ (t2tb1(v12) = v14) | ~ (mem(elt1,
% 33.22/5.51 | v15, v10) = 0) | ~ elt(v13) | ~ elt(v12) | ? [v16: any]
% 33.22/5.51 | : ? [v17: any] : (le(v12, v13) = v17 & mem(elt1, v14,
% 33.22/5.51 | all_126_3) = v16 & ( ~ (v16 = 0) | v17 = 0))) & ! [v12:
% 33.22/5.51 | elt] : ! [v13: elt] : ! [v14: uni] : ! [v15: uni] : ( ~
% 33.22/5.51 | (t2tb1(v13) = v15) | ~ (t2tb1(v12) = v14) | ~ (mem(elt1,
% 33.22/5.51 | v15, v7) = 0) | ~ elt(v13) | ~ elt(v12) | ? [v16: any]
% 33.22/5.51 | : ? [v17: any] : (le(v12, v13) = v17 & mem(elt1, v14,
% 33.22/5.51 | all_126_3) = v16 & ( ~ (v16 = 0) | v17 = 0))) & ? [v12:
% 33.22/5.51 | list_elt] : ? [v13: uni] : ? [v14: uni] : ? [v15: list_elt]
% 33.22/5.51 | : ? [v16: int] : ( ~ (v16 = 0) & sorted(v15) = 0 & tb2t(v14) =
% 33.22/5.51 | v15 & t2tb(v12) = v13 & permut(elt1, v13, v11) = 0 &
% 33.22/5.51 | permut(elt1, v13, all_128_1) = v16 & reverse(elt1, v13) = v14
% 33.22/5.51 | & list_elt(v15) & list_elt(v12) & uni(v14) & uni(v13)))))
% 33.22/5.51 |
% 33.22/5.51 | DELTA: instantiating (28) with fresh symbols all_131_0, all_131_1, all_131_2,
% 33.22/5.51 | all_131_3, all_131_4, all_131_5 gives:
% 33.22/5.52 | (29) $lesseq(2, all_128_3) & prefix(elt1, $difference(all_128_7,
% 33.22/5.52 | all_128_3), all_131_4) = all_131_2 & tb2t(all_131_1) = all_128_0 &
% 33.22/5.52 | tb2t(all_131_3) = all_128_6 & t2tb(all_131_5) = all_131_4 &
% 33.22/5.52 | infix_plpl(elt1, all_128_2, all_131_2) = all_131_1 & infix_plpl(elt1,
% 33.22/5.52 | all_128_2, all_131_4) = all_131_3 & length(elt1, all_131_4) =
% 33.22/5.52 | all_131_0 & list_elt(all_131_5) & uni(all_131_1) & uni(all_131_2) &
% 33.22/5.52 | uni(all_131_3) & uni(all_131_4) & ? [v0: list_elt] : ? [v1: uni] :
% 33.22/5.52 | ? [v2: uni] : ($lesseq(all_128_7, $sum(all_131_0, all_128_3)) &
% 33.22/5.52 | $lesseq(2, $difference(all_128_7, all_128_3)) & sorted(v0) = 0 &
% 33.22/5.52 | t2tb(v0) = v1 & permut(elt1, v1, all_128_2) = 0 & infix_plpl(elt1,
% 33.22/5.52 | all_126_3, v1) = v2 & list_elt(v0) & uni(v2) & uni(v1) & ? [v3:
% 33.22/5.52 | list_elt] : ? [v4: uni] : ? [v5: uni] : (all_126_0 = 0 &
% 33.22/5.52 | sorted(v3) = 0 & t2tb(v3) = v4 & permut(elt1, v4, all_131_2) = 0 &
% 33.22/5.52 | infix_plpl(elt1, v2, v4) = v5 & list_elt(v3) & uni(v5) & uni(v4) &
% 33.22/5.52 | ! [v6: elt] : ! [v7: elt] : ! [v8: uni] : ! [v9: uni] : ( ~
% 33.22/5.52 | (t2tb1(v7) = v9) | ~ (t2tb1(v6) = v8) | ~ (mem(elt1, v9, v4) =
% 33.22/5.52 | 0) | ~ elt(v7) | ~ elt(v6) | ? [v10: any] : ? [v11: any] :
% 33.22/5.52 | (le(v6, v7) = v11 & mem(elt1, v8, all_126_3) = v10 & ( ~ (v10 =
% 33.22/5.52 | 0) | v11 = 0))) & ! [v6: elt] : ! [v7: elt] : ! [v8:
% 33.22/5.52 | uni] : ! [v9: uni] : ( ~ (t2tb1(v7) = v9) | ~ (t2tb1(v6) = v8)
% 33.22/5.52 | | ~ (mem(elt1, v9, v1) = 0) | ~ elt(v7) | ~ elt(v6) | ?
