TSTP Solution File: KLE093+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE093+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 : n002.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 05:34:31 EDT 2023
% Result : Theorem 27.70s 4.48s
% Output : Proof 120.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE093+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 12:12:50 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.13/1.06 Prover 1: Preprocessing ...
% 2.13/1.06 Prover 4: Preprocessing ...
% 2.71/1.11 Prover 3: Preprocessing ...
% 2.71/1.11 Prover 0: Preprocessing ...
% 2.71/1.11 Prover 2: Preprocessing ...
% 2.71/1.11 Prover 6: Preprocessing ...
% 2.71/1.12 Prover 5: Preprocessing ...
% 4.72/1.43 Prover 6: Constructing countermodel ...
% 4.72/1.45 Prover 3: Constructing countermodel ...
% 4.72/1.45 Prover 1: Constructing countermodel ...
% 4.72/1.47 Prover 5: Proving ...
% 5.39/1.48 Prover 4: Constructing countermodel ...
% 5.46/1.49 Prover 0: Proving ...
% 6.35/1.65 Prover 2: Proving ...
% 8.27/1.91 Prover 3: gave up
% 8.27/1.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.27/1.93 Prover 7: Preprocessing ...
% 9.09/2.02 Prover 7: Constructing countermodel ...
% 10.28/2.18 Prover 6: gave up
% 10.28/2.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.28/2.20 Prover 8: Preprocessing ...
% 11.31/2.30 Prover 8: Warning: ignoring some quantifiers
% 11.31/2.30 Prover 8: Constructing countermodel ...
% 12.25/2.41 Prover 1: gave up
% 12.55/2.43 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 12.55/2.46 Prover 9: Preprocessing ...
% 13.03/2.56 Prover 9: Constructing countermodel ...
% 15.51/2.87 Prover 8: gave up
% 15.83/2.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.83/2.91 Prover 10: Preprocessing ...
% 16.44/2.96 Prover 10: Constructing countermodel ...
% 20.03/3.44 Prover 10: gave up
% 20.03/3.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 20.16/3.47 Prover 11: Preprocessing ...
% 20.96/3.57 Prover 11: Constructing countermodel ...
% 27.70/4.47 Prover 0: proved (3845ms)
% 27.70/4.47
% 27.70/4.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.70/4.48
% 27.70/4.49 Prover 9: stopped
% 27.70/4.49 Prover 2: stopped
% 27.70/4.51 Prover 5: stopped
% 27.70/4.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 27.70/4.51 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 27.70/4.51 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 27.70/4.51 Prover 16: Preprocessing ...
% 27.70/4.52 Prover 13: Preprocessing ...
% 28.39/4.54 Prover 19: Preprocessing ...
% 28.39/4.57 Prover 16: Warning: ignoring some quantifiers
% 28.39/4.57 Prover 16: Constructing countermodel ...
% 28.86/4.61 Prover 13: Warning: ignoring some quantifiers
% 28.86/4.62 Prover 13: Constructing countermodel ...
% 28.86/4.62 Prover 19: Warning: ignoring some quantifiers
% 28.86/4.62 Prover 19: Constructing countermodel ...
% 31.18/4.95 Prover 19: gave up
% 31.75/4.99 Prover 13: gave up
% 81.15/12.15 Prover 16: stopped
% 118.56/22.12 Prover 11: Found proof (size 783)
% 118.56/22.12 Prover 11: proved (18672ms)
% 118.56/22.12 Prover 4: stopped
% 118.56/22.12 Prover 7: stopped
% 118.56/22.12
% 118.56/22.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 118.56/22.13
% 119.23/22.30 % SZS output start Proof for theBenchmark
% 119.23/22.30 Assumptions after simplification:
% 119.23/22.30 ---------------------------------
% 119.23/22.30
% 119.23/22.30 (additive_associativity)
% 119.23/22.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 119.23/22.33 (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 119.23/22.33 | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 & addition(v1, v0) = v5 &
% 119.23/22.33 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 119.23/22.33 : ! [v4: $i] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~
% 119.23/22.33 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 &
% 119.23/22.33 addition(v2, v1) = v5 & $i(v5) & $i(v4)))
% 119.23/22.33
% 119.23/22.33 (additive_commutativity)
% 119.23/22.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~
% 119.23/22.33 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 119.23/22.33 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 119.23/22.33 (addition(v1, v0) = v2 & $i(v2)))
% 119.23/22.33
% 119.23/22.33 (additive_idempotence)
% 119.23/22.34 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~ $i(v0))
% 119.23/22.34
% 119.23/22.34 (additive_identity)
% 119.23/22.34 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1)
% 119.23/22.34 | ~ $i(v0))
% 119.23/22.34
% 119.23/22.34 (domain1)
% 119.23/22.34 ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 119.23/22.34 (multiplication(v1, v0) = v2 & addition(v0, v2) = v2 & $i(v2)))
% 119.23/22.34
% 119.23/22.34 (domain2)
% 119.23/22.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (domain(v1) = v2)
% 119.23/22.34 | ~ (multiplication(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 119.23/22.34 ? [v5: $i] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) =
% 119.23/22.34 v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 119.23/22.34 (multiplication(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 119.23/22.34 [v4: $i] : ? [v5: $i] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) =
% 119.23/22.34 v4 & multiplication(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3)))
% 119.23/22.34
% 119.23/22.34 (domain3)
% 119.23/22.34 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) |
% 119.23/22.34 addition(v1, one) = one)
% 119.23/22.34
% 119.23/22.34 (domain4)
% 119.23/22.34 domain(zero) = zero & $i(zero)
% 119.23/22.34
% 119.23/22.34 (domain5)
% 119.23/22.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 119.23/22.35 (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ~
% 119.23/22.35 $i(v1) | ~ $i(v0) | ? [v5: $i] : (domain(v5) = v4 & addition(v0, v1) = v5
% 119.23/22.35 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 119.23/22.35 (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i]
% 119.23/22.35 : ? [v5: $i] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 &
% 119.23/22.35 addition(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3)))
% 119.23/22.35
% 119.23/22.35 (goals)
% 119.23/22.35 $i(one) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = one) &
% 119.23/22.35 domain(v1) = v2 & star(v0) = v1 & $i(v2) & $i(v1) & $i(v0))
% 119.23/22.35
% 119.23/22.35 (multiplicative_right_identity)
% 119.23/22.35 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 119.23/22.35 v1) | ~ $i(v0))
% 119.23/22.35
% 119.23/22.35 (order)
% 119.23/22.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (addition(v0, v1) =
% 119.23/22.35 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1) =
% 119.23/22.35 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0,
% 119.23/22.35 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 119.23/22.35 addition(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 119.23/22.35 (leq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | addition(v0, v1) = v1) & ! [v0:
% 119.23/22.35 $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = v1) | ~ $i(v1) | ~ $i(v0) |
% 119.23/22.35 leq(v0, v1) = 0)
% 119.23/22.35
% 119.23/22.35 (right_annihilation)
% 119.23/22.35 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(v0,
% 119.23/22.35 zero) = v1) | ~ $i(v0))
% 119.23/22.35
% 119.23/22.35 (star_induction_left)
% 119.23/22.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 119.23/22.36 int] : (v5 = 0 | ~ (star(v0) = v3) | ~ (leq(v4, v1) = v5) | ~
% 119.23/22.36 (multiplication(v3, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 119.23/22.36 $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & leq(v7, v1) = v8 &
% 119.23/22.36 multiplication(v0, v1) = v6 & addition(v6, v2) = v7 & $i(v7) & $i(v6))) &
% 119.23/22.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 119.23/22.36 (multiplication(v0, v1) = v3) | ~ (addition(v3, v2) = v4) | ~ $i(v2) | ~
% 119.23/22.36 $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: int]
% 119.23/22.36 : ((v8 = 0 & star(v0) = v6 & leq(v7, v1) = 0 & multiplication(v6, v2) = v7 &
% 119.23/22.36 $i(v7) & $i(v6)) | ( ~ (v5 = 0) & leq(v4, v1) = v5)))
% 119.23/22.36
% 119.23/22.36 (star_unfold_left)
% 119.23/22.36 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ?
% 119.23/22.36 [v2: $i] : ? [v3: $i] : (leq(v3, v1) = 0 & multiplication(v1, v0) = v2 &
% 119.23/22.36 addition(one, v2) = v3 & $i(v3) & $i(v2)))
% 119.23/22.36
% 119.23/22.36 (star_unfold_right)
% 119.23/22.36 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ?
% 119.23/22.36 [v2: $i] : ? [v3: $i] : (leq(v3, v1) = 0 & multiplication(v0, v1) = v2 &
% 119.23/22.36 addition(one, v2) = v3 & $i(v3) & $i(v2)))
% 119.23/22.36
% 119.23/22.36 (function-axioms)
% 119.23/22.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 119.23/22.37 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 119.23/22.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 119.23/22.37 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 119.23/22.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 119.23/22.37 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 119.23/22.37 [v2: $i] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) & ! [v0:
% 119.23/22.37 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (star(v2) = v1) | ~
% 119.23/22.37 (star(v2) = v0))
% 119.23/22.37
% 119.23/22.37 Further assumptions not needed in the proof:
% 119.23/22.37 --------------------------------------------
% 119.23/22.37 left_annihilation, left_distributivity, multiplicative_associativity,
% 119.23/22.37 multiplicative_left_identity, right_distributivity, star_induction_right
% 119.23/22.37
% 119.23/22.37 Those formulas are unsatisfiable:
% 119.23/22.37 ---------------------------------
% 119.23/22.37
% 119.23/22.37 Begin of proof
% 119.23/22.37 |
% 119.23/22.37 | ALPHA: (additive_commutativity) implies:
% 119.23/22.37 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) |
% 119.23/22.37 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2)))
% 119.23/22.37 |
% 119.23/22.37 | ALPHA: (additive_associativity) implies:
% 119.23/22.37 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 119.23/22.37 | ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~ $i(v2) |
% 119.23/22.37 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 &
% 119.23/22.37 | addition(v2, v1) = v5 & $i(v5) & $i(v4)))
% 119.23/22.37 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 119.23/22.37 | ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) |
% 119.23/22.38 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 &
% 119.23/22.38 | addition(v1, v0) = v5 & $i(v5) & $i(v4)))
% 119.23/22.38 |
% 119.23/22.38 | ALPHA: (additive_identity) implies:
% 119.23/22.38 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) |
% 119.23/22.38 | ~ $i(v0))
% 119.23/22.38 |
% 119.23/22.38 | ALPHA: (multiplicative_right_identity) implies:
% 119.23/22.38 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 119.23/22.38 | v1) | ~ $i(v0))
% 119.23/22.38 |
% 119.23/22.38 | ALPHA: (right_annihilation) implies:
% 119.23/22.38 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(v0, zero) =
% 119.23/22.38 | v1) | ~ $i(v0))
% 119.23/22.38 |
% 119.23/22.38 | ALPHA: (order) implies:
% 119.23/22.38 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = v1) | ~ $i(v1) |
% 119.23/22.38 | ~ $i(v0) | leq(v0, v1) = 0)
% 119.23/22.38 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v0, v1) = 0) | ~ $i(v1) | ~
% 119.23/22.38 | $i(v0) | addition(v0, v1) = v1)
% 119.23/22.38 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (addition(v0,
% 119.23/22.38 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 119.23/22.38 | leq(v0, v1) = v3))
% 119.23/22.38 |
% 119.23/22.38 | ALPHA: (star_unfold_right) implies:
% 119.23/22.38 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2:
% 119.23/22.38 | $i] : ? [v3: $i] : (leq(v3, v1) = 0 & multiplication(v0, v1) = v2
% 119.23/22.38 | & addition(one, v2) = v3 & $i(v3) & $i(v2)))
% 119.23/22.38 |
% 119.23/22.38 | ALPHA: (star_unfold_left) implies:
% 119.23/22.38 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2:
% 119.23/22.38 | $i] : ? [v3: $i] : (leq(v3, v1) = 0 & multiplication(v1, v0) = v2
% 119.23/22.38 | & addition(one, v2) = v3 & $i(v3) & $i(v2)))
% 119.23/22.38 |
% 119.23/22.38 | ALPHA: (star_induction_left) implies:
% 119.23/22.38 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 119.23/22.38 | ( ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v2) = v4) | ~
% 119.23/22.38 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: $i] : ?
% 119.23/22.38 | [v7: $i] : ? [v8: int] : ((v8 = 0 & star(v0) = v6 & leq(v7, v1) = 0
% 119.23/22.38 | & multiplication(v6, v2) = v7 & $i(v7) & $i(v6)) | ( ~ (v5 = 0)
% 119.23/22.38 | & leq(v4, v1) = v5)))
% 119.23/22.38 |
% 119.23/22.38 | ALPHA: (domain2) implies:
% 119.23/22.39 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (multiplication(v0, v1)
% 119.23/22.39 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ?
% 119.23/22.39 | [v5: $i] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 &
% 119.23/22.39 | multiplication(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3)))
% 119.23/22.39 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 119.23/22.39 | (domain(v1) = v2) | ~ (multiplication(v0, v2) = v3) | ~ $i(v1) |
% 119.23/22.39 | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : (domain(v4) = v5 & domain(v3)
% 119.23/22.39 | = v5 & multiplication(v0, v1) = v4 & $i(v5) & $i(v4)))
% 119.23/22.39 |
% 119.23/22.39 | ALPHA: (domain3) implies:
% 119.23/22.39 | (15) ! [v0: $i] : ! [v1: $i] : ( ~ (domain(v0) = v1) | ~ $i(v0) |
% 119.23/22.39 | addition(v1, one) = one)
% 119.23/22.39 |
% 119.23/22.39 | ALPHA: (domain4) implies:
% 119.23/22.39 | (16) $i(zero)
% 119.23/22.39 | (17) domain(zero) = zero
% 119.23/22.39 |
% 119.23/22.39 | ALPHA: (domain5) implies:
% 119.23/22.39 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2)
% 119.23/22.39 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 119.23/22.39 | (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4,
% 119.23/22.39 | v5) = v3 & $i(v5) & $i(v4) & $i(v3)))
% 119.23/22.39 |
% 119.23/22.39 | ALPHA: (goals) implies:
% 119.23/22.39 | (19) $i(one)
% 119.23/22.39 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = one) & domain(v1)
% 119.23/22.39 | = v2 & star(v0) = v1 & $i(v2) & $i(v1) & $i(v0))
% 119.23/22.39 |
% 119.23/22.39 | ALPHA: (function-axioms) implies:
% 119.23/22.39 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (domain(v2) =
% 119.23/22.39 | v1) | ~ (domain(v2) = v0))
% 119.23/22.39 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 119.23/22.39 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 119.23/22.39 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 119.23/22.39 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 119.23/22.39 | (24) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 119.23/22.39 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) =
% 119.23/22.39 | v0))
% 119.23/22.39 |
% 119.23/22.39 | DELTA: instantiating (20) with fresh symbols all_24_0, all_24_1, all_24_2
% 119.23/22.39 | gives:
% 119.23/22.39 | (25) ~ (all_24_0 = one) & domain(all_24_1) = all_24_0 & star(all_24_2) =
% 119.23/22.39 | all_24_1 & $i(all_24_0) & $i(all_24_1) & $i(all_24_2)
% 119.23/22.39 |
% 119.23/22.39 | ALPHA: (25) implies:
% 119.23/22.39 | (26) ~ (all_24_0 = one)
% 119.23/22.39 | (27) $i(all_24_2)
% 119.23/22.39 | (28) $i(all_24_1)
% 119.23/22.39 | (29) $i(all_24_0)
% 119.23/22.39 | (30) star(all_24_2) = all_24_1
% 119.23/22.39 | (31) domain(all_24_1) = all_24_0
% 119.23/22.39 |
% 119.23/22.40 | GROUND_INST: instantiating (11) with all_24_2, all_24_1, simplifying with
% 119.23/22.40 | (27), (30) gives:
% 119.23/22.40 | (32) ? [v0: $i] : ? [v1: $i] : (leq(v1, all_24_1) = 0 &
% 119.23/22.40 | multiplication(all_24_1, all_24_2) = v0 & addition(one, v0) = v1 &
% 119.23/22.40 | $i(v1) & $i(v0))
% 119.23/22.40 |
% 119.23/22.40 | GROUND_INST: instantiating (10) with all_24_2, all_24_1, simplifying with
% 119.23/22.40 | (27), (30) gives:
% 119.23/22.40 | (33) ? [v0: $i] : ? [v1: $i] : (leq(v1, all_24_1) = 0 &
% 119.23/22.40 | multiplication(all_24_2, all_24_1) = v0 & addition(one, v0) = v1 &
% 119.23/22.40 | $i(v1) & $i(v0))
% 119.23/22.40 |
% 119.23/22.40 | GROUND_INST: instantiating (15) with zero, zero, simplifying with (16), (17)
% 119.23/22.40 | gives:
% 119.23/22.40 | (34) addition(zero, one) = one
% 119.23/22.40 |
% 119.23/22.40 | GROUND_INST: instantiating (domain1) with zero, zero, simplifying with (16),
% 119.23/22.40 | (17) gives:
% 119.23/22.40 | (35) ? [v0: $i] : (multiplication(zero, zero) = v0 & addition(zero, v0) =
% 119.23/22.40 | v0 & $i(v0))
% 119.23/22.40 |
% 119.23/22.40 | GROUND_INST: instantiating (15) with all_24_1, all_24_0, simplifying with
% 119.23/22.40 | (28), (31) gives:
% 119.23/22.40 | (36) addition(all_24_0, one) = one
% 119.23/22.40 |
% 119.23/22.40 | GROUND_INST: instantiating (domain1) with all_24_1, all_24_0, simplifying with
% 119.23/22.40 | (28), (31) gives:
% 119.23/22.40 | (37) ? [v0: $i] : (multiplication(all_24_0, all_24_1) = v0 &
% 119.23/22.40 | addition(all_24_1, v0) = v0 & $i(v0))
% 119.23/22.40 |
% 119.23/22.40 | DELTA: instantiating (35) with fresh symbol all_32_0 gives:
% 119.23/22.40 | (38) multiplication(zero, zero) = all_32_0 & addition(zero, all_32_0) =
% 119.23/22.40 | all_32_0 & $i(all_32_0)
% 119.23/22.40 |
% 119.23/22.40 | ALPHA: (38) implies:
% 119.23/22.40 | (39) $i(all_32_0)
% 119.23/22.40 | (40) addition(zero, all_32_0) = all_32_0
% 119.23/22.40 | (41) multiplication(zero, zero) = all_32_0
% 119.23/22.40 |
% 119.23/22.40 | DELTA: instantiating (37) with fresh symbol all_34_0 gives:
% 119.23/22.40 | (42) multiplication(all_24_0, all_24_1) = all_34_0 & addition(all_24_1,
% 119.23/22.40 | all_34_0) = all_34_0 & $i(all_34_0)
% 119.23/22.40 |
% 119.23/22.40 | ALPHA: (42) implies:
% 119.23/22.40 | (43) $i(all_34_0)
% 119.23/22.40 | (44) addition(all_24_1, all_34_0) = all_34_0
% 119.23/22.40 | (45) multiplication(all_24_0, all_24_1) = all_34_0
% 119.23/22.40 |
% 119.23/22.40 | DELTA: instantiating (33) with fresh symbols all_36_0, all_36_1 gives:
% 119.23/22.40 | (46) leq(all_36_0, all_24_1) = 0 & multiplication(all_24_2, all_24_1) =
% 119.23/22.40 | all_36_1 & addition(one, all_36_1) = all_36_0 & $i(all_36_0) &
% 119.23/22.40 | $i(all_36_1)
% 119.23/22.40 |
% 119.23/22.40 | ALPHA: (46) implies:
% 119.23/22.40 | (47) $i(all_36_1)
% 119.23/22.40 | (48) addition(one, all_36_1) = all_36_0
% 119.23/22.40 | (49) multiplication(all_24_2, all_24_1) = all_36_1
% 119.23/22.40 | (50) leq(all_36_0, all_24_1) = 0
% 119.23/22.40 |
% 119.23/22.40 | DELTA: instantiating (32) with fresh symbols all_38_0, all_38_1 gives:
% 119.23/22.40 | (51) leq(all_38_0, all_24_1) = 0 & multiplication(all_24_1, all_24_2) =
% 119.23/22.40 | all_38_1 & addition(one, all_38_1) = all_38_0 & $i(all_38_0) &
% 119.23/22.40 | $i(all_38_1)
% 119.23/22.40 |
% 119.23/22.40 | ALPHA: (51) implies:
% 119.23/22.40 | (52) $i(all_38_1)
% 119.23/22.40 | (53) addition(one, all_38_1) = all_38_0
% 119.23/22.40 | (54) multiplication(all_24_1, all_24_2) = all_38_1
% 119.23/22.40 | (55) leq(all_38_0, all_24_1) = 0
% 119.23/22.40 |
% 119.23/22.41 | GROUND_INST: instantiating (2) with one, zero, zero, one, one, simplifying
