TSTP Solution File: KLE139+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE139+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 : n007.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 05:34:38 EDT 2023
% Result : Theorem 20.72s 3.54s
% Output : Proof 52.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE139+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 11:04:28 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.44/0.62 ________ _____
% 0.44/0.62 ___ __ \_________(_)________________________________
% 0.44/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.44/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.44/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.44/0.62
% 0.44/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.44/0.62 (2023-06-19)
% 0.44/0.62
% 0.44/0.62 (c) Philipp Rümmer, 2009-2023
% 0.44/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.44/0.62 Amanda Stjerna.
% 0.44/0.62 Free software under BSD-3-Clause.
% 0.44/0.62
% 0.44/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.44/0.62
% 0.44/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.61/0.64 Running up to 7 provers in parallel.
% 0.61/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.61/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.61/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.61/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.61/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.61/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.61/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.52/1.15 Prover 1: Preprocessing ...
% 2.52/1.15 Prover 4: Preprocessing ...
% 3.10/1.23 Prover 5: Preprocessing ...
% 3.10/1.23 Prover 6: Preprocessing ...
% 3.10/1.23 Prover 3: Preprocessing ...
% 3.10/1.23 Prover 2: Preprocessing ...
% 3.10/1.23 Prover 0: Preprocessing ...
% 5.37/1.55 Prover 6: Constructing countermodel ...
% 5.69/1.58 Prover 3: Constructing countermodel ...
% 5.69/1.61 Prover 1: Constructing countermodel ...
% 5.69/1.61 Prover 4: Constructing countermodel ...
% 5.69/1.63 Prover 5: Proving ...
% 5.69/1.64 Prover 0: Proving ...
% 6.98/1.75 Prover 3: gave up
% 6.98/1.75 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.98/1.75 Prover 1: gave up
% 7.09/1.77 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.09/1.78 Prover 2: Proving ...
% 7.09/1.81 Prover 6: gave up
% 7.50/1.82 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 7.50/1.82 Prover 7: Preprocessing ...
% 7.50/1.82 Prover 8: Preprocessing ...
% 7.50/1.85 Prover 9: Preprocessing ...
% 7.81/1.92 Prover 8: Warning: ignoring some quantifiers
% 7.81/1.93 Prover 8: Constructing countermodel ...
% 8.80/1.99 Prover 7: Constructing countermodel ...
% 8.80/2.00 Prover 9: Constructing countermodel ...
% 9.38/2.09 Prover 8: gave up
% 9.38/2.10 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.82/2.14 Prover 10: Preprocessing ...
% 10.86/2.27 Prover 10: Constructing countermodel ...
% 11.58/2.36 Prover 10: gave up
% 11.58/2.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.58/2.39 Prover 11: Preprocessing ...
% 13.11/2.55 Prover 11: Constructing countermodel ...
% 20.72/3.54 Prover 0: proved (2892ms)
% 20.72/3.54
% 20.72/3.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.72/3.54
% 20.72/3.54 Prover 9: stopped
% 20.72/3.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 20.72/3.54 Prover 5: stopped
% 20.72/3.54 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 20.72/3.55 Prover 2: stopped
% 20.72/3.55 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 20.72/3.57 Prover 19: Preprocessing ...
% 20.72/3.57 Prover 16: Preprocessing ...
% 20.72/3.58 Prover 13: Preprocessing ...
% 21.32/3.64 Prover 16: Warning: ignoring some quantifiers
% 21.32/3.65 Prover 16: Constructing countermodel ...
% 21.32/3.66 Prover 19: Warning: ignoring some quantifiers
% 21.78/3.67 Prover 19: Constructing countermodel ...
% 21.78/3.70 Prover 13: Warning: ignoring some quantifiers
% 21.78/3.71 Prover 13: Constructing countermodel ...
% 21.78/3.73 Prover 19: gave up
% 21.78/3.75 Prover 13: gave up
% 50.91/7.84 Prover 11: Found proof (size 460)
% 50.91/7.84 Prover 11: proved (5476ms)
% 50.91/7.85 Prover 7: stopped
% 50.91/7.85 Prover 16: stopped
% 50.91/7.85 Prover 4: stopped
% 50.91/7.85
% 50.91/7.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.91/7.85
% 51.63/8.03 % SZS output start Proof for theBenchmark
% 51.63/8.03 Assumptions after simplification:
% 51.63/8.03 ---------------------------------
% 51.63/8.03
% 51.63/8.03 (additive_associativity)
% 51.74/8.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 51.74/8.06 (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 51.74/8.06 | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 & addition(v1, v0) = v5 &
% 51.74/8.06 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 51.74/8.06 : ! [v4: $i] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~
% 51.74/8.06 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 &
% 51.74/8.06 addition(v2, v1) = v5 & $i(v5) & $i(v4)))
% 51.74/8.06
% 51.74/8.06 (additive_commutativity)
% 51.74/8.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~
% 51.74/8.06 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 51.74/8.06 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 51.74/8.06 (addition(v1, v0) = v2 & $i(v2)))
% 51.74/8.06
% 51.74/8.06 (additive_identity)
% 51.74/8.07 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1)
% 51.74/8.07 | ~ $i(v0))
% 51.74/8.07
% 51.74/8.07 (distributivity1)
% 51.74/8.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 51.74/8.07 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) |
% 51.74/8.07 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 51.74/8.07 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5))) &
% 51.74/8.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 51.74/8.07 (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~ $i(v2) | ~
% 51.74/8.07 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v0, v2) =
% 51.74/8.07 v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5)
% 51.74/8.07 & $i(v4)))
% 51.74/8.07
% 51.74/8.07 (distributivity2)
% 51.74/8.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 51.74/8.07 $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) |
% 51.74/8.07 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 51.74/8.07 : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5))) &
% 51.74/8.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 51.74/8.07 (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ $i(v2) | ~
% 51.74/8.07 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v1, v2) =
% 51.74/8.07 v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5)
% 51.74/8.07 & $i(v4)))
% 51.74/8.07
% 51.74/8.07 (goals)
% 51.74/8.07 $i(one) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 51.74/8.07 v1) & strong_iteration(v0) = v1 & multiplication(v1, v0) = v2 &
% 51.74/8.07 addition(v2, one) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 51.74/8.07
% 51.74/8.08 (infty_unfold1)
% 51.74/8.08 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~
% 51.74/8.08 $i(v0) | ? [v2: $i] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1
% 51.74/8.08 & $i(v2) & $i(v1)))
% 51.74/8.08
% 51.74/8.08 (isolation)
% 51.74/8.08 $i(zero) & ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~
% 51.74/8.08 $i(v0) | ? [v2: $i] : ? [v3: $i] : (star(v0) = v2 & multiplication(v1,
% 51.74/8.08 zero) = v3 & addition(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & !
% 51.74/8.08 [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 51.74/8.08 [v3: $i] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 &
% 51.74/8.08 addition(v1, v3) = v2 & $i(v3) & $i(v2)))
% 51.74/8.08
% 51.74/8.08 (left_annihilation)
% 51.74/8.08 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero,
% 51.74/8.08 v0) = v1) | ~ $i(v0))
% 51.74/8.08
% 51.74/8.08 (multiplicative_associativity)
% 51.74/8.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 51.74/8.08 (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ $i(v2)
% 51.74/8.08 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1, v2) = v5 &
% 51.74/8.08 multiplication(v0, v5) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1:
% 51.74/8.08 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (multiplication(v1, v2)
% 51.74/8.08 = v3) | ~ (multiplication(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 51.74/8.08 $i(v0) | ? [v5: $i] : (multiplication(v5, v2) = v4 & multiplication(v0, v1)
% 51.74/8.08 = v5 & $i(v5) & $i(v4)))
% 51.74/8.08
% 51.74/8.08 (multiplicative_left_identity)
% 51.74/8.08 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(one, v0) =
% 51.74/8.08 v1) | ~ $i(v0))
% 51.74/8.08
% 51.74/8.08 (multiplicative_right_identity)
% 51.74/8.08 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 51.74/8.08 v1) | ~ $i(v0))
% 51.74/8.08
% 51.74/8.08 (star_unfold1)
% 51.74/8.08 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ?
% 51.74/8.08 [v2: $i] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1 & $i(v2) &
% 51.74/8.08 $i(v1)))
% 51.74/8.08
% 51.74/8.08 (star_unfold2)
% 51.74/8.09 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ?
% 51.74/8.09 [v2: $i] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1 & $i(v2) &
% 51.74/8.09 $i(v1)))
% 51.74/8.09
% 51.74/8.09 (function-axioms)
% 51.74/8.09 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 51.74/8.09 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 51.74/8.09 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 51.74/8.09 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 51.74/8.09 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 51.74/8.09 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 51.74/8.09 [v2: $i] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~
% 51.74/8.09 (strong_iteration(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 51.74/8.09 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0))
% 51.74/8.09
% 51.74/8.09 Further assumptions not needed in the proof:
% 51.74/8.09 --------------------------------------------
% 51.74/8.09 idempotence, infty_coinduction, order, star_induction1, star_induction2
% 51.74/8.09
% 51.74/8.09 Those formulas are unsatisfiable:
% 51.74/8.09 ---------------------------------
% 51.74/8.09
% 51.74/8.09 Begin of proof
% 51.74/8.09 |
% 51.74/8.09 | ALPHA: (additive_commutativity) implies:
% 51.74/8.09 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) |
% 51.74/8.09 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2)))
% 51.74/8.09 |
% 51.74/8.09 | ALPHA: (additive_associativity) implies:
% 51.74/8.09 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 51.74/8.09 | ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~ $i(v2) |
% 51.74/8.09 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 &
% 51.74/8.09 | addition(v2, v1) = v5 & $i(v5) & $i(v4)))
% 51.74/8.09 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 51.74/8.09 | ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) |
% 51.74/8.09 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 &
% 51.74/8.09 | addition(v1, v0) = v5 & $i(v5) & $i(v4)))
% 51.74/8.09 |
% 51.74/8.09 | ALPHA: (additive_identity) implies:
% 51.74/8.10 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, zero) = v1) |
% 51.74/8.10 | ~ $i(v0))
% 51.74/8.10 |
% 51.74/8.10 | ALPHA: (multiplicative_associativity) implies:
% 51.74/8.10 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 51.74/8.10 | ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) |
% 51.74/8.10 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v5,
% 51.74/8.10 | v2) = v4 & multiplication(v0, v1) = v5 & $i(v5) & $i(v4)))
% 51.74/8.10 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 51.74/8.10 | ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) |
% 51.74/8.10 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1,
% 51.74/8.10 | v2) = v5 & multiplication(v0, v5) = v4 & $i(v5) & $i(v4)))
% 51.74/8.10 |
% 51.74/8.10 | ALPHA: (multiplicative_right_identity) implies:
% 51.74/8.10 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 51.74/8.10 | v1) | ~ $i(v0))
% 51.74/8.10 |
% 51.74/8.10 | ALPHA: (multiplicative_left_identity) implies:
% 51.74/8.10 | (8) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(one, v0) =
% 51.74/8.10 | v1) | ~ $i(v0))
% 51.74/8.10 |
% 51.74/8.10 | ALPHA: (distributivity1) implies:
% 51.74/8.10 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 51.74/8.10 | ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~
% 51.74/8.10 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] :
% 51.74/8.10 | (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 &
% 51.74/8.10 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4)))
% 51.74/8.10 |
% 51.74/8.10 | ALPHA: (distributivity2) implies:
% 51.74/8.10 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 51.74/8.10 | ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~
