TSTP Solution File: KLE151+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE151+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:34:42 EDT 2023
% Result : Theorem 27.82s 4.37s
% Output : Proof 95.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE151+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 10:52:16 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.47/0.65 ________ _____
% 0.47/0.65 ___ __ \_________(_)________________________________
% 0.47/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.47/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.47/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.47/0.65
% 0.47/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.47/0.65 (2023-06-19)
% 0.47/0.65
% 0.47/0.65 (c) Philipp Rümmer, 2009-2023
% 0.47/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.47/0.65 Amanda Stjerna.
% 0.47/0.65 Free software under BSD-3-Clause.
% 0.47/0.65
% 0.47/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.47/0.65
% 0.47/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.47/0.67 Running up to 7 provers in parallel.
% 0.76/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.76/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.76/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.76/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.76/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.76/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.76/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.18/1.04 Prover 1: Preprocessing ...
% 2.18/1.04 Prover 4: Preprocessing ...
% 2.86/1.08 Prover 5: Preprocessing ...
% 2.86/1.08 Prover 3: Preprocessing ...
% 2.86/1.08 Prover 0: Preprocessing ...
% 2.86/1.08 Prover 2: Preprocessing ...
% 2.86/1.08 Prover 6: Preprocessing ...
% 4.80/1.38 Prover 1: Constructing countermodel ...
% 4.80/1.40 Prover 3: Constructing countermodel ...
% 4.80/1.40 Prover 6: Constructing countermodel ...
% 5.22/1.42 Prover 5: Proving ...
% 5.54/1.45 Prover 0: Proving ...
% 5.54/1.46 Prover 4: Constructing countermodel ...
% 6.22/1.55 Prover 2: Proving ...
% 7.03/1.68 Prover 3: gave up
% 7.03/1.70 Prover 1: gave up
% 7.03/1.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.45/1.72 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.45/1.77 Prover 8: Preprocessing ...
% 7.45/1.78 Prover 7: Preprocessing ...
% 7.91/1.87 Prover 8: Warning: ignoring some quantifiers
% 7.91/1.88 Prover 8: Constructing countermodel ...
% 7.91/1.88 Prover 7: Constructing countermodel ...
% 9.18/2.02 Prover 8: gave up
% 9.18/2.02 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 9.92/2.07 Prover 9: Preprocessing ...
% 11.13/2.22 Prover 9: Constructing countermodel ...
% 11.50/2.27 Prover 6: gave up
% 11.50/2.29 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.50/2.31 Prover 10: Preprocessing ...
% 12.58/2.42 Prover 10: Constructing countermodel ...
% 12.58/2.43 Prover 10: gave up
% 12.58/2.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.58/2.45 Prover 11: Preprocessing ...
% 13.20/2.51 Prover 11: Constructing countermodel ...
% 27.82/4.37 Prover 0: proved (3697ms)
% 27.82/4.37
% 27.82/4.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.82/4.37
% 27.82/4.37 Prover 5: stopped
% 27.82/4.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 27.82/4.38 Prover 2: stopped
% 27.82/4.38 Prover 9: stopped
% 27.82/4.38 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 27.90/4.38 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 27.90/4.40 Prover 13: Preprocessing ...
% 27.90/4.40 Prover 19: Preprocessing ...
% 27.90/4.40 Prover 16: Preprocessing ...
% 28.20/4.50 Prover 16: Warning: ignoring some quantifiers
% 28.20/4.50 Prover 13: Warning: ignoring some quantifiers
% 28.20/4.50 Prover 16: Constructing countermodel ...
% 28.20/4.50 Prover 19: Warning: ignoring some quantifiers
% 28.20/4.50 Prover 13: Constructing countermodel ...
% 28.86/4.52 Prover 19: Constructing countermodel ...
