TSTP Solution File: KLE010+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE010+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n021.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 05:34:11 EDT 2023
% Result : Theorem 231.57s 31.66s
% Output : Proof 233.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE010+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 12:22:59 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.52/0.62 Running up to 7 provers in parallel.
% 0.52/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.52/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.52/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.52/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.52/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.52/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.52/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.38/1.03 Prover 4: Preprocessing ...
% 2.38/1.03 Prover 1: Preprocessing ...
% 2.92/1.08 Prover 5: Preprocessing ...
% 2.92/1.08 Prover 3: Preprocessing ...
% 2.92/1.08 Prover 0: Preprocessing ...
% 2.92/1.08 Prover 2: Preprocessing ...
% 2.92/1.10 Prover 6: Preprocessing ...
% 5.29/1.42 Prover 3: Constructing countermodel ...
% 5.29/1.42 Prover 1: Constructing countermodel ...
% 5.44/1.43 Prover 6: Proving ...
% 5.44/1.46 Prover 4: Constructing countermodel ...
% 5.44/1.48 Prover 5: Proving ...
% 5.44/1.48 Prover 0: Proving ...
% 5.44/1.50 Prover 2: Proving ...
% 72.89/10.31 Prover 2: stopped
% 72.89/10.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 73.24/10.34 Prover 7: Preprocessing ...
% 74.28/10.42 Prover 7: Constructing countermodel ...
% 100.86/13.98 Prover 5: stopped
% 100.86/13.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 101.50/14.02 Prover 8: Preprocessing ...
% 102.04/14.05 Prover 8: Warning: ignoring some quantifiers
% 102.04/14.05 Prover 8: Constructing countermodel ...
% 116.45/15.97 Prover 1: stopped
% 116.45/15.97 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 116.45/15.99 Prover 9: Preprocessing ...
% 116.45/16.03 Prover 9: Constructing countermodel ...
% 130.81/17.87 Prover 6: stopped
% 130.81/17.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 131.33/17.92 Prover 10: Preprocessing ...
% 131.75/17.97 Prover 10: Constructing countermodel ...
% 224.85/30.85 Prover 7: stopped
% 224.85/30.85 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 224.85/30.88 Prover 11: Preprocessing ...
% 226.10/30.94 Prover 11: Constructing countermodel ...
% 231.49/31.63 Prover 10: Found proof (size 1201)
% 231.49/31.63 Prover 10: proved (13740ms)
% 231.49/31.63 Prover 9: stopped
% 231.49/31.63 Prover 0: stopped
% 231.49/31.63 Prover 11: stopped
% 231.49/31.63 Prover 8: stopped
% 231.49/31.63 Prover 4: stopped
% 231.57/31.65 Prover 3: stopped
% 231.57/31.66
% 231.57/31.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 231.57/31.66
% 232.12/32.10 % SZS output start Proof for theBenchmark
% 232.12/32.10 Assumptions after simplification:
% 232.12/32.10 ---------------------------------
% 232.12/32.10
% 232.12/32.10 (additive_associativity)
% 232.12/32.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 232.12/32.13 (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 232.12/32.13 | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 & addition(v1, v0) = v5 &
% 232.12/32.13 $i(v5) & $i(v4)))
% 232.12/32.13
% 232.12/32.13 (additive_commutativity)
% 232.12/32.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~
% 232.12/32.13 $i(v1) | ~ $i(v0) | (addition(v1, v0) = v2 & $i(v2)))
% 232.12/32.13
% 232.12/32.13 (additive_idempotence)
% 232.12/32.14 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~ $i(v0))
% 232.12/32.14
% 232.12/32.14 (goals)
% 232.12/32.14 $i(one) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 232.12/32.14 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 232.12/32.14 [v10: $i] : ? [v11: $i] : ? [v12: $i] : (c(v1) = v3 & c(v0) = v8 &
% 232.12/32.14 multiplication(v8, v3) = v11 & multiplication(v8, v1) = v9 &
% 232.12/32.14 multiplication(v3, v0) = v4 & multiplication(v1, v0) = v2 &
% 232.12/32.14 multiplication(v0, v1) = v6 & addition(v10, v11) = v12 & addition(v7, v9) =
% 232.12/32.14 v10 & addition(v5, v6) = v7 & addition(v2, v4) = v5 & $i(v12) & $i(v11) &
% 232.12/32.14 $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 232.12/32.14 $i(v2) & $i(v1) & $i(v0) & test(v1) & test(v0) & ( ~ leq(v12, one) | ~
% 232.12/32.14 leq(one, v12)))
% 232.12/32.14
% 232.12/32.14 (left_distributivity)
% 232.12/32.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 232.12/32.14 $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) |
% 232.12/32.14 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 232.12/32.14 : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5)))
% 232.12/32.14
% 232.12/32.14 (multiplicative_associativity)
% 232.12/32.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 232.12/32.15 (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ $i(v2)
% 232.12/32.15 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1, v2) = v5 &
% 232.12/32.15 multiplication(v0, v5) = v4 & $i(v5) & $i(v4)))
% 232.12/32.15
% 232.12/32.15 (multiplicative_left_identity)
% 232.12/32.15 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(one, v0) =
% 232.12/32.15 v1) | ~ $i(v0))
% 232.12/32.15
% 232.12/32.15 (multiplicative_right_identity)
% 232.12/32.15 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 232.12/32.15 v1) | ~ $i(v0))
% 232.12/32.15
% 232.12/32.15 (order)
% 232.12/32.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (addition(v0, v1) =
% 232.12/32.15 v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1)) & ! [v0: $i] : ! [v1: $i]
% 232.12/32.15 : ( ~ (addition(v0, v1) = v1) | ~ $i(v1) | ~ $i(v0) | leq(v0, v1))
% 232.12/32.15
% 232.12/32.15 (right_distributivity)
% 232.12/32.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 232.12/32.15 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) |
% 232.12/32.15 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 232.12/32.15 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5)))
% 232.12/32.15
% 232.12/32.15 (test_2)
% 232.12/32.16 $i(one) & $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = one | ~
% 232.12/32.16 (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0)) &
% 232.12/32.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~
% 232.12/32.16 $i(v1) | ~ $i(v0) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero
% 232.12/32.16 & multiplication(v0, v1) = zero)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 232.12/32.16 (addition(v0, v1) = one) | ~ $i(v1) | ~ $i(v0) | complement(v1, v0) | ?
% 232.12/32.16 [v2: $i] : ? [v3: $i] : (( ~ (v3 = zero) & multiplication(v1, v0) = v3 &
% 232.12/32.16 $i(v3)) | ( ~ (v2 = zero) & multiplication(v0, v1) = v2 & $i(v2))))
% 232.12/32.16
% 232.12/32.16 (test_3)
% 232.12/32.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (c(v0) = v2) | ~
% 232.12/32.16 $i(v1) | ~ $i(v0) | ~ complement(v0, v1) | ~ test(v0)) & ! [v0: $i] : !
% 232.12/32.16 [v1: $i] : ( ~ (c(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ test(v0) |
% 232.12/32.16 complement(v0, v1))
% 232.12/32.16
% 232.12/32.16 (function-axioms)
% 232.43/32.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 232.43/32.16 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 232.43/32.16 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 232.43/32.16 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 232.43/32.16 [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0))
% 232.43/32.16
% 232.43/32.16 Further assumptions not needed in the proof:
% 232.43/32.16 --------------------------------------------
% 232.43/32.16 additive_identity, left_annihilation, right_annihilation, test_1, test_4
% 232.43/32.16
% 232.43/32.16 Those formulas are unsatisfiable:
% 232.43/32.16 ---------------------------------
% 232.43/32.16
% 232.43/32.16 Begin of proof
% 232.43/32.17 |
% 232.43/32.17 | ALPHA: (multiplicative_right_identity) implies:
% 232.43/32.17 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 232.43/32.17 | v1) | ~ $i(v0))
% 232.43/32.17 |
% 232.43/32.17 | ALPHA: (multiplicative_left_identity) implies:
% 232.43/32.17 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(one, v0) =
% 232.43/32.17 | v1) | ~ $i(v0))
% 232.43/32.17 |
% 232.43/32.17 | ALPHA: (order) implies:
% 232.43/32.17 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = v1) | ~ $i(v1) |
% 232.43/32.17 | ~ $i(v0) | leq(v0, v1))
% 232.43/32.17 |
% 232.43/32.17 | ALPHA: (test_2) implies:
% 232.43/32.17 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = one) | ~ $i(v1) |
% 232.43/32.17 | ~ $i(v0) | complement(v1, v0) | ? [v2: $i] : ? [v3: $i] : (( ~ (v3
% 232.43/32.17 | = zero) & multiplication(v1, v0) = v3 & $i(v3)) | ( ~ (v2 =
% 232.43/32.17 | zero) & multiplication(v0, v1) = v2 & $i(v2))))
% 232.43/32.17 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) |
% 232.43/32.17 | ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0) | (multiplication(v1,
% 232.43/32.17 | v0) = zero & multiplication(v0, v1) = zero))
% 232.43/32.17 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = one | ~ (addition(v0,
% 232.43/32.17 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ complement(v1, v0))
% 232.43/32.17 |
% 232.43/32.17 | ALPHA: (test_3) implies:
% 232.43/32.17 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (c(v0) = v1) | ~ $i(v1) | ~ $i(v0) |
% 232.43/32.17 | ~ test(v0) | complement(v0, v1))
% 232.43/32.17 |
% 232.43/32.17 | ALPHA: (goals) implies:
% 232.43/32.18 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 232.43/32.18 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 232.43/32.18 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : (c(v1) = v3 & c(v0) = v8 &
% 232.43/32.18 | multiplication(v8, v3) = v11 & multiplication(v8, v1) = v9 &
% 232.43/32.18 | multiplication(v3, v0) = v4 & multiplication(v1, v0) = v2 &
% 232.43/32.18 | multiplication(v0, v1) = v6 & addition(v10, v11) = v12 & addition(v7,
% 232.43/32.18 | v9) = v10 & addition(v5, v6) = v7 & addition(v2, v4) = v5 & $i(v12)
% 232.43/32.18 | & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 232.43/32.18 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & test(v1) & test(v0) & (
% 232.43/32.18 | ~ leq(v12, one) | ~ leq(one, v12)))
% 232.43/32.18 |
% 232.43/32.18 | ALPHA: (function-axioms) implies:
% 232.43/32.18 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 232.43/32.18 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 232.43/32.18 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 232.43/32.18 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 232.43/32.18 |
% 232.43/32.18 | DELTA: instantiating (8) with fresh symbols all_20_0, all_20_1, all_20_2,
% 232.43/32.18 | all_20_3, all_20_4, all_20_5, all_20_6, all_20_7, all_20_8, all_20_9,
% 232.43/32.18 | all_20_10, all_20_11, all_20_12 gives:
% 232.43/32.18 | (11) c(all_20_11) = all_20_9 & c(all_20_12) = all_20_4 &
% 232.43/32.18 | multiplication(all_20_4, all_20_9) = all_20_1 &
% 232.43/32.18 | multiplication(all_20_4, all_20_11) = all_20_3 &
% 232.43/32.18 | multiplication(all_20_9, all_20_12) = all_20_8 &
% 232.43/32.18 | multiplication(all_20_11, all_20_12) = all_20_10 &
% 232.43/32.18 | multiplication(all_20_12, all_20_11) = all_20_6 & addition(all_20_2,
% 232.43/32.18 | all_20_1) = all_20_0 & addition(all_20_5, all_20_3) = all_20_2 &
% 232.43/32.18 | addition(all_20_7, all_20_6) = all_20_5 & addition(all_20_10,
% 232.43/32.18 | all_20_8) = all_20_7 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) &
% 232.43/32.18 | $i(all_20_3) & $i(all_20_4) & $i(all_20_5) & $i(all_20_6) &
% 232.43/32.18 | $i(all_20_7) & $i(all_20_8) & $i(all_20_9) & $i(all_20_10) &
% 232.43/32.18 | $i(all_20_11) & $i(all_20_12) & test(all_20_11) & test(all_20_12) & (
% 232.43/32.19 | ~ leq(all_20_0, one) | ~ leq(one, all_20_0))
% 232.43/32.19 |
% 232.43/32.19 | ALPHA: (11) implies:
% 232.43/32.19 | (12) test(all_20_12)
% 232.43/32.19 | (13) test(all_20_11)
% 232.43/32.19 | (14) $i(all_20_12)
% 232.43/32.19 | (15) $i(all_20_11)
% 232.43/32.19 | (16) $i(all_20_10)
% 232.43/32.19 | (17) $i(all_20_9)
% 232.43/32.19 | (18) $i(all_20_8)
% 232.43/32.19 | (19) $i(all_20_6)
% 232.43/32.19 | (20) $i(all_20_4)
% 232.43/32.19 | (21) $i(all_20_3)
% 232.43/32.19 | (22) $i(all_20_1)
% 232.43/32.19 | (23) addition(all_20_10, all_20_8) = all_20_7
% 232.43/32.19 | (24) addition(all_20_7, all_20_6) = all_20_5
% 232.43/32.19 | (25) addition(all_20_5, all_20_3) = all_20_2
% 232.43/32.19 | (26) addition(all_20_2, all_20_1) = all_20_0
% 232.43/32.19 | (27) multiplication(all_20_12, all_20_11) = all_20_6
% 232.43/32.19 | (28) multiplication(all_20_11, all_20_12) = all_20_10
% 232.43/32.19 | (29) multiplication(all_20_9, all_20_12) = all_20_8
% 232.43/32.19 | (30) multiplication(all_20_4, all_20_11) = all_20_3
% 232.43/32.19 | (31) multiplication(all_20_4, all_20_9) = all_20_1
% 232.43/32.19 | (32) c(all_20_12) = all_20_4
% 232.43/32.19 | (33) c(all_20_11) = all_20_9
% 232.43/32.19 | (34) ~ leq(all_20_0, one) | ~ leq(one, all_20_0)
% 232.43/32.19 |
% 232.43/32.19 | GROUND_INST: instantiating (additive_commutativity) with all_20_10, all_20_8,
% 232.43/32.19 | all_20_7, simplifying with (16), (18), (23) gives:
% 232.43/32.19 | (35) addition(all_20_8, all_20_10) = all_20_7 & $i(all_20_7)
% 232.43/32.19 |
% 232.43/32.19 | ALPHA: (35) implies:
% 232.43/32.19 | (36) $i(all_20_7)
% 232.43/32.19 | (37) addition(all_20_8, all_20_10) = all_20_7
% 232.43/32.19 |
% 232.43/32.19 | GROUND_INST: instantiating (additive_associativity) with all_20_6, all_20_8,
% 232.43/32.19 | all_20_10, all_20_7, all_20_5, simplifying with (16), (18), (19),
% 232.43/32.19 | (23), (24) gives:
% 232.43/32.19 | (38) ? [v0: $i] : (addition(all_20_8, all_20_6) = v0 & addition(all_20_10,
% 232.43/32.19 | v0) = all_20_5 & $i(v0) & $i(all_20_5))
% 232.43/32.19 |
% 232.43/32.19 | GROUND_INST: instantiating (additive_commutativity) with all_20_7, all_20_6,
% 232.43/32.19 | all_20_5, simplifying with (19), (24), (36) gives:
% 232.43/32.19 | (39) addition(all_20_6, all_20_7) = all_20_5 & $i(all_20_5)
% 232.43/32.19 |
% 232.43/32.19 | ALPHA: (39) implies:
% 232.43/32.19 | (40) $i(all_20_5)
% 232.43/32.19 | (41) addition(all_20_6, all_20_7) = all_20_5
% 232.43/32.19 |
% 232.43/32.19 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_6,
% 232.43/32.19 | all_20_7, all_20_5, all_20_2, simplifying with (19), (21), (24),
% 232.43/32.19 | (25), (36) gives:
% 232.43/32.20 | (42) ? [v0: $i] : (addition(all_20_6, all_20_3) = v0 & addition(all_20_7,
% 232.43/32.20 | v0) = all_20_2 & $i(v0) & $i(all_20_2))
% 232.43/32.20 |
% 232.43/32.20 | GROUND_INST: instantiating (additive_commutativity) with all_20_5, all_20_3,
% 232.43/32.20 | all_20_2, simplifying with (21), (25), (40) gives:
% 232.43/32.20 | (43) addition(all_20_3, all_20_5) = all_20_2 & $i(all_20_2)
% 232.43/32.20 |
% 232.43/32.20 | ALPHA: (43) implies:
% 232.43/32.20 | (44) addition(all_20_3, all_20_5) = all_20_2
% 232.43/32.20 |
% 232.43/32.20 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_3,
% 232.43/32.20 | all_20_5, all_20_2, all_20_0, simplifying with (21), (22), (25),
% 232.43/32.20 | (26), (40) gives:
% 232.43/32.20 | (45) ? [v0: $i] : (addition(all_20_3, all_20_1) = v0 & addition(all_20_5,
% 232.43/32.20 | v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 232.43/32.20 |
% 232.43/32.20 | GROUND_INST: instantiating (left_distributivity) with all_20_11, all_20_9,
% 232.43/32.20 | all_20_12, all_20_10, all_20_8, all_20_7, simplifying with (14),
% 232.43/32.20 | (15), (17), (23), (28), (29) gives:
% 232.43/32.20 | (46) ? [v0: $i] : (multiplication(v0, all_20_12) = all_20_7 &
% 232.43/32.20 | addition(all_20_11, all_20_9) = v0 & $i(v0) & $i(all_20_7))
% 232.43/32.20 |
% 232.43/32.20 | GROUND_INST: instantiating (7) with all_20_12, all_20_4, simplifying with
% 232.43/32.20 | (12), (14), (20), (32) gives:
% 232.43/32.20 | (47) complement(all_20_12, all_20_4)
% 232.43/32.20 |
% 232.43/32.20 | GROUND_INST: instantiating (7) with all_20_11, all_20_9, simplifying with
% 232.43/32.20 | (13), (15), (17), (33) gives:
% 232.43/32.20 | (48) complement(all_20_11, all_20_9)
% 232.43/32.20 |
% 232.43/32.20 | DELTA: instantiating (45) with fresh symbol all_32_0 gives:
% 232.43/32.20 | (49) addition(all_20_3, all_20_1) = all_32_0 & addition(all_20_5, all_32_0)
% 232.43/32.20 | = all_20_0 & $i(all_32_0) & $i(all_20_0)
% 232.43/32.20 |
% 232.43/32.20 | ALPHA: (49) implies:
% 232.43/32.20 | (50) $i(all_32_0)
% 232.43/32.20 | (51) addition(all_20_5, all_32_0) = all_20_0
% 232.43/32.20 | (52) addition(all_20_3, all_20_1) = all_32_0
% 232.43/32.20 |
% 232.43/32.20 | DELTA: instantiating (46) with fresh symbol all_34_0 gives:
% 232.43/32.20 | (53) multiplication(all_34_0, all_20_12) = all_20_7 & addition(all_20_11,
% 232.43/32.20 | all_20_9) = all_34_0 & $i(all_34_0) & $i(all_20_7)
% 232.43/32.20 |
% 232.43/32.20 | ALPHA: (53) implies:
% 232.43/32.20 | (54) addition(all_20_11, all_20_9) = all_34_0
% 232.43/32.20 |
% 232.43/32.20 | DELTA: instantiating (42) with fresh symbol all_36_0 gives:
% 232.43/32.20 | (55) addition(all_20_6, all_20_3) = all_36_0 & addition(all_20_7, all_36_0)
% 232.43/32.20 | = all_20_2 & $i(all_36_0) & $i(all_20_2)
% 232.43/32.20 |
% 232.43/32.20 | ALPHA: (55) implies:
% 232.43/32.20 | (56) $i(all_36_0)
% 232.43/32.20 | (57) addition(all_20_7, all_36_0) = all_20_2
% 232.43/32.20 | (58) addition(all_20_6, all_20_3) = all_36_0
% 232.43/32.20 |
