TSTP Solution File: SWW629_2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW629_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 00:50:57 EDT 2023
% Result : Theorem 17.70s 3.07s
% Output : Proof 25.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWW629_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Sun Aug 27 21:44:45 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.50 ________ _____
% 0.14/0.50 ___ __ \_________(_)________________________________
% 0.14/0.50 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.50 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.50 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.50
% 0.14/0.50 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.50 (2023-06-19)
% 0.14/0.50
% 0.14/0.50 (c) Philipp Rümmer, 2009-2023
% 0.14/0.50 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.50 Amanda Stjerna.
% 0.14/0.50 Free software under BSD-3-Clause.
% 0.14/0.50
% 0.14/0.50 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.50
% 0.14/0.51 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.52 Running up to 7 provers in parallel.
% 0.14/0.53 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.53 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.53 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.53 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.53 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.53 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.14/0.53 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.97/1.22 Prover 5: Preprocessing ...
% 3.97/1.22 Prover 0: Preprocessing ...
% 3.97/1.22 Prover 1: Preprocessing ...
% 3.97/1.22 Prover 6: Preprocessing ...
% 3.97/1.22 Prover 2: Preprocessing ...
% 3.97/1.22 Prover 4: Preprocessing ...
% 3.97/1.22 Prover 3: Preprocessing ...
% 10.64/2.19 Prover 1: Warning: ignoring some quantifiers
% 10.64/2.21 Prover 5: Proving ...
% 10.64/2.22 Prover 4: Warning: ignoring some quantifiers
% 10.64/2.24 Prover 3: Warning: ignoring some quantifiers
% 11.59/2.26 Prover 1: Constructing countermodel ...
% 11.59/2.27 Prover 3: Constructing countermodel ...
% 11.59/2.27 Prover 6: Proving ...
% 11.59/2.28 Prover 4: Constructing countermodel ...
% 11.59/2.30 Prover 0: Proving ...
% 12.16/2.34 Prover 2: Proving ...
% 17.70/3.07 Prover 3: proved (2540ms)
% 17.70/3.07
% 17.70/3.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.70/3.07
% 17.70/3.07 Prover 2: stopped
% 17.70/3.07 Prover 5: stopped
% 17.70/3.07 Prover 6: stopped
% 17.70/3.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 17.70/3.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 17.70/3.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.70/3.08 Prover 0: stopped
% 17.70/3.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 17.70/3.09 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 19.19/3.27 Prover 8: Preprocessing ...
% 19.19/3.28 Prover 11: Preprocessing ...
% 19.19/3.30 Prover 7: Preprocessing ...
% 19.19/3.31 Prover 10: Preprocessing ...
% 19.63/3.35 Prover 13: Preprocessing ...
% 19.91/3.42 Prover 8: Warning: ignoring some quantifiers
% 19.91/3.44 Prover 8: Constructing countermodel ...
% 19.91/3.48 Prover 7: Warning: ignoring some quantifiers
% 19.91/3.50 Prover 10: Warning: ignoring some quantifiers
% 19.91/3.53 Prover 7: Constructing countermodel ...
% 19.91/3.53 Prover 10: Constructing countermodel ...
% 19.91/3.55 Prover 13: Warning: ignoring some quantifiers
% 21.16/3.58 Prover 13: Constructing countermodel ...
% 21.16/3.59 Prover 11: Warning: ignoring some quantifiers
% 21.16/3.62 Prover 11: Constructing countermodel ...
% 25.31/4.09 Prover 10: Found proof (size 77)
% 25.31/4.09 Prover 10: proved (1025ms)
% 25.31/4.10 Prover 11: stopped
% 25.31/4.10 Prover 7: stopped
% 25.31/4.10 Prover 1: stopped
% 25.31/4.10 Prover 8: stopped
% 25.31/4.10 Prover 13: Found proof (size 79)
% 25.31/4.10 Prover 13: proved (1009ms)
% 25.31/4.11 Prover 4: stopped
% 25.31/4.11
% 25.31/4.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.31/4.11
% 25.31/4.12 % SZS output start Proof for theBenchmark
% 25.31/4.12 Assumptions after simplification:
% 25.31/4.12 ---------------------------------
% 25.31/4.12
% 25.31/4.12 (append_assoc)
% 25.31/4.14 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : !
% 25.31/4.14 [v5: uni] : ( ~ (infix_plpl(v0, v4, v3) = v5) | ~ (infix_plpl(v0, v1, v2) =
% 25.31/4.14 v4) | ~ ty(v0) | ~ uni(v3) | ~ uni(v2) | ~ uni(v1) | ? [v6: uni] :
% 25.31/4.14 (infix_plpl(v0, v2, v3) = v6 & infix_plpl(v0, v1, v6) = v5 & uni(v6) &
% 25.31/4.14 uni(v5)))
% 25.31/4.14
% 25.31/4.14 (append_l_nil)
% 25.31/4.14 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : (v3 = v1 | ~
% 25.31/4.14 (infix_plpl(v0, v1, v2) = v3) | ~ (nil(v0) = v2) | ~ ty(v0) | ~ uni(v1))
% 25.31/4.14
% 25.31/4.14 (bridgeR)
% 25.31/4.14 ! [v0: uni] : ! [v1: list_elt] : ( ~ (tb2t(v0) = v1) | ~ uni(v0) | t2tb(v1)
% 25.31/4.14 = v0)
% 25.31/4.14
% 25.31/4.14 (length_nil)
% 25.31/4.14 ! [v0: ty] : ! [v1: uni] : ! [v2: int] : (v2 = 0 | ~ (length2(v0, v1) =
% 25.31/4.14 v2) | ~ ty(v0) | ~ uni(v1) | ? [v3: uni] : ( ~ (v3 = v1) & nil(v0) = v3
% 25.31/4.14 & uni(v3))) & ! [v0: ty] : ! [v1: uni] : ( ~ (length2(v0, v1) = 0) | ~
% 25.31/4.14 ty(v0) | ~ uni(v1) | nil(v0) = v1)
% 25.31/4.14
% 25.31/4.14 (nil_sort1)
% 25.31/4.14 ! [v0: ty] : ! [v1: ty] : ( ~ (list(v0) = v1) | ~ ty(v0) | ? [v2: uni] :
% 25.31/4.14 (nil(v0) = v2 & uni(v2) & sort1(v1, v2)))
% 25.31/4.14
% 25.31/4.14 (permut_append)
% 25.31/4.14 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : !
