TSTP Solution File: KLE150+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE150+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n017.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 24.17s 3.94s
% Output : Proof 78.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE150+2 : 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 : n017.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 10:39:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.11/1.07 Prover 1: Preprocessing ...
% 2.11/1.07 Prover 4: Preprocessing ...
% 2.96/1.11 Prover 5: Preprocessing ...
% 2.96/1.11 Prover 0: Preprocessing ...
% 2.96/1.11 Prover 3: Preprocessing ...
% 2.96/1.11 Prover 2: Preprocessing ...
% 2.96/1.11 Prover 6: Preprocessing ...
% 4.32/1.40 Prover 6: Constructing countermodel ...
% 4.32/1.42 Prover 1: Constructing countermodel ...
% 4.32/1.42 Prover 3: Constructing countermodel ...
% 5.39/1.45 Prover 4: Constructing countermodel ...
% 5.65/1.47 Prover 0: Proving ...
% 5.65/1.48 Prover 5: Proving ...
% 5.89/1.52 Prover 2: Proving ...
% 6.73/1.64 Prover 3: gave up
% 6.73/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.73/1.68 Prover 7: Preprocessing ...
% 7.88/1.77 Prover 7: Constructing countermodel ...
% 8.34/1.93 Prover 6: gave up
% 8.34/1.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.34/1.97 Prover 8: Preprocessing ...
% 9.36/2.05 Prover 8: Warning: ignoring some quantifiers
% 9.92/2.06 Prover 8: Constructing countermodel ...
% 12.27/2.38 Prover 8: gave up
% 12.27/2.38 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 12.27/2.40 Prover 9: Preprocessing ...
% 13.25/2.49 Prover 9: Constructing countermodel ...
% 16.30/2.94 Prover 1: gave up
% 17.02/2.97 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 17.16/3.01 Prover 10: Preprocessing ...
% 17.45/3.06 Prover 10: Constructing countermodel ...
% 17.45/3.09 Prover 10: gave up
% 17.45/3.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 18.06/3.11 Prover 11: Preprocessing ...
% 18.06/3.18 Prover 11: Constructing countermodel ...
% 24.17/3.93 Prover 9: proved (1552ms)
% 24.17/3.94
% 24.17/3.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.17/3.94
% 24.17/3.94 Prover 5: stopped
% 24.50/3.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.50/3.96 Prover 2: stopped
% 24.50/3.97 Prover 13: Preprocessing ...
% 24.50/3.97 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 24.50/3.97 Prover 0: stopped
% 24.50/3.97 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 24.50/3.97 Prover 16: Preprocessing ...
% 24.50/3.99 Prover 19: Preprocessing ...
% 24.95/4.01 Prover 13: Warning: ignoring some quantifiers
% 24.95/4.02 Prover 13: Constructing countermodel ...
% 24.95/4.02 Prover 16: Warning: ignoring some quantifiers
% 24.95/4.02 Prover 19: Warning: ignoring some quantifiers
% 24.95/4.02 Prover 16: Constructing countermodel ...
% 24.95/4.03 Prover 19: Constructing countermodel ...
% 24.95/4.04 Prover 13: gave up
% 25.37/4.09 Prover 19: gave up
% 26.74/4.28 Prover 16: gave up
% 77.11/14.04 Prover 4: Found proof (size 140)
% 77.11/14.04 Prover 4: proved (13393ms)
% 77.11/14.04 Prover 7: stopped
% 77.11/14.04 Prover 11: stopped
% 77.11/14.04
% 77.11/14.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 77.11/14.04
% 77.48/14.09 % SZS output start Proof for theBenchmark
% 77.48/14.10 Assumptions after simplification:
% 77.48/14.10 ---------------------------------
% 77.48/14.10
% 77.48/14.10 (additive_associativity)
% 77.48/14.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 77.48/14.15 (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 77.48/14.15 | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 & addition(v1, v0) = v5 &
% 77.48/14.15 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 77.48/14.15 : ! [v4: $i] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~
% 77.48/14.15 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 &
% 77.48/14.15 addition(v2, v1) = v5 & $i(v5) & $i(v4)))
% 77.48/14.15
% 77.48/14.15 (additive_commutativity)
% 77.48/14.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~
% 77.48/14.15 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 77.48/14.15 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 77.48/14.15 (addition(v1, v0) = v2 & $i(v2)))
% 77.48/14.15
% 77.48/14.15 (distributivity1)
% 77.48/14.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 77.48/14.15 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) |
% 77.48/14.15 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 77.48/14.15 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5))) &
% 77.48/14.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 77.48/14.15 (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~ $i(v2) | ~
% 77.48/14.15 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v0, v2) =
% 77.48/14.15 v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5)
% 77.48/14.15 & $i(v4)))
% 77.48/14.15
% 77.48/14.15 (distributivity2)
% 77.48/14.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 77.48/14.16 $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) |
% 77.48/14.16 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 77.48/14.16 : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5))) &
% 77.48/14.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 77.48/14.16 (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ $i(v2) | ~
% 77.48/14.16 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v1, v2) =
% 77.48/14.16 v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5)
% 77.48/14.16 & $i(v4)))
% 77.48/14.16
% 77.48/14.16 (goals)
% 77.48/14.16 $i(one) & $i(zero) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 77.48/14.16 ? [v4: any] : ? [v5: any] : (strong_iteration(v1) = v2 & leq(v3, v2) = v5 &
% 77.48/14.16 leq(v2, v3) = v4 & multiplication(v0, zero) = v1 & addition(one, v1) = v3 &
% 77.48/14.16 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v5 = 0) | ~ (v4 = 0)))
% 77.48/14.16
% 77.48/14.16 (idempotence)
% 77.48/14.16 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~ $i(v0))
% 77.48/14.16
% 77.48/14.16 (infty_coinduction)
% 77.48/14.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 77.48/14.17 int] : (v5 = 0 | ~ (strong_iteration(v0) = v3) | ~ (leq(v2, v4) = v5) | ~
% 77.48/14.17 (multiplication(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 77.48/14.17 $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & leq(v2, v7) = v8 &
% 77.48/14.17 multiplication(v0, v2) = v6 & addition(v6, v1) = v7 & $i(v7) & $i(v6))) &
% 77.48/14.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 77.48/14.17 (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ~ $i(v2) | ~
% 77.48/14.17 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any]
% 77.48/14.17 : (strong_iteration(v0) = v6 & leq(v2, v7) = v8 & leq(v2, v4) = v5 &
% 77.48/14.17 multiplication(v6, v1) = v7 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v8 = 0)))
% 77.48/14.17
% 77.48/14.17 (infty_unfold1)
% 77.48/14.17 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~
% 77.48/14.17 $i(v0) | ? [v2: $i] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1
% 77.48/14.17 & $i(v2) & $i(v1)))
% 77.48/14.17
% 77.48/14.17 (isolation)
% 77.48/14.17 $i(zero) & ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~
% 77.48/14.17 $i(v0) | ? [v2: $i] : ? [v3: $i] : (star(v0) = v2 & multiplication(v1,
% 77.48/14.17 zero) = v3 & addition(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & !
% 77.48/14.17 [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 77.48/14.17 [v3: $i] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 &
% 77.48/14.17 addition(v1, v3) = v2 & $i(v3) & $i(v2)))
% 77.48/14.17
% 77.48/14.17 (left_annihilation)
% 77.48/14.17 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero,
% 77.48/14.17 v0) = v1) | ~ $i(v0))
% 77.48/14.17
% 77.48/14.17 (multiplicative_associativity)
% 77.48/14.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 77.48/14.17 (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ $i(v2)
% 77.48/14.17 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1, v2) = v5 &
% 77.48/14.17 multiplication(v0, v5) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1:
% 77.48/14.18 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (multiplication(v1, v2)
% 77.48/14.18 = v3) | ~ (multiplication(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 77.48/14.18 $i(v0) | ? [v5: $i] : (multiplication(v5, v2) = v4 & multiplication(v0, v1)
% 77.48/14.18 = v5 & $i(v5) & $i(v4)))
% 77.48/14.18
% 77.48/14.18 (multiplicative_right_identity)
% 77.90/14.18 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 77.90/14.18 v1) | ~ $i(v0))
% 77.90/14.18
% 77.90/14.18 (order)
% 77.90/14.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (addition(v0, v1) =
% 77.90/14.18 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1) =
% 77.90/14.18 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0,
% 77.90/14.18 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 77.90/14.18 addition(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 77.90/14.18 (leq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | addition(v0, v1) = v1) & ! [v0:
% 77.90/14.18 $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = v1) | ~ $i(v1) | ~ $i(v0) |
% 77.90/14.18 leq(v0, v1) = 0)
% 77.90/14.18
% 77.90/14.18 (star_induction1)
% 77.90/14.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 77.90/14.18 int] : (v5 = 0 | ~ (leq(v4, v2) = v5) | ~ (star(v0) = v3) | ~
% 77.90/14.18 (multiplication(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 77.90/14.18 $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & leq(v7, v2) = v8 &
% 77.90/14.18 multiplication(v0, v2) = v6 & addition(v6, v1) = v7 & $i(v7) & $i(v6))) &
% 77.90/14.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 77.90/14.18 (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ~ $i(v2) | ~
% 77.90/14.18 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any]
% 77.90/14.18 : (leq(v7, v2) = v8 & leq(v4, v2) = v5 & star(v0) = v6 & multiplication(v6,
% 77.90/14.18 v1) = v7 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v8 = 0)))
% 77.90/14.18
% 77.90/14.18 (star_induction2)
% 77.90/14.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 77.90/14.19 int] : (v5 = 0 | ~ (leq(v4, v2) = v5) | ~ (star(v0) = v3) | ~
% 77.90/14.19 (multiplication(v1, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 77.90/14.19 $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & leq(v7, v2) = v8 &
% 77.90/14.19 multiplication(v2, v0) = v6 & addition(v6, v1) = v7 & $i(v7) & $i(v6))) &
% 77.90/14.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 77.90/14.19 (multiplication(v2, v0) = v3) | ~ (addition(v3, v1) = v4) | ~ $i(v2) | ~
% 77.90/14.19 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any]
% 77.90/14.19 : (leq(v7, v2) = v8 & leq(v4, v2) = v5 & star(v0) = v6 & multiplication(v1,
% 77.90/14.19 v6) = v7 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v8 = 0)))
% 77.90/14.19
% 77.90/14.19 (star_unfold2)
% 77.90/14.19 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ?
% 77.90/14.19 [v2: $i] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1 & $i(v2) &
% 77.90/14.19 $i(v1)))
% 77.90/14.19
% 77.90/14.19 (function-axioms)
% 77.90/14.19 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 77.90/14.19 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 77.90/14.19 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 77.90/14.19 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 77.90/14.19 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 77.90/14.19 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 77.90/14.19 [v2: $i] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~
% 77.90/14.19 (strong_iteration(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 77.90/14.19 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0))
% 77.90/14.19
% 77.90/14.19 Further assumptions not needed in the proof:
% 77.90/14.19 --------------------------------------------
% 77.90/14.19 additive_identity, multiplicative_left_identity, star_unfold1
% 77.90/14.19
% 77.90/14.19 Those formulas are unsatisfiable:
% 77.90/14.19 ---------------------------------
% 77.90/14.19
% 77.90/14.19 Begin of proof
% 77.97/14.19 |
% 77.97/14.19 | ALPHA: (additive_commutativity) implies:
% 77.97/14.19 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) |
% 77.97/14.19 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2)))
% 77.97/14.19 |
% 77.97/14.19 | ALPHA: (additive_associativity) implies:
% 77.97/14.19 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 77.97/14.19 | ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) |
% 77.97/14.19 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 &
% 77.97/14.19 | addition(v1, v0) = v5 & $i(v5) & $i(v4)))
% 77.97/14.19 |
% 77.97/14.19 | ALPHA: (multiplicative_associativity) implies:
% 77.97/14.19 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 77.97/14.19 | ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) |
% 77.97/14.19 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1,
% 77.97/14.19 | v2) = v5 & multiplication(v0, v5) = v4 & $i(v5) & $i(v4)))
% 77.97/14.19 |
% 77.97/14.19 | ALPHA: (multiplicative_right_identity) implies:
% 77.97/14.19 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 77.97/14.19 | v1) | ~ $i(v0))
% 77.97/14.19 |
% 77.97/14.19 | ALPHA: (distributivity1) implies:
% 77.97/14.20 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 77.97/14.20 | ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~
% 77.97/14.20 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] :
% 77.97/14.20 | (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 &
% 77.97/14.20 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4)))
% 77.97/14.20 |
% 77.97/14.20 | ALPHA: (distributivity2) implies:
% 77.97/14.20 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 77.97/14.20 | ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~
% 77.97/14.20 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] :
% 77.97/14.20 | (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 &
% 77.97/14.20 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4)))
% 77.97/14.20 |
% 77.97/14.20 | ALPHA: (left_annihilation) implies:
% 77.97/14.20 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero, v0) =
% 77.97/14.20 | v1) | ~ $i(v0))
% 77.97/14.20 |
% 77.97/14.20 | ALPHA: (star_unfold2) implies:
% 77.97/14.20 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2:
% 77.97/14.20 | $i] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1 &
% 77.97/14.20 | $i(v2) & $i(v1)))
% 77.97/14.20 |
% 77.97/14.20 | ALPHA: (star_induction1) implies:
% 77.97/14.20 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 77.97/14.20 | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ~
% 77.97/14.20 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7:
% 77.97/14.20 | $i] : ? [v8: any] : (leq(v7, v2) = v8 & leq(v4, v2) = v5 &
% 77.97/14.20 | star(v0) = v6 & multiplication(v6, v1) = v7 & $i(v7) & $i(v6) & ( ~
% 77.97/14.20 | (v5 = 0) | v8 = 0)))
% 77.97/14.20 |
% 77.97/14.20 | ALPHA: (star_induction2) implies:
% 77.97/14.20 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 77.97/14.20 | ( ~ (multiplication(v2, v0) = v3) | ~ (addition(v3, v1) = v4) | ~
% 77.97/14.20 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ?