% 119.23/22.41 | with (16), (19), (34) gives:
% 119.23/22.41 | (56) ? [v0: $i] : (addition(v0, one) = one & addition(zero, zero) = v0 &
% 119.23/22.41 | $i(v0))
% 119.23/22.41 |
% 119.23/22.41 | GROUND_INST: instantiating (1) with one, zero, one, simplifying with (16),
% 119.23/22.41 | (19), (34) gives:
% 119.23/22.41 | (57) addition(one, zero) = one
% 119.23/22.41 |
% 119.23/22.41 | GROUND_INST: instantiating (18) with zero, one, one, simplifying with (16),
% 119.23/22.41 | (19), (34) gives:
% 119.23/22.41 | (58) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(one) = v2 &
% 119.23/22.41 | domain(one) = v0 & domain(zero) = v1 & addition(v1, v2) = v0 &
% 119.23/22.41 | $i(v2) & $i(v1) & $i(v0))
% 119.23/22.41 |
% 119.23/22.41 | GROUND_INST: instantiating (2) with all_32_0, zero, zero, all_32_0, all_32_0,
% 119.23/22.41 | simplifying with (16), (39), (40) gives:
% 119.23/22.41 | (59) ? [v0: $i] : (addition(v0, all_32_0) = all_32_0 & addition(zero,
% 119.23/22.41 | zero) = v0 & $i(v0))
% 119.23/22.41 |
% 119.23/22.41 | GROUND_INST: instantiating (7) with zero, all_32_0, simplifying with (16),
% 119.23/22.41 | (39), (40) gives:
% 119.23/22.41 | (60) leq(zero, all_32_0) = 0
% 119.23/22.41 |
% 119.23/22.41 | GROUND_INST: instantiating (18) with zero, all_32_0, all_32_0, simplifying
% 119.23/22.41 | with (16), (39), (40) gives:
% 119.23/22.41 | (61) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_32_0) = v2 &
% 119.23/22.41 | domain(all_32_0) = v0 & domain(zero) = v1 & addition(v1, v2) = v0 &
% 119.23/22.41 | $i(v2) & $i(v1) & $i(v0))
% 119.23/22.41 |
% 119.23/22.41 | GROUND_INST: instantiating (3) with all_36_1, one, zero, one, all_36_0,
% 119.23/22.41 | simplifying with (16), (19), (34), (47), (48) gives:
% 119.23/22.41 | (62) ? [v0: $i] : (addition(one, all_36_1) = v0 & addition(zero, v0) =
% 119.23/22.41 | all_36_0 & $i(v0) & $i(all_36_0))
% 119.23/22.41 |
% 119.23/22.41 | GROUND_INST: instantiating (1) with all_36_1, one, all_36_0, simplifying with
% 119.23/22.41 | (19), (47), (48) gives:
% 119.23/22.41 | (63) addition(all_36_1, one) = all_36_0 & $i(all_36_0)
% 119.23/22.41 |
% 119.23/22.41 | ALPHA: (63) implies:
% 119.23/22.41 | (64) $i(all_36_0)
% 119.23/22.41 | (65) addition(all_36_1, one) = all_36_0
% 119.23/22.41 |
% 119.23/22.41 | GROUND_INST: instantiating (18) with one, all_36_1, all_36_0, simplifying with
% 119.23/22.41 | (19), (47), (48) gives:
% 119.23/22.41 | (66) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_36_0) = v0 &
% 119.23/22.41 | domain(all_36_1) = v2 & domain(one) = v1 & addition(v1, v2) = v0 &
% 119.23/22.41 | $i(v2) & $i(v1) & $i(v0))
% 119.23/22.41 |
% 119.23/22.41 | GROUND_INST: instantiating (3) with all_38_1, one, zero, one, all_38_0,
% 119.23/22.41 | simplifying with (16), (19), (34), (52), (53) gives:
% 119.23/22.41 | (67) ? [v0: $i] : (addition(one, all_38_1) = v0 & addition(zero, v0) =
% 119.23/22.41 | all_38_0 & $i(v0) & $i(all_38_0))
% 119.23/22.41 |
% 119.23/22.41 | GROUND_INST: instantiating (1) with all_38_1, one, all_38_0, simplifying with
% 119.23/22.41 | (19), (52), (53) gives:
% 119.23/22.41 | (68) addition(all_38_1, one) = all_38_0 & $i(all_38_0)
% 119.23/22.41 |
% 119.23/22.41 | ALPHA: (68) implies:
% 119.23/22.41 | (69) $i(all_38_0)
% 119.23/22.41 | (70) addition(all_38_1, one) = all_38_0
% 119.23/22.41 |
% 119.23/22.42 | GROUND_INST: instantiating (18) with one, all_38_1, all_38_0, simplifying with
% 119.23/22.42 | (19), (52), (53) gives:
% 119.23/22.42 | (71) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_38_0) = v0 &
% 119.23/22.42 | domain(all_38_1) = v2 & domain(one) = v1 & addition(v1, v2) = v0 &
% 119.23/22.42 | $i(v2) & $i(v1) & $i(v0))
% 119.23/22.42 |
% 119.23/22.42 | GROUND_INST: instantiating (2) with all_34_0, all_24_1, all_24_1, all_34_0,
% 119.23/22.42 | all_34_0, simplifying with (28), (43), (44) gives:
% 119.23/22.42 | (72) ? [v0: $i] : (addition(v0, all_34_0) = all_34_0 & addition(all_24_1,
% 119.23/22.42 | all_24_1) = v0 & $i(v0))
% 119.23/22.42 |
% 119.23/22.42 | GROUND_INST: instantiating (1) with all_34_0, all_24_1, all_34_0, simplifying
% 119.23/22.42 | with (28), (43), (44) gives:
% 119.23/22.42 | (73) addition(all_34_0, all_24_1) = all_34_0
% 119.23/22.42 |
% 119.23/22.42 | GROUND_INST: instantiating (18) with all_24_1, all_34_0, all_34_0, simplifying
% 119.23/22.42 | with (28), (43), (44) gives:
% 119.23/22.42 | (74) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_34_0) = v2 &
% 119.23/22.42 | domain(all_34_0) = v0 & domain(all_24_1) = v1 & addition(v1, v2) =
% 119.23/22.42 | v0 & $i(v2) & $i(v1) & $i(v0))
% 119.23/22.42 |
% 119.23/22.42 | GROUND_INST: instantiating (2) with one, all_24_0, all_24_0, one, one,
% 119.23/22.42 | simplifying with (19), (29), (36) gives:
% 119.23/22.42 | (75) ? [v0: $i] : (addition(v0, one) = one & addition(all_24_0, all_24_0)
% 119.23/22.42 | = v0 & $i(v0))
% 119.23/22.42 |
% 119.23/22.42 | GROUND_INST: instantiating (3) with all_38_1, one, all_24_0, one, all_38_0,
% 119.23/22.42 | simplifying with (19), (29), (36), (52), (53) gives:
% 119.23/22.42 | (76) ? [v0: $i] : (addition(all_24_0, v0) = all_38_0 & addition(one,
% 119.23/22.42 | all_38_1) = v0 & $i(v0) & $i(all_38_0))
% 119.23/22.42 |
% 119.23/22.42 | GROUND_INST: instantiating (3) with all_36_1, one, all_24_0, one, all_36_0,
% 119.23/22.42 | simplifying with (19), (29), (36), (47), (48) gives:
% 119.23/22.42 | (77) ? [v0: $i] : (addition(all_24_0, v0) = all_36_0 & addition(one,
% 119.23/22.42 | all_36_1) = v0 & $i(v0) & $i(all_36_0))
% 119.23/22.42 |
% 119.23/22.42 | GROUND_INST: instantiating (2) with one, zero, all_24_0, one, one, simplifying
% 119.23/22.42 | with (16), (19), (29), (34), (36) gives:
% 119.23/22.42 | (78) ? [v0: $i] : (addition(v0, one) = one & addition(all_24_0, zero) = v0
% 119.23/22.42 | & $i(v0))
% 119.23/22.42 |
% 119.23/22.42 | GROUND_INST: instantiating (2) with one, all_24_0, zero, one, one, simplifying
% 119.23/22.42 | with (16), (19), (29), (34), (36) gives:
% 119.23/22.42 | (79) ? [v0: $i] : (addition(v0, one) = one & addition(zero, all_24_0) = v0
% 119.23/22.42 | & $i(v0))
% 119.23/22.42 |
% 119.23/22.42 | GROUND_INST: instantiating (1) with one, all_24_0, one, simplifying with (19),
% 119.23/22.42 | (29), (36) gives:
% 119.23/22.42 | (80) addition(one, all_24_0) = one
% 119.23/22.42 |
% 119.23/22.42 | GROUND_INST: instantiating (18) with all_24_0, one, one, simplifying with
% 119.23/22.42 | (19), (29), (36) gives:
% 119.23/22.43 | (81) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_24_0) = v1 &
% 119.23/22.43 | domain(one) = v2 & domain(one) = v0 & addition(v1, v2) = v0 & $i(v2)
% 119.23/22.43 | & $i(v1) & $i(v0))
% 119.23/22.43 |
% 119.81/22.43 | GROUND_INST: instantiating (14) with zero, zero, zero, all_32_0, simplifying
% 119.81/22.43 | with (16), (17), (41) gives:
% 119.81/22.43 | (82) ? [v0: $i] : ? [v1: $i] : (domain(v0) = v1 & domain(all_32_0) = v1 &
% 119.81/22.43 | multiplication(zero, zero) = v0 & $i(v1) & $i(v0))
% 119.81/22.43 |
% 119.81/22.43 | GROUND_INST: instantiating (6) with zero, all_32_0, simplifying with (16),
% 119.81/22.43 | (41) gives:
% 119.81/22.43 | (83) all_32_0 = zero
% 119.81/22.43 |
% 119.81/22.43 | GROUND_INST: instantiating (13) with zero, zero, all_32_0, simplifying with
% 119.81/22.43 | (16), (41) gives:
% 119.81/22.43 | (84) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(v2) = v0 &
% 119.81/22.43 | domain(all_32_0) = v0 & domain(zero) = v1 & multiplication(zero, v1)
% 119.81/22.43 | = v2 & $i(v2) & $i(v1) & $i(v0))
% 119.81/22.43 |
% 119.81/22.43 | GROUND_INST: instantiating (13) with all_24_2, all_24_1, all_36_1, simplifying
% 119.81/22.43 | with (27), (28), (49) gives:
% 119.81/22.43 | (85) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(v2) = v0 &
% 119.81/22.43 | domain(all_36_1) = v0 & domain(all_24_1) = v1 &
% 119.81/22.43 | multiplication(all_24_2, v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 119.81/22.43 |
% 119.81/22.43 | GROUND_INST: instantiating (13) with all_24_1, all_24_2, all_38_1, simplifying
% 119.81/22.43 | with (27), (28), (54) gives:
% 119.81/22.43 | (86) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(v2) = v0 &
% 119.81/22.43 | domain(all_38_1) = v0 & domain(all_24_2) = v1 &
% 119.81/22.43 | multiplication(all_24_1, v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 119.81/22.43 |
% 119.81/22.43 | GROUND_INST: instantiating (13) with all_24_0, all_24_1, all_34_0, simplifying
% 119.81/22.43 | with (28), (29), (45) gives:
% 119.81/22.43 | (87) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(v2) = v0 &
% 119.81/22.43 | domain(all_34_0) = v0 & domain(all_24_1) = v1 &
% 119.81/22.43 | multiplication(all_24_0, v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 119.81/22.43 |
% 119.81/22.43 | GROUND_INST: instantiating (8) with all_36_0, all_24_1, simplifying with (28),
% 119.81/22.43 | (50), (64) gives:
% 119.81/22.43 | (88) addition(all_36_0, all_24_1) = all_24_1
% 119.81/22.43 |
% 119.81/22.43 | GROUND_INST: instantiating (8) with all_38_0, all_24_1, simplifying with (28),
% 119.81/22.43 | (55), (69) gives:
% 119.81/22.43 | (89) addition(all_38_0, all_24_1) = all_24_1
% 119.81/22.43 |
% 119.81/22.43 | DELTA: instantiating (79) with fresh symbol all_46_0 gives:
% 119.81/22.43 | (90) addition(all_46_0, one) = one & addition(zero, all_24_0) = all_46_0 &
% 119.81/22.43 | $i(all_46_0)
% 119.81/22.43 |
% 119.81/22.43 | ALPHA: (90) implies:
% 119.81/22.43 | (91) addition(zero, all_24_0) = all_46_0
% 119.81/22.43 | (92) addition(all_46_0, one) = one
% 119.81/22.43 |
% 119.81/22.43 | DELTA: instantiating (78) with fresh symbol all_48_0 gives:
% 119.81/22.43 | (93) addition(all_48_0, one) = one & addition(all_24_0, zero) = all_48_0 &
% 119.81/22.43 | $i(all_48_0)
% 119.81/22.43 |
% 119.81/22.43 | ALPHA: (93) implies:
% 119.81/22.43 | (94) addition(all_24_0, zero) = all_48_0
% 119.81/22.43 | (95) addition(all_48_0, one) = one
% 119.81/22.43 |
% 119.81/22.43 | DELTA: instantiating (56) with fresh symbol all_50_0 gives:
% 119.81/22.43 | (96) addition(all_50_0, one) = one & addition(zero, zero) = all_50_0 &
% 119.81/22.43 | $i(all_50_0)
% 119.81/22.43 |
% 119.81/22.43 | ALPHA: (96) implies:
% 119.81/22.43 | (97) addition(zero, zero) = all_50_0
% 119.81/22.44 | (98) addition(all_50_0, one) = one
% 119.81/22.44 |
% 119.81/22.44 | DELTA: instantiating (72) with fresh symbol all_52_0 gives:
% 119.81/22.44 | (99) addition(all_52_0, all_34_0) = all_34_0 & addition(all_24_1, all_24_1)
% 119.81/22.44 | = all_52_0 & $i(all_52_0)
% 119.81/22.44 |
% 119.81/22.44 | ALPHA: (99) implies:
% 119.81/22.44 | (100) $i(all_52_0)
% 119.81/22.44 | (101) addition(all_24_1, all_24_1) = all_52_0
% 119.81/22.44 | (102) addition(all_52_0, all_34_0) = all_34_0
% 119.81/22.44 |
% 119.81/22.44 | DELTA: instantiating (59) with fresh symbol all_54_0 gives:
% 119.81/22.44 | (103) addition(all_54_0, all_32_0) = all_32_0 & addition(zero, zero) =
% 119.81/22.44 | all_54_0 & $i(all_54_0)
% 119.81/22.44 |
% 119.81/22.44 | ALPHA: (103) implies:
% 119.81/22.44 | (104) addition(zero, zero) = all_54_0
% 119.81/22.44 |
% 119.81/22.44 | DELTA: instantiating (75) with fresh symbol all_56_0 gives:
% 119.81/22.44 | (105) addition(all_56_0, one) = one & addition(all_24_0, all_24_0) =
% 119.81/22.44 | all_56_0 & $i(all_56_0)
% 119.81/22.44 |
% 119.81/22.44 | ALPHA: (105) implies:
% 119.81/22.44 | (106) $i(all_56_0)
% 119.81/22.44 | (107) addition(all_24_0, all_24_0) = all_56_0
% 119.81/22.44 | (108) addition(all_56_0, one) = one
% 119.81/22.44 |
% 119.81/22.44 | DELTA: instantiating (62) with fresh symbol all_58_0 gives:
% 119.81/22.44 | (109) addition(one, all_36_1) = all_58_0 & addition(zero, all_58_0) =
% 119.81/22.44 | all_36_0 & $i(all_58_0) & $i(all_36_0)
% 119.81/22.44 |
% 119.81/22.44 | ALPHA: (109) implies:
% 119.81/22.44 | (110) $i(all_58_0)
% 119.81/22.44 | (111) addition(zero, all_58_0) = all_36_0
% 119.81/22.44 | (112) addition(one, all_36_1) = all_58_0
% 119.81/22.44 |
% 119.81/22.44 | DELTA: instantiating (77) with fresh symbol all_60_0 gives:
% 119.81/22.44 | (113) addition(all_24_0, all_60_0) = all_36_0 & addition(one, all_36_1) =
% 119.81/22.44 | all_60_0 & $i(all_60_0) & $i(all_36_0)
% 119.81/22.44 |
% 119.81/22.44 | ALPHA: (113) implies:
% 119.81/22.44 | (114) addition(one, all_36_1) = all_60_0
% 119.81/22.44 | (115) addition(all_24_0, all_60_0) = all_36_0
% 119.81/22.44 |
% 119.81/22.44 | DELTA: instantiating (76) with fresh symbol all_62_0 gives:
% 119.81/22.44 | (116) addition(all_24_0, all_62_0) = all_38_0 & addition(one, all_38_1) =
% 119.81/22.44 | all_62_0 & $i(all_62_0) & $i(all_38_0)
% 119.81/22.44 |
% 119.81/22.44 | ALPHA: (116) implies:
% 119.81/22.44 | (117) $i(all_62_0)
% 119.81/22.44 | (118) addition(one, all_38_1) = all_62_0
% 119.81/22.44 | (119) addition(all_24_0, all_62_0) = all_38_0
% 119.81/22.44 |
% 119.81/22.44 | DELTA: instantiating (67) with fresh symbol all_64_0 gives:
% 119.81/22.44 | (120) addition(one, all_38_1) = all_64_0 & addition(zero, all_64_0) =
% 119.81/22.44 | all_38_0 & $i(all_64_0) & $i(all_38_0)
% 119.81/22.44 |
% 119.81/22.44 | ALPHA: (120) implies:
% 119.81/22.44 | (121) addition(zero, all_64_0) = all_38_0
% 119.81/22.44 | (122) addition(one, all_38_1) = all_64_0
% 119.81/22.44 |
% 119.81/22.44 | DELTA: instantiating (82) with fresh symbols all_66_0, all_66_1 gives:
% 119.81/22.44 | (123) domain(all_66_1) = all_66_0 & domain(all_32_0) = all_66_0 &
% 119.81/22.44 | multiplication(zero, zero) = all_66_1 & $i(all_66_0) & $i(all_66_1)
% 119.81/22.44 |
% 119.81/22.44 | ALPHA: (123) implies:
% 119.81/22.44 | (124) multiplication(zero, zero) = all_66_1
% 119.81/22.44 | (125) domain(all_32_0) = all_66_0
% 119.81/22.44 |
% 119.81/22.44 | DELTA: instantiating (81) with fresh symbols all_68_0, all_68_1, all_68_2
% 119.81/22.44 | gives:
% 119.81/22.44 | (126) domain(all_24_0) = all_68_1 & domain(one) = all_68_0 & domain(one) =
% 119.81/22.44 | all_68_2 & addition(all_68_1, all_68_0) = all_68_2 & $i(all_68_0) &
% 119.81/22.44 | $i(all_68_1) & $i(all_68_2)
% 119.81/22.44 |
% 119.81/22.44 | ALPHA: (126) implies:
% 119.81/22.44 | (127) $i(all_68_1)
% 119.81/22.44 | (128) $i(all_68_0)
% 119.81/22.44 | (129) addition(all_68_1, all_68_0) = all_68_2
% 119.81/22.44 | (130) domain(one) = all_68_2
% 119.81/22.44 | (131) domain(one) = all_68_0
% 119.81/22.44 | (132) domain(all_24_0) = all_68_1
% 119.81/22.44 |
% 119.81/22.44 | DELTA: instantiating (85) with fresh symbols all_70_0, all_70_1, all_70_2
% 119.81/22.44 | gives:
% 119.81/22.44 | (133) domain(all_70_0) = all_70_2 & domain(all_36_1) = all_70_2 &
% 119.81/22.44 | domain(all_24_1) = all_70_1 & multiplication(all_24_2, all_70_1) =
% 119.81/22.44 | all_70_0 & $i(all_70_0) & $i(all_70_1) & $i(all_70_2)
% 119.81/22.44 |
% 119.81/22.44 | ALPHA: (133) implies:
% 119.81/22.44 | (134) $i(all_70_1)
% 119.81/22.44 | (135) $i(all_70_0)
% 119.81/22.44 | (136) multiplication(all_24_2, all_70_1) = all_70_0
% 119.81/22.44 | (137) domain(all_24_1) = all_70_1
% 119.81/22.44 | (138) domain(all_36_1) = all_70_2
% 119.81/22.44 | (139) domain(all_70_0) = all_70_2
% 119.81/22.44 |
% 119.81/22.44 | DELTA: instantiating (74) with fresh symbols all_72_0, all_72_1, all_72_2
% 119.81/22.44 | gives:
% 119.81/22.45 | (140) domain(all_34_0) = all_72_0 & domain(all_34_0) = all_72_2 &
% 119.81/22.45 | domain(all_24_1) = all_72_1 & addition(all_72_1, all_72_0) = all_72_2
% 119.81/22.45 | & $i(all_72_0) & $i(all_72_1) & $i(all_72_2)
% 119.81/22.45 |
% 119.81/22.45 | ALPHA: (140) implies:
% 119.81/22.45 | (141) $i(all_72_0)
% 119.81/22.45 | (142) addition(all_72_1, all_72_0) = all_72_2
% 119.81/22.45 | (143) domain(all_24_1) = all_72_1
% 119.81/22.45 | (144) domain(all_34_0) = all_72_2
% 119.81/22.45 | (145) domain(all_34_0) = all_72_0
% 119.81/22.45 |
% 119.81/22.45 | DELTA: instantiating (71) with fresh symbols all_74_0, all_74_1, all_74_2
% 119.81/22.45 | gives:
% 119.81/22.45 | (146) domain(all_38_0) = all_74_2 & domain(all_38_1) = all_74_0 &
% 119.81/22.45 | domain(one) = all_74_1 & addition(all_74_1, all_74_0) = all_74_2 &
% 119.81/22.45 | $i(all_74_0) & $i(all_74_1) & $i(all_74_2)
% 119.81/22.45 |
% 119.81/22.45 | ALPHA: (146) implies:
% 119.81/22.45 | (147) addition(all_74_1, all_74_0) = all_74_2
% 119.81/22.45 | (148) domain(one) = all_74_1
% 119.81/22.45 | (149) domain(all_38_1) = all_74_0
% 119.81/22.45 | (150) domain(all_38_0) = all_74_2
% 119.81/22.45 |
% 119.81/22.45 | DELTA: instantiating (66) with fresh symbols all_76_0, all_76_1, all_76_2
% 119.81/22.45 | gives:
% 119.81/22.45 | (151) domain(all_36_0) = all_76_2 & domain(all_36_1) = all_76_0 &
% 119.81/22.45 | domain(one) = all_76_1 & addition(all_76_1, all_76_0) = all_76_2 &
% 119.81/22.45 | $i(all_76_0) & $i(all_76_1) & $i(all_76_2)
% 119.81/22.45 |
% 119.81/22.45 | ALPHA: (151) implies:
% 119.81/22.45 | (152) $i(all_76_0)
% 119.81/22.45 | (153) addition(all_76_1, all_76_0) = all_76_2
% 119.81/22.45 | (154) domain(one) = all_76_1
% 119.81/22.45 | (155) domain(all_36_1) = all_76_0
% 119.81/22.45 | (156) domain(all_36_0) = all_76_2
% 119.81/22.45 |
% 119.81/22.45 | DELTA: instantiating (84) with fresh symbols all_78_0, all_78_1, all_78_2
% 119.81/22.45 | gives:
% 119.81/22.45 | (157) domain(all_78_0) = all_78_2 & domain(all_32_0) = all_78_2 &
% 119.81/22.45 | domain(zero) = all_78_1 & multiplication(zero, all_78_1) = all_78_0 &
% 119.81/22.45 | $i(all_78_0) & $i(all_78_1) & $i(all_78_2)
% 119.81/22.45 |
% 119.81/22.45 | ALPHA: (157) implies:
% 119.81/22.45 | (158) $i(all_78_0)
% 119.81/22.45 | (159) multiplication(zero, all_78_1) = all_78_0
% 119.81/22.45 | (160) domain(zero) = all_78_1
% 119.81/22.45 | (161) domain(all_32_0) = all_78_2
% 119.81/22.45 | (162) domain(all_78_0) = all_78_2
% 119.81/22.45 |
% 119.81/22.45 | DELTA: instantiating (87) with fresh symbols all_80_0, all_80_1, all_80_2
% 119.81/22.45 | gives:
% 119.81/22.45 | (163) domain(all_80_0) = all_80_2 & domain(all_34_0) = all_80_2 &
% 119.81/22.45 | domain(all_24_1) = all_80_1 & multiplication(all_24_0, all_80_1) =
% 119.81/22.45 | all_80_0 & $i(all_80_0) & $i(all_80_1) & $i(all_80_2)
% 119.81/22.45 |
% 119.81/22.45 | ALPHA: (163) implies:
% 119.81/22.45 | (164) $i(all_80_0)
% 119.81/22.45 | (165) multiplication(all_24_0, all_80_1) = all_80_0
% 119.81/22.45 | (166) domain(all_24_1) = all_80_1
% 119.81/22.45 | (167) domain(all_34_0) = all_80_2
% 119.81/22.45 | (168) domain(all_80_0) = all_80_2
% 119.81/22.45 |
% 119.81/22.45 | DELTA: instantiating (86) with fresh symbols all_82_0, all_82_1, all_82_2
% 119.81/22.45 | gives:
% 119.81/22.45 | (169) domain(all_82_0) = all_82_2 & domain(all_38_1) = all_82_2 &
% 119.81/22.45 | domain(all_24_2) = all_82_1 & multiplication(all_24_1, all_82_1) =
% 119.81/22.45 | all_82_0 & $i(all_82_0) & $i(all_82_1) & $i(all_82_2)
% 119.81/22.45 |
% 119.81/22.45 | ALPHA: (169) implies:
% 119.81/22.45 | (170) $i(all_82_2)
% 119.81/22.45 | (171) $i(all_82_1)
% 119.81/22.45 | (172) $i(all_82_0)
% 119.81/22.45 | (173) domain(all_24_2) = all_82_1
% 119.81/22.45 | (174) domain(all_38_1) = all_82_2
% 119.81/22.45 | (175) domain(all_82_0) = all_82_2
% 119.81/22.45 |
% 119.81/22.45 | DELTA: instantiating (61) with fresh symbols all_84_0, all_84_1, all_84_2
% 119.81/22.45 | gives:
% 119.81/22.45 | (176) domain(all_32_0) = all_84_0 & domain(all_32_0) = all_84_2 &
% 119.81/22.45 | domain(zero) = all_84_1 & addition(all_84_1, all_84_0) = all_84_2 &