% 33.22/5.52 | [v10: any] : ? [v11: any] : (le(v6, v7) = v11 & mem(elt1, v8,
% 33.22/5.52 | all_126_3) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ? [v6:
% 33.22/5.52 | list_elt] : ? [v7: uni] : ? [v8: uni] : ? [v9: list_elt] : ?
% 33.22/5.52 | [v10: int] : ( ~ (v10 = 0) & sorted(v9) = 0 & tb2t(v8) = v9 &
% 33.22/5.52 | t2tb(v6) = v7 & permut(elt1, v7, v5) = 0 & permut(elt1, v7,
% 33.22/5.52 | all_128_1) = v10 & reverse(elt1, v7) = v8 & list_elt(v9) &
% 33.22/5.52 | list_elt(v6) & uni(v8) & uni(v7))))
% 33.22/5.52 |
% 33.22/5.52 | ALPHA: (29) implies:
% 33.22/5.52 | (30) $lesseq(2, all_128_3)
% 33.22/5.52 | (31) uni(all_131_3)
% 33.22/5.52 | (32) uni(all_131_2)
% 33.22/5.52 | (33) uni(all_131_1)
% 33.22/5.52 | (34) infix_plpl(elt1, all_128_2, all_131_2) = all_131_1
% 33.22/5.52 | (35) tb2t(all_131_3) = all_128_6
% 33.22/5.52 | (36) tb2t(all_131_1) = all_128_0
% 33.22/5.52 | (37) ? [v0: list_elt] : ? [v1: uni] : ? [v2: uni] : ($lesseq(all_128_7,
% 33.22/5.52 | $sum(all_131_0, all_128_3)) & $lesseq(2, $difference(all_128_7,
% 33.22/5.52 | all_128_3)) & sorted(v0) = 0 & t2tb(v0) = v1 & permut(elt1, v1,
% 33.22/5.52 | all_128_2) = 0 & infix_plpl(elt1, all_126_3, v1) = v2 &
% 33.22/5.52 | list_elt(v0) & uni(v2) & uni(v1) & ? [v3: list_elt] : ? [v4: uni]
% 33.22/5.52 | : ? [v5: uni] : (all_126_0 = 0 & sorted(v3) = 0 & t2tb(v3) = v4 &
% 33.22/5.52 | permut(elt1, v4, all_131_2) = 0 & infix_plpl(elt1, v2, v4) = v5 &
% 33.22/5.52 | list_elt(v3) & uni(v5) & uni(v4) & ! [v6: elt] : ! [v7: elt] :
% 33.22/5.52 | ! [v8: uni] : ! [v9: uni] : ( ~ (t2tb1(v7) = v9) | ~ (t2tb1(v6)
% 33.22/5.52 | = v8) | ~ (mem(elt1, v9, v4) = 0) | ~ elt(v7) | ~ elt(v6) |
% 33.22/5.52 | ? [v10: any] : ? [v11: any] : (le(v6, v7) = v11 & mem(elt1,
% 33.22/5.52 | v8, all_126_3) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v6:
% 33.22/5.53 | elt] : ! [v7: elt] : ! [v8: uni] : ! [v9: uni] : ( ~
% 33.22/5.53 | (t2tb1(v7) = v9) | ~ (t2tb1(v6) = v8) | ~ (mem(elt1, v9, v1) =
% 33.22/5.53 | 0) | ~ elt(v7) | ~ elt(v6) | ? [v10: any] : ? [v11: any] :
% 33.22/5.53 | (le(v6, v7) = v11 & mem(elt1, v8, all_126_3) = v10 & ( ~ (v10 =
% 33.22/5.53 | 0) | v11 = 0))) & ? [v6: list_elt] : ? [v7: uni] : ?