% 232.43/32.20 | DELTA: instantiating (38) with fresh symbol all_38_0 gives:
% 232.43/32.20 | (59) addition(all_20_8, all_20_6) = all_38_0 & addition(all_20_10,
% 232.43/32.20 | all_38_0) = all_20_5 & $i(all_38_0) & $i(all_20_5)
% 232.43/32.20 |
% 232.43/32.20 | ALPHA: (59) implies:
% 232.43/32.20 | (60) $i(all_38_0)
% 232.43/32.20 | (61) addition(all_20_10, all_38_0) = all_20_5
% 232.43/32.20 | (62) addition(all_20_8, all_20_6) = all_38_0
% 232.43/32.20 |
% 232.43/32.20 | GROUND_INST: instantiating (additive_commutativity) with all_20_11, all_20_9,
% 232.43/32.20 | all_34_0, simplifying with (15), (17), (54) gives:
% 232.43/32.20 | (63) addition(all_20_9, all_20_11) = all_34_0 & $i(all_34_0)
% 232.43/32.20 |
% 232.43/32.20 | ALPHA: (63) implies:
% 232.43/32.20 | (64) addition(all_20_9, all_20_11) = all_34_0
% 232.43/32.20 |
% 232.43/32.21 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_38_0,
% 232.43/32.21 | all_20_10, all_20_5, all_20_2, simplifying with (16), (21), (25),
% 232.43/32.21 | (60), (61) gives:
% 232.43/32.21 | (65) ? [v0: $i] : (addition(all_38_0, all_20_3) = v0 & addition(all_20_10,
% 232.43/32.21 | v0) = all_20_2 & $i(v0) & $i(all_20_2))
% 232.43/32.21 |
% 232.43/32.21 | GROUND_INST: instantiating (additive_commutativity) with all_20_10, all_38_0,
% 232.43/32.21 | all_20_5, simplifying with (16), (60), (61) gives:
% 232.43/32.21 | (66) addition(all_38_0, all_20_10) = all_20_5 & $i(all_20_5)
% 232.43/32.21 |
% 232.43/32.21 | ALPHA: (66) implies:
% 232.43/32.21 | (67) addition(all_38_0, all_20_10) = all_20_5
% 232.43/32.21 |
% 232.43/32.21 | GROUND_INST: instantiating (left_distributivity) with all_20_9, all_20_11,
% 232.43/32.21 | all_20_12, all_20_8, all_20_10, all_20_7, simplifying with (14),
% 232.43/32.21 | (15), (17), (28), (29), (37) gives:
% 232.43/32.21 | (68) ? [v0: $i] : (multiplication(v0, all_20_12) = all_20_7 &
% 232.43/32.21 | addition(all_20_9, all_20_11) = v0 & $i(v0) & $i(all_20_7))
% 232.43/32.21 |
% 232.43/32.21 | GROUND_INST: instantiating (additive_associativity) with all_20_6, all_20_10,
% 232.43/32.21 | all_20_8, all_20_7, all_20_5, simplifying with (16), (18), (19),
% 232.43/32.21 | (24), (37) gives:
% 232.43/32.21 | (69) ? [v0: $i] : (addition(all_20_8, v0) = all_20_5 & addition(all_20_10,
% 232.43/32.21 | all_20_6) = v0 & $i(v0) & $i(all_20_5))
% 232.43/32.21 |
% 232.43/32.21 | GROUND_INST: instantiating (additive_commutativity) with all_20_8, all_20_6,
% 232.43/32.21 | all_38_0, simplifying with (18), (19), (62) gives:
% 232.43/32.21 | (70) addition(all_20_6, all_20_8) = all_38_0 & $i(all_38_0)
% 232.43/32.21 |
% 232.43/32.21 | ALPHA: (70) implies:
% 232.43/32.21 | (71) addition(all_20_6, all_20_8) = all_38_0
% 232.43/32.21 |
% 232.43/32.21 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_36_0,
% 232.43/32.21 | all_20_7, all_20_2, all_20_0, simplifying with (22), (26), (36),
% 232.43/32.21 | (56), (57) gives:
% 232.43/32.21 | (72) ? [v0: $i] : (addition(all_36_0, all_20_1) = v0 & addition(all_20_7,
% 232.43/32.21 | v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 232.43/32.21 |
% 232.43/32.21 | GROUND_INST: instantiating (additive_associativity) with all_36_0, all_20_8,
% 232.43/32.21 | all_20_10, all_20_7, all_20_2, simplifying with (16), (18), (23),
% 232.43/32.21 | (56), (57) gives:
% 232.43/32.21 | (73) ? [v0: $i] : (addition(all_20_8, all_36_0) = v0 & addition(all_20_10,
% 232.43/32.21 | v0) = all_20_2 & $i(v0) & $i(all_20_2))
% 232.43/32.21 |
% 232.43/32.21 | GROUND_INST: instantiating (additive_associativity) with all_36_0, all_20_10,
% 232.43/32.21 | all_20_8, all_20_7, all_20_2, simplifying with (16), (18), (37),
% 232.43/32.21 | (56), (57) gives:
% 232.43/32.21 | (74) ? [v0: $i] : (addition(all_20_8, v0) = all_20_2 & addition(all_20_10,
% 232.43/32.21 | all_36_0) = v0 & $i(v0) & $i(all_20_2))
% 232.43/32.21 |
% 232.43/32.21 | GROUND_INST: instantiating (additive_commutativity) with all_20_7, all_36_0,
% 232.43/32.21 | all_20_2, simplifying with (36), (56), (57) gives:
% 232.43/32.21 | (75) addition(all_36_0, all_20_7) = all_20_2 & $i(all_20_2)
% 232.43/32.21 |
% 232.43/32.21 | ALPHA: (75) implies:
% 232.43/32.21 | (76) addition(all_36_0, all_20_7) = all_20_2
% 232.43/32.21 |
% 232.43/32.21 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_7,
% 232.43/32.21 | all_20_6, all_20_5, all_20_2, simplifying with (19), (21), (25),
% 232.43/32.21 | (36), (41) gives:
% 232.43/32.21 | (77) ? [v0: $i] : (addition(all_20_6, v0) = all_20_2 & addition(all_20_7,
% 232.43/32.22 | all_20_3) = v0 & $i(v0) & $i(all_20_2))
% 232.43/32.22 |
% 232.43/32.22 | GROUND_INST: instantiating (left_distributivity) with all_20_12, all_20_4,
% 232.43/32.22 | all_20_11, all_20_6, all_20_3, all_36_0, simplifying with (14),
% 232.43/32.22 | (15), (20), (27), (30), (58) gives:
% 232.43/32.22 | (78) ? [v0: $i] : (multiplication(v0, all_20_11) = all_36_0 &
% 232.43/32.22 | addition(all_20_12, all_20_4) = v0 & $i(v0) & $i(all_36_0))
% 232.43/32.22 |
% 232.43/32.22 | GROUND_INST: instantiating (additive_commutativity) with all_20_6, all_20_3,
% 232.43/32.22 | all_36_0, simplifying with (19), (21), (58) gives:
% 232.43/32.22 | (79) addition(all_20_3, all_20_6) = all_36_0 & $i(all_36_0)
% 232.43/32.22 |
% 232.43/32.22 | ALPHA: (79) implies:
% 232.43/32.22 | (80) addition(all_20_3, all_20_6) = all_36_0
% 232.43/32.22 |
% 232.43/32.22 | GROUND_INST: instantiating (additive_associativity) with all_32_0, all_20_6,
% 232.43/32.22 | all_20_7, all_20_5, all_20_0, simplifying with (19), (24), (36),
% 232.43/32.22 | (50), (51) gives:
% 232.43/32.22 | (81) ? [v0: $i] : (addition(all_20_6, all_32_0) = v0 & addition(all_20_7,
% 232.43/32.22 | v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 232.43/32.22 |
% 232.43/32.22 | GROUND_INST: instantiating (additive_associativity) with all_32_0, all_20_7,
% 232.43/32.22 | all_20_6, all_20_5, all_20_0, simplifying with (19), (36), (41),
% 232.43/32.22 | (50), (51) gives:
% 232.43/32.22 | (82) ? [v0: $i] : (addition(all_20_6, v0) = all_20_0 & addition(all_20_7,
% 232.43/32.22 | all_32_0) = v0 & $i(v0) & $i(all_20_0))
% 232.43/32.22 |
% 232.43/32.22 | GROUND_INST: instantiating (additive_associativity) with all_32_0, all_38_0,
% 232.43/32.22 | all_20_10, all_20_5, all_20_0, simplifying with (16), (50), (51),
% 232.43/32.22 | (60), (61) gives:
% 232.43/32.22 | (83) ? [v0: $i] : (addition(all_38_0, all_32_0) = v0 & addition(all_20_10,
% 232.43/32.22 | v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 232.43/32.22 |
% 232.43/32.22 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_5,
% 232.43/32.22 | all_20_3, all_20_2, all_20_0, simplifying with (21), (22), (26),
% 232.43/32.22 | (40), (44) gives:
% 232.43/32.22 | (84) ? [v0: $i] : (addition(all_20_3, v0) = all_20_0 & addition(all_20_5,
% 232.43/32.22 | all_20_1) = v0 & $i(v0) & $i(all_20_0))
% 232.43/32.22 |
% 232.43/32.22 | GROUND_INST: instantiating (right_distributivity) with all_20_4, all_20_11,
% 232.43/32.22 | all_20_9, all_20_3, all_20_1, all_32_0, simplifying with (15),
% 232.43/32.22 | (17), (20), (30), (31), (52) gives:
% 232.43/32.22 | (85) ? [v0: $i] : (multiplication(all_20_4, v0) = all_32_0 &
% 232.43/32.22 | addition(all_20_11, all_20_9) = v0 & $i(v0) & $i(all_32_0))
% 232.43/32.22 |
% 232.43/32.22 | GROUND_INST: instantiating (additive_commutativity) with all_20_3, all_20_1,
% 232.43/32.22 | all_32_0, simplifying with (21), (22), (52) gives:
% 232.43/32.22 | (86) addition(all_20_1, all_20_3) = all_32_0 & $i(all_32_0)
% 232.43/32.22 |
% 232.43/32.22 | ALPHA: (86) implies:
% 232.43/32.22 | (87) addition(all_20_1, all_20_3) = all_32_0
% 232.43/32.22 |
% 232.43/32.22 | DELTA: instantiating (85) with fresh symbol all_46_0 gives:
% 232.43/32.22 | (88) multiplication(all_20_4, all_46_0) = all_32_0 & addition(all_20_11,
% 232.43/32.22 | all_20_9) = all_46_0 & $i(all_46_0) & $i(all_32_0)
% 232.43/32.22 |
% 232.43/32.22 | ALPHA: (88) implies:
% 232.43/32.22 | (89) addition(all_20_11, all_20_9) = all_46_0
% 232.43/32.22 | (90) multiplication(all_20_4, all_46_0) = all_32_0
% 232.43/32.22 |
% 232.43/32.22 | DELTA: instantiating (84) with fresh symbol all_48_0 gives:
% 232.43/32.22 | (91) addition(all_20_3, all_48_0) = all_20_0 & addition(all_20_5, all_20_1)
% 232.43/32.22 | = all_48_0 & $i(all_48_0) & $i(all_20_0)
% 232.43/32.22 |
% 232.43/32.22 | ALPHA: (91) implies:
% 232.43/32.22 | (92) addition(all_20_5, all_20_1) = all_48_0
% 232.43/32.22 | (93) addition(all_20_3, all_48_0) = all_20_0
% 232.43/32.22 |
% 232.43/32.22 | DELTA: instantiating (74) with fresh symbol all_50_0 gives:
% 232.43/32.22 | (94) addition(all_20_8, all_50_0) = all_20_2 & addition(all_20_10,
% 232.43/32.23 | all_36_0) = all_50_0 & $i(all_50_0) & $i(all_20_2)
% 232.43/32.23 |
% 232.43/32.23 | ALPHA: (94) implies:
% 232.43/32.23 | (95) addition(all_20_10, all_36_0) = all_50_0
% 232.43/32.23 | (96) addition(all_20_8, all_50_0) = all_20_2
% 232.43/32.23 |
% 232.43/32.23 | DELTA: instantiating (73) with fresh symbol all_52_0 gives:
% 232.43/32.23 | (97) addition(all_20_8, all_36_0) = all_52_0 & addition(all_20_10,
% 232.43/32.23 | all_52_0) = all_20_2 & $i(all_52_0) & $i(all_20_2)
% 232.43/32.23 |
% 232.43/32.23 | ALPHA: (97) implies:
% 232.43/32.23 | (98) $i(all_52_0)
% 232.43/32.23 | (99) addition(all_20_10, all_52_0) = all_20_2
% 232.43/32.23 | (100) addition(all_20_8, all_36_0) = all_52_0
% 232.43/32.23 |
% 232.43/32.23 | DELTA: instantiating (82) with fresh symbol all_54_0 gives:
% 232.43/32.23 | (101) addition(all_20_6, all_54_0) = all_20_0 & addition(all_20_7,
% 232.43/32.23 | all_32_0) = all_54_0 & $i(all_54_0) & $i(all_20_0)
% 232.43/32.23 |
% 232.43/32.23 | ALPHA: (101) implies:
% 232.43/32.23 | (102) addition(all_20_7, all_32_0) = all_54_0
% 232.43/32.23 |
% 232.43/32.23 | DELTA: instantiating (65) with fresh symbol all_56_0 gives:
% 232.43/32.23 | (103) addition(all_38_0, all_20_3) = all_56_0 & addition(all_20_10,
% 232.43/32.23 | all_56_0) = all_20_2 & $i(all_56_0) & $i(all_20_2)
% 232.43/32.23 |
% 232.43/32.23 | ALPHA: (103) implies:
% 232.43/32.23 | (104) $i(all_56_0)
% 232.43/32.23 | (105) addition(all_20_10, all_56_0) = all_20_2
% 232.43/32.23 | (106) addition(all_38_0, all_20_3) = all_56_0
% 232.43/32.23 |
% 232.43/32.23 | DELTA: instantiating (77) with fresh symbol all_58_0 gives:
% 232.43/32.23 | (107) addition(all_20_6, all_58_0) = all_20_2 & addition(all_20_7,
% 232.43/32.23 | all_20_3) = all_58_0 & $i(all_58_0) & $i(all_20_2)
% 232.43/32.23 |
% 232.43/32.23 | ALPHA: (107) implies:
% 232.43/32.23 | (108) addition(all_20_7, all_20_3) = all_58_0
% 232.43/32.23 | (109) addition(all_20_6, all_58_0) = all_20_2
% 232.43/32.23 |
% 232.43/32.23 | DELTA: instantiating (69) with fresh symbol all_60_0 gives:
% 232.43/32.23 | (110) addition(all_20_8, all_60_0) = all_20_5 & addition(all_20_10,
% 232.43/32.23 | all_20_6) = all_60_0 & $i(all_60_0) & $i(all_20_5)
% 232.43/32.23 |
% 232.43/32.23 | ALPHA: (110) implies:
% 232.43/32.23 | (111) addition(all_20_10, all_20_6) = all_60_0
% 232.43/32.23 | (112) addition(all_20_8, all_60_0) = all_20_5
% 232.43/32.23 |
% 232.43/32.23 | DELTA: instantiating (78) with fresh symbol all_62_0 gives:
% 232.43/32.23 | (113) multiplication(all_62_0, all_20_11) = all_36_0 & addition(all_20_12,
% 232.43/32.23 | all_20_4) = all_62_0 & $i(all_62_0) & $i(all_36_0)
% 232.43/32.23 |
% 232.43/32.23 | ALPHA: (113) implies:
% 232.43/32.23 | (114) addition(all_20_12, all_20_4) = all_62_0
% 232.43/32.23 |
% 232.43/32.23 | DELTA: instantiating (72) with fresh symbol all_64_0 gives:
% 232.43/32.23 | (115) addition(all_36_0, all_20_1) = all_64_0 & addition(all_20_7,
% 232.43/32.23 | all_64_0) = all_20_0 & $i(all_64_0) & $i(all_20_0)
% 232.43/32.23 |
% 232.43/32.23 | ALPHA: (115) implies:
% 232.43/32.23 | (116) $i(all_64_0)
% 232.43/32.23 | (117) addition(all_20_7, all_64_0) = all_20_0
% 232.43/32.23 | (118) addition(all_36_0, all_20_1) = all_64_0
% 232.43/32.23 |
% 232.43/32.23 | DELTA: instantiating (83) with fresh symbol all_66_0 gives:
% 232.43/32.23 | (119) addition(all_38_0, all_32_0) = all_66_0 & addition(all_20_10,
% 232.43/32.23 | all_66_0) = all_20_0 & $i(all_66_0) & $i(all_20_0)
% 232.43/32.23 |
% 232.43/32.23 | ALPHA: (119) implies:
% 232.43/32.23 | (120) $i(all_66_0)
% 232.43/32.23 | (121) addition(all_20_10, all_66_0) = all_20_0
% 232.43/32.23 | (122) addition(all_38_0, all_32_0) = all_66_0
% 232.43/32.23 |
% 232.43/32.23 | DELTA: instantiating (68) with fresh symbol all_68_0 gives:
% 232.43/32.23 | (123) multiplication(all_68_0, all_20_12) = all_20_7 & addition(all_20_9,
% 232.43/32.23 | all_20_11) = all_68_0 & $i(all_68_0) & $i(all_20_7)
% 232.43/32.23 |
% 232.43/32.23 | ALPHA: (123) implies:
% 232.43/32.23 | (124) addition(all_20_9, all_20_11) = all_68_0
% 232.43/32.23 | (125) multiplication(all_68_0, all_20_12) = all_20_7
% 232.43/32.23 |
% 232.43/32.23 | DELTA: instantiating (81) with fresh symbol all_70_0 gives:
% 232.43/32.23 | (126) addition(all_20_6, all_32_0) = all_70_0 & addition(all_20_7,
% 232.43/32.23 | all_70_0) = all_20_0 & $i(all_70_0) & $i(all_20_0)
% 232.43/32.23 |
% 232.43/32.23 | ALPHA: (126) implies:
% 232.43/32.23 | (127) $i(all_70_0)
% 232.43/32.23 | (128) addition(all_20_7, all_70_0) = all_20_0
% 232.43/32.23 | (129) addition(all_20_6, all_32_0) = all_70_0
% 232.43/32.23 |
% 232.43/32.23 | GROUND_INST: instantiating (9) with all_34_0, all_46_0, all_20_9, all_20_11,
% 232.43/32.23 | simplifying with (54), (89) gives:
% 232.43/32.23 | (130) all_46_0 = all_34_0
% 232.43/32.23 |
% 232.43/32.23 | GROUND_INST: instantiating (9) with all_34_0, all_68_0, all_20_11, all_20_9,
% 232.43/32.23 | simplifying with (64), (124) gives:
% 232.43/32.23 | (131) all_68_0 = all_34_0
% 232.43/32.23 |
% 232.43/32.23 | REDUCE: (125), (131) imply:
% 232.43/32.23 | (132) multiplication(all_34_0, all_20_12) = all_20_7
% 232.43/32.23 |
% 232.43/32.23 | REDUCE: (90), (130) imply:
% 232.43/32.23 | (133) multiplication(all_20_4, all_34_0) = all_32_0
% 232.43/32.23 |
% 232.43/32.23 | GROUND_INST: instantiating (additive_commutativity) with all_20_12, all_20_4,
% 232.43/32.23 | all_62_0, simplifying with (14), (20), (114) gives:
% 232.43/32.24 | (134) addition(all_20_4, all_20_12) = all_62_0 & $i(all_62_0)
% 232.43/32.24 |
% 232.43/32.24 | ALPHA: (134) implies:
% 232.43/32.24 | (135) addition(all_20_4, all_20_12) = all_62_0
% 232.43/32.24 |
% 232.43/32.24 | GROUND_INST: instantiating (additive_commutativity) with all_20_10, all_20_6,
% 232.43/32.24 | all_60_0, simplifying with (16), (19), (111) gives:
% 232.43/32.24 | (136) addition(all_20_6, all_20_10) = all_60_0 & $i(all_60_0)
% 232.43/32.24 |
% 232.43/32.24 | ALPHA: (136) implies:
% 232.43/32.24 | (137) $i(all_60_0)
% 232.43/32.24 | (138) addition(all_20_6, all_20_10) = all_60_0
% 232.43/32.24 |
% 232.43/32.24 | GROUND_INST: instantiating (additive_commutativity) with all_20_10, all_36_0,
% 232.43/32.24 | all_50_0, simplifying with (16), (56), (95) gives:
% 232.43/32.24 | (139) addition(all_36_0, all_20_10) = all_50_0 & $i(all_50_0)
% 232.43/32.24 |
% 232.43/32.24 | ALPHA: (139) implies:
% 232.43/32.24 | (140) $i(all_50_0)
% 232.43/32.24 | (141) addition(all_36_0, all_20_10) = all_50_0
% 232.43/32.24 |
% 232.43/32.24 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_52_0,
% 232.43/32.24 | all_20_10, all_20_2, all_20_0, simplifying with (16), (22), (26),
% 232.43/32.24 | (98), (99) gives:
% 232.43/32.24 | (142) ? [v0: $i] : (addition(all_52_0, all_20_1) = v0 &
% 232.43/32.24 | addition(all_20_10, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 232.43/32.24 |
% 232.43/32.24 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_56_0,
% 232.43/32.24 | all_20_10, all_20_2, all_20_0, simplifying with (16), (22), (26),
% 232.43/32.24 | (104), (105) gives:
% 232.43/32.24 | (143) ? [v0: $i] : (addition(all_56_0, all_20_1) = v0 &
% 232.43/32.24 | addition(all_20_10, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 232.43/32.24 |
% 232.43/32.24 | GROUND_INST: instantiating (additive_commutativity) with all_20_10, all_56_0,
% 232.43/32.24 | all_20_2, simplifying with (16), (104), (105) gives:
% 232.43/32.24 | (144) addition(all_56_0, all_20_10) = all_20_2 & $i(all_20_2)
% 232.43/32.24 |
% 232.43/32.24 | ALPHA: (144) implies:
% 232.43/32.24 | (145) addition(all_56_0, all_20_10) = all_20_2
% 232.43/32.24 |
% 232.43/32.24 | GROUND_INST: instantiating (additive_commutativity) with all_20_10, all_66_0,
% 232.43/32.24 | all_20_0, simplifying with (16), (120), (121) gives:
% 232.43/32.24 | (146) addition(all_66_0, all_20_10) = all_20_0 & $i(all_20_0)
% 232.43/32.24 |
% 232.43/32.24 | ALPHA: (146) implies:
% 232.43/32.24 | (147) addition(all_66_0, all_20_10) = all_20_0
% 232.43/32.24 |
% 232.43/32.24 | GROUND_INST: instantiating (6) with all_20_9, all_20_11, all_34_0, simplifying
% 232.43/32.24 | with (15), (17), (48), (64) gives:
% 232.83/32.24 | (148) all_34_0 = one
% 232.83/32.24 |
% 232.83/32.24 | GROUND_INST: instantiating (additive_commutativity) with all_20_8, all_36_0,
% 232.83/32.24 | all_52_0, simplifying with (18), (56), (100) gives:
% 232.83/32.24 | (149) addition(all_36_0, all_20_8) = all_52_0 & $i(all_52_0)
% 232.83/32.24 |
% 232.83/32.24 | ALPHA: (149) implies:
% 232.83/32.24 | (150) addition(all_36_0, all_20_8) = all_52_0
% 232.83/32.24 |
% 232.83/32.24 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_50_0,
% 232.83/32.24 | all_20_8, all_20_2, all_20_0, simplifying with (18), (22), (26),
% 232.83/32.24 | (96), (140) gives:
% 232.83/32.24 | (151) ? [v0: $i] : (addition(all_50_0, all_20_1) = v0 & addition(all_20_8,