% 28.86/4.52 Prover 13: gave up
% 29.39/4.59 Prover 19: gave up
% 77.87/12.08 Prover 16: stopped
% 95.17/16.65 Prover 11: Found proof (size 59)
% 95.17/16.65 Prover 11: proved (14217ms)
% 95.17/16.65 Prover 7: stopped
% 95.17/16.65 Prover 4: stopped
% 95.17/16.65
% 95.17/16.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 95.17/16.65
% 95.17/16.66 % SZS output start Proof for theBenchmark
% 95.34/16.66 Assumptions after simplification:
% 95.34/16.66 ---------------------------------
% 95.34/16.66
% 95.34/16.66 (additive_commutativity)
% 95.34/16.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~
% 95.34/16.69 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 95.34/16.69 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 95.34/16.69 (addition(v1, v0) = v2 & $i(v2)))
% 95.34/16.69
% 95.34/16.69 (distributivity1)
% 95.34/16.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 95.34/16.69 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) |
% 95.34/16.69 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 95.34/16.69 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5))) &
% 95.34/16.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 95.34/16.69 (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~ $i(v2) | ~
% 95.34/16.69 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v0, v2) =
% 95.34/16.69 v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5)
% 95.34/16.69 & $i(v4)))
% 95.34/16.69
% 95.34/16.69 (goals)
% 95.34/16.70 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 95.34/16.70 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 95.34/16.70 strong_iteration(v5) = v6 & strong_iteration(v2) = v3 & leq(v4, v7) = v8 &
% 95.34/16.70 multiplication(v6, v0) = v7 & multiplication(v1, v0) = v2 &
% 95.34/16.70 multiplication(v0, v3) = v4 & multiplication(v0, v1) = v5 & $i(v7) & $i(v6)
% 95.34/16.70 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 95.34/16.70
% 95.34/16.70 (idempotence)
% 95.34/16.70 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~ $i(v0))
% 95.34/16.70
% 95.34/16.70 (infty_coinduction)
% 95.34/16.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 95.34/16.70 int] : (v5 = 0 | ~ (strong_iteration(v0) = v3) | ~ (leq(v2, v4) = v5) | ~
% 95.34/16.70 (multiplication(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 95.34/16.70 $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & leq(v2, v7) = v8 &
% 95.34/16.70 multiplication(v0, v2) = v6 & addition(v6, v1) = v7 & $i(v7) & $i(v6))) &
% 95.34/16.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 95.34/16.70 (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ~ $i(v2) | ~
% 95.34/16.70 $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: int]
% 95.34/16.70 : ((v8 = 0 & strong_iteration(v0) = v6 & leq(v2, v7) = 0 &
% 95.34/16.70 multiplication(v6, v1) = v7 & $i(v7) & $i(v6)) | ( ~ (v5 = 0) & leq(v2,
% 95.34/16.70 v4) = v5)))
% 95.34/16.70
% 95.34/16.70 (infty_unfold1)
% 95.34/16.70 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~
% 95.34/16.70 $i(v0) | ? [v2: $i] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1
% 95.34/16.70 & $i(v2) & $i(v1)))
% 95.34/16.70
% 95.34/16.70 (isolation)
% 95.34/16.71 $i(zero) & ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~
% 95.34/16.71 $i(v0) | ? [v2: $i] : ? [v3: $i] : (star(v0) = v2 & multiplication(v1,
% 95.34/16.71 zero) = v3 & addition(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & !
% 95.34/16.71 [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 95.34/16.71 [v3: $i] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 &
% 95.34/16.71 addition(v1, v3) = v2 & $i(v3) & $i(v2)))
% 95.34/16.71
% 95.34/16.71 (multiplicative_associativity)
% 95.34/16.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 95.34/16.71 (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ $i(v2)
% 95.34/16.71 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1, v2) = v5 &
% 95.34/16.71 multiplication(v0, v5) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1:
% 95.34/16.71 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (multiplication(v1, v2)
% 95.34/16.71 = v3) | ~ (multiplication(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 95.34/16.71 $i(v0) | ? [v5: $i] : (multiplication(v5, v2) = v4 & multiplication(v0, v1)
% 95.34/16.71 = v5 & $i(v5) & $i(v4)))