% 25.31/4.14 [v5: uni] : ! [v6: uni] : ( ~ (infix_plpl(v0, v3, v4) = v6) | ~
% 25.31/4.14 (infix_plpl(v0, v1, v2) = v5) | ~ ty(v0) | ~ uni(v4) | ~ uni(v3) | ~
% 25.31/4.14 uni(v2) | ~ uni(v1) | ~ permut(v0, v2, v4) | ~ permut(v0, v1, v3) |
% 25.31/4.14 permut(v0, v5, v6))
% 25.31/4.14
% 25.31/4.14 (permut_append_swap)
% 25.31/4.14 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ( ~ (infix_plpl(v0,
% 25.31/4.14 v1, v2) = v3) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v4: uni] :
% 25.31/4.14 (infix_plpl(v0, v2, v1) = v4 & uni(v4) & permut(v0, v3, v4)))
% 25.31/4.14
% 25.31/4.14 (permut_assoc)
% 25.31/4.14 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : !
% 25.31/4.15 [v5: uni] : ( ~ (infix_plpl(v0, v4, v3) = v5) | ~ (infix_plpl(v0, v1, v2) =
% 25.31/4.15 v4) | ~ ty(v0) | ~ uni(v3) | ~ uni(v2) | ~ uni(v1) | ? [v6: uni] : ?
% 25.31/4.15 [v7: uni] : (infix_plpl(v0, v2, v3) = v6 & infix_plpl(v0, v1, v6) = v7 &
% 25.31/4.15 uni(v7) & uni(v6) & permut(v0, v5, v7)))
% 25.31/4.15
% 25.31/4.15 (permut_trans)
% 25.31/4.15 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ( ~ ty(v0) | ~
% 25.31/4.15 uni(v3) | ~ uni(v2) | ~ uni(v1) | ~ permut(v0, v2, v3) | ~ permut(v0,
% 25.31/4.15 v1, v2) | permut(v0, v1, v3))
% 25.31/4.15
% 25.31/4.15 (sorted_Nil)
% 25.31/4.15 ty(elt) & ? [v0: uni] : ? [v1: list_elt] : (tb2t(v0) = v1 & nil(elt) = v0 &
% 25.31/4.15 list_elt(v1) & uni(v0) & sorted1(v1))
% 25.31/4.15
% 25.31/4.15 (sorted_One)
% 25.31/4.15 ty(elt) & ? [v0: uni] : (nil(elt) = v0 & uni(v0) & ! [v1: elt1] : ! [v2:
% 25.31/4.15 uni] : ( ~ (t2tb1(v1) = v2) | ~ elt1(v1) | ? [v3: uni] : ? [v4:
% 25.31/4.15 list_elt] : (tb2t(v3) = v4 & cons(elt, v2, v0) = v3 & list_elt(v4) &
% 25.31/4.15 uni(v3) & sorted1(v4))))
% 25.31/4.15
% 25.31/4.15 (sorted_inversion)
% 25.31/4.15 ty(elt) & ? [v0: uni] : ? [v1: list_elt] : (tb2t(v0) = v1 & nil(elt) = v0 &
% 25.31/4.15 list_elt(v1) & uni(v0) & ! [v2: list_elt] : (v2 = v1 | ~ list_elt(v2) | ~
% 25.31/4.15 sorted1(v2) | ? [v3: elt1] : ? [v4: elt1] : ? [v5: list_elt] : ? [v6:
% 25.31/4.15 uni] : ? [v7: uni] : ? [v8: uni] : ? [v9: list_elt] : ? [v10: uni] :
% 25.31/4.15 ? [v11: uni] : ? [v12: list_elt] : ? [v13: elt1] : ? [v14: uni] : ?
% 25.31/4.15 [v15: uni] : ? [v16: list_elt] : (list_elt(v5) & elt1(v13) & elt1(v4) &
% 25.31/4.15 elt1(v3) & ((v16 = v2 & t2tb1(v13) = v14 & tb2t(v15) = v2 & cons(elt,
% 25.31/4.15 v14, v0) = v15 & uni(v15) & uni(v14)) | (v12 = v2 & t2tb1(v4) = v6
% 25.31/4.15 & t2tb1(v3) = v10 & tb2t(v11) = v2 & tb2t(v8) = v9 & t2tb(v5) = v7 &
% 25.31/4.15 cons(elt, v10, v8) = v11 & cons(elt, v6, v7) = v8 & list_elt(v9) &
% 25.31/4.15 uni(v11) & uni(v10) & uni(v8) & uni(v7) & uni(v6) & sorted1(v9) &
% 25.31/4.15 le1(v3, v4))))))
% 25.31/4.15
% 25.31/4.15 (t2tb_sort)
% 25.31/4.15 ty(elt) & ? [v0: ty] : (list(elt) = v0 & ty(v0) & ! [v1: list_elt] : ! [v2:
% 25.31/4.15 uni] : ( ~ (t2tb(v1) = v2) | ~ list_elt(v1) | sort1(v0, v2)))
% 25.31/4.15
% 25.31/4.15 (wP_parameter_mergesort)
% 25.31/4.15 bool1(true1) & ty(elt) & ? [v0: uni] : ? [v1: list_elt] : ? [v2: list_elt]
% 25.31/4.15 : ? [v3: uni] : ? [v4: int] : ? [v5: list_elt] : ? [v6: list_elt] : ?
% 25.31/4.15 [v7: uni] : ? [v8: uni] : ? [v9: uni] : ? [v10: uni] : ? [v11: uni] : ?