% 33.22/5.53 | [v8: uni] : ? [v9: list_elt] : ? [v10: int] : ( ~ (v10 = 0) &
% 33.22/5.53 | sorted(v9) = 0 & tb2t(v8) = v9 & t2tb(v6) = v7 & permut(elt1,
% 33.22/5.53 | v7, v5) = 0 & permut(elt1, v7, all_128_1) = v10 &
% 33.22/5.53 | reverse(elt1, v7) = v8 & list_elt(v9) & list_elt(v6) & uni(v8) &
% 33.22/5.53 | uni(v7))))
% 33.22/5.53 |
% 33.22/5.53 | DELTA: instantiating (37) with fresh symbols all_133_0, all_133_1, all_133_2
% 33.22/5.53 | gives:
% 33.22/5.53 | (38) $lesseq(all_128_7, $sum(all_131_0, all_128_3)) & $lesseq(2,
% 33.22/5.53 | $difference(all_128_7, all_128_3)) & sorted(all_133_2) = 0 &
% 33.22/5.53 | t2tb(all_133_2) = all_133_1 & permut(elt1, all_133_1, all_128_2) = 0 &
% 33.22/5.53 | infix_plpl(elt1, all_126_3, all_133_1) = all_133_0 &
% 33.22/5.53 | list_elt(all_133_2) & uni(all_133_0) & uni(all_133_1) & ? [v0:
% 33.22/5.53 | list_elt] : ? [v1: uni] : ? [v2: uni] : (all_126_0 = 0 &
% 33.22/5.53 | sorted(v0) = 0 & t2tb(v0) = v1 & permut(elt1, v1, all_131_2) = 0 &
% 33.22/5.53 | infix_plpl(elt1, all_133_0, v1) = v2 & list_elt(v0) & uni(v2) &
% 33.22/5.53 | uni(v1) & ! [v3: elt] : ! [v4: elt] : ! [v5: uni] : ! [v6: uni]
% 33.22/5.53 | : ( ~ (t2tb1(v4) = v6) | ~ (t2tb1(v3) = v5) | ~ (mem(elt1, v6, v1)
% 33.22/5.53 | = 0) | ~ elt(v4) | ~ elt(v3) | ? [v7: any] : ? [v8: any] :
% 33.22/5.53 | (le(v3, v4) = v8 & mem(elt1, v5, all_126_3) = v7 & ( ~ (v7 = 0) |
% 33.22/5.53 | v8 = 0))) & ! [v3: elt] : ! [v4: elt] : ! [v5: uni] : !
% 33.22/5.53 | [v6: uni] : ( ~ (t2tb1(v4) = v6) | ~ (t2tb1(v3) = v5) | ~
% 33.22/5.53 | (mem(elt1, v6, all_133_1) = 0) | ~ elt(v4) | ~ elt(v3) | ? [v7:
% 33.22/5.53 | any] : ? [v8: any] : (le(v3, v4) = v8 & mem(elt1, v5,
% 33.22/5.53 | all_126_3) = v7 & ( ~ (v7 = 0) | v8 = 0))) & ? [v3: list_elt]
% 33.22/5.53 | : ? [v4: uni] : ? [v5: uni] : ? [v6: list_elt] : ? [v7: int] : (
% 33.22/5.53 | ~ (v7 = 0) & sorted(v6) = 0 & tb2t(v5) = v6 & t2tb(v3) = v4 &
% 33.22/5.53 | permut(elt1, v4, v2) = 0 & permut(elt1, v4, all_128_1) = v7 &
% 33.22/5.53 | reverse(elt1, v4) = v5 & list_elt(v6) & list_elt(v3) & uni(v5) &
% 33.22/5.53 | uni(v4)))
% 33.22/5.53 |
% 33.22/5.53 | ALPHA: (38) implies:
% 33.22/5.53 | (39) uni(all_133_1)
% 33.22/5.53 | (40) uni(all_133_0)
% 33.22/5.53 | (41) infix_plpl(elt1, all_126_3, all_133_1) = all_133_0
% 33.22/5.53 | (42) permut(elt1, all_133_1, all_128_2) = 0
% 33.22/5.53 | (43) ? [v0: list_elt] : ? [v1: uni] : ? [v2: uni] : (all_126_0 = 0 &
% 33.22/5.53 | sorted(v0) = 0 & t2tb(v0) = v1 & permut(elt1, v1, all_131_2) = 0 &
% 33.22/5.53 | infix_plpl(elt1, all_133_0, v1) = v2 & list_elt(v0) & uni(v2) &
% 33.22/5.53 | uni(v1) & ! [v3: elt] : ! [v4: elt] : ! [v5: uni] : ! [v6: uni]
% 33.22/5.53 | : ( ~ (t2tb1(v4) = v6) | ~ (t2tb1(v3) = v5) | ~ (mem(elt1, v6, v1)
% 33.22/5.53 | = 0) | ~ elt(v4) | ~ elt(v3) | ? [v7: any] : ? [v8: any] :
% 33.22/5.53 | (le(v3, v4) = v8 & mem(elt1, v5, all_126_3) = v7 & ( ~ (v7 = 0) |
% 33.22/5.53 | v8 = 0))) & ! [v3: elt] : ! [v4: elt] : ! [v5: uni] : !