% 51.74/8.10 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] :
% 51.74/8.10 | (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 &
% 51.74/8.10 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4)))
% 51.74/8.10 |
% 51.74/8.10 | ALPHA: (left_annihilation) implies:
% 51.74/8.10 | (11) ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero, v0)
% 51.74/8.10 | = v1) | ~ $i(v0))
% 51.74/8.10 |
% 51.74/8.10 | ALPHA: (star_unfold1) implies:
% 51.74/8.10 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2:
% 51.74/8.10 | $i] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1 &
% 51.74/8.10 | $i(v2) & $i(v1)))
% 51.74/8.10 |
% 51.74/8.10 | ALPHA: (star_unfold2) implies:
% 51.74/8.10 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2:
% 51.74/8.10 | $i] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1 &
% 51.74/8.10 | $i(v2) & $i(v1)))
% 51.74/8.10 |
% 51.74/8.10 | ALPHA: (infty_unfold1) implies:
% 51.74/8.10 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~
% 51.74/8.10 | $i(v0) | ? [v2: $i] : (multiplication(v0, v1) = v2 & addition(v2,
% 51.74/8.10 | one) = v1 & $i(v2) & $i(v1)))
% 51.74/8.10 |
% 51.74/8.10 | ALPHA: (isolation) implies:
% 51.74/8.11 | (15) $i(zero)
% 51.74/8.11 | (16) ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~
% 51.74/8.11 | $i(v0) | ? [v2: $i] : ? [v3: $i] : (star(v0) = v2 &
% 51.74/8.11 | multiplication(v1, zero) = v3 & addition(v2, v3) = v1 & $i(v3) &
% 51.74/8.11 | $i(v2) & $i(v1)))
% 51.74/8.11 |
% 51.74/8.11 | ALPHA: (goals) implies:
% 51.74/8.11 | (17) $i(one)
% 51.74/8.11 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v1)
% 51.74/8.11 | & strong_iteration(v0) = v1 & multiplication(v1, v0) = v2 &
% 51.74/8.11 | addition(v2, one) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 51.74/8.11 |
% 51.74/8.11 | ALPHA: (function-axioms) implies:
% 51.74/8.11 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 51.74/8.11 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 51.74/8.11 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 51.74/8.11 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 51.74/8.11 |
% 51.74/8.11 | DELTA: instantiating (18) with fresh symbols all_22_0, all_22_1, all_22_2,
% 51.74/8.11 | all_22_3 gives:
% 51.74/8.11 | (21) ~ (all_22_0 = all_22_2) & strong_iteration(all_22_3) = all_22_2 &
% 51.74/8.11 | multiplication(all_22_2, all_22_3) = all_22_1 & addition(all_22_1,
% 51.74/8.11 | one) = all_22_0 & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) &
% 51.74/8.11 | $i(all_22_3)
% 51.74/8.11 |
% 51.74/8.11 | ALPHA: (21) implies:
% 51.74/8.11 | (22) ~ (all_22_0 = all_22_2)
% 51.74/8.11 | (23) $i(all_22_3)
% 51.74/8.11 | (24) $i(all_22_1)
% 51.74/8.11 | (25) addition(all_22_1, one) = all_22_0
% 51.74/8.11 | (26) multiplication(all_22_2, all_22_3) = all_22_1
% 51.74/8.11 | (27) strong_iteration(all_22_3) = all_22_2
% 51.74/8.11 |
% 51.74/8.11 | GROUND_INST: instantiating (1) with one, all_22_1, all_22_0, simplifying with
% 51.74/8.11 | (17), (24), (25) gives:
% 51.74/8.11 | (28) addition(one, all_22_1) = all_22_0 & $i(all_22_0)
% 51.74/8.11 |
% 51.74/8.11 | ALPHA: (28) implies:
% 51.74/8.11 | (29) addition(one, all_22_1) = all_22_0
% 51.74/8.11 |
% 51.74/8.11 | GROUND_INST: instantiating (16) with all_22_3, all_22_2, simplifying with
% 51.74/8.11 | (23), (27) gives:
% 51.74/8.11 | (30) ? [v0: $i] : ? [v1: $i] : (star(all_22_3) = v0 &
% 51.74/8.11 | multiplication(all_22_2, zero) = v1 & addition(v0, v1) = all_22_2 &
% 51.74/8.11 | $i(v1) & $i(v0) & $i(all_22_2))
% 51.74/8.11 |
% 51.74/8.11 | GROUND_INST: instantiating (14) with all_22_3, all_22_2, simplifying with
% 51.74/8.11 | (23), (27) gives:
% 51.74/8.11 | (31) ? [v0: $i] : (multiplication(all_22_3, all_22_2) = v0 & addition(v0,
% 51.74/8.11 | one) = all_22_2 & $i(v0) & $i(all_22_2))
% 51.74/8.11 |
% 51.74/8.11 | DELTA: instantiating (31) with fresh symbol all_30_0 gives:
% 51.74/8.11 | (32) multiplication(all_22_3, all_22_2) = all_30_0 & addition(all_30_0,
% 51.74/8.11 | one) = all_22_2 & $i(all_30_0) & $i(all_22_2)
% 51.74/8.11 |
% 51.74/8.11 | ALPHA: (32) implies:
% 51.74/8.11 | (33) $i(all_30_0)
% 51.74/8.12 | (34) addition(all_30_0, one) = all_22_2
% 51.74/8.12 | (35) multiplication(all_22_3, all_22_2) = all_30_0
% 51.74/8.12 |
% 51.74/8.12 | DELTA: instantiating (30) with fresh symbols all_32_0, all_32_1 gives:
% 51.74/8.12 | (36) star(all_22_3) = all_32_1 & multiplication(all_22_2, zero) = all_32_0
% 51.74/8.12 | & addition(all_32_1, all_32_0) = all_22_2 & $i(all_32_0) &
% 51.74/8.12 | $i(all_32_1) & $i(all_22_2)
% 51.74/8.12 |
% 51.74/8.12 | ALPHA: (36) implies:
% 51.74/8.12 | (37) $i(all_32_1)
% 51.74/8.12 | (38) $i(all_32_0)
% 51.74/8.12 | (39) addition(all_32_1, all_32_0) = all_22_2
% 51.74/8.12 | (40) multiplication(all_22_2, zero) = all_32_0
% 51.74/8.12 | (41) star(all_22_3) = all_32_1
% 51.74/8.12 |
% 51.74/8.12 | GROUND_INST: instantiating (10) with all_30_0, one, all_22_3, all_22_2,
% 51.74/8.12 | all_22_1, simplifying with (17), (23), (26), (33), (34) gives:
% 51.74/8.12 | (42) ? [v0: $i] : ? [v1: $i] : (multiplication(all_30_0, all_22_3) = v0 &
% 51.74/8.12 | multiplication(one, all_22_3) = v1 & addition(v0, v1) = all_22_1 &
% 51.74/8.12 | $i(v1) & $i(v0) & $i(all_22_1))
% 51.74/8.12 |
% 51.74/8.12 | GROUND_INST: instantiating (1) with one, all_30_0, all_22_2, simplifying with
% 51.74/8.12 | (17), (33), (34) gives:
% 51.74/8.12 | (43) addition(one, all_30_0) = all_22_2 & $i(all_22_2)
% 51.74/8.12 |
% 51.74/8.12 | ALPHA: (43) implies:
% 51.74/8.12 | (44) addition(one, all_30_0) = all_22_2
% 51.74/8.12 |
% 51.74/8.12 | GROUND_INST: instantiating (10) with all_32_1, all_32_0, all_22_3, all_22_2,
% 51.74/8.12 | all_22_1, simplifying with (23), (26), (37), (38), (39) gives:
% 51.74/8.12 | (45) ? [v0: $i] : ? [v1: $i] : (multiplication(all_32_0, all_22_3) = v1 &
% 51.74/8.12 | multiplication(all_32_1, all_22_3) = v0 & addition(v0, v1) =
% 51.74/8.12 | all_22_1 & $i(v1) & $i(v0) & $i(all_22_1))
% 51.74/8.12 |
% 51.74/8.12 | GROUND_INST: instantiating (1) with all_32_0, all_32_1, all_22_2, simplifying
% 51.74/8.12 | with (37), (38), (39) gives:
% 51.74/8.12 | (46) addition(all_32_0, all_32_1) = all_22_2 & $i(all_22_2)
% 51.74/8.12 |
% 51.74/8.12 | ALPHA: (46) implies:
% 51.74/8.12 | (47) $i(all_22_2)
% 51.74/8.12 | (48) addition(all_32_0, all_32_1) = all_22_2
% 51.74/8.12 |
% 51.74/8.12 | GROUND_INST: instantiating (9) with all_22_3, all_32_1, all_32_0, all_22_2,
% 51.74/8.12 | all_30_0, simplifying with (23), (35), (37), (38), (39) gives:
% 51.74/8.12 | (49) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_3, all_32_0) = v1 &
% 51.74/8.12 | multiplication(all_22_3, all_32_1) = v0 & addition(v0, v1) =
% 51.74/8.12 | all_30_0 & $i(v1) & $i(v0) & $i(all_30_0))
% 51.74/8.12 |
% 51.74/8.12 | GROUND_INST: instantiating (9) with all_22_3, all_30_0, one, all_22_2,
% 51.74/8.12 | all_30_0, simplifying with (17), (23), (33), (34), (35) gives:
% 51.74/8.12 | (50) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_3, all_30_0) = v0 &
% 51.74/8.12 | multiplication(all_22_3, one) = v1 & addition(v0, v1) = all_30_0 &
% 51.74/8.12 | $i(v1) & $i(v0))
% 51.74/8.12 |
% 51.74/8.12 | GROUND_INST: instantiating (10) with all_32_1, all_32_0, zero, all_22_2,
% 51.74/8.12 | all_32_0, simplifying with (15), (37), (38), (39), (40) gives:
% 51.74/8.13 | (51) ? [v0: $i] : ? [v1: $i] : (multiplication(all_32_0, zero) = v1 &
% 51.74/8.13 | multiplication(all_32_1, zero) = v0 & addition(v0, v1) = all_32_0 &
% 51.74/8.13 | $i(v1) & $i(v0))
% 51.74/8.13 |
% 51.74/8.13 | GROUND_INST: instantiating (10) with all_30_0, one, zero, all_22_2, all_32_0,
% 51.74/8.13 | simplifying with (15), (17), (33), (34), (40) gives:
% 51.74/8.13 | (52) ? [v0: $i] : ? [v1: $i] : (multiplication(all_30_0, zero) = v0 &
% 51.74/8.13 | multiplication(one, zero) = v1 & addition(v0, v1) = all_32_0 &
% 51.74/8.13 | $i(v1) & $i(v0) & $i(all_32_0))
% 51.74/8.13 |
% 51.74/8.13 | GROUND_INST: instantiating (13) with all_22_3, all_32_1, simplifying with
% 51.74/8.13 | (23), (41) gives:
% 51.74/8.13 | (53) ? [v0: $i] : (multiplication(all_32_1, all_22_3) = v0 & addition(one,
% 51.74/8.13 | v0) = all_32_1 & $i(v0) & $i(all_32_1))
% 51.74/8.13 |
% 51.74/8.13 | GROUND_INST: instantiating (12) with all_22_3, all_32_1, simplifying with
% 51.74/8.13 | (23), (41) gives:
% 52.10/8.13 | (54) ? [v0: $i] : (multiplication(all_22_3, all_32_1) = v0 & addition(one,
% 52.10/8.13 | v0) = all_32_1 & $i(v0) & $i(all_32_1))
% 52.10/8.13 |
% 52.10/8.13 | DELTA: instantiating (54) with fresh symbol all_43_0 gives:
% 52.10/8.13 | (55) multiplication(all_22_3, all_32_1) = all_43_0 & addition(one,
% 52.10/8.13 | all_43_0) = all_32_1 & $i(all_43_0) & $i(all_32_1)
% 52.10/8.13 |
% 52.10/8.13 | ALPHA: (55) implies:
% 52.10/8.13 | (56) addition(one, all_43_0) = all_32_1
% 52.10/8.13 | (57) multiplication(all_22_3, all_32_1) = all_43_0
% 52.10/8.13 |
% 52.10/8.13 | DELTA: instantiating (53) with fresh symbol all_45_0 gives:
% 52.10/8.13 | (58) multiplication(all_32_1, all_22_3) = all_45_0 & addition(one,
% 52.10/8.13 | all_45_0) = all_32_1 & $i(all_45_0) & $i(all_32_1)
% 52.10/8.13 |
% 52.10/8.13 | ALPHA: (58) implies:
% 52.10/8.13 | (59) addition(one, all_45_0) = all_32_1
% 52.10/8.13 | (60) multiplication(all_32_1, all_22_3) = all_45_0
% 52.10/8.13 |
% 52.10/8.13 | DELTA: instantiating (50) with fresh symbols all_47_0, all_47_1 gives:
% 52.10/8.13 | (61) multiplication(all_22_3, all_30_0) = all_47_1 &
% 52.10/8.13 | multiplication(all_22_3, one) = all_47_0 & addition(all_47_1,
% 52.10/8.13 | all_47_0) = all_30_0 & $i(all_47_0) & $i(all_47_1)
% 52.10/8.13 |
% 52.10/8.13 | ALPHA: (61) implies:
% 52.10/8.13 | (62) $i(all_47_1)
% 52.10/8.13 | (63) $i(all_47_0)
% 52.10/8.13 | (64) addition(all_47_1, all_47_0) = all_30_0
% 52.10/8.13 | (65) multiplication(all_22_3, one) = all_47_0
% 52.10/8.13 | (66) multiplication(all_22_3, all_30_0) = all_47_1
% 52.10/8.13 |
% 52.10/8.13 | DELTA: instantiating (51) with fresh symbols all_49_0, all_49_1 gives:
% 52.10/8.13 | (67) multiplication(all_32_0, zero) = all_49_0 & multiplication(all_32_1,
% 52.10/8.13 | zero) = all_49_1 & addition(all_49_1, all_49_0) = all_32_0 &
% 52.10/8.13 | $i(all_49_0) & $i(all_49_1)
% 52.10/8.13 |
% 52.10/8.13 | ALPHA: (67) implies:
% 52.10/8.13 | (68) $i(all_49_1)
% 52.10/8.13 | (69) $i(all_49_0)
% 52.10/8.13 | (70) addition(all_49_1, all_49_0) = all_32_0
% 52.10/8.13 | (71) multiplication(all_32_1, zero) = all_49_1
% 52.10/8.13 | (72) multiplication(all_32_0, zero) = all_49_0
% 52.10/8.13 |
% 52.10/8.13 | DELTA: instantiating (49) with fresh symbols all_51_0, all_51_1 gives:
% 52.10/8.13 | (73) multiplication(all_22_3, all_32_0) = all_51_0 &
% 52.10/8.13 | multiplication(all_22_3, all_32_1) = all_51_1 & addition(all_51_1,
% 52.10/8.13 | all_51_0) = all_30_0 & $i(all_51_0) & $i(all_51_1) & $i(all_30_0)
% 52.10/8.13 |
% 52.10/8.13 | ALPHA: (73) implies:
% 52.10/8.13 | (74) $i(all_51_1)
% 52.10/8.13 | (75) $i(all_51_0)
% 52.10/8.13 | (76) addition(all_51_1, all_51_0) = all_30_0
% 52.10/8.13 | (77) multiplication(all_22_3, all_32_1) = all_51_1
% 52.10/8.13 | (78) multiplication(all_22_3, all_32_0) = all_51_0
% 52.10/8.13 |
% 52.10/8.13 | DELTA: instantiating (52) with fresh symbols all_53_0, all_53_1 gives:
% 52.10/8.14 | (79) multiplication(all_30_0, zero) = all_53_1 & multiplication(one, zero)
% 52.10/8.14 | = all_53_0 & addition(all_53_1, all_53_0) = all_32_0 & $i(all_53_0) &
% 52.10/8.14 | $i(all_53_1) & $i(all_32_0)
% 52.10/8.14 |
% 52.10/8.14 | ALPHA: (79) implies:
% 52.10/8.14 | (80) $i(all_53_1)
% 52.10/8.14 | (81) $i(all_53_0)
% 52.10/8.14 | (82) addition(all_53_1, all_53_0) = all_32_0
% 52.10/8.14 | (83) multiplication(one, zero) = all_53_0
% 52.10/8.14 | (84) multiplication(all_30_0, zero) = all_53_1
% 52.10/8.14 |
% 52.10/8.14 | DELTA: instantiating (45) with fresh symbols all_55_0, all_55_1 gives:
% 52.10/8.14 | (85) multiplication(all_32_0, all_22_3) = all_55_0 &
% 52.10/8.14 | multiplication(all_32_1, all_22_3) = all_55_1 & addition(all_55_1,
% 52.10/8.14 | all_55_0) = all_22_1 & $i(all_55_0) & $i(all_55_1) & $i(all_22_1)
% 52.10/8.14 |
% 52.10/8.14 | ALPHA: (85) implies:
% 52.10/8.14 | (86) $i(all_55_1)
% 52.10/8.14 | (87) $i(all_55_0)
% 52.10/8.14 | (88) addition(all_55_1, all_55_0) = all_22_1
% 52.10/8.14 | (89) multiplication(all_32_1, all_22_3) = all_55_1
% 52.10/8.14 | (90) multiplication(all_32_0, all_22_3) = all_55_0
% 52.10/8.14 |
% 52.10/8.14 | DELTA: instantiating (42) with fresh symbols all_57_0, all_57_1 gives:
% 52.10/8.14 | (91) multiplication(all_30_0, all_22_3) = all_57_1 & multiplication(one,
% 52.10/8.14 | all_22_3) = all_57_0 & addition(all_57_1, all_57_0) = all_22_1 &
% 52.10/8.14 | $i(all_57_0) & $i(all_57_1) & $i(all_22_1)
% 52.10/8.14 |
% 52.10/8.14 | ALPHA: (91) implies:
% 52.10/8.14 | (92) multiplication(one, all_22_3) = all_57_0
% 52.10/8.14 | (93) multiplication(all_30_0, all_22_3) = all_57_1
% 52.10/8.14 |