% 232.83/32.24 | v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 232.83/32.24 |
% 232.83/32.24 | GROUND_INST: instantiating (additive_commutativity) with all_20_8, all_50_0,
% 232.83/32.24 | all_20_2, simplifying with (18), (96), (140) gives:
% 232.83/32.24 | (152) addition(all_50_0, all_20_8) = all_20_2 & $i(all_20_2)
% 232.83/32.24 |
% 232.83/32.24 | ALPHA: (152) implies:
% 232.83/32.24 | (153) addition(all_50_0, all_20_8) = all_20_2
% 232.83/32.24 |
% 232.83/32.24 | GROUND_INST: instantiating (additive_associativity) with all_32_0, all_60_0,
% 232.83/32.24 | all_20_8, all_20_5, all_20_0, simplifying with (18), (50), (51),
% 232.83/32.24 | (112), (137) gives:
% 232.83/32.25 | (154) ? [v0: $i] : (addition(all_60_0, all_32_0) = v0 & addition(all_20_8,
% 232.83/32.25 | v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 232.83/32.25 |
% 232.83/32.25 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_60_0,
% 232.83/32.25 | all_20_8, all_20_5, all_20_2, simplifying with (18), (21), (25),
% 232.83/32.25 | (112), (137) gives:
% 232.83/32.25 | (155) ? [v0: $i] : (addition(all_60_0, all_20_3) = v0 & addition(all_20_8,
% 232.83/32.25 | v0) = all_20_2 & $i(v0) & $i(all_20_2))
% 232.83/32.25 |
% 232.83/32.25 | GROUND_INST: instantiating (additive_commutativity) with all_20_8, all_60_0,
% 232.83/32.25 | all_20_5, simplifying with (18), (112), (137) gives:
% 232.83/32.25 | (156) addition(all_60_0, all_20_8) = all_20_5 & $i(all_20_5)
% 232.83/32.25 |
% 232.83/32.25 | ALPHA: (156) implies:
% 232.83/32.25 | (157) addition(all_60_0, all_20_8) = all_20_5
% 232.83/32.25 |
% 232.83/32.25 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_10,
% 232.83/32.25 | all_20_8, all_20_7, all_58_0, simplifying with (16), (18), (21),
% 232.83/32.25 | (37), (108) gives:
% 232.83/32.25 | (158) ? [v0: $i] : (addition(all_20_8, v0) = all_58_0 &
% 232.83/32.25 | addition(all_20_10, all_20_3) = v0 & $i(v0) & $i(all_58_0))
% 232.83/32.25 |
% 232.83/32.25 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_8,
% 232.83/32.25 | all_20_10, all_20_7, all_58_0, simplifying with (16), (18), (21),
% 232.83/32.25 | (23), (108) gives:
% 232.83/32.25 | (159) ? [v0: $i] : (addition(all_20_8, all_20_3) = v0 &
% 232.83/32.25 | addition(all_20_10, v0) = all_58_0 & $i(v0) & $i(all_58_0))
% 232.83/32.25 |
% 232.83/32.25 | GROUND_INST: instantiating (additive_commutativity) with all_20_7, all_20_3,
% 232.83/32.25 | all_58_0, simplifying with (21), (36), (108) gives:
% 232.83/32.25 | (160) addition(all_20_3, all_20_7) = all_58_0 & $i(all_58_0)
% 232.83/32.25 |
% 232.83/32.25 | ALPHA: (160) implies:
% 232.83/32.25 | (161) $i(all_58_0)
% 232.83/32.25 | (162) addition(all_20_3, all_20_7) = all_58_0
% 232.83/32.25 |
% 232.83/32.25 | GROUND_INST: instantiating (additive_associativity) with all_32_0, all_20_10,
% 232.83/32.25 | all_20_8, all_20_7, all_54_0, simplifying with (16), (18), (37),
% 232.83/32.25 | (50), (102) gives:
% 232.83/32.25 | (163) ? [v0: $i] : (addition(all_20_8, v0) = all_54_0 &
% 232.83/32.25 | addition(all_20_10, all_32_0) = v0 & $i(v0) & $i(all_54_0))
% 232.83/32.25 |
% 232.83/32.25 | GROUND_INST: instantiating (additive_associativity) with all_32_0, all_20_8,
% 232.83/32.25 | all_20_10, all_20_7, all_54_0, simplifying with (16), (18), (23),
% 232.83/32.25 | (50), (102) gives:
% 232.83/32.25 | (164) ? [v0: $i] : (addition(all_20_8, all_32_0) = v0 &
% 232.83/32.25 | addition(all_20_10, v0) = all_54_0 & $i(v0) & $i(all_54_0))
% 232.83/32.25 |
% 232.83/32.25 | GROUND_INST: instantiating (additive_commutativity) with all_20_7, all_32_0,
% 232.83/32.25 | all_54_0, simplifying with (36), (50), (102) gives:
% 232.83/32.25 | (165) addition(all_32_0, all_20_7) = all_54_0 & $i(all_54_0)
% 232.83/32.25 |
% 232.83/32.25 | ALPHA: (165) implies:
% 232.83/32.25 | (166) addition(all_32_0, all_20_7) = all_54_0
% 232.83/32.25 |
% 232.83/32.25 | GROUND_INST: instantiating (additive_associativity) with all_64_0, all_20_10,
% 232.83/32.25 | all_20_8, all_20_7, all_20_0, simplifying with (16), (18), (37),
% 232.83/32.25 | (116), (117) gives:
% 232.83/32.25 | (167) ? [v0: $i] : (addition(all_20_8, v0) = all_20_0 &
% 232.83/32.25 | addition(all_20_10, all_64_0) = v0 & $i(v0) & $i(all_20_0))
% 232.83/32.25 |
% 232.83/32.25 | GROUND_INST: instantiating (additive_associativity) with all_64_0, all_20_8,
% 232.83/32.25 | all_20_10, all_20_7, all_20_0, simplifying with (16), (18), (23),
% 232.83/32.25 | (116), (117) gives:
% 232.83/32.26 | (168) ? [v0: $i] : (addition(all_20_8, all_64_0) = v0 &
% 232.83/32.26 | addition(all_20_10, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 232.83/32.26 |
% 232.83/32.26 | GROUND_INST: instantiating (additive_associativity) with all_70_0, all_20_10,
% 232.83/32.26 | all_20_8, all_20_7, all_20_0, simplifying with (16), (18), (37),
% 232.83/32.26 | (127), (128) gives:
% 232.83/32.26 | (169) ? [v0: $i] : (addition(all_20_8, v0) = all_20_0 &
% 232.83/32.26 | addition(all_20_10, all_70_0) = v0 & $i(v0) & $i(all_20_0))
% 232.83/32.26 |
% 232.83/32.26 | GROUND_INST: instantiating (additive_commutativity) with all_20_7, all_70_0,
% 232.83/32.26 | all_20_0, simplifying with (36), (127), (128) gives:
% 232.83/32.26 | (170) addition(all_70_0, all_20_7) = all_20_0 & $i(all_20_0)
% 232.83/32.26 |
% 232.83/32.26 | ALPHA: (170) implies:
% 232.83/32.26 | (171) addition(all_70_0, all_20_7) = all_20_0
% 232.83/32.26 |
% 232.83/32.26 | GROUND_INST: instantiating (additive_commutativity) with all_20_6, all_32_0,
% 232.83/32.26 | all_70_0, simplifying with (19), (50), (129) gives:
% 232.83/32.26 | (172) addition(all_32_0, all_20_6) = all_70_0 & $i(all_70_0)
% 232.83/32.26 |
% 232.83/32.26 | ALPHA: (172) implies:
% 232.83/32.26 | (173) addition(all_32_0, all_20_6) = all_70_0
% 232.83/32.26 |
% 232.83/32.26 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_58_0,
% 232.83/32.26 | all_20_6, all_20_2, all_20_0, simplifying with (19), (22), (26),
% 232.83/32.26 | (109), (161) gives:
% 232.83/32.26 | (174) ? [v0: $i] : (addition(all_58_0, all_20_1) = v0 & addition(all_20_6,
% 232.83/32.26 | v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 232.83/32.26 |
% 232.83/32.26 | GROUND_INST: instantiating (additive_commutativity) with all_20_6, all_58_0,
% 232.83/32.26 | all_20_2, simplifying with (19), (109), (161) gives:
% 232.83/32.26 | (175) addition(all_58_0, all_20_6) = all_20_2 & $i(all_20_2)
% 232.83/32.26 |
% 232.83/32.26 | ALPHA: (175) implies:
% 232.83/32.26 | (176) addition(all_58_0, all_20_6) = all_20_2
% 232.83/32.26 |
% 232.83/32.26 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_7,
% 232.83/32.26 | all_20_6, all_20_5, all_48_0, simplifying with (19), (22), (36),
% 232.83/32.26 | (41), (92) gives:
% 232.83/32.26 | (177) ? [v0: $i] : (addition(all_20_6, v0) = all_48_0 & addition(all_20_7,
% 232.83/32.26 | all_20_1) = v0 & $i(v0) & $i(all_48_0))
% 232.83/32.26 |
% 232.83/32.26 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_6,
% 232.83/32.26 | all_20_7, all_20_5, all_48_0, simplifying with (19), (22), (24),
% 232.83/32.26 | (36), (92) gives:
% 232.83/32.26 | (178) ? [v0: $i] : (addition(all_20_6, all_20_1) = v0 & addition(all_20_7,
% 232.83/32.26 | v0) = all_48_0 & $i(v0) & $i(all_48_0))
% 232.83/32.26 |
% 232.83/32.26 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_38_0,
% 232.83/32.26 | all_20_10, all_20_5, all_48_0, simplifying with (16), (22), (60),
% 232.83/32.26 | (61), (92) gives:
% 232.83/32.26 | (179) ? [v0: $i] : (addition(all_38_0, all_20_1) = v0 &
% 232.83/32.26 | addition(all_20_10, v0) = all_48_0 & $i(v0) & $i(all_48_0))
% 232.83/32.26 |
% 232.83/32.26 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_60_0,
% 232.83/32.26 | all_20_8, all_20_5, all_48_0, simplifying with (18), (22), (92),
% 232.83/32.26 | (112), (137) gives:
% 232.83/32.26 | (180) ? [v0: $i] : (addition(all_60_0, all_20_1) = v0 & addition(all_20_8,
% 232.83/32.26 | v0) = all_48_0 & $i(v0) & $i(all_48_0))
% 232.83/32.26 |
% 232.83/32.26 | GROUND_INST: instantiating (additive_commutativity) with all_20_5, all_20_1,
% 232.83/32.26 | all_48_0, simplifying with (22), (40), (92) gives:
% 232.83/32.26 | (181) addition(all_20_1, all_20_5) = all_48_0 & $i(all_48_0)
% 232.83/32.26 |
% 232.83/32.26 | ALPHA: (181) implies:
% 232.83/32.26 | (182) $i(all_48_0)
% 232.83/32.26 |
% 232.83/32.26 | GROUND_INST: instantiating (left_distributivity) with all_20_4, all_20_12,
% 232.83/32.27 | all_20_11, all_20_3, all_20_6, all_36_0, simplifying with (14),
% 232.83/32.27 | (15), (20), (27), (30), (80) gives:
% 232.83/32.27 | (183) ? [v0: $i] : (multiplication(v0, all_20_11) = all_36_0 &
% 232.83/32.27 | addition(all_20_4, all_20_12) = v0 & $i(v0) & $i(all_36_0))
% 232.83/32.27 |
% 232.83/32.27 | GROUND_INST: instantiating (additive_commutativity) with all_20_3, all_48_0,
% 232.83/32.27 | all_20_0, simplifying with (21), (93), (182) gives:
% 232.83/32.27 | (184) addition(all_48_0, all_20_3) = all_20_0 & $i(all_20_0)
% 232.83/32.27 |
% 232.83/32.27 | ALPHA: (184) implies:
% 232.83/32.27 | (185) addition(all_48_0, all_20_3) = all_20_0
% 232.83/32.27 |
% 232.83/32.27 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_7,
% 232.83/32.27 | all_36_0, all_20_2, all_20_0, simplifying with (22), (26), (36),
% 232.83/32.27 | (56), (76) gives:
% 232.83/32.27 | (186) ? [v0: $i] : (addition(all_36_0, v0) = all_20_0 & addition(all_20_7,
% 232.83/32.27 | all_20_1) = v0 & $i(v0) & $i(all_20_0))
% 232.83/32.27 |
% 232.83/32.27 | GROUND_INST: instantiating (additive_associativity) with all_20_7, all_20_3,
% 232.83/32.27 | all_20_6, all_36_0, all_20_2, simplifying with (19), (21), (36),
% 232.83/32.27 | (58), (76) gives:
% 232.83/32.27 | (187) ? [v0: $i] : (addition(all_20_3, all_20_7) = v0 & addition(all_20_6,
% 232.83/32.27 | v0) = all_20_2 & $i(v0) & $i(all_20_2))
% 232.83/32.27 |
% 232.83/32.27 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_3,
% 232.83/32.27 | all_20_6, all_36_0, all_64_0, simplifying with (19), (21), (22),
% 232.83/32.27 | (58), (118) gives:
% 232.83/32.27 | (188) ? [v0: $i] : (addition(all_20_3, all_20_1) = v0 & addition(all_20_6,
% 232.83/32.27 | v0) = all_64_0 & $i(v0) & $i(all_64_0))
% 232.83/32.27 |
% 232.83/32.27 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_6,
% 232.83/32.27 | all_20_3, all_36_0, all_64_0, simplifying with (19), (21), (22),
% 232.83/32.27 | (80), (118) gives:
% 232.83/32.27 | (189) ? [v0: $i] : (addition(all_20_3, v0) = all_64_0 & addition(all_20_6,
% 232.83/32.27 | all_20_1) = v0 & $i(v0) & $i(all_64_0))
% 232.83/32.27 |
% 232.83/32.27 | GROUND_INST: instantiating (additive_associativity) with all_32_0, all_20_10,
% 232.83/32.27 | all_38_0, all_20_5, all_20_0, simplifying with (16), (50), (51),
% 232.83/32.27 | (60), (67) gives:
% 232.83/32.27 | (190) ? [v0: $i] : (addition(all_38_0, v0) = all_20_0 &
% 232.83/32.27 | addition(all_20_10, all_32_0) = v0 & $i(v0) & $i(all_20_0))
% 232.83/32.27 |
% 232.83/32.27 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_10,
% 232.83/32.27 | all_38_0, all_20_5, all_20_2, simplifying with (16), (21), (25),
% 232.83/32.27 | (60), (67) gives:
% 232.83/32.27 | (191) ? [v0: $i] : (addition(all_38_0, v0) = all_20_2 &
% 232.83/32.27 | addition(all_20_10, all_20_3) = v0 & $i(v0) & $i(all_20_2))
% 232.83/32.27 |
% 232.83/32.27 | GROUND_INST: instantiating (additive_associativity) with all_20_10, all_20_6,
% 232.83/32.27 | all_20_8, all_38_0, all_20_5, simplifying with (16), (18), (19),
% 232.83/32.27 | (62), (67) gives:
% 232.83/32.27 | (192) ? [v0: $i] : (addition(all_20_6, all_20_10) = v0 &
% 232.83/32.27 | addition(all_20_8, v0) = all_20_5 & $i(v0) & $i(all_20_5))
% 232.83/32.27 |
% 232.83/32.27 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_10,
% 232.83/32.27 | all_38_0, all_20_5, all_48_0, simplifying with (16), (22), (60),
% 232.83/32.27 | (67), (92) gives:
% 232.83/32.27 | (193) ? [v0: $i] : (addition(all_38_0, v0) = all_48_0 &
% 232.83/32.27 | addition(all_20_10, all_20_1) = v0 & $i(v0) & $i(all_48_0))
% 232.83/32.27 |
% 232.83/32.27 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_6,
% 232.83/32.27 | all_20_8, all_38_0, all_56_0, simplifying with (18), (19), (21),
% 232.83/32.27 | (62), (106) gives:
% 232.83/32.28 | (194) ? [v0: $i] : (addition(all_20_6, all_20_3) = v0 & addition(all_20_8,
% 232.83/32.28 | v0) = all_56_0 & $i(v0) & $i(all_56_0))
% 232.83/32.28 |
% 232.83/32.28 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_8,
% 232.83/32.28 | all_20_6, all_38_0, all_56_0, simplifying with (18), (19), (21),
% 232.83/32.28 | (71), (106) gives:
% 232.83/32.28 | (195) ? [v0: $i] : (addition(all_20_6, v0) = all_56_0 & addition(all_20_8,
% 232.83/32.28 | all_20_3) = v0 & $i(v0) & $i(all_56_0))
% 232.83/32.28 |
% 232.83/32.28 | GROUND_INST: instantiating (additive_commutativity) with all_38_0, all_20_3,
% 232.83/32.28 | all_56_0, simplifying with (21), (60), (106) gives:
% 232.83/32.28 | (196) addition(all_20_3, all_38_0) = all_56_0 & $i(all_56_0)
% 232.83/32.28 |
% 232.83/32.28 | ALPHA: (196) implies:
% 232.83/32.28 | (197) addition(all_20_3, all_38_0) = all_56_0
% 232.83/32.28 |
% 232.83/32.28 | GROUND_INST: instantiating (additive_associativity) with all_32_0, all_20_6,
% 232.83/32.28 | all_20_8, all_38_0, all_66_0, simplifying with (18), (19), (50),
% 232.83/32.28 | (62), (122) gives:
% 232.83/32.28 | (198) ? [v0: $i] : (addition(all_20_6, all_32_0) = v0 & addition(all_20_8,
% 232.83/32.28 | v0) = all_66_0 & $i(v0) & $i(all_66_0))
% 232.83/32.28 |
% 232.83/32.28 | GROUND_INST: instantiating (additive_associativity) with all_32_0, all_20_8,
% 232.83/32.28 | all_20_6, all_38_0, all_66_0, simplifying with (18), (19), (50),
% 232.83/32.28 | (71), (122) gives:
% 232.83/32.28 | (199) ? [v0: $i] : (addition(all_20_6, v0) = all_66_0 & addition(all_20_8,
% 232.83/32.28 | all_32_0) = v0 & $i(v0) & $i(all_66_0))
% 232.83/32.28 |
% 232.83/32.28 | DELTA: instantiating (195) with fresh symbol all_86_0 gives:
% 232.83/32.28 | (200) addition(all_20_6, all_86_0) = all_56_0 & addition(all_20_8,
% 232.83/32.28 | all_20_3) = all_86_0 & $i(all_86_0) & $i(all_56_0)
% 232.83/32.28 |
% 232.83/32.28 | ALPHA: (200) implies:
% 232.83/32.28 | (201) addition(all_20_8, all_20_3) = all_86_0
% 233.03/32.28 | (202) addition(all_20_6, all_86_0) = all_56_0
% 233.03/32.28 |
% 233.03/32.28 | DELTA: instantiating (155) with fresh symbol all_88_0 gives:
% 233.03/32.28 | (203) addition(all_60_0, all_20_3) = all_88_0 & addition(all_20_8,
% 233.03/32.28 | all_88_0) = all_20_2 & $i(all_88_0) & $i(all_20_2)
% 233.03/32.28 |
% 233.03/32.28 | ALPHA: (203) implies:
% 233.03/32.28 | (204) $i(all_88_0)
% 233.03/32.28 | (205) addition(all_20_8, all_88_0) = all_20_2
% 233.03/32.28 | (206) addition(all_60_0, all_20_3) = all_88_0
% 233.03/32.28 |
% 233.03/32.28 | DELTA: instantiating (194) with fresh symbol all_90_0 gives:
% 233.03/32.28 | (207) addition(all_20_6, all_20_3) = all_90_0 & addition(all_20_8,
% 233.03/32.28 | all_90_0) = all_56_0 & $i(all_90_0) & $i(all_56_0)
% 233.03/32.28 |
% 233.03/32.28 | ALPHA: (207) implies:
% 233.03/32.28 | (208) $i(all_90_0)
% 233.03/32.28 | (209) addition(all_20_8, all_90_0) = all_56_0
% 233.03/32.28 | (210) addition(all_20_6, all_20_3) = all_90_0
% 233.03/32.28 |
% 233.03/32.28 | DELTA: instantiating (159) with fresh symbol all_92_0 gives:
% 233.03/32.28 | (211) addition(all_20_8, all_20_3) = all_92_0 & addition(all_20_10,
% 233.03/32.28 | all_92_0) = all_58_0 & $i(all_92_0) & $i(all_58_0)
% 233.03/32.28 |
% 233.03/32.28 | ALPHA: (211) implies:
% 233.03/32.28 | (212) addition(all_20_10, all_92_0) = all_58_0
% 233.03/32.28 | (213) addition(all_20_8, all_20_3) = all_92_0
% 233.03/32.28 |
% 233.03/32.28 | DELTA: instantiating (158) with fresh symbol all_94_0 gives:
% 233.03/32.28 | (214) addition(all_20_8, all_94_0) = all_58_0 & addition(all_20_10,
% 233.03/32.28 | all_20_3) = all_94_0 & $i(all_94_0) & $i(all_58_0)
% 233.03/32.28 |
% 233.03/32.28 | ALPHA: (214) implies:
% 233.03/32.28 | (215) addition(all_20_10, all_20_3) = all_94_0
% 233.03/32.28 | (216) addition(all_20_8, all_94_0) = all_58_0
% 233.03/32.28 |
% 233.03/32.28 | DELTA: instantiating (168) with fresh symbol all_96_0 gives:
% 233.03/32.28 | (217) addition(all_20_8, all_64_0) = all_96_0 & addition(all_20_10,
% 233.03/32.28 | all_96_0) = all_20_0 & $i(all_96_0) & $i(all_20_0)
% 233.03/32.28 |
% 233.03/32.28 | ALPHA: (217) implies:
% 233.03/32.28 | (218) addition(all_20_8, all_64_0) = all_96_0
% 233.03/32.28 |
% 233.03/32.28 | DELTA: instantiating (180) with fresh symbol all_98_0 gives:
% 233.03/32.28 | (219) addition(all_60_0, all_20_1) = all_98_0 & addition(all_20_8,
% 233.03/32.28 | all_98_0) = all_48_0 & $i(all_98_0) & $i(all_48_0)
% 233.03/32.28 |
% 233.03/32.28 | ALPHA: (219) implies:
% 233.03/32.28 | (220) $i(all_98_0)
% 233.03/32.28 | (221) addition(all_20_8, all_98_0) = all_48_0
% 233.03/32.28 | (222) addition(all_60_0, all_20_1) = all_98_0
% 233.03/32.28 |
% 233.03/32.28 | DELTA: instantiating (177) with fresh symbol all_100_0 gives:
% 233.03/32.28 | (223) addition(all_20_6, all_100_0) = all_48_0 & addition(all_20_7,
% 233.03/32.28 | all_20_1) = all_100_0 & $i(all_100_0) & $i(all_48_0)
% 233.03/32.28 |
% 233.03/32.28 | ALPHA: (223) implies:
% 233.03/32.28 | (224) addition(all_20_7, all_20_1) = all_100_0
% 233.03/32.28 | (225) addition(all_20_6, all_100_0) = all_48_0
% 233.03/32.28 |
% 233.03/32.28 | DELTA: instantiating (199) with fresh symbol all_102_0 gives:
% 233.03/32.28 | (226) addition(all_20_6, all_102_0) = all_66_0 & addition(all_20_8,
% 233.03/32.28 | all_32_0) = all_102_0 & $i(all_102_0) & $i(all_66_0)