% 33.22/5.53 | [v6: uni] : ( ~ (t2tb1(v4) = v6) | ~ (t2tb1(v3) = v5) | ~
% 33.22/5.53 | (mem(elt1, v6, all_133_1) = 0) | ~ elt(v4) | ~ elt(v3) | ? [v7:
% 33.22/5.53 | any] : ? [v8: any] : (le(v3, v4) = v8 & mem(elt1, v5,
% 33.22/5.53 | all_126_3) = v7 & ( ~ (v7 = 0) | v8 = 0))) & ? [v3: list_elt]
% 33.22/5.53 | : ? [v4: uni] : ? [v5: uni] : ? [v6: list_elt] : ? [v7: int] : (
% 33.22/5.53 | ~ (v7 = 0) & sorted(v6) = 0 & tb2t(v5) = v6 & t2tb(v3) = v4 &
% 33.22/5.53 | permut(elt1, v4, v2) = 0 & permut(elt1, v4, all_128_1) = v7 &
% 33.22/5.53 | reverse(elt1, v4) = v5 & list_elt(v6) & list_elt(v3) & uni(v5) &
% 33.22/5.53 | uni(v4)))
% 33.22/5.53 |
% 33.22/5.53 | DELTA: instantiating (43) with fresh symbols all_136_0, all_136_1, all_136_2
% 33.22/5.53 | gives:
% 33.44/5.54 | (44) all_126_0 = 0 & sorted(all_136_2) = 0 & t2tb(all_136_2) = all_136_1 &
% 33.44/5.54 | permut(elt1, all_136_1, all_131_2) = 0 & infix_plpl(elt1, all_133_0,
% 33.44/5.54 | all_136_1) = all_136_0 & list_elt(all_136_2) & uni(all_136_0) &
% 33.44/5.54 | uni(all_136_1) & ! [v0: elt] : ! [v1: elt] : ! [v2: uni] : ! [v3:
% 33.44/5.54 | uni] : ( ~ (t2tb1(v1) = v3) | ~ (t2tb1(v0) = v2) | ~ (mem(elt1,
% 33.44/5.54 | v3, all_136_1) = 0) | ~ elt(v1) | ~ elt(v0) | ? [v4: any] :
% 33.44/5.54 | ? [v5: any] : (le(v0, v1) = v5 & mem(elt1, v2, all_126_3) = v4 & ( ~
% 33.44/5.54 | (v4 = 0) | v5 = 0))) & ! [v0: elt] : ! [v1: elt] : ! [v2:
% 33.44/5.54 | uni] : ! [v3: uni] : ( ~ (t2tb1(v1) = v3) | ~ (t2tb1(v0) = v2) |
% 33.44/5.54 | ~ (mem(elt1, v3, all_133_1) = 0) | ~ elt(v1) | ~ elt(v0) | ? [v4:
% 33.44/5.54 | any] : ? [v5: any] : (le(v0, v1) = v5 & mem(elt1, v2, all_126_3)
% 33.44/5.54 | = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0: list_elt] : ? [v1: uni]
% 33.44/5.54 | : ? [v2: uni] : ? [v3: list_elt] : ? [v4: int] : ( ~ (v4 = 0) &
% 33.44/5.54 | sorted(v3) = 0 & tb2t(v2) = v3 & t2tb(v0) = v1 & permut(elt1, v1,
% 33.44/5.54 | all_136_0) = 0 & permut(elt1, v1, all_128_1) = v4 & reverse(elt1,
% 33.44/5.54 | v1) = v2 & list_elt(v3) & list_elt(v0) & uni(v2) & uni(v1))
% 33.44/5.54 |
% 33.44/5.54 | ALPHA: (44) implies:
% 33.44/5.54 | (45) uni(all_136_1)
% 33.44/5.54 | (46) uni(all_136_0)
% 33.44/5.54 | (47) infix_plpl(elt1, all_133_0, all_136_1) = all_136_0
% 33.44/5.54 | (48) permut(elt1, all_136_1, all_131_2) = 0
% 33.44/5.54 | (49) ? [v0: list_elt] : ? [v1: uni] : ? [v2: uni] : ? [v3: list_elt] :
% 33.44/5.54 | ? [v4: int] : ( ~ (v4 = 0) & sorted(v3) = 0 & tb2t(v2) = v3 & t2tb(v0)
% 33.44/5.54 | = v1 & permut(elt1, v1, all_136_0) = 0 & permut(elt1, v1, all_128_1)
% 33.44/5.54 | = v4 & reverse(elt1, v1) = v2 & list_elt(v3) & list_elt(v0) &
% 33.44/5.54 | uni(v2) & uni(v1))
% 33.44/5.54 |
% 33.44/5.54 | DELTA: instantiating (49) with fresh symbols all_139_0, all_139_1, all_139_2,
% 33.44/5.54 | all_139_3, all_139_4 gives:
% 33.44/5.54 | (50) ~ (all_139_0 = 0) & sorted(all_139_1) = 0 & tb2t(all_139_2) =
% 33.44/5.54 | all_139_1 & t2tb(all_139_4) = all_139_3 & permut(elt1, all_139_3,
% 33.44/5.54 | all_136_0) = 0 & permut(elt1, all_139_3, all_128_1) = all_139_0 &
% 33.44/5.54 | reverse(elt1, all_139_3) = all_139_2 & list_elt(all_139_1) &