% 52.10/8.14 | GROUND_INST: instantiating (20) with all_43_0, all_51_1, all_32_1, all_22_3,
% 52.10/8.14 | simplifying with (57), (77) gives:
% 52.10/8.14 | (94) all_51_1 = all_43_0
% 52.10/8.14 |
% 52.10/8.14 | GROUND_INST: instantiating (20) with all_45_0, all_55_1, all_22_3, all_32_1,
% 52.10/8.14 | simplifying with (60), (89) gives:
% 52.10/8.14 | (95) all_55_1 = all_45_0
% 52.10/8.14 |
% 52.10/8.14 | REDUCE: (88), (95) imply:
% 52.10/8.14 | (96) addition(all_45_0, all_55_0) = all_22_1
% 52.10/8.14 |
% 52.10/8.14 | REDUCE: (76), (94) imply:
% 52.10/8.14 | (97) addition(all_43_0, all_51_0) = all_30_0
% 52.10/8.14 |
% 52.10/8.14 | REDUCE: (86), (95) imply:
% 52.10/8.14 | (98) $i(all_45_0)
% 52.10/8.14 |
% 52.10/8.14 | REDUCE: (74), (94) imply:
% 52.10/8.14 | (99) $i(all_43_0)
% 52.10/8.14 |
% 52.10/8.14 | GROUND_INST: instantiating (10) with one, all_30_0, all_22_3, all_22_2,
% 52.10/8.14 | all_22_1, simplifying with (17), (23), (26), (33), (44) gives:
% 52.10/8.14 | (100) ? [v0: $i] : ? [v1: $i] : (multiplication(all_30_0, all_22_3) = v1
% 52.10/8.14 | & multiplication(one, all_22_3) = v0 & addition(v0, v1) = all_22_1
% 52.10/8.14 | & $i(v1) & $i(v0) & $i(all_22_1))
% 52.10/8.14 |
% 52.10/8.14 | GROUND_INST: instantiating (10) with one, all_30_0, zero, all_22_2, all_32_0,
% 52.10/8.14 | simplifying with (15), (17), (33), (40), (44) gives:
% 52.10/8.14 | (101) ? [v0: $i] : ? [v1: $i] : (multiplication(all_30_0, zero) = v1 &
% 52.10/8.14 | multiplication(one, zero) = v0 & addition(v0, v1) = all_32_0 &
% 52.10/8.14 | $i(v1) & $i(v0) & $i(all_32_0))
% 52.10/8.14 |
% 52.10/8.15 | GROUND_INST: instantiating (9) with all_22_3, one, all_30_0, all_22_2,
% 52.10/8.15 | all_30_0, simplifying with (17), (23), (33), (35), (44) gives:
% 52.10/8.15 | (102) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_3, all_30_0) = v1
% 52.10/8.15 | & multiplication(all_22_3, one) = v0 & addition(v0, v1) = all_30_0
% 52.10/8.15 | & $i(v1) & $i(v0))
% 52.10/8.15 |
% 52.10/8.15 | GROUND_INST: instantiating (3) with all_32_0, all_43_0, one, all_32_1,
% 52.10/8.15 | all_22_2, simplifying with (17), (38), (39), (56), (99) gives:
% 52.10/8.15 | (103) ? [v0: $i] : (addition(all_43_0, all_32_0) = v0 & addition(one, v0)
% 52.10/8.15 | = all_22_2 & $i(v0) & $i(all_22_2))
% 52.10/8.15 |
% 52.10/8.15 | GROUND_INST: instantiating (1) with all_45_0, one, all_32_1, simplifying with
% 52.10/8.15 | (17), (59), (98) gives:
% 52.10/8.15 | (104) addition(all_45_0, one) = all_32_1 & $i(all_32_1)
% 52.10/8.15 |
% 52.10/8.15 | GROUND_INST: instantiating (10) with all_32_0, all_32_1, all_22_3, all_22_2,
% 52.10/8.15 | all_22_1, simplifying with (23), (26), (37), (38), (48) gives:
% 52.10/8.15 | (105) ? [v0: $i] : ? [v1: $i] : (multiplication(all_32_0, all_22_3) = v0
% 52.10/8.15 | & multiplication(all_32_1, all_22_3) = v1 & addition(v0, v1) =
% 52.10/8.15 | all_22_1 & $i(v1) & $i(v0) & $i(all_22_1))
% 52.10/8.15 |
% 52.10/8.15 | GROUND_INST: instantiating (10) with all_32_0, all_32_1, zero, all_22_2,
% 52.10/8.15 | all_32_0, simplifying with (15), (37), (38), (40), (48) gives:
% 52.10/8.15 | (106) ? [v0: $i] : ? [v1: $i] : (multiplication(all_32_0, zero) = v0 &
% 52.10/8.15 | multiplication(all_32_1, zero) = v1 & addition(v0, v1) = all_32_0 &
% 52.10/8.15 | $i(v1) & $i(v0))
% 52.10/8.15 |
% 52.10/8.15 | GROUND_INST: instantiating (9) with all_22_3, all_32_0, all_32_1, all_22_2,
% 52.10/8.15 | all_30_0, simplifying with (23), (35), (37), (38), (48) gives:
% 52.10/8.15 | (107) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_3, all_32_0) = v0
% 52.10/8.15 | & multiplication(all_22_3, all_32_1) = v1 & addition(v0, v1) =
% 52.10/8.15 | all_30_0 & $i(v1) & $i(v0) & $i(all_30_0))
% 52.10/8.15 |
% 52.10/8.15 | GROUND_INST: instantiating (2) with all_45_0, one, all_32_0, all_32_1,
% 52.10/8.15 | all_22_2, simplifying with (17), (38), (48), (59), (98) gives:
% 52.10/8.15 | (108) ? [v0: $i] : (addition(v0, all_45_0) = all_22_2 & addition(all_32_0,
% 52.10/8.15 | one) = v0 & $i(v0) & $i(all_22_2))
% 52.10/8.15 |
% 52.10/8.15 | GROUND_INST: instantiating (2) with all_43_0, one, all_32_0, all_32_1,
% 52.10/8.15 | all_22_2, simplifying with (17), (38), (48), (56), (99) gives:
% 52.10/8.15 | (109) ? [v0: $i] : (addition(v0, all_43_0) = all_22_2 & addition(all_32_0,
% 52.10/8.15 | one) = v0 & $i(v0) & $i(all_22_2))
% 52.10/8.15 |
% 52.10/8.15 | GROUND_INST: instantiating (2) with all_51_0, all_43_0, one, all_30_0,
% 52.10/8.15 | all_22_2, simplifying with (17), (44), (75), (97), (99) gives:
% 52.10/8.15 | (110) ? [v0: $i] : (addition(v0, all_51_0) = all_22_2 & addition(one,
% 52.10/8.15 | all_43_0) = v0 & $i(v0) & $i(all_22_2))
% 52.10/8.15 |
% 52.10/8.15 | GROUND_INST: instantiating (2) with all_55_0, all_45_0, one, all_22_1,
% 52.10/8.15 | all_22_0, simplifying with (17), (29), (87), (96), (98) gives:
% 52.10/8.15 | (111) ? [v0: $i] : (addition(v0, all_55_0) = all_22_0 & addition(one,
% 52.10/8.15 | all_45_0) = v0 & $i(v0) & $i(all_22_0))
% 52.10/8.15 |
% 52.10/8.15 | GROUND_INST: instantiating (2) with all_49_0, all_49_1, all_32_1, all_32_0,
% 52.10/8.15 | all_22_2, simplifying with (37), (39), (68), (69), (70) gives:
% 52.10/8.15 | (112) ? [v0: $i] : (addition(v0, all_49_0) = all_22_2 & addition(all_32_1,
% 52.10/8.15 | all_49_1) = v0 & $i(v0) & $i(all_22_2))
% 52.10/8.15 |
% 52.10/8.15 | GROUND_INST: instantiating (3) with all_32_1, all_49_0, all_49_1, all_32_0,
% 52.10/8.15 | all_22_2, simplifying with (37), (48), (68), (69), (70) gives:
% 52.10/8.16 | (113) ? [v0: $i] : (addition(all_49_0, all_32_1) = v0 & addition(all_49_1,
% 52.10/8.16 | v0) = all_22_2 & $i(v0) & $i(all_22_2))
% 52.10/8.16 |
% 52.10/8.16 | GROUND_INST: instantiating (2) with all_53_0, all_53_1, all_32_1, all_32_0,
% 52.10/8.16 | all_22_2, simplifying with (37), (39), (80), (81), (82) gives:
% 52.10/8.16 | (114) ? [v0: $i] : (addition(v0, all_53_0) = all_22_2 & addition(all_32_1,
% 52.10/8.16 | all_53_1) = v0 & $i(v0) & $i(all_22_2))
% 52.10/8.16 |
% 52.10/8.16 | GROUND_INST: instantiating (3) with all_32_1, all_53_0, all_53_1, all_32_0,
% 52.10/8.16 | all_22_2, simplifying with (37), (48), (80), (81), (82) gives:
% 52.10/8.16 | (115) ? [v0: $i] : (addition(all_53_0, all_32_1) = v0 & addition(all_53_1,
% 52.10/8.16 | v0) = all_22_2 & $i(v0) & $i(all_22_2))
% 52.10/8.16 |
% 52.10/8.16 | GROUND_INST: instantiating (8) with zero, all_53_0, simplifying with (15),
% 52.10/8.16 | (83) gives:
% 52.10/8.16 | (116) all_53_0 = zero
% 52.10/8.16 |
% 52.10/8.16 | GROUND_INST: instantiating (8) with all_22_3, all_57_0, simplifying with (23),
% 52.10/8.16 | (92) gives:
% 52.10/8.16 | (117) all_57_0 = all_22_3
% 52.10/8.16 |
% 52.10/8.16 | GROUND_INST: instantiating (7) with all_22_3, all_47_0, simplifying with (23),
% 52.10/8.16 | (65) gives:
% 52.10/8.16 | (118) all_47_0 = all_22_3
% 52.10/8.16 |
% 52.10/8.16 | GROUND_INST: instantiating (5) with all_22_3, all_22_3, all_22_2, all_30_0,
% 52.10/8.16 | all_47_1, simplifying with (23), (35), (47), (66) gives:
% 52.10/8.16 | (119) ? [v0: $i] : (multiplication(v0, all_22_2) = all_47_1 &
% 52.10/8.16 | multiplication(all_22_3, all_22_3) = v0 & $i(v0) & $i(all_47_1))
% 52.10/8.16 |
% 52.10/8.16 | GROUND_INST: instantiating (9) with all_22_3, all_47_1, all_47_0, all_30_0,
% 52.10/8.16 | all_47_1, simplifying with (23), (62), (63), (64), (66) gives:
% 52.10/8.16 | (120) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_3, all_47_0) = v1
% 52.10/8.16 | & multiplication(all_22_3, all_47_1) = v0 & addition(v0, v1) =
% 52.10/8.16 | all_47_1 & $i(v1) & $i(v0))
% 52.10/8.16 |
% 52.10/8.16 | GROUND_INST: instantiating (9) with all_22_3, one, all_45_0, all_32_1,
% 52.10/8.16 | all_43_0, simplifying with (17), (23), (57), (59), (98) gives:
% 52.10/8.16 | (121) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_3, all_45_0) = v1
% 52.10/8.16 | & multiplication(all_22_3, one) = v0 & addition(v0, v1) = all_43_0
% 52.10/8.16 | & $i(v1) & $i(v0) & $i(all_43_0))
% 52.10/8.16 |
% 52.10/8.16 | GROUND_INST: instantiating (9) with all_22_3, one, all_43_0, all_32_1,
% 52.10/8.16 | all_43_0, simplifying with (17), (23), (56), (57), (99) gives:
% 52.10/8.16 | (122) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_3, all_43_0) = v1
% 52.10/8.16 | & multiplication(all_22_3, one) = v0 & addition(v0, v1) = all_43_0
% 52.10/8.16 | & $i(v1) & $i(v0))
% 52.10/8.16 |
% 52.10/8.16 | GROUND_INST: instantiating (5) with all_22_3, all_22_2, zero, all_32_0,
% 52.10/8.16 | all_51_0, simplifying with (15), (23), (40), (47), (78) gives:
% 52.10/8.16 | (123) ? [v0: $i] : (multiplication(v0, zero) = all_51_0 &
% 52.10/8.16 | multiplication(all_22_3, all_22_2) = v0 & $i(v0) & $i(all_51_0))
% 52.10/8.16 |
% 52.10/8.16 | GROUND_INST: instantiating (9) with all_22_3, all_53_1, all_53_0, all_32_0,
% 52.10/8.16 | all_51_0, simplifying with (23), (78), (80), (81), (82) gives:
% 52.10/8.16 | (124) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_3, all_53_0) = v1
% 52.10/8.16 | & multiplication(all_22_3, all_53_1) = v0 & addition(v0, v1) =
% 52.10/8.16 | all_51_0 & $i(v1) & $i(v0) & $i(all_51_0))
% 52.10/8.16 |
% 52.10/8.16 | GROUND_INST: instantiating (6) with all_22_3, all_22_2, zero, all_30_0,
% 52.10/8.16 | all_53_1, simplifying with (15), (23), (35), (47), (84) gives:
% 52.10/8.16 | (125) ? [v0: $i] : (multiplication(all_22_2, zero) = v0 &
% 52.10/8.16 | multiplication(all_22_3, v0) = all_53_1 & $i(v0) & $i(all_53_1))
% 52.10/8.16 |
% 52.10/8.16 | GROUND_INST: instantiating (10) with all_47_1, all_47_0, zero, all_30_0,
% 52.10/8.16 | all_53_1, simplifying with (15), (62), (63), (64), (84) gives:
% 52.10/8.16 | (126) ? [v0: $i] : ? [v1: $i] : (multiplication(all_47_0, zero) = v1 &
% 52.10/8.16 | multiplication(all_47_1, zero) = v0 & addition(v0, v1) = all_53_1 &
% 52.10/8.16 | $i(v1) & $i(v0) & $i(all_53_1))
% 52.10/8.16 |
% 52.10/8.16 | GROUND_INST: instantiating (10) with all_43_0, all_51_0, zero, all_30_0,
% 52.10/8.16 | all_53_1, simplifying with (15), (75), (84), (97), (99) gives:
% 52.10/8.16 | (127) ? [v0: $i] : ? [v1: $i] : (multiplication(all_51_0, zero) = v1 &
% 52.10/8.16 | multiplication(all_43_0, zero) = v0 & addition(v0, v1) = all_53_1 &
% 52.10/8.16 | $i(v1) & $i(v0) & $i(all_53_1))
% 52.10/8.16 |
% 52.10/8.17 | GROUND_INST: instantiating (10) with all_47_1, all_47_0, all_22_3, all_30_0,
% 52.10/8.17 | all_57_1, simplifying with (23), (62), (63), (64), (93) gives:
% 52.10/8.17 | (128) ? [v0: $i] : ? [v1: $i] : (multiplication(all_47_0, all_22_3) = v1
% 52.10/8.17 | & multiplication(all_47_1, all_22_3) = v0 & addition(v0, v1) =
% 52.10/8.17 | all_57_1 & $i(v1) & $i(v0) & $i(all_57_1))
% 52.10/8.17 |
% 52.10/8.17 | GROUND_INST: instantiating (10) with all_43_0, all_51_0, all_22_3, all_30_0,
% 52.10/8.17 | all_57_1, simplifying with (23), (75), (93), (97), (99) gives:
% 52.10/8.17 | (129) ? [v0: $i] : ? [v1: $i] : (multiplication(all_51_0, all_22_3) = v1
% 52.10/8.17 | & multiplication(all_43_0, all_22_3) = v0 & addition(v0, v1) =
% 52.10/8.17 | all_57_1 & $i(v1) & $i(v0) & $i(all_57_1))
% 52.10/8.17 |
% 52.10/8.17 | GROUND_INST: instantiating (10) with one, all_45_0, zero, all_32_1, all_49_1,
% 52.10/8.17 | simplifying with (15), (17), (59), (71), (98) gives:
% 52.10/8.17 | (130) ? [v0: $i] : ? [v1: $i] : (multiplication(all_45_0, zero) = v1 &
% 52.10/8.17 | multiplication(one, zero) = v0 & addition(v0, v1) = all_49_1 &
% 52.10/8.17 | $i(v1) & $i(v0) & $i(all_49_1))
% 52.10/8.17 |
% 52.10/8.17 | GROUND_INST: instantiating (10) with one, all_43_0, zero, all_32_1, all_49_1,
% 52.10/8.17 | simplifying with (15), (17), (56), (71), (99) gives:
% 52.10/8.17 | (131) ? [v0: $i] : ? [v1: $i] : (multiplication(all_43_0, zero) = v1 &
% 52.10/8.17 | multiplication(one, zero) = v0 & addition(v0, v1) = all_49_1 &
% 52.10/8.17 | $i(v1) & $i(v0) & $i(all_49_1))
% 52.10/8.17 |
% 52.10/8.17 | GROUND_INST: instantiating (10) with one, all_43_0, all_22_3, all_32_1,
% 52.10/8.17 | all_45_0, simplifying with (17), (23), (56), (60), (99) gives:
% 52.10/8.17 | (132) ? [v0: $i] : ? [v1: $i] : (multiplication(all_43_0, all_22_3) = v1
% 52.10/8.17 | & multiplication(one, all_22_3) = v0 & addition(v0, v1) = all_45_0
% 52.10/8.17 | & $i(v1) & $i(v0) & $i(all_45_0))
% 52.10/8.17 |
% 52.10/8.17 | GROUND_INST: instantiating (6) with all_22_2, zero, zero, all_32_0, all_49_0,
% 52.10/8.17 | simplifying with (15), (40), (47), (72) gives:
% 52.10/8.17 | (133) ? [v0: $i] : (multiplication(all_22_2, v0) = all_49_0 &
% 52.10/8.17 | multiplication(zero, zero) = v0 & $i(v0) & $i(all_49_0))
% 52.10/8.17 |
% 52.10/8.17 | GROUND_INST: instantiating (10) with all_53_1, all_53_0, zero, all_32_0,
% 52.10/8.17 | all_49_0, simplifying with (15), (72), (80), (81), (82) gives:
% 52.10/8.17 | (134) ? [v0: $i] : ? [v1: $i] : (multiplication(all_53_0, zero) = v1 &
% 52.10/8.17 | multiplication(all_53_1, zero) = v0 & addition(v0, v1) = all_49_0 &
% 52.10/8.17 | $i(v1) & $i(v0) & $i(all_49_0))
% 52.10/8.17 |
% 52.31/8.17 | GROUND_INST: instantiating (6) with all_22_2, zero, all_22_3, all_32_0,