% 233.03/32.28 |
% 233.03/32.28 | ALPHA: (226) implies:
% 233.03/32.28 | (227) addition(all_20_8, all_32_0) = all_102_0
% 233.03/32.28 |
% 233.03/32.28 | DELTA: instantiating (186) with fresh symbol all_104_0 gives:
% 233.03/32.28 | (228) addition(all_36_0, all_104_0) = all_20_0 & addition(all_20_7,
% 233.03/32.28 | all_20_1) = all_104_0 & $i(all_104_0) & $i(all_20_0)
% 233.03/32.28 |
% 233.03/32.28 | ALPHA: (228) implies:
% 233.03/32.29 | (229) addition(all_20_7, all_20_1) = all_104_0
% 233.03/32.29 | (230) addition(all_36_0, all_104_0) = all_20_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (188) with fresh symbol all_108_0 gives:
% 233.03/32.29 | (231) addition(all_20_3, all_20_1) = all_108_0 & addition(all_20_6,
% 233.03/32.29 | all_108_0) = all_64_0 & $i(all_108_0) & $i(all_64_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (231) implies:
% 233.03/32.29 | (232) $i(all_108_0)
% 233.03/32.29 | (233) addition(all_20_6, all_108_0) = all_64_0
% 233.03/32.29 | (234) addition(all_20_3, all_20_1) = all_108_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (179) with fresh symbol all_110_0 gives:
% 233.03/32.29 | (235) addition(all_38_0, all_20_1) = all_110_0 & addition(all_20_10,
% 233.03/32.29 | all_110_0) = all_48_0 & $i(all_110_0) & $i(all_48_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (235) implies:
% 233.03/32.29 | (236) $i(all_110_0)
% 233.03/32.29 | (237) addition(all_20_10, all_110_0) = all_48_0
% 233.03/32.29 | (238) addition(all_38_0, all_20_1) = all_110_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (178) with fresh symbol all_112_0 gives:
% 233.03/32.29 | (239) addition(all_20_6, all_20_1) = all_112_0 & addition(all_20_7,
% 233.03/32.29 | all_112_0) = all_48_0 & $i(all_112_0) & $i(all_48_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (239) implies:
% 233.03/32.29 | (240) addition(all_20_7, all_112_0) = all_48_0
% 233.03/32.29 | (241) addition(all_20_6, all_20_1) = all_112_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (174) with fresh symbol all_114_0 gives:
% 233.03/32.29 | (242) addition(all_58_0, all_20_1) = all_114_0 & addition(all_20_6,
% 233.03/32.29 | all_114_0) = all_20_0 & $i(all_114_0) & $i(all_20_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (242) implies:
% 233.03/32.29 | (243) $i(all_114_0)
% 233.03/32.29 | (244) addition(all_20_6, all_114_0) = all_20_0
% 233.03/32.29 | (245) addition(all_58_0, all_20_1) = all_114_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (154) with fresh symbol all_116_0 gives:
% 233.03/32.29 | (246) addition(all_60_0, all_32_0) = all_116_0 & addition(all_20_8,
% 233.03/32.29 | all_116_0) = all_20_0 & $i(all_116_0) & $i(all_20_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (246) implies:
% 233.03/32.29 | (247) addition(all_60_0, all_32_0) = all_116_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (164) with fresh symbol all_120_0 gives:
% 233.03/32.29 | (248) addition(all_20_8, all_32_0) = all_120_0 & addition(all_20_10,
% 233.03/32.29 | all_120_0) = all_54_0 & $i(all_120_0) & $i(all_54_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (248) implies:
% 233.03/32.29 | (249) addition(all_20_8, all_32_0) = all_120_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (169) with fresh symbol all_122_0 gives:
% 233.03/32.29 | (250) addition(all_20_8, all_122_0) = all_20_0 & addition(all_20_10,
% 233.03/32.29 | all_70_0) = all_122_0 & $i(all_122_0) & $i(all_20_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (250) implies:
% 233.03/32.29 | (251) addition(all_20_10, all_70_0) = all_122_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (167) with fresh symbol all_124_0 gives:
% 233.03/32.29 | (252) addition(all_20_8, all_124_0) = all_20_0 & addition(all_20_10,
% 233.03/32.29 | all_64_0) = all_124_0 & $i(all_124_0) & $i(all_20_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (252) implies:
% 233.03/32.29 | (253) addition(all_20_10, all_64_0) = all_124_0
% 233.03/32.29 | (254) addition(all_20_8, all_124_0) = all_20_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (151) with fresh symbol all_126_0 gives:
% 233.03/32.29 | (255) addition(all_50_0, all_20_1) = all_126_0 & addition(all_20_8,
% 233.03/32.29 | all_126_0) = all_20_0 & $i(all_126_0) & $i(all_20_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (255) implies:
% 233.03/32.29 | (256) addition(all_50_0, all_20_1) = all_126_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (143) with fresh symbol all_128_0 gives:
% 233.03/32.29 | (257) addition(all_56_0, all_20_1) = all_128_0 & addition(all_20_10,
% 233.03/32.29 | all_128_0) = all_20_0 & $i(all_128_0) & $i(all_20_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (257) implies:
% 233.03/32.29 | (258) addition(all_56_0, all_20_1) = all_128_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (142) with fresh symbol all_130_0 gives:
% 233.03/32.29 | (259) addition(all_52_0, all_20_1) = all_130_0 & addition(all_20_10,
% 233.03/32.29 | all_130_0) = all_20_0 & $i(all_130_0) & $i(all_20_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (259) implies:
% 233.03/32.29 | (260) $i(all_130_0)
% 233.03/32.29 | (261) addition(all_20_10, all_130_0) = all_20_0
% 233.03/32.29 | (262) addition(all_52_0, all_20_1) = all_130_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (163) with fresh symbol all_132_0 gives:
% 233.03/32.29 | (263) addition(all_20_8, all_132_0) = all_54_0 & addition(all_20_10,
% 233.03/32.29 | all_32_0) = all_132_0 & $i(all_132_0) & $i(all_54_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (263) implies:
% 233.03/32.29 | (264) addition(all_20_10, all_32_0) = all_132_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (187) with fresh symbol all_134_0 gives:
% 233.03/32.29 | (265) addition(all_20_3, all_20_7) = all_134_0 & addition(all_20_6,
% 233.03/32.29 | all_134_0) = all_20_2 & $i(all_134_0) & $i(all_20_2)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (265) implies:
% 233.03/32.29 | (266) addition(all_20_3, all_20_7) = all_134_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (189) with fresh symbol all_136_0 gives:
% 233.03/32.29 | (267) addition(all_20_3, all_136_0) = all_64_0 & addition(all_20_6,
% 233.03/32.29 | all_20_1) = all_136_0 & $i(all_136_0) & $i(all_64_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (267) implies:
% 233.03/32.29 | (268) $i(all_136_0)
% 233.03/32.29 | (269) addition(all_20_6, all_20_1) = all_136_0
% 233.03/32.29 | (270) addition(all_20_3, all_136_0) = all_64_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (183) with fresh symbol all_138_0 gives:
% 233.03/32.29 | (271) multiplication(all_138_0, all_20_11) = all_36_0 & addition(all_20_4,
% 233.03/32.29 | all_20_12) = all_138_0 & $i(all_138_0) & $i(all_36_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (271) implies:
% 233.03/32.29 | (272) addition(all_20_4, all_20_12) = all_138_0
% 233.03/32.29 | (273) multiplication(all_138_0, all_20_11) = all_36_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (198) with fresh symbol all_140_0 gives:
% 233.03/32.29 | (274) addition(all_20_6, all_32_0) = all_140_0 & addition(all_20_8,
% 233.03/32.29 | all_140_0) = all_66_0 & $i(all_140_0) & $i(all_66_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (274) implies:
% 233.03/32.29 | (275) $i(all_140_0)
% 233.03/32.29 | (276) addition(all_20_8, all_140_0) = all_66_0
% 233.03/32.29 | (277) addition(all_20_6, all_32_0) = all_140_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (193) with fresh symbol all_142_0 gives:
% 233.03/32.29 | (278) addition(all_38_0, all_142_0) = all_48_0 & addition(all_20_10,
% 233.03/32.29 | all_20_1) = all_142_0 & $i(all_142_0) & $i(all_48_0)
% 233.03/32.29 |
% 233.03/32.29 | ALPHA: (278) implies:
% 233.03/32.29 | (279) addition(all_20_10, all_20_1) = all_142_0
% 233.03/32.29 | (280) addition(all_38_0, all_142_0) = all_48_0
% 233.03/32.29 |
% 233.03/32.29 | DELTA: instantiating (192) with fresh symbol all_144_0 gives:
% 233.03/32.30 | (281) addition(all_20_6, all_20_10) = all_144_0 & addition(all_20_8,
% 233.03/32.30 | all_144_0) = all_20_5 & $i(all_144_0) & $i(all_20_5)
% 233.03/32.30 |
% 233.03/32.30 | ALPHA: (281) implies:
% 233.03/32.30 | (282) $i(all_144_0)
% 233.03/32.30 | (283) addition(all_20_6, all_20_10) = all_144_0
% 233.03/32.30 |
% 233.03/32.30 | DELTA: instantiating (191) with fresh symbol all_146_0 gives:
% 233.03/32.30 | (284) addition(all_38_0, all_146_0) = all_20_2 & addition(all_20_10,
% 233.03/32.30 | all_20_3) = all_146_0 & $i(all_146_0) & $i(all_20_2)
% 233.03/32.30 |
% 233.03/32.30 | ALPHA: (284) implies:
% 233.03/32.30 | (285) addition(all_20_10, all_20_3) = all_146_0
% 233.03/32.30 | (286) addition(all_38_0, all_146_0) = all_20_2
% 233.03/32.30 |
% 233.03/32.30 | DELTA: instantiating (190) with fresh symbol all_148_0 gives:
% 233.03/32.30 | (287) addition(all_38_0, all_148_0) = all_20_0 & addition(all_20_10,
% 233.03/32.30 | all_32_0) = all_148_0 & $i(all_148_0) & $i(all_20_0)
% 233.03/32.30 |
% 233.03/32.30 | ALPHA: (287) implies:
% 233.03/32.30 | (288) addition(all_20_10, all_32_0) = all_148_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (132), (148) imply:
% 233.03/32.30 | (289) multiplication(one, all_20_12) = all_20_7
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (133), (148) imply:
% 233.03/32.30 | (290) multiplication(all_20_4, one) = all_32_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (64), (148) imply:
% 233.03/32.30 | (291) addition(all_20_9, all_20_11) = one
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (54), (148) imply:
% 233.03/32.30 | (292) addition(all_20_11, all_20_9) = one
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_94_0, all_146_0, all_20_3, all_20_10,
% 233.03/32.30 | simplifying with (215), (285) gives:
% 233.03/32.30 | (293) all_146_0 = all_94_0
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_132_0, all_148_0, all_32_0, all_20_10,
% 233.03/32.30 | simplifying with (264), (288) gives:
% 233.03/32.30 | (294) all_148_0 = all_132_0
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_86_0, all_92_0, all_20_3, all_20_8,
% 233.03/32.30 | simplifying with (201), (213) gives:
% 233.03/32.30 | (295) all_92_0 = all_86_0
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_102_0, all_120_0, all_32_0, all_20_8,
% 233.03/32.30 | simplifying with (227), (249) gives:
% 233.03/32.30 | (296) all_120_0 = all_102_0
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_100_0, all_104_0, all_20_1, all_20_7,
% 233.03/32.30 | simplifying with (224), (229) gives:
% 233.03/32.30 | (297) all_104_0 = all_100_0
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_60_0, all_144_0, all_20_10, all_20_6,
% 233.03/32.30 | simplifying with (138), (283) gives:
% 233.03/32.30 | (298) all_144_0 = all_60_0
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_36_0, all_90_0, all_20_3, all_20_6,
% 233.03/32.30 | simplifying with (58), (210) gives:
% 233.03/32.30 | (299) all_90_0 = all_36_0
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_112_0, all_136_0, all_20_1, all_20_6,
% 233.03/32.30 | simplifying with (241), (269) gives:
% 233.03/32.30 | (300) all_136_0 = all_112_0
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_70_0, all_140_0, all_32_0, all_20_6,
% 233.03/32.30 | simplifying with (129), (277) gives:
% 233.03/32.30 | (301) all_140_0 = all_70_0
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_62_0, all_138_0, all_20_12, all_20_4,
% 233.03/32.30 | simplifying with (135), (272) gives:
% 233.03/32.30 | (302) all_138_0 = all_62_0
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_58_0, all_134_0, all_20_7, all_20_3,
% 233.03/32.30 | simplifying with (162), (266) gives:
% 233.03/32.30 | (303) all_134_0 = all_58_0
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_32_0, all_108_0, all_20_1, all_20_3,
% 233.03/32.30 | simplifying with (52), (234) gives:
% 233.03/32.30 | (304) all_108_0 = all_32_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (273), (302) imply:
% 233.03/32.30 | (305) multiplication(all_62_0, all_20_11) = all_36_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (286), (293) imply:
% 233.03/32.30 | (306) addition(all_38_0, all_94_0) = all_20_2
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (230), (297) imply:
% 233.03/32.30 | (307) addition(all_36_0, all_100_0) = all_20_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (270), (300) imply:
% 233.03/32.30 | (308) addition(all_20_3, all_112_0) = all_64_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (233), (304) imply:
% 233.03/32.30 | (309) addition(all_20_6, all_32_0) = all_64_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (276), (301) imply:
% 233.03/32.30 | (310) addition(all_20_8, all_70_0) = all_66_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (209), (299) imply:
% 233.03/32.30 | (311) addition(all_20_8, all_36_0) = all_56_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (212), (295) imply:
% 233.03/32.30 | (312) addition(all_20_10, all_86_0) = all_58_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (268), (300) imply:
% 233.03/32.30 | (313) $i(all_112_0)
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_52_0, all_56_0, all_36_0, all_20_8,
% 233.03/32.30 | simplifying with (100), (311) gives:
% 233.03/32.30 | (314) all_56_0 = all_52_0
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_70_0, all_64_0, all_32_0, all_20_6,
% 233.03/32.30 | simplifying with (129), (309) gives:
% 233.03/32.30 | (315) all_70_0 = all_64_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (171), (315) imply:
% 233.03/32.30 | (316) addition(all_64_0, all_20_7) = all_20_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (258), (314) imply:
% 233.03/32.30 | (317) addition(all_52_0, all_20_1) = all_128_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (145), (314) imply:
% 233.03/32.30 | (318) addition(all_52_0, all_20_10) = all_20_2
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (106), (314) imply:
% 233.03/32.30 | (319) addition(all_38_0, all_20_3) = all_52_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (173), (315) imply:
% 233.03/32.30 | (320) addition(all_32_0, all_20_6) = all_64_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (197), (314) imply:
% 233.03/32.30 | (321) addition(all_20_3, all_38_0) = all_52_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (202), (314) imply:
% 233.03/32.30 | (322) addition(all_20_6, all_86_0) = all_52_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (310), (315) imply:
% 233.03/32.30 | (323) addition(all_20_8, all_64_0) = all_66_0
% 233.03/32.30 |
% 233.03/32.30 | REDUCE: (251), (315) imply:
% 233.03/32.30 | (324) addition(all_20_10, all_64_0) = all_122_0
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_124_0, all_122_0, all_64_0, all_20_10,
% 233.03/32.30 | simplifying with (253), (324) gives:
% 233.03/32.30 | (325) all_124_0 = all_122_0
% 233.03/32.30 |
% 233.03/32.30 | GROUND_INST: instantiating (9) with all_96_0, all_66_0, all_64_0, all_20_8,
% 233.03/32.30 | simplifying with (218), (323) gives:
% 233.03/32.30 | (326) all_96_0 = all_66_0
% 233.03/32.30 |
% 233.03/32.31 | GROUND_INST: instantiating (9) with all_130_0, all_128_0, all_20_1, all_52_0,
% 233.03/32.31 | simplifying with (262), (317) gives:
% 233.03/32.31 | (327) all_130_0 = all_128_0
% 233.03/32.31 |
% 233.03/32.31 | REDUCE: (254), (325) imply:
% 233.03/32.31 | (328) addition(all_20_8, all_122_0) = all_20_0
% 233.03/32.31 |
% 233.03/32.31 | REDUCE: (261), (327) imply:
% 233.03/32.31 | (329) addition(all_20_10, all_128_0) = all_20_0
% 233.03/32.31 |
% 233.03/32.31 | REDUCE: (260), (327) imply:
% 233.03/32.31 | (330) $i(all_128_0)
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_commutativity) with all_20_10, all_20_3,
% 233.03/32.31 | all_94_0, simplifying with (16), (21), (215) gives:
% 233.03/32.31 | (331) addition(all_20_3, all_20_10) = all_94_0 & $i(all_94_0)
% 233.03/32.31 |
% 233.03/32.31 | ALPHA: (331) implies:
% 233.03/32.31 | (332) $i(all_94_0)
% 233.03/32.31 | (333) addition(all_20_3, all_20_10) = all_94_0
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_commutativity) with all_20_10, all_20_1,
% 233.03/32.31 | all_142_0, simplifying with (16), (22), (279) gives:
% 233.03/32.31 | (334) addition(all_20_1, all_20_10) = all_142_0 & $i(all_142_0)
% 233.03/32.31 |
% 233.03/32.31 | ALPHA: (334) implies:
% 233.03/32.31 | (335) $i(all_142_0)
% 233.03/32.31 | (336) addition(all_20_1, all_20_10) = all_142_0
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_commutativity) with all_20_10, all_32_0,
% 233.03/32.31 | all_132_0, simplifying with (16), (50), (264) gives:
% 233.03/32.31 | (337) addition(all_32_0, all_20_10) = all_132_0 & $i(all_132_0)
% 233.03/32.31 |
% 233.03/32.31 | ALPHA: (337) implies:
% 233.03/32.31 | (338) addition(all_32_0, all_20_10) = all_132_0
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_commutativity) with all_20_10, all_64_0,
% 233.03/32.31 | all_122_0, simplifying with (16), (116), (324) gives:
% 233.03/32.31 | (339) addition(all_64_0, all_20_10) = all_122_0 & $i(all_122_0)
% 233.03/32.31 |
% 233.03/32.31 | ALPHA: (339) implies:
% 233.03/32.31 | (340) $i(all_122_0)
% 233.03/32.31 | (341) addition(all_64_0, all_20_10) = all_122_0
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_commutativity) with all_20_10, all_110_0,
% 233.03/32.31 | all_48_0, simplifying with (16), (236), (237) gives:
% 233.03/32.31 | (342) addition(all_110_0, all_20_10) = all_48_0 & $i(all_48_0)
% 233.03/32.31 |
% 233.03/32.31 | ALPHA: (342) implies:
% 233.03/32.31 | (343) addition(all_110_0, all_20_10) = all_48_0