% 77.97/14.20 | [v7: $i] : ? [v8: any] : (leq(v7, v2) = v8 & leq(v4, v2) = v5 &
% 77.97/14.20 | star(v0) = v6 & multiplication(v1, v6) = v7 & $i(v7) & $i(v6) & (
% 77.97/14.20 | ~ (v5 = 0) | v8 = 0)))
% 77.97/14.20 |
% 77.97/14.20 | ALPHA: (infty_unfold1) implies:
% 77.97/14.20 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~
% 77.97/14.20 | $i(v0) | ? [v2: $i] : (multiplication(v0, v1) = v2 & addition(v2,
% 77.97/14.20 | one) = v1 & $i(v2) & $i(v1)))
% 77.97/14.20 |
% 77.97/14.20 | ALPHA: (infty_coinduction) implies:
% 77.97/14.20 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 77.97/14.21 | ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ~
% 77.97/14.21 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ?
% 77.97/14.21 | [v7: $i] : ? [v8: any] : (strong_iteration(v0) = v6 & leq(v2, v7) =
% 77.97/14.21 | v8 & leq(v2, v4) = v5 & multiplication(v6, v1) = v7 & $i(v7) &
% 77.97/14.21 | $i(v6) & ( ~ (v5 = 0) | v8 = 0)))
% 77.97/14.21 |
% 77.97/14.21 | ALPHA: (isolation) implies:
% 77.97/14.21 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~
% 77.97/14.21 | $i(v0) | ? [v2: $i] : ? [v3: $i] : (star(v0) = v2 &
% 77.97/14.21 | multiplication(v1, zero) = v3 & addition(v2, v3) = v1 & $i(v3) &
% 77.97/14.21 | $i(v2) & $i(v1)))
% 77.97/14.21 |
% 77.97/14.21 | ALPHA: (order) implies:
% 77.97/14.21 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) =
% 77.97/14.21 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 77.97/14.21 | addition(v0, v1) = v3 & $i(v3)))
% 77.97/14.21 |
% 77.97/14.21 | ALPHA: (goals) implies:
% 77.97/14.21 | (15) $i(zero)
% 77.97/14.21 | (16) $i(one)
% 77.97/14.21 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] :
% 77.97/14.21 | ? [v5: any] : (strong_iteration(v1) = v2 & leq(v3, v2) = v5 & leq(v2,
% 77.97/14.21 | v3) = v4 & multiplication(v0, zero) = v1 & addition(one, v1) = v3
% 77.97/14.21 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v5 = 0) | ~ (v4 = 0)))
% 77.97/14.21 |
% 77.97/14.21 | ALPHA: (function-axioms) implies:
% 77.97/14.21 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 77.97/14.21 | (strong_iteration(v2) = v1) | ~ (strong_iteration(v2) = v0))
% 78.08/14.21 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 78.08/14.21 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 78.08/14.21 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 78.08/14.21 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 78.08/14.21 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 78.08/14.21 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) =
% 78.08/14.21 | v0))
% 78.08/14.21 |
% 78.08/14.21 | DELTA: instantiating (17) with fresh symbols all_22_0, all_22_1, all_22_2,
% 78.08/14.21 | all_22_3, all_22_4, all_22_5 gives:
% 78.08/14.21 | (22) strong_iteration(all_22_4) = all_22_3 & leq(all_22_2, all_22_3) =
% 78.08/14.21 | all_22_0 & leq(all_22_3, all_22_2) = all_22_1 &
% 78.08/14.21 | multiplication(all_22_5, zero) = all_22_4 & addition(one, all_22_4) =
% 78.08/14.21 | all_22_2 & $i(all_22_2) & $i(all_22_3) & $i(all_22_4) & $i(all_22_5) &
% 78.08/14.21 | ( ~ (all_22_0 = 0) | ~ (all_22_1 = 0))
% 78.08/14.21 |
% 78.08/14.21 | ALPHA: (22) implies:
% 78.08/14.21 | (23) $i(all_22_5)
% 78.08/14.21 | (24) $i(all_22_4)
% 78.08/14.21 | (25) $i(all_22_3)
% 78.08/14.21 | (26) addition(one, all_22_4) = all_22_2
% 78.08/14.21 | (27) multiplication(all_22_5, zero) = all_22_4
% 78.08/14.21 | (28) leq(all_22_3, all_22_2) = all_22_1
% 78.08/14.22 | (29) leq(all_22_2, all_22_3) = all_22_0
% 78.08/14.22 | (30) strong_iteration(all_22_4) = all_22_3
% 78.08/14.22 | (31) ~ (all_22_0 = 0) | ~ (all_22_1 = 0)
% 78.08/14.22 |
% 78.08/14.22 | GROUND_INST: instantiating (1) with all_22_4, one, all_22_2, simplifying with
% 78.08/14.22 | (16), (24), (26) gives:
% 78.11/14.22 | (32) addition(all_22_4, one) = all_22_2 & $i(all_22_2)
% 78.11/14.22 |
% 78.11/14.22 | ALPHA: (32) implies:
% 78.11/14.22 | (33) $i(all_22_2)
% 78.11/14.22 | (34) addition(all_22_4, one) = all_22_2
% 78.11/14.22 |
% 78.11/14.22 | GROUND_INST: instantiating (14) with all_22_3, all_22_2, all_22_1, simplifying
% 78.11/14.22 | with (25), (28), (33) gives:
% 78.11/14.22 | (35) all_22_1 = 0 | ? [v0: any] : ( ~ (v0 = all_22_2) & addition(all_22_3,
% 78.11/14.22 | all_22_2) = v0 & $i(v0))
% 78.11/14.22 |
% 78.11/14.22 | GROUND_INST: instantiating (14) with all_22_2, all_22_3, all_22_0, simplifying