% 95.34/16.71
% 95.34/16.71 (multiplicative_right_identity)
% 95.34/16.71 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 95.34/16.71 v1) | ~ $i(v0))
% 95.34/16.71
% 95.34/16.71 (order)
% 95.34/16.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (addition(v0, v1) =
% 95.34/16.71 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1) =
% 95.34/16.71 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0,
% 95.34/16.71 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 95.34/16.71 addition(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 95.34/16.71 (leq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | addition(v0, v1) = v1) & ! [v0:
% 95.34/16.71 $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = v1) | ~ $i(v1) | ~ $i(v0) |
% 95.34/16.71 leq(v0, v1) = 0)
% 95.34/16.71
% 95.34/16.71 (function-axioms)
% 95.34/16.72 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 95.34/16.72 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 95.34/16.72 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 95.34/16.72 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 95.34/16.72 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 95.34/16.72 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 95.34/16.72 [v2: $i] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~
% 95.34/16.72 (strong_iteration(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 95.34/16.72 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0))
% 95.34/16.72
% 95.34/16.72 Further assumptions not needed in the proof:
% 95.34/16.72 --------------------------------------------
% 95.34/16.72 additive_associativity, additive_identity, distributivity2, left_annihilation,
% 95.34/16.72 multiplicative_left_identity, star_induction1, star_induction2, star_unfold1,
% 95.34/16.72 star_unfold2
% 95.34/16.72
% 95.34/16.72 Those formulas are unsatisfiable:
% 95.34/16.72 ---------------------------------
% 95.34/16.72
% 95.34/16.72 Begin of proof
% 95.34/16.72 |
% 95.34/16.72 | ALPHA: (additive_commutativity) implies:
% 95.34/16.72 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) |
% 95.34/16.72 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2)))
% 95.34/16.72 |
% 95.34/16.72 | ALPHA: (multiplicative_associativity) implies:
% 95.34/16.72 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 95.34/16.72 | ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) |
% 95.34/16.72 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1,
% 95.34/16.72 | v2) = v5 & multiplication(v0, v5) = v4 & $i(v5) & $i(v4)))
% 95.34/16.72 |
% 95.34/16.72 | ALPHA: (multiplicative_right_identity) implies:
% 95.34/16.72 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 95.34/16.72 | v1) | ~ $i(v0))
% 95.34/16.72 |
% 95.34/16.72 | ALPHA: (distributivity1) implies:
% 95.34/16.72 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 95.34/16.72 | ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~
% 95.34/16.72 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] :
% 95.34/16.72 | (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 &
% 95.34/16.72 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4)))
% 95.34/16.72 |
% 95.34/16.72 | ALPHA: (infty_unfold1) implies:
% 95.34/16.72 | (5) $i(one)
% 95.34/16.73 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~ $i(v0)
% 95.34/16.73 | | ? [v2: $i] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1
% 95.34/16.73 | & $i(v2) & $i(v1)))
% 95.34/16.73 |
% 95.34/16.73 | ALPHA: (infty_coinduction) implies:
% 95.34/16.73 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 95.34/16.73 | ! [v5: int] : (v5 = 0 | ~ (strong_iteration(v0) = v3) | ~ (leq(v2,
% 95.34/16.73 | v4) = v5) | ~ (multiplication(v3, v1) = v4) | ~ $i(v2) | ~
% 95.34/16.73 | $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~
% 95.34/16.73 | (v8 = 0) & leq(v2, v7) = v8 & multiplication(v0, v2) = v6 &
% 95.34/16.73 | addition(v6, v1) = v7 & $i(v7) & $i(v6)))
% 95.34/16.73 |
% 95.34/16.73 | ALPHA: (isolation) implies:
% 95.34/16.73 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~ $i(v0)
% 95.34/16.73 | | ? [v2: $i] : ? [v3: $i] : (star(v0) = v2 & multiplication(v1,
% 95.34/16.73 | zero) = v3 & addition(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1)))
% 95.34/16.73 |
% 95.34/16.73 | ALPHA: (order) implies:
% 95.34/16.73 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) =
% 95.34/16.73 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 95.34/16.73 | addition(v0, v1) = v3 & $i(v3)))
% 95.34/16.73 |
% 95.34/16.73 | ALPHA: (function-axioms) implies:
% 95.34/16.73 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 95.34/16.73 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 95.34/16.73 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 95.34/16.73 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 95.34/16.73 |
% 95.34/16.73 | DELTA: instantiating (goals) with fresh symbols all_22_0, all_22_1, all_22_2,
% 95.34/16.73 | all_22_3, all_22_4, all_22_5, all_22_6, all_22_7, all_22_8 gives:
% 95.34/16.73 | (12) ~ (all_22_0 = 0) & strong_iteration(all_22_3) = all_22_2 &
% 95.34/16.73 | strong_iteration(all_22_6) = all_22_5 & leq(all_22_4, all_22_1) =
% 95.34/16.73 | all_22_0 & multiplication(all_22_2, all_22_8) = all_22_1 &
% 95.34/16.73 | multiplication(all_22_7, all_22_8) = all_22_6 &
% 95.34/16.73 | multiplication(all_22_8, all_22_5) = all_22_4 &
% 95.34/16.73 | multiplication(all_22_8, all_22_7) = all_22_3 & $i(all_22_1) &
% 95.34/16.73 | $i(all_22_2) & $i(all_22_3) & $i(all_22_4) & $i(all_22_5) &
% 95.34/16.73 | $i(all_22_6) & $i(all_22_7) & $i(all_22_8)
% 95.34/16.73 |
% 95.34/16.73 | ALPHA: (12) implies:
% 95.34/16.73 | (13) ~ (all_22_0 = 0)
% 95.34/16.73 | (14) $i(all_22_8)
% 95.34/16.73 | (15) $i(all_22_7)
% 95.34/16.73 | (16) $i(all_22_6)
% 95.34/16.73 | (17) $i(all_22_4)
% 95.34/16.73 | (18) $i(all_22_3)
% 95.34/16.73 | (19) multiplication(all_22_8, all_22_7) = all_22_3
% 95.34/16.73 | (20) multiplication(all_22_8, all_22_5) = all_22_4
% 95.34/16.73 | (21) multiplication(all_22_7, all_22_8) = all_22_6
% 95.34/16.73 | (22) multiplication(all_22_2, all_22_8) = all_22_1
% 95.34/16.73 | (23) leq(all_22_4, all_22_1) = all_22_0
% 95.34/16.73 | (24) strong_iteration(all_22_6) = all_22_5
% 95.34/16.73 | (25) strong_iteration(all_22_3) = all_22_2
% 95.34/16.73 |
% 95.34/16.73 | GROUND_INST: instantiating (8) with all_22_6, all_22_5, simplifying with (16),
% 95.34/16.73 | (24) gives:
% 95.34/16.73 | (26) ? [v0: $i] : ? [v1: $i] : (star(all_22_6) = v0 &
% 95.34/16.73 | multiplication(all_22_5, zero) = v1 & addition(v0, v1) = all_22_5 &
% 95.34/16.73 | $i(v1) & $i(v0) & $i(all_22_5))
% 95.34/16.73 |
% 95.34/16.73 | GROUND_INST: instantiating (6) with all_22_6, all_22_5, simplifying with (16),
% 95.34/16.73 | (24) gives:
% 95.34/16.74 | (27) ? [v0: $i] : (multiplication(all_22_6, all_22_5) = v0 & addition(v0,
% 95.34/16.74 | one) = all_22_5 & $i(v0) & $i(all_22_5))
% 95.34/16.74 |
% 95.34/16.74 | GROUND_INST: instantiating (7) with all_22_3, all_22_8, all_22_4, all_22_2,
% 95.34/16.74 | all_22_1, all_22_0, simplifying with (14), (17), (18), (22),
% 95.34/16.74 | (23), (25) gives:
% 95.34/16.74 | (28) all_22_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0)
% 95.34/16.74 | & leq(all_22_4, v1) = v2 & multiplication(all_22_3, all_22_4) = v0 &
% 95.34/16.74 | addition(v0, all_22_8) = v1 & $i(v1) & $i(v0))
% 95.34/16.74 |
% 95.34/16.74 | DELTA: instantiating (27) with fresh symbol all_31_0 gives:
% 95.34/16.74 | (29) multiplication(all_22_6, all_22_5) = all_31_0 & addition(all_31_0,
% 95.34/16.74 | one) = all_22_5 & $i(all_31_0) & $i(all_22_5)
% 95.34/16.74 |
% 95.34/16.74 | ALPHA: (29) implies:
% 95.34/16.74 | (30) $i(all_31_0)
% 95.34/16.74 | (31) addition(all_31_0, one) = all_22_5
% 95.34/16.74 | (32) multiplication(all_22_6, all_22_5) = all_31_0
% 95.34/16.74 |
% 95.34/16.74 | DELTA: instantiating (26) with fresh symbols all_33_0, all_33_1 gives:
% 95.34/16.74 | (33) star(all_22_6) = all_33_1 & multiplication(all_22_5, zero) = all_33_0
% 95.34/16.74 | & addition(all_33_1, all_33_0) = all_22_5 & $i(all_33_0) &
% 95.34/16.74 | $i(all_33_1) & $i(all_22_5)
% 95.34/16.74 |
% 95.34/16.74 | ALPHA: (33) implies:
% 95.34/16.74 | (34) $i(all_33_1)
% 95.34/16.74 | (35) $i(all_33_0)
% 95.34/16.74 | (36) addition(all_33_1, all_33_0) = all_22_5
% 95.34/16.74 |
% 95.34/16.74 | BETA: splitting (28) gives:
% 95.34/16.74 |
% 95.34/16.74 | Case 1:
% 95.34/16.74 | |
% 95.34/16.74 | | (37) all_22_0 = 0
% 95.34/16.74 | |
% 95.34/16.74 | | REDUCE: (13), (37) imply:
% 95.34/16.74 | | (38) $false
% 95.73/16.74 | |
% 95.73/16.74 | | CLOSE: (38) is inconsistent.