% 119.81/22.45 | $i(all_84_0) & $i(all_84_1) & $i(all_84_2)
% 119.81/22.45 |
% 119.81/22.45 | ALPHA: (176) implies:
% 119.81/22.45 | (177) domain(zero) = all_84_1
% 119.81/22.45 | (178) domain(all_32_0) = all_84_2
% 119.81/22.45 | (179) domain(all_32_0) = all_84_0
% 119.81/22.45 |
% 119.81/22.45 | DELTA: instantiating (58) with fresh symbols all_86_0, all_86_1, all_86_2
% 119.81/22.45 | gives:
% 119.81/22.45 | (180) domain(one) = all_86_0 & domain(one) = all_86_2 & domain(zero) =
% 119.81/22.45 | all_86_1 & addition(all_86_1, all_86_0) = all_86_2 & $i(all_86_0) &
% 119.81/22.45 | $i(all_86_1) & $i(all_86_2)
% 119.81/22.45 |
% 119.81/22.45 | ALPHA: (180) implies:
% 119.81/22.45 | (181) addition(all_86_1, all_86_0) = all_86_2
% 119.81/22.45 | (182) domain(zero) = all_86_1
% 119.81/22.45 | (183) domain(one) = all_86_2
% 119.81/22.45 | (184) domain(one) = all_86_0
% 119.81/22.45 |
% 119.81/22.45 | REDUCE: (83), (179) imply:
% 119.81/22.46 | (185) domain(zero) = all_84_0
% 119.81/22.46 |
% 119.81/22.46 | REDUCE: (83), (178) imply:
% 119.81/22.46 | (186) domain(zero) = all_84_2
% 119.81/22.46 |
% 119.81/22.46 | REDUCE: (83), (161) imply:
% 119.81/22.46 | (187) domain(zero) = all_78_2
% 119.81/22.46 |
% 119.81/22.46 | REDUCE: (83), (125) imply:
% 119.81/22.46 | (188) domain(zero) = all_66_0
% 119.81/22.46 |
% 119.81/22.46 | REDUCE: (60), (83) imply:
% 119.81/22.46 | (189) leq(zero, zero) = 0
% 119.81/22.46 |
% 119.81/22.46 | REDUCE: (41), (83) imply:
% 119.81/22.46 | (190) multiplication(zero, zero) = zero
% 119.81/22.46 |
% 119.81/22.46 | REDUCE: (40), (83) imply:
% 119.81/22.46 | (191) addition(zero, zero) = zero
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (22) with all_50_0, all_54_0, zero, zero,
% 119.81/22.46 | simplifying with (97), (104) gives:
% 119.81/22.46 | (192) all_54_0 = all_50_0
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (22) with zero, all_54_0, zero, zero, simplifying
% 119.81/22.46 | with (104), (191) gives:
% 119.81/22.46 | (193) all_54_0 = zero
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (22) with all_36_0, all_60_0, all_36_1, one,
% 119.81/22.46 | simplifying with (48), (114) gives:
% 119.81/22.46 | (194) all_60_0 = all_36_0
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (22) with all_58_0, all_60_0, all_36_1, one,
% 119.81/22.46 | simplifying with (112), (114) gives:
% 119.81/22.46 | (195) all_60_0 = all_58_0
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (22) with all_38_0, all_64_0, all_38_1, one,
% 119.81/22.46 | simplifying with (53), (122) gives:
% 119.81/22.46 | (196) all_64_0 = all_38_0
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (22) with all_62_0, all_64_0, all_38_1, one,
% 119.81/22.46 | simplifying with (118), (122) gives:
% 119.81/22.46 | (197) all_64_0 = all_62_0
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (23) with zero, all_66_1, zero, zero, simplifying
% 119.81/22.46 | with (124), (190) gives:
% 119.81/22.46 | (198) all_66_1 = zero
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_78_2, all_78_1, zero, simplifying
% 119.81/22.46 | with (160), (187) gives:
% 119.81/22.46 | (199) all_78_1 = all_78_2
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with zero, all_84_1, zero, simplifying with
% 119.81/22.46 | (17), (177) gives:
% 119.81/22.46 | (200) all_84_1 = zero
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_78_1, all_84_1, zero, simplifying
% 119.81/22.46 | with (160), (177) gives:
% 119.81/22.46 | (201) all_84_1 = all_78_1
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_84_0, all_86_1, zero, simplifying
% 119.81/22.46 | with (182), (185) gives:
% 119.81/22.46 | (202) all_86_1 = all_84_0
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_84_2, all_86_1, zero, simplifying
% 119.81/22.46 | with (182), (186) gives:
% 119.81/22.46 | (203) all_86_1 = all_84_2
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_78_1, all_86_1, zero, simplifying
% 119.81/22.46 | with (160), (182) gives:
% 119.81/22.46 | (204) all_86_1 = all_78_1
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_66_0, all_86_1, zero, simplifying
% 119.81/22.46 | with (182), (188) gives:
% 119.81/22.46 | (205) all_86_1 = all_66_0
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_68_2, all_76_1, one, simplifying with
% 119.81/22.46 | (130), (154) gives:
% 119.81/22.46 | (206) all_76_1 = all_68_2
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_76_1, all_86_2, one, simplifying with
% 119.81/22.46 | (154), (183) gives:
% 119.81/22.46 | (207) all_86_2 = all_76_1
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_74_1, all_86_2, one, simplifying with
% 119.81/22.46 | (148), (183) gives:
% 119.81/22.46 | (208) all_86_2 = all_74_1
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_86_2, all_86_0, one, simplifying with
% 119.81/22.46 | (183), (184) gives:
% 119.81/22.46 | (209) all_86_0 = all_86_2
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_68_0, all_86_0, one, simplifying with
% 119.81/22.46 | (131), (184) gives:
% 119.81/22.46 | (210) all_86_0 = all_68_0
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_24_0, all_72_1, all_24_1, simplifying
% 119.81/22.46 | with (31), (143) gives:
% 119.81/22.46 | (211) all_72_1 = all_24_0
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_72_1, all_80_1, all_24_1, simplifying
% 119.81/22.46 | with (143), (166) gives:
% 119.81/22.46 | (212) all_80_1 = all_72_1
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_70_1, all_80_1, all_24_1, simplifying
% 119.81/22.46 | with (137), (166) gives:
% 119.81/22.46 | (213) all_80_1 = all_70_1
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_72_0, all_80_2, all_34_0, simplifying
% 119.81/22.46 | with (145), (167) gives:
% 119.81/22.46 | (214) all_80_2 = all_72_0
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_72_2, all_80_2, all_34_0, simplifying
% 119.81/22.46 | with (144), (167) gives:
% 119.81/22.46 | (215) all_80_2 = all_72_2
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_70_2, all_76_0, all_36_1, simplifying
% 119.81/22.46 | with (138), (155) gives:
% 119.81/22.46 | (216) all_76_0 = all_70_2
% 119.81/22.46 |
% 119.81/22.46 | GROUND_INST: instantiating (21) with all_74_0, all_82_2, all_38_1, simplifying
% 119.81/22.46 | with (149), (174) gives:
% 119.81/22.46 | (217) all_82_2 = all_74_0
% 119.81/22.46 |
% 119.81/22.46 | COMBINE_EQS: (209), (210) imply:
% 119.81/22.46 | (218) all_86_2 = all_68_0
% 119.81/22.46 |
% 119.81/22.46 | SIMP: (218) implies:
% 119.81/22.46 | (219) all_86_2 = all_68_0
% 119.81/22.46 |
% 119.81/22.46 | COMBINE_EQS: (202), (204) imply:
% 119.81/22.46 | (220) all_84_0 = all_78_1
% 119.81/22.46 |
% 119.81/22.46 | COMBINE_EQS: (202), (203) imply:
% 119.81/22.47 | (221) all_84_0 = all_84_2
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (202), (205) imply:
% 119.81/22.47 | (222) all_84_0 = all_66_0
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (207), (208) imply:
% 119.81/22.47 | (223) all_76_1 = all_74_1
% 119.81/22.47 |
% 119.81/22.47 | SIMP: (223) implies:
% 119.81/22.47 | (224) all_76_1 = all_74_1
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (208), (219) imply:
% 119.81/22.47 | (225) all_74_1 = all_68_0
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (220), (221) imply:
% 119.81/22.47 | (226) all_84_2 = all_78_1
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (221), (222) imply:
% 119.81/22.47 | (227) all_84_2 = all_66_0
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (200), (201) imply:
% 119.81/22.47 | (228) all_78_1 = zero
% 119.81/22.47 |
% 119.81/22.47 | SIMP: (228) implies:
% 119.81/22.47 | (229) all_78_1 = zero
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (226), (227) imply:
% 119.81/22.47 | (230) all_78_1 = all_66_0
% 119.81/22.47 |
% 119.81/22.47 | SIMP: (230) implies:
% 119.81/22.47 | (231) all_78_1 = all_66_0
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (212), (213) imply:
% 119.81/22.47 | (232) all_72_1 = all_70_1
% 119.81/22.47 |
% 119.81/22.47 | SIMP: (232) implies:
% 119.81/22.47 | (233) all_72_1 = all_70_1
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (214), (215) imply:
% 119.81/22.47 | (234) all_72_0 = all_72_2
% 119.81/22.47 |
% 119.81/22.47 | SIMP: (234) implies:
% 119.81/22.47 | (235) all_72_0 = all_72_2
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (199), (229) imply:
% 119.81/22.47 | (236) all_78_2 = zero
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (199), (231) imply:
% 119.81/22.47 | (237) all_78_2 = all_66_0
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (236), (237) imply:
% 119.81/22.47 | (238) all_66_0 = zero
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (206), (224) imply:
% 119.81/22.47 | (239) all_74_1 = all_68_2
% 119.81/22.47 |
% 119.81/22.47 | SIMP: (239) implies:
% 119.81/22.47 | (240) all_74_1 = all_68_2
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (225), (240) imply:
% 119.81/22.47 | (241) all_68_0 = all_68_2
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (211), (233) imply:
% 119.81/22.47 | (242) all_70_1 = all_24_0
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (196), (197) imply:
% 119.81/22.47 | (243) all_62_0 = all_38_0
% 119.81/22.47 |
% 119.81/22.47 | SIMP: (243) implies:
% 119.81/22.47 | (244) all_62_0 = all_38_0
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (194), (195) imply:
% 119.81/22.47 | (245) all_58_0 = all_36_0
% 119.81/22.47 |
% 119.81/22.47 | SIMP: (245) implies:
% 119.81/22.47 | (246) all_58_0 = all_36_0
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (192), (193) imply:
% 119.81/22.47 | (247) all_50_0 = zero
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (213), (242) imply:
% 119.81/22.47 | (248) all_80_1 = all_24_0
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (227), (238) imply:
% 119.81/22.47 | (249) all_84_2 = zero
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (221), (249) imply:
% 119.81/22.47 | (250) all_84_0 = zero
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (208), (240) imply:
% 119.81/22.47 | (251) all_86_2 = all_68_2
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (202), (250) imply:
% 119.81/22.47 | (252) all_86_1 = zero
% 119.81/22.47 |
% 119.81/22.47 | COMBINE_EQS: (210), (241) imply:
% 119.81/22.47 | (253) all_86_0 = all_68_2
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (175), (217) imply:
% 119.81/22.47 | (254) domain(all_82_0) = all_74_0
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (168), (215) imply:
% 119.81/22.47 | (255) domain(all_80_0) = all_72_2
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (162), (236) imply:
% 119.81/22.47 | (256) domain(all_78_0) = zero
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (165), (248) imply:
% 119.81/22.47 | (257) multiplication(all_24_0, all_24_0) = all_80_0
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (136), (242) imply:
% 119.81/22.47 | (258) multiplication(all_24_2, all_24_0) = all_70_0
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (159), (229) imply:
% 119.81/22.47 | (259) multiplication(zero, zero) = all_78_0
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (181), (251), (252), (253) imply:
% 119.81/22.47 | (260) addition(zero, all_68_2) = all_68_2
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (153), (206), (216) imply:
% 119.81/22.47 | (261) addition(all_68_2, all_70_2) = all_76_2
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (147), (240) imply:
% 119.81/22.47 | (262) addition(all_68_2, all_74_0) = all_74_2
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (142), (211), (235) imply:
% 119.81/22.47 | (263) addition(all_24_0, all_72_2) = all_72_2
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (129), (241) imply:
% 119.81/22.47 | (264) addition(all_68_1, all_68_2) = all_68_2
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (119), (244) imply:
% 119.81/22.47 | (265) addition(all_24_0, all_38_0) = all_38_0
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (115), (194) imply:
% 119.81/22.47 | (266) addition(all_24_0, all_36_0) = all_36_0
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (121), (196) imply:
% 119.81/22.47 | (267) addition(zero, all_38_0) = all_38_0
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (111), (246) imply:
% 119.81/22.47 | (268) addition(zero, all_36_0) = all_36_0
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (170), (217) imply:
% 119.81/22.47 | (269) $i(all_74_0)
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (152), (216) imply:
% 119.81/22.47 | (270) $i(all_70_2)
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (141), (235) imply:
% 119.81/22.47 | (271) $i(all_72_2)
% 119.81/22.47 |
% 119.81/22.47 | REDUCE: (128), (241) imply:
% 119.81/22.47 | (272) $i(all_68_2)
% 119.81/22.47 |
% 119.81/22.47 | GROUND_INST: instantiating (23) with zero, all_78_0, zero, zero, simplifying
% 119.81/22.47 | with (190), (259) gives:
% 119.81/22.47 | (273) all_78_0 = zero
% 119.81/22.47 |
% 119.81/22.47 | GROUND_INST: instantiating (1) with all_24_0, zero, all_46_0, simplifying with
% 119.81/22.47 | (16), (29), (91) gives:
% 119.81/22.47 | (274) addition(all_24_0, zero) = all_46_0 & $i(all_46_0)
% 119.81/22.47 |
% 119.81/22.47 | ALPHA: (274) implies:
% 119.81/22.47 | (275) $i(all_46_0)
% 119.81/22.47 | (276) addition(all_24_0, zero) = all_46_0
% 119.81/22.47 |
% 119.81/22.47 | GROUND_INST: instantiating (18) with zero, all_24_0, all_46_0, simplifying
% 119.81/22.47 | with (16), (29), (91) gives:
% 119.81/22.48 | (277) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_46_0) = v0 &
% 119.81/22.48 | domain(all_24_0) = v2 & domain(zero) = v1 & addition(v1, v2) = v0 &
% 119.81/22.48 | $i(v2) & $i(v1) & $i(v0))
% 119.81/22.48 |
% 119.81/22.48 | GROUND_INST: instantiating (18) with zero, all_36_0, all_36_0, simplifying
% 119.81/22.48 | with (16), (64), (268) gives:
% 119.81/22.48 | (278) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_36_0) = v2 &
% 119.81/22.48 | domain(all_36_0) = v0 & domain(zero) = v1 & addition(v1, v2) = v0 &
% 119.81/22.48 | $i(v2) & $i(v1) & $i(v0))
% 119.81/22.48 |
% 119.81/22.48 | GROUND_INST: instantiating (18) with zero, all_38_0, all_38_0, simplifying
% 119.81/22.48 | with (16), (69), (267) gives:
% 119.81/22.48 | (279) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_38_0) = v2 &
% 119.81/22.48 | domain(all_38_0) = v0 & domain(zero) = v1 & addition(v1, v2) = v0 &
% 119.81/22.48 | $i(v2) & $i(v1) & $i(v0))
% 119.81/22.48 |
% 119.81/22.48 | GROUND_INST: instantiating (18) with zero, all_68_2, all_68_2, simplifying
% 119.81/22.48 | with (16), (260), (272) gives:
% 119.81/22.48 | (280) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_68_2) = v2 &
% 119.81/22.48 | domain(all_68_2) = v0 & domain(zero) = v1 & addition(v1, v2) = v0 &
% 119.81/22.48 | $i(v2) & $i(v1) & $i(v0))
% 119.81/22.48 |
% 119.81/22.48 | GROUND_INST: instantiating (18) with one, zero, one, simplifying with (16),
% 119.81/22.48 | (19), (57) gives:
% 119.81/22.48 | (281) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(one) = v1 &
% 119.81/22.48 | domain(one) = v0 & domain(zero) = v2 & addition(v1, v2) = v0 &
% 119.81/22.48 | $i(v2) & $i(v1) & $i(v0))
% 119.81/22.48 |
% 119.81/22.48 | GROUND_INST: instantiating (3) with all_24_0, all_24_0, one, one, one,
% 119.81/22.48 | simplifying with (19), (29), (80) gives:
% 120.15/22.48 | (282) ? [v0: $i] : (addition(all_24_0, all_24_0) = v0 & addition(one, v0)
% 120.15/22.48 | = one & $i(v0))
% 120.15/22.48 |
% 120.15/22.48 | GROUND_INST: instantiating (3) with zero, all_24_0, one, one, one, simplifying
% 120.15/22.48 | with (16), (19), (29), (57), (80) gives:
% 120.15/22.48 | (283) ? [v0: $i] : (addition(all_24_0, zero) = v0 & addition(one, v0) =
% 120.15/22.48 | one & $i(v0))
% 120.15/22.48 |
% 120.15/22.48 | GROUND_INST: instantiating (18) with one, all_24_0, one, simplifying with
% 120.15/22.48 | (19), (29), (80) gives:
% 120.15/22.48 | (284) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_24_0) = v2 &
% 120.15/22.48 | domain(one) = v1 & domain(one) = v0 & addition(v1, v2) = v0 &
% 120.15/22.48 | $i(v2) & $i(v1) & $i(v0))
% 120.15/22.48 |
% 120.15/22.48 | GROUND_INST: instantiating (additive_idempotence) with all_24_1, all_52_0,
% 120.15/22.48 | simplifying with (28), (101) gives:
% 120.15/22.48 | (285) all_52_0 = all_24_1
% 120.15/22.48 |
% 120.15/22.48 | GROUND_INST: instantiating (18) with all_24_1, all_24_1, all_52_0, simplifying
% 120.15/22.48 | with (28), (101) gives:
% 120.15/22.48 | (286) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_52_0) = v0 &
% 120.15/22.48 | domain(all_24_1) = v2 & domain(all_24_1) = v1 & addition(v1, v2) =
% 120.15/22.48 | v0 & $i(v2) & $i(v1) & $i(v0))
% 120.15/22.48 |
% 120.15/22.48 | GROUND_INST: instantiating (2) with zero, zero, all_24_0, zero, all_48_0,
% 120.15/22.48 | simplifying with (16), (29), (94), (191) gives:
% 120.15/22.48 | (287) ? [v0: $i] : (addition(v0, zero) = all_48_0 & addition(all_24_0,
% 120.15/22.48 | zero) = v0 & $i(v0) & $i(all_48_0))
% 120.15/22.48 |
% 120.15/22.48 | GROUND_INST: instantiating (4) with all_24_0, all_48_0, simplifying with (29),
% 120.15/22.48 | (94) gives:
% 120.15/22.48 | (288) all_48_0 = all_24_0
% 120.15/22.48 |
% 120.15/22.48 | GROUND_INST: instantiating (1) with zero, all_24_0, all_48_0, simplifying with
% 120.15/22.48 | (16), (29), (94) gives:
% 120.15/22.48 | (289) addition(zero, all_24_0) = all_48_0 & $i(all_48_0)
% 120.15/22.48 |
% 120.15/22.48 | ALPHA: (289) implies:
% 120.15/22.48 | (290) $i(all_48_0)
% 120.15/22.48 |
% 120.15/22.48 | GROUND_INST: instantiating (18) with all_24_0, zero, all_48_0, simplifying
% 120.15/22.48 | with (16), (29), (94) gives:
% 120.15/22.48 | (291) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_48_0) = v0 &
% 120.15/22.48 | domain(all_24_0) = v1 & domain(zero) = v2 & addition(v1, v2) = v0 &
% 120.15/22.48 | $i(v2) & $i(v1) & $i(v0))
% 120.15/22.48 |
% 120.15/22.48 | GROUND_INST: instantiating (additive_idempotence) with all_24_0, all_56_0,
% 120.15/22.48 | simplifying with (29), (107) gives:
% 120.15/22.48 | (292) all_56_0 = all_24_0
% 120.15/22.48 |
% 120.15/22.48 | GROUND_INST: instantiating (18) with all_24_0, all_24_0, all_56_0, simplifying
% 120.15/22.48 | with (29), (107) gives:
% 120.15/22.48 | (293) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_56_0) = v0 &
% 120.15/22.48 | domain(all_24_0) = v2 & domain(all_24_0) = v1 & addition(v1, v2) =
% 120.15/22.48 | v0 & $i(v2) & $i(v1) & $i(v0))
% 120.15/22.48 |
% 120.15/22.48 | GROUND_INST: instantiating (2) with all_36_0, all_24_0, all_24_0, all_36_0,
% 120.15/22.48 | all_36_0, simplifying with (29), (64), (266) gives:
% 120.15/22.48 | (294) ? [v0: $i] : (addition(v0, all_36_0) = all_36_0 & addition(all_24_0,
% 120.15/22.48 | all_24_0) = v0 & $i(v0))
% 120.15/22.48 |
% 120.15/22.48 | GROUND_INST: instantiating (2) with all_36_0, zero, all_24_0, all_36_0,
% 120.15/22.48 | all_36_0, simplifying with (16), (29), (64), (266), (268) gives:
% 120.15/22.48 | (295) ? [v0: $i] : (addition(v0, all_36_0) = all_36_0 & addition(all_24_0,
% 120.15/22.48 | zero) = v0 & $i(v0))
% 120.15/22.48 |
% 120.15/22.49 | GROUND_INST: instantiating (18) with all_24_0, all_36_0, all_36_0, simplifying
% 120.15/22.49 | with (29), (64), (266) gives:
% 120.15/22.49 | (296) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_36_0) = v2 &
% 120.15/22.49 | domain(all_36_0) = v0 & domain(all_24_0) = v1 & addition(v1, v2) =