% 25.31/4.15 [v12: int] : ? [v13: int] : ? [v14: int] : ? [v15: list_elt] : ? [v16:
% 25.31/4.15 uni] : ? [v17: list_elt] : ? [v18: uni] : ? [v19: uni] : ? [v20:
% 25.31/4.15 list_elt] : ? [v21: uni] : ($lesseq(2, v4) & tb2t(v0) = v1 & t2tb(v20) =
% 25.31/4.15 v21 & t2tb(v17) = v18 & t2tb(v15) = v16 & t2tb(v6) = v7 & t2tb(v5) = v8 &
% 25.31/4.15 t2tb(v2) = v3 & t2tb(v1) = v10 & infix_plpl(elt, v16, v18) = v19 &
% 25.31/4.15 infix_plpl(elt, v9, v10) = v11 & infix_plpl(elt, v7, v8) = v9 & length2(elt,
% 25.31/4.15 v8) = v13 & length2(elt, v7) = v12 & length2(elt, v3) = v4 & nil(elt) = v0
% 25.31/4.15 & list_elt(v20) & list_elt(v17) & list_elt(v15) & list_elt(v6) &
% 25.31/4.15 list_elt(v5) & list_elt(v2) & list_elt(v1) & uni(v21) & uni(v19) & uni(v18)
% 25.31/4.15 & uni(v16) & uni(v11) & uni(v10) & uni(v9) & uni(v8) & uni(v7) & uni(v3) &
% 25.31/4.15 uni(v0) & sorted1(v20) & sorted1(v17) & sorted1(v15) & permut(elt, v21, v19)
% 25.31/4.15 & permut(elt, v18, v8) & permut(elt, v16, v7) & permut(elt, v11, v3) &
% 25.31/4.15 permut(elt, v9, v3) & ~ permut(elt, v21, v3) & (v13 = v12 | (v14 = 0 &
% 25.31/4.15 $difference(v13, v12) = -1 & length2(elt, v10) = 0)))
% 25.31/4.15
% 25.31/4.15 (function-axioms)
% 25.31/4.16 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : !
% 25.31/4.16 [v5: ty] : ! [v6: ty] : (v1 = v0 | ~ (match_list1(v6, v5, v4, v3, v2) = v1)
% 25.31/4.16 | ~ (match_list1(v6, v5, v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] :
% 25.31/4.16 ! [v2: uni] : ! [v3: uni] : ! [v4: bool1] : ! [v5: ty] : (v1 = v0 | ~
% 25.31/4.16 (match_bool1(v5, v4, v3, v2) = v1) | ~ (match_bool1(v5, v4, v3, v2) = v0))
% 25.31/4.16 & ! [v0: int] : ! [v1: int] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] :
% 25.31/4.16 (v1 = v0 | ~ (num_occ1(v4, v3, v2) = v1) | ~ (num_occ1(v4, v3, v2) = v0)) &
% 25.31/4.16 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : (v1 =
% 25.31/4.16 v0 | ~ (infix_plpl(v4, v3, v2) = v1) | ~ (infix_plpl(v4, v3, v2) = v0)) &
% 25.31/4.16 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : (v1 =
% 25.31/4.16 v0 | ~ (cons(v4, v3, v2) = v1) | ~ (cons(v4, v3, v2) = v0)) & ! [v0: int]
% 25.31/4.16 : ! [v1: int] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (length3(v3, v2) =
% 25.31/4.16 v1) | ~ (length3(v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2:
% 25.31/4.16 uni] : ! [v3: ty] : (v1 = v0 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) =
% 25.31/4.16 v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0
% 25.31/4.16 | ~ (mk_t(v3, v2) = v1) | ~ (mk_t(v3, v2) = v0)) & ! [v0: uni] : ! [v1:
% 25.31/4.16 uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (reverse(v3, v2) = v1) |
% 25.31/4.16 ~ (reverse(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: uni] : !
% 25.31/4.16 [v3: ty] : (v1 = v0 | ~ (length2(v3, v2) = v1) | ~ (length2(v3, v2) = v0)) &
% 25.31/4.16 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~
% 25.31/4.16 (cons_proj_21(v3, v2) = v1) | ~ (cons_proj_21(v3, v2) = v0)) & ! [v0: uni]
% 25.31/4.16 : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (cons_proj_11(v3,
% 25.31/4.16 v2) = v1) | ~ (cons_proj_11(v3, v2) = v0)) & ! [v0: elt1] : ! [v1:
% 25.31/4.16 elt1] : ! [v2: uni] : (v1 = v0 | ~ (tb2t1(v2) = v1) | ~ (tb2t1(v2) = v0))
% 25.31/4.16 & ! [v0: uni] : ! [v1: uni] : ! [v2: elt1] : (v1 = v0 | ~ (t2tb1(v2) = v1)
% 25.31/4.16 | ~ (t2tb1(v2) = v0)) & ! [v0: list_elt] : ! [v1: list_elt] : ! [v2:
% 25.31/4.16 uni] : (v1 = v0 | ~ (tb2t(v2) = v1) | ~ (tb2t(v2) = v0)) & ! [v0: uni] :
% 25.31/4.16 ! [v1: uni] : ! [v2: list_elt] : (v1 = v0 | ~ (t2tb(v2) = v1) | ~ (t2tb(v2)
% 25.31/4.16 = v0)) & ! [v0: ty] : ! [v1: ty] : ! [v2: ty] : (v1 = v0 | ~ (t(v2) =
% 25.31/4.16 v1) | ~ (t(v2) = v0)) & ! [v0: ty] : ! [v1: ty] : ! [v2: ty] : (v1 =
% 25.31/4.16 v0 | ~ (list(v2) = v1) | ~ (list(v2) = v0)) & ! [v0: uni] : ! [v1: uni]