% 78.11/14.22 | with (25), (29), (33) gives:
% 78.11/14.22 | (36) all_22_0 = 0 | ? [v0: any] : ( ~ (v0 = all_22_3) & addition(all_22_2,
% 78.11/14.22 | all_22_3) = v0 & $i(v0))
% 78.11/14.22 |
% 78.11/14.22 | GROUND_INST: instantiating (13) with all_22_4, all_22_3, simplifying with
% 78.11/14.22 | (24), (30) gives:
% 78.11/14.22 | (37) ? [v0: $i] : ? [v1: $i] : (star(all_22_4) = v0 &
% 78.11/14.22 | multiplication(all_22_3, zero) = v1 & addition(v0, v1) = all_22_3 &
% 78.11/14.22 | $i(v1) & $i(v0) & $i(all_22_3))
% 78.11/14.22 |
% 78.11/14.22 | GROUND_INST: instantiating (11) with all_22_4, all_22_3, simplifying with
% 78.11/14.22 | (24), (30) gives:
% 78.11/14.22 | (38) ? [v0: $i] : (multiplication(all_22_4, all_22_3) = v0 & addition(v0,
% 78.11/14.22 | one) = all_22_3 & $i(v0) & $i(all_22_3))
% 78.11/14.22 |
% 78.11/14.22 | DELTA: instantiating (38) with fresh symbol all_30_0 gives:
% 78.11/14.22 | (39) multiplication(all_22_4, all_22_3) = all_30_0 & addition(all_30_0,
% 78.11/14.22 | one) = all_22_3 & $i(all_30_0) & $i(all_22_3)
% 78.11/14.22 |
% 78.11/14.22 | ALPHA: (39) implies:
% 78.11/14.22 | (40) $i(all_30_0)
% 78.11/14.22 | (41) addition(all_30_0, one) = all_22_3
% 78.11/14.22 | (42) multiplication(all_22_4, all_22_3) = all_30_0
% 78.11/14.22 |
% 78.11/14.22 | DELTA: instantiating (37) with fresh symbols all_32_0, all_32_1 gives:
% 78.11/14.22 | (43) star(all_22_4) = all_32_1 & multiplication(all_22_3, zero) = all_32_0
% 78.11/14.22 | & addition(all_32_1, all_32_0) = all_22_3 & $i(all_32_0) &
% 78.11/14.22 | $i(all_32_1) & $i(all_22_3)
% 78.11/14.22 |
% 78.11/14.22 | ALPHA: (43) implies:
% 78.11/14.22 | (44) $i(all_32_1)
% 78.11/14.22 | (45) $i(all_32_0)
% 78.11/14.22 | (46) addition(all_32_1, all_32_0) = all_22_3
% 78.11/14.22 | (47) multiplication(all_22_3, zero) = all_32_0
% 78.11/14.22 | (48) star(all_22_4) = all_32_1
% 78.11/14.22 |
% 78.11/14.22 | GROUND_INST: instantiating (1) with all_32_0, all_32_1, all_22_3, simplifying
% 78.11/14.22 | with (44), (45), (46) gives:
% 78.11/14.22 | (49) addition(all_32_0, all_32_1) = all_22_3 & $i(all_22_3)
% 78.11/14.22 |
% 78.11/14.22 | ALPHA: (49) implies:
% 78.11/14.22 | (50) addition(all_32_0, all_32_1) = all_22_3
% 78.11/14.22 |
% 78.11/14.22 | GROUND_INST: instantiating (3) with all_22_5, zero, all_22_3, all_22_4,
% 78.11/14.22 | all_30_0, simplifying with (15), (23), (25), (27), (42) gives:
% 78.11/14.23 | (51) ? [v0: $i] : (multiplication(all_22_5, v0) = all_30_0 &
% 78.11/14.23 | multiplication(zero, all_22_3) = v0 & $i(v0) & $i(all_30_0))
% 78.11/14.23 |
% 78.11/14.23 | GROUND_INST: instantiating (12) with all_22_4, one, all_22_3, all_30_0,
% 78.11/14.23 | all_22_3, simplifying with (16), (24), (25), (41), (42) gives:
% 78.11/14.23 | (52) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] :
% 78.11/14.23 | (strong_iteration(all_22_4) = v1 & leq(all_22_3, v2) = v3 &
% 78.11/14.23 | leq(all_22_3, all_22_3) = v0 & multiplication(v1, one) = v2 & $i(v2)
% 78.11/14.23 | & $i(v1) & ( ~ (v0 = 0) | v3 = 0))
% 78.11/14.23 |
% 78.11/14.23 | GROUND_INST: instantiating (9) with all_22_4, one, all_22_3, all_30_0,
% 78.11/14.23 | all_22_3, simplifying with (16), (24), (25), (41), (42) gives:
% 78.11/14.23 | (53) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : (leq(v2,
% 78.11/14.23 | all_22_3) = v3 & leq(all_22_3, all_22_3) = v0 & star(all_22_4) =
% 78.11/14.23 | v1 & multiplication(v1, one) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) |
% 78.11/14.23 | v3 = 0))
% 78.11/14.23 |
% 78.11/14.23 | GROUND_INST: instantiating (5) with all_22_4, all_30_0, one, all_22_3,
% 78.11/14.23 | all_30_0, simplifying with (16), (24), (40), (41), (42) gives:
% 78.11/14.23 | (54) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_4, all_30_0) = v0 &
% 78.11/14.23 | multiplication(all_22_4, one) = v1 & addition(v0, v1) = all_30_0 &
% 78.11/14.23 | $i(v1) & $i(v0))
% 78.11/14.23 |
% 78.11/14.23 | GROUND_INST: instantiating (6) with all_30_0, one, zero, all_22_3, all_32_0,
% 78.11/14.23 | simplifying with (15), (16), (40), (41), (47) gives:
% 78.11/14.23 | (55) ? [v0: $i] : ? [v1: $i] : (multiplication(all_30_0, zero) = v0 &
% 78.11/14.23 | multiplication(one, zero) = v1 & addition(v0, v1) = all_32_0 &
% 78.11/14.23 | $i(v1) & $i(v0) & $i(all_32_0))
% 78.11/14.23 |
% 78.11/14.23 | GROUND_INST: instantiating (8) with all_22_4, all_32_1, simplifying with (24),
% 78.11/14.23 | (48) gives:
% 78.11/14.23 | (56) ? [v0: $i] : (multiplication(all_32_1, all_22_4) = v0 & addition(one,
% 78.11/14.23 | v0) = all_32_1 & $i(v0) & $i(all_32_1))
% 78.11/14.23 |
% 78.11/14.23 | DELTA: instantiating (56) with fresh symbol all_42_0 gives:
% 78.11/14.23 | (57) multiplication(all_32_1, all_22_4) = all_42_0 & addition(one,
% 78.11/14.23 | all_42_0) = all_32_1 & $i(all_42_0) & $i(all_32_1)
% 78.11/14.23 |
% 78.11/14.23 | ALPHA: (57) implies:
% 78.11/14.23 | (58) $i(all_42_0)
% 78.11/14.23 | (59) addition(one, all_42_0) = all_32_1
% 78.11/14.23 |
% 78.11/14.23 | DELTA: instantiating (51) with fresh symbol all_44_0 gives:
% 78.11/14.23 | (60) multiplication(all_22_5, all_44_0) = all_30_0 & multiplication(zero,
% 78.11/14.23 | all_22_3) = all_44_0 & $i(all_44_0) & $i(all_30_0)
% 78.11/14.23 |
% 78.11/14.23 | ALPHA: (60) implies:
% 78.11/14.23 | (61) multiplication(zero, all_22_3) = all_44_0
% 78.11/14.23 | (62) multiplication(all_22_5, all_44_0) = all_30_0
% 78.11/14.23 |
% 78.11/14.23 | DELTA: instantiating (54) with fresh symbols all_48_0, all_48_1 gives:
% 78.11/14.23 | (63) multiplication(all_22_4, all_30_0) = all_48_1 &
% 78.11/14.23 | multiplication(all_22_4, one) = all_48_0 & addition(all_48_1,
% 78.11/14.23 | all_48_0) = all_30_0 & $i(all_48_0) & $i(all_48_1)
% 78.11/14.23 |
% 78.11/14.23 | ALPHA: (63) implies:
% 78.11/14.23 | (64) $i(all_48_1)
% 78.11/14.23 | (65) $i(all_48_0)
% 78.11/14.23 | (66) addition(all_48_1, all_48_0) = all_30_0
% 78.11/14.23 | (67) multiplication(all_22_4, one) = all_48_0
% 78.11/14.23 |
% 78.11/14.23 | DELTA: instantiating (55) with fresh symbols all_50_0, all_50_1 gives:
% 78.11/14.24 | (68) multiplication(all_30_0, zero) = all_50_1 & multiplication(one, zero)
% 78.11/14.24 | = all_50_0 & addition(all_50_1, all_50_0) = all_32_0 & $i(all_50_0) &
% 78.11/14.24 | $i(all_50_1) & $i(all_32_0)
% 78.11/14.24 |
% 78.11/14.24 | DELTA: instantiating (53) with fresh symbols all_56_0, all_56_1, all_56_2,
% 78.11/14.24 | all_56_3 gives:
% 78.11/14.24 | (69) leq(all_56_1, all_22_3) = all_56_0 & leq(all_22_3, all_22_3) =
% 78.11/14.24 | all_56_3 & star(all_22_4) = all_56_2 & multiplication(all_56_2, one) =
% 78.11/14.24 | all_56_1 & $i(all_56_1) & $i(all_56_2) & ( ~ (all_56_3 = 0) | all_56_0
% 78.11/14.24 | = 0)
% 78.11/14.24 |
% 78.11/14.24 | ALPHA: (69) implies:
% 78.11/14.24 | (70) leq(all_22_3, all_22_3) = all_56_3
% 78.11/14.24 |
% 78.11/14.24 | DELTA: instantiating (52) with fresh symbols all_58_0, all_58_1, all_58_2,
% 78.11/14.24 | all_58_3 gives:
% 78.11/14.24 | (71) strong_iteration(all_22_4) = all_58_2 & leq(all_22_3, all_58_1) =
% 78.11/14.24 | all_58_0 & leq(all_22_3, all_22_3) = all_58_3 &
% 78.11/14.24 | multiplication(all_58_2, one) = all_58_1 & $i(all_58_1) & $i(all_58_2)
% 78.11/14.24 | & ( ~ (all_58_3 = 0) | all_58_0 = 0)
% 78.11/14.24 |
% 78.11/14.24 | ALPHA: (71) implies:
% 78.11/14.24 | (72) $i(all_58_2)
% 78.11/14.24 | (73) $i(all_58_1)
% 78.11/14.24 | (74) multiplication(all_58_2, one) = all_58_1
% 78.11/14.24 | (75) leq(all_22_3, all_22_3) = all_58_3
% 78.11/14.24 | (76) leq(all_22_3, all_58_1) = all_58_0
% 78.11/14.24 | (77) strong_iteration(all_22_4) = all_58_2
% 78.11/14.24 |
% 78.11/14.24 | GROUND_INST: instantiating (21) with all_56_3, all_58_3, all_22_3, all_22_3,
% 78.11/14.24 | simplifying with (70), (75) gives:
% 78.11/14.24 | (78) all_58_3 = all_56_3
% 78.11/14.24 |
% 78.11/14.24 | GROUND_INST: instantiating (18) with all_22_3, all_58_2, all_22_4, simplifying
% 78.11/14.24 | with (30), (77) gives:
% 78.11/14.24 | (79) all_58_2 = all_22_3
% 78.11/14.24 |
% 78.11/14.24 | REDUCE: (74), (79) imply:
% 78.11/14.24 | (80) multiplication(all_22_3, one) = all_58_1
% 78.11/14.24 |
% 78.11/14.24 | GROUND_INST: instantiating (2) with all_32_0, all_42_0, one, all_32_1,
% 78.11/14.24 | all_22_3, simplifying with (16), (45), (46), (58), (59) gives:
% 78.11/14.24 | (81) ? [v0: $i] : (addition(all_42_0, all_32_0) = v0 & addition(one, v0) =
% 78.11/14.24 | all_22_3 & $i(v0) & $i(all_22_3))
% 78.11/14.24 |
% 78.11/14.24 | GROUND_INST: instantiating (1) with all_42_0, one, all_32_1, simplifying with
% 78.11/14.24 | (16), (58), (59) gives:
% 78.11/14.24 | (82) addition(all_42_0, one) = all_32_1 & $i(all_32_1)
% 78.11/14.24 |
% 78.11/14.24 | GROUND_INST: instantiating (10) with zero, all_32_1, all_22_3, all_32_0,
% 78.11/14.24 | all_22_3, simplifying with (15), (25), (44), (47), (50) gives:
% 78.11/14.24 | (83) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : (leq(v2,
% 78.11/14.24 | all_22_3) = v3 & leq(all_22_3, all_22_3) = v0 & star(zero) = v1 &
% 78.11/14.24 | multiplication(all_32_1, v1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) |
% 78.11/14.24 | v3 = 0))
% 78.11/14.24 |
% 78.11/14.24 | GROUND_INST: instantiating (2) with one, all_48_0, all_48_1, all_30_0,
% 78.11/14.24 | all_22_3, simplifying with (16), (41), (64), (65), (66) gives:
% 78.11/14.24 | (84) ? [v0: $i] : (addition(all_48_0, one) = v0 & addition(all_48_1, v0) =
% 78.11/14.24 | all_22_3 & $i(v0) & $i(all_22_3))
% 78.11/14.24 |
% 78.11/14.24 | GROUND_INST: instantiating (7) with all_22_3, all_44_0, simplifying with (25),
% 78.11/14.24 | (61) gives:
% 78.11/14.24 | (85) all_44_0 = zero
% 78.11/14.24 |
% 78.11/14.24 | GROUND_INST: instantiating (4) with all_22_4, all_48_0, simplifying with (24),
% 78.11/14.24 | (67) gives:
% 78.11/14.24 | (86) all_48_0 = all_22_4
% 78.11/14.24 |
% 78.11/14.25 | GROUND_INST: instantiating (4) with all_22_3, all_58_1, simplifying with (25),
% 78.11/14.25 | (80) gives:
% 78.11/14.25 | (87) all_58_1 = all_22_3
% 78.11/14.25 |
% 78.11/14.25 | GROUND_INST: instantiating (14) with all_22_3, all_22_3, all_56_3, simplifying
% 78.11/14.25 | with (25), (70) gives:
% 78.11/14.25 | (88) all_56_3 = 0 | ? [v0: any] : ( ~ (v0 = all_22_3) & addition(all_22_3,
% 78.11/14.25 | all_22_3) = v0 & $i(v0))
% 78.11/14.25 |
% 78.11/14.25 | GROUND_INST: instantiating (14) with all_22_3, all_58_1, all_58_0, simplifying
% 78.11/14.25 | with (25), (73), (76) gives:
% 78.11/14.25 | (89) all_58_0 = 0 | ? [v0: any] : ( ~ (v0 = all_58_1) & addition(all_22_3,
% 78.11/14.25 | all_58_1) = v0 & $i(v0))
% 78.11/14.25 |
% 78.11/14.25 | DELTA: instantiating (81) with fresh symbol all_94_0 gives:
% 78.11/14.25 | (90) addition(all_42_0, all_32_0) = all_94_0 & addition(one, all_94_0) =
% 78.11/14.25 | all_22_3 & $i(all_94_0) & $i(all_22_3)
% 78.11/14.25 |
% 78.11/14.25 | ALPHA: (90) implies:
% 78.11/14.25 | (91) $i(all_94_0)
% 78.11/14.25 | (92) addition(one, all_94_0) = all_22_3
% 78.11/14.25 |
% 78.11/14.25 | DELTA: instantiating (84) with fresh symbol all_124_0 gives:
% 78.11/14.25 | (93) addition(all_48_0, one) = all_124_0 & addition(all_48_1, all_124_0) =
% 78.11/14.25 | all_22_3 & $i(all_124_0) & $i(all_22_3)
% 78.11/14.25 |
% 78.11/14.25 | ALPHA: (93) implies:
% 78.11/14.25 | (94) addition(all_48_0, one) = all_124_0
% 78.11/14.25 |
% 78.11/14.25 | DELTA: instantiating (83) with fresh symbols all_216_0, all_216_1, all_216_2,
% 78.11/14.25 | all_216_3 gives:
% 78.11/14.25 | (95) leq(all_216_1, all_22_3) = all_216_0 & leq(all_22_3, all_22_3) =
% 78.11/14.25 | all_216_3 & star(zero) = all_216_2 & multiplication(all_32_1,
% 78.11/14.25 | all_216_2) = all_216_1 & $i(all_216_1) & $i(all_216_2) & ( ~
% 78.11/14.25 | (all_216_3 = 0) | all_216_0 = 0)
% 78.11/14.25 |
% 78.11/14.25 | ALPHA: (95) implies:
% 78.11/14.25 | (96) leq(all_22_3, all_22_3) = all_216_3
% 78.11/14.25 |
% 78.11/14.25 | REDUCE: (76), (87) imply:
% 78.11/14.25 | (97) leq(all_22_3, all_22_3) = all_58_0
% 78.11/14.25 |
% 78.11/14.25 | REDUCE: (62), (85) imply:
% 78.11/14.25 | (98) multiplication(all_22_5, zero) = all_30_0
% 78.11/14.25 |
% 78.11/14.25 | REDUCE: (86), (94) imply:
% 78.11/14.25 | (99) addition(all_22_4, one) = all_124_0
% 78.11/14.25 |
% 78.11/14.25 | GROUND_INST: instantiating (19) with all_22_2, all_124_0, one, all_22_4,
% 78.11/14.25 | simplifying with (34), (99) gives:
% 78.11/14.25 | (100) all_124_0 = all_22_2
% 78.11/14.25 |
% 78.11/14.25 | GROUND_INST: instantiating (20) with all_22_4, all_30_0, zero, all_22_5,
% 78.11/14.25 | simplifying with (27), (98) gives:
% 78.11/14.25 | (101) all_30_0 = all_22_4
% 78.11/14.25 |
% 78.11/14.25 | GROUND_INST: instantiating (21) with all_56_3, all_216_3, all_22_3, all_22_3,
% 78.11/14.25 | simplifying with (70), (96) gives:
% 78.11/14.25 | (102) all_216_3 = all_56_3
% 78.11/14.25 |
% 78.11/14.25 | GROUND_INST: instantiating (21) with all_58_0, all_216_3, all_22_3, all_22_3,
% 78.11/14.25 | simplifying with (96), (97) gives:
% 78.11/14.25 | (103) all_216_3 = all_58_0
% 78.11/14.25 |
% 78.11/14.25 | COMBINE_EQS: (102), (103) imply:
% 78.11/14.25 | (104) all_58_0 = all_56_3
% 78.11/14.25 |
% 78.11/14.25 | SIMP: (104) implies:
% 78.11/14.25 | (105) all_58_0 = all_56_3
% 78.11/14.25 |