% 33.44/5.54 | list_elt(all_139_4) & uni(all_139_2) & uni(all_139_3)
% 33.44/5.54 |
% 33.44/5.54 | ALPHA: (50) implies:
% 33.44/5.54 | (51) ~ (all_139_0 = 0)
% 33.44/5.54 | (52) uni(all_139_3)
% 33.44/5.54 | (53) permut(elt1, all_139_3, all_128_1) = all_139_0
% 33.44/5.54 | (54) permut(elt1, all_139_3, all_136_0) = 0
% 33.44/5.54 |
% 33.44/5.54 | GROUND_INST: instantiating (8) with all_120_0, all_123_1, elt1, simplifying
% 33.44/5.54 | with (16), (18) gives:
% 33.44/5.54 | (55) all_123_1 = all_120_0
% 33.44/5.54 |
% 33.44/5.54 | GROUND_INST: instantiating (8) with all_123_1, all_126_3, elt1, simplifying
% 33.44/5.54 | with (18), (20) gives:
% 33.44/5.54 | (56) all_126_3 = all_123_1
% 33.44/5.54 |
% 33.44/5.54 | GROUND_INST: instantiating (8) with all_110_1, all_126_3, elt1, simplifying
% 33.44/5.54 | with (13), (20) gives:
% 33.48/5.54 | (57) all_126_3 = all_110_1
% 33.48/5.54 |
% 33.48/5.54 | COMBINE_EQS: (56), (57) imply:
% 33.48/5.54 | (58) all_123_1 = all_110_1
% 33.48/5.54 |
% 33.48/5.54 | SIMP: (58) implies:
% 33.48/5.54 | (59) all_123_1 = all_110_1
% 33.48/5.54 |
% 33.48/5.54 | COMBINE_EQS: (55), (59) imply:
% 33.48/5.54 | (60) all_120_0 = all_110_1
% 33.48/5.54 |
% 33.48/5.54 | SIMP: (60) implies:
% 33.48/5.54 | (61) all_120_0 = all_110_1
% 33.48/5.54 |
% 33.48/5.54 | REDUCE: (41), (57) imply:
% 33.48/5.54 | (62) infix_plpl(elt1, all_110_1, all_133_1) = all_133_0
% 33.48/5.54 |
% 33.48/5.54 | REDUCE: (15), (61) imply:
% 33.48/5.54 | (63) uni(all_110_1)
% 33.48/5.54 |
% 33.48/5.54 | GROUND_INST: instantiating (2) with elt1, all_133_1, all_110_1, all_133_0,
% 33.48/5.54 | simplifying with (6), (13), (39), (62) gives:
% 33.48/5.54 | (64) all_133_0 = all_133_1
% 33.48/5.54 |
% 33.48/5.54 | GROUND_INST: instantiating (append_assoc) with elt1, all_110_1, all_133_1,
% 33.48/5.54 | all_136_1, all_133_0, all_136_0, simplifying with (6), (39),
% 33.48/5.54 | (45), (47), (62), (63) gives:
% 33.48/5.54 | (65) ? [v0: uni] : (infix_plpl(elt1, all_133_1, all_136_1) = v0 &
% 33.48/5.54 | infix_plpl(elt1, all_110_1, v0) = all_136_0 & uni(v0) &
% 33.48/5.54 | uni(all_136_0))
% 33.48/5.54 |
% 33.48/5.55 | GROUND_INST: instantiating (permut_length) with elt1, all_133_1, all_128_2,
% 33.48/5.55 | simplifying with (6), (23), (39), (42) gives:
% 33.48/5.55 | (66) ? [v0: int] : (length(elt1, all_133_1) = v0 & length(elt1, all_128_2)
% 33.48/5.55 | = v0)
% 33.48/5.55 |
% 33.48/5.55 | GROUND_INST: instantiating (permut_trans) with elt1, all_139_3, all_136_0,
% 33.48/5.55 | all_128_1, all_139_0, simplifying with (6), (24), (46), (52),
% 33.48/5.55 | (53), (54) gives:
% 33.48/5.55 | (67) all_139_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & permut(elt1, all_136_0,
% 33.48/5.55 | all_128_1) = v0)
% 33.48/5.55 |
% 33.48/5.55 | GROUND_INST: instantiating (bridgeR) with all_128_1, all_128_0, simplifying
% 33.48/5.55 | with (24), (26) gives:
% 33.48/5.55 | (68) t2tb(all_128_0) = all_128_1
% 33.48/5.55 |
% 33.48/5.55 | GROUND_INST: instantiating (bridgeR) with all_131_3, all_128_6, simplifying
% 33.48/5.55 | with (31), (35) gives:
% 33.48/5.55 | (69) t2tb(all_128_6) = all_131_3
% 33.48/5.55 |
% 33.48/5.55 | GROUND_INST: instantiating (bridgeR) with all_131_1, all_128_0, simplifying