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_commutativity) with all_20_10, all_128_0,
% 233.03/32.31 | all_20_0, simplifying with (16), (329), (330) gives:
% 233.03/32.31 | (344) addition(all_128_0, all_20_10) = all_20_0 & $i(all_20_0)
% 233.03/32.31 |
% 233.03/32.31 | ALPHA: (344) implies:
% 233.03/32.31 | (345) addition(all_128_0, all_20_10) = all_20_0
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_commutativity) with all_20_8, all_20_3,
% 233.03/32.31 | all_86_0, simplifying with (18), (21), (201) gives:
% 233.03/32.31 | (346) addition(all_20_3, all_20_8) = all_86_0 & $i(all_86_0)
% 233.03/32.31 |
% 233.03/32.31 | ALPHA: (346) implies:
% 233.03/32.31 | (347) $i(all_86_0)
% 233.03/32.31 | (348) addition(all_20_3, all_20_8) = all_86_0
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_commutativity) with all_20_8, all_32_0,
% 233.03/32.31 | all_102_0, simplifying with (18), (50), (227) gives:
% 233.03/32.31 | (349) addition(all_32_0, all_20_8) = all_102_0 & $i(all_102_0)
% 233.03/32.31 |
% 233.03/32.31 | ALPHA: (349) implies:
% 233.03/32.31 | (350) addition(all_32_0, all_20_8) = all_102_0
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_commutativity) with all_20_8, all_64_0,
% 233.03/32.31 | all_66_0, simplifying with (18), (116), (323) gives:
% 233.03/32.31 | (351) addition(all_64_0, all_20_8) = all_66_0 & $i(all_66_0)
% 233.03/32.31 |
% 233.03/32.31 | ALPHA: (351) implies:
% 233.03/32.31 | (352) addition(all_64_0, all_20_8) = all_66_0
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_88_0,
% 233.03/32.31 | all_20_8, all_20_2, all_20_0, simplifying with (18), (22), (26),
% 233.03/32.31 | (204), (205) gives:
% 233.03/32.31 | (353) ? [v0: $i] : (addition(all_88_0, all_20_1) = v0 & addition(all_20_8,
% 233.03/32.31 | v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_commutativity) with all_20_8, all_94_0,
% 233.03/32.31 | all_58_0, simplifying with (18), (216), (332) gives:
% 233.03/32.31 | (354) addition(all_94_0, all_20_8) = all_58_0 & $i(all_58_0)
% 233.03/32.31 |
% 233.03/32.31 | ALPHA: (354) implies:
% 233.03/32.31 | (355) addition(all_94_0, all_20_8) = all_58_0
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_commutativity) with all_20_8, all_98_0,
% 233.03/32.31 | all_48_0, simplifying with (18), (220), (221) gives:
% 233.03/32.31 | (356) addition(all_98_0, all_20_8) = all_48_0 & $i(all_48_0)
% 233.03/32.31 |
% 233.03/32.31 | ALPHA: (356) implies:
% 233.03/32.31 | (357) addition(all_98_0, all_20_8) = all_48_0
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_commutativity) with all_20_8, all_122_0,
% 233.03/32.31 | all_20_0, simplifying with (18), (328), (340) gives:
% 233.03/32.31 | (358) addition(all_122_0, all_20_8) = all_20_0 & $i(all_20_0)
% 233.03/32.31 |
% 233.03/32.31 | ALPHA: (358) implies:
% 233.03/32.31 | (359) addition(all_122_0, all_20_8) = all_20_0
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_10,
% 233.03/32.31 | all_20_8, all_20_7, all_100_0, simplifying with (16), (18), (22),
% 233.03/32.31 | (37), (224) gives:
% 233.03/32.31 | (360) ? [v0: $i] : (addition(all_20_8, v0) = all_100_0 &
% 233.03/32.31 | addition(all_20_10, all_20_1) = v0 & $i(v0) & $i(all_100_0))
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_8,
% 233.03/32.31 | all_20_10, all_20_7, all_100_0, simplifying with (16), (18),
% 233.03/32.31 | (22), (23), (224) gives:
% 233.03/32.31 | (361) ? [v0: $i] : (addition(all_20_8, all_20_1) = v0 &
% 233.03/32.31 | addition(all_20_10, v0) = all_100_0 & $i(v0) & $i(all_100_0))
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_commutativity) with all_20_7, all_20_1,
% 233.03/32.31 | all_100_0, simplifying with (22), (36), (224) gives:
% 233.03/32.31 | (362) addition(all_20_1, all_20_7) = all_100_0 & $i(all_100_0)
% 233.03/32.31 |
% 233.03/32.31 | ALPHA: (362) implies:
% 233.03/32.31 | (363) $i(all_100_0)
% 233.03/32.31 | (364) addition(all_20_1, all_20_7) = all_100_0
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_associativity) with all_112_0, all_20_10,
% 233.03/32.31 | all_20_8, all_20_7, all_48_0, simplifying with (16), (18), (37),
% 233.03/32.31 | (240), (313) gives:
% 233.03/32.31 | (365) ? [v0: $i] : (addition(all_20_8, v0) = all_48_0 &
% 233.03/32.31 | addition(all_20_10, all_112_0) = v0 & $i(v0) & $i(all_48_0))
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_associativity) with all_112_0, all_20_8,
% 233.03/32.31 | all_20_10, all_20_7, all_48_0, simplifying with (16), (18), (23),
% 233.03/32.31 | (240), (313) gives:
% 233.03/32.31 | (366) ? [v0: $i] : (addition(all_20_8, all_112_0) = v0 &
% 233.03/32.31 | addition(all_20_10, v0) = all_48_0 & $i(v0) & $i(all_48_0))
% 233.03/32.31 |
% 233.03/32.31 | GROUND_INST: instantiating (additive_commutativity) with all_20_6, all_20_1,
% 233.03/32.31 | all_112_0, simplifying with (19), (22), (241) gives:
% 233.03/32.31 | (367) addition(all_20_1, all_20_6) = all_112_0 & $i(all_112_0)
% 233.03/32.31 |
% 233.03/32.31 | ALPHA: (367) implies:
% 233.03/32.31 | (368) addition(all_20_1, all_20_6) = all_112_0
% 233.03/32.31 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_commutativity) with all_20_6, all_86_0,
% 233.03/32.32 | all_52_0, simplifying with (19), (322), (347) gives:
% 233.03/32.32 | (369) addition(all_86_0, all_20_6) = all_52_0 & $i(all_52_0)
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_commutativity) with all_20_6, all_114_0,
% 233.03/32.32 | all_20_0, simplifying with (19), (243), (244) gives:
% 233.03/32.32 | (370) addition(all_114_0, all_20_6) = all_20_0 & $i(all_20_0)
% 233.03/32.32 |
% 233.03/32.32 | ALPHA: (370) implies:
% 233.03/32.32 | (371) addition(all_114_0, all_20_6) = all_20_0
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (6) with all_20_4, all_20_12, all_62_0, simplifying
% 233.03/32.32 | with (14), (20), (47), (135) gives:
% 233.03/32.32 | (372) all_62_0 = one
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (5) with all_20_4, all_20_12, all_62_0, simplifying
% 233.03/32.32 | with (14), (20), (47), (135) gives:
% 233.03/32.32 | (373) multiplication(all_20_4, all_20_12) = zero &
% 233.03/32.32 | multiplication(all_20_12, all_20_4) = zero
% 233.03/32.32 |
% 233.03/32.32 | ALPHA: (373) implies:
% 233.03/32.32 | (374) multiplication(all_20_12, all_20_4) = zero
% 233.03/32.32 | (375) multiplication(all_20_4, all_20_12) = zero
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_commutativity) with all_20_3, all_112_0,
% 233.03/32.32 | all_64_0, simplifying with (21), (308), (313) gives:
% 233.03/32.32 | (376) addition(all_112_0, all_20_3) = all_64_0 & $i(all_64_0)
% 233.03/32.32 |
% 233.03/32.32 | ALPHA: (376) implies:
% 233.03/32.32 | (377) addition(all_112_0, all_20_3) = all_64_0
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_7, all_20_3,
% 233.03/32.32 | all_20_1, all_32_0, all_54_0, simplifying with (21), (22), (36),
% 233.03/32.32 | (87), (166) gives:
% 233.03/32.32 | (378) ? [v0: $i] : (addition(all_20_1, v0) = all_54_0 & addition(all_20_3,
% 233.03/32.32 | all_20_7) = v0 & $i(v0) & $i(all_54_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_7, all_20_1,
% 233.03/32.32 | all_20_3, all_32_0, all_54_0, simplifying with (21), (22), (36),
% 233.03/32.32 | (52), (166) gives:
% 233.03/32.32 | (379) ? [v0: $i] : (addition(all_20_1, all_20_7) = v0 & addition(all_20_3,
% 233.03/32.32 | v0) = all_54_0 & $i(v0) & $i(all_54_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_6, all_20_1,
% 233.03/32.32 | all_20_3, all_32_0, all_64_0, simplifying with (19), (21), (22),
% 233.03/32.32 | (52), (320) gives:
% 233.03/32.32 | (380) ? [v0: $i] : (addition(all_20_1, all_20_6) = v0 & addition(all_20_3,
% 233.03/32.32 | v0) = all_64_0 & $i(v0) & $i(all_64_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_10, all_20_6,
% 233.03/32.32 | all_20_3, all_36_0, all_50_0, simplifying with (16), (19), (21),
% 233.03/32.32 | (80), (141) gives:
% 233.03/32.32 | (381) ? [v0: $i] : (addition(all_20_3, v0) = all_50_0 & addition(all_20_6,
% 233.03/32.32 | all_20_10) = v0 & $i(v0) & $i(all_50_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_10, all_20_3,
% 233.03/32.32 | all_20_6, all_36_0, all_50_0, simplifying with (16), (19), (21),
% 233.03/32.32 | (58), (141) gives:
% 233.03/32.32 | (382) ? [v0: $i] : (addition(all_20_3, all_20_10) = v0 &
% 233.03/32.32 | addition(all_20_6, v0) = all_50_0 & $i(v0) & $i(all_50_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_8, all_20_3,
% 233.03/32.32 | all_20_6, all_36_0, all_52_0, simplifying with (18), (19), (21),
% 233.03/32.32 | (58), (150) gives:
% 233.03/32.32 | (383) ? [v0: $i] : (addition(all_20_3, all_20_8) = v0 & addition(all_20_6,
% 233.03/32.32 | v0) = all_52_0 & $i(v0) & $i(all_52_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_100_0, all_20_3,
% 233.03/32.32 | all_20_6, all_36_0, all_20_0, simplifying with (19), (21), (58),
% 233.03/32.32 | (307), (363) gives:
% 233.03/32.32 | (384) ? [v0: $i] : (addition(all_20_3, all_100_0) = v0 &
% 233.03/32.32 | addition(all_20_6, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_8,
% 233.03/32.32 | all_20_6, all_38_0, all_110_0, simplifying with (18), (19), (22),
% 233.03/32.32 | (71), (238) gives:
% 233.03/32.32 | (385) ? [v0: $i] : (addition(all_20_6, v0) = all_110_0 &
% 233.03/32.32 | addition(all_20_8, all_20_1) = v0 & $i(v0) & $i(all_110_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_6,
% 233.03/32.32 | all_20_8, all_38_0, all_110_0, simplifying with (18), (19), (22),
% 233.03/32.32 | (62), (238) gives:
% 233.03/32.32 | (386) ? [v0: $i] : (addition(all_20_6, all_20_1) = v0 & addition(all_20_8,
% 233.03/32.32 | v0) = all_110_0 & $i(v0) & $i(all_110_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_commutativity) with all_38_0, all_20_1,
% 233.03/32.32 | all_110_0, simplifying with (22), (60), (238) gives:
% 233.03/32.32 | (387) addition(all_20_1, all_38_0) = all_110_0 & $i(all_110_0)
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_94_0, all_20_6,
% 233.03/32.32 | all_20_8, all_38_0, all_20_2, simplifying with (18), (19), (62),
% 233.03/32.32 | (306), (332) gives:
% 233.03/32.32 | (388) ? [v0: $i] : (addition(all_20_6, all_94_0) = v0 & addition(all_20_8,
% 233.03/32.32 | v0) = all_20_2 & $i(v0) & $i(all_20_2))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_142_0, all_20_8,
% 233.03/32.32 | all_20_6, all_38_0, all_48_0, simplifying with (18), (19), (71),
% 233.03/32.32 | (280), (335) gives:
% 233.03/32.32 | (389) ? [v0: $i] : (addition(all_20_6, v0) = all_48_0 & addition(all_20_8,
% 233.03/32.32 | all_142_0) = v0 & $i(v0) & $i(all_48_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_142_0,
% 233.03/32.32 | all_38_0, all_48_0, all_20_0, simplifying with (21), (60), (185),
% 233.03/32.32 | (280), (335) gives:
% 233.03/32.32 | (390) ? [v0: $i] : (addition(all_142_0, all_20_3) = v0 &
% 233.03/32.32 | addition(all_38_0, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_100_0,
% 233.03/32.32 | all_20_6, all_48_0, all_20_0, simplifying with (19), (21), (185),
% 233.03/32.32 | (225), (363) gives:
% 233.03/32.32 | (391) ? [v0: $i] : (addition(all_100_0, all_20_3) = v0 &
% 233.03/32.32 | addition(all_20_6, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_112_0,
% 233.03/32.32 | all_20_7, all_48_0, all_20_0, simplifying with (21), (36), (185),
% 233.03/32.32 | (240), (313) gives:
% 233.03/32.32 | (392) ? [v0: $i] : (addition(all_112_0, all_20_3) = v0 &
% 233.03/32.32 | addition(all_20_7, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_98_0,
% 233.03/32.32 | all_20_8, all_48_0, all_20_0, simplifying with (18), (21), (185),
% 233.03/32.32 | (220), (221) gives:
% 233.03/32.32 | (393) ? [v0: $i] : (addition(all_98_0, all_20_3) = v0 & addition(all_20_8,
% 233.03/32.32 | v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_110_0,
% 233.03/32.32 | all_20_10, all_48_0, all_20_0, simplifying with (16), (21),
% 233.03/32.32 | (185), (236), (237) gives:
% 233.03/32.32 | (394) ? [v0: $i] : (addition(all_110_0, all_20_3) = v0 &
% 233.03/32.32 | addition(all_20_10, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_8,
% 233.03/32.32 | all_50_0, all_20_2, all_20_0, simplifying with (18), (22), (26),
% 233.03/32.32 | (140), (153) gives:
% 233.03/32.32 | (395) ? [v0: $i] : (addition(all_50_0, v0) = all_20_0 & addition(all_20_8,
% 233.03/32.32 | all_20_1) = v0 & $i(v0) & $i(all_20_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_36_0,
% 233.03/32.32 | all_20_10, all_50_0, all_126_0, simplifying with (16), (22),
% 233.03/32.32 | (56), (95), (256) gives:
% 233.03/32.32 | (396) ? [v0: $i] : (addition(all_36_0, all_20_1) = v0 &
% 233.03/32.32 | addition(all_20_10, v0) = all_126_0 & $i(v0) & $i(all_126_0))
% 233.03/32.32 |
% 233.03/32.32 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_10,
% 233.03/32.32 | all_36_0, all_50_0, all_126_0, simplifying with (16), (22), (56),
% 233.03/32.32 | (141), (256) gives:
% 233.03/32.33 | (397) ? [v0: $i] : (addition(all_36_0, v0) = all_126_0 &
% 233.03/32.33 | addition(all_20_10, all_20_1) = v0 & $i(v0) & $i(all_126_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_10,
% 233.03/32.33 | all_52_0, all_20_2, all_20_0, simplifying with (16), (22), (26),
% 233.03/32.33 | (98), (318) gives:
% 233.03/32.33 | (398) ? [v0: $i] : (addition(all_52_0, v0) = all_20_0 &
% 233.03/32.33 | addition(all_20_10, all_20_1) = v0 & $i(v0) & $i(all_20_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_10, all_20_3,
% 233.03/32.33 | all_38_0, all_52_0, all_20_2, simplifying with (16), (21), (60),
% 233.03/32.33 | (318), (319) gives:
% 233.03/32.33 | (399) ? [v0: $i] : (addition(all_38_0, v0) = all_20_2 & addition(all_20_3,
% 233.03/32.33 | all_20_10) = v0 & $i(v0) & $i(all_20_2))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_36_0,
% 233.03/32.33 | all_20_8, all_52_0, all_128_0, simplifying with (18), (22), (56),
% 233.03/32.33 | (100), (317) gives:
% 233.03/32.33 | (400) ? [v0: $i] : (addition(all_36_0, all_20_1) = v0 & addition(all_20_8,
% 233.03/32.33 | v0) = all_128_0 & $i(v0) & $i(all_128_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_3,
% 233.03/32.33 | all_38_0, all_52_0, all_128_0, simplifying with (21), (22), (60),
% 233.03/32.33 | (317), (319) gives:
% 233.03/32.33 | (401) ? [v0: $i] : (addition(all_38_0, v0) = all_128_0 &
% 233.03/32.33 | addition(all_20_3, all_20_1) = v0 & $i(v0) & $i(all_128_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_8,
% 233.03/32.33 | all_36_0, all_52_0, all_128_0, simplifying with (18), (22), (56),
% 233.03/32.33 | (150), (317) gives:
% 233.03/32.33 | (402) ? [v0: $i] : (addition(all_36_0, v0) = all_128_0 &
% 233.03/32.33 | addition(all_20_8, all_20_1) = v0 & $i(v0) & $i(all_128_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_38_0,
% 233.03/32.33 | all_20_3, all_52_0, all_128_0, simplifying with (21), (22), (60),
% 233.03/32.33 | (317), (321) gives:
% 233.03/32.33 | (403) ? [v0: $i] : (addition(all_38_0, all_20_1) = v0 & addition(all_20_3,
% 233.03/32.33 | v0) = all_128_0 & $i(v0) & $i(all_128_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_86_0,
% 233.03/32.33 | all_20_6, all_52_0, all_128_0, simplifying with (19), (22),
% 233.03/32.33 | (317), (322), (347) gives:
% 233.03/32.33 | (404) ? [v0: $i] : (addition(all_86_0, all_20_1) = v0 & addition(all_20_6,
% 233.03/32.33 | v0) = all_128_0 & $i(v0) & $i(all_128_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_6,
% 233.03/32.33 | all_58_0, all_20_2, all_20_0, simplifying with (19), (22), (26),
% 233.03/32.33 | (161), (176) gives:
% 233.03/32.33 | (405) ? [v0: $i] : (addition(all_58_0, v0) = all_20_0 & addition(all_20_6,
% 233.03/32.33 | all_20_1) = v0 & $i(v0) & $i(all_20_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_6, all_94_0,
% 233.03/32.33 | all_20_8, all_58_0, all_20_2, simplifying with (18), (19), (176),
% 233.03/32.33 | (216), (332) gives:
% 233.03/32.33 | (406) ? [v0: $i] : (addition(all_94_0, all_20_6) = v0 & addition(all_20_8,
% 233.03/32.33 | v0) = all_20_2 & $i(v0) & $i(all_20_2))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_3,
% 233.03/32.33 | all_20_7, all_58_0, all_114_0, simplifying with (21), (22), (36),
% 233.03/32.33 | (108), (245) gives:
% 233.03/32.33 | (407) ? [v0: $i] : (addition(all_20_3, all_20_1) = v0 & addition(all_20_7,
% 233.03/32.33 | v0) = all_114_0 & $i(v0) & $i(all_114_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_7,
% 233.03/32.33 | all_20_3, all_58_0, all_114_0, simplifying with (21), (22), (36),
% 233.03/32.33 | (162), (245) gives:
% 233.03/32.33 | (408) ? [v0: $i] : (addition(all_20_3, v0) = all_114_0 &
% 233.03/32.33 | addition(all_20_7, all_20_1) = v0 & $i(v0) & $i(all_114_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_86_0,
% 233.03/32.33 | all_20_10, all_58_0, all_114_0, simplifying with (16), (22),
% 233.03/32.33 | (245), (312), (347) gives:
% 233.03/32.33 | (409) ? [v0: $i] : (addition(all_86_0, all_20_1) = v0 &
% 233.03/32.33 | addition(all_20_10, v0) = all_114_0 & $i(v0) & $i(all_114_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_commutativity) with all_58_0, all_20_1,
% 233.03/32.33 | all_114_0, simplifying with (22), (161), (245) gives:
% 233.03/32.33 | (410) addition(all_20_1, all_58_0) = all_114_0 & $i(all_114_0)
% 233.03/32.33 |
% 233.03/32.33 | ALPHA: (410) implies:
% 233.03/32.33 | (411) addition(all_20_1, all_58_0) = all_114_0
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_8,
% 233.03/32.33 | all_60_0, all_20_5, all_48_0, simplifying with (18), (22), (92),
% 233.03/32.33 | (137), (157) gives:
% 233.03/32.33 | (412) ? [v0: $i] : (addition(all_60_0, v0) = all_48_0 & addition(all_20_8,