% 78.11/14.25 | REDUCE: (41), (101) imply:
% 78.11/14.25 | (106) addition(all_22_4, one) = all_22_3
% 78.11/14.25 |
% 78.11/14.25 | GROUND_INST: instantiating (19) with all_22_2, all_22_3, one, all_22_4,
% 78.11/14.25 | simplifying with (34), (106) gives:
% 78.11/14.25 | (107) all_22_2 = all_22_3
% 78.11/14.25 |
% 78.11/14.25 | REDUCE: (29), (107) imply:
% 78.11/14.25 | (108) leq(all_22_3, all_22_3) = all_22_0
% 78.11/14.25 |
% 78.11/14.25 | REDUCE: (28), (107) imply:
% 78.11/14.25 | (109) leq(all_22_3, all_22_3) = all_22_1
% 78.11/14.25 |
% 78.11/14.25 | GROUND_INST: instantiating (21) with all_56_3, all_22_1, all_22_3, all_22_3,
% 78.11/14.25 | simplifying with (70), (109) gives:
% 78.11/14.25 | (110) all_56_3 = all_22_1
% 78.11/14.25 |
% 78.11/14.25 | GROUND_INST: instantiating (21) with all_56_3, all_22_0, all_22_3, all_22_3,
% 78.11/14.25 | simplifying with (70), (108) gives:
% 78.11/14.25 | (111) all_56_3 = all_22_0
% 78.11/14.25 |
% 78.11/14.25 | COMBINE_EQS: (110), (111) imply:
% 78.11/14.25 | (112) all_22_0 = all_22_1
% 78.11/14.25 |
% 78.11/14.25 | COMBINE_EQS: (105), (110) imply:
% 78.11/14.26 | (113) all_58_0 = all_22_1
% 78.11/14.26 |
% 78.11/14.26 | BETA: splitting (31) gives:
% 78.11/14.26 |
% 78.11/14.26 | Case 1:
% 78.11/14.26 | |
% 78.11/14.26 | | (114) ~ (all_22_0 = 0)
% 78.11/14.26 | |
% 78.11/14.26 | | REDUCE: (112), (114) imply:
% 78.11/14.26 | | (115) ~ (all_22_1 = 0)
% 78.11/14.26 | |
% 78.11/14.26 | | BETA: splitting (35) gives:
% 78.11/14.26 | |
% 78.11/14.26 | | Case 1:
% 78.11/14.26 | | |
% 78.11/14.26 | | | (116) all_22_1 = 0
% 78.11/14.26 | | |
% 78.11/14.26 | | | REDUCE: (115), (116) imply:
% 78.11/14.26 | | | (117) $false
% 78.11/14.26 | | |
% 78.11/14.26 | | | CLOSE: (117) is inconsistent.
% 78.11/14.26 | | |
% 78.11/14.26 | | Case 2:
% 78.11/14.26 | | |
% 78.11/14.26 | | | (118) ? [v0: any] : ( ~ (v0 = all_22_2) & addition(all_22_3, all_22_2)
% 78.11/14.26 | | | = v0 & $i(v0))
% 78.11/14.26 | | |
% 78.11/14.26 | | | DELTA: instantiating (118) with fresh symbol all_256_0 gives:
% 78.11/14.26 | | | (119) ~ (all_256_0 = all_22_2) & addition(all_22_3, all_22_2) =
% 78.11/14.26 | | | all_256_0 & $i(all_256_0)
% 78.11/14.26 | | |
% 78.11/14.26 | | | ALPHA: (119) implies:
% 78.11/14.26 | | | (120) addition(all_22_3, all_22_2) = all_256_0
% 78.11/14.26 | | |
% 78.11/14.26 | | | REDUCE: (107), (120) imply:
% 78.11/14.26 | | | (121) addition(all_22_3, all_22_3) = all_256_0
% 78.11/14.26 | | |
% 78.11/14.26 | | | BETA: splitting (36) gives:
% 78.11/14.26 | | |
% 78.11/14.26 | | | Case 1:
% 78.11/14.26 | | | |
% 78.11/14.26 | | | | (122) all_22_0 = 0
% 78.11/14.26 | | | |
% 78.11/14.26 | | | | COMBINE_EQS: (112), (122) imply:
% 78.11/14.26 | | | | (123) all_22_1 = 0
% 78.11/14.26 | | | |
% 78.11/14.26 | | | | SIMP: (123) implies:
% 78.11/14.26 | | | | (124) all_22_1 = 0
% 78.11/14.26 | | | |
% 78.11/14.26 | | | | REDUCE: (115), (124) imply:
% 78.11/14.26 | | | | (125) $false
% 78.11/14.26 | | | |
% 78.11/14.26 | | | | CLOSE: (125) is inconsistent.
% 78.11/14.26 | | | |
% 78.11/14.26 | | | Case 2:
% 78.11/14.26 | | | |
% 78.11/14.26 | | | | (126) ? [v0: any] : ( ~ (v0 = all_22_3) & addition(all_22_2,
% 78.11/14.26 | | | | all_22_3) = v0 & $i(v0))
% 78.11/14.26 | | | |
% 78.11/14.26 | | | | DELTA: instantiating (126) with fresh symbol all_261_0 gives:
% 78.11/14.26 | | | | (127) ~ (all_261_0 = all_22_3) & addition(all_22_2, all_22_3) =
% 78.11/14.26 | | | | all_261_0 & $i(all_261_0)
% 78.11/14.26 | | | |
% 78.11/14.26 | | | | ALPHA: (127) implies:
% 78.11/14.26 | | | | (128) ~ (all_261_0 = all_22_3)
% 78.11/14.26 | | | | (129) addition(all_22_2, all_22_3) = all_261_0
% 78.11/14.26 | | | |
% 78.11/14.26 | | | | REDUCE: (107), (129) imply:
% 78.11/14.26 | | | | (130) addition(all_22_3, all_22_3) = all_261_0
% 78.11/14.26 | | | |
% 78.11/14.26 | | | | BETA: splitting (89) gives:
% 78.11/14.26 | | | |
% 78.11/14.26 | | | | Case 1:
% 78.11/14.26 | | | | |
% 78.11/14.26 | | | | | (131) all_58_0 = 0
% 78.11/14.26 | | | | |
% 78.11/14.26 | | | | | COMBINE_EQS: (113), (131) imply:
% 78.11/14.27 | | | | | (132) all_22_1 = 0
% 78.11/14.27 | | | | |
% 78.11/14.27 | | | | | SIMP: (132) implies:
% 78.11/14.27 | | | | | (133) all_22_1 = 0
% 78.11/14.27 | | | | |
% 78.11/14.27 | | | | | REDUCE: (115), (133) imply:
% 78.11/14.27 | | | | | (134) $false
% 78.11/14.27 | | | | |
% 78.11/14.27 | | | | | CLOSE: (134) is inconsistent.