% 25.31/4.16 : ! [v2: ty] : (v1 = v0 | ~ (nil(v2) = v1) | ~ (nil(v2) = v0)) & ! [v0:
% 25.31/4.16 uni] : ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~ (witness1(v2) = v1) | ~
% 25.31/4.16 (witness1(v2) = v0))
% 25.31/4.16
% 25.31/4.16 Further assumptions not needed in the proof:
% 25.31/4.16 --------------------------------------------
% 25.31/4.16 append_Num_Occ, append_length, bool_inversion, bridgeL, bridgeL1, bridgeR1,
% 25.31/4.16 compatOrderMult, cons_proj_1_def1, cons_proj_1_sort1, cons_proj_2_def1,
% 25.31/4.16 cons_proj_2_sort1, cons_sort1, elts_def1, elts_sort1, infix_plpl_def,
% 25.31/4.16 infix_plpl_sort1, length_def, length_def1, length_nonnegative, list_inversion1,
% 25.31/4.16 match_bool_False, match_bool_True, match_bool_sort1, match_list_Cons1,
% 25.31/4.16 match_list_Nil1, match_list_sort1, mem_Num_Occ, mem_append, mem_decomp, mem_def,
% 25.31/4.16 mk_t_sort1, nil_Cons1, num_occ_def, permut_cons, permut_cons_append, permut_def,
% 25.31/4.16 permut_length, permut_mem, permut_refl, permut_swap, permut_sym, refl1,
% 25.31/4.16 reverse_append, reverse_cons, reverse_def, reverse_length, reverse_mem,
% 25.31/4.16 reverse_num_occ, reverse_reverse, reverse_sort1, sorted_Two, sorted_append,
% 25.31/4.16 sorted_mem, t2tb_sort1, t_inversion1, total1, trans1, true_False,
% 25.31/4.16 tuple0_inversion, witness_sort1
% 25.31/4.16
% 25.31/4.16 Those formulas are unsatisfiable:
% 25.31/4.16 ---------------------------------
% 25.31/4.16
% 25.31/4.16 Begin of proof
% 25.31/4.16 |
% 25.31/4.16 | ALPHA: (length_nil) implies:
% 25.31/4.16 | (1) ! [v0: ty] : ! [v1: uni] : ! [v2: int] : (v2 = 0 | ~ (length2(v0,
% 25.31/4.16 | v1) = v2) | ~ ty(v0) | ~ uni(v1) | ? [v3: uni] : ( ~ (v3 = v1)
% 25.31/4.16 | & nil(v0) = v3 & uni(v3)))
% 25.31/4.16 |
% 25.31/4.16 | ALPHA: (t2tb_sort) implies:
% 25.31/4.16 | (2) ? [v0: ty] : (list(elt) = v0 & ty(v0) & ! [v1: list_elt] : ! [v2:
% 25.31/4.16 | uni] : ( ~ (t2tb(v1) = v2) | ~ list_elt(v1) | sort1(v0, v2)))
% 25.31/4.16 |
% 25.31/4.16 | ALPHA: (sorted_Nil) implies:
% 25.31/4.16 | (3) ? [v0: uni] : ? [v1: list_elt] : (tb2t(v0) = v1 & nil(elt) = v0 &
% 25.31/4.16 | list_elt(v1) & uni(v0) & sorted1(v1))
% 25.31/4.16 |
% 25.31/4.16 | ALPHA: (sorted_One) implies:
% 25.31/4.16 | (4) ? [v0: uni] : (nil(elt) = v0 & uni(v0) & ! [v1: elt1] : ! [v2: uni]
% 25.31/4.17 | : ( ~ (t2tb1(v1) = v2) | ~ elt1(v1) | ? [v3: uni] : ? [v4:
% 25.31/4.17 | list_elt] : (tb2t(v3) = v4 & cons(elt, v2, v0) = v3 &
% 25.31/4.17 | list_elt(v4) & uni(v3) & sorted1(v4))))
% 25.31/4.17 |
% 25.31/4.17 | ALPHA: (sorted_inversion) implies:
% 25.31/4.17 | (5) ? [v0: uni] : ? [v1: list_elt] : (tb2t(v0) = v1 & nil(elt) = v0 &
% 25.31/4.17 | list_elt(v1) & uni(v0) & ! [v2: list_elt] : (v2 = v1 | ~
% 25.31/4.17 | list_elt(v2) | ~ sorted1(v2) | ? [v3: elt1] : ? [v4: elt1] : ?
% 25.31/4.17 | [v5: list_elt] : ? [v6: uni] : ? [v7: uni] : ? [v8: uni] : ?
% 25.31/4.17 | [v9: list_elt] : ? [v10: uni] : ? [v11: uni] : ? [v12: list_elt]
% 25.31/4.17 | : ? [v13: elt1] : ? [v14: uni] : ? [v15: uni] : ? [v16:
% 25.31/4.17 | list_elt] : (list_elt(v5) & elt1(v13) & elt1(v4) & elt1(v3) &
% 25.31/4.17 | ((v16 = v2 & t2tb1(v13) = v14 & tb2t(v15) = v2 & cons(elt, v14,
% 25.31/4.17 | v0) = v15 & uni(v15) & uni(v14)) | (v12 = v2 & t2tb1(v4) =
% 25.31/4.17 | v6 & t2tb1(v3) = v10 & tb2t(v11) = v2 & tb2t(v8) = v9 &
% 25.31/4.17 | t2tb(v5) = v7 & cons(elt, v10, v8) = v11 & cons(elt, v6, v7)
% 25.31/4.17 | = v8 & list_elt(v9) & uni(v11) & uni(v10) & uni(v8) & uni(v7)
% 25.31/4.17 | & uni(v6) & sorted1(v9) & le1(v3, v4))))))
% 25.31/4.17 |
% 25.31/4.17 | ALPHA: (wP_parameter_mergesort) implies:
% 25.31/4.17 | (6) ty(elt)
% 25.31/4.17 | (7) ? [v0: uni] : ? [v1: list_elt] : ? [v2: list_elt] : ? [v3: uni] :
% 25.31/4.17 | ? [v4: int] : ? [v5: list_elt] : ? [v6: list_elt] : ? [v7: uni] : ?