% 33.48/5.55 | with (33), (36) gives:
% 33.48/5.55 | (70) t2tb(all_128_0) = all_131_1
% 33.48/5.55 |
% 33.48/5.55 | DELTA: instantiating (66) with fresh symbol all_164_0 gives:
% 33.48/5.55 | (71) length(elt1, all_133_1) = all_164_0 & length(elt1, all_128_2) =
% 33.48/5.55 | all_164_0
% 33.48/5.55 |
% 33.48/5.55 | ALPHA: (71) implies:
% 33.48/5.55 | (72) length(elt1, all_128_2) = all_164_0
% 33.48/5.55 |
% 33.48/5.55 | DELTA: instantiating (65) with fresh symbol all_171_0 gives:
% 33.48/5.55 | (73) infix_plpl(elt1, all_133_1, all_136_1) = all_171_0 & infix_plpl(elt1,
% 33.48/5.55 | all_110_1, all_171_0) = all_136_0 & uni(all_171_0) & uni(all_136_0)
% 33.48/5.55 |
% 33.48/5.55 | ALPHA: (73) implies:
% 33.48/5.55 | (74) infix_plpl(elt1, all_133_1, all_136_1) = all_171_0
% 33.48/5.55 |
% 33.48/5.55 | REDUCE: (47), (64) imply:
% 33.48/5.55 | (75) infix_plpl(elt1, all_133_1, all_136_1) = all_136_0
% 33.48/5.55 |
% 33.48/5.55 | BETA: splitting (67) gives:
% 33.48/5.55 |
% 33.48/5.55 | Case 1:
% 33.48/5.55 | |
% 33.48/5.55 | | (76) all_139_0 = 0
% 33.48/5.55 | |
% 33.48/5.55 | | REDUCE: (51), (76) imply:
% 33.48/5.55 | | (77) $false
% 33.48/5.55 | |
% 33.48/5.55 | | CLOSE: (77) is inconsistent.
% 33.48/5.55 | |
% 33.48/5.55 | Case 2:
% 33.48/5.55 | |
% 33.48/5.55 | | (78) ? [v0: int] : ( ~ (v0 = 0) & permut(elt1, all_136_0, all_128_1) =
% 33.48/5.55 | | v0)
% 33.48/5.55 | |
% 33.48/5.55 | | DELTA: instantiating (78) with fresh symbol all_196_0 gives:
% 33.48/5.55 | | (79) ~ (all_196_0 = 0) & permut(elt1, all_136_0, all_128_1) = all_196_0
% 33.48/5.55 | |
% 33.48/5.55 | | ALPHA: (79) implies:
% 33.48/5.55 | | (80) ~ (all_196_0 = 0)
% 33.48/5.55 | | (81) permut(elt1, all_136_0, all_128_1) = all_196_0
% 33.48/5.55 | |
% 33.48/5.55 | | GROUND_INST: instantiating (10) with all_136_0, all_171_0, all_136_1,
% 33.48/5.55 | | all_133_1, elt1, simplifying with (74), (75) gives:
% 33.48/5.55 | | (82) all_171_0 = all_136_0
% 33.48/5.55 | |
% 33.48/5.56 | | GROUND_INST: instantiating (9) with all_128_5, all_131_3, all_128_6,
% 33.48/5.56 | | simplifying with (25), (69) gives:
% 33.48/5.56 | | (83) all_131_3 = all_128_5
% 33.48/5.56 | |
% 33.48/5.56 | | GROUND_INST: instantiating (9) with all_128_1, all_131_1, all_128_0,
% 33.48/5.56 | | simplifying with (68), (70) gives:
% 33.48/5.56 | | (84) all_131_1 = all_128_1
% 33.48/5.56 | |
% 33.48/5.56 | | REDUCE: (34), (84) imply:
% 33.48/5.56 | | (85) infix_plpl(elt1, all_128_2, all_131_2) = all_128_1
% 33.48/5.56 | |
% 33.48/5.56 | | REDUCE: (31), (83) imply:
% 33.48/5.56 | | (86) uni(all_128_5)
% 33.48/5.56 | |
% 33.48/5.56 | | GROUND_INST: instantiating (prefix_length) with elt1, all_128_3, all_128_5,
% 33.48/5.56 | | all_128_2, all_164_0, simplifying with (6), (27), (72), (86)
% 33.48/5.56 | | gives:
% 33.48/5.56 | | (87) all_164_0 = all_128_3 | ~ ($lesseq(0, all_128_3)) | ? [v0: int] :
% 33.48/5.56 | | ($lesseq(1, $difference(all_128_3, v0)) & length(elt1, all_128_5) =
% 33.48/5.56 | | v0)
% 33.48/5.56 | |
% 33.48/5.56 | | GROUND_INST: instantiating (1) with elt1, all_128_2, all_164_0, simplifying
% 33.48/5.56 | | with (6), (23), (72) gives:
% 33.48/5.56 | | (88) all_164_0 = 0 | ? [v0: any] : ( ~ (v0 = all_128_2) & nil(elt1) = v0
% 33.48/5.56 | | & uni(v0))
% 33.48/5.56 | |
% 33.48/5.56 | | GROUND_INST: instantiating (permut_append) with elt1, all_133_1, all_136_1,
% 33.48/5.56 | | all_128_2, all_131_2, all_136_0, all_128_1, all_196_0,
% 33.48/5.56 | | simplifying with (6), (23), (32), (39), (45), (75), (81), (85)
% 33.48/5.56 | | gives:
% 33.48/5.56 | | (89) all_196_0 = 0 | ? [v0: any] : ? [v1: any] : (permut(elt1,
% 33.48/5.56 | | all_136_1, all_131_2) = v1 & permut(elt1, all_133_1, all_128_2)
% 33.48/5.56 | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 33.48/5.56 | |
% 33.48/5.56 | | BETA: splitting (89) gives:
% 33.48/5.56 | |
% 33.48/5.56 | | Case 1:
% 33.48/5.56 | | |
% 33.48/5.56 | | | (90) all_196_0 = 0
% 33.48/5.56 | | |
% 33.48/5.56 | | | REDUCE: (80), (90) imply:
% 33.48/5.56 | | | (91) $false
% 33.48/5.56 | | |
% 33.48/5.56 | | | CLOSE: (91) is inconsistent.
% 33.48/5.56 | | |
% 33.48/5.56 | | Case 2:
% 33.48/5.56 | | |
% 33.48/5.56 | | | (92) ? [v0: any] : ? [v1: any] : (permut(elt1, all_136_1, all_131_2)
% 33.48/5.56 | | | = v1 & permut(elt1, all_133_1, all_128_2) = v0 & ( ~ (v1 = 0) |
% 33.48/5.56 | | | ~ (v0 = 0)))
% 33.48/5.56 | | |
% 33.48/5.56 | | | DELTA: instantiating (92) with fresh symbols all_251_0, all_251_1 gives:
% 33.48/5.56 | | | (93) permut(elt1, all_136_1, all_131_2) = all_251_0 & permut(elt1,
% 33.48/5.56 | | | all_133_1, all_128_2) = all_251_1 & ( ~ (all_251_0 = 0) | ~
% 33.48/5.56 | | | (all_251_1 = 0))
% 33.48/5.56 | | |
% 33.48/5.56 | | | ALPHA: (93) implies:
% 33.48/5.56 | | | (94) permut(elt1, all_133_1, all_128_2) = all_251_1
% 33.48/5.56 | | | (95) permut(elt1, all_136_1, all_131_2) = all_251_0
% 33.48/5.56 | | | (96) ~ (all_251_0 = 0) | ~ (all_251_1 = 0)
% 33.48/5.56 | | |
% 33.48/5.56 | | | BETA: splitting (87) gives:
% 33.48/5.56 | | |
% 33.48/5.56 | | | Case 1:
% 33.48/5.56 | | | |
% 33.48/5.56 | | | | (97) $lesseq(all_128_3, -1)
% 33.48/5.56 | | | |
% 33.48/5.56 | | | | COMBINE_INEQS: (30), (97) imply:
% 33.48/5.56 | | | | (98) $false
% 33.48/5.56 | | | |
% 33.48/5.56 | | | | CLOSE: (98) is inconsistent.
% 33.48/5.56 | | | |
% 33.48/5.56 | | | Case 2:
% 33.48/5.56 | | | |
% 33.48/5.56 | | | | (99) all_164_0 = all_128_3 | ? [v0: int] : ($lesseq(1,
% 33.48/5.56 | | | | $difference(all_128_3, v0)) & length(elt1, all_128_5) = v0)
% 33.48/5.56 | | | |
% 33.48/5.56 | | | | BETA: splitting (99) gives:
% 33.48/5.56 | | | |
% 33.48/5.56 | | | | Case 1:
% 33.48/5.56 | | | | |
% 33.48/5.56 | | | | | (100) all_164_0 = all_128_3
% 33.48/5.56 | | | | |
% 33.48/5.56 | | | | | BETA: splitting (88) gives:
% 33.48/5.56 | | | | |
% 33.48/5.56 | | | | | Case 1:
% 33.48/5.56 | | | | | |
% 33.48/5.56 | | | | | | (101) all_164_0 = 0
% 33.48/5.56 | | | | | |
% 33.48/5.56 | | | | | | COMBINE_EQS: (100), (101) imply:
% 33.48/5.56 | | | | | | (102) all_128_3 = 0
% 33.48/5.56 | | | | | |
% 33.48/5.56 | | | | | | SIMP: (102) implies:
% 33.48/5.56 | | | | | | (103) all_128_3 = 0
% 33.48/5.56 | | | | | |
% 33.48/5.56 | | | | | | REDUCE: (30), (103) imply:
% 33.48/5.56 | | | | | | (104) $false
% 33.48/5.56 | | | | | |
% 33.48/5.56 | | | | | | CLOSE: (104) is inconsistent.