% 52.31/8.17 | all_55_0, simplifying with (15), (23), (40), (47), (90) gives:
% 52.31/8.17 | (135) ? [v0: $i] : (multiplication(all_22_2, v0) = all_55_0 &
% 52.31/8.17 | multiplication(zero, all_22_3) = v0 & $i(v0) & $i(all_55_0))
% 52.31/8.17 |
% 52.31/8.17 | GROUND_INST: instantiating (10) with all_53_1, all_53_0, all_22_3, all_32_0,
% 52.31/8.17 | all_55_0, simplifying with (23), (80), (81), (82), (90) gives:
% 52.31/8.17 | (136) ? [v0: $i] : ? [v1: $i] : (multiplication(all_53_0, all_22_3) = v1
% 52.31/8.17 | & multiplication(all_53_1, all_22_3) = v0 & addition(v0, v1) =
% 52.31/8.17 | all_55_0 & $i(v1) & $i(v0) & $i(all_55_0))
% 52.31/8.17 |
% 52.31/8.17 | DELTA: instantiating (113) with fresh symbol all_72_0 gives:
% 52.31/8.17 | (137) addition(all_49_0, all_32_1) = all_72_0 & addition(all_49_1,
% 52.31/8.17 | all_72_0) = all_22_2 & $i(all_72_0) & $i(all_22_2)
% 52.31/8.17 |
% 52.31/8.17 | ALPHA: (137) implies:
% 52.31/8.17 | (138) addition(all_49_0, all_32_1) = all_72_0
% 52.31/8.17 |
% 52.31/8.17 | DELTA: instantiating (110) with fresh symbol all_78_0 gives:
% 52.31/8.17 | (139) addition(all_78_0, all_51_0) = all_22_2 & addition(one, all_43_0) =
% 52.31/8.17 | all_78_0 & $i(all_78_0) & $i(all_22_2)
% 52.31/8.17 |
% 52.31/8.17 | ALPHA: (139) implies:
% 52.31/8.17 | (140) $i(all_78_0)
% 52.31/8.17 | (141) addition(one, all_43_0) = all_78_0
% 52.31/8.17 | (142) addition(all_78_0, all_51_0) = all_22_2
% 52.31/8.17 |
% 52.31/8.17 | DELTA: instantiating (119) with fresh symbol all_80_0 gives:
% 52.31/8.17 | (143) multiplication(all_80_0, all_22_2) = all_47_1 &
% 52.31/8.17 | multiplication(all_22_3, all_22_3) = all_80_0 & $i(all_80_0) &
% 52.31/8.17 | $i(all_47_1)
% 52.31/8.17 |
% 52.31/8.17 | ALPHA: (143) implies:
% 52.31/8.17 | (144) multiplication(all_22_3, all_22_3) = all_80_0
% 52.31/8.17 | (145) multiplication(all_80_0, all_22_2) = all_47_1
% 52.31/8.17 |
% 52.31/8.17 | DELTA: instantiating (115) with fresh symbol all_82_0 gives:
% 52.31/8.17 | (146) addition(all_53_0, all_32_1) = all_82_0 & addition(all_53_1,
% 52.31/8.17 | all_82_0) = all_22_2 & $i(all_82_0) & $i(all_22_2)
% 52.31/8.17 |
% 52.31/8.17 | ALPHA: (146) implies:
% 52.31/8.17 | (147) addition(all_53_1, all_82_0) = all_22_2
% 52.31/8.17 | (148) addition(all_53_0, all_32_1) = all_82_0
% 52.31/8.17 |
% 52.31/8.17 | DELTA: instantiating (111) with fresh symbol all_84_0 gives:
% 52.31/8.17 | (149) addition(all_84_0, all_55_0) = all_22_0 & addition(one, all_45_0) =
% 52.31/8.17 | all_84_0 & $i(all_84_0) & $i(all_22_0)
% 52.31/8.17 |
% 52.31/8.17 | ALPHA: (149) implies:
% 52.31/8.18 | (150) addition(one, all_45_0) = all_84_0
% 52.31/8.18 | (151) addition(all_84_0, all_55_0) = all_22_0
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (103) with fresh symbol all_88_0 gives:
% 52.31/8.18 | (152) addition(all_43_0, all_32_0) = all_88_0 & addition(one, all_88_0) =
% 52.31/8.18 | all_22_2 & $i(all_88_0) & $i(all_22_2)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (152) implies:
% 52.31/8.18 | (153) $i(all_88_0)
% 52.31/8.18 | (154) addition(one, all_88_0) = all_22_2
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (135) with fresh symbol all_90_0 gives:
% 52.31/8.18 | (155) multiplication(all_22_2, all_90_0) = all_55_0 & multiplication(zero,
% 52.31/8.18 | all_22_3) = all_90_0 & $i(all_90_0) & $i(all_55_0)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (155) implies:
% 52.31/8.18 | (156) multiplication(zero, all_22_3) = all_90_0
% 52.31/8.18 | (157) multiplication(all_22_2, all_90_0) = all_55_0
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (125) with fresh symbol all_94_0 gives:
% 52.31/8.18 | (158) multiplication(all_22_2, zero) = all_94_0 & multiplication(all_22_3,
% 52.31/8.18 | all_94_0) = all_53_1 & $i(all_94_0) & $i(all_53_1)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (158) implies:
% 52.31/8.18 | (159) $i(all_94_0)
% 52.31/8.18 | (160) multiplication(all_22_3, all_94_0) = all_53_1
% 52.31/8.18 | (161) multiplication(all_22_2, zero) = all_94_0
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (123) with fresh symbol all_96_0 gives:
% 52.31/8.18 | (162) multiplication(all_96_0, zero) = all_51_0 & multiplication(all_22_3,
% 52.31/8.18 | all_22_2) = all_96_0 & $i(all_96_0) & $i(all_51_0)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (162) implies:
% 52.31/8.18 | (163) multiplication(all_22_3, all_22_2) = all_96_0
% 52.31/8.18 | (164) multiplication(all_96_0, zero) = all_51_0
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (133) with fresh symbol all_98_0 gives:
% 52.31/8.18 | (165) multiplication(all_22_2, all_98_0) = all_49_0 & multiplication(zero,
% 52.31/8.18 | zero) = all_98_0 & $i(all_98_0) & $i(all_49_0)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (165) implies:
% 52.31/8.18 | (166) multiplication(zero, zero) = all_98_0
% 52.31/8.18 | (167) multiplication(all_22_2, all_98_0) = all_49_0
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (112) with fresh symbol all_102_0 gives:
% 52.31/8.18 | (168) addition(all_102_0, all_49_0) = all_22_2 & addition(all_32_1,
% 52.31/8.18 | all_49_1) = all_102_0 & $i(all_102_0) & $i(all_22_2)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (168) implies:
% 52.31/8.18 | (169) addition(all_32_1, all_49_1) = all_102_0
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (109) with fresh symbol all_108_0 gives:
% 52.31/8.18 | (170) addition(all_108_0, all_43_0) = all_22_2 & addition(all_32_0, one) =
% 52.31/8.18 | all_108_0 & $i(all_108_0) & $i(all_22_2)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (170) implies:
% 52.31/8.18 | (171) addition(all_32_0, one) = all_108_0
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (114) with fresh symbol all_110_0 gives:
% 52.31/8.18 | (172) addition(all_110_0, all_53_0) = all_22_2 & addition(all_32_1,
% 52.31/8.18 | all_53_1) = all_110_0 & $i(all_110_0) & $i(all_22_2)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (172) implies:
% 52.31/8.18 | (173) addition(all_32_1, all_53_1) = all_110_0
% 52.31/8.18 | (174) addition(all_110_0, all_53_0) = all_22_2
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (108) with fresh symbol all_112_0 gives:
% 52.31/8.18 | (175) addition(all_112_0, all_45_0) = all_22_2 & addition(all_32_0, one) =
% 52.31/8.18 | all_112_0 & $i(all_112_0) & $i(all_22_2)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (175) implies:
% 52.31/8.18 | (176) addition(all_32_0, one) = all_112_0
% 52.31/8.18 | (177) addition(all_112_0, all_45_0) = all_22_2
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (120) with fresh symbols all_116_0, all_116_1 gives:
% 52.31/8.18 | (178) multiplication(all_22_3, all_47_0) = all_116_0 &
% 52.31/8.18 | multiplication(all_22_3, all_47_1) = all_116_1 & addition(all_116_1,
% 52.31/8.18 | all_116_0) = all_47_1 & $i(all_116_0) & $i(all_116_1)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (178) implies:
% 52.31/8.18 | (179) $i(all_116_0)
% 52.31/8.18 | (180) multiplication(all_22_3, all_47_0) = all_116_0
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (106) with fresh symbols all_118_0, all_118_1 gives:
% 52.31/8.18 | (181) multiplication(all_32_0, zero) = all_118_1 & multiplication(all_32_1,
% 52.31/8.18 | zero) = all_118_0 & addition(all_118_1, all_118_0) = all_32_0 &
% 52.31/8.18 | $i(all_118_0) & $i(all_118_1)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (181) implies:
% 52.31/8.18 | (182) multiplication(all_32_0, zero) = all_118_1
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (102) with fresh symbols all_122_0, all_122_1 gives:
% 52.31/8.18 | (183) multiplication(all_22_3, all_30_0) = all_122_0 &
% 52.31/8.18 | multiplication(all_22_3, one) = all_122_1 & addition(all_122_1,
% 52.31/8.18 | all_122_0) = all_30_0 & $i(all_122_0) & $i(all_122_1)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (183) implies:
% 52.31/8.18 | (184) $i(all_122_1)
% 52.31/8.18 | (185) multiplication(all_22_3, one) = all_122_1
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (122) with fresh symbols all_126_0, all_126_1 gives:
% 52.31/8.18 | (186) multiplication(all_22_3, all_43_0) = all_126_0 &
% 52.31/8.18 | multiplication(all_22_3, one) = all_126_1 & addition(all_126_1,
% 52.31/8.18 | all_126_0) = all_43_0 & $i(all_126_0) & $i(all_126_1)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (186) implies:
% 52.31/8.18 | (187) multiplication(all_22_3, one) = all_126_1
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (129) with fresh symbols all_128_0, all_128_1 gives:
% 52.31/8.18 | (188) multiplication(all_51_0, all_22_3) = all_128_0 &
% 52.31/8.18 | multiplication(all_43_0, all_22_3) = all_128_1 & addition(all_128_1,
% 52.31/8.18 | all_128_0) = all_57_1 & $i(all_128_0) & $i(all_128_1) &
% 52.31/8.18 | $i(all_57_1)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (188) implies:
% 52.31/8.18 | (189) multiplication(all_43_0, all_22_3) = all_128_1
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (128) with fresh symbols all_130_0, all_130_1 gives:
% 52.31/8.18 | (190) multiplication(all_47_0, all_22_3) = all_130_0 &
% 52.31/8.18 | multiplication(all_47_1, all_22_3) = all_130_1 & addition(all_130_1,
% 52.31/8.18 | all_130_0) = all_57_1 & $i(all_130_0) & $i(all_130_1) &
% 52.31/8.18 | $i(all_57_1)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (190) implies:
% 52.31/8.18 | (191) multiplication(all_47_0, all_22_3) = all_130_0
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (131) with fresh symbols all_134_0, all_134_1 gives:
% 52.31/8.18 | (192) multiplication(all_43_0, zero) = all_134_0 & multiplication(one,
% 52.31/8.18 | zero) = all_134_1 & addition(all_134_1, all_134_0) = all_49_1 &
% 52.31/8.18 | $i(all_134_0) & $i(all_134_1) & $i(all_49_1)
% 52.31/8.18 |
% 52.31/8.18 | ALPHA: (192) implies:
% 52.31/8.18 | (193) $i(all_134_1)
% 52.31/8.18 | (194) addition(all_134_1, all_134_0) = all_49_1
% 52.31/8.18 | (195) multiplication(one, zero) = all_134_1
% 52.31/8.18 | (196) multiplication(all_43_0, zero) = all_134_0
% 52.31/8.18 |
% 52.31/8.18 | DELTA: instantiating (130) with fresh symbols all_136_0, all_136_1 gives:
% 52.31/8.19 | (197) multiplication(all_45_0, zero) = all_136_0 & multiplication(one,
% 52.31/8.19 | zero) = all_136_1 & addition(all_136_1, all_136_0) = all_49_1 &
% 52.31/8.19 | $i(all_136_0) & $i(all_136_1) & $i(all_49_1)
% 52.31/8.19 |
% 52.31/8.19 | ALPHA: (197) implies:
% 52.31/8.19 | (198) $i(all_136_0)
% 52.31/8.19 | (199) addition(all_136_1, all_136_0) = all_49_1
% 52.31/8.19 | (200) multiplication(one, zero) = all_136_1
% 52.31/8.19 |
% 52.31/8.19 | DELTA: instantiating (136) with fresh symbols all_138_0, all_138_1 gives:
% 52.31/8.19 | (201) multiplication(all_53_0, all_22_3) = all_138_0 &
% 52.31/8.19 | multiplication(all_53_1, all_22_3) = all_138_1 & addition(all_138_1,
% 52.31/8.19 | all_138_0) = all_55_0 & $i(all_138_0) & $i(all_138_1) &
% 52.31/8.19 | $i(all_55_0)
% 52.31/8.19 |
% 52.31/8.19 | ALPHA: (201) implies:
% 52.31/8.19 | (202) $i(all_138_0)
% 52.31/8.19 | (203) multiplication(all_53_0, all_22_3) = all_138_0
% 52.31/8.19 |
% 52.31/8.19 | DELTA: instantiating (127) with fresh symbols all_142_0, all_142_1 gives:
% 52.31/8.19 | (204) multiplication(all_51_0, zero) = all_142_0 & multiplication(all_43_0,
% 52.31/8.19 | zero) = all_142_1 & addition(all_142_1, all_142_0) = all_53_1 &
% 52.31/8.19 | $i(all_142_0) & $i(all_142_1) & $i(all_53_1)
% 52.31/8.19 |
% 52.31/8.19 | ALPHA: (204) implies:
% 52.31/8.19 | (205) $i(all_142_1)
% 52.31/8.19 | (206) addition(all_142_1, all_142_0) = all_53_1
% 52.31/8.19 | (207) multiplication(all_43_0, zero) = all_142_1
% 52.31/8.19 | (208) multiplication(all_51_0, zero) = all_142_0
% 52.31/8.19 |
% 52.31/8.19 | DELTA: instantiating (124) with fresh symbols all_144_0, all_144_1 gives:
% 52.31/8.19 | (209) multiplication(all_22_3, all_53_0) = all_144_0 &
% 52.31/8.19 | multiplication(all_22_3, all_53_1) = all_144_1 & addition(all_144_1,
% 52.31/8.19 | all_144_0) = all_51_0 & $i(all_144_0) & $i(all_144_1) &
% 52.31/8.19 | $i(all_51_0)
% 52.31/8.19 |
% 52.31/8.19 | ALPHA: (209) implies:
% 52.31/8.19 | (210) multiplication(all_22_3, all_53_0) = all_144_0
% 52.31/8.19 |
% 52.31/8.19 | DELTA: instantiating (132) with fresh symbols all_146_0, all_146_1 gives:
% 52.31/8.19 | (211) multiplication(all_43_0, all_22_3) = all_146_0 & multiplication(one,
% 52.31/8.19 | all_22_3) = all_146_1 & addition(all_146_1, all_146_0) = all_45_0 &
% 52.31/8.19 | $i(all_146_0) & $i(all_146_1) & $i(all_45_0)
% 52.31/8.19 |
% 52.31/8.19 | ALPHA: (211) implies:
% 52.31/8.19 | (212) $i(all_146_0)
% 52.31/8.19 | (213) addition(all_146_1, all_146_0) = all_45_0
% 52.31/8.19 | (214) multiplication(one, all_22_3) = all_146_1
% 52.31/8.19 | (215) multiplication(all_43_0, all_22_3) = all_146_0
% 52.31/8.19 |
% 52.31/8.19 | DELTA: instantiating (121) with fresh symbols all_148_0, all_148_1 gives:
% 52.31/8.19 | (216) multiplication(all_22_3, all_45_0) = all_148_0 &