% 25.31/4.17 | [v8: uni] : ? [v9: uni] : ? [v10: uni] : ? [v11: uni] : ? [v12:
% 25.31/4.17 | int] : ? [v13: int] : ? [v14: int] : ? [v15: list_elt] : ? [v16:
% 25.31/4.17 | uni] : ? [v17: list_elt] : ? [v18: uni] : ? [v19: uni] : ? [v20:
% 25.31/4.17 | list_elt] : ? [v21: uni] : ($lesseq(2, v4) & tb2t(v0) = v1 &
% 25.31/4.17 | t2tb(v20) = v21 & t2tb(v17) = v18 & t2tb(v15) = v16 & t2tb(v6) = v7 &
% 25.31/4.17 | t2tb(v5) = v8 & t2tb(v2) = v3 & t2tb(v1) = v10 & infix_plpl(elt, v16,
% 25.31/4.17 | v18) = v19 & infix_plpl(elt, v9, v10) = v11 & infix_plpl(elt, v7,
% 25.31/4.17 | v8) = v9 & length2(elt, v8) = v13 & length2(elt, v7) = v12 &
% 25.31/4.17 | length2(elt, v3) = v4 & nil(elt) = v0 & list_elt(v20) & list_elt(v17)
% 25.31/4.17 | & list_elt(v15) & list_elt(v6) & list_elt(v5) & list_elt(v2) &
% 25.31/4.17 | list_elt(v1) & uni(v21) & uni(v19) & uni(v18) & uni(v16) & uni(v11) &
% 25.31/4.17 | uni(v10) & uni(v9) & uni(v8) & uni(v7) & uni(v3) & uni(v0) &
% 25.31/4.17 | sorted1(v20) & sorted1(v17) & sorted1(v15) & permut(elt, v21, v19) &
% 25.31/4.17 | permut(elt, v18, v8) & permut(elt, v16, v7) & permut(elt, v11, v3) &
% 25.31/4.17 | permut(elt, v9, v3) & ~ permut(elt, v21, v3) & (v13 = v12 | (v14 = 0
% 25.31/4.17 | & $difference(v13, v12) = -1 & length2(elt, v10) = 0)))
% 25.31/4.17 |
% 25.31/4.17 | ALPHA: (function-axioms) implies:
% 25.31/4.17 | (8) ! [v0: uni] : ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~ (nil(v2) =
% 25.31/4.17 | v1) | ~ (nil(v2) = v0))
% 25.31/4.17 | (9) ! [v0: uni] : ! [v1: uni] : ! [v2: list_elt] : (v1 = v0 | ~
% 25.31/4.17 | (t2tb(v2) = v1) | ~ (t2tb(v2) = v0))
% 25.31/4.17 | (10) ! [v0: list_elt] : ! [v1: list_elt] : ! [v2: uni] : (v1 = v0 | ~
% 25.31/4.17 | (tb2t(v2) = v1) | ~ (tb2t(v2) = v0))
% 25.31/4.17 | (11) ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4:
% 25.31/4.17 | ty] : (v1 = v0 | ~ (infix_plpl(v4, v3, v2) = v1) | ~
% 25.31/4.17 | (infix_plpl(v4, v3, v2) = v0))
% 25.31/4.17 |
% 25.31/4.17 | DELTA: instantiating (3) with fresh symbols all_83_0, all_83_1 gives:
% 25.31/4.17 | (12) tb2t(all_83_1) = all_83_0 & nil(elt) = all_83_1 & list_elt(all_83_0) &
% 25.31/4.17 | uni(all_83_1) & sorted1(all_83_0)
% 25.31/4.17 |
% 25.31/4.17 | ALPHA: (12) implies:
% 25.31/4.17 | (13) nil(elt) = all_83_1
% 25.31/4.17 | (14) tb2t(all_83_1) = all_83_0
% 25.31/4.17 |
% 25.31/4.17 | DELTA: instantiating (2) with fresh symbol all_85_0 gives:
% 25.31/4.17 | (15) list(elt) = all_85_0 & ty(all_85_0) & ! [v0: list_elt] : ! [v1: uni]
% 25.31/4.17 | : ( ~ (t2tb(v0) = v1) | ~ list_elt(v0) | sort1(all_85_0, v1))
% 25.31/4.17 |
% 25.31/4.17 | ALPHA: (15) implies:
% 25.31/4.17 | (16) list(elt) = all_85_0
% 25.31/4.17 |
% 25.31/4.17 | DELTA: instantiating (4) with fresh symbol all_90_0 gives:
% 25.31/4.18 | (17) nil(elt) = all_90_0 & uni(all_90_0) & ! [v0: elt1] : ! [v1: uni] : (
% 25.31/4.18 | ~ (t2tb1(v0) = v1) | ~ elt1(v0) | ? [v2: uni] : ? [v3: list_elt]
% 25.31/4.18 | : (tb2t(v2) = v3 & cons(elt, v1, all_90_0) = v2 & list_elt(v3) &
% 25.31/4.18 | uni(v2) & sorted1(v3)))
% 25.31/4.18 |
% 25.31/4.18 | ALPHA: (17) implies:
% 25.31/4.18 | (18) uni(all_90_0)
% 25.31/4.18 | (19) nil(elt) = all_90_0
% 25.31/4.18 |
% 25.31/4.18 | DELTA: instantiating (5) with fresh symbols all_93_0, all_93_1 gives:
% 25.31/4.18 | (20) tb2t(all_93_1) = all_93_0 & nil(elt) = all_93_1 & list_elt(all_93_0) &
% 25.31/4.18 | uni(all_93_1) & ! [v0: any] : (v0 = all_93_0 | ~ list_elt(v0) | ~
% 25.31/4.18 | sorted1(v0) | ? [v1: elt1] : ? [v2: elt1] : ? [v3: list_elt] : ?
% 25.31/4.18 | [v4: uni] : ? [v5: uni] : ? [v6: uni] : ? [v7: list_elt] : ?
% 25.31/4.18 | [v8: uni] : ? [v9: uni] : ? [v10: any] : ? [v11: elt1] : ? [v12:
% 25.31/4.18 | uni] : ? [v13: uni] : ? [v14: any] : (list_elt(v3) & elt1(v11) &
% 25.31/4.18 | elt1(v2) & elt1(v1) & ((v14 = v0 & t2tb1(v11) = v12 & tb2t(v13) =
% 25.31/4.18 | v0 & cons(elt, v12, all_93_1) = v13 & uni(v13) & uni(v12)) |
% 25.31/4.18 | (v10 = v0 & t2tb1(v2) = v4 & t2tb1(v1) = v8 & tb2t(v9) = v0 &
% 25.31/4.18 | tb2t(v6) = v7 & t2tb(v3) = v5 & cons(elt, v8, v6) = v9 &
% 25.31/4.18 | cons(elt, v4, v5) = v6 & list_elt(v7) & uni(v9) & uni(v8) &
% 25.31/4.18 | uni(v6) & uni(v5) & uni(v4) & sorted1(v7) & le1(v1, v2)))))
% 25.31/4.18 |
% 25.31/4.18 | ALPHA: (20) implies:
% 25.31/4.18 | (21) nil(elt) = all_93_1
% 25.31/4.18 | (22) tb2t(all_93_1) = all_93_0
% 25.31/4.18 |