% 33.48/5.56 | | | | | |
% 33.48/5.56 | | | | | Case 2:
% 33.48/5.56 | | | | | |
% 33.48/5.56 | | | | | |
% 33.48/5.56 | | | | | | GROUND_INST: instantiating (11) with 0, all_251_1, all_128_2,
% 33.48/5.56 | | | | | | all_133_1, elt1, simplifying with (42), (94) gives:
% 33.48/5.56 | | | | | | (105) all_251_1 = 0
% 33.48/5.56 | | | | | |
% 33.48/5.56 | | | | | | GROUND_INST: instantiating (11) with 0, all_251_0, all_131_2,
% 33.48/5.56 | | | | | | all_136_1, elt1, simplifying with (48), (95) gives:
% 33.48/5.56 | | | | | | (106) all_251_0 = 0
% 33.48/5.56 | | | | | |
% 33.48/5.56 | | | | | | REF_CLOSE: (96), (105), (106) are inconsistent by sub-proof #1.
% 33.48/5.56 | | | | | |
% 33.48/5.56 | | | | | End of split
% 33.48/5.56 | | | | |
% 33.48/5.56 | | | | Case 2:
% 33.48/5.56 | | | | |
% 33.48/5.56 | | | | |
% 33.48/5.57 | | | | | GROUND_INST: instantiating (11) with 0, all_251_1, all_128_2,
% 33.48/5.57 | | | | | all_133_1, elt1, simplifying with (42), (94) gives:
% 33.48/5.57 | | | | | (107) all_251_1 = 0
% 33.48/5.57 | | | | |
% 33.48/5.57 | | | | | GROUND_INST: instantiating (11) with 0, all_251_0, all_131_2,
% 33.48/5.57 | | | | | all_136_1, elt1, simplifying with (48), (95) gives:
% 33.48/5.57 | | | | | (108) all_251_0 = 0
% 33.48/5.57 | | | | |
% 33.48/5.57 | | | | | REF_CLOSE: (96), (107), (108) are inconsistent by sub-proof #1.
% 33.48/5.57 | | | | |
% 33.48/5.57 | | | | End of split
% 33.48/5.57 | | | |
% 33.48/5.57 | | | End of split
% 33.48/5.57 | | |
% 33.48/5.57 | | End of split
% 33.48/5.57 | |
% 33.48/5.57 | End of split
% 33.48/5.57 |
% 33.48/5.57 End of proof
% 33.48/5.57
% 33.48/5.57 Sub-proof #1 shows that the following formulas are inconsistent:
% 33.48/5.57 ----------------------------------------------------------------
% 33.48/5.57 (1) ~ (all_251_0 = 0) | ~ (all_251_1 = 0)
% 33.48/5.57 (2) all_251_0 = 0
% 33.48/5.57 (3) all_251_1 = 0
% 33.48/5.57
% 33.48/5.57 Begin of proof
% 33.48/5.57 |
% 33.48/5.57 | BETA: splitting (1) gives:
% 33.48/5.57 |
% 33.48/5.57 | Case 1:
% 33.48/5.57 | |
% 33.48/5.57 | | (4) ~ (all_251_0 = 0)
% 33.48/5.57 | |
% 33.48/5.57 | | REDUCE: (2), (4) imply:
% 33.48/5.57 | | (5) $false
% 33.48/5.57 | |
% 33.48/5.57 | | CLOSE: (5) is inconsistent.
% 33.48/5.57 | |
% 33.48/5.57 | Case 2:
% 33.48/5.57 | |
% 33.48/5.57 | | (6) ~ (all_251_1 = 0)
% 33.48/5.57 | |
% 33.48/5.57 | | REDUCE: (3), (6) imply:
% 33.48/5.57 | | (7) $false
% 33.48/5.57 | |
% 33.48/5.57 | | CLOSE: (7) is inconsistent.
% 33.48/5.57 | |
% 33.48/5.57 | End of split
% 33.48/5.57 |
% 33.48/5.57 End of proof
% 33.48/5.57 % SZS output end Proof for theBenchmark
% 33.48/5.57
% 33.48/5.57 4937ms
%------------------------------------------------------------------------------