% 52.31/8.19 | multiplication(all_22_3, one) = all_148_1 & addition(all_148_1,
% 52.31/8.19 | all_148_0) = all_43_0 & $i(all_148_0) & $i(all_148_1) &
% 52.31/8.19 | $i(all_43_0)
% 52.31/8.19 |
% 52.31/8.19 | ALPHA: (216) implies:
% 52.31/8.19 | (217) $i(all_148_0)
% 52.31/8.19 | (218) addition(all_148_1, all_148_0) = all_43_0
% 52.31/8.19 | (219) multiplication(all_22_3, one) = all_148_1
% 52.31/8.19 |
% 52.31/8.19 | DELTA: instantiating (107) with fresh symbols all_150_0, all_150_1 gives:
% 52.31/8.19 | (220) multiplication(all_22_3, all_32_0) = all_150_1 &
% 52.31/8.19 | multiplication(all_22_3, all_32_1) = all_150_0 & addition(all_150_1,
% 52.31/8.19 | all_150_0) = all_30_0 & $i(all_150_0) & $i(all_150_1) &
% 52.31/8.19 | $i(all_30_0)
% 52.31/8.19 |
% 52.31/8.19 | ALPHA: (220) implies:
% 52.31/8.19 | (221) addition(all_150_1, all_150_0) = all_30_0
% 52.31/8.19 | (222) multiplication(all_22_3, all_32_1) = all_150_0
% 52.31/8.19 | (223) multiplication(all_22_3, all_32_0) = all_150_1
% 52.31/8.19 |
% 52.31/8.19 | DELTA: instantiating (134) with fresh symbols all_154_0, all_154_1 gives:
% 52.31/8.19 | (224) multiplication(all_53_0, zero) = all_154_0 & multiplication(all_53_1,
% 52.31/8.19 | zero) = all_154_1 & addition(all_154_1, all_154_0) = all_49_0 &
% 52.31/8.19 | $i(all_154_0) & $i(all_154_1) & $i(all_49_0)
% 52.31/8.19 |
% 52.31/8.19 | ALPHA: (224) implies:
% 52.31/8.19 | (225) $i(all_154_1)
% 52.31/8.19 | (226) $i(all_154_0)
% 52.31/8.19 | (227) addition(all_154_1, all_154_0) = all_49_0
% 52.31/8.19 | (228) multiplication(all_53_1, zero) = all_154_1
% 52.31/8.19 | (229) multiplication(all_53_0, zero) = all_154_0
% 52.31/8.19 |
% 52.31/8.19 | DELTA: instantiating (101) with fresh symbols all_156_0, all_156_1 gives:
% 52.31/8.19 | (230) multiplication(all_30_0, zero) = all_156_0 & multiplication(one,
% 52.31/8.19 | zero) = all_156_1 & addition(all_156_1, all_156_0) = all_32_0 &
% 52.31/8.19 | $i(all_156_0) & $i(all_156_1) & $i(all_32_0)
% 52.31/8.19 |
% 52.31/8.19 | ALPHA: (230) implies:
% 52.31/8.19 | (231) $i(all_156_0)
% 52.31/8.19 | (232) addition(all_156_1, all_156_0) = all_32_0
% 52.31/8.19 | (233) multiplication(one, zero) = all_156_1
% 52.31/8.19 | (234) multiplication(all_30_0, zero) = all_156_0
% 52.31/8.19 |
% 52.31/8.19 | DELTA: instantiating (100) with fresh symbols all_158_0, all_158_1 gives:
% 52.31/8.19 | (235) multiplication(all_30_0, all_22_3) = all_158_0 & multiplication(one,
% 52.31/8.19 | all_22_3) = all_158_1 & addition(all_158_1, all_158_0) = all_22_1 &
% 52.31/8.19 | $i(all_158_0) & $i(all_158_1) & $i(all_22_1)
% 52.31/8.19 |
% 52.31/8.19 | ALPHA: (235) implies:
% 52.31/8.19 | (236) multiplication(one, all_22_3) = all_158_1
% 52.31/8.19 |
% 52.31/8.19 | DELTA: instantiating (105) with fresh symbols all_160_0, all_160_1 gives:
% 52.31/8.19 | (237) multiplication(all_32_0, all_22_3) = all_160_1 &
% 52.31/8.19 | multiplication(all_32_1, all_22_3) = all_160_0 & addition(all_160_1,
% 52.31/8.19 | all_160_0) = all_22_1 & $i(all_160_0) & $i(all_160_1) &
% 52.31/8.19 | $i(all_22_1)
% 52.31/8.19 |
% 52.31/8.19 | ALPHA: (237) implies:
% 52.31/8.19 | (238) $i(all_160_1)
% 52.31/8.19 | (239) multiplication(all_32_0, all_22_3) = all_160_1
% 52.31/8.19 |
% 52.31/8.19 | DELTA: instantiating (126) with fresh symbols all_162_0, all_162_1 gives:
% 52.31/8.19 | (240) multiplication(all_47_0, zero) = all_162_0 & multiplication(all_47_1,
% 52.31/8.19 | zero) = all_162_1 & addition(all_162_1, all_162_0) = all_53_1 &
% 52.31/8.19 | $i(all_162_0) & $i(all_162_1) & $i(all_53_1)
% 52.31/8.19 |
% 52.31/8.19 | ALPHA: (240) implies:
% 52.31/8.19 | (241) $i(all_162_1)
% 52.31/8.19 | (242) $i(all_162_0)
% 52.31/8.19 | (243) addition(all_162_1, all_162_0) = all_53_1
% 52.31/8.19 | (244) multiplication(all_47_1, zero) = all_162_1
% 52.31/8.19 | (245) multiplication(all_47_0, zero) = all_162_0
% 52.31/8.19 |
% 52.31/8.19 | REDUCE: (116), (203) imply:
% 52.31/8.19 | (246) multiplication(zero, all_22_3) = all_138_0
% 52.31/8.19 |
% 52.31/8.19 | REDUCE: (116), (229) imply:
% 52.31/8.19 | (247) multiplication(zero, zero) = all_154_0
% 52.31/8.19 |
% 52.31/8.19 | REDUCE: (118), (191) imply:
% 52.31/8.19 | (248) multiplication(all_22_3, all_22_3) = all_130_0
% 52.31/8.19 |
% 52.31/8.19 | REDUCE: (118), (245) imply:
% 52.31/8.19 | (249) multiplication(all_22_3, zero) = all_162_0
% 52.31/8.19 |
% 52.31/8.19 | REDUCE: (116), (210) imply:
% 52.31/8.19 | (250) multiplication(all_22_3, zero) = all_144_0
% 52.31/8.19 |
% 52.31/8.19 | REDUCE: (118), (180) imply:
% 52.31/8.19 | (251) multiplication(all_22_3, all_22_3) = all_116_0
% 52.31/8.19 |
% 52.31/8.19 | REDUCE: (65), (118) imply:
% 52.31/8.19 | (252) multiplication(all_22_3, one) = all_22_3
% 52.31/8.19 |
% 52.31/8.19 | REDUCE: (92), (117) imply:
% 52.31/8.20 | (253) multiplication(one, all_22_3) = all_22_3
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (83), (116) imply:
% 52.31/8.20 | (254) multiplication(one, zero) = zero
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (116), (174) imply:
% 52.31/8.20 | (255) addition(all_110_0, zero) = all_22_2
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (116), (148) imply:
% 52.31/8.20 | (256) addition(zero, all_32_1) = all_82_0
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (82), (116) imply:
% 52.31/8.20 | (257) addition(all_53_1, zero) = all_32_0
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (19) with all_32_1, all_78_0, all_43_0, one,
% 52.31/8.20 | simplifying with (56), (141) gives:
% 52.31/8.20 | (258) all_78_0 = all_32_1
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (19) with all_32_1, all_84_0, all_45_0, one,
% 52.31/8.20 | simplifying with (59), (150) gives:
% 52.31/8.20 | (259) all_84_0 = all_32_1
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (19) with all_108_0, all_112_0, one, all_32_0,
% 52.31/8.20 | simplifying with (171), (176) gives:
% 52.31/8.20 | (260) all_112_0 = all_108_0
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_98_0, all_154_0, zero, zero,
% 52.31/8.20 | simplifying with (166), (247) gives:
% 52.31/8.20 | (261) all_154_0 = all_98_0
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_90_0, all_138_0, all_22_3, zero,
% 52.31/8.20 | simplifying with (156), (246) gives:
% 52.31/8.20 | (262) all_138_0 = all_90_0
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_136_1, all_156_1, zero, one,
% 52.31/8.20 | simplifying with (200), (233) gives:
% 52.31/8.20 | (263) all_156_1 = all_136_1
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_134_1, all_156_1, zero, one,
% 52.31/8.20 | simplifying with (195), (233) gives:
% 52.31/8.20 | (264) all_156_1 = all_134_1
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with zero, all_156_1, zero, one, simplifying
% 52.31/8.20 | with (233), (254) gives:
% 52.31/8.20 | (265) all_156_1 = zero
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_146_1, all_158_1, all_22_3, one,
% 52.31/8.20 | simplifying with (214), (236) gives:
% 52.31/8.20 | (266) all_158_1 = all_146_1
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_22_3, all_158_1, all_22_3, one,
% 52.31/8.20 | simplifying with (236), (253) gives:
% 52.31/8.20 | (267) all_158_1 = all_22_3
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_144_0, all_162_0, zero, all_22_3,
% 52.31/8.20 | simplifying with (249), (250) gives:
% 52.31/8.20 | (268) all_162_0 = all_144_0
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_122_1, all_126_1, one, all_22_3,
% 52.31/8.20 | simplifying with (185), (187) gives:
% 52.31/8.20 | (269) all_126_1 = all_122_1
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_126_1, all_148_1, one, all_22_3,
% 52.31/8.20 | simplifying with (187), (219) gives:
% 52.31/8.20 | (270) all_148_1 = all_126_1
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_22_3, all_148_1, one, all_22_3,
% 52.31/8.20 | simplifying with (219), (252) gives:
% 52.31/8.20 | (271) all_148_1 = all_22_3
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_116_0, all_130_0, all_22_3, all_22_3,
% 52.31/8.20 | simplifying with (248), (251) gives:
% 52.31/8.20 | (272) all_130_0 = all_116_0
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_80_0, all_130_0, all_22_3, all_22_3,
% 52.31/8.20 | simplifying with (144), (248) gives:
% 52.31/8.20 | (273) all_130_0 = all_80_0
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_30_0, all_96_0, all_22_2, all_22_3,
% 52.31/8.20 | simplifying with (35), (163) gives:
% 52.31/8.20 | (274) all_96_0 = all_30_0
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_43_0, all_150_0, all_32_1, all_22_3,
% 52.31/8.20 | simplifying with (57), (222) gives:
% 52.31/8.20 | (275) all_150_0 = all_43_0
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_51_0, all_150_1, all_32_0, all_22_3,
% 52.31/8.20 | simplifying with (78), (223) gives:
% 52.31/8.20 | (276) all_150_1 = all_51_0
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_32_0, all_94_0, zero, all_22_2,
% 52.31/8.20 | simplifying with (40), (161) gives:
% 52.31/8.20 | (277) all_94_0 = all_32_0
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_53_1, all_156_0, zero, all_30_0,
% 52.31/8.20 | simplifying with (84), (234) gives:
% 52.31/8.20 | (278) all_156_0 = all_53_1
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_49_0, all_118_1, zero, all_32_0,
% 52.31/8.20 | simplifying with (72), (182) gives:
% 52.31/8.20 | (279) all_118_1 = all_49_0
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_55_0, all_160_1, all_22_3, all_32_0,
% 52.31/8.20 | simplifying with (90), (239) gives:
% 52.31/8.20 | (280) all_160_1 = all_55_0
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_134_0, all_142_1, zero, all_43_0,
% 52.31/8.20 | simplifying with (196), (207) gives:
% 52.31/8.20 | (281) all_142_1 = all_134_0
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_128_1, all_146_0, all_22_3, all_43_0,
% 52.31/8.20 | simplifying with (189), (215) gives:
% 52.31/8.20 | (282) all_146_0 = all_128_1
% 52.31/8.20 |
% 52.31/8.20 | COMBINE_EQS: (266), (267) imply:
% 52.31/8.20 | (283) all_146_1 = all_22_3
% 52.31/8.20 |
% 52.31/8.20 | SIMP: (283) implies:
% 52.31/8.20 | (284) all_146_1 = all_22_3
% 52.31/8.20 |
% 52.31/8.20 | COMBINE_EQS: (263), (265) imply:
% 52.31/8.20 | (285) all_136_1 = zero
% 52.31/8.20 |
% 52.31/8.20 | COMBINE_EQS: (263), (264) imply:
% 52.31/8.20 | (286) all_136_1 = all_134_1
% 52.31/8.20 |
% 52.31/8.20 | COMBINE_EQS: (270), (271) imply:
% 52.31/8.20 | (287) all_126_1 = all_22_3
% 52.31/8.20 |
% 52.31/8.20 | SIMP: (287) implies:
% 52.31/8.20 | (288) all_126_1 = all_22_3
% 52.31/8.20 |
% 52.31/8.20 | COMBINE_EQS: (285), (286) imply:
% 52.31/8.20 | (289) all_134_1 = zero
% 52.31/8.20 |
% 52.31/8.20 | SIMP: (289) implies:
% 52.31/8.20 | (290) all_134_1 = zero
% 52.31/8.20 |
% 52.31/8.20 | COMBINE_EQS: (272), (273) imply:
% 52.31/8.20 | (291) all_116_0 = all_80_0
% 52.31/8.20 |
% 52.31/8.20 | COMBINE_EQS: (269), (288) imply:
% 52.31/8.20 | (292) all_122_1 = all_22_3
% 52.31/8.20 |
% 52.31/8.20 | SIMP: (292) implies:
% 52.31/8.20 | (293) all_122_1 = all_22_3
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (164), (274) imply:
% 52.31/8.20 | (294) multiplication(all_30_0, zero) = all_51_0
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (160), (277) imply:
% 52.31/8.20 | (295) multiplication(all_22_3, all_32_0) = all_53_1
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (243), (268) imply:
% 52.31/8.20 | (296) addition(all_162_1, all_144_0) = all_53_1
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (232), (265), (278) imply:
% 52.31/8.20 | (297) addition(zero, all_53_1) = all_32_0
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (227), (261) imply:
% 52.31/8.20 | (298) addition(all_154_1, all_98_0) = all_49_0
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (221), (275), (276) imply:
% 52.31/8.20 | (299) addition(all_51_0, all_43_0) = all_30_0
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (218), (271) imply:
% 52.31/8.20 | (300) addition(all_22_3, all_148_0) = all_43_0
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (213), (282), (284) imply:
% 52.31/8.20 | (301) addition(all_22_3, all_128_1) = all_45_0
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (206), (281) imply:
% 52.31/8.20 | (302) addition(all_134_0, all_142_0) = all_53_1
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (199), (285) imply:
% 52.31/8.20 | (303) addition(zero, all_136_0) = all_49_1
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (194), (290) imply:
% 52.31/8.20 | (304) addition(zero, all_134_0) = all_49_1
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (177), (260) imply:
% 52.31/8.20 | (305) addition(all_108_0, all_45_0) = all_22_2
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (151), (259) imply:
% 52.31/8.20 | (306) addition(all_32_1, all_55_0) = all_22_0
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (142), (258) imply:
% 52.31/8.20 | (307) addition(all_32_1, all_51_0) = all_22_2