% 25.31/4.18 | DELTA: instantiating (7) with fresh symbols all_96_0, all_96_1, all_96_2,
% 25.31/4.18 | all_96_3, all_96_4, all_96_5, all_96_6, all_96_7, all_96_8, all_96_9,
% 25.31/4.18 | all_96_10, all_96_11, all_96_12, all_96_13, all_96_14, all_96_15,
% 25.31/4.18 | all_96_16, all_96_17, all_96_18, all_96_19, all_96_20, all_96_21 gives:
% 25.31/4.18 | (23) $lesseq(2, all_96_17) & tb2t(all_96_21) = all_96_20 & t2tb(all_96_1) =
% 25.31/4.18 | all_96_0 & t2tb(all_96_4) = all_96_3 & t2tb(all_96_6) = all_96_5 &
% 25.31/4.18 | t2tb(all_96_15) = all_96_14 & t2tb(all_96_16) = all_96_13 &
% 25.31/4.18 | t2tb(all_96_19) = all_96_18 & t2tb(all_96_20) = all_96_11 &
% 25.31/4.18 | infix_plpl(elt, all_96_5, all_96_3) = all_96_2 & infix_plpl(elt,
% 25.31/4.18 | all_96_12, all_96_11) = all_96_10 & infix_plpl(elt, all_96_14,
% 25.31/4.18 | all_96_13) = all_96_12 & length2(elt, all_96_13) = all_96_8 &
% 25.31/4.18 | length2(elt, all_96_14) = all_96_9 & length2(elt, all_96_18) =
% 25.31/4.18 | all_96_17 & nil(elt) = all_96_21 & list_elt(all_96_1) &
% 25.31/4.18 | list_elt(all_96_4) & list_elt(all_96_6) & list_elt(all_96_15) &
% 25.31/4.18 | list_elt(all_96_16) & list_elt(all_96_19) & list_elt(all_96_20) &
% 25.31/4.18 | uni(all_96_0) & uni(all_96_2) & uni(all_96_3) & uni(all_96_5) &
% 25.31/4.18 | uni(all_96_10) & uni(all_96_11) & uni(all_96_12) & uni(all_96_13) &
% 25.31/4.18 | uni(all_96_14) & uni(all_96_18) & uni(all_96_21) & sorted1(all_96_1) &
% 25.31/4.18 | sorted1(all_96_4) & sorted1(all_96_6) & permut(elt, all_96_0,
% 25.31/4.18 | all_96_2) & permut(elt, all_96_3, all_96_13) & permut(elt, all_96_5,
% 25.31/4.18 | all_96_14) & permut(elt, all_96_10, all_96_18) & permut(elt,
% 25.31/4.18 | all_96_12, all_96_18) & ~ permut(elt, all_96_0, all_96_18) &
% 25.31/4.18 | (all_96_8 = all_96_9 | (all_96_7 = 0 & $difference(all_96_8, all_96_9)
% 25.31/4.18 | = -1 & length2(elt, all_96_11) = 0))
% 25.31/4.18 |
% 25.31/4.18 | ALPHA: (23) implies:
% 25.31/4.18 | (24) $lesseq(2, all_96_17)
% 25.31/4.18 | (25) ~ permut(elt, all_96_0, all_96_18)
% 25.31/4.18 | (26) permut(elt, all_96_10, all_96_18)
% 25.31/4.18 | (27) permut(elt, all_96_5, all_96_14)
% 25.31/4.18 | (28) permut(elt, all_96_3, all_96_13)
% 25.31/4.18 | (29) permut(elt, all_96_0, all_96_2)
% 25.31/4.18 | (30) uni(all_96_18)
% 25.31/4.18 | (31) uni(all_96_14)
% 25.31/4.18 | (32) uni(all_96_13)
% 25.31/4.18 | (33) uni(all_96_12)
% 25.31/4.18 | (34) uni(all_96_11)
% 25.31/4.18 | (35) uni(all_96_5)
% 25.31/4.18 | (36) uni(all_96_3)
% 25.31/4.18 | (37) uni(all_96_2)
% 25.31/4.18 | (38) uni(all_96_0)
% 25.31/4.18 | (39) nil(elt) = all_96_21
% 25.31/4.18 | (40) length2(elt, all_96_18) = all_96_17
% 25.31/4.18 | (41) infix_plpl(elt, all_96_14, all_96_13) = all_96_12
% 25.31/4.18 | (42) infix_plpl(elt, all_96_12, all_96_11) = all_96_10
% 25.31/4.18 | (43) infix_plpl(elt, all_96_5, all_96_3) = all_96_2
% 25.31/4.18 | (44) t2tb(all_96_20) = all_96_11
% 25.31/4.18 | (45) tb2t(all_96_21) = all_96_20
% 25.31/4.18 |
% 25.31/4.18 | GROUND_INST: instantiating (8) with all_90_0, all_93_1, elt, simplifying with
% 25.31/4.18 | (19), (21) gives:
% 25.31/4.19 | (46) all_93_1 = all_90_0
% 25.31/4.19 |
% 25.31/4.19 | GROUND_INST: instantiating (8) with all_93_1, all_96_21, elt, simplifying with
% 25.31/4.19 | (21), (39) gives:
% 25.31/4.19 | (47) all_96_21 = all_93_1
% 25.31/4.19 |
% 25.31/4.19 | GROUND_INST: instantiating (8) with all_83_1, all_96_21, elt, simplifying with
% 25.31/4.19 | (13), (39) gives:
% 25.31/4.19 | (48) all_96_21 = all_83_1
% 25.31/4.19 |
% 25.31/4.19 | COMBINE_EQS: (47), (48) imply:
% 25.31/4.19 | (49) all_93_1 = all_83_1
% 25.31/4.19 |
% 25.31/4.19 | SIMP: (49) implies:
% 25.31/4.19 | (50) all_93_1 = all_83_1
% 25.31/4.19 |
% 25.31/4.19 | COMBINE_EQS: (46), (50) imply:
% 25.31/4.19 | (51) all_90_0 = all_83_1
% 25.31/4.19 |
% 25.31/4.19 | REDUCE: (45), (48) imply:
% 25.31/4.19 | (52) tb2t(all_83_1) = all_96_20
% 25.31/4.19 |
% 25.31/4.19 | REDUCE: (22), (50) imply:
% 25.31/4.19 | (53) tb2t(all_83_1) = all_93_0
% 25.31/4.19 |
% 25.31/4.19 | REDUCE: (18), (51) imply:
% 25.31/4.19 | (54) uni(all_83_1)
% 25.31/4.19 |
% 25.31/4.19 | GROUND_INST: instantiating (10) with all_83_0, all_96_20, all_83_1,
% 25.31/4.19 | simplifying with (14), (52) gives:
% 25.31/4.19 | (55) all_96_20 = all_83_0
% 25.31/4.19 |
% 25.31/4.19 | GROUND_INST: instantiating (10) with all_93_0, all_96_20, all_83_1,