% 120.15/22.49 | v0 & $i(v2) & $i(v1) & $i(v0))
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (2) with all_38_0, all_24_0, all_24_0, all_38_0,
% 120.15/22.49 | all_38_0, simplifying with (29), (69), (265) gives:
% 120.15/22.49 | (297) ? [v0: $i] : (addition(v0, all_38_0) = all_38_0 & addition(all_24_0,
% 120.15/22.49 | all_24_0) = v0 & $i(v0))
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (2) with all_38_0, zero, all_24_0, all_38_0,
% 120.15/22.49 | all_38_0, simplifying with (16), (29), (69), (265), (267) gives:
% 120.15/22.49 | (298) ? [v0: $i] : (addition(v0, all_38_0) = all_38_0 & addition(all_24_0,
% 120.15/22.49 | zero) = v0 & $i(v0))
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (18) with all_24_0, all_38_0, all_38_0, simplifying
% 120.15/22.49 | with (29), (69), (265) gives:
% 120.15/22.49 | (299) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_38_0) = v2 &
% 120.15/22.49 | domain(all_38_0) = v0 & domain(all_24_0) = v1 & addition(v1, v2) =
% 120.15/22.49 | v0 & $i(v2) & $i(v1) & $i(v0))
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (2) with all_72_2, all_24_0, all_24_0, all_72_2,
% 120.15/22.49 | all_72_2, simplifying with (29), (263), (271) gives:
% 120.15/22.49 | (300) ? [v0: $i] : (addition(v0, all_72_2) = all_72_2 & addition(all_24_0,
% 120.15/22.49 | all_24_0) = v0 & $i(v0))
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (18) with all_24_0, all_72_2, all_72_2, simplifying
% 120.15/22.49 | with (29), (263), (271) gives:
% 120.15/22.49 | (301) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_72_2) = v2 &
% 120.15/22.49 | domain(all_72_2) = v0 & domain(all_24_0) = v1 & addition(v1, v2) =
% 120.15/22.49 | v0 & $i(v2) & $i(v1) & $i(v0))
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (18) with all_34_0, all_24_1, all_34_0, simplifying
% 120.15/22.49 | with (28), (43), (73) gives:
% 120.15/22.49 | (302) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_34_0) = v1 &
% 120.15/22.49 | domain(all_34_0) = v0 & domain(all_24_1) = v2 & addition(v1, v2) =
% 120.15/22.49 | v0 & $i(v2) & $i(v1) & $i(v0))
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (18) with all_36_1, one, all_36_0, simplifying with
% 120.15/22.49 | (19), (47), (65) gives:
% 120.15/22.49 | (303) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_36_0) = v0 &
% 120.15/22.49 | domain(all_36_1) = v1 & domain(one) = v2 & addition(v1, v2) = v0 &
% 120.15/22.49 | $i(v2) & $i(v1) & $i(v0))
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (18) with all_36_0, all_24_1, all_24_1, simplifying
% 120.15/22.49 | with (28), (64), (88) gives:
% 120.15/22.49 | (304) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_36_0) = v1 &
% 120.15/22.49 | domain(all_24_1) = v2 & domain(all_24_1) = v0 & addition(v1, v2) =
% 120.15/22.49 | v0 & $i(v2) & $i(v1) & $i(v0))
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (18) with all_38_1, one, all_38_0, simplifying with
% 120.15/22.49 | (19), (52), (70) gives:
% 120.15/22.49 | (305) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_38_0) = v0 &
% 120.15/22.49 | domain(all_38_1) = v1 & domain(one) = v2 & addition(v1, v2) = v0 &
% 120.15/22.49 | $i(v2) & $i(v1) & $i(v0))
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (18) with all_38_0, all_24_1, all_24_1, simplifying
% 120.15/22.49 | with (28), (69), (89) gives:
% 120.15/22.49 | (306) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_38_0) = v1 &
% 120.15/22.49 | domain(all_24_1) = v2 & domain(all_24_1) = v0 & addition(v1, v2) =
% 120.15/22.49 | v0 & $i(v2) & $i(v1) & $i(v0))
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (2) with one, all_24_0, all_46_0, one, one,
% 120.15/22.49 | simplifying with (19), (29), (36), (92), (275) gives:
% 120.15/22.49 | (307) ? [v0: $i] : (addition(v0, one) = one & addition(all_46_0, all_24_0)
% 120.15/22.49 | = v0 & $i(v0))
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (2) with one, all_46_0, all_46_0, one, one,
% 120.15/22.49 | simplifying with (19), (92), (275) gives:
% 120.15/22.49 | (308) ? [v0: $i] : (addition(v0, one) = one & addition(all_46_0, all_46_0)
% 120.15/22.49 | = v0 & $i(v0))
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (1) with one, all_46_0, one, simplifying with (19),
% 120.15/22.49 | (92), (275) gives:
% 120.15/22.49 | (309) addition(one, all_46_0) = one
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (18) with all_46_0, one, one, simplifying with
% 120.15/22.49 | (19), (92), (275) gives:
% 120.15/22.49 | (310) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_46_0) = v1 &
% 120.15/22.49 | domain(one) = v2 & domain(one) = v0 & addition(v1, v2) = v0 &
% 120.15/22.49 | $i(v2) & $i(v1) & $i(v0))
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (2) with one, all_24_0, all_48_0, one, one,
% 120.15/22.49 | simplifying with (19), (29), (36), (95), (290) gives:
% 120.15/22.49 | (311) ? [v0: $i] : (addition(v0, one) = one & addition(all_48_0, all_24_0)
% 120.15/22.49 | = v0 & $i(v0))
% 120.15/22.49 |
% 120.15/22.49 | GROUND_INST: instantiating (2) with one, all_48_0, all_24_0, one, one,
% 120.15/22.49 | simplifying with (19), (29), (36), (95), (290) gives:
% 120.15/22.49 | (312) ? [v0: $i] : (addition(v0, one) = one & addition(all_24_0, all_48_0)
% 120.15/22.49 | = v0 & $i(v0))
% 120.15/22.49 |
% 120.15/22.50 | GROUND_INST: instantiating (2) with one, zero, all_48_0, one, one, simplifying
% 120.15/22.50 | with (16), (19), (34), (95), (290) gives:
% 120.15/22.50 | (313) ? [v0: $i] : (addition(v0, one) = one & addition(all_48_0, zero) =
% 120.15/22.50 | v0 & $i(v0))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (2) with one, all_48_0, all_48_0, one, one,
% 120.15/22.50 | simplifying with (19), (95), (290) gives:
% 120.15/22.50 | (314) ? [v0: $i] : (addition(v0, one) = one & addition(all_48_0, all_48_0)
% 120.15/22.50 | = v0 & $i(v0))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (2) with one, all_46_0, all_48_0, one, one,
% 120.15/22.50 | simplifying with (19), (92), (95), (275), (290) gives:
% 120.15/22.50 | (315) ? [v0: $i] : (addition(v0, one) = one & addition(all_48_0, all_46_0)
% 120.15/22.50 | = v0 & $i(v0))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (2) with one, all_48_0, all_46_0, one, one,
% 120.15/22.50 | simplifying with (19), (92), (95), (275), (290) gives:
% 120.15/22.50 | (316) ? [v0: $i] : (addition(v0, one) = one & addition(all_46_0, all_48_0)
% 120.15/22.50 | = v0 & $i(v0))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (18) with all_48_0, one, one, simplifying with
% 120.15/22.50 | (19), (95), (290) gives:
% 120.15/22.50 | (317) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_48_0) = v1 &
% 120.15/22.50 | domain(one) = v2 & domain(one) = v0 & addition(v1, v2) = v0 &
% 120.15/22.50 | $i(v2) & $i(v1) & $i(v0))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (18) with all_52_0, all_34_0, all_34_0, simplifying
% 120.15/22.50 | with (43), (100), (102) gives:
% 120.15/22.50 | (318) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_52_0) = v1 &
% 120.15/22.50 | domain(all_34_0) = v2 & domain(all_34_0) = v0 & addition(v1, v2) =
% 120.15/22.50 | v0 & $i(v2) & $i(v1) & $i(v0))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (2) with one, all_24_0, all_56_0, one, one,
% 120.15/22.50 | simplifying with (19), (29), (36), (106), (108) gives:
% 120.15/22.50 | (319) ? [v0: $i] : (addition(v0, one) = one & addition(all_56_0, all_24_0)
% 120.15/22.50 | = v0 & $i(v0))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (2) with one, all_56_0, all_24_0, one, one,
% 120.15/22.50 | simplifying with (19), (29), (36), (106), (108) gives:
% 120.15/22.50 | (320) ? [v0: $i] : (addition(v0, one) = one & addition(all_24_0, all_56_0)
% 120.15/22.50 | = v0 & $i(v0))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (2) with one, zero, all_56_0, one, one, simplifying
% 120.15/22.50 | with (16), (19), (34), (106), (108) gives:
% 120.15/22.50 | (321) ? [v0: $i] : (addition(v0, one) = one & addition(all_56_0, zero) =
% 120.15/22.50 | v0 & $i(v0))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (2) with one, all_56_0, all_56_0, one, one,
% 120.15/22.50 | simplifying with (19), (106), (108) gives:
% 120.15/22.50 | (322) ? [v0: $i] : (addition(v0, one) = one & addition(all_56_0, all_56_0)
% 120.15/22.50 | = v0 & $i(v0))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (2) with one, all_48_0, all_56_0, one, one,
% 120.15/22.50 | simplifying with (19), (95), (106), (108), (290) gives:
% 120.15/22.50 | (323) ? [v0: $i] : (addition(v0, one) = one & addition(all_56_0, all_48_0)
% 120.15/22.50 | = v0 & $i(v0))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (2) with one, all_56_0, all_48_0, one, one,
% 120.15/22.50 | simplifying with (19), (95), (106), (108), (290) gives:
% 120.15/22.50 | (324) ? [v0: $i] : (addition(v0, one) = one & addition(all_48_0, all_56_0)
% 120.15/22.50 | = v0 & $i(v0))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (2) with one, all_56_0, all_46_0, one, one,
% 120.15/22.50 | simplifying with (19), (92), (106), (108), (275) gives:
% 120.15/22.50 | (325) ? [v0: $i] : (addition(v0, one) = one & addition(all_46_0, all_56_0)
% 120.15/22.50 | = v0 & $i(v0))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (18) with all_56_0, one, one, simplifying with
% 120.15/22.50 | (19), (106), (108) gives:
% 120.15/22.50 | (326) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(all_56_0) = v1 &
% 120.15/22.50 | domain(one) = v2 & domain(one) = v0 & addition(v1, v2) = v0 &
% 120.15/22.50 | $i(v2) & $i(v1) & $i(v0))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (3) with all_70_2, all_68_2, zero, all_68_2,
% 120.15/22.50 | all_76_2, simplifying with (16), (260), (261), (270), (272)
% 120.15/22.50 | gives:
% 120.15/22.50 | (327) ? [v0: $i] : (addition(all_68_2, all_70_2) = v0 & addition(zero, v0)
% 120.15/22.50 | = all_76_2 & $i(v0) & $i(all_76_2))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (3) with all_74_0, all_68_2, zero, all_68_2,
% 120.15/22.50 | all_74_2, simplifying with (16), (260), (262), (269), (272)
% 120.15/22.50 | gives:
% 120.15/22.50 | (328) ? [v0: $i] : (addition(all_68_2, all_74_0) = v0 & addition(zero, v0)
% 120.15/22.50 | = all_74_2 & $i(v0) & $i(all_74_2))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (3) with all_74_0, all_68_2, all_68_1, all_68_2,
% 120.15/22.50 | all_74_2, simplifying with (127), (262), (264), (269), (272)
% 120.15/22.50 | gives:
% 120.15/22.50 | (329) ? [v0: $i] : (addition(all_68_1, v0) = all_74_2 & addition(all_68_2,
% 120.15/22.50 | all_74_0) = v0 & $i(v0) & $i(all_74_2))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (3) with all_70_2, all_68_2, all_68_1, all_68_2,
% 120.15/22.50 | all_76_2, simplifying with (127), (261), (264), (270), (272)
% 120.15/22.50 | gives:
% 120.15/22.50 | (330) ? [v0: $i] : (addition(all_68_1, v0) = all_76_2 & addition(all_68_2,
% 120.15/22.50 | all_70_2) = v0 & $i(v0) & $i(all_76_2))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (2) with all_68_2, all_68_1, zero, all_68_2,
% 120.15/22.50 | all_68_2, simplifying with (16), (127), (260), (264), (272)
% 120.15/22.50 | gives:
% 120.15/22.50 | (331) ? [v0: $i] : (addition(v0, all_68_2) = all_68_2 & addition(zero,
% 120.15/22.50 | all_68_1) = v0 & $i(v0))
% 120.15/22.50 |
% 120.15/22.50 | GROUND_INST: instantiating (12) with zero, zero, zero, zero, zero, simplifying
% 120.15/22.50 | with (16), (190), (191) gives:
% 120.15/22.51 | (332) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ((v3 = 0 &
% 120.15/22.51 | star(zero) = v1 & leq(v2, zero) = 0 & multiplication(v1, zero) =
% 120.15/22.51 | v2 & $i(v2) & $i(v1)) | ( ~ (v0 = 0) & leq(zero, zero) = v0))
% 120.15/22.51 |
% 120.15/22.51 | GROUND_INST: instantiating (13) with all_24_2, all_24_0, all_70_0, simplifying
% 120.15/22.51 | with (27), (29), (258) gives:
% 120.15/22.51 | (333) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(v2) = v0 &
% 120.15/22.51 | domain(all_70_0) = v0 & domain(all_24_0) = v1 &
% 120.15/22.51 | multiplication(all_24_2, v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 120.15/22.51 |
% 120.15/22.51 | GROUND_INST: instantiating (13) with all_24_0, all_24_0, all_80_0, simplifying
% 120.15/22.51 | with (29), (257) gives:
% 120.15/22.51 | (334) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (domain(v2) = v0 &
% 120.15/22.51 | domain(all_80_0) = v0 & domain(all_24_0) = v1 &
% 120.15/22.51 | multiplication(all_24_0, v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 120.15/22.51 |
% 120.15/22.51 | GROUND_INST: instantiating (15) with one, all_68_2, simplifying with (19),
% 120.15/22.51 | (130) gives:
% 120.15/22.51 | (335) addition(all_68_2, one) = one
% 120.15/22.51 |
% 120.15/22.51 | GROUND_INST: instantiating (domain1) with one, all_68_2, simplifying with
% 120.15/22.51 | (19), (130) gives:
% 120.15/22.51 | (336) ? [v0: $i] : (multiplication(all_68_2, one) = v0 & addition(one, v0)
% 120.15/22.51 | = v0 & $i(v0))
% 120.15/22.51 |
% 120.15/22.51 | GROUND_INST: instantiating (15) with all_24_2, all_82_1, simplifying with
% 120.15/22.51 | (27), (173) gives:
% 120.15/22.51 | (337) addition(all_82_1, one) = one
% 120.15/22.51 |
% 120.15/22.51 | GROUND_INST: instantiating (15) with all_24_0, all_68_1, simplifying with
% 120.15/22.51 | (29), (132) gives:
% 120.15/22.51 | (338) addition(all_68_1, one) = one
% 120.15/22.51 |
% 120.15/22.51 | GROUND_INST: instantiating (15) with all_36_0, all_76_2, simplifying with
% 120.15/22.51 | (64), (156) gives:
% 120.15/22.51 | (339) addition(all_76_2, one) = one
% 120.15/22.51 |
% 120.15/22.51 | GROUND_INST: instantiating (15) with all_38_0, all_74_2, simplifying with
% 120.15/22.51 | (69), (150) gives:
% 120.15/22.51 | (340) addition(all_74_2, one) = one
% 120.15/22.51 |
% 120.15/22.51 | GROUND_INST: instantiating (15) with all_70_0, all_70_2, simplifying with
% 120.15/22.51 | (135), (139) gives:
% 120.15/22.51 | (341) addition(all_70_2, one) = one
% 120.15/22.51 |
% 120.15/22.51 | GROUND_INST: instantiating (15) with all_80_0, all_72_2, simplifying with
% 120.15/22.51 | (164), (255) gives:
% 120.15/22.51 | (342) addition(all_72_2, one) = one
% 120.15/22.51 |
% 120.15/22.51 | GROUND_INST: instantiating (15) with all_82_0, all_74_0, simplifying with
% 120.15/22.51 | (172), (254) gives:
% 120.15/22.51 | (343) addition(all_74_0, one) = one
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (319) with fresh symbol all_102_0 gives:
% 120.15/22.51 | (344) addition(all_102_0, one) = one & addition(all_56_0, all_24_0) =
% 120.15/22.51 | all_102_0 & $i(all_102_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (344) implies:
% 120.15/22.51 | (345) addition(all_56_0, all_24_0) = all_102_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (331) with fresh symbol all_106_0 gives:
% 120.15/22.51 | (346) addition(all_106_0, all_68_2) = all_68_2 & addition(zero, all_68_1) =
% 120.15/22.51 | all_106_0 & $i(all_106_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (346) implies:
% 120.15/22.51 | (347) $i(all_106_0)
% 120.15/22.51 | (348) addition(zero, all_68_1) = all_106_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (313) with fresh symbol all_110_0 gives:
% 120.15/22.51 | (349) addition(all_110_0, one) = one & addition(all_48_0, zero) = all_110_0
% 120.15/22.51 | & $i(all_110_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (349) implies:
% 120.15/22.51 | (350) addition(all_48_0, zero) = all_110_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (312) with fresh symbol all_112_0 gives:
% 120.15/22.51 | (351) addition(all_112_0, one) = one & addition(all_24_0, all_48_0) =
% 120.15/22.51 | all_112_0 & $i(all_112_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (351) implies:
% 120.15/22.51 | (352) addition(all_24_0, all_48_0) = all_112_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (300) with fresh symbol all_114_0 gives:
% 120.15/22.51 | (353) addition(all_114_0, all_72_2) = all_72_2 & addition(all_24_0,
% 120.15/22.51 | all_24_0) = all_114_0 & $i(all_114_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (353) implies:
% 120.15/22.51 | (354) addition(all_24_0, all_24_0) = all_114_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (311) with fresh symbol all_116_0 gives:
% 120.15/22.51 | (355) addition(all_116_0, one) = one & addition(all_48_0, all_24_0) =
% 120.15/22.51 | all_116_0 & $i(all_116_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (355) implies:
% 120.15/22.51 | (356) addition(all_48_0, all_24_0) = all_116_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (283) with fresh symbol all_118_0 gives:
% 120.15/22.51 | (357) addition(all_24_0, zero) = all_118_0 & addition(one, all_118_0) = one
% 120.15/22.51 | & $i(all_118_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (357) implies:
% 120.15/22.51 | (358) addition(all_24_0, zero) = all_118_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (316) with fresh symbol all_144_0 gives:
% 120.15/22.51 | (359) addition(all_144_0, one) = one & addition(all_46_0, all_48_0) =
% 120.15/22.51 | all_144_0 & $i(all_144_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (359) implies:
% 120.15/22.51 | (360) addition(all_46_0, all_48_0) = all_144_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (315) with fresh symbol all_146_0 gives:
% 120.15/22.51 | (361) addition(all_146_0, one) = one & addition(all_48_0, all_46_0) =
% 120.15/22.51 | all_146_0 & $i(all_146_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (361) implies:
% 120.15/22.51 | (362) addition(all_48_0, all_46_0) = all_146_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (314) with fresh symbol all_148_0 gives:
% 120.15/22.51 | (363) addition(all_148_0, one) = one & addition(all_48_0, all_48_0) =
% 120.15/22.51 | all_148_0 & $i(all_148_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (363) implies:
% 120.15/22.51 | (364) addition(all_48_0, all_48_0) = all_148_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (295) with fresh symbol all_150_0 gives:
% 120.15/22.51 | (365) addition(all_150_0, all_36_0) = all_36_0 & addition(all_24_0, zero) =
% 120.15/22.51 | all_150_0 & $i(all_150_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (365) implies:
% 120.15/22.51 | (366) addition(all_24_0, zero) = all_150_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (324) with fresh symbol all_156_0 gives:
% 120.15/22.51 | (367) addition(all_156_0, one) = one & addition(all_48_0, all_56_0) =
% 120.15/22.51 | all_156_0 & $i(all_156_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (367) implies:
% 120.15/22.51 | (368) addition(all_48_0, all_56_0) = all_156_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (323) with fresh symbol all_158_0 gives:
% 120.15/22.51 | (369) addition(all_158_0, one) = one & addition(all_56_0, all_48_0) =
% 120.15/22.51 | all_158_0 & $i(all_158_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (369) implies:
% 120.15/22.51 | (370) addition(all_56_0, all_48_0) = all_158_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (321) with fresh symbol all_160_0 gives:
% 120.15/22.51 | (371) addition(all_160_0, one) = one & addition(all_56_0, zero) = all_160_0
% 120.15/22.51 | & $i(all_160_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (371) implies:
% 120.15/22.51 | (372) addition(all_56_0, zero) = all_160_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (322) with fresh symbol all_162_0 gives:
% 120.15/22.51 | (373) addition(all_162_0, one) = one & addition(all_56_0, all_56_0) =
% 120.15/22.51 | all_162_0 & $i(all_162_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (373) implies:
% 120.15/22.51 | (374) addition(all_56_0, all_56_0) = all_162_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (320) with fresh symbol all_166_0 gives:
% 120.15/22.51 | (375) addition(all_166_0, one) = one & addition(all_24_0, all_56_0) =
% 120.15/22.51 | all_166_0 & $i(all_166_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (375) implies:
% 120.15/22.51 | (376) addition(all_24_0, all_56_0) = all_166_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (336) with fresh symbol all_168_0 gives:
% 120.15/22.51 | (377) multiplication(all_68_2, one) = all_168_0 & addition(one, all_168_0)
% 120.15/22.51 | = all_168_0 & $i(all_168_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (377) implies:
% 120.15/22.51 | (378) $i(all_168_0)
% 120.15/22.51 | (379) addition(one, all_168_0) = all_168_0
% 120.15/22.51 | (380) multiplication(all_68_2, one) = all_168_0
% 120.15/22.51 |
% 120.15/22.51 | DELTA: instantiating (294) with fresh symbol all_172_0 gives:
% 120.15/22.51 | (381) addition(all_172_0, all_36_0) = all_36_0 & addition(all_24_0,
% 120.15/22.51 | all_24_0) = all_172_0 & $i(all_172_0)
% 120.15/22.51 |
% 120.15/22.51 | ALPHA: (381) implies:
% 120.15/22.52 | (382) addition(all_24_0, all_24_0) = all_172_0
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (325) with fresh symbol all_176_0 gives:
% 120.15/22.52 | (383) addition(all_176_0, one) = one & addition(all_46_0, all_56_0) =
% 120.15/22.52 | all_176_0 & $i(all_176_0)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (383) implies:
% 120.15/22.52 | (384) $i(all_176_0)
% 120.15/22.52 | (385) addition(all_46_0, all_56_0) = all_176_0
% 120.15/22.52 | (386) addition(all_176_0, one) = one
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (282) with fresh symbol all_186_0 gives:
% 120.15/22.52 | (387) addition(all_24_0, all_24_0) = all_186_0 & addition(one, all_186_0) =
% 120.15/22.52 | one & $i(all_186_0)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (387) implies:
% 120.15/22.52 | (388) addition(all_24_0, all_24_0) = all_186_0
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (298) with fresh symbol all_202_0 gives:
% 120.15/22.52 | (389) addition(all_202_0, all_38_0) = all_38_0 & addition(all_24_0, zero) =
% 120.15/22.52 | all_202_0 & $i(all_202_0)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (389) implies:
% 120.15/22.52 | (390) addition(all_24_0, zero) = all_202_0
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (297) with fresh symbol all_204_0 gives:
% 120.15/22.52 | (391) addition(all_204_0, all_38_0) = all_38_0 & addition(all_24_0,
% 120.15/22.52 | all_24_0) = all_204_0 & $i(all_204_0)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (391) implies:
% 120.15/22.52 | (392) addition(all_24_0, all_24_0) = all_204_0
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (308) with fresh symbol all_208_0 gives:
% 120.15/22.52 | (393) addition(all_208_0, one) = one & addition(all_46_0, all_46_0) =
% 120.15/22.52 | all_208_0 & $i(all_208_0)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (393) implies:
% 120.15/22.52 | (394) addition(all_46_0, all_46_0) = all_208_0
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (307) with fresh symbol all_214_0 gives:
% 120.15/22.52 | (395) addition(all_214_0, one) = one & addition(all_46_0, all_24_0) =
% 120.15/22.52 | all_214_0 & $i(all_214_0)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (395) implies:
% 120.15/22.52 | (396) addition(all_46_0, all_24_0) = all_214_0
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (287) with fresh symbol all_236_0 gives:
% 120.15/22.52 | (397) addition(all_236_0, zero) = all_48_0 & addition(all_24_0, zero) =
% 120.15/22.52 | all_236_0 & $i(all_236_0) & $i(all_48_0)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (397) implies:
% 120.15/22.52 | (398) addition(all_24_0, zero) = all_236_0
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (328) with fresh symbol all_250_0 gives:
% 120.15/22.52 | (399) addition(all_68_2, all_74_0) = all_250_0 & addition(zero, all_250_0)
% 120.15/22.52 | = all_74_2 & $i(all_250_0) & $i(all_74_2)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (399) implies:
% 120.15/22.52 | (400) $i(all_250_0)
% 120.15/22.52 | (401) addition(all_68_2, all_74_0) = all_250_0
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (327) with fresh symbol all_254_0 gives:
% 120.15/22.52 | (402) addition(all_68_2, all_70_2) = all_254_0 & addition(zero, all_254_0)
% 120.15/22.52 | = all_76_2 & $i(all_254_0) & $i(all_76_2)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (402) implies:
% 120.15/22.52 | (403) $i(all_254_0)
% 120.15/22.52 | (404) addition(all_68_2, all_70_2) = all_254_0
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (330) with fresh symbol all_270_0 gives:
% 120.15/22.52 | (405) addition(all_68_1, all_270_0) = all_76_2 & addition(all_68_2,
% 120.15/22.52 | all_70_2) = all_270_0 & $i(all_270_0) & $i(all_76_2)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (405) implies:
% 120.15/22.52 | (406) addition(all_68_2, all_70_2) = all_270_0
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (329) with fresh symbol all_302_0 gives:
% 120.15/22.52 | (407) addition(all_68_1, all_302_0) = all_74_2 & addition(all_68_2,
% 120.15/22.52 | all_74_0) = all_302_0 & $i(all_302_0) & $i(all_74_2)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (407) implies:
% 120.15/22.52 | (408) addition(all_68_2, all_74_0) = all_302_0
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (304) with fresh symbols all_338_0, all_338_1, all_338_2
% 120.15/22.52 | gives:
% 120.15/22.52 | (409) domain(all_36_0) = all_338_1 & domain(all_24_1) = all_338_0 &
% 120.15/22.52 | domain(all_24_1) = all_338_2 & addition(all_338_1, all_338_0) =
% 120.15/22.52 | all_338_2 & $i(all_338_0) & $i(all_338_1) & $i(all_338_2)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (409) implies:
% 120.15/22.52 | (410) domain(all_24_1) = all_338_2
% 120.15/22.52 | (411) domain(all_24_1) = all_338_0
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (301) with fresh symbols all_340_0, all_340_1, all_340_2
% 120.15/22.52 | gives:
% 120.15/22.52 | (412) domain(all_72_2) = all_340_0 & domain(all_72_2) = all_340_2 &
% 120.15/22.52 | domain(all_24_0) = all_340_1 & addition(all_340_1, all_340_0) =
% 120.15/22.52 | all_340_2 & $i(all_340_0) & $i(all_340_1) & $i(all_340_2)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (412) implies:
% 120.15/22.52 | (413) domain(all_24_0) = all_340_1
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (299) with fresh symbols all_342_0, all_342_1, all_342_2
% 120.15/22.52 | gives:
% 120.15/22.52 | (414) domain(all_38_0) = all_342_0 & domain(all_38_0) = all_342_2 &
% 120.15/22.52 | domain(all_24_0) = all_342_1 & addition(all_342_1, all_342_0) =
% 120.15/22.52 | all_342_2 & $i(all_342_0) & $i(all_342_1) & $i(all_342_2)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (414) implies:
% 120.15/22.52 | (415) domain(all_24_0) = all_342_1
% 120.15/22.52 | (416) domain(all_38_0) = all_342_2
% 120.15/22.52 | (417) domain(all_38_0) = all_342_0
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (326) with fresh symbols all_344_0, all_344_1, all_344_2
% 120.15/22.52 | gives:
% 120.15/22.52 | (418) domain(all_56_0) = all_344_1 & domain(one) = all_344_0 & domain(one)
% 120.15/22.52 | = all_344_2 & addition(all_344_1, all_344_0) = all_344_2 &
% 120.15/22.52 | $i(all_344_0) & $i(all_344_1) & $i(all_344_2)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (418) implies:
% 120.15/22.52 | (419) $i(all_344_2)
% 120.15/22.52 | (420) domain(one) = all_344_2
% 120.15/22.52 | (421) domain(one) = all_344_0
% 120.15/22.52 | (422) domain(all_56_0) = all_344_1
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (278) with fresh symbols all_346_0, all_346_1, all_346_2
% 120.15/22.52 | gives:
% 120.15/22.52 | (423) domain(all_36_0) = all_346_0 & domain(all_36_0) = all_346_2 &
% 120.15/22.52 | domain(zero) = all_346_1 & addition(all_346_1, all_346_0) = all_346_2
% 120.15/22.52 | & $i(all_346_0) & $i(all_346_1) & $i(all_346_2)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (423) implies:
% 120.15/22.52 | (424) $i(all_346_1)
% 120.15/22.52 | (425) domain(zero) = all_346_1
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (305) with fresh symbols all_348_0, all_348_1, all_348_2
% 120.15/22.52 | gives:
% 120.15/22.52 | (426) domain(all_38_0) = all_348_2 & domain(all_38_1) = all_348_1 &
% 120.15/22.52 | domain(one) = all_348_0 & addition(all_348_1, all_348_0) = all_348_2
% 120.15/22.52 | & $i(all_348_0) & $i(all_348_1) & $i(all_348_2)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (426) implies:
% 120.15/22.52 | (427) $i(all_348_1)
% 120.15/22.52 | (428) addition(all_348_1, all_348_0) = all_348_2
% 120.15/22.52 | (429) domain(one) = all_348_0
% 120.15/22.52 | (430) domain(all_38_1) = all_348_1
% 120.15/22.52 | (431) domain(all_38_0) = all_348_2
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (310) with fresh symbols all_350_0, all_350_1, all_350_2
% 120.15/22.52 | gives:
% 120.15/22.52 | (432) domain(all_46_0) = all_350_1 & domain(one) = all_350_0 & domain(one)
% 120.15/22.52 | = all_350_2 & addition(all_350_1, all_350_0) = all_350_2 &
% 120.15/22.52 | $i(all_350_0) & $i(all_350_1) & $i(all_350_2)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (432) implies:
% 120.15/22.52 | (433) domain(one) = all_350_2
% 120.15/22.52 | (434) domain(one) = all_350_0
% 120.15/22.52 | (435) domain(all_46_0) = all_350_1
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (279) with fresh symbols all_352_0, all_352_1, all_352_2
% 120.15/22.52 | gives:
% 120.15/22.52 | (436) domain(all_38_0) = all_352_0 & domain(all_38_0) = all_352_2 &
% 120.15/22.52 | domain(zero) = all_352_1 & addition(all_352_1, all_352_0) = all_352_2
% 120.15/22.52 | & $i(all_352_0) & $i(all_352_1) & $i(all_352_2)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (436) implies:
% 120.15/22.52 | (437) domain(zero) = all_352_1
% 120.15/22.52 | (438) domain(all_38_0) = all_352_2
% 120.15/22.52 | (439) domain(all_38_0) = all_352_0
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (317) with fresh symbols all_356_0, all_356_1, all_356_2
% 120.15/22.52 | gives:
% 120.15/22.52 | (440) domain(all_48_0) = all_356_1 & domain(one) = all_356_0 & domain(one)
% 120.15/22.52 | = all_356_2 & addition(all_356_1, all_356_0) = all_356_2 &
% 120.15/22.52 | $i(all_356_0) & $i(all_356_1) & $i(all_356_2)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (440) implies:
% 120.15/22.52 | (441) domain(one) = all_356_2
% 120.15/22.52 | (442) domain(one) = all_356_0
% 120.15/22.52 | (443) domain(all_48_0) = all_356_1
% 120.15/22.52 |
% 120.15/22.52 | DELTA: instantiating (333) with fresh symbols all_358_0, all_358_1, all_358_2
% 120.15/22.52 | gives:
% 120.15/22.52 | (444) domain(all_358_0) = all_358_2 & domain(all_70_0) = all_358_2 &
% 120.15/22.52 | domain(all_24_0) = all_358_1 & multiplication(all_24_2, all_358_1) =
% 120.15/22.52 | all_358_0 & $i(all_358_0) & $i(all_358_1) & $i(all_358_2)
% 120.15/22.52 |
% 120.15/22.52 | ALPHA: (444) implies:
% 120.15/22.52 | (445) $i(all_358_2)
% 120.15/22.53 | (446) domain(all_24_0) = all_358_1
% 120.15/22.53 | (447) domain(all_70_0) = all_358_2
% 120.15/22.53 |
% 120.15/22.53 | DELTA: instantiating (291) with fresh symbols all_360_0, all_360_1, all_360_2
% 120.15/22.53 | gives:
% 120.15/22.53 | (448) domain(all_48_0) = all_360_2 & domain(all_24_0) = all_360_1 &
% 120.15/22.53 | domain(zero) = all_360_0 & addition(all_360_1, all_360_0) = all_360_2
% 120.15/22.53 | & $i(all_360_0) & $i(all_360_1) & $i(all_360_2)
% 120.15/22.53 |
% 120.15/22.53 | ALPHA: (448) implies:
% 120.15/22.53 | (449) domain(zero) = all_360_0
% 120.15/22.53 | (450) domain(all_24_0) = all_360_1
% 120.15/22.53 | (451) domain(all_48_0) = all_360_2
% 120.15/22.53 |
% 120.15/22.53 | DELTA: instantiating (303) with fresh symbols all_362_0, all_362_1, all_362_2
% 120.15/22.53 | gives:
% 120.15/22.53 | (452) domain(all_36_0) = all_362_2 & domain(all_36_1) = all_362_1 &
% 120.15/22.53 | domain(one) = all_362_0 & addition(all_362_1, all_362_0) = all_362_2
% 120.15/22.53 | & $i(all_362_0) & $i(all_362_1) & $i(all_362_2)
% 120.15/22.53 |
% 120.15/22.53 | ALPHA: (452) implies:
% 120.15/22.53 | (453) domain(one) = all_362_0
% 120.15/22.53 |
% 120.15/22.53 | DELTA: instantiating (277) with fresh symbols all_364_0, all_364_1, all_364_2
% 120.15/22.53 | gives:
% 120.15/22.53 | (454) domain(all_46_0) = all_364_2 & domain(all_24_0) = all_364_0 &
% 120.15/22.53 | domain(zero) = all_364_1 & addition(all_364_1, all_364_0) = all_364_2
% 120.15/22.53 | & $i(all_364_0) & $i(all_364_1) & $i(all_364_2)
% 120.15/22.53 |
% 120.15/22.53 | ALPHA: (454) implies:
% 120.15/22.53 | (455) addition(all_364_1, all_364_0) = all_364_2
% 120.15/22.53 | (456) domain(zero) = all_364_1
% 120.15/22.53 | (457) domain(all_24_0) = all_364_0
% 120.15/22.53 | (458) domain(all_46_0) = all_364_2
% 120.15/22.53 |
% 120.15/22.53 | DELTA: instantiating (302) with fresh symbols all_366_0, all_366_1, all_366_2
% 120.15/22.53 | gives:
% 120.15/22.53 | (459) domain(all_34_0) = all_366_1 & domain(all_34_0) = all_366_2 &
% 120.15/22.53 | domain(all_24_1) = all_366_0 & addition(all_366_1, all_366_0) =
% 120.15/22.53 | all_366_2 & $i(all_366_0) & $i(all_366_1) & $i(all_366_2)
% 120.15/22.53 |
% 120.15/22.53 | ALPHA: (459) implies:
% 120.15/22.53 | (460) $i(all_366_2)
% 120.15/22.53 | (461) domain(all_24_1) = all_366_0
% 120.15/22.53 | (462) domain(all_34_0) = all_366_2
% 120.15/22.53 | (463) domain(all_34_0) = all_366_1
% 120.15/22.53 |
% 120.15/22.53 | DELTA: instantiating (281) with fresh symbols all_368_0, all_368_1, all_368_2
% 120.15/22.53 | gives:
% 120.15/22.53 | (464) domain(one) = all_368_1 & domain(one) = all_368_2 & domain(zero) =
% 120.15/22.53 | all_368_0 & addition(all_368_1, all_368_0) = all_368_2 &
% 120.15/22.53 | $i(all_368_0) & $i(all_368_1) & $i(all_368_2)
% 120.15/22.53 |
% 120.15/22.53 | ALPHA: (464) implies:
% 120.15/22.53 | (465) domain(zero) = all_368_0
% 120.15/22.53 | (466) domain(one) = all_368_2
% 120.15/22.53 | (467) domain(one) = all_368_1
% 120.15/22.53 |
% 120.15/22.53 | DELTA: instantiating (293) with fresh symbols all_370_0, all_370_1, all_370_2
% 120.15/22.53 | gives:
% 120.15/22.53 | (468) domain(all_56_0) = all_370_2 & domain(all_24_0) = all_370_0 &
% 120.15/22.53 | domain(all_24_0) = all_370_1 & addition(all_370_1, all_370_0) =
% 120.15/22.53 | all_370_2 & $i(all_370_0) & $i(all_370_1) & $i(all_370_2)
% 120.15/22.53 |
% 120.15/22.53 | ALPHA: (468) implies:
% 120.15/22.53 | (469) domain(all_24_0) = all_370_1
% 120.15/22.53 | (470) domain(all_24_0) = all_370_0
% 120.15/22.53 | (471) domain(all_56_0) = all_370_2
% 120.15/22.53 |
% 120.15/22.53 | DELTA: instantiating (334) with fresh symbols all_372_0, all_372_1, all_372_2
% 120.15/22.53 | gives:
% 120.15/22.53 | (472) domain(all_372_0) = all_372_2 & domain(all_80_0) = all_372_2 &
% 120.15/22.53 | domain(all_24_0) = all_372_1 & multiplication(all_24_0, all_372_1) =
% 120.15/22.53 | all_372_0 & $i(all_372_0) & $i(all_372_1) & $i(all_372_2)
% 120.15/22.53 |
% 120.15/22.53 | ALPHA: (472) implies:
% 120.15/22.53 | (473) domain(all_24_0) = all_372_1
% 120.15/22.53 |
% 120.15/22.53 | DELTA: instantiating (280) with fresh symbols all_376_0, all_376_1, all_376_2
% 120.15/22.53 | gives:
% 120.15/22.53 | (474) domain(all_68_2) = all_376_0 & domain(all_68_2) = all_376_2 &
% 120.15/22.53 | domain(zero) = all_376_1 & addition(all_376_1, all_376_0) = all_376_2
% 120.15/22.53 | & $i(all_376_0) & $i(all_376_1) & $i(all_376_2)
% 120.15/22.53 |
% 120.15/22.53 | ALPHA: (474) implies:
% 120.15/22.53 | (475) domain(zero) = all_376_1
% 120.15/22.53 |
% 120.15/22.53 | DELTA: instantiating (296) with fresh symbols all_378_0, all_378_1, all_378_2
% 120.15/22.53 | gives:
% 120.15/22.53 | (476) domain(all_36_0) = all_378_0 & domain(all_36_0) = all_378_2 &
% 120.15/22.53 | domain(all_24_0) = all_378_1 & addition(all_378_1, all_378_0) =
% 120.15/22.53 | all_378_2 & $i(all_378_0) & $i(all_378_1) & $i(all_378_2)
% 120.15/22.53 |
% 120.15/22.53 | ALPHA: (476) implies:
% 120.15/22.53 | (477) domain(all_24_0) = all_378_1
% 120.15/22.53 |
% 120.15/22.53 | DELTA: instantiating (284) with fresh symbols all_380_0, all_380_1, all_380_2
% 120.15/22.53 | gives:
% 120.15/22.53 | (478) domain(all_24_0) = all_380_0 & domain(one) = all_380_1 & domain(one)
% 120.15/22.53 | = all_380_2 & addition(all_380_1, all_380_0) = all_380_2 &
% 120.15/22.53 | $i(all_380_0) & $i(all_380_1) & $i(all_380_2)
% 120.15/22.53 |
% 120.15/22.53 | ALPHA: (478) implies:
% 120.15/22.53 | (479) domain(one) = all_380_2
% 120.15/22.53 | (480) domain(one) = all_380_1
% 120.15/22.53 | (481) domain(all_24_0) = all_380_0
% 120.15/22.53 |
% 120.15/22.53 | DELTA: instantiating (286) with fresh symbols all_382_0, all_382_1, all_382_2
% 120.15/22.53 | gives:
% 120.15/22.53 | (482) domain(all_52_0) = all_382_2 & domain(all_24_1) = all_382_0 &
% 120.15/22.53 | domain(all_24_1) = all_382_1 & addition(all_382_1, all_382_0) =
% 120.15/22.53 | all_382_2 & $i(all_382_0) & $i(all_382_1) & $i(all_382_2)
% 120.15/22.53 |
% 120.15/22.53 | ALPHA: (482) implies:
% 120.15/22.53 | (483) domain(all_24_1) = all_382_1
% 120.15/22.53 | (484) domain(all_24_1) = all_382_0
% 120.15/22.53 | (485) domain(all_52_0) = all_382_2
% 120.15/22.53 |
% 120.15/22.53 | DELTA: instantiating (306) with fresh symbols all_384_0, all_384_1, all_384_2
% 120.15/22.53 | gives:
% 120.15/22.53 | (486) domain(all_38_0) = all_384_1 & domain(all_24_1) = all_384_0 &
% 120.15/22.53 | domain(all_24_1) = all_384_2 & addition(all_384_1, all_384_0) =
% 120.15/22.53 | all_384_2 & $i(all_384_0) & $i(all_384_1) & $i(all_384_2)
% 120.15/22.53 |
% 120.15/22.53 | ALPHA: (486) implies:
% 120.15/22.53 | (487) addition(all_384_1, all_384_0) = all_384_2
% 120.15/22.53 | (488) domain(all_24_1) = all_384_2
% 120.15/22.53 | (489) domain(all_24_1) = all_384_0
% 120.15/22.53 | (490) domain(all_38_0) = all_384_1
% 120.15/22.53 |
% 120.15/22.53 | DELTA: instantiating (318) with fresh symbols all_388_0, all_388_1, all_388_2
% 120.15/22.53 | gives:
% 120.15/22.53 | (491) domain(all_52_0) = all_388_1 & domain(all_34_0) = all_388_0 &
% 120.15/22.53 | domain(all_34_0) = all_388_2 & addition(all_388_1, all_388_0) =
% 120.15/22.53 | all_388_2 & $i(all_388_0) & $i(all_388_1) & $i(all_388_2)
% 120.15/22.53 |
% 120.15/22.53 | ALPHA: (491) implies:
% 120.15/22.53 | (492) domain(all_34_0) = all_388_2
% 120.15/22.53 | (493) domain(all_34_0) = all_388_0
% 120.15/22.53 | (494) domain(all_52_0) = all_388_1
% 120.15/22.53 |
% 120.15/22.53 | DELTA: instantiating (332) with fresh symbols all_390_0, all_390_1, all_390_2,
% 120.15/22.53 | all_390_3 gives:
% 120.15/22.53 | (495) (all_390_0 = 0 & star(zero) = all_390_2 & leq(all_390_1, zero) = 0 &
% 120.15/22.53 | multiplication(all_390_2, zero) = all_390_1 & $i(all_390_1) &
% 120.15/22.53 | $i(all_390_2)) | ( ~ (all_390_3 = 0) & leq(zero, zero) = all_390_3)
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (292), (471) imply:
% 120.15/22.53 | (496) domain(all_24_0) = all_370_2
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (292), (422) imply:
% 120.15/22.53 | (497) domain(all_24_0) = all_344_1
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (285), (494) imply:
% 120.15/22.53 | (498) domain(all_24_1) = all_388_1
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (285), (485) imply:
% 120.15/22.53 | (499) domain(all_24_1) = all_382_2
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (288), (451) imply:
% 120.15/22.53 | (500) domain(all_24_0) = all_360_2
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (288), (443) imply:
% 120.15/22.53 | (501) domain(all_24_0) = all_356_1
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (292), (374) imply:
% 120.15/22.53 | (502) addition(all_24_0, all_24_0) = all_162_0
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (288), (292), (370) imply:
% 120.15/22.53 | (503) addition(all_24_0, all_24_0) = all_158_0
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (292), (345) imply:
% 120.15/22.53 | (504) addition(all_24_0, all_24_0) = all_102_0
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (292), (372) imply:
% 120.15/22.53 | (505) addition(all_24_0, zero) = all_160_0
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (288), (292), (368) imply:
% 120.15/22.53 | (506) addition(all_24_0, all_24_0) = all_156_0
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (288), (364) imply:
% 120.15/22.53 | (507) addition(all_24_0, all_24_0) = all_148_0
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (288), (362) imply:
% 120.15/22.53 | (508) addition(all_24_0, all_46_0) = all_146_0
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (288), (356) imply:
% 120.15/22.53 | (509) addition(all_24_0, all_24_0) = all_116_0
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (288), (350) imply:
% 120.15/22.53 | (510) addition(all_24_0, zero) = all_110_0
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (292), (385) imply:
% 120.15/22.53 | (511) addition(all_46_0, all_24_0) = all_176_0
% 120.15/22.53 |
% 120.15/22.53 | REDUCE: (288), (360) imply:
% 120.15/22.54 | (512) addition(all_46_0, all_24_0) = all_144_0
% 120.15/22.54 |
% 120.15/22.54 | REDUCE: (292), (376) imply:
% 120.15/22.54 | (513) addition(all_24_0, all_24_0) = all_166_0
% 120.15/22.54 |
% 120.15/22.54 | REDUCE: (288), (352) imply:
% 120.15/22.54 | (514) addition(all_24_0, all_24_0) = all_112_0
% 120.15/22.54 |
% 120.15/22.54 | REDUCE: (107), (292) imply:
% 120.15/22.54 | (515) addition(all_24_0, all_24_0) = all_24_0
% 120.15/22.54 |
% 120.15/22.54 | REDUCE: (94), (288) imply:
% 120.15/22.54 | (516) addition(all_24_0, zero) = all_24_0
% 120.15/22.54 |
% 120.15/22.54 | BETA: splitting (495) gives:
% 120.15/22.54 |
% 120.15/22.54 | Case 1:
% 120.15/22.54 | |
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_118_0, all_150_0, zero, all_24_0,
% 120.15/22.54 | | simplifying with (358), (366) gives:
% 120.15/22.54 | | (517) all_150_0 = all_118_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_118_0, all_160_0, zero, all_24_0,
% 120.15/22.54 | | simplifying with (358), (505) gives:
% 120.15/22.54 | | (518) all_160_0 = all_118_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_46_0, all_160_0, zero, all_24_0,
% 120.15/22.54 | | simplifying with (276), (505) gives:
% 120.15/22.54 | | (519) all_160_0 = all_46_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_160_0, all_202_0, zero, all_24_0,
% 120.15/22.54 | | simplifying with (390), (505) gives:
% 120.15/22.54 | | (520) all_202_0 = all_160_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_110_0, all_202_0, zero, all_24_0,
% 120.15/22.54 | | simplifying with (390), (510) gives:
% 120.15/22.54 | | (521) all_202_0 = all_110_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_150_0, all_236_0, zero, all_24_0,
% 120.15/22.54 | | simplifying with (366), (398) gives:
% 120.15/22.54 | | (522) all_236_0 = all_150_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_24_0, all_236_0, zero, all_24_0,
% 120.15/22.54 | | simplifying with (398), (516) gives:
% 120.15/22.54 | | (523) all_236_0 = all_24_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_116_0, all_156_0, all_24_0,
% 120.15/22.54 | | all_24_0, simplifying with (506), (509) gives:
% 120.15/22.54 | | (524) all_156_0 = all_116_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_112_0, all_156_0, all_24_0,
% 120.15/22.54 | | all_24_0, simplifying with (506), (514) gives:
% 120.15/22.54 | | (525) all_156_0 = all_112_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_156_0, all_158_0, all_24_0,
% 120.15/22.54 | | all_24_0, simplifying with (503), (506) gives:
% 120.15/22.54 | | (526) all_158_0 = all_156_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_158_0, all_162_0, all_24_0,
% 120.15/22.54 | | all_24_0, simplifying with (502), (503) gives:
% 120.15/22.54 | | (527) all_162_0 = all_158_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_172_0, all_186_0, all_24_0,
% 120.15/22.54 | | all_24_0, simplifying with (382), (388) gives:
% 120.15/22.54 | | (528) all_186_0 = all_172_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_162_0, all_186_0, all_24_0,
% 120.15/22.54 | | all_24_0, simplifying with (388), (502) gives:
% 120.15/22.54 | | (529) all_186_0 = all_162_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_148_0, all_186_0, all_24_0,
% 120.15/22.54 | | all_24_0, simplifying with (388), (507) gives:
% 120.15/22.54 | | (530) all_186_0 = all_148_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_166_0, all_204_0, all_24_0,
% 120.15/22.54 | | all_24_0, simplifying with (392), (513) gives:
% 120.15/22.54 | | (531) all_204_0 = all_166_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_156_0, all_204_0, all_24_0,
% 120.15/22.54 | | all_24_0, simplifying with (392), (506) gives:
% 120.15/22.54 | | (532) all_204_0 = all_156_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_114_0, all_204_0, all_24_0,
% 120.15/22.54 | | all_24_0, simplifying with (354), (392) gives:
% 120.15/22.54 | | (533) all_204_0 = all_114_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_102_0, all_204_0, all_24_0,
% 120.15/22.54 | | all_24_0, simplifying with (392), (504) gives:
% 120.15/22.54 | | (534) all_204_0 = all_102_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_24_0, all_204_0, all_24_0,
% 120.15/22.54 | | all_24_0, simplifying with (392), (515) gives:
% 120.15/22.54 | | (535) all_204_0 = all_24_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_176_0, all_214_0, all_24_0,
% 120.15/22.54 | | all_46_0, simplifying with (396), (511) gives:
% 120.15/22.54 | | (536) all_214_0 = all_176_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_144_0, all_214_0, all_24_0,
% 120.15/22.54 | | all_46_0, simplifying with (396), (512) gives:
% 120.15/22.54 | | (537) all_214_0 = all_144_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_76_2, all_270_0, all_70_2,
% 120.15/22.54 | | all_68_2, simplifying with (261), (406) gives:
% 120.15/22.54 | | (538) all_270_0 = all_76_2
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_254_0, all_270_0, all_70_2,
% 120.15/22.54 | | all_68_2, simplifying with (404), (406) gives:
% 120.15/22.54 | | (539) all_270_0 = all_254_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_74_2, all_302_0, all_74_0,
% 120.15/22.54 | | all_68_2, simplifying with (262), (408) gives:
% 120.15/22.54 | | (540) all_302_0 = all_74_2
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (22) with all_250_0, all_302_0, all_74_0,
% 120.15/22.54 | | all_68_2, simplifying with (401), (408) gives:
% 120.15/22.54 | | (541) all_302_0 = all_250_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with zero, all_352_1, zero, simplifying with
% 120.15/22.54 | | (17), (437) gives:
% 120.15/22.54 | | (542) all_352_1 = zero
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_352_1, all_360_0, zero, simplifying
% 120.15/22.54 | | with (437), (449) gives:
% 120.15/22.54 | | (543) all_360_0 = all_352_1
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_360_0, all_364_1, zero, simplifying
% 120.15/22.54 | | with (449), (456) gives:
% 120.15/22.54 | | (544) all_364_1 = all_360_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_364_1, all_368_0, zero, simplifying
% 120.15/22.54 | | with (456), (465) gives:
% 120.15/22.54 | | (545) all_368_0 = all_364_1
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_368_0, all_376_1, zero, simplifying
% 120.15/22.54 | | with (465), (475) gives:
% 120.15/22.54 | | (546) all_376_1 = all_368_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_346_1, all_376_1, zero, simplifying
% 120.15/22.54 | | with (425), (475) gives:
% 120.15/22.54 | | (547) all_376_1 = all_346_1
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_344_2, all_348_0, one, simplifying
% 120.15/22.54 | | with (420), (429) gives:
% 120.15/22.54 | | (548) all_348_0 = all_344_2
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_348_0, all_350_2, one, simplifying
% 120.15/22.54 | | with (429), (433) gives:
% 120.15/22.54 | | (549) all_350_2 = all_348_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_68_2, all_356_2, one, simplifying
% 120.15/22.54 | | with (130), (441) gives:
% 120.15/22.54 | | (550) all_356_2 = all_68_2
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_350_2, all_356_2, one, simplifying
% 120.15/22.54 | | with (433), (441) gives:
% 120.15/22.54 | | (551) all_356_2 = all_350_2
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_356_2, all_362_0, one, simplifying
% 120.15/22.54 | | with (441), (453) gives:
% 120.15/22.54 | | (552) all_362_0 = all_356_2
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_362_0, all_368_2, one, simplifying
% 120.15/22.54 | | with (453), (466) gives:
% 120.15/22.54 | | (553) all_368_2 = all_362_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_368_2, all_368_1, one, simplifying
% 120.15/22.54 | | with (466), (467) gives:
% 120.15/22.54 | | (554) all_368_1 = all_368_2
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_356_0, all_380_2, one, simplifying
% 120.15/22.54 | | with (442), (479) gives:
% 120.15/22.54 | | (555) all_380_2 = all_356_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_350_2, all_380_2, one, simplifying
% 120.15/22.54 | | with (433), (479) gives:
% 120.15/22.54 | | (556) all_380_2 = all_350_2
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_344_0, all_380_2, one, simplifying
% 120.15/22.54 | | with (421), (479) gives:
% 120.15/22.54 | | (557) all_380_2 = all_344_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_368_1, all_380_1, one, simplifying
% 120.15/22.54 | | with (467), (480) gives:
% 120.15/22.54 | | (558) all_380_1 = all_368_1
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_350_0, all_380_1, one, simplifying
% 120.15/22.54 | | with (434), (480) gives:
% 120.15/22.54 | | (559) all_380_1 = all_350_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_24_0, all_338_0, all_24_1,
% 120.15/22.54 | | simplifying with (31), (411) gives:
% 120.15/22.54 | | (560) all_338_0 = all_24_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_338_0, all_366_0, all_24_1,
% 120.15/22.54 | | simplifying with (411), (461) gives:
% 120.15/22.54 | | (561) all_366_0 = all_338_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_366_0, all_382_2, all_24_1,
% 120.15/22.54 | | simplifying with (461), (499) gives:
% 120.15/22.54 | | (562) all_382_2 = all_366_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_382_2, all_382_1, all_24_1,
% 120.15/22.54 | | simplifying with (483), (499) gives:
% 120.15/22.54 | | (563) all_382_1 = all_382_2
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_384_2, all_384_0, all_24_1,
% 120.15/22.54 | | simplifying with (488), (489) gives:
% 120.15/22.54 | | (564) all_384_0 = all_384_2
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_382_0, all_384_0, all_24_1,
% 120.15/22.54 | | simplifying with (484), (489) gives:
% 120.15/22.54 | | (565) all_384_0 = all_382_0
% 120.15/22.54 | |
% 120.15/22.54 | | GROUND_INST: instantiating (21) with all_382_1, all_384_0, all_24_1,
% 120.15/22.54 | | simplifying with (483), (489) gives:
% 120.15/22.54 | | (566) all_384_0 = all_382_1
% 120.15/22.54 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_384_2, all_388_1, all_24_1,
% 120.15/22.55 | | simplifying with (488), (498) gives:
% 120.15/22.55 | | (567) all_388_1 = all_384_2
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_338_2, all_388_1, all_24_1,
% 120.15/22.55 | | simplifying with (410), (498) gives:
% 120.15/22.55 | | (568) all_388_1 = all_338_2
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_68_1, all_342_1, all_24_0,
% 120.15/22.55 | | simplifying with (132), (415) gives:
% 120.15/22.55 | | (569) all_342_1 = all_68_1
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_342_1, all_356_1, all_24_0,
% 120.15/22.55 | | simplifying with (415), (501) gives:
% 120.15/22.55 | | (570) all_356_1 = all_342_1
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_340_1, all_356_1, all_24_0,
% 120.15/22.55 | | simplifying with (413), (501) gives:
% 120.15/22.55 | | (571) all_356_1 = all_340_1
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_356_1, all_358_1, all_24_0,
% 120.15/22.55 | | simplifying with (446), (501) gives:
% 120.15/22.55 | | (572) all_358_1 = all_356_1
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_358_1, all_360_2, all_24_0,
% 120.15/22.55 | | simplifying with (446), (500) gives:
% 120.15/22.55 | | (573) all_360_2 = all_358_1
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_360_2, all_360_1, all_24_0,
% 120.15/22.55 | | simplifying with (450), (500) gives:
% 120.15/22.55 | | (574) all_360_1 = all_360_2
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_360_1, all_364_0, all_24_0,
% 120.15/22.55 | | simplifying with (450), (457) gives:
% 120.15/22.55 | | (575) all_364_0 = all_360_1
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_364_0, all_370_2, all_24_0,
% 120.15/22.55 | | simplifying with (457), (496) gives:
% 120.15/22.55 | | (576) all_370_2 = all_364_0
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_370_2, all_370_1, all_24_0,
% 120.15/22.55 | | simplifying with (469), (496) gives:
% 120.15/22.55 | | (577) all_370_1 = all_370_2
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_370_1, all_370_0, all_24_0,
% 120.15/22.55 | | simplifying with (469), (470) gives:
% 120.15/22.55 | | (578) all_370_0 = all_370_1
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_370_0, all_372_1, all_24_0,
% 120.15/22.55 | | simplifying with (470), (473) gives:
% 120.15/22.55 | | (579) all_372_1 = all_370_0
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_372_1, all_378_1, all_24_0,
% 120.15/22.55 | | simplifying with (473), (477) gives:
% 120.15/22.55 | | (580) all_378_1 = all_372_1
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_378_1, all_380_0, all_24_0,
% 120.15/22.55 | | simplifying with (477), (481) gives:
% 120.15/22.55 | | (581) all_380_0 = all_378_1
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_344_1, all_380_0, all_24_0,
% 120.15/22.55 | | simplifying with (481), (497) gives:
% 120.15/22.55 | | (582) all_380_0 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_72_2, all_366_1, all_34_0,
% 120.15/22.55 | | simplifying with (144), (463) gives:
% 120.15/22.55 | | (583) all_366_1 = all_72_2
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_366_1, all_388_2, all_34_0,
% 120.15/22.55 | | simplifying with (463), (492) gives:
% 120.15/22.55 | | (584) all_388_2 = all_366_1
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_388_2, all_388_0, all_34_0,
% 120.15/22.55 | | simplifying with (492), (493) gives:
% 120.15/22.55 | | (585) all_388_0 = all_388_2
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_366_2, all_388_0, all_34_0,
% 120.15/22.55 | | simplifying with (462), (493) gives:
% 120.15/22.55 | | (586) all_388_0 = all_366_2
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_74_0, all_348_1, all_38_1,
% 120.15/22.55 | | simplifying with (149), (430) gives:
% 120.15/22.55 | | (587) all_348_1 = all_74_0
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_74_2, all_348_2, all_38_0,
% 120.15/22.55 | | simplifying with (150), (431) gives:
% 120.15/22.55 | | (588) all_348_2 = all_74_2
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_342_0, all_348_2, all_38_0,
% 120.15/22.55 | | simplifying with (417), (431) gives:
% 120.15/22.55 | | (589) all_348_2 = all_342_0
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_348_2, all_352_2, all_38_0,
% 120.15/22.55 | | simplifying with (431), (438) gives:
% 120.15/22.55 | | (590) all_352_2 = all_348_2
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_352_0, all_384_1, all_38_0,
% 120.15/22.55 | | simplifying with (439), (490) gives:
% 120.15/22.55 | | (591) all_384_1 = all_352_0
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_352_2, all_384_1, all_38_0,
% 120.15/22.55 | | simplifying with (438), (490) gives:
% 120.15/22.55 | | (592) all_384_1 = all_352_2
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_342_2, all_384_1, all_38_0,
% 120.15/22.55 | | simplifying with (416), (490) gives:
% 120.15/22.55 | | (593) all_384_1 = all_342_2
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_350_1, all_364_2, all_46_0,
% 120.15/22.55 | | simplifying with (435), (458) gives:
% 120.15/22.55 | | (594) all_364_2 = all_350_1
% 120.15/22.55 | |
% 120.15/22.55 | | GROUND_INST: instantiating (21) with all_70_2, all_358_2, all_70_0,
% 120.15/22.55 | | simplifying with (139), (447) gives:
% 120.15/22.55 | | (595) all_358_2 = all_70_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (585), (586) imply:
% 120.15/22.55 | | (596) all_388_2 = all_366_2
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (596) implies:
% 120.15/22.55 | | (597) all_388_2 = all_366_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (567), (568) imply:
% 120.15/22.55 | | (598) all_384_2 = all_338_2
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (598) implies:
% 120.15/22.55 | | (599) all_384_2 = all_338_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (584), (597) imply:
% 120.15/22.55 | | (600) all_366_1 = all_366_2
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (600) implies:
% 120.15/22.55 | | (601) all_366_1 = all_366_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (565), (566) imply:
% 120.15/22.55 | | (602) all_382_0 = all_382_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (564), (565) imply:
% 120.15/22.55 | | (603) all_384_2 = all_382_0
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (603) implies:
% 120.15/22.55 | | (604) all_384_2 = all_382_0
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (591), (593) imply:
% 120.15/22.55 | | (605) all_352_0 = all_342_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (591), (592) imply:
% 120.15/22.55 | | (606) all_352_0 = all_352_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (599), (604) imply:
% 120.15/22.55 | | (607) all_382_0 = all_338_2
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (607) implies:
% 120.15/22.55 | | (608) all_382_0 = all_338_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (602), (608) imply:
% 120.15/22.55 | | (609) all_382_1 = all_338_2
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (609) implies:
% 120.15/22.55 | | (610) all_382_1 = all_338_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (563), (610) imply:
% 120.15/22.55 | | (611) all_382_2 = all_338_2
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (611) implies:
% 120.15/22.55 | | (612) all_382_2 = all_338_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (562), (612) imply:
% 120.15/22.55 | | (613) all_366_0 = all_338_2
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (613) implies:
% 120.15/22.55 | | (614) all_366_0 = all_338_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (581), (582) imply:
% 120.15/22.55 | | (615) all_378_1 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (615) implies:
% 120.15/22.55 | | (616) all_378_1 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (558), (559) imply:
% 120.15/22.55 | | (617) all_368_1 = all_350_0
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (617) implies:
% 120.15/22.55 | | (618) all_368_1 = all_350_0
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (555), (557) imply:
% 120.15/22.55 | | (619) all_356_0 = all_344_0
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (555), (556) imply:
% 120.15/22.55 | | (620) all_356_0 = all_350_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (580), (616) imply:
% 120.15/22.55 | | (621) all_372_1 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (621) implies:
% 120.15/22.55 | | (622) all_372_1 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (546), (547) imply:
% 120.15/22.55 | | (623) all_368_0 = all_346_1
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (623) implies:
% 120.15/22.55 | | (624) all_368_0 = all_346_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (579), (622) imply:
% 120.15/22.55 | | (625) all_370_0 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (625) implies:
% 120.15/22.55 | | (626) all_370_0 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (578), (626) imply:
% 120.15/22.55 | | (627) all_370_1 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (627) implies:
% 120.15/22.55 | | (628) all_370_1 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (577), (628) imply:
% 120.15/22.55 | | (629) all_370_2 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (629) implies:
% 120.15/22.55 | | (630) all_370_2 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (576), (630) imply:
% 120.15/22.55 | | (631) all_364_0 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (631) implies:
% 120.15/22.55 | | (632) all_364_0 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (545), (624) imply:
% 120.15/22.55 | | (633) all_364_1 = all_346_1
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (633) implies:
% 120.15/22.55 | | (634) all_364_1 = all_346_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (554), (618) imply:
% 120.15/22.55 | | (635) all_368_2 = all_350_0
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (635) implies:
% 120.15/22.55 | | (636) all_368_2 = all_350_0
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (553), (636) imply:
% 120.15/22.55 | | (637) all_362_0 = all_350_0
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (637) implies:
% 120.15/22.55 | | (638) all_362_0 = all_350_0
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (561), (614) imply:
% 120.15/22.55 | | (639) all_338_0 = all_338_2
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (639) implies:
% 120.15/22.55 | | (640) all_338_0 = all_338_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (583), (601) imply:
% 120.15/22.55 | | (641) all_366_2 = all_72_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (575), (632) imply:
% 120.15/22.55 | | (642) all_360_1 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (642) implies:
% 120.15/22.55 | | (643) all_360_1 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (544), (634) imply:
% 120.15/22.55 | | (644) all_360_0 = all_346_1
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (644) implies:
% 120.15/22.55 | | (645) all_360_0 = all_346_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (552), (638) imply:
% 120.15/22.55 | | (646) all_356_2 = all_350_0
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (646) implies:
% 120.15/22.55 | | (647) all_356_2 = all_350_0
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (543), (645) imply:
% 120.15/22.55 | | (648) all_352_1 = all_346_1
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (648) implies:
% 120.15/22.55 | | (649) all_352_1 = all_346_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (574), (643) imply:
% 120.15/22.55 | | (650) all_360_2 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (650) implies:
% 120.15/22.55 | | (651) all_360_2 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (573), (651) imply:
% 120.15/22.55 | | (652) all_358_1 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (652) implies:
% 120.15/22.55 | | (653) all_358_1 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (572), (653) imply:
% 120.15/22.55 | | (654) all_356_1 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (654) implies:
% 120.15/22.55 | | (655) all_356_1 = all_344_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (619), (620) imply:
% 120.15/22.55 | | (656) all_350_2 = all_344_0
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (656) implies:
% 120.15/22.55 | | (657) all_350_2 = all_344_0
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (571), (655) imply:
% 120.15/22.55 | | (658) all_344_1 = all_340_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (570), (655) imply:
% 120.15/22.55 | | (659) all_344_1 = all_342_1
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (550), (647) imply:
% 120.15/22.55 | | (660) all_350_0 = all_68_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (551), (647) imply:
% 120.15/22.55 | | (661) all_350_0 = all_350_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (605), (606) imply:
% 120.15/22.55 | | (662) all_352_2 = all_342_2
% 120.15/22.55 | |
% 120.15/22.55 | | SIMP: (662) implies:
% 120.15/22.55 | | (663) all_352_2 = all_342_2
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (542), (649) imply:
% 120.15/22.55 | | (664) all_346_1 = zero
% 120.15/22.55 | |
% 120.15/22.55 | | COMBINE_EQS: (590), (663) imply:
% 120.15/22.55 | | (665) all_348_2 = all_342_2
% 120.15/22.56 | |
% 120.15/22.56 | | SIMP: (665) implies:
% 120.15/22.56 | | (666) all_348_2 = all_342_2
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (660), (661) imply:
% 120.15/22.56 | | (667) all_350_2 = all_68_2
% 120.15/22.56 | |
% 120.15/22.56 | | SIMP: (667) implies:
% 120.15/22.56 | | (668) all_350_2 = all_68_2
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (549), (657) imply:
% 120.15/22.56 | | (669) all_348_0 = all_344_0
% 120.15/22.56 | |
% 120.15/22.56 | | SIMP: (669) implies:
% 120.15/22.56 | | (670) all_348_0 = all_344_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (657), (668) imply:
% 120.15/22.56 | | (671) all_344_0 = all_68_2
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (548), (670) imply:
% 120.15/22.56 | | (672) all_344_0 = all_344_2
% 120.15/22.56 | |
% 120.15/22.56 | | SIMP: (672) implies:
% 120.15/22.56 | | (673) all_344_0 = all_344_2
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (588), (589) imply:
% 120.15/22.56 | | (674) all_342_0 = all_74_2
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (589), (666) imply:
% 120.15/22.56 | | (675) all_342_0 = all_342_2
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (671), (673) imply:
% 120.15/22.56 | | (676) all_344_2 = all_68_2
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (658), (659) imply:
% 120.15/22.56 | | (677) all_342_1 = all_340_1
% 120.15/22.56 | |
% 120.15/22.56 | | SIMP: (677) implies:
% 120.15/22.56 | | (678) all_342_1 = all_340_1
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (674), (675) imply:
% 120.15/22.56 | | (679) all_342_2 = all_74_2
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (569), (678) imply:
% 120.15/22.56 | | (680) all_340_1 = all_68_1
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (560), (640) imply:
% 120.15/22.56 | | (681) all_338_2 = all_24_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (540), (541) imply:
% 120.15/22.56 | | (682) all_250_0 = all_74_2
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (538), (539) imply:
% 120.15/22.56 | | (683) all_254_0 = all_76_2
% 120.15/22.56 | |
% 120.15/22.56 | | SIMP: (683) implies:
% 120.15/22.56 | | (684) all_254_0 = all_76_2
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (522), (523) imply:
% 120.15/22.56 | | (685) all_150_0 = all_24_0
% 120.15/22.56 | |
% 120.15/22.56 | | SIMP: (685) implies:
% 120.15/22.56 | | (686) all_150_0 = all_24_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (536), (537) imply:
% 120.15/22.56 | | (687) all_176_0 = all_144_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (531), (535) imply:
% 120.15/22.56 | | (688) all_166_0 = all_24_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (531), (532) imply:
% 120.15/22.56 | | (689) all_166_0 = all_156_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (531), (533) imply:
% 120.15/22.56 | | (690) all_166_0 = all_114_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (531), (534) imply:
% 120.15/22.56 | | (691) all_166_0 = all_102_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (520), (521) imply:
% 120.15/22.56 | | (692) all_160_0 = all_110_0
% 120.15/22.56 | |
% 120.15/22.56 | | SIMP: (692) implies:
% 120.15/22.56 | | (693) all_160_0 = all_110_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (528), (530) imply:
% 120.15/22.56 | | (694) all_172_0 = all_148_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (528), (529) imply:
% 120.15/22.56 | | (695) all_172_0 = all_162_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (694), (695) imply:
% 120.15/22.56 | | (696) all_162_0 = all_148_0
% 120.15/22.56 | |
% 120.15/22.56 | | SIMP: (696) implies:
% 120.15/22.56 | | (697) all_162_0 = all_148_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (688), (690) imply:
% 120.15/22.56 | | (698) all_114_0 = all_24_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (690), (691) imply:
% 120.15/22.56 | | (699) all_114_0 = all_102_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (689), (690) imply:
% 120.15/22.56 | | (700) all_156_0 = all_114_0
% 120.15/22.56 | |
% 120.15/22.56 | | SIMP: (700) implies:
% 120.15/22.56 | | (701) all_156_0 = all_114_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (527), (697) imply:
% 120.15/22.56 | | (702) all_158_0 = all_148_0
% 120.15/22.56 | |
% 120.15/22.56 | | SIMP: (702) implies:
% 120.15/22.56 | | (703) all_158_0 = all_148_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (518), (693) imply:
% 120.15/22.56 | | (704) all_118_0 = all_110_0
% 120.15/22.56 | |
% 120.15/22.56 | | SIMP: (704) implies:
% 120.15/22.56 | | (705) all_118_0 = all_110_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (519), (693) imply:
% 120.15/22.56 | | (706) all_110_0 = all_46_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (526), (703) imply:
% 120.15/22.56 | | (707) all_156_0 = all_148_0
% 120.15/22.56 | |
% 120.15/22.56 | | SIMP: (707) implies:
% 120.15/22.56 | | (708) all_156_0 = all_148_0
% 120.15/22.56 | |
% 120.15/22.56 | | COMBINE_EQS: (524), (708) imply:
% 120.55/22.56 | | (709) all_148_0 = all_116_0
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (525), (708) imply:
% 120.55/22.56 | | (710) all_148_0 = all_112_0
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (701), (708) imply:
% 120.55/22.56 | | (711) all_148_0 = all_114_0
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (517), (686) imply:
% 120.55/22.56 | | (712) all_118_0 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | SIMP: (712) implies:
% 120.55/22.56 | | (713) all_118_0 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (709), (710) imply:
% 120.55/22.56 | | (714) all_116_0 = all_112_0
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (709), (711) imply:
% 120.55/22.56 | | (715) all_116_0 = all_114_0
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (705), (713) imply:
% 120.55/22.56 | | (716) all_110_0 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | SIMP: (716) implies:
% 120.55/22.56 | | (717) all_110_0 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (714), (715) imply:
% 120.55/22.56 | | (718) all_114_0 = all_112_0
% 120.55/22.56 | |
% 120.55/22.56 | | SIMP: (718) implies:
% 120.55/22.56 | | (719) all_114_0 = all_112_0
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (699), (719) imply:
% 120.55/22.56 | | (720) all_112_0 = all_102_0
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (698), (719) imply:
% 120.55/22.56 | | (721) all_112_0 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (720), (721) imply:
% 120.55/22.56 | | (722) all_102_0 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (706), (717) imply:
% 120.55/22.56 | | (723) all_46_0 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | SIMP: (723) implies:
% 120.55/22.56 | | (724) all_46_0 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (658), (680) imply:
% 120.55/22.56 | | (725) all_344_1 = all_68_1
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (548), (676) imply:
% 120.55/22.56 | | (726) all_348_0 = all_68_2
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (605), (679) imply:
% 120.55/22.56 | | (727) all_352_0 = all_74_2
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (634), (664) imply:
% 120.55/22.56 | | (728) all_364_1 = zero
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (632), (725) imply:
% 120.55/22.56 | | (729) all_364_0 = all_68_1
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (608), (681) imply:
% 120.55/22.56 | | (730) all_382_0 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (599), (681) imply:
% 120.55/22.56 | | (731) all_384_2 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (591), (727) imply:
% 120.55/22.56 | | (732) all_384_1 = all_74_2
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (565), (730) imply:
% 120.55/22.56 | | (733) all_384_0 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | REDUCE: (435), (724) imply:
% 120.55/22.56 | | (734) domain(all_24_0) = all_350_1
% 120.55/22.56 | |
% 120.55/22.56 | | REDUCE: (487), (731), (732), (733) imply:
% 120.55/22.56 | | (735) addition(all_74_2, all_24_0) = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | REDUCE: (455), (594), (728), (729) imply:
% 120.55/22.56 | | (736) addition(zero, all_68_1) = all_350_1
% 120.55/22.56 | |
% 120.55/22.56 | | REDUCE: (428), (587), (588), (726) imply:
% 120.55/22.56 | | (737) addition(all_74_0, all_68_2) = all_74_2
% 120.55/22.56 | |
% 120.55/22.56 | | REDUCE: (386), (687) imply:
% 120.55/22.56 | | (738) addition(all_144_0, one) = one
% 120.55/22.56 | |
% 120.55/22.56 | | REDUCE: (394), (724) imply:
% 120.55/22.56 | | (739) addition(all_24_0, all_24_0) = all_208_0
% 120.55/22.56 | |
% 120.55/22.56 | | REDUCE: (512), (724) imply:
% 120.55/22.56 | | (740) addition(all_24_0, all_24_0) = all_144_0
% 120.55/22.56 | |
% 120.55/22.56 | | REDUCE: (508), (724) imply:
% 120.55/22.56 | | (741) addition(all_24_0, all_24_0) = all_146_0
% 120.55/22.56 | |
% 120.55/22.56 | | REDUCE: (403), (684) imply:
% 120.55/22.56 | | (742) $i(all_76_2)
% 120.55/22.56 | |
% 120.55/22.56 | | REDUCE: (400), (682) imply:
% 120.55/22.56 | | (743) $i(all_74_2)
% 120.55/22.56 | |
% 120.55/22.56 | | REDUCE: (384), (687) imply:
% 120.55/22.56 | | (744) $i(all_144_0)
% 120.55/22.56 | |
% 120.55/22.56 | | GROUND_INST: instantiating (22) with all_106_0, all_350_1, all_68_1, zero,
% 120.55/22.56 | | simplifying with (348), (736) gives:
% 120.55/22.56 | | (745) all_350_1 = all_106_0
% 120.55/22.56 | |
% 120.55/22.56 | | GROUND_INST: instantiating (22) with all_144_0, all_146_0, all_24_0,
% 120.55/22.56 | | all_24_0, simplifying with (740), (741) gives:
% 120.55/22.56 | | (746) all_146_0 = all_144_0
% 120.55/22.56 | |
% 120.55/22.56 | | GROUND_INST: instantiating (22) with all_24_0, all_208_0, all_24_0,
% 120.55/22.56 | | all_24_0, simplifying with (515), (739) gives:
% 120.55/22.56 | | (747) all_208_0 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | GROUND_INST: instantiating (22) with all_146_0, all_208_0, all_24_0,
% 120.55/22.56 | | all_24_0, simplifying with (739), (741) gives:
% 120.55/22.56 | | (748) all_208_0 = all_146_0
% 120.55/22.56 | |
% 120.55/22.56 | | GROUND_INST: instantiating (21) with all_68_1, all_350_1, all_24_0,
% 120.55/22.56 | | simplifying with (132), (734) gives:
% 120.55/22.56 | | (749) all_350_1 = all_68_1
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (745), (749) imply:
% 120.55/22.56 | | (750) all_106_0 = all_68_1
% 120.55/22.56 | |
% 120.55/22.56 | | SIMP: (750) implies:
% 120.55/22.56 | | (751) all_106_0 = all_68_1
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (747), (748) imply:
% 120.55/22.56 | | (752) all_146_0 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | SIMP: (752) implies:
% 120.55/22.56 | | (753) all_146_0 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | COMBINE_EQS: (746), (753) imply:
% 120.55/22.56 | | (754) all_144_0 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | SIMP: (754) implies:
% 120.55/22.56 | | (755) all_144_0 = all_24_0
% 120.55/22.56 | |
% 120.55/22.56 | | GROUND_INST: instantiating (3) with all_168_0, one, all_24_0, one,
% 120.55/22.56 | | all_168_0, simplifying with (19), (29), (36), (378), (379)
% 120.55/22.56 | | gives:
% 120.55/22.56 | | (756) ? [v0: $i] : (addition(all_24_0, v0) = all_168_0 & addition(one,
% 120.55/22.56 | | all_168_0) = v0 & $i(v0))
% 120.55/22.56 | |
% 120.55/22.56 | | GROUND_INST: instantiating (3) with all_168_0, all_24_0, one, one,
% 120.55/22.56 | | all_168_0, simplifying with (19), (29), (80), (378), (379)
% 120.55/22.56 | | gives:
% 120.55/22.56 | | (757) ? [v0: $i] : (addition(all_24_0, all_168_0) = v0 & addition(one,
% 120.55/22.56 | | v0) = all_168_0 & $i(v0))
% 120.55/22.56 | |
% 120.55/22.56 | | GROUND_INST: instantiating (3) with all_168_0, one, zero, one, all_168_0,
% 120.55/22.56 | | simplifying with (16), (19), (34), (378), (379) gives:
% 120.55/22.56 | | (758) ? [v0: $i] : (addition(one, all_168_0) = v0 & addition(zero, v0) =
% 120.55/22.56 | | all_168_0 & $i(v0))
% 120.55/22.56 | |
% 120.55/22.56 | | GROUND_INST: instantiating (3) with all_168_0, one, all_68_2, one,
% 120.55/22.56 | | all_168_0, simplifying with (19), (272), (335), (378), (379)
% 120.55/22.56 | | gives:
% 120.55/22.57 | | (759) ? [v0: $i] : (addition(all_68_2, v0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = v0 & $i(v0))
% 120.55/22.57 | |
% 120.55/22.57 | | GROUND_INST: instantiating (1) with one, all_68_2, one, simplifying with
% 120.55/22.57 | | (19), (272), (335) gives:
% 120.55/22.57 | | (760) addition(one, all_68_2) = one
% 120.55/22.57 | |
% 120.55/22.57 | | GROUND_INST: instantiating (3) with all_168_0, one, all_68_1, one,
% 120.55/22.57 | | all_168_0, simplifying with (19), (127), (338), (378), (379)
% 120.55/22.57 | | gives:
% 120.55/22.57 | | (761) ? [v0: $i] : (addition(all_68_1, v0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = v0 & $i(v0))
% 120.55/22.57 | |
% 120.55/22.57 | | GROUND_INST: instantiating (3) with all_168_0, one, all_70_2, one,
% 120.55/22.57 | | all_168_0, simplifying with (19), (270), (341), (378), (379)
% 120.55/22.57 | | gives:
% 120.55/22.57 | | (762) ? [v0: $i] : (addition(all_70_2, v0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = v0 & $i(v0))
% 120.55/22.57 | |
% 120.55/22.57 | | GROUND_INST: instantiating (3) with all_168_0, one, all_72_2, one,
% 120.55/22.57 | | all_168_0, simplifying with (19), (271), (342), (378), (379)