% 95.73/16.74 | |
% 95.73/16.74 | Case 2:
% 95.73/16.74 | |
% 95.73/16.74 | | (39) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 95.73/16.74 | | leq(all_22_4, v1) = v2 & multiplication(all_22_3, all_22_4) = v0 &
% 95.73/16.74 | | addition(v0, all_22_8) = v1 & $i(v1) & $i(v0))
% 95.73/16.74 | |
% 95.73/16.74 | | DELTA: instantiating (39) with fresh symbols all_46_0, all_46_1, all_46_2
% 95.73/16.74 | | gives:
% 95.73/16.74 | | (40) ~ (all_46_0 = 0) & leq(all_22_4, all_46_1) = all_46_0 &
% 95.73/16.74 | | multiplication(all_22_3, all_22_4) = all_46_2 & addition(all_46_2,
% 95.73/16.74 | | all_22_8) = all_46_1 & $i(all_46_1) & $i(all_46_2)
% 95.73/16.74 | |
% 95.73/16.74 | | ALPHA: (40) implies:
% 95.73/16.74 | | (41) ~ (all_46_0 = 0)
% 95.73/16.74 | | (42) $i(all_46_2)
% 95.73/16.74 | | (43) addition(all_46_2, all_22_8) = all_46_1
% 95.73/16.74 | | (44) multiplication(all_22_3, all_22_4) = all_46_2
% 95.73/16.74 | | (45) leq(all_22_4, all_46_1) = all_46_0
% 95.73/16.74 | |
% 95.73/16.74 | | GROUND_INST: instantiating (4) with all_22_8, all_31_0, one, all_22_5,
% 95.73/16.74 | | all_22_4, simplifying with (5), (14), (20), (30), (31) gives:
% 95.73/16.74 | | (46) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_8, all_31_0) = v0
% 95.73/16.74 | | & multiplication(all_22_8, one) = v1 & addition(v0, v1) = all_22_4
% 95.73/16.74 | | & $i(v1) & $i(v0) & $i(all_22_4))
% 95.73/16.74 | |
% 95.73/16.74 | | GROUND_INST: instantiating (1) with all_33_0, all_33_1, all_22_5,
% 95.73/16.74 | | simplifying with (34), (35), (36) gives:
% 95.73/16.74 | | (47) addition(all_33_0, all_33_1) = all_22_5 & $i(all_22_5)
% 95.73/16.74 | |
% 95.73/16.74 | | ALPHA: (47) implies:
% 95.73/16.74 | | (48) $i(all_22_5)
% 95.73/16.74 | |
% 95.73/16.74 | | GROUND_INST: instantiating (1) with all_22_8, all_46_2, all_46_1,
% 95.73/16.74 | | simplifying with (14), (42), (43) gives:
% 95.73/16.75 | | (49) addition(all_22_8, all_46_2) = all_46_1 & $i(all_46_1)
% 95.73/16.75 | |
% 95.73/16.75 | | ALPHA: (49) implies:
% 95.73/16.75 | | (50) $i(all_46_1)
% 95.73/16.75 | |
% 95.73/16.75 | | GROUND_INST: instantiating (2) with all_22_7, all_22_8, all_22_5, all_22_6,
% 95.73/16.75 | | all_31_0, simplifying with (14), (15), (21), (32), (48) gives:
% 95.73/16.75 | | (51) ? [v0: $i] : (multiplication(all_22_7, v0) = all_31_0 &
% 95.73/16.75 | | multiplication(all_22_8, all_22_5) = v0 & $i(v0) & $i(all_31_0))
% 95.73/16.75 | |