% 25.31/4.19 | simplifying with (52), (53) gives:
% 25.31/4.19 | (56) all_96_20 = all_93_0
% 25.31/4.19 |
% 25.31/4.19 | COMBINE_EQS: (55), (56) imply:
% 25.31/4.19 | (57) all_93_0 = all_83_0
% 25.31/4.19 |
% 25.31/4.19 | REDUCE: (44), (55) imply:
% 25.31/4.19 | (58) t2tb(all_83_0) = all_96_11
% 25.31/4.19 |
% 25.31/4.19 | GROUND_INST: instantiating (nil_sort1) with elt, all_85_0, simplifying with
% 25.31/4.19 | (6), (16) gives:
% 25.31/4.19 | (59) ? [v0: uni] : (nil(elt) = v0 & uni(v0) & sort1(all_85_0, v0))
% 25.31/4.19 |
% 25.31/4.19 | GROUND_INST: instantiating (1) with elt, all_96_18, all_96_17, simplifying
% 25.31/4.19 | with (6), (30), (40) gives:
% 25.31/4.19 | (60) all_96_17 = 0 | ? [v0: any] : ( ~ (v0 = all_96_18) & nil(elt) = v0 &
% 25.31/4.19 | uni(v0))
% 25.31/4.19 |
% 25.31/4.19 | GROUND_INST: instantiating (permut_append_swap) with elt, all_96_14,
% 25.31/4.19 | all_96_13, all_96_12, simplifying with (6), (31), (32), (41)
% 25.31/4.19 | gives:
% 25.31/4.19 | (61) ? [v0: uni] : (infix_plpl(elt, all_96_13, all_96_14) = v0 & uni(v0) &
% 25.31/4.19 | permut(elt, all_96_12, v0))
% 25.31/4.19 |
% 25.31/4.19 | GROUND_INST: instantiating (permut_assoc) with elt, all_96_14, all_96_13,
% 25.31/4.19 | all_96_11, all_96_12, all_96_10, simplifying with (6), (31),
% 25.31/4.19 | (32), (34), (41), (42) gives:
% 25.31/4.19 | (62) ? [v0: uni] : ? [v1: uni] : (infix_plpl(elt, all_96_13, all_96_11) =
% 25.31/4.19 | v0 & infix_plpl(elt, all_96_14, v0) = v1 & uni(v1) & uni(v0) &
% 25.31/4.19 | permut(elt, all_96_10, v1))
% 25.31/4.19 |
% 25.31/4.19 | GROUND_INST: instantiating (append_assoc) with elt, all_96_14, all_96_13,
% 25.31/4.19 | all_96_11, all_96_12, all_96_10, simplifying with (6), (31),
% 25.31/4.19 | (32), (34), (41), (42) gives:
% 25.31/4.19 | (63) ? [v0: uni] : (infix_plpl(elt, all_96_13, all_96_11) = v0 &
% 25.31/4.19 | infix_plpl(elt, all_96_14, v0) = all_96_10 & uni(v0) &
% 25.31/4.19 | uni(all_96_10))
% 25.31/4.19 |
% 25.31/4.20 | GROUND_INST: instantiating (permut_append) with elt, all_96_5, all_96_3,
% 25.31/4.20 | all_96_14, all_96_13, all_96_2, all_96_12, simplifying with (6),
% 25.31/4.20 | (27), (28), (31), (32), (35), (36), (41), (43) gives:
% 25.31/4.20 | (64) permut(elt, all_96_2, all_96_12)
% 25.31/4.20 |
% 25.31/4.20 | GROUND_INST: instantiating (bridgeR) with all_83_1, all_83_0, simplifying with
% 25.31/4.20 | (14), (54) gives:
% 25.31/4.20 | (65) t2tb(all_83_0) = all_83_1
% 25.31/4.20 |
% 25.31/4.20 | DELTA: instantiating (59) with fresh symbol all_120_0 gives:
% 25.31/4.20 | (66) nil(elt) = all_120_0 & uni(all_120_0) & sort1(all_85_0, all_120_0)
% 25.31/4.20 |
% 25.31/4.20 | ALPHA: (66) implies:
% 25.31/4.20 | (67) nil(elt) = all_120_0
% 25.31/4.20 |
% 25.31/4.20 | DELTA: instantiating (61) with fresh symbol all_130_0 gives:
% 25.31/4.20 | (68) infix_plpl(elt, all_96_13, all_96_14) = all_130_0 & uni(all_130_0) &
% 25.31/4.20 | permut(elt, all_96_12, all_130_0)
% 25.31/4.20 |
% 25.31/4.20 | ALPHA: (68) implies:
% 25.31/4.20 | (69) infix_plpl(elt, all_96_13, all_96_14) = all_130_0
% 25.31/4.20 |
% 25.31/4.20 | DELTA: instantiating (63) with fresh symbol all_132_0 gives:
% 25.31/4.20 | (70) infix_plpl(elt, all_96_13, all_96_11) = all_132_0 & infix_plpl(elt,
% 25.31/4.20 | all_96_14, all_132_0) = all_96_10 & uni(all_132_0) & uni(all_96_10)
% 25.31/4.20 |
% 25.31/4.20 | ALPHA: (70) implies:
% 25.31/4.20 | (71) infix_plpl(elt, all_96_14, all_132_0) = all_96_10
% 25.31/4.20 | (72) infix_plpl(elt, all_96_13, all_96_11) = all_132_0
% 25.31/4.20 |
% 25.31/4.20 | DELTA: instantiating (62) with fresh symbols all_134_0, all_134_1 gives:
% 25.31/4.20 | (73) infix_plpl(elt, all_96_13, all_96_11) = all_134_1 & infix_plpl(elt,
% 25.31/4.20 | all_96_14, all_134_1) = all_134_0 & uni(all_134_0) & uni(all_134_1)
% 25.31/4.20 | & permut(elt, all_96_10, all_134_0)
% 25.31/4.20 |
% 25.31/4.20 | ALPHA: (73) implies:
% 25.31/4.20 | (74) infix_plpl(elt, all_96_14, all_134_1) = all_134_0
% 25.31/4.20 | (75) infix_plpl(elt, all_96_13, all_96_11) = all_134_1
% 25.31/4.20 |
% 25.31/4.20 | BETA: splitting (60) gives:
% 25.31/4.20 |
% 25.31/4.20 | Case 1:
% 25.31/4.20 | |
% 25.31/4.20 | | (76) all_96_17 = 0
% 25.31/4.20 | |
% 25.31/4.20 | | REDUCE: (24), (76) imply:
% 25.31/4.20 | | (77) $false
% 25.31/4.20 | |
% 25.31/4.20 | | CLOSE: (77) is inconsistent.