% 78.11/14.27 | | | | |
% 78.11/14.27 | | | | Case 2:
% 78.11/14.27 | | | | |
% 78.11/14.27 | | | | | (135) ~ (all_58_0 = 0)
% 78.11/14.27 | | | | | (136) ? [v0: any] : ( ~ (v0 = all_58_1) & addition(all_22_3,
% 78.11/14.27 | | | | | all_58_1) = v0 & $i(v0))
% 78.11/14.27 | | | | |
% 78.11/14.27 | | | | | DELTA: instantiating (136) with fresh symbol all_266_0 gives:
% 78.11/14.27 | | | | | (137) ~ (all_266_0 = all_58_1) & addition(all_22_3, all_58_1) =
% 78.11/14.27 | | | | | all_266_0 & $i(all_266_0)
% 78.11/14.27 | | | | |
% 78.11/14.27 | | | | | ALPHA: (137) implies:
% 78.11/14.27 | | | | | (138) addition(all_22_3, all_58_1) = all_266_0
% 78.11/14.27 | | | | |
% 78.11/14.27 | | | | | REDUCE: (87), (138) imply:
% 78.11/14.27 | | | | | (139) addition(all_22_3, all_22_3) = all_266_0
% 78.11/14.27 | | | | |
% 78.11/14.27 | | | | | BETA: splitting (88) gives:
% 78.11/14.27 | | | | |
% 78.11/14.27 | | | | | Case 1:
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | (140) all_56_3 = 0
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | COMBINE_EQS: (110), (140) imply:
% 78.11/14.27 | | | | | | (141) all_22_1 = 0
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | SIMP: (141) implies:
% 78.11/14.27 | | | | | | (142) all_22_1 = 0
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | REDUCE: (115), (142) imply:
% 78.11/14.27 | | | | | | (143) $false
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | CLOSE: (143) is inconsistent.
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | Case 2:
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | (144) ? [v0: any] : ( ~ (v0 = all_22_3) & addition(all_22_3,
% 78.11/14.27 | | | | | | all_22_3) = v0 & $i(v0))
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | DELTA: instantiating (144) with fresh symbol all_271_0 gives:
% 78.11/14.27 | | | | | | (145) ~ (all_271_0 = all_22_3) & addition(all_22_3, all_22_3) =
% 78.11/14.27 | | | | | | all_271_0 & $i(all_271_0)
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | ALPHA: (145) implies:
% 78.11/14.27 | | | | | | (146) addition(all_22_3, all_22_3) = all_271_0
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | GROUND_INST: instantiating (19) with all_261_0, all_266_0, all_22_3,
% 78.11/14.27 | | | | | | all_22_3, simplifying with (130), (139) gives:
% 78.11/14.27 | | | | | | (147) all_266_0 = all_261_0
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | GROUND_INST: instantiating (19) with all_266_0, all_271_0, all_22_3,
% 78.11/14.27 | | | | | | all_22_3, simplifying with (139), (146) gives:
% 78.11/14.27 | | | | | | (148) all_271_0 = all_266_0
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | GROUND_INST: instantiating (19) with all_256_0, all_271_0, all_22_3,
% 78.11/14.27 | | | | | | all_22_3, simplifying with (121), (146) gives:
% 78.11/14.27 | | | | | | (149) all_271_0 = all_256_0
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | COMBINE_EQS: (148), (149) imply:
% 78.11/14.27 | | | | | | (150) all_266_0 = all_256_0
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | SIMP: (150) implies:
% 78.11/14.27 | | | | | | (151) all_266_0 = all_256_0
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | COMBINE_EQS: (147), (151) imply:
% 78.11/14.27 | | | | | | (152) all_261_0 = all_256_0
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | SIMP: (152) implies:
% 78.11/14.27 | | | | | | (153) all_261_0 = all_256_0
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | REDUCE: (128), (153) imply:
% 78.11/14.27 | | | | | | (154) ~ (all_256_0 = all_22_3)
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | GROUND_INST: instantiating (1) with all_94_0, one, all_22_3,
% 78.11/14.27 | | | | | | simplifying with (16), (91), (92) gives:
% 78.11/14.27 | | | | | | (155) addition(all_94_0, one) = all_22_3 & $i(all_22_3)
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | GROUND_INST: instantiating (idempotence) with all_22_3, all_256_0,
% 78.11/14.27 | | | | | | simplifying with (25), (121) gives:
% 78.11/14.27 | | | | | | (156) all_256_0 = all_22_3
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | REDUCE: (154), (156) imply:
% 78.11/14.27 | | | | | | (157) $false
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | | CLOSE: (157) is inconsistent.
% 78.11/14.27 | | | | | |
% 78.11/14.27 | | | | | End of split
% 78.11/14.27 | | | | |
% 78.11/14.27 | | | | End of split
% 78.11/14.27 | | | |
% 78.11/14.27 | | | End of split
% 78.11/14.27 | | |
% 78.11/14.27 | | End of split
% 78.11/14.27 | |
% 78.11/14.27 | Case 2:
% 78.11/14.27 | |
% 78.11/14.27 | | (158) all_22_0 = 0
% 78.11/14.27 | | (159) ~ (all_22_1 = 0)
% 78.11/14.27 | |
% 78.11/14.27 | | COMBINE_EQS: (112), (158) imply:
% 78.11/14.27 | | (160) all_22_1 = 0
% 78.11/14.27 | |
% 78.11/14.27 | | SIMP: (160) implies:
% 78.11/14.27 | | (161) all_22_1 = 0
% 78.11/14.27 | |
% 78.11/14.27 | | REDUCE: (159), (161) imply:
% 78.11/14.27 | | (162) $false
% 78.11/14.27 | |
% 78.11/14.27 | | CLOSE: (162) is inconsistent.
% 78.11/14.27 | |
% 78.11/14.27 | End of split
% 78.11/14.27 |
% 78.11/14.27 End of proof
% 78.11/14.27 % SZS output end Proof for theBenchmark
% 78.11/14.27
% 78.11/14.27 13650ms
%------------------------------------------------------------------------------