% 95.73/16.75 | | GROUND_INST: instantiating (2) with all_22_8, all_22_7, all_22_4, all_22_3,
% 95.73/16.75 | | all_46_2, simplifying with (14), (15), (17), (19), (44) gives:
% 95.73/16.75 | | (52) ? [v0: $i] : (multiplication(all_22_7, all_22_4) = v0 &
% 95.73/16.75 | | multiplication(all_22_8, v0) = all_46_2 & $i(v0) & $i(all_46_2))
% 95.73/16.75 | |
% 95.73/16.75 | | GROUND_INST: instantiating (9) with all_22_4, all_46_1, all_46_0,
% 95.73/16.75 | | simplifying with (17), (45), (50) gives:
% 95.73/16.75 | | (53) all_46_0 = 0 | ? [v0: any] : ( ~ (v0 = all_46_1) &
% 95.73/16.75 | | addition(all_22_4, all_46_1) = v0 & $i(v0))
% 95.73/16.75 | |
% 95.73/16.75 | | DELTA: instantiating (51) with fresh symbol all_60_0 gives:
% 95.73/16.75 | | (54) multiplication(all_22_7, all_60_0) = all_31_0 &
% 95.73/16.75 | | multiplication(all_22_8, all_22_5) = all_60_0 & $i(all_60_0) &
% 95.73/16.75 | | $i(all_31_0)
% 95.73/16.75 | |
% 95.73/16.75 | | ALPHA: (54) implies:
% 95.73/16.75 | | (55) multiplication(all_22_8, all_22_5) = all_60_0
% 95.73/16.75 | | (56) multiplication(all_22_7, all_60_0) = all_31_0
% 95.73/16.75 | |
% 95.73/16.75 | | DELTA: instantiating (52) with fresh symbol all_62_0 gives:
% 95.73/16.75 | | (57) multiplication(all_22_7, all_22_4) = all_62_0 &
% 95.73/16.75 | | multiplication(all_22_8, all_62_0) = all_46_2 & $i(all_62_0) &
% 95.73/16.75 | | $i(all_46_2)
% 95.73/16.75 | |
% 95.73/16.75 | | ALPHA: (57) implies:
% 95.73/16.75 | | (58) multiplication(all_22_8, all_62_0) = all_46_2
% 95.73/16.75 | | (59) multiplication(all_22_7, all_22_4) = all_62_0
% 95.73/16.75 | |
% 95.73/16.75 | | DELTA: instantiating (46) with fresh symbols all_80_0, all_80_1 gives:
% 95.73/16.75 | | (60) multiplication(all_22_8, all_31_0) = all_80_1 &
% 95.73/16.75 | | multiplication(all_22_8, one) = all_80_0 & addition(all_80_1,
% 95.73/16.75 | | all_80_0) = all_22_4 & $i(all_80_0) & $i(all_80_1) & $i(all_22_4)
% 95.73/16.75 | |
% 95.73/16.75 | | ALPHA: (60) implies:
% 95.73/16.75 | | (61) addition(all_80_1, all_80_0) = all_22_4
% 95.73/16.75 | | (62) multiplication(all_22_8, one) = all_80_0
% 95.73/16.75 | | (63) multiplication(all_22_8, all_31_0) = all_80_1
% 95.73/16.75 | |
% 95.73/16.75 | | BETA: splitting (53) gives:
% 95.73/16.75 | |
% 95.73/16.75 | | Case 1:
% 95.73/16.75 | | |
% 95.73/16.75 | | | (64) all_46_0 = 0
% 95.73/16.75 | | |
% 95.73/16.75 | | | REDUCE: (41), (64) imply:
% 95.73/16.75 | | | (65) $false
% 95.73/16.75 | | |
% 95.73/16.75 | | | CLOSE: (65) is inconsistent.