% 25.31/4.20 | |
% 25.31/4.20 | Case 2:
% 25.31/4.20 | |
% 25.31/4.20 | | (78) ? [v0: any] : ( ~ (v0 = all_96_18) & nil(elt) = v0 & uni(v0))
% 25.31/4.20 | |
% 25.31/4.20 | | DELTA: instantiating (78) with fresh symbol all_143_0 gives:
% 25.31/4.20 | | (79) ~ (all_143_0 = all_96_18) & nil(elt) = all_143_0 & uni(all_143_0)
% 25.31/4.20 | |
% 25.31/4.20 | | ALPHA: (79) implies:
% 25.31/4.20 | | (80) nil(elt) = all_143_0
% 25.31/4.20 | |
% 25.31/4.21 | | GROUND_INST: instantiating (8) with all_83_1, all_143_0, elt, simplifying
% 25.31/4.21 | | with (13), (80) gives:
% 25.31/4.21 | | (81) all_143_0 = all_83_1
% 25.31/4.21 | |
% 25.31/4.21 | | GROUND_INST: instantiating (8) with all_120_0, all_143_0, elt, simplifying
% 25.31/4.21 | | with (67), (80) gives:
% 25.31/4.21 | | (82) all_143_0 = all_120_0
% 25.31/4.21 | |
% 25.31/4.21 | | GROUND_INST: instantiating (11) with all_132_0, all_134_1, all_96_11,
% 25.31/4.21 | | all_96_13, elt, simplifying with (72), (75) gives:
% 25.31/4.21 | | (83) all_134_1 = all_132_0
% 25.31/4.21 | |
% 25.31/4.21 | | GROUND_INST: instantiating (9) with all_96_11, all_83_1, all_83_0,
% 25.31/4.21 | | simplifying with (58), (65) gives:
% 25.31/4.21 | | (84) all_96_11 = all_83_1
% 25.31/4.21 | |
% 25.31/4.21 | | COMBINE_EQS: (81), (82) imply:
% 25.31/4.21 | | (85) all_120_0 = all_83_1
% 25.31/4.21 | |
% 25.31/4.21 | | REDUCE: (42), (84) imply:
% 25.31/4.21 | | (86) infix_plpl(elt, all_96_12, all_83_1) = all_96_10
% 25.31/4.21 | |
% 25.31/4.21 | | REDUCE: (72), (84) imply:
% 25.31/4.21 | | (87) infix_plpl(elt, all_96_13, all_83_1) = all_132_0
% 25.31/4.21 | |
% 25.31/4.21 | | REDUCE: (74), (83) imply:
% 25.31/4.21 | | (88) infix_plpl(elt, all_96_14, all_132_0) = all_134_0
% 25.31/4.21 | |
% 25.31/4.21 | | GROUND_INST: instantiating (11) with all_96_10, all_134_0, all_132_0,
% 25.31/4.21 | | all_96_14, elt, simplifying with (71), (88) gives:
% 25.31/4.21 | | (89) all_134_0 = all_96_10
% 25.31/4.21 | |
% 25.31/4.21 | | GROUND_INST: instantiating (permut_trans) with elt, all_96_0, all_96_2,
% 25.31/4.21 | | all_96_12, simplifying with (6), (29), (33), (37), (38), (64)
% 25.31/4.21 | | gives:
% 25.31/4.21 | | (90) permut(elt, all_96_0, all_96_12)
% 25.31/4.21 | |
% 25.31/4.21 | | GROUND_INST: instantiating (append_l_nil) with elt, all_96_13, all_83_1,
% 25.31/4.21 | | all_132_0, simplifying with (6), (13), (32), (87) gives:
% 25.31/4.21 | | (91) all_132_0 = all_96_13
% 25.31/4.21 | |
% 25.31/4.21 | | GROUND_INST: instantiating (permut_append_swap) with elt, all_96_13,
% 25.31/4.21 | | all_96_14, all_130_0, simplifying with (6), (31), (32), (69)
% 25.31/4.21 | | gives:
% 25.31/4.21 | | (92) ? [v0: uni] : (infix_plpl(elt, all_96_14, all_96_13) = v0 & uni(v0)
% 25.31/4.21 | | & permut(elt, all_130_0, v0))
% 25.31/4.21 | |
% 25.31/4.21 | | GROUND_INST: instantiating (append_l_nil) with elt, all_96_12, all_83_1,
% 25.31/4.21 | | all_96_10, simplifying with (6), (13), (33), (86) gives:
% 25.31/4.21 | | (93) all_96_10 = all_96_12
% 25.31/4.21 | |
% 25.31/4.21 | | DELTA: instantiating (92) with fresh symbol all_167_0 gives:
% 25.31/4.21 | | (94) infix_plpl(elt, all_96_14, all_96_13) = all_167_0 & uni(all_167_0) &
% 25.31/4.21 | | permut(elt, all_130_0, all_167_0)
% 25.31/4.21 | |
% 25.31/4.21 | | ALPHA: (94) implies:
% 25.31/4.21 | | (95) uni(all_167_0)
% 25.31/4.21 | | (96) infix_plpl(elt, all_96_14, all_96_13) = all_167_0
% 25.31/4.21 | |
% 25.31/4.21 | | REDUCE: (26), (93) imply:
% 25.31/4.21 | | (97) permut(elt, all_96_12, all_96_18)
% 25.31/4.21 | |
% 25.31/4.21 | | GROUND_INST: instantiating (11) with all_96_12, all_167_0, all_96_13,
% 25.31/4.21 | | all_96_14, elt, simplifying with (41), (96) gives:
% 25.31/4.21 | | (98) all_167_0 = all_96_12
% 25.31/4.21 | |
% 25.31/4.21 | | GROUND_INST: instantiating (permut_trans) with elt, all_96_0, all_96_12,
% 25.31/4.21 | | all_96_18, simplifying with (6), (25), (30), (33), (38), (90),
% 25.31/4.21 | | (97) gives:
% 25.31/4.21 | | (99) $false
% 25.31/4.21 | |
% 25.31/4.21 | | CLOSE: (99) is inconsistent.
% 25.31/4.21 | |
% 25.31/4.21 | End of split
% 25.31/4.21 |
% 25.31/4.21 End of proof
% 25.31/4.21 % SZS output end Proof for theBenchmark
% 25.31/4.21
% 25.31/4.21 3707ms
%------------------------------------------------------------------------------