% 120.55/22.57 | | gives:
% 120.55/22.57 | | (763) ? [v0: $i] : (addition(all_72_2, v0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = v0 & $i(v0))
% 120.55/22.57 | |
% 120.55/22.57 | | GROUND_INST: instantiating (2) with one, all_74_2, all_24_0, one, one,
% 120.55/22.57 | | simplifying with (19), (29), (36), (340), (743) gives:
% 120.55/22.57 | | (764) ? [v0: $i] : (addition(v0, one) = one & addition(all_24_0,
% 120.55/22.57 | | all_74_2) = v0 & $i(v0))
% 120.55/22.57 | |
% 120.55/22.57 | | GROUND_INST: instantiating (3) with all_168_0, one, all_74_2, one,
% 120.55/22.57 | | all_168_0, simplifying with (19), (340), (378), (379), (743)
% 120.55/22.57 | | gives:
% 120.55/22.57 | | (765) ? [v0: $i] : (addition(all_74_2, v0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = v0 & $i(v0))
% 120.55/22.57 | |
% 120.55/22.57 | | GROUND_INST: instantiating (2) with all_24_0, all_74_2, all_24_0, all_24_0,
% 120.55/22.57 | | all_24_0, simplifying with (29), (515), (735), (743) gives:
% 120.55/22.57 | | (766) ? [v0: $i] : (addition(v0, all_24_0) = all_24_0 &
% 120.55/22.57 | | addition(all_24_0, all_74_2) = v0 & $i(v0))
% 120.55/22.57 | |
% 120.55/22.57 | | GROUND_INST: instantiating (1) with all_24_0, all_74_2, all_24_0,
% 120.55/22.57 | | simplifying with (29), (735), (743) gives:
% 120.55/22.57 | | (767) addition(all_24_0, all_74_2) = all_24_0
% 120.55/22.57 | |
% 120.55/22.57 | | GROUND_INST: instantiating (2) with one, zero, all_74_0, one, one,
% 120.55/22.57 | | simplifying with (16), (19), (34), (269), (343) gives:
% 120.55/22.57 | | (768) ? [v0: $i] : (addition(v0, one) = one & addition(all_74_0, zero) =
% 120.55/22.57 | | v0 & $i(v0))
% 120.55/22.57 | |
% 120.55/22.57 | | GROUND_INST: instantiating (3) with all_168_0, one, all_74_0, one,
% 120.55/22.57 | | all_168_0, simplifying with (19), (269), (343), (378), (379)
% 120.55/22.57 | | gives:
% 120.55/22.57 | | (769) ? [v0: $i] : (addition(all_74_0, v0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = v0 & $i(v0))
% 120.55/22.57 | |
% 120.55/22.57 | | GROUND_INST: instantiating (2) with all_68_2, zero, all_74_0, all_68_2,
% 120.55/22.57 | | all_74_2, simplifying with (16), (260), (269), (272), (737)
% 120.55/22.57 | | gives:
% 120.55/22.57 | | (770) ? [v0: $i] : (addition(v0, all_68_2) = all_74_2 &
% 120.55/22.57 | | addition(all_74_0, zero) = v0 & $i(v0) & $i(all_74_2))
% 120.55/22.57 | |
% 120.55/22.57 | | GROUND_INST: instantiating (9) with all_74_0, all_68_2, all_74_2,
% 120.55/22.57 | | simplifying with (269), (272), (737) gives:
% 120.55/22.57 | | (771) all_74_2 = all_68_2 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_74_0,
% 120.55/22.57 | | all_68_2) = v0)
% 120.55/22.57 | |
% 120.55/22.57 | | GROUND_INST: instantiating (3) with all_168_0, one, all_76_2, one,
% 120.55/22.57 | | all_168_0, simplifying with (19), (339), (378), (379), (742)
% 120.55/22.57 | | gives:
% 120.55/22.57 | | (772) ? [v0: $i] : (addition(all_76_2, v0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = v0 & $i(v0))
% 120.55/22.57 | |
% 120.55/22.57 | | GROUND_INST: instantiating (3) with all_168_0, one, all_82_1, one,
% 120.55/22.57 | | all_168_0, simplifying with (19), (171), (337), (378), (379)
% 120.55/22.57 | | gives:
% 120.55/22.57 | | (773) ? [v0: $i] : (addition(all_82_1, v0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = v0 & $i(v0))
% 120.55/22.57 | |
% 120.55/22.57 | | GROUND_INST: instantiating (5) with all_68_2, all_168_0, simplifying with
% 120.55/22.57 | | (272), (380) gives:
% 120.55/22.57 | | (774) all_168_0 = all_68_2
% 120.55/22.57 | |
% 120.55/22.57 | | DELTA: instantiating (758) with fresh symbol all_591_0 gives:
% 120.55/22.57 | | (775) addition(one, all_168_0) = all_591_0 & addition(zero, all_591_0) =
% 120.55/22.57 | | all_168_0 & $i(all_591_0)
% 120.55/22.57 | |
% 120.55/22.57 | | ALPHA: (775) implies:
% 120.55/22.57 | | (776) addition(one, all_168_0) = all_591_0
% 120.55/22.57 | |
% 120.55/22.57 | | DELTA: instantiating (773) with fresh symbol all_691_0 gives:
% 120.55/22.57 | | (777) addition(all_82_1, all_691_0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = all_691_0 & $i(all_691_0)
% 120.55/22.57 | |
% 120.55/22.57 | | ALPHA: (777) implies:
% 120.55/22.57 | | (778) addition(one, all_168_0) = all_691_0
% 120.55/22.57 | |
% 120.55/22.57 | | DELTA: instantiating (757) with fresh symbol all_791_0 gives:
% 120.55/22.57 | | (779) addition(all_24_0, all_168_0) = all_791_0 & addition(one,
% 120.55/22.57 | | all_791_0) = all_168_0 & $i(all_791_0)
% 120.55/22.57 | |
% 120.55/22.57 | | ALPHA: (779) implies:
% 120.55/22.57 | | (780) addition(all_24_0, all_168_0) = all_791_0
% 120.55/22.57 | |
% 120.55/22.57 | | DELTA: instantiating (772) with fresh symbol all_809_0 gives:
% 120.55/22.57 | | (781) addition(all_76_2, all_809_0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = all_809_0 & $i(all_809_0)
% 120.55/22.57 | |
% 120.55/22.57 | | ALPHA: (781) implies:
% 120.55/22.57 | | (782) addition(one, all_168_0) = all_809_0
% 120.55/22.57 | |
% 120.55/22.57 | | DELTA: instantiating (756) with fresh symbol all_815_0 gives:
% 120.55/22.57 | | (783) addition(all_24_0, all_815_0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = all_815_0 & $i(all_815_0)
% 120.55/22.57 | |
% 120.55/22.57 | | ALPHA: (783) implies:
% 120.55/22.57 | | (784) addition(one, all_168_0) = all_815_0
% 120.55/22.57 | | (785) addition(all_24_0, all_815_0) = all_168_0
% 120.55/22.57 | |
% 120.55/22.57 | | DELTA: instantiating (762) with fresh symbol all_837_0 gives:
% 120.55/22.57 | | (786) addition(all_70_2, all_837_0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = all_837_0 & $i(all_837_0)
% 120.55/22.57 | |
% 120.55/22.57 | | ALPHA: (786) implies:
% 120.55/22.57 | | (787) addition(one, all_168_0) = all_837_0
% 120.55/22.57 | |
% 120.55/22.57 | | DELTA: instantiating (765) with fresh symbol all_993_0 gives:
% 120.55/22.57 | | (788) addition(all_74_2, all_993_0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = all_993_0 & $i(all_993_0)
% 120.55/22.57 | |
% 120.55/22.57 | | ALPHA: (788) implies:
% 120.55/22.57 | | (789) addition(one, all_168_0) = all_993_0
% 120.55/22.57 | |
% 120.55/22.57 | | DELTA: instantiating (764) with fresh symbol all_995_0 gives:
% 120.55/22.57 | | (790) addition(all_995_0, one) = one & addition(all_24_0, all_74_2) =
% 120.55/22.57 | | all_995_0 & $i(all_995_0)
% 120.55/22.57 | |
% 120.55/22.57 | | ALPHA: (790) implies:
% 120.55/22.57 | | (791) addition(all_24_0, all_74_2) = all_995_0
% 120.55/22.57 | |
% 120.55/22.57 | | DELTA: instantiating (759) with fresh symbol all_1091_0 gives:
% 120.55/22.57 | | (792) addition(all_68_2, all_1091_0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = all_1091_0 & $i(all_1091_0)
% 120.55/22.57 | |
% 120.55/22.57 | | ALPHA: (792) implies:
% 120.55/22.57 | | (793) addition(one, all_168_0) = all_1091_0
% 120.55/22.57 | |
% 120.55/22.57 | | DELTA: instantiating (761) with fresh symbol all_1093_0 gives:
% 120.55/22.57 | | (794) addition(all_68_1, all_1093_0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = all_1093_0 & $i(all_1093_0)
% 120.55/22.57 | |
% 120.55/22.57 | | ALPHA: (794) implies:
% 120.55/22.57 | | (795) addition(one, all_168_0) = all_1093_0
% 120.55/22.57 | |
% 120.55/22.57 | | DELTA: instantiating (769) with fresh symbol all_1095_0 gives:
% 120.55/22.57 | | (796) addition(all_74_0, all_1095_0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = all_1095_0 & $i(all_1095_0)
% 120.55/22.57 | |
% 120.55/22.57 | | ALPHA: (796) implies:
% 120.55/22.57 | | (797) addition(one, all_168_0) = all_1095_0
% 120.55/22.57 | |
% 120.55/22.57 | | DELTA: instantiating (763) with fresh symbol all_1105_0 gives:
% 120.55/22.57 | | (798) addition(all_72_2, all_1105_0) = all_168_0 & addition(one,
% 120.55/22.57 | | all_168_0) = all_1105_0 & $i(all_1105_0)
% 120.55/22.57 | |
% 120.55/22.57 | | ALPHA: (798) implies:
% 120.55/22.57 | | (799) addition(one, all_168_0) = all_1105_0
% 120.55/22.57 | |
% 120.55/22.57 | | DELTA: instantiating (766) with fresh symbol all_1129_0 gives:
% 120.55/22.57 | | (800) addition(all_1129_0, all_24_0) = all_24_0 & addition(all_24_0,
% 120.55/22.57 | | all_74_2) = all_1129_0 & $i(all_1129_0)
% 120.55/22.57 | |
% 120.55/22.57 | | ALPHA: (800) implies:
% 120.55/22.57 | | (801) addition(all_24_0, all_74_2) = all_1129_0
% 120.55/22.57 | |
% 120.55/22.57 | | DELTA: instantiating (768) with fresh symbol all_1191_0 gives:
% 120.55/22.57 | | (802) addition(all_1191_0, one) = one & addition(all_74_0, zero) =
% 120.55/22.57 | | all_1191_0 & $i(all_1191_0)
% 120.55/22.57 | |
% 120.55/22.57 | | ALPHA: (802) implies:
% 120.55/22.57 | | (803) addition(all_74_0, zero) = all_1191_0
% 120.55/22.57 | | (804) addition(all_1191_0, one) = one
% 120.55/22.57 | |
% 120.55/22.57 | | DELTA: instantiating (770) with fresh symbol all_2273_0 gives:
% 120.55/22.57 | | (805) addition(all_2273_0, all_68_2) = all_74_2 & addition(all_74_0,
% 120.55/22.57 | | zero) = all_2273_0 & $i(all_2273_0) & $i(all_74_2)
% 120.55/22.57 | |
% 120.55/22.57 | | ALPHA: (805) implies:
% 120.55/22.57 | | (806) addition(all_74_0, zero) = all_2273_0
% 120.55/22.57 | | (807) addition(all_2273_0, all_68_2) = all_74_2
% 120.55/22.57 | |
% 120.55/22.57 | | REDUCE: (774), (785) imply:
% 120.55/22.57 | | (808) addition(all_24_0, all_815_0) = all_68_2
% 120.55/22.57 | |
% 120.55/22.57 | | REDUCE: (774), (780) imply:
% 120.55/22.57 | | (809) addition(all_24_0, all_68_2) = all_791_0
% 120.55/22.57 | |
% 120.55/22.57 | | REDUCE: (774), (799) imply:
% 120.55/22.57 | | (810) addition(one, all_68_2) = all_1105_0
% 120.55/22.57 | |
% 120.55/22.57 | | REDUCE: (774), (797) imply:
% 120.55/22.57 | | (811) addition(one, all_68_2) = all_1095_0
% 120.55/22.57 | |
% 120.55/22.57 | | REDUCE: (774), (795) imply:
% 120.55/22.57 | | (812) addition(one, all_68_2) = all_1093_0
% 120.55/22.57 | |
% 120.55/22.57 | | REDUCE: (774), (793) imply:
% 120.55/22.57 | | (813) addition(one, all_68_2) = all_1091_0
% 120.55/22.57 | |
% 120.55/22.57 | | REDUCE: (774), (789) imply:
% 120.55/22.57 | | (814) addition(one, all_68_2) = all_993_0
% 120.55/22.57 | |
% 120.55/22.57 | | REDUCE: (774), (787) imply:
% 120.55/22.57 | | (815) addition(one, all_68_2) = all_837_0
% 120.55/22.57 | |
% 120.55/22.57 | | REDUCE: (774), (784) imply:
% 120.55/22.57 | | (816) addition(one, all_68_2) = all_815_0
% 120.55/22.57 | |
% 120.55/22.57 | | REDUCE: (774), (782) imply:
% 120.55/22.58 | | (817) addition(one, all_68_2) = all_809_0
% 120.55/22.58 | |
% 120.55/22.58 | | REDUCE: (774), (778) imply:
% 120.55/22.58 | | (818) addition(one, all_68_2) = all_691_0
% 120.55/22.58 | |
% 120.55/22.58 | | REDUCE: (774), (776) imply:
% 120.55/22.58 | | (819) addition(one, all_68_2) = all_591_0
% 120.55/22.58 | |
% 120.55/22.58 | | REDUCE: (379), (774) imply:
% 120.55/22.58 | | (820) addition(one, all_68_2) = all_68_2
% 120.55/22.58 | |
% 120.55/22.58 | | GROUND_INST: instantiating (22) with all_591_0, all_691_0, all_68_2, one,
% 120.55/22.58 | | simplifying with (818), (819) gives:
% 120.55/22.58 | | (821) all_691_0 = all_591_0
% 120.55/22.58 | |
% 120.55/22.58 | | GROUND_INST: instantiating (22) with all_691_0, all_809_0, all_68_2, one,
% 120.55/22.58 | | simplifying with (817), (818) gives:
% 120.55/22.58 | | (822) all_809_0 = all_691_0
% 120.55/22.58 | |
% 120.55/22.58 | | GROUND_INST: instantiating (22) with all_691_0, all_837_0, all_68_2, one,
% 120.55/22.58 | | simplifying with (815), (818) gives:
% 120.55/22.58 | | (823) all_837_0 = all_691_0
% 120.55/22.58 | |
% 120.55/22.58 | | GROUND_INST: instantiating (22) with all_837_0, all_993_0, all_68_2, one,
% 120.55/22.58 | | simplifying with (814), (815) gives:
% 120.55/22.58 | | (824) all_993_0 = all_837_0
% 120.55/22.58 | |
% 120.55/22.58 | | GROUND_INST: instantiating (22) with all_1091_0, all_1093_0, all_68_2, one,
% 120.55/22.58 | | simplifying with (812), (813) gives:
% 120.55/22.58 | | (825) all_1093_0 = all_1091_0
% 120.55/22.58 | |
% 120.55/22.58 | | GROUND_INST: instantiating (22) with all_993_0, all_1093_0, all_68_2, one,
% 120.55/22.58 | | simplifying with (812), (814) gives:
% 120.55/22.58 | | (826) all_1093_0 = all_993_0
% 120.55/22.58 | |
% 120.55/22.58 | | GROUND_INST: instantiating (22) with all_815_0, all_1093_0, all_68_2, one,
% 120.55/22.58 | | simplifying with (812), (816) gives:
% 120.55/22.58 | | (827) all_1093_0 = all_815_0
% 120.55/22.58 | |
% 120.55/22.58 | | GROUND_INST: instantiating (22) with all_809_0, all_1095_0, all_68_2, one,
% 120.55/22.58 | | simplifying with (811), (817) gives:
% 120.55/22.58 | | (828) all_1095_0 = all_809_0
% 120.55/22.58 | |
% 120.55/22.58 | | GROUND_INST: instantiating (22) with all_68_2, all_1095_0, all_68_2, one,
% 120.55/22.58 | | simplifying with (811), (820) gives:
% 120.55/22.58 | | (829) all_1095_0 = all_68_2
% 120.55/22.58 | |
% 120.55/22.58 | | GROUND_INST: instantiating (22) with all_837_0, all_1105_0, all_68_2, one,
% 120.55/22.58 | | simplifying with (810), (815) gives:
% 120.55/22.58 | | (830) all_1105_0 = all_837_0
% 120.55/22.58 | |
% 120.55/22.58 | | GROUND_INST: instantiating (22) with one, all_1105_0, all_68_2, one,
% 120.55/22.58 | | simplifying with (760), (810) gives:
% 120.55/22.58 | | (831) all_1105_0 = one
% 120.55/22.58 | |
% 120.55/22.58 | | GROUND_INST: instantiating (22) with all_995_0, all_1129_0, all_74_2,
% 120.55/22.58 | | all_24_0, simplifying with (791), (801) gives:
% 120.55/22.58 | | (832) all_1129_0 = all_995_0
% 120.55/22.58 | |
% 120.55/22.58 | | GROUND_INST: instantiating (22) with all_24_0, all_1129_0, all_74_2,
% 120.55/22.58 | | all_24_0, simplifying with (767), (801) gives:
% 120.55/22.58 | | (833) all_1129_0 = all_24_0
% 120.55/22.58 | |
% 120.55/22.58 | | GROUND_INST: instantiating (22) with all_1191_0, all_2273_0, zero, all_74_0,
% 120.55/22.58 | | simplifying with (803), (806) gives:
% 120.55/22.58 | | (834) all_2273_0 = all_1191_0
% 120.55/22.58 | |
% 120.55/22.58 | | COMBINE_EQS: (832), (833) imply:
% 120.64/22.58 | | (835) all_995_0 = all_24_0
% 120.64/22.58 | |
% 120.64/22.58 | | SIMP: (835) implies:
% 120.64/22.58 | | (836) all_995_0 = all_24_0
% 120.64/22.58 | |
% 120.64/22.58 | | COMBINE_EQS: (830), (831) imply:
% 120.64/22.58 | | (837) all_837_0 = one
% 120.64/22.58 | |
% 120.64/22.58 | | SIMP: (837) implies:
% 120.64/22.58 | | (838) all_837_0 = one
% 120.64/22.58 | |
% 120.64/22.58 | | COMBINE_EQS: (828), (829) imply:
% 120.64/22.58 | | (839) all_809_0 = all_68_2
% 120.64/22.58 | |
% 120.64/22.58 | | SIMP: (839) implies:
% 120.64/22.58 | | (840) all_809_0 = all_68_2
% 120.64/22.58 | |
% 120.64/22.58 | | COMBINE_EQS: (825), (827) imply:
% 120.64/22.58 | | (841) all_1091_0 = all_815_0
% 120.64/22.58 | |
% 120.64/22.58 | | COMBINE_EQS: (825), (826) imply:
% 120.64/22.58 | | (842) all_1091_0 = all_993_0
% 120.64/22.58 | |
% 120.64/22.58 | | COMBINE_EQS: (841), (842) imply:
% 120.64/22.58 | | (843) all_993_0 = all_815_0
% 120.64/22.58 | |
% 120.64/22.58 | | SIMP: (843) implies:
% 120.64/22.58 | | (844) all_993_0 = all_815_0
% 120.64/22.58 | |
% 120.64/22.58 | | COMBINE_EQS: (824), (844) imply:
% 120.64/22.58 | | (845) all_837_0 = all_815_0
% 120.64/22.58 | |
% 120.64/22.58 | | SIMP: (845) implies:
% 120.64/22.58 | | (846) all_837_0 = all_815_0
% 120.64/22.58 | |
% 120.64/22.58 | | COMBINE_EQS: (823), (846) imply:
% 120.64/22.58 | | (847) all_815_0 = all_691_0
% 120.64/22.58 | |
% 120.64/22.58 | | COMBINE_EQS: (838), (846) imply:
% 120.64/22.58 | | (848) all_815_0 = one
% 120.64/22.58 | |
% 120.64/22.58 | | COMBINE_EQS: (847), (848) imply:
% 120.64/22.58 | | (849) all_691_0 = one
% 120.64/22.58 | |
% 120.64/22.58 | | SIMP: (849) implies:
% 120.64/22.58 | | (850) all_691_0 = one
% 120.64/22.58 | |
% 120.64/22.58 | | COMBINE_EQS: (822), (840) imply:
% 120.64/22.58 | | (851) all_691_0 = all_68_2
% 120.64/22.58 | |
% 120.64/22.58 | | SIMP: (851) implies:
% 120.64/22.58 | | (852) all_691_0 = all_68_2
% 120.64/22.58 | |
% 120.64/22.58 | | COMBINE_EQS: (821), (850) imply:
% 120.64/22.58 | | (853) all_591_0 = one
% 120.64/22.58 | |
% 120.64/22.58 | | COMBINE_EQS: (821), (852) imply:
% 120.64/22.58 | | (854) all_591_0 = all_68_2
% 120.64/22.58 | |
% 120.64/22.58 | | COMBINE_EQS: (853), (854) imply:
% 120.64/22.58 | | (855) all_68_2 = one
% 120.64/22.58 | |
% 120.64/22.58 | | SIMP: (855) implies:
% 120.64/22.58 | | (856) all_68_2 = one
% 120.64/22.58 | |
% 120.64/22.58 | | REDUCE: (807), (834), (856) imply:
% 120.64/22.58 | | (857) addition(all_1191_0, one) = all_74_2
% 120.64/22.58 | |
% 120.64/22.58 | | REDUCE: (809), (856) imply:
% 120.64/22.58 | | (858) addition(all_24_0, one) = all_791_0
% 120.64/22.58 | |
% 120.64/22.58 | | BETA: splitting (771) gives:
% 120.64/22.58 | |
% 120.64/22.58 | | Case 1:
% 120.64/22.58 | | |
% 120.64/22.58 | | | (859) all_74_2 = all_68_2
% 120.64/22.58 | | |
% 120.64/22.58 | | | COMBINE_EQS: (856), (859) imply:
% 120.64/22.58 | | | (860) all_74_2 = one
% 120.64/22.58 | | |
% 120.64/22.58 | | | REDUCE: (767), (860) imply:
% 120.64/22.58 | | | (861) addition(all_24_0, one) = all_24_0
% 120.64/22.58 | | |
% 120.64/22.58 | | | GROUND_INST: instantiating (22) with one, all_791_0, one, all_24_0,
% 120.64/22.58 | | | simplifying with (36), (858) gives:
% 120.64/22.58 | | | (862) all_791_0 = one
% 120.64/22.58 | | |
% 120.64/22.58 | | | GROUND_INST: instantiating (22) with all_24_0, all_791_0, one, all_24_0,
% 120.64/22.58 | | | simplifying with (858), (861) gives:
% 120.64/22.58 | | | (863) all_791_0 = all_24_0
% 120.64/22.58 | | |
% 120.64/22.58 | | | COMBINE_EQS: (862), (863) imply:
% 120.64/22.58 | | | (864) all_24_0 = one
% 120.64/22.58 | | |
% 120.64/22.58 | | | REDUCE: (26), (864) imply:
% 120.64/22.58 | | | (865) $false
% 120.64/22.58 | | |
% 120.64/22.58 | | | CLOSE: (865) is inconsistent.
% 120.64/22.58 | | |
% 120.64/22.58 | | Case 2:
% 120.64/22.58 | | |
% 120.64/22.58 | | | (866) ~ (all_74_2 = all_68_2)
% 120.64/22.58 | | |
% 120.64/22.58 | | | REDUCE: (856), (866) imply:
% 120.64/22.58 | | | (867) ~ (all_74_2 = one)
% 120.64/22.58 | | |
% 120.64/22.58 | | | GROUND_INST: instantiating (22) with one, all_74_2, one, all_1191_0,
% 120.64/22.58 | | | simplifying with (804), (857) gives:
% 120.64/22.58 | | | (868) all_74_2 = one
% 120.64/22.58 | | |
% 120.64/22.58 | | | REDUCE: (867), (868) imply:
% 120.64/22.58 | | | (869) $false
% 120.64/22.58 | | |
% 120.64/22.58 | | | CLOSE: (869) is inconsistent.
% 120.64/22.58 | | |
% 120.64/22.58 | | End of split
% 120.64/22.58 | |
% 120.64/22.59 | Case 2:
% 120.64/22.59 | |
% 120.64/22.59 | | (870) ~ (all_390_3 = 0) & leq(zero, zero) = all_390_3
% 120.64/22.59 | |
% 120.64/22.59 | | ALPHA: (870) implies:
% 120.64/22.59 | | (871) ~ (all_390_3 = 0)
% 120.64/22.59 | | (872) leq(zero, zero) = all_390_3
% 120.64/22.59 | |
% 120.64/22.59 | | GROUND_INST: instantiating (24) with 0, all_390_3, zero, zero, simplifying
% 120.64/22.59 | | with (189), (872) gives:
% 120.64/22.59 | | (873) all_390_3 = 0
% 120.64/22.59 | |
% 120.64/22.59 | | REDUCE: (871), (873) imply:
% 120.64/22.59 | | (874) $false
% 120.64/22.59 | |
% 120.64/22.59 | | CLOSE: (874) is inconsistent.
% 120.64/22.59 | |
% 120.64/22.59 | End of split
% 120.64/22.59 |
% 120.64/22.59 End of proof
% 120.64/22.59 % SZS output end Proof for theBenchmark
% 120.64/22.59
% 120.64/22.59 21983ms
%------------------------------------------------------------------------------