% 95.73/16.75 | | |
% 95.73/16.75 | | Case 2:
% 95.73/16.75 | | |
% 95.73/16.75 | | | (66) ? [v0: any] : ( ~ (v0 = all_46_1) & addition(all_22_4, all_46_1)
% 95.73/16.75 | | | = v0 & $i(v0))
% 95.73/16.75 | | |
% 95.73/16.75 | | | DELTA: instantiating (66) with fresh symbol all_109_0 gives:
% 95.73/16.75 | | | (67) ~ (all_109_0 = all_46_1) & addition(all_22_4, all_46_1) =
% 95.73/16.75 | | | all_109_0 & $i(all_109_0)
% 95.73/16.75 | | |
% 95.73/16.75 | | | ALPHA: (67) implies:
% 95.73/16.75 | | | (68) ~ (all_109_0 = all_46_1)
% 95.73/16.75 | | | (69) addition(all_22_4, all_46_1) = all_109_0
% 95.73/16.75 | | |
% 95.73/16.75 | | | GROUND_INST: instantiating (11) with all_22_4, all_60_0, all_22_5,
% 95.73/16.75 | | | all_22_8, simplifying with (20), (55) gives:
% 95.73/16.75 | | | (70) all_60_0 = all_22_4
% 95.73/16.75 | | |
% 95.73/16.75 | | | REDUCE: (56), (70) imply:
% 95.73/16.75 | | | (71) multiplication(all_22_7, all_22_4) = all_31_0
% 95.73/16.75 | | |
% 95.73/16.75 | | | GROUND_INST: instantiating (11) with all_62_0, all_31_0, all_22_4,
% 95.73/16.75 | | | all_22_7, simplifying with (59), (71) gives:
% 95.73/16.75 | | | (72) all_62_0 = all_31_0
% 95.73/16.75 | | |
% 95.73/16.75 | | | REDUCE: (58), (72) imply:
% 95.73/16.75 | | | (73) multiplication(all_22_8, all_31_0) = all_46_2
% 95.73/16.75 | | |
% 95.73/16.75 | | | GROUND_INST: instantiating (11) with all_80_1, all_46_2, all_31_0,
% 95.73/16.75 | | | all_22_8, simplifying with (63), (73) gives:
% 95.73/16.75 | | | (74) all_80_1 = all_46_2
% 95.73/16.75 | | |
% 95.73/16.76 | | | REDUCE: (61), (74) imply:
% 95.73/16.76 | | | (75) addition(all_46_2, all_80_0) = all_22_4
% 95.73/16.76 | | |
% 95.73/16.76 | | | GROUND_INST: instantiating (3) with all_22_8, all_80_0, simplifying with
% 95.73/16.76 | | | (14), (62) gives:
% 95.73/16.76 | | | (76) all_80_0 = all_22_8
% 95.73/16.76 | | |
% 95.73/16.76 | | | REDUCE: (75), (76) imply:
% 95.73/16.76 | | | (77) addition(all_46_2, all_22_8) = all_22_4
% 95.73/16.76 | | |
% 95.73/16.76 | | | GROUND_INST: instantiating (10) with all_46_1, all_22_4, all_22_8,
% 95.73/16.76 | | | all_46_2, simplifying with (43), (77) gives:
% 95.73/16.76 | | | (78) all_46_1 = all_22_4
% 95.73/16.76 | | |
% 95.73/16.76 | | | REDUCE: (68), (78) imply:
% 95.73/16.76 | | | (79) ~ (all_109_0 = all_22_4)
% 95.73/16.76 | | |
% 95.73/16.76 | | | REDUCE: (69), (78) imply:
% 95.73/16.76 | | | (80) addition(all_22_4, all_22_4) = all_109_0
% 95.73/16.76 | | |
% 95.73/16.76 | | | GROUND_INST: instantiating (idempotence) with all_22_4, all_109_0,
% 95.73/16.76 | | | simplifying with (17), (80) gives:
% 95.73/16.76 | | | (81) all_109_0 = all_22_4
% 95.73/16.76 | | |
% 95.73/16.76 | | | REDUCE: (79), (81) imply:
% 95.73/16.76 | | | (82) $false
% 95.73/16.76 | | |
% 95.73/16.76 | | | CLOSE: (82) is inconsistent.
% 95.73/16.76 | | |
% 95.73/16.76 | | End of split
% 95.73/16.76 | |
% 95.73/16.76 | End of split
% 95.73/16.76 |
% 95.73/16.76 End of proof
% 95.73/16.76 % SZS output end Proof for theBenchmark
% 95.73/16.76
% 95.73/16.76 16102ms
%------------------------------------------------------------------------------