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (242), (268) imply:
% 52.31/8.20 | (308) $i(all_144_0)
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (226), (261) imply:
% 52.31/8.20 | (309) $i(all_98_0)
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (212), (282) imply:
% 52.31/8.20 | (310) $i(all_128_1)
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (205), (281) imply:
% 52.31/8.20 | (311) $i(all_134_0)
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (202), (262) imply:
% 52.31/8.20 | (312) $i(all_90_0)
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (179), (291) imply:
% 52.31/8.20 | (313) $i(all_80_0)
% 52.31/8.20 |
% 52.31/8.20 | GROUND_INST: instantiating (20) with all_53_1, all_51_0, zero, all_30_0,
% 52.31/8.20 | simplifying with (84), (294) gives:
% 52.31/8.20 | (314) all_53_1 = all_51_0
% 52.31/8.20 |
% 52.31/8.20 | REDUCE: (228), (314) imply:
% 52.31/8.21 | (315) multiplication(all_51_0, zero) = all_154_1
% 52.31/8.21 |
% 52.31/8.21 | REDUCE: (296), (314) imply:
% 52.31/8.21 | (316) addition(all_162_1, all_144_0) = all_51_0
% 52.31/8.21 |
% 52.31/8.21 | REDUCE: (302), (314) imply:
% 52.31/8.21 | (317) addition(all_134_0, all_142_0) = all_51_0
% 52.31/8.21 |
% 52.31/8.21 | REDUCE: (147), (314) imply:
% 52.31/8.21 | (318) addition(all_51_0, all_82_0) = all_22_2
% 52.31/8.21 |
% 52.31/8.21 | REDUCE: (257), (314) imply:
% 52.31/8.21 | (319) addition(all_51_0, zero) = all_32_0
% 52.31/8.21 |
% 52.31/8.21 | REDUCE: (173), (314) imply:
% 52.31/8.21 | (320) addition(all_32_1, all_51_0) = all_110_0
% 52.31/8.21 |
% 52.31/8.21 | REDUCE: (297), (314) imply:
% 52.31/8.21 | (321) addition(zero, all_51_0) = all_32_0
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (19) with all_22_2, all_110_0, all_51_0, all_32_1,
% 52.31/8.21 | simplifying with (307), (320) gives:
% 52.31/8.21 | (322) all_110_0 = all_22_2
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (20) with all_142_0, all_154_1, zero, all_51_0,
% 52.31/8.21 | simplifying with (208), (315) gives:
% 52.31/8.21 | (323) all_154_1 = all_142_0
% 52.31/8.21 |
% 52.31/8.21 | REDUCE: (298), (323) imply:
% 52.31/8.21 | (324) addition(all_142_0, all_98_0) = all_49_0
% 52.31/8.21 |
% 52.31/8.21 | REDUCE: (255), (322) imply:
% 52.31/8.21 | (325) addition(all_22_2, zero) = all_22_2
% 52.31/8.21 |
% 52.31/8.21 | REDUCE: (225), (323) imply:
% 52.31/8.21 | (326) $i(all_142_0)
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (1) with all_32_1, zero, all_82_0, simplifying with
% 52.31/8.21 | (15), (37), (256) gives:
% 52.31/8.21 | (327) addition(all_32_1, zero) = all_82_0 & $i(all_82_0)
% 52.31/8.21 |
% 52.31/8.21 | ALPHA: (327) implies:
% 52.31/8.21 | (328) $i(all_82_0)
% 52.31/8.21 | (329) addition(all_32_1, zero) = all_82_0
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (10) with zero, all_51_0, zero, all_32_0, all_49_0,
% 52.31/8.21 | simplifying with (15), (72), (75), (321) gives:
% 52.31/8.21 | (330) ? [v0: $i] : ? [v1: $i] : (multiplication(all_51_0, zero) = v1 &
% 52.31/8.21 | multiplication(zero, zero) = v0 & addition(v0, v1) = all_49_0 &
% 52.31/8.21 | $i(v1) & $i(v0) & $i(all_49_0))
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (2) with all_51_0, zero, all_32_1, all_32_0,
% 52.31/8.21 | all_22_2, simplifying with (15), (37), (39), (75), (321) gives:
% 52.31/8.21 | (331) ? [v0: $i] : (addition(v0, all_51_0) = all_22_2 & addition(all_32_1,
% 52.31/8.21 | zero) = v0 & $i(v0) & $i(all_22_2))
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (1) with all_88_0, one, all_22_2, simplifying with
% 52.31/8.21 | (17), (153), (154) gives:
% 52.31/8.21 | (332) addition(all_88_0, one) = all_22_2 & $i(all_22_2)
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (1) with all_128_1, all_22_3, all_45_0, simplifying
% 52.31/8.21 | with (23), (301), (310) gives:
% 52.31/8.21 | (333) addition(all_128_1, all_22_3) = all_45_0 & $i(all_45_0)
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (1) with all_148_0, all_22_3, all_43_0, simplifying
% 52.31/8.21 | with (23), (217), (300) gives:
% 52.31/8.21 | (334) addition(all_148_0, all_22_3) = all_43_0 & $i(all_43_0)
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (10) with all_22_2, zero, zero, all_22_2, all_32_0,
% 52.31/8.21 | simplifying with (15), (40), (47), (325) gives:
% 52.31/8.21 | (335) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_2, zero) = v0 &
% 52.31/8.21 | multiplication(zero, zero) = v1 & addition(v0, v1) = all_32_0 &
% 52.31/8.21 | $i(v1) & $i(v0) & $i(all_32_0))
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (3) with zero, all_32_1, all_32_0, all_22_2,
% 52.31/8.21 | all_22_2, simplifying with (15), (37), (38), (48), (325) gives:
% 52.31/8.21 | (336) ? [v0: $i] : (addition(all_32_0, v0) = all_22_2 & addition(all_32_1,
% 52.31/8.21 | zero) = v0 & $i(v0) & $i(all_22_2))
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (2) with all_136_0, zero, all_32_1, all_49_1,
% 52.31/8.21 | all_102_0, simplifying with (15), (37), (169), (198), (303)
% 52.31/8.21 | gives:
% 52.31/8.21 | (337) ? [v0: $i] : (addition(v0, all_136_0) = all_102_0 &
% 52.31/8.21 | addition(all_32_1, zero) = v0 & $i(v0) & $i(all_102_0))
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (2) with all_134_0, zero, all_32_1, all_49_1,
% 52.31/8.21 | all_102_0, simplifying with (15), (37), (169), (304), (311)
% 52.31/8.21 | gives:
% 52.31/8.21 | (338) ? [v0: $i] : (addition(v0, all_134_0) = all_102_0 &
% 52.31/8.21 | addition(all_32_1, zero) = v0 & $i(v0) & $i(all_102_0))
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (10) with all_32_1, all_51_0, zero, all_22_2,
% 52.31/8.21 | all_32_0, simplifying with (15), (37), (40), (75), (307) gives:
% 52.31/8.21 | (339) ? [v0: $i] : ? [v1: $i] : (multiplication(all_51_0, zero) = v1 &
% 52.31/8.21 | multiplication(all_32_1, zero) = v0 & addition(v0, v1) = all_32_0 &
% 52.31/8.21 | $i(v1) & $i(v0) & $i(all_32_0))
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (1) with all_55_0, all_32_1, all_22_0, simplifying
% 52.31/8.21 | with (37), (87), (306) gives:
% 52.31/8.21 | (340) addition(all_55_0, all_32_1) = all_22_0 & $i(all_22_0)
% 52.31/8.21 |
% 52.31/8.21 | ALPHA: (340) implies:
% 52.31/8.21 | (341) addition(all_55_0, all_32_1) = all_22_0
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (1) with one, all_32_0, all_108_0, simplifying with
% 52.31/8.21 | (17), (38), (171) gives:
% 52.31/8.21 | (342) addition(one, all_32_0) = all_108_0 & $i(all_108_0)
% 52.31/8.21 |
% 52.31/8.21 | ALPHA: (342) implies:
% 52.31/8.21 | (343) $i(all_108_0)
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (4) with all_51_0, all_32_0, simplifying with (75),
% 52.31/8.21 | (319) gives:
% 52.31/8.21 | (344) all_51_0 = all_32_0
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (10) with all_51_0, all_82_0, zero, all_22_2,
% 52.31/8.21 | all_32_0, simplifying with (15), (40), (75), (318), (328) gives:
% 52.31/8.21 | (345) ? [v0: $i] : ? [v1: $i] : (multiplication(all_82_0, zero) = v1 &
% 52.31/8.21 | multiplication(all_51_0, zero) = v0 & addition(v0, v1) = all_32_0 &
% 52.31/8.21 | $i(v1) & $i(v0) & $i(all_32_0))
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (1) with all_45_0, all_108_0, all_22_2, simplifying
% 52.31/8.21 | with (98), (305), (343) gives:
% 52.31/8.21 | (346) addition(all_45_0, all_108_0) = all_22_2 & $i(all_22_2)
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (3) with all_82_0, all_142_0, all_134_0, all_51_0,
% 52.31/8.21 | all_22_2, simplifying with (311), (317), (318), (326), (328)
% 52.31/8.21 | gives:
% 52.31/8.21 | (347) ? [v0: $i] : (addition(all_142_0, all_82_0) = v0 &
% 52.31/8.21 | addition(all_134_0, v0) = all_22_2 & $i(v0) & $i(all_22_2))
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (3) with all_32_1, all_98_0, all_142_0, all_49_0,
% 52.31/8.21 | all_72_0, simplifying with (37), (138), (309), (324), (326)
% 52.31/8.21 | gives:
% 52.31/8.21 | (348) ? [v0: $i] : (addition(all_142_0, v0) = all_72_0 &
% 52.31/8.21 | addition(all_98_0, all_32_1) = v0 & $i(v0) & $i(all_72_0))
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (1) with all_144_0, all_162_1, all_51_0,
% 52.31/8.21 | simplifying with (241), (308), (316) gives:
% 52.31/8.21 | (349) addition(all_144_0, all_162_1) = all_51_0 & $i(all_51_0)
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (11) with zero, all_98_0, simplifying with (15),
% 52.31/8.21 | (166) gives:
% 52.31/8.21 | (350) all_98_0 = zero
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (11) with all_22_3, all_90_0, simplifying with
% 52.31/8.21 | (23), (156) gives:
% 52.31/8.21 | (351) all_90_0 = zero
% 52.31/8.21 |
% 52.31/8.21 | GROUND_INST: instantiating (10) with all_32_0, all_32_1, all_90_0, all_22_2,
% 52.31/8.21 | all_55_0, simplifying with (37), (38), (48), (157), (312) gives:
% 52.31/8.22 | (352) ? [v0: $i] : ? [v1: $i] : (multiplication(all_32_0, all_90_0) = v0
% 52.31/8.22 | & multiplication(all_32_1, all_90_0) = v1 & addition(v0, v1) =
% 52.31/8.22 | all_55_0 & $i(v1) & $i(v0) & $i(all_55_0))
% 52.31/8.22 |
% 52.31/8.22 | GROUND_INST: instantiating (10) with all_32_1, all_32_0, all_90_0, all_22_2,
% 52.31/8.22 | all_55_0, simplifying with (37), (38), (39), (157), (312) gives:
% 52.31/8.22 | (353) ? [v0: $i] : ? [v1: $i] : (multiplication(all_32_0, all_90_0) = v1
% 52.31/8.22 | & multiplication(all_32_1, all_90_0) = v0 & addition(v0, v1) =
% 52.31/8.22 | all_55_0 & $i(v1) & $i(v0) & $i(all_55_0))
% 52.31/8.22 |
% 52.31/8.22 | GROUND_INST: instantiating (10) with all_51_0, all_82_0, all_90_0, all_22_2,
% 52.31/8.22 | all_55_0, simplifying with (75), (157), (312), (318), (328)
% 52.31/8.22 | gives:
% 52.31/8.22 | (354) ? [v0: $i] : ? [v1: $i] : (multiplication(all_82_0, all_90_0) = v1
% 52.31/8.22 | & multiplication(all_51_0, all_90_0) = v0 & addition(v0, v1) =
% 52.31/8.22 | all_55_0 & $i(v1) & $i(v0) & $i(all_55_0))
% 52.31/8.22 |
% 52.31/8.22 | GROUND_INST: instantiating (10) with all_32_1, all_51_0, all_90_0, all_22_2,
% 52.31/8.22 | all_55_0, simplifying with (37), (75), (157), (307), (312) gives:
% 52.31/8.22 | (355) ? [v0: $i] : ? [v1: $i] : (multiplication(all_51_0, all_90_0) = v1
% 52.31/8.22 | & multiplication(all_32_1, all_90_0) = v0 & addition(v0, v1) =
% 52.31/8.22 | all_55_0 & $i(v1) & $i(v0) & $i(all_55_0))
% 52.31/8.22 |
% 52.31/8.22 | GROUND_INST: instantiating (10) with all_22_2, zero, all_90_0, all_22_2,
% 52.31/8.22 | all_55_0, simplifying with (15), (47), (157), (312), (325) gives:
% 52.31/8.22 | (356) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_2, all_90_0) = v0
% 52.31/8.22 | & multiplication(zero, all_90_0) = v1 & addition(v0, v1) = all_55_0
% 52.31/8.22 | & $i(v1) & $i(v0) & $i(all_55_0))
% 52.31/8.22 |
% 52.31/8.22 | GROUND_INST: instantiating (10) with all_32_0, all_32_1, all_98_0, all_22_2,
% 52.31/8.22 | all_49_0, simplifying with (37), (38), (48), (167), (309) gives:
% 52.31/8.22 | (357) ? [v0: $i] : ? [v1: $i] : (multiplication(all_32_0, all_98_0) = v0
% 52.31/8.22 | & multiplication(all_32_1, all_98_0) = v1 & addition(v0, v1) =
% 52.31/8.22 | all_49_0 & $i(v1) & $i(v0) & $i(all_49_0))
% 52.31/8.22 |
% 52.31/8.22 | GROUND_INST: instantiating (10) with all_32_1, all_32_0, all_98_0, all_22_2,
% 52.31/8.22 | all_49_0, simplifying with (37), (38), (39), (167), (309) gives:
% 52.31/8.22 | (358) ? [v0: $i] : ? [v1: $i] : (multiplication(all_32_0, all_98_0) = v1
% 52.31/8.22 | & multiplication(all_32_1, all_98_0) = v0 & addition(v0, v1) =
% 52.31/8.22 | all_49_0 & $i(v1) & $i(v0) & $i(all_49_0))
% 52.31/8.22 |
% 52.31/8.22 | GROUND_INST: instantiating (10) with all_51_0, all_82_0, all_98_0, all_22_2,
% 52.31/8.22 | all_49_0, simplifying with (75), (167), (309), (318), (328)
% 52.31/8.22 | gives:
% 52.31/8.22 | (359) ? [v0: $i] : ? [v1: $i] : (multiplication(all_82_0, all_98_0) = v1
% 52.31/8.22 | & multiplication(all_51_0, all_98_0) = v0 & addition(v0, v1) =
% 52.31/8.22 | all_49_0 & $i(v1) & $i(v0) & $i(all_49_0))
% 52.31/8.22 |
% 52.31/8.22 | GROUND_INST: instantiating (10) with all_32_1, all_51_0, all_98_0, all_22_2,
% 52.31/8.22 | all_49_0, simplifying with (37), (75), (167), (307), (309) gives:
% 52.31/8.22 | (360) ? [v0: $i] : ? [v1: $i] : (multiplication(all_51_0, all_98_0) = v1
% 52.31/8.22 | & multiplication(all_32_1, all_98_0) = v0 & addition(v0, v1) =
% 52.31/8.22 | all_49_0 & $i(v1) & $i(v0) & $i(all_49_0))
% 52.31/8.22 |
% 52.31/8.22 | GROUND_INST: instantiating (10) with all_22_2, zero, all_98_0, all_22_2,
% 52.31/8.22 | all_49_0, simplifying with (15), (47), (167), (309), (325) gives:
% 52.31/8.22 | (361) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_2, all_98_0) = v0
% 52.31/8.22 | & multiplication(zero, all_98_0) = v1 & addition(v0, v1) = all_49_0
% 52.31/8.22 | & $i(v1) & $i(v0) & $i(all_49_0))
% 52.31/8.22 |
% 52.31/8.22 | GROUND_INST: instantiating (10) with all_51_0, all_43_0, zero, all_30_0,
% 52.31/8.22 | all_51_0, simplifying with (15), (75), (99), (294), (299) gives:
% 52.31/8.22 | (362) ? [v0: $i] : ? [v1: $i] : (multiplication(all_51_0, zero) = v0 &
% 52.31/8.22 | multiplication(all_43_0, zero) = v1 & addition(v0, v1) = all_51_0 &
% 52.31/8.22 | $i(v1) & $i(v0))
% 52.31/8.22 |
% 52.31/8.22 | GROUND_INST: instantiating (6) with all_22_3, all_32_0, zero, all_51_0,
% 52.31/8.22 | all_142_0, simplifying with (15), (23), (38), (78), (208) gives:
% 52.31/8.22 | (363) ? [v0: $i] : (multiplication(all_32_0, zero) = v0 &
% 52.31/8.22 | multiplication(all_22_3, v0) = all_142_0 & $i(v0) & $i(all_142_0))
% 52.31/8.22 |
% 52.31/8.22 | GROUND_INST: instantiating (6) with all_80_0, all_22_2, zero, all_47_1,
% 52.31/8.22 | all_162_1, simplifying with (15), (47), (145), (244), (313)
% 52.31/8.22 | gives:
% 52.31/8.22 | (364) ? [v0: $i] : (multiplication(all_80_0, v0) = all_162_1 &
% 52.31/8.22 | multiplication(all_22_2, zero) = v0 & $i(v0) & $i(all_162_1))
% 52.31/8.22 |
% 52.31/8.22 | DELTA: instantiating (336) with fresh symbol all_217_0 gives:
% 52.31/8.22 | (365) addition(all_32_0, all_217_0) = all_22_2 & addition(all_32_1, zero) =
% 52.31/8.22 | all_217_0 & $i(all_217_0) & $i(all_22_2)
% 52.31/8.22 |
% 52.31/8.22 | ALPHA: (365) implies:
% 52.31/8.22 | (366) addition(all_32_1, zero) = all_217_0
% 52.31/8.22 | (367) addition(all_32_0, all_217_0) = all_22_2
% 52.31/8.22 |
% 52.31/8.22 | DELTA: instantiating (347) with fresh symbol all_237_0 gives:
% 52.31/8.22 | (368) addition(all_142_0, all_82_0) = all_237_0 & addition(all_134_0,
% 52.31/8.22 | all_237_0) = all_22_2 & $i(all_237_0) & $i(all_22_2)
% 52.31/8.22 |
% 52.31/8.22 | ALPHA: (368) implies:
% 52.31/8.22 | (369) addition(all_142_0, all_82_0) = all_237_0
% 52.31/8.22 |
% 52.31/8.22 | DELTA: instantiating (331) with fresh symbol all_325_0 gives:
% 52.31/8.22 | (370) addition(all_325_0, all_51_0) = all_22_2 & addition(all_32_1, zero) =
% 52.31/8.22 | all_325_0 & $i(all_325_0) & $i(all_22_2)
% 52.31/8.22 |
% 52.31/8.22 | ALPHA: (370) implies:
% 52.31/8.22 | (371) addition(all_32_1, zero) = all_325_0
% 52.31/8.22 |
% 52.31/8.22 | DELTA: instantiating (364) with fresh symbol all_361_0 gives:
% 52.31/8.22 | (372) multiplication(all_80_0, all_361_0) = all_162_1 &
% 52.31/8.22 | multiplication(all_22_2, zero) = all_361_0 & $i(all_361_0) &
% 52.31/8.22 | $i(all_162_1)
% 52.31/8.22 |
% 52.31/8.22 | ALPHA: (372) implies:
% 52.31/8.22 | (373) multiplication(all_22_2, zero) = all_361_0
% 52.31/8.22 |
% 52.31/8.22 | DELTA: instantiating (363) with fresh symbol all_533_0 gives:
% 52.31/8.22 | (374) multiplication(all_32_0, zero) = all_533_0 & multiplication(all_22_3,
% 52.31/8.22 | all_533_0) = all_142_0 & $i(all_533_0) & $i(all_142_0)
% 52.31/8.22 |
% 52.31/8.22 | ALPHA: (374) implies:
% 52.31/8.22 | (375) multiplication(all_32_0, zero) = all_533_0
% 52.31/8.22 |
% 52.31/8.22 | DELTA: instantiating (348) with fresh symbol all_557_0 gives:
% 52.31/8.22 | (376) addition(all_142_0, all_557_0) = all_72_0 & addition(all_98_0,
% 52.31/8.22 | all_32_1) = all_557_0 & $i(all_557_0) & $i(all_72_0)
% 52.31/8.22 |
% 52.31/8.22 | ALPHA: (376) implies:
% 52.31/8.22 | (377) addition(all_98_0, all_32_1) = all_557_0
% 52.31/8.22 | (378) addition(all_142_0, all_557_0) = all_72_0
% 52.31/8.22 |
% 52.31/8.22 | DELTA: instantiating (338) with fresh symbol all_669_0 gives:
% 52.31/8.22 | (379) addition(all_669_0, all_134_0) = all_102_0 & addition(all_32_1, zero)
% 52.31/8.22 | = all_669_0 & $i(all_669_0) & $i(all_102_0)
% 52.31/8.22 |
% 52.31/8.22 | ALPHA: (379) implies:
% 52.31/8.22 | (380) addition(all_32_1, zero) = all_669_0
% 52.31/8.22 |
% 52.31/8.22 | DELTA: instantiating (337) with fresh symbol all_681_0 gives:
% 52.31/8.22 | (381) addition(all_681_0, all_136_0) = all_102_0 & addition(all_32_1, zero)
% 52.31/8.22 | = all_681_0 & $i(all_681_0) & $i(all_102_0)
% 52.31/8.22 |
% 52.31/8.22 | ALPHA: (381) implies:
% 52.31/8.22 | (382) addition(all_32_1, zero) = all_681_0
% 52.31/8.22 |
% 52.31/8.22 | DELTA: instantiating (362) with fresh symbols all_731_0, all_731_1 gives:
% 52.31/8.22 | (383) multiplication(all_51_0, zero) = all_731_1 & multiplication(all_43_0,
% 52.31/8.22 | zero) = all_731_0 & addition(all_731_1, all_731_0) = all_51_0 &
% 52.31/8.22 | $i(all_731_0) & $i(all_731_1)
% 52.31/8.22 |
% 52.31/8.22 | ALPHA: (383) implies:
% 52.31/8.22 | (384) multiplication(all_51_0, zero) = all_731_1
% 52.31/8.22 |
% 52.31/8.22 | DELTA: instantiating (356) with fresh symbols all_737_0, all_737_1 gives:
% 52.31/8.23 | (385) multiplication(all_22_2, all_90_0) = all_737_1 & multiplication(zero,
% 52.31/8.23 | all_90_0) = all_737_0 & addition(all_737_1, all_737_0) = all_55_0 &
% 52.31/8.23 | $i(all_737_0) & $i(all_737_1) & $i(all_55_0)
% 52.31/8.23 |
% 52.31/8.23 | ALPHA: (385) implies:
% 52.31/8.23 | (386) multiplication(all_22_2, all_90_0) = all_737_1
% 52.31/8.23 |
% 52.31/8.23 | DELTA: instantiating (355) with fresh symbols all_739_0, all_739_1 gives:
% 52.31/8.23 | (387) multiplication(all_51_0, all_90_0) = all_739_0 &
% 52.31/8.23 | multiplication(all_32_1, all_90_0) = all_739_1 & addition(all_739_1,
% 52.31/8.23 | all_739_0) = all_55_0 & $i(all_739_0) & $i(all_739_1) &
% 52.31/8.23 | $i(all_55_0)
% 52.31/8.23 |
% 52.31/8.23 | ALPHA: (387) implies:
% 52.31/8.23 | (388) multiplication(all_51_0, all_90_0) = all_739_0
% 52.31/8.23 |
% 52.31/8.23 | DELTA: instantiating (339) with fresh symbols all_741_0, all_741_1 gives:
% 52.31/8.23 | (389) multiplication(all_51_0, zero) = all_741_0 & multiplication(all_32_1,
% 52.31/8.23 | zero) = all_741_1 & addition(all_741_1, all_741_0) = all_32_0 &
% 52.31/8.23 | $i(all_741_0) & $i(all_741_1) & $i(all_32_0)
% 52.31/8.23 |
% 52.31/8.23 | ALPHA: (389) implies:
% 52.31/8.23 | (390) multiplication(all_51_0, zero) = all_741_0
% 52.31/8.23 |
% 52.31/8.23 | DELTA: instantiating (345) with fresh symbols all_763_0, all_763_1 gives:
% 52.31/8.23 | (391) multiplication(all_82_0, zero) = all_763_0 & multiplication(all_51_0,
% 52.31/8.23 | zero) = all_763_1 & addition(all_763_1, all_763_0) = all_32_0 &
% 52.31/8.23 | $i(all_763_0) & $i(all_763_1) & $i(all_32_0)
% 52.31/8.23 |
% 52.31/8.23 | ALPHA: (391) implies:
% 52.31/8.23 | (392) multiplication(all_51_0, zero) = all_763_1
% 52.31/8.23 |
% 52.31/8.23 | DELTA: instantiating (359) with fresh symbols all_843_0, all_843_1 gives:
% 52.31/8.23 | (393) multiplication(all_82_0, all_98_0) = all_843_0 &
% 52.31/8.23 | multiplication(all_51_0, all_98_0) = all_843_1 & addition(all_843_1,
% 52.31/8.23 | all_843_0) = all_49_0 & $i(all_843_0) & $i(all_843_1) &
% 52.31/8.23 | $i(all_49_0)
% 52.31/8.23 |
% 52.31/8.23 | ALPHA: (393) implies:
% 52.31/8.23 | (394) multiplication(all_51_0, all_98_0) = all_843_1
% 52.31/8.23 |
% 52.31/8.23 | DELTA: instantiating (358) with fresh symbols all_847_0, all_847_1 gives:
% 52.31/8.23 | (395) multiplication(all_32_0, all_98_0) = all_847_0 &
% 52.31/8.23 | multiplication(all_32_1, all_98_0) = all_847_1 & addition(all_847_1,
% 52.31/8.23 | all_847_0) = all_49_0 & $i(all_847_0) & $i(all_847_1) &
% 52.31/8.23 | $i(all_49_0)
% 52.31/8.23 |
% 52.31/8.23 | ALPHA: (395) implies:
% 52.31/8.23 | (396) multiplication(all_32_0, all_98_0) = all_847_0
% 52.31/8.23 |
% 52.31/8.23 | DELTA: instantiating (357) with fresh symbols all_867_0, all_867_1 gives:
% 52.31/8.23 | (397) multiplication(all_32_0, all_98_0) = all_867_1 &
% 52.31/8.23 | multiplication(all_32_1, all_98_0) = all_867_0 & addition(all_867_1,
% 52.31/8.23 | all_867_0) = all_49_0 & $i(all_867_0) & $i(all_867_1) &
% 52.31/8.23 | $i(all_49_0)
% 52.31/8.23 |
% 52.31/8.23 | ALPHA: (397) implies:
% 52.31/8.23 | (398) multiplication(all_32_0, all_98_0) = all_867_1
% 52.31/8.23 |
% 52.31/8.23 | DELTA: instantiating (361) with fresh symbols all_871_0, all_871_1 gives:
% 52.31/8.23 | (399) multiplication(all_22_2, all_98_0) = all_871_1 & multiplication(zero,
% 52.31/8.23 | all_98_0) = all_871_0 & addition(all_871_1, all_871_0) = all_49_0 &
% 52.31/8.23 | $i(all_871_0) & $i(all_871_1) & $i(all_49_0)
% 52.31/8.23 |
% 52.31/8.23 | ALPHA: (399) implies:
% 52.31/8.23 | (400) multiplication(all_22_2, all_98_0) = all_871_1
% 52.31/8.23 |
% 52.31/8.23 | DELTA: instantiating (335) with fresh symbols all_881_0, all_881_1 gives:
% 52.31/8.23 | (401) multiplication(all_22_2, zero) = all_881_1 & multiplication(zero,
% 52.31/8.23 | zero) = all_881_0 & addition(all_881_1, all_881_0) = all_32_0 &
% 52.31/8.23 | $i(all_881_0) & $i(all_881_1) & $i(all_32_0)
% 52.31/8.23 |
% 52.31/8.23 | ALPHA: (401) implies:
% 52.31/8.23 | (402) multiplication(all_22_2, zero) = all_881_1
% 52.31/8.23 |
% 52.31/8.23 | DELTA: instantiating (360) with fresh symbols all_907_0, all_907_1 gives:
% 52.31/8.23 | (403) multiplication(all_51_0, all_98_0) = all_907_0 &
% 52.31/8.23 | multiplication(all_32_1, all_98_0) = all_907_1 & addition(all_907_1,
% 52.31/8.23 | all_907_0) = all_49_0 & $i(all_907_0) & $i(all_907_1) &
% 52.31/8.23 | $i(all_49_0)
% 52.31/8.23 |
% 52.31/8.23 | ALPHA: (403) implies:
% 52.31/8.23 | (404) multiplication(all_51_0, all_98_0) = all_907_0
% 52.31/8.23 |
% 52.31/8.23 | DELTA: instantiating (354) with fresh symbols all_923_0, all_923_1 gives:
% 52.31/8.23 | (405) multiplication(all_82_0, all_90_0) = all_923_0 &
% 52.31/8.23 | multiplication(all_51_0, all_90_0) = all_923_1 & addition(all_923_1,
% 52.31/8.23 | all_923_0) = all_55_0 & $i(all_923_0) & $i(all_923_1) &
% 52.31/8.23 | $i(all_55_0)
% 52.31/8.23 |
% 52.31/8.23 | ALPHA: (405) implies:
% 52.31/8.23 | (406) multiplication(all_51_0, all_90_0) = all_923_1
% 52.31/8.23 |
% 52.31/8.23 | DELTA: instantiating (330) with fresh symbols all_939_0, all_939_1 gives:
% 52.31/8.23 | (407) multiplication(all_51_0, zero) = all_939_0 & multiplication(zero,
% 52.31/8.23 | zero) = all_939_1 & addition(all_939_1, all_939_0) = all_49_0 &
% 52.31/8.23 | $i(all_939_0) & $i(all_939_1) & $i(all_49_0)
% 52.31/8.23 |
% 52.31/8.23 | ALPHA: (407) implies:
% 52.31/8.23 | (408) multiplication(all_51_0, zero) = all_939_0
% 52.31/8.23 |
% 52.31/8.23 | DELTA: instantiating (353) with fresh symbols all_981_0, all_981_1 gives:
% 52.31/8.23 | (409) multiplication(all_32_0, all_90_0) = all_981_0 &
% 52.31/8.23 | multiplication(all_32_1, all_90_0) = all_981_1 & addition(all_981_1,
% 52.31/8.23 | all_981_0) = all_55_0 & $i(all_981_0) & $i(all_981_1) &
% 52.31/8.23 | $i(all_55_0)
% 52.31/8.23 |
% 52.31/8.23 | ALPHA: (409) implies:
% 52.31/8.23 | (410) multiplication(all_32_0, all_90_0) = all_981_0
% 52.31/8.23 |
% 52.31/8.23 | DELTA: instantiating (352) with fresh symbols all_983_0, all_983_1 gives:
% 52.31/8.23 | (411) multiplication(all_32_0, all_90_0) = all_983_1 &
% 52.31/8.23 | multiplication(all_32_1, all_90_0) = all_983_0 & addition(all_983_1,
% 52.31/8.23 | all_983_0) = all_55_0 & $i(all_983_0) & $i(all_983_1) &
% 52.31/8.23 | $i(all_55_0)
% 52.31/8.23 |
% 52.31/8.23 | ALPHA: (411) implies:
% 52.31/8.23 | (412) multiplication(all_32_0, all_90_0) = all_983_1
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (344), (350), (404) imply:
% 52.31/8.23 | (413) multiplication(all_32_0, zero) = all_907_0
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (344), (350), (394) imply:
% 52.31/8.23 | (414) multiplication(all_32_0, zero) = all_843_1
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (344), (351), (406) imply:
% 52.31/8.23 | (415) multiplication(all_32_0, zero) = all_923_1
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (344), (351), (388) imply:
% 52.31/8.23 | (416) multiplication(all_32_0, zero) = all_739_0
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (344), (408) imply:
% 52.31/8.23 | (417) multiplication(all_32_0, zero) = all_939_0
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (344), (392) imply:
% 52.31/8.23 | (418) multiplication(all_32_0, zero) = all_763_1
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (344), (390) imply:
% 52.31/8.23 | (419) multiplication(all_32_0, zero) = all_741_0
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (344), (384) imply:
% 52.31/8.23 | (420) multiplication(all_32_0, zero) = all_731_1
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (208), (344) imply:
% 52.31/8.23 | (421) multiplication(all_32_0, zero) = all_142_0
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (350), (398) imply:
% 52.31/8.23 | (422) multiplication(all_32_0, zero) = all_867_1
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (350), (396) imply:
% 52.31/8.23 | (423) multiplication(all_32_0, zero) = all_847_0
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (351), (412) imply:
% 52.31/8.23 | (424) multiplication(all_32_0, zero) = all_983_1
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (351), (410) imply:
% 52.31/8.23 | (425) multiplication(all_32_0, zero) = all_981_0
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (350), (400) imply:
% 52.31/8.23 | (426) multiplication(all_22_2, zero) = all_871_1
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (167), (350) imply:
% 52.31/8.23 | (427) multiplication(all_22_2, zero) = all_49_0
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (351), (386) imply:
% 52.31/8.23 | (428) multiplication(all_22_2, zero) = all_737_1
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (157), (351) imply:
% 52.31/8.23 | (429) multiplication(all_22_2, zero) = all_55_0
% 52.31/8.23 |
% 52.31/8.23 | REDUCE: (350), (377) imply:
% 52.31/8.23 | (430) addition(zero, all_32_1) = all_557_0
% 52.31/8.23 |
% 52.31/8.23 | GROUND_INST: instantiating (19) with all_82_0, all_557_0, all_32_1, zero,
% 52.31/8.23 | simplifying with (256), (430) gives:
% 52.31/8.23 | (431) all_557_0 = all_82_0
% 52.31/8.23 |
% 52.31/8.23 | GROUND_INST: instantiating (19) with all_82_0, all_325_0, zero, all_32_1,
% 52.31/8.23 | simplifying with (329), (371) gives:
% 52.31/8.23 | (432) all_325_0 = all_82_0
% 52.31/8.23 |
% 52.31/8.23 | GROUND_INST: instantiating (19) with all_325_0, all_669_0, zero, all_32_1,
% 52.31/8.23 | simplifying with (371), (380) gives:
% 52.31/8.23 | (433) all_669_0 = all_325_0
% 52.31/8.23 |
% 52.31/8.23 | GROUND_INST: instantiating (19) with all_669_0, all_681_0, zero, all_32_1,
% 52.31/8.23 | simplifying with (380), (382) gives:
% 52.31/8.23 | (434) all_681_0 = all_669_0
% 52.31/8.23 |
% 52.31/8.23 | GROUND_INST: instantiating (19) with all_217_0, all_681_0, zero, all_32_1,
% 52.31/8.23 | simplifying with (366), (382) gives:
% 52.31/8.23 | (435) all_681_0 = all_217_0
% 52.31/8.23 |
% 52.31/8.23 | GROUND_INST: instantiating (20) with all_32_0, all_737_1, zero, all_22_2,
% 52.31/8.23 | simplifying with (40), (428) gives:
% 52.31/8.23 | (436) all_737_1 = all_32_0
% 52.31/8.23 |
% 52.31/8.23 | GROUND_INST: instantiating (20) with all_49_0, all_737_1, zero, all_22_2,
% 52.31/8.23 | simplifying with (427), (428) gives:
% 52.31/8.23 | (437) all_737_1 = all_49_0
% 52.31/8.23 |
% 52.31/8.23 | GROUND_INST: instantiating (20) with all_737_1, all_871_1, zero, all_22_2,
% 52.31/8.23 | simplifying with (426), (428) gives:
% 52.31/8.23 | (438) all_871_1 = all_737_1
% 52.31/8.23 |
% 52.31/8.23 | GROUND_INST: instantiating (20) with all_55_0, all_871_1, zero, all_22_2,
% 52.31/8.23 | simplifying with (426), (429) gives:
% 52.31/8.23 | (439) all_871_1 = all_55_0
% 52.31/8.23 |
% 52.31/8.23 | GROUND_INST: instantiating (20) with all_737_1, all_881_1, zero, all_22_2,
% 52.31/8.23 | simplifying with (402), (428) gives:
% 52.31/8.23 | (440) all_881_1 = all_737_1
% 52.31/8.23 |
% 52.31/8.23 | GROUND_INST: instantiating (20) with all_361_0, all_881_1, zero, all_22_2,
% 52.31/8.23 | simplifying with (373), (402) gives:
% 52.31/8.23 | (441) all_881_1 = all_361_0
% 52.31/8.23 |
% 52.31/8.23 | GROUND_INST: instantiating (20) with all_49_0, all_533_0, zero, all_32_0,
% 52.31/8.23 | simplifying with (72), (375) gives:
% 52.31/8.23 | (442) all_533_0 = all_49_0
% 52.31/8.23 |
% 52.31/8.23 | GROUND_INST: instantiating (20) with all_731_1, all_847_0, zero, all_32_0,
% 52.31/8.23 | simplifying with (420), (423) gives:
% 52.31/8.24 | (443) all_847_0 = all_731_1
% 52.31/8.24 |
% 52.31/8.24 | GROUND_INST: instantiating (20) with all_739_0, all_867_1, zero, all_32_0,
% 52.31/8.24 | simplifying with (416), (422) gives:
% 52.31/8.24 | (444) all_867_1 = all_739_0
% 52.31/8.24 |
% 52.31/8.24 | GROUND_INST: instantiating (20) with all_533_0, all_867_1, zero, all_32_0,
% 52.31/8.24 | simplifying with (375), (422) gives:
% 52.31/8.24 | (445) all_867_1 = all_533_0
% 52.31/8.24 |
% 52.31/8.24 | GROUND_INST: instantiating (20) with all_142_0, all_867_1, zero, all_32_0,
% 52.31/8.24 | simplifying with (421), (422) gives:
% 52.31/8.24 | (446) all_867_1 = all_142_0
% 52.31/8.24 |
% 52.31/8.24 | GROUND_INST: instantiating (20) with all_907_0, all_923_1, zero, all_32_0,
% 52.31/8.24 | simplifying with (413), (415) gives:
% 52.31/8.24 | (447) all_923_1 = all_907_0
% 52.31/8.24 |
% 52.31/8.24 | GROUND_INST: instantiating (20) with all_741_0, all_923_1, zero, all_32_0,
% 52.31/8.24 | simplifying with (415), (419) gives:
% 52.31/8.24 | (448) all_923_1 = all_741_0
% 52.31/8.24 |
% 52.31/8.24 | GROUND_INST: instantiating (20) with all_867_1, all_981_0, zero, all_32_0,
% 52.31/8.24 | simplifying with (422), (425) gives:
% 52.31/8.24 | (449) all_981_0 = all_867_1
% 52.31/8.24 |
% 52.31/8.24 | GROUND_INST: instantiating (20) with all_847_0, all_981_0, zero, all_32_0,
% 52.31/8.24 | simplifying with (423), (425) gives:
% 52.31/8.24 | (450) all_981_0 = all_847_0
% 52.31/8.24 |
% 52.31/8.24 | GROUND_INST: instantiating (20) with all_763_1, all_981_0, zero, all_32_0,
% 52.31/8.24 | simplifying with (418), (425) gives:
% 52.31/8.24 | (451) all_981_0 = all_763_1
% 52.31/8.24 |
% 52.31/8.24 | GROUND_INST: instantiating (20) with all_981_0, all_983_1, zero, all_32_0,
% 52.31/8.24 | simplifying with (424), (425) gives:
% 52.31/8.24 | (452) all_983_1 = all_981_0
% 52.31/8.24 |
% 52.31/8.24 | GROUND_INST: instantiating (20) with all_939_0, all_983_1, zero, all_32_0,
% 52.31/8.24 | simplifying with (417), (424) gives:
% 52.31/8.24 | (453) all_983_1 = all_939_0
% 52.31/8.24 |
% 52.31/8.24 | GROUND_INST: instantiating (20) with all_923_1, all_983_1, zero, all_32_0,
% 52.31/8.24 | simplifying with (415), (424) gives:
% 52.31/8.24 | (454) all_983_1 = all_923_1
% 52.31/8.24 |
% 52.31/8.24 | GROUND_INST: instantiating (20) with all_843_1, all_983_1, zero, all_32_0,
% 52.31/8.24 | simplifying with (414), (424) gives:
% 52.31/8.24 | (455) all_983_1 = all_843_1
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (452), (453) imply:
% 52.31/8.24 | (456) all_981_0 = all_939_0
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (456) implies:
% 52.31/8.24 | (457) all_981_0 = all_939_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (453), (455) imply:
% 52.31/8.24 | (458) all_939_0 = all_843_1
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (453), (454) imply:
% 52.31/8.24 | (459) all_939_0 = all_923_1
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (450), (451) imply:
% 52.31/8.24 | (460) all_847_0 = all_763_1
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (460) implies:
% 52.31/8.24 | (461) all_847_0 = all_763_1
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (449), (451) imply:
% 52.31/8.24 | (462) all_867_1 = all_763_1
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (462) implies:
% 52.31/8.24 | (463) all_867_1 = all_763_1
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (451), (457) imply:
% 52.31/8.24 | (464) all_939_0 = all_763_1
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (464) implies:
% 52.31/8.24 | (465) all_939_0 = all_763_1
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (458), (465) imply:
% 52.31/8.24 | (466) all_843_1 = all_763_1
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (458), (459) imply:
% 52.31/8.24 | (467) all_923_1 = all_843_1
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (467) implies:
% 52.31/8.24 | (468) all_923_1 = all_843_1
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (447), (448) imply:
% 52.31/8.24 | (469) all_907_0 = all_741_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (447), (468) imply:
% 52.31/8.24 | (470) all_907_0 = all_843_1
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (469), (470) imply:
% 52.31/8.24 | (471) all_843_1 = all_741_0
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (471) implies:
% 52.31/8.24 | (472) all_843_1 = all_741_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (440), (441) imply:
% 52.31/8.24 | (473) all_737_1 = all_361_0
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (473) implies:
% 52.31/8.24 | (474) all_737_1 = all_361_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (438), (439) imply:
% 52.31/8.24 | (475) all_737_1 = all_55_0
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (475) implies:
% 52.31/8.24 | (476) all_737_1 = all_55_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (444), (445) imply:
% 52.31/8.24 | (477) all_739_0 = all_533_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (444), (463) imply:
% 52.31/8.24 | (478) all_763_1 = all_739_0
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (478) implies:
% 52.31/8.24 | (479) all_763_1 = all_739_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (444), (446) imply:
% 52.31/8.24 | (480) all_739_0 = all_142_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (443), (461) imply:
% 52.31/8.24 | (481) all_763_1 = all_731_1
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (481) implies:
% 52.31/8.24 | (482) all_763_1 = all_731_1
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (466), (472) imply:
% 52.31/8.24 | (483) all_763_1 = all_741_0
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (483) implies:
% 52.31/8.24 | (484) all_763_1 = all_741_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (479), (484) imply:
% 52.31/8.24 | (485) all_741_0 = all_739_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (482), (484) imply:
% 52.31/8.24 | (486) all_741_0 = all_731_1
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (485), (486) imply:
% 52.31/8.24 | (487) all_739_0 = all_731_1
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (487) implies:
% 52.31/8.24 | (488) all_739_0 = all_731_1
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (477), (488) imply:
% 52.31/8.24 | (489) all_731_1 = all_533_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (480), (488) imply:
% 52.31/8.24 | (490) all_731_1 = all_142_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (436), (474) imply:
% 52.31/8.24 | (491) all_361_0 = all_32_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (474), (476) imply:
% 52.31/8.24 | (492) all_361_0 = all_55_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (437), (474) imply:
% 52.31/8.24 | (493) all_361_0 = all_49_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (489), (490) imply:
% 52.31/8.24 | (494) all_533_0 = all_142_0
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (494) implies:
% 52.31/8.24 | (495) all_533_0 = all_142_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (434), (435) imply:
% 52.31/8.24 | (496) all_669_0 = all_217_0
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (496) implies:
% 52.31/8.24 | (497) all_669_0 = all_217_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (433), (497) imply:
% 52.31/8.24 | (498) all_325_0 = all_217_0
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (498) implies:
% 52.31/8.24 | (499) all_325_0 = all_217_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (442), (495) imply:
% 52.31/8.24 | (500) all_142_0 = all_49_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (492), (493) imply:
% 52.31/8.24 | (501) all_55_0 = all_49_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (491), (492) imply:
% 52.31/8.24 | (502) all_55_0 = all_32_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (432), (499) imply:
% 52.31/8.24 | (503) all_217_0 = all_82_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (501), (502) imply:
% 52.31/8.24 | (504) all_49_0 = all_32_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (500), (504) imply:
% 52.31/8.24 | (505) all_142_0 = all_32_0
% 52.31/8.24 |
% 52.31/8.24 | REDUCE: (378), (431), (505) imply:
% 52.31/8.24 | (506) addition(all_32_0, all_82_0) = all_72_0
% 52.31/8.24 |
% 52.31/8.24 | REDUCE: (369), (505) imply:
% 52.31/8.24 | (507) addition(all_32_0, all_82_0) = all_237_0
% 52.31/8.24 |
% 52.31/8.24 | REDUCE: (341), (502) imply:
% 52.31/8.24 | (508) addition(all_32_0, all_32_1) = all_22_0
% 52.31/8.24 |
% 52.31/8.24 | REDUCE: (138), (504) imply:
% 52.31/8.24 | (509) addition(all_32_0, all_32_1) = all_72_0
% 52.31/8.24 |
% 52.31/8.24 | REDUCE: (367), (503) imply:
% 52.31/8.24 | (510) addition(all_32_0, all_82_0) = all_22_2
% 52.31/8.24 |
% 52.31/8.24 | GROUND_INST: instantiating (19) with all_22_0, all_72_0, all_32_1, all_32_0,
% 52.31/8.24 | simplifying with (508), (509) gives:
% 52.31/8.24 | (511) all_72_0 = all_22_0
% 52.31/8.24 |
% 52.31/8.24 | GROUND_INST: instantiating (19) with all_22_2, all_237_0, all_82_0, all_32_0,
% 52.31/8.24 | simplifying with (507), (510) gives:
% 52.31/8.24 | (512) all_237_0 = all_22_2
% 52.31/8.24 |
% 52.31/8.24 | GROUND_INST: instantiating (19) with all_72_0, all_237_0, all_82_0, all_32_0,
% 52.31/8.24 | simplifying with (506), (507) gives:
% 52.31/8.24 | (513) all_237_0 = all_72_0
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (512), (513) imply:
% 52.31/8.24 | (514) all_72_0 = all_22_2
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (514) implies:
% 52.31/8.24 | (515) all_72_0 = all_22_2
% 52.31/8.24 |
% 52.31/8.24 | COMBINE_EQS: (511), (515) imply:
% 52.31/8.24 | (516) all_22_0 = all_22_2
% 52.31/8.24 |
% 52.31/8.24 | SIMP: (516) implies:
% 52.31/8.24 | (517) all_22_0 = all_22_2
% 52.31/8.24 |
% 52.31/8.24 | REDUCE: (22), (517) imply:
% 52.31/8.24 | (518) $false
% 52.31/8.24 |
% 52.31/8.24 | CLOSE: (518) is inconsistent.
% 52.31/8.24 |
% 52.31/8.24 End of proof
% 52.31/8.24 % SZS output end Proof for theBenchmark
% 52.31/8.24
% 52.31/8.24 7624ms
%------------------------------------------------------------------------------