% 233.03/32.33 | all_20_1) = v0 & $i(v0) & $i(all_48_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_6,
% 233.03/32.33 | all_20_10, all_60_0, all_88_0, simplifying with (16), (19), (21),
% 233.03/32.33 | (111), (206) gives:
% 233.03/32.33 | (413) ? [v0: $i] : (addition(all_20_6, all_20_3) = v0 &
% 233.03/32.33 | addition(all_20_10, v0) = all_88_0 & $i(v0) & $i(all_88_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_10,
% 233.03/32.33 | all_20_6, all_60_0, all_88_0, simplifying with (16), (19), (21),
% 233.03/32.33 | (138), (206) gives:
% 233.03/32.33 | (414) ? [v0: $i] : (addition(all_20_6, v0) = all_88_0 &
% 233.03/32.33 | addition(all_20_10, all_20_3) = v0 & $i(v0) & $i(all_88_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_6,
% 233.03/32.33 | all_20_10, all_60_0, all_98_0, simplifying with (16), (19), (22),
% 233.03/32.33 | (111), (222) gives:
% 233.03/32.33 | (415) ? [v0: $i] : (addition(all_20_6, all_20_1) = v0 &
% 233.03/32.33 | addition(all_20_10, v0) = all_98_0 & $i(v0) & $i(all_98_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_10,
% 233.03/32.33 | all_20_6, all_60_0, all_98_0, simplifying with (16), (19), (22),
% 233.03/32.33 | (138), (222) gives:
% 233.03/32.33 | (416) ? [v0: $i] : (addition(all_20_6, v0) = all_98_0 &
% 233.03/32.33 | addition(all_20_10, all_20_1) = v0 & $i(v0) & $i(all_98_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_32_0, all_20_6,
% 233.03/32.33 | all_20_10, all_60_0, all_116_0, simplifying with (16), (19),
% 233.03/32.33 | (50), (111), (247) gives:
% 233.03/32.33 | (417) ? [v0: $i] : (addition(all_20_6, all_32_0) = v0 &
% 233.03/32.33 | addition(all_20_10, v0) = all_116_0 & $i(v0) & $i(all_116_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_7, all_20_1,
% 233.03/32.33 | all_36_0, all_64_0, all_20_0, simplifying with (22), (36), (56),
% 233.03/32.33 | (118), (316) gives:
% 233.03/32.33 | (418) ? [v0: $i] : (addition(all_36_0, v0) = all_20_0 & addition(all_20_1,
% 233.03/32.33 | all_20_7) = v0 & $i(v0) & $i(all_20_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_10, all_32_0,
% 233.03/32.33 | all_38_0, all_66_0, all_20_0, simplifying with (16), (50), (60),
% 233.03/32.33 | (122), (147) gives:
% 233.03/32.33 | (419) ? [v0: $i] : (addition(all_38_0, v0) = all_20_0 & addition(all_32_0,
% 233.03/32.33 | all_20_10) = v0 & $i(v0) & $i(all_20_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (additive_associativity) with all_20_10, all_64_0,
% 233.03/32.33 | all_20_8, all_66_0, all_20_0, simplifying with (16), (18), (116),
% 233.03/32.33 | (147), (323) gives:
% 233.03/32.33 | (420) ? [v0: $i] : (addition(all_64_0, all_20_10) = v0 &
% 233.03/32.33 | addition(all_20_8, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (2) with all_20_12, all_20_7, simplifying with
% 233.03/32.33 | (14), (289) gives:
% 233.03/32.33 | (421) all_20_7 = all_20_12
% 233.03/32.33 |
% 233.03/32.33 | GROUND_INST: instantiating (1) with all_20_4, all_32_0, simplifying with (20),
% 233.03/32.33 | (290) gives:
% 233.03/32.33 | (422) all_32_0 = all_20_4
% 233.03/32.33 |
% 233.03/32.33 | DELTA: instantiating (378) with fresh symbol all_172_0 gives:
% 233.03/32.33 | (423) addition(all_20_1, all_172_0) = all_54_0 & addition(all_20_3,
% 233.03/32.33 | all_20_7) = all_172_0 & $i(all_172_0) & $i(all_54_0)
% 233.03/32.33 |
% 233.03/32.33 | ALPHA: (423) implies:
% 233.03/32.33 | (424) $i(all_172_0)
% 233.03/32.33 | (425) addition(all_20_3, all_20_7) = all_172_0
% 233.03/32.33 |
% 233.03/32.33 | DELTA: instantiating (388) with fresh symbol all_174_0 gives:
% 233.03/32.33 | (426) addition(all_20_6, all_94_0) = all_174_0 & addition(all_20_8,
% 233.03/32.33 | all_174_0) = all_20_2 & $i(all_174_0) & $i(all_20_2)
% 233.03/32.33 |
% 233.03/32.33 | ALPHA: (426) implies:
% 233.03/32.33 | (427) addition(all_20_6, all_94_0) = all_174_0
% 233.03/32.33 |
% 233.03/32.33 | DELTA: instantiating (403) with fresh symbol all_178_0 gives:
% 233.03/32.34 | (428) addition(all_38_0, all_20_1) = all_178_0 & addition(all_20_3,
% 233.03/32.34 | all_178_0) = all_128_0 & $i(all_178_0) & $i(all_128_0)
% 233.03/32.34 |
% 233.03/32.34 | ALPHA: (428) implies:
% 233.28/32.34 | (429) addition(all_20_3, all_178_0) = all_128_0
% 233.28/32.34 | (430) addition(all_38_0, all_20_1) = all_178_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (401) with fresh symbol all_180_0 gives:
% 233.28/32.34 | (431) addition(all_38_0, all_180_0) = all_128_0 & addition(all_20_3,
% 233.28/32.34 | all_20_1) = all_180_0 & $i(all_180_0) & $i(all_128_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (431) implies:
% 233.28/32.34 | (432) $i(all_180_0)
% 233.28/32.34 | (433) addition(all_20_3, all_20_1) = all_180_0
% 233.28/32.34 | (434) addition(all_38_0, all_180_0) = all_128_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (400) with fresh symbol all_182_0 gives:
% 233.28/32.34 | (435) addition(all_36_0, all_20_1) = all_182_0 & addition(all_20_8,
% 233.28/32.34 | all_182_0) = all_128_0 & $i(all_182_0) & $i(all_128_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (435) implies:
% 233.28/32.34 | (436) addition(all_36_0, all_20_1) = all_182_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (380) with fresh symbol all_184_0 gives:
% 233.28/32.34 | (437) addition(all_20_1, all_20_6) = all_184_0 & addition(all_20_3,
% 233.28/32.34 | all_184_0) = all_64_0 & $i(all_184_0) & $i(all_64_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (437) implies:
% 233.28/32.34 | (438) $i(all_184_0)
% 233.28/32.34 | (439) addition(all_20_3, all_184_0) = all_64_0
% 233.28/32.34 | (440) addition(all_20_1, all_20_6) = all_184_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (385) with fresh symbol all_186_0 gives:
% 233.28/32.34 | (441) addition(all_20_6, all_186_0) = all_110_0 & addition(all_20_8,
% 233.28/32.34 | all_20_1) = all_186_0 & $i(all_186_0) & $i(all_110_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (441) implies:
% 233.28/32.34 | (442) addition(all_20_8, all_20_1) = all_186_0
% 233.28/32.34 | (443) addition(all_20_6, all_186_0) = all_110_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (386) with fresh symbol all_188_0 gives:
% 233.28/32.34 | (444) addition(all_20_6, all_20_1) = all_188_0 & addition(all_20_8,
% 233.28/32.34 | all_188_0) = all_110_0 & $i(all_188_0) & $i(all_110_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (444) implies:
% 233.28/32.34 | (445) addition(all_20_8, all_188_0) = all_110_0
% 233.28/32.34 | (446) addition(all_20_6, all_20_1) = all_188_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (379) with fresh symbol all_190_0 gives:
% 233.28/32.34 | (447) addition(all_20_1, all_20_7) = all_190_0 & addition(all_20_3,
% 233.28/32.34 | all_190_0) = all_54_0 & $i(all_190_0) & $i(all_54_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (447) implies:
% 233.28/32.34 | (448) addition(all_20_3, all_190_0) = all_54_0
% 233.28/32.34 | (449) addition(all_20_1, all_20_7) = all_190_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (419) with fresh symbol all_196_0 gives:
% 233.28/32.34 | (450) addition(all_38_0, all_196_0) = all_20_0 & addition(all_32_0,
% 233.28/32.34 | all_20_10) = all_196_0 & $i(all_196_0) & $i(all_20_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (450) implies:
% 233.28/32.34 | (451) addition(all_32_0, all_20_10) = all_196_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (417) with fresh symbol all_202_0 gives:
% 233.28/32.34 | (452) addition(all_20_6, all_32_0) = all_202_0 & addition(all_20_10,
% 233.28/32.34 | all_202_0) = all_116_0 & $i(all_202_0) & $i(all_116_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (452) implies:
% 233.28/32.34 | (453) addition(all_20_10, all_202_0) = all_116_0
% 233.28/32.34 | (454) addition(all_20_6, all_32_0) = all_202_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (416) with fresh symbol all_208_0 gives:
% 233.28/32.34 | (455) addition(all_20_6, all_208_0) = all_98_0 & addition(all_20_10,
% 233.28/32.34 | all_20_1) = all_208_0 & $i(all_208_0) & $i(all_98_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (455) implies:
% 233.28/32.34 | (456) $i(all_208_0)
% 233.28/32.34 | (457) addition(all_20_10, all_20_1) = all_208_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (415) with fresh symbol all_210_0 gives:
% 233.28/32.34 | (458) addition(all_20_6, all_20_1) = all_210_0 & addition(all_20_10,
% 233.28/32.34 | all_210_0) = all_98_0 & $i(all_210_0) & $i(all_98_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (458) implies:
% 233.28/32.34 | (459) addition(all_20_10, all_210_0) = all_98_0
% 233.28/32.34 | (460) addition(all_20_6, all_20_1) = all_210_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (407) with fresh symbol all_214_0 gives:
% 233.28/32.34 | (461) addition(all_20_3, all_20_1) = all_214_0 & addition(all_20_7,
% 233.28/32.34 | all_214_0) = all_114_0 & $i(all_214_0) & $i(all_114_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (461) implies:
% 233.28/32.34 | (462) addition(all_20_7, all_214_0) = all_114_0
% 233.28/32.34 | (463) addition(all_20_3, all_20_1) = all_214_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (406) with fresh symbol all_216_0 gives:
% 233.28/32.34 | (464) addition(all_94_0, all_20_6) = all_216_0 & addition(all_20_8,
% 233.28/32.34 | all_216_0) = all_20_2 & $i(all_216_0) & $i(all_20_2)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (464) implies:
% 233.28/32.34 | (465) addition(all_94_0, all_20_6) = all_216_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (405) with fresh symbol all_218_0 gives:
% 233.28/32.34 | (466) addition(all_58_0, all_218_0) = all_20_0 & addition(all_20_6,
% 233.28/32.34 | all_20_1) = all_218_0 & $i(all_218_0) & $i(all_20_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (466) implies:
% 233.28/32.34 | (467) addition(all_20_6, all_20_1) = all_218_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (408) with fresh symbol all_220_0 gives:
% 233.28/32.34 | (468) addition(all_20_3, all_220_0) = all_114_0 & addition(all_20_7,
% 233.28/32.34 | all_20_1) = all_220_0 & $i(all_220_0) & $i(all_114_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (468) implies:
% 233.28/32.34 | (469) addition(all_20_7, all_20_1) = all_220_0
% 233.28/32.34 | (470) addition(all_20_3, all_220_0) = all_114_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (399) with fresh symbol all_224_0 gives:
% 233.28/32.34 | (471) addition(all_38_0, all_224_0) = all_20_2 & addition(all_20_3,
% 233.28/32.34 | all_20_10) = all_224_0 & $i(all_224_0) & $i(all_20_2)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (471) implies:
% 233.28/32.34 | (472) $i(all_224_0)
% 233.28/32.34 | (473) addition(all_20_3, all_20_10) = all_224_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (404) with fresh symbol all_226_0 gives:
% 233.28/32.34 | (474) addition(all_86_0, all_20_1) = all_226_0 & addition(all_20_6,
% 233.28/32.34 | all_226_0) = all_128_0 & $i(all_226_0) & $i(all_128_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (474) implies:
% 233.28/32.34 | (475) addition(all_86_0, all_20_1) = all_226_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (418) with fresh symbol all_230_0 gives:
% 233.28/32.34 | (476) addition(all_36_0, all_230_0) = all_20_0 & addition(all_20_1,
% 233.28/32.34 | all_20_7) = all_230_0 & $i(all_230_0) & $i(all_20_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (476) implies:
% 233.28/32.34 | (477) addition(all_20_1, all_20_7) = all_230_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (414) with fresh symbol all_234_0 gives:
% 233.28/32.34 | (478) addition(all_20_6, all_234_0) = all_88_0 & addition(all_20_10,
% 233.28/32.34 | all_20_3) = all_234_0 & $i(all_234_0) & $i(all_88_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (478) implies:
% 233.28/32.34 | (479) addition(all_20_10, all_20_3) = all_234_0
% 233.28/32.34 | (480) addition(all_20_6, all_234_0) = all_88_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (384) with fresh symbol all_236_0 gives:
% 233.28/32.34 | (481) addition(all_20_3, all_100_0) = all_236_0 & addition(all_20_6,
% 233.28/32.34 | all_236_0) = all_20_0 & $i(all_236_0) & $i(all_20_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (481) implies:
% 233.28/32.34 | (482) addition(all_20_3, all_100_0) = all_236_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (382) with fresh symbol all_238_0 gives:
% 233.28/32.34 | (483) addition(all_20_3, all_20_10) = all_238_0 & addition(all_20_6,
% 233.28/32.34 | all_238_0) = all_50_0 & $i(all_238_0) & $i(all_50_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (483) implies:
% 233.28/32.34 | (484) addition(all_20_6, all_238_0) = all_50_0
% 233.28/32.34 | (485) addition(all_20_3, all_20_10) = all_238_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (381) with fresh symbol all_240_0 gives:
% 233.28/32.34 | (486) addition(all_20_3, all_240_0) = all_50_0 & addition(all_20_6,
% 233.28/32.34 | all_20_10) = all_240_0 & $i(all_240_0) & $i(all_50_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (486) implies:
% 233.28/32.34 | (487) $i(all_240_0)
% 233.28/32.34 | (488) addition(all_20_6, all_20_10) = all_240_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (383) with fresh symbol all_242_0 gives:
% 233.28/32.34 | (489) addition(all_20_3, all_20_8) = all_242_0 & addition(all_20_6,
% 233.28/32.34 | all_242_0) = all_52_0 & $i(all_242_0) & $i(all_52_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (489) implies:
% 233.28/32.34 | (490) addition(all_20_3, all_20_8) = all_242_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (353) with fresh symbol all_244_0 gives:
% 233.28/32.34 | (491) addition(all_88_0, all_20_1) = all_244_0 & addition(all_20_8,
% 233.28/32.34 | all_244_0) = all_20_0 & $i(all_244_0) & $i(all_20_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (491) implies:
% 233.28/32.34 | (492) addition(all_88_0, all_20_1) = all_244_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (366) with fresh symbol all_246_0 gives:
% 233.28/32.34 | (493) addition(all_20_8, all_112_0) = all_246_0 & addition(all_20_10,
% 233.28/32.34 | all_246_0) = all_48_0 & $i(all_246_0) & $i(all_48_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (493) implies:
% 233.28/32.34 | (494) addition(all_20_8, all_112_0) = all_246_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (365) with fresh symbol all_248_0 gives:
% 233.28/32.34 | (495) addition(all_20_8, all_248_0) = all_48_0 & addition(all_20_10,
% 233.28/32.34 | all_112_0) = all_248_0 & $i(all_248_0) & $i(all_48_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (495) implies:
% 233.28/32.34 | (496) addition(all_20_10, all_112_0) = all_248_0
% 233.28/32.34 |
% 233.28/32.34 | DELTA: instantiating (413) with fresh symbol all_250_0 gives:
% 233.28/32.34 | (497) addition(all_20_6, all_20_3) = all_250_0 & addition(all_20_10,
% 233.28/32.34 | all_250_0) = all_88_0 & $i(all_250_0) & $i(all_88_0)
% 233.28/32.34 |
% 233.28/32.34 | ALPHA: (497) implies:
% 233.28/32.34 | (498) $i(all_250_0)
% 233.28/32.34 | (499) addition(all_20_6, all_20_3) = all_250_0
% 233.28/32.34 |
% 233.28/32.35 | DELTA: instantiating (402) with fresh symbol all_254_0 gives:
% 233.28/32.35 | (500) addition(all_36_0, all_254_0) = all_128_0 & addition(all_20_8,
% 233.28/32.35 | all_20_1) = all_254_0 & $i(all_254_0) & $i(all_128_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (500) implies:
% 233.28/32.35 | (501) $i(all_254_0)
% 233.28/32.35 | (502) addition(all_20_8, all_20_1) = all_254_0
% 233.28/32.35 | (503) addition(all_36_0, all_254_0) = all_128_0
% 233.28/32.35 |
% 233.28/32.35 | DELTA: instantiating (397) with fresh symbol all_256_0 gives:
% 233.28/32.35 | (504) addition(all_36_0, all_256_0) = all_126_0 & addition(all_20_10,
% 233.28/32.35 | all_20_1) = all_256_0 & $i(all_256_0) & $i(all_126_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (504) implies:
% 233.28/32.35 | (505) addition(all_20_10, all_20_1) = all_256_0
% 233.28/32.35 |
% 233.28/32.35 | DELTA: instantiating (396) with fresh symbol all_258_0 gives:
% 233.28/32.35 | (506) addition(all_36_0, all_20_1) = all_258_0 & addition(all_20_10,
% 233.28/32.35 | all_258_0) = all_126_0 & $i(all_258_0) & $i(all_126_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (506) implies:
% 233.28/32.35 | (507) addition(all_20_10, all_258_0) = all_126_0
% 233.28/32.35 | (508) addition(all_36_0, all_20_1) = all_258_0
% 233.28/32.35 |
% 233.28/32.35 | DELTA: instantiating (393) with fresh symbol all_260_0 gives:
% 233.28/32.35 | (509) addition(all_98_0, all_20_3) = all_260_0 & addition(all_20_8,
% 233.28/32.35 | all_260_0) = all_20_0 & $i(all_260_0) & $i(all_20_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (509) implies:
% 233.28/32.35 | (510) addition(all_98_0, all_20_3) = all_260_0
% 233.28/32.35 |
% 233.28/32.35 | DELTA: instantiating (391) with fresh symbol all_262_0 gives:
% 233.28/32.35 | (511) addition(all_100_0, all_20_3) = all_262_0 & addition(all_20_6,
% 233.28/32.35 | all_262_0) = all_20_0 & $i(all_262_0) & $i(all_20_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (511) implies:
% 233.28/32.35 | (512) $i(all_262_0)
% 233.28/32.35 | (513) addition(all_20_6, all_262_0) = all_20_0
% 233.28/32.35 | (514) addition(all_100_0, all_20_3) = all_262_0
% 233.28/32.35 |
% 233.28/32.35 | DELTA: instantiating (361) with fresh symbol all_264_0 gives:
% 233.28/32.35 | (515) addition(all_20_8, all_20_1) = all_264_0 & addition(all_20_10,
% 233.28/32.35 | all_264_0) = all_100_0 & $i(all_264_0) & $i(all_100_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (515) implies:
% 233.28/32.35 | (516) addition(all_20_10, all_264_0) = all_100_0
% 233.28/32.35 | (517) addition(all_20_8, all_20_1) = all_264_0
% 233.28/32.35 |
% 233.28/32.35 | DELTA: instantiating (389) with fresh symbol all_266_0 gives:
% 233.28/32.35 | (518) addition(all_20_6, all_266_0) = all_48_0 & addition(all_20_8,
% 233.28/32.35 | all_142_0) = all_266_0 & $i(all_266_0) & $i(all_48_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (518) implies:
% 233.28/32.35 | (519) addition(all_20_8, all_142_0) = all_266_0
% 233.28/32.35 |
% 233.28/32.35 | DELTA: instantiating (360) with fresh symbol all_268_0 gives:
% 233.28/32.35 | (520) addition(all_20_8, all_268_0) = all_100_0 & addition(all_20_10,
% 233.28/32.35 | all_20_1) = all_268_0 & $i(all_268_0) & $i(all_100_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (520) implies:
% 233.28/32.35 | (521) addition(all_20_10, all_20_1) = all_268_0
% 233.28/32.35 | (522) addition(all_20_8, all_268_0) = all_100_0
% 233.28/32.35 |
% 233.28/32.35 | DELTA: instantiating (390) with fresh symbol all_270_0 gives:
% 233.28/32.35 | (523) addition(all_142_0, all_20_3) = all_270_0 & addition(all_38_0,
% 233.28/32.35 | all_270_0) = all_20_0 & $i(all_270_0) & $i(all_20_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (523) implies:
% 233.28/32.35 | (524) addition(all_142_0, all_20_3) = all_270_0
% 233.28/32.35 |
% 233.28/32.35 | DELTA: instantiating (392) with fresh symbol all_272_0 gives:
% 233.28/32.35 | (525) addition(all_112_0, all_20_3) = all_272_0 & addition(all_20_7,
% 233.28/32.35 | all_272_0) = all_20_0 & $i(all_272_0) & $i(all_20_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (525) implies:
% 233.28/32.35 | (526) addition(all_112_0, all_20_3) = all_272_0
% 233.28/32.35 |
% 233.28/32.35 | DELTA: instantiating (395) with fresh symbol all_274_0 gives:
% 233.28/32.35 | (527) addition(all_50_0, all_274_0) = all_20_0 & addition(all_20_8,
% 233.28/32.35 | all_20_1) = all_274_0 & $i(all_274_0) & $i(all_20_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (527) implies:
% 233.28/32.35 | (528) addition(all_20_8, all_20_1) = all_274_0
% 233.28/32.35 | (529) addition(all_50_0, all_274_0) = all_20_0
% 233.28/32.35 |
% 233.28/32.35 | DELTA: instantiating (394) with fresh symbol all_276_0 gives:
% 233.28/32.35 | (530) addition(all_110_0, all_20_3) = all_276_0 & addition(all_20_10,
% 233.28/32.35 | all_276_0) = all_20_0 & $i(all_276_0) & $i(all_20_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (530) implies:
% 233.28/32.35 | (531) $i(all_276_0)
% 233.28/32.35 | (532) addition(all_20_10, all_276_0) = all_20_0
% 233.28/32.35 | (533) addition(all_110_0, all_20_3) = all_276_0
% 233.28/32.35 |
% 233.28/32.35 | DELTA: instantiating (398) with fresh symbol all_278_0 gives:
% 233.28/32.35 | (534) addition(all_52_0, all_278_0) = all_20_0 & addition(all_20_10,
% 233.28/32.35 | all_20_1) = all_278_0 & $i(all_278_0) & $i(all_20_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (534) implies:
% 233.28/32.35 | (535) addition(all_20_10, all_20_1) = all_278_0
% 233.28/32.35 |
% 233.28/32.35 | DELTA: instantiating (420) with fresh symbol all_280_0 gives:
% 233.28/32.35 | (536) addition(all_64_0, all_20_10) = all_280_0 & addition(all_20_8,
% 233.28/32.35 | all_280_0) = all_20_0 & $i(all_280_0) & $i(all_20_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (536) implies:
% 233.28/32.35 | (537) addition(all_64_0, all_20_10) = all_280_0
% 233.28/32.35 |
% 233.28/32.35 | DELTA: instantiating (409) with fresh symbol all_282_0 gives:
% 233.28/32.35 | (538) addition(all_86_0, all_20_1) = all_282_0 & addition(all_20_10,
% 233.28/32.35 | all_282_0) = all_114_0 & $i(all_282_0) & $i(all_114_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (538) implies:
% 233.28/32.35 | (539) addition(all_86_0, all_20_1) = all_282_0
% 233.28/32.35 |
% 233.28/32.35 | DELTA: instantiating (412) with fresh symbol all_284_0 gives:
% 233.28/32.35 | (540) addition(all_60_0, all_284_0) = all_48_0 & addition(all_20_8,
% 233.28/32.35 | all_20_1) = all_284_0 & $i(all_284_0) & $i(all_48_0)
% 233.28/32.35 |
% 233.28/32.35 | ALPHA: (540) implies:
% 233.28/32.35 | (541) addition(all_20_8, all_20_1) = all_284_0
% 233.28/32.35 | (542) addition(all_60_0, all_284_0) = all_48_0
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (305), (372) imply:
% 233.28/32.35 | (543) multiplication(one, all_20_11) = all_36_0
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (290), (422) imply:
% 233.28/32.35 | (544) multiplication(all_20_4, one) = all_20_4
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (289), (421) imply:
% 233.28/32.35 | (545) multiplication(one, all_20_12) = all_20_12
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (316), (421) imply:
% 233.28/32.35 | (546) addition(all_64_0, all_20_12) = all_20_0
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (122), (422) imply:
% 233.28/32.35 | (547) addition(all_38_0, all_20_4) = all_66_0
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (166), (421), (422) imply:
% 233.28/32.35 | (548) addition(all_20_4, all_20_12) = all_54_0
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (350), (422) imply:
% 233.28/32.35 | (549) addition(all_20_4, all_20_8) = all_102_0
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (422), (451) imply:
% 233.28/32.35 | (550) addition(all_20_4, all_20_10) = all_196_0
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (338), (422) imply:
% 233.28/32.35 | (551) addition(all_20_4, all_20_10) = all_132_0
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (87), (422) imply:
% 233.28/32.35 | (552) addition(all_20_1, all_20_3) = all_20_4
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (421), (477) imply:
% 233.28/32.35 | (553) addition(all_20_1, all_20_12) = all_230_0
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (421), (449) imply:
% 233.28/32.35 | (554) addition(all_20_1, all_20_12) = all_190_0
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (364), (421) imply:
% 233.28/32.35 | (555) addition(all_20_1, all_20_12) = all_100_0
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (52), (422) imply:
% 233.28/32.35 | (556) addition(all_20_3, all_20_1) = all_20_4
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (421), (425) imply:
% 233.28/32.35 | (557) addition(all_20_3, all_20_12) = all_172_0
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (162), (421) imply:
% 233.28/32.35 | (558) addition(all_20_3, all_20_12) = all_58_0
% 233.28/32.35 |
% 233.28/32.35 | REDUCE: (135), (372) imply:
% 233.28/32.35 | (559) addition(all_20_4, all_20_12) = one
% 233.28/32.35 |
% 233.37/32.35 | REDUCE: (422), (454) imply:
% 233.37/32.35 | (560) addition(all_20_6, all_20_4) = all_202_0
% 233.37/32.35 |
% 233.37/32.35 | REDUCE: (309), (422) imply:
% 233.37/32.35 | (561) addition(all_20_6, all_20_4) = all_64_0
% 233.37/32.35 |
% 233.37/32.35 | REDUCE: (421), (462) imply:
% 233.37/32.35 | (562) addition(all_20_12, all_214_0) = all_114_0
% 233.37/32.35 |
% 233.37/32.35 | REDUCE: (421), (469) imply:
% 233.37/32.35 | (563) addition(all_20_12, all_20_1) = all_220_0
% 233.37/32.35 |
% 233.37/32.35 | REDUCE: (224), (421) imply:
% 233.37/32.35 | (564) addition(all_20_12, all_20_1) = all_100_0
% 233.37/32.35 |
% 233.37/32.35 | REDUCE: (108), (421) imply:
% 233.37/32.35 | (565) addition(all_20_12, all_20_3) = all_58_0
% 233.37/32.35 |
% 233.37/32.35 | GROUND_INST: instantiating (9) with all_100_0, all_220_0, all_20_1, all_20_12,
% 233.37/32.35 | simplifying with (563), (564) gives:
% 233.37/32.35 | (566) all_220_0 = all_100_0
% 233.37/32.35 |
% 233.37/32.35 | GROUND_INST: instantiating (9) with all_94_0, all_234_0, all_20_3, all_20_10,
% 233.37/32.35 | simplifying with (215), (479) gives:
% 233.37/32.35 | (567) all_234_0 = all_94_0
% 233.37/32.35 |
% 233.37/32.35 | GROUND_INST: instantiating (9) with all_142_0, all_268_0, all_20_1, all_20_10,
% 233.37/32.35 | simplifying with (279), (521) gives:
% 233.37/32.35 | (568) all_268_0 = all_142_0
% 233.37/32.35 |
% 233.37/32.35 | GROUND_INST: instantiating (9) with all_256_0, all_268_0, all_20_1, all_20_10,
% 233.37/32.35 | simplifying with (505), (521) gives:
% 233.37/32.35 | (569) all_268_0 = all_256_0
% 233.37/32.35 |
% 233.37/32.35 | GROUND_INST: instantiating (9) with all_268_0, all_278_0, all_20_1, all_20_10,
% 233.37/32.35 | simplifying with (521), (535) gives:
% 233.37/32.35 | (570) all_278_0 = all_268_0
% 233.37/32.35 |
% 233.37/32.35 | GROUND_INST: instantiating (9) with all_208_0, all_278_0, all_20_1, all_20_10,
% 233.37/32.35 | simplifying with (457), (535) gives:
% 233.37/32.35 | (571) all_278_0 = all_208_0
% 233.37/32.35 |
% 233.37/32.35 | GROUND_INST: instantiating (9) with all_254_0, all_264_0, all_20_1, all_20_8,
% 233.37/32.35 | simplifying with (502), (517) gives:
% 233.37/32.35 | (572) all_264_0 = all_254_0
% 233.37/32.35 |
% 233.37/32.35 | GROUND_INST: instantiating (9) with all_264_0, all_274_0, all_20_1, all_20_8,
% 233.37/32.35 | simplifying with (517), (528) gives:
% 233.37/32.35 | (573) all_274_0 = all_264_0
% 233.37/32.35 |
% 233.37/32.35 | GROUND_INST: instantiating (9) with all_274_0, all_284_0, all_20_1, all_20_8,
% 233.37/32.35 | simplifying with (528), (541) gives:
% 233.37/32.35 | (574) all_284_0 = all_274_0
% 233.37/32.35 |
% 233.37/32.35 | GROUND_INST: instantiating (9) with all_186_0, all_284_0, all_20_1, all_20_8,
% 233.37/32.35 | simplifying with (442), (541) gives:
% 233.37/32.35 | (575) all_284_0 = all_186_0
% 233.37/32.35 |
% 233.37/32.35 | GROUND_INST: instantiating (9) with all_60_0, all_240_0, all_20_10, all_20_6,
% 233.37/32.35 | simplifying with (138), (488) gives:
% 233.37/32.35 | (576) all_240_0 = all_60_0
% 233.37/32.35 |
% 233.37/32.35 | GROUND_INST: instantiating (9) with all_64_0, all_202_0, all_20_4, all_20_6,
% 233.37/32.35 | simplifying with (560), (561) gives:
% 233.37/32.36 | (577) all_202_0 = all_64_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_36_0, all_250_0, all_20_3, all_20_6,
% 233.37/32.36 | simplifying with (58), (499) gives:
% 233.37/32.36 | (578) all_250_0 = all_36_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_112_0, all_218_0, all_20_1, all_20_6,
% 233.37/32.36 | simplifying with (241), (467) gives:
% 233.37/32.36 | (579) all_218_0 = all_112_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_210_0, all_218_0, all_20_1, all_20_6,
% 233.37/32.36 | simplifying with (460), (467) gives:
% 233.37/32.36 | (580) all_218_0 = all_210_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_188_0, all_218_0, all_20_1, all_20_6,
% 233.37/32.36 | simplifying with (446), (467) gives:
% 233.37/32.36 | (581) all_218_0 = all_188_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with one, all_54_0, all_20_12, all_20_4,
% 233.37/32.36 | simplifying with (548), (559) gives:
% 233.37/32.36 | (582) all_54_0 = one
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_132_0, all_196_0, all_20_10, all_20_4,
% 233.37/32.36 | simplifying with (550), (551) gives:
% 233.37/32.36 | (583) all_196_0 = all_132_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_58_0, all_172_0, all_20_12, all_20_3,
% 233.37/32.36 | simplifying with (557), (558) gives:
% 233.37/32.36 | (584) all_172_0 = all_58_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_224_0, all_238_0, all_20_10, all_20_3,
% 233.37/32.36 | simplifying with (473), (485) gives:
% 233.37/32.36 | (585) all_238_0 = all_224_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_94_0, all_238_0, all_20_10, all_20_3,
% 233.37/32.36 | simplifying with (333), (485) gives:
% 233.37/32.36 | (586) all_238_0 = all_94_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_86_0, all_242_0, all_20_8, all_20_3,
% 233.37/32.36 | simplifying with (348), (490) gives:
% 233.37/32.36 | (587) all_242_0 = all_86_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_180_0, all_214_0, all_20_1, all_20_3,
% 233.37/32.36 | simplifying with (433), (463) gives:
% 233.37/32.36 | (588) all_214_0 = all_180_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_20_4, all_214_0, all_20_1, all_20_3,
% 233.37/32.36 | simplifying with (463), (556) gives:
% 233.37/32.36 | (589) all_214_0 = all_20_4
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_190_0, all_230_0, all_20_12, all_20_1,
% 233.37/32.36 | simplifying with (553), (554) gives:
% 233.37/32.36 | (590) all_230_0 = all_190_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_100_0, all_230_0, all_20_12, all_20_1,
% 233.37/32.36 | simplifying with (553), (555) gives:
% 233.37/32.36 | (591) all_230_0 = all_100_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_112_0, all_184_0, all_20_6, all_20_1,
% 233.37/32.36 | simplifying with (368), (440) gives:
% 233.37/32.36 | (592) all_184_0 = all_112_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_64_0, all_258_0, all_20_1, all_36_0,
% 233.37/32.36 | simplifying with (118), (508) gives:
% 233.37/32.36 | (593) all_258_0 = all_64_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_182_0, all_258_0, all_20_1, all_36_0,
% 233.37/32.36 | simplifying with (436), (508) gives:
% 233.37/32.36 | (594) all_258_0 = all_182_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_110_0, all_178_0, all_20_1, all_38_0,
% 233.37/32.36 | simplifying with (238), (430) gives:
% 233.37/32.36 | (595) all_178_0 = all_110_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_122_0, all_280_0, all_20_10, all_64_0,
% 233.37/32.36 | simplifying with (341), (537) gives:
% 233.37/32.36 | (596) all_280_0 = all_122_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_226_0, all_282_0, all_20_1, all_86_0,
% 233.37/32.36 | simplifying with (475), (539) gives:
% 233.37/32.36 | (597) all_282_0 = all_226_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_64_0, all_272_0, all_20_3, all_112_0,
% 233.37/32.36 | simplifying with (377), (526) gives:
% 233.37/32.36 | (598) all_272_0 = all_64_0
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (574), (575) imply:
% 233.37/32.36 | (599) all_274_0 = all_186_0
% 233.37/32.36 |
% 233.37/32.36 | SIMP: (599) implies:
% 233.37/32.36 | (600) all_274_0 = all_186_0
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (570), (571) imply:
% 233.37/32.36 | (601) all_268_0 = all_208_0
% 233.37/32.36 |
% 233.37/32.36 | SIMP: (601) implies:
% 233.37/32.36 | (602) all_268_0 = all_208_0
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (573), (600) imply:
% 233.37/32.36 | (603) all_264_0 = all_186_0
% 233.37/32.36 |
% 233.37/32.36 | SIMP: (603) implies:
% 233.37/32.36 | (604) all_264_0 = all_186_0
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (568), (569) imply:
% 233.37/32.36 | (605) all_256_0 = all_142_0
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (569), (602) imply:
% 233.37/32.36 | (606) all_256_0 = all_208_0
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (572), (604) imply:
% 233.37/32.36 | (607) all_254_0 = all_186_0
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (593), (594) imply:
% 233.37/32.36 | (608) all_182_0 = all_64_0
% 233.37/32.36 |
% 233.37/32.36 | SIMP: (608) implies:
% 233.37/32.36 | (609) all_182_0 = all_64_0
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (605), (606) imply:
% 233.37/32.36 | (610) all_208_0 = all_142_0
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (585), (586) imply:
% 233.37/32.36 | (611) all_224_0 = all_94_0
% 233.37/32.36 |
% 233.37/32.36 | SIMP: (611) implies:
% 233.37/32.36 | (612) all_224_0 = all_94_0
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (590), (591) imply:
% 233.37/32.36 | (613) all_190_0 = all_100_0
% 233.37/32.36 |
% 233.37/32.36 | SIMP: (613) implies:
% 233.37/32.36 | (614) all_190_0 = all_100_0
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (579), (580) imply:
% 233.37/32.36 | (615) all_210_0 = all_112_0
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (580), (581) imply:
% 233.37/32.36 | (616) all_210_0 = all_188_0
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (588), (589) imply:
% 233.37/32.36 | (617) all_180_0 = all_20_4
% 233.37/32.36 |
% 233.37/32.36 | SIMP: (617) implies:
% 233.37/32.36 | (618) all_180_0 = all_20_4
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (615), (616) imply:
% 233.37/32.36 | (619) all_188_0 = all_112_0
% 233.37/32.36 |
% 233.37/32.36 | SIMP: (619) implies:
% 233.37/32.36 | (620) all_188_0 = all_112_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (542), (575) imply:
% 233.37/32.36 | (621) addition(all_60_0, all_186_0) = all_48_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (529), (600) imply:
% 233.37/32.36 | (622) addition(all_50_0, all_186_0) = all_20_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (434), (618) imply:
% 233.37/32.36 | (623) addition(all_38_0, all_20_4) = all_128_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (503), (607) imply:
% 233.37/32.36 | (624) addition(all_36_0, all_186_0) = all_128_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (470), (566) imply:
% 233.37/32.36 | (625) addition(all_20_3, all_100_0) = all_114_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (448), (582), (614) imply:
% 233.37/32.36 | (626) addition(all_20_3, all_100_0) = one
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (429), (595) imply:
% 233.37/32.36 | (627) addition(all_20_3, all_110_0) = all_128_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (484), (586) imply:
% 233.37/32.36 | (628) addition(all_20_6, all_94_0) = all_50_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (480), (567) imply:
% 233.37/32.36 | (629) addition(all_20_6, all_94_0) = all_88_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (522), (568) imply:
% 233.37/32.36 | (630) addition(all_20_8, all_142_0) = all_100_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (445), (620) imply:
% 233.37/32.36 | (631) addition(all_20_8, all_112_0) = all_110_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (516), (604) imply:
% 233.37/32.36 | (632) addition(all_20_10, all_186_0) = all_100_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (507), (593) imply:
% 233.37/32.36 | (633) addition(all_20_10, all_64_0) = all_126_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (459), (615) imply:
% 233.37/32.36 | (634) addition(all_20_10, all_112_0) = all_98_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (453), (577) imply:
% 233.37/32.36 | (635) addition(all_20_10, all_64_0) = all_116_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (562), (589) imply:
% 233.37/32.36 | (636) addition(all_20_12, all_20_4) = all_114_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (501), (607) imply:
% 233.37/32.36 | (637) $i(all_186_0)
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_122_0, all_126_0, all_64_0, all_20_10,
% 233.37/32.36 | simplifying with (324), (633) gives:
% 233.37/32.36 | (638) all_126_0 = all_122_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_116_0, all_126_0, all_64_0, all_20_10,
% 233.37/32.36 | simplifying with (633), (635) gives:
% 233.37/32.36 | (639) all_126_0 = all_116_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_248_0, all_98_0, all_112_0, all_20_10,
% 233.37/32.36 | simplifying with (496), (634) gives:
% 233.37/32.36 | (640) all_248_0 = all_98_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_246_0, all_110_0, all_112_0, all_20_8,
% 233.37/32.36 | simplifying with (494), (631) gives:
% 233.37/32.36 | (641) all_246_0 = all_110_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_266_0, all_100_0, all_142_0, all_20_8,
% 233.37/32.36 | simplifying with (519), (630) gives:
% 233.37/32.36 | (642) all_266_0 = all_100_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_174_0, all_50_0, all_94_0, all_20_6,
% 233.37/32.36 | simplifying with (427), (628) gives:
% 233.37/32.36 | (643) all_174_0 = all_50_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_174_0, all_88_0, all_94_0, all_20_6,
% 233.37/32.36 | simplifying with (427), (629) gives:
% 233.37/32.36 | (644) all_174_0 = all_88_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_236_0, one, all_100_0, all_20_3,
% 233.37/32.36 | simplifying with (482), (626) gives:
% 233.37/32.36 | (645) all_236_0 = one
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_236_0, all_114_0, all_100_0, all_20_3,
% 233.37/32.36 | simplifying with (482), (625) gives:
% 233.37/32.36 | (646) all_236_0 = all_114_0
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_66_0, all_128_0, all_20_4, all_38_0,
% 233.37/32.36 | simplifying with (547), (623) gives:
% 233.37/32.36 | (647) all_128_0 = all_66_0
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (645), (646) imply:
% 233.37/32.36 | (648) all_114_0 = one
% 233.37/32.36 |
% 233.37/32.36 | SIMP: (648) implies:
% 233.37/32.36 | (649) all_114_0 = one
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (643), (644) imply:
% 233.37/32.36 | (650) all_88_0 = all_50_0
% 233.37/32.36 |
% 233.37/32.36 | COMBINE_EQS: (638), (639) imply:
% 233.37/32.36 | (651) all_122_0 = all_116_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (359), (651) imply:
% 233.37/32.36 | (652) addition(all_116_0, all_20_8) = all_20_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (371), (649) imply:
% 233.37/32.36 | (653) addition(one, all_20_6) = all_20_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (492), (650) imply:
% 233.37/32.36 | (654) addition(all_50_0, all_20_1) = all_244_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (341), (651) imply:
% 233.37/32.36 | (655) addition(all_64_0, all_20_10) = all_116_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (245), (649) imply:
% 233.37/32.36 | (656) addition(all_58_0, all_20_1) = one
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (256), (639) imply:
% 233.37/32.36 | (657) addition(all_50_0, all_20_1) = all_116_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (624), (647) imply:
% 233.37/32.36 | (658) addition(all_36_0, all_186_0) = all_66_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (411), (649) imply:
% 233.37/32.36 | (659) addition(all_20_1, all_58_0) = one
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (627), (647) imply:
% 233.37/32.36 | (660) addition(all_20_3, all_110_0) = all_66_0
% 233.37/32.36 |
% 233.37/32.36 | REDUCE: (636), (649) imply:
% 233.37/32.36 | (661) addition(all_20_12, all_20_4) = one
% 233.37/32.36 |
% 233.37/32.36 | GROUND_INST: instantiating (9) with all_116_0, all_244_0, all_20_1, all_50_0,
% 233.37/32.36 | simplifying with (654), (657) gives:
% 233.37/32.36 | (662) all_244_0 = all_116_0
% 233.37/32.36 |
% 233.37/32.36 | BETA: splitting (34) gives:
% 233.37/32.36 |
% 233.37/32.37 | Case 1:
% 233.37/32.37 | |
% 233.37/32.37 | | (663) ~ leq(all_20_0, one)
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_associativity) with all_20_6,
% 233.37/32.37 | | all_20_11, all_20_9, one, all_20_0, simplifying with (15),
% 233.37/32.37 | | (17), (19), (291), (653) gives:
% 233.37/32.37 | | (664) ? [v0: $i] : (addition(all_20_9, v0) = all_20_0 &
% 233.37/32.37 | | addition(all_20_11, all_20_6) = v0 & $i(v0) & $i(all_20_0))
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_associativity) with all_20_6, all_20_9,
% 233.37/32.37 | | all_20_11, one, all_20_0, simplifying with (15), (17), (19),
% 233.37/32.37 | | (292), (653) gives:
% 233.37/32.37 | | (665) ? [v0: $i] : (addition(all_20_9, all_20_6) = v0 &
% 233.37/32.37 | | addition(all_20_11, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_commutativity) with all_20_10,
% 233.37/32.37 | | all_186_0, all_100_0, simplifying with (16), (632), (637)
% 233.37/32.37 | | gives:
% 233.37/32.37 | | (666) addition(all_186_0, all_20_10) = all_100_0 & $i(all_100_0)
% 233.37/32.37 | |
% 233.37/32.37 | | ALPHA: (666) implies:
% 233.37/32.37 | | (667) addition(all_186_0, all_20_10) = all_100_0
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_commutativity) with all_20_10,
% 233.37/32.37 | | all_276_0, all_20_0, simplifying with (16), (531), (532) gives:
% 233.37/32.37 | | (668) addition(all_276_0, all_20_10) = all_20_0 & $i(all_20_0)
% 233.37/32.37 | |
% 233.37/32.37 | | ALPHA: (668) implies:
% 233.37/32.37 | | (669) addition(all_276_0, all_20_10) = all_20_0
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_commutativity) with all_20_8, all_20_1,
% 233.37/32.37 | | all_186_0, simplifying with (18), (22), (442) gives:
% 233.37/32.37 | | (670) addition(all_20_1, all_20_8) = all_186_0 & $i(all_186_0)
% 233.37/32.37 | |
% 233.37/32.37 | | ALPHA: (670) implies:
% 233.37/32.37 | | (671) addition(all_20_1, all_20_8) = all_186_0
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_commutativity) with all_20_8,
% 233.37/32.37 | | all_112_0, all_110_0, simplifying with (18), (313), (631)
% 233.37/32.37 | | gives:
% 233.37/32.37 | | (672) addition(all_112_0, all_20_8) = all_110_0 & $i(all_110_0)
% 233.37/32.37 | |
% 233.37/32.37 | | ALPHA: (672) implies:
% 233.37/32.37 | | (673) addition(all_112_0, all_20_8) = all_110_0
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_commutativity) with all_20_8,
% 233.37/32.37 | | all_142_0, all_100_0, simplifying with (18), (335), (630)
% 233.37/32.37 | | gives:
% 233.37/32.37 | | (674) addition(all_142_0, all_20_8) = all_100_0 & $i(all_100_0)
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_commutativity) with all_20_6, all_94_0,
% 233.37/32.37 | | all_50_0, simplifying with (19), (332), (628) gives:
% 233.37/32.37 | | (675) addition(all_94_0, all_20_6) = all_50_0 & $i(all_50_0)
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_commutativity) with all_20_6,
% 233.37/32.37 | | all_186_0, all_110_0, simplifying with (19), (443), (637)
% 233.37/32.37 | | gives:
% 233.37/32.37 | | (676) addition(all_186_0, all_20_6) = all_110_0 & $i(all_110_0)
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_commutativity) with all_20_6,
% 233.37/32.37 | | all_262_0, all_20_0, simplifying with (19), (512), (513) gives:
% 233.37/32.37 | | (677) addition(all_262_0, all_20_6) = all_20_0 & $i(all_20_0)
% 233.37/32.37 | |
% 233.37/32.37 | | ALPHA: (677) implies:
% 233.37/32.37 | | (678) addition(all_262_0, all_20_6) = all_20_0
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_associativity) with all_20_8, all_20_1,
% 233.37/32.37 | | all_20_3, all_20_4, all_102_0, simplifying with (18), (21),
% 233.37/32.37 | | (22), (549), (556) gives:
% 233.37/32.37 | | (679) ? [v0: $i] : (addition(all_20_1, all_20_8) = v0 &
% 233.37/32.37 | | addition(all_20_3, v0) = all_102_0 & $i(v0) & $i(all_102_0))
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_commutativity) with all_20_3,
% 233.37/32.37 | | all_100_0, one, simplifying with (21), (363), (626) gives:
% 233.37/32.37 | | (680) addition(all_100_0, all_20_3) = one & $i(one)
% 233.37/32.37 | |
% 233.37/32.37 | | ALPHA: (680) implies:
% 233.37/32.37 | | (681) $i(one)
% 233.37/32.37 | | (682) addition(all_100_0, all_20_3) = one
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_commutativity) with all_20_3,
% 233.37/32.37 | | all_110_0, all_66_0, simplifying with (21), (236), (660) gives:
% 233.37/32.37 | | (683) addition(all_110_0, all_20_3) = all_66_0 & $i(all_66_0)
% 233.37/32.37 | |
% 233.37/32.37 | | ALPHA: (683) implies:
% 233.37/32.37 | | (684) addition(all_110_0, all_20_3) = all_66_0
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_associativity) with all_20_10,
% 233.37/32.37 | | all_20_3, all_20_1, all_20_4, all_132_0, simplifying with (16),
% 233.37/32.37 | | (21), (22), (551), (552) gives:
% 233.37/32.37 | | (685) ? [v0: $i] : (addition(all_20_1, v0) = all_132_0 &
% 233.37/32.37 | | addition(all_20_3, all_20_10) = v0 & $i(v0) & $i(all_132_0))
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (4) with all_20_1, all_58_0, simplifying with
% 233.37/32.37 | | (22), (161), (659) gives:
% 233.37/32.37 | | (686) complement(all_58_0, all_20_1) | ? [v0: $i] : ? [v1: $i] : (( ~
% 233.37/32.37 | | (v1 = zero) & multiplication(all_58_0, all_20_1) = v1 & $i(v1))
% 233.37/32.37 | | | ( ~ (v0 = zero) & multiplication(all_20_1, all_58_0) = v0 &
% 233.37/32.37 | | $i(v0)))
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_associativity) with all_20_10,
% 233.37/32.37 | | all_186_0, all_36_0, all_66_0, all_20_0, simplifying with (16),
% 233.37/32.37 | | (56), (147), (637), (658) gives:
% 233.37/32.37 | | (687) ? [v0: $i] : (addition(all_186_0, all_20_10) = v0 &
% 233.37/32.37 | | addition(all_36_0, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_associativity) with all_186_0,
% 233.37/32.37 | | all_94_0, all_20_6, all_50_0, all_20_0, simplifying with (19),
% 233.37/32.37 | | (332), (622), (628), (637) gives:
% 233.37/32.37 | | (688) ? [v0: $i] : (addition(all_94_0, all_186_0) = v0 &
% 233.37/32.37 | | addition(all_20_6, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (4) with all_58_0, all_20_1, simplifying with
% 233.37/32.37 | | (22), (161), (656) gives:
% 233.37/32.37 | | (689) complement(all_20_1, all_58_0) | ? [v0: $i] : ? [v1: $i] : (( ~
% 233.37/32.37 | | (v1 = zero) & multiplication(all_20_1, all_58_0) = v1 & $i(v1))
% 233.37/32.37 | | | ( ~ (v0 = zero) & multiplication(all_58_0, all_20_1) = v0 &
% 233.37/32.37 | | $i(v0)))
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_associativity) with all_20_3,
% 233.37/32.37 | | all_186_0, all_60_0, all_48_0, all_20_0, simplifying with (21),
% 233.37/32.37 | | (137), (185), (621), (637) gives:
% 233.37/32.37 | | (690) ? [v0: $i] : (addition(all_186_0, all_20_3) = v0 &
% 233.37/32.37 | | addition(all_60_0, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_associativity) with all_20_8, all_20_1,
% 233.37/32.37 | | all_36_0, all_64_0, all_66_0, simplifying with (18), (22),
% 233.37/32.37 | | (56), (118), (352) gives:
% 233.37/32.37 | | (691) ? [v0: $i] : (addition(all_36_0, v0) = all_66_0 &
% 233.37/32.37 | | addition(all_20_1, all_20_8) = v0 & $i(v0) & $i(all_66_0))
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_associativity) with all_20_8,
% 233.37/32.37 | | all_112_0, all_20_3, all_64_0, all_66_0, simplifying with (18),
% 233.37/32.37 | | (21), (308), (313), (352) gives:
% 233.37/32.37 | | (692) ? [v0: $i] : (addition(all_112_0, all_20_8) = v0 &
% 233.37/32.37 | | addition(all_20_3, v0) = all_66_0 & $i(v0) & $i(all_66_0))
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_8,
% 233.37/32.37 | | all_20_3, all_86_0, all_226_0, simplifying with (18), (21),
% 233.37/32.37 | | (22), (348), (475) gives:
% 233.37/32.37 | | (693) ? [v0: $i] : (addition(all_20_3, v0) = all_226_0 &
% 233.37/32.37 | | addition(all_20_8, all_20_1) = v0 & $i(v0) & $i(all_226_0))
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_8,
% 233.37/32.37 | | all_94_0, all_58_0, one, simplifying with (18), (22), (332),
% 233.37/32.37 | | (355), (656) gives:
% 233.37/32.37 | | (694) ? [v0: $i] : (addition(all_94_0, v0) = one & addition(all_20_8,
% 233.37/32.37 | | all_20_1) = v0 & $i(v0) & $i(one))
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_associativity) with all_20_6, all_20_3,
% 233.37/32.37 | | all_20_10, all_94_0, all_216_0, simplifying with (16), (19),
% 233.37/32.37 | | (21), (215), (465) gives:
% 233.37/32.37 | | (695) ? [v0: $i] : (addition(all_20_3, all_20_6) = v0 &
% 233.37/32.37 | | addition(all_20_10, v0) = all_216_0 & $i(v0) & $i(all_216_0))
% 233.37/32.37 | |
% 233.37/32.37 | | GROUND_INST: instantiating (additive_associativity) with all_20_8, all_20_1,
% 233.37/32.37 | | all_60_0, all_98_0, all_48_0, simplifying with (18), (22),
% 233.37/32.37 | | (137), (222), (357) gives:
% 233.37/32.37 | | (696) ? [v0: $i] : (addition(all_60_0, v0) = all_48_0 &
% 233.37/32.37 | | addition(all_20_1, all_20_8) = v0 & $i(v0) & $i(all_48_0))
% 233.37/32.38 | |
% 233.37/32.38 | | GROUND_INST: instantiating (additive_associativity) with all_20_8,
% 233.37/32.38 | | all_112_0, all_20_10, all_98_0, all_48_0, simplifying with
% 233.37/32.38 | | (16), (18), (313), (357), (634) gives:
% 233.37/32.38 | | (697) ? [v0: $i] : (addition(all_112_0, all_20_8) = v0 &
% 233.37/32.38 | | addition(all_20_10, v0) = all_48_0 & $i(v0) & $i(all_48_0))
% 233.37/32.38 | |
% 233.37/32.38 | | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_1,
% 233.37/32.38 | | all_60_0, all_98_0, all_260_0, simplifying with (21), (22),
% 233.37/32.38 | | (137), (222), (510) gives:
% 233.37/32.38 | | (698) ? [v0: $i] : (addition(all_60_0, v0) = all_260_0 &
% 233.37/32.38 | | addition(all_20_1, all_20_3) = v0 & $i(v0) & $i(all_260_0))
% 233.37/32.38 | |
% 233.37/32.38 | | GROUND_INST: instantiating (additive_associativity) with all_20_3,
% 233.37/32.38 | | all_20_12, all_20_1, all_100_0, all_262_0, simplifying with
% 233.37/32.38 | | (14), (21), (22), (514), (555) gives:
% 233.37/32.39 | | (699) ? [v0: $i] : (addition(all_20_1, v0) = all_262_0 &
% 233.37/32.39 | | addition(all_20_12, all_20_3) = v0 & $i(v0) & $i(all_262_0))
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (additive_associativity) with all_20_3,
% 233.37/32.39 | | all_186_0, all_20_10, all_100_0, all_262_0, simplifying with
% 233.37/32.39 | | (16), (21), (514), (632), (637) gives:
% 233.37/32.39 | | (700) ? [v0: $i] : (addition(all_186_0, all_20_3) = v0 &
% 233.37/32.39 | | addition(all_20_10, v0) = all_262_0 & $i(v0) & $i(all_262_0))
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_1,
% 233.37/32.39 | | all_20_12, all_100_0, all_262_0, simplifying with (14), (21),
% 233.37/32.39 | | (22), (514), (564) gives:
% 233.37/32.39 | | (701) ? [v0: $i] : (addition(all_20_1, all_20_3) = v0 &
% 233.37/32.39 | | addition(all_20_12, v0) = all_262_0 & $i(v0) & $i(all_262_0))
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (additive_associativity) with all_20_3,
% 233.37/32.39 | | all_20_10, all_110_0, all_48_0, all_20_0, simplifying with
% 233.37/32.39 | | (16), (21), (185), (236), (343) gives:
% 233.37/32.39 | | (702) ? [v0: $i] : (addition(all_110_0, v0) = all_20_0 &
% 233.37/32.39 | | addition(all_20_10, all_20_3) = v0 & $i(v0) & $i(all_20_0))
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (additive_associativity) with all_20_10,
% 233.37/32.39 | | all_186_0, all_20_6, all_110_0, all_48_0, simplifying with
% 233.37/32.39 | | (16), (19), (343), (443), (637) gives:
% 233.37/32.39 | | (703) ? [v0: $i] : (addition(all_186_0, all_20_10) = v0 &
% 233.37/32.39 | | addition(all_20_6, v0) = all_48_0 & $i(v0) & $i(all_48_0))
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_1,
% 233.37/32.39 | | all_38_0, all_110_0, all_276_0, simplifying with (21), (22),
% 233.37/32.39 | | (60), (238), (533) gives:
% 233.37/32.39 | | (704) ? [v0: $i] : (addition(all_38_0, v0) = all_276_0 &
% 233.37/32.39 | | addition(all_20_1, all_20_3) = v0 & $i(v0) & $i(all_276_0))
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (additive_associativity) with all_20_3,
% 233.37/32.39 | | all_186_0, all_20_6, all_110_0, all_276_0, simplifying with
% 233.37/32.39 | | (19), (21), (443), (533), (637) gives:
% 233.37/32.39 | | (705) ? [v0: $i] : (addition(all_186_0, all_20_3) = v0 &
% 233.37/32.39 | | addition(all_20_6, v0) = all_276_0 & $i(v0) & $i(all_276_0))
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (additive_associativity) with all_20_10,
% 233.37/32.39 | | all_20_3, all_112_0, all_64_0, all_116_0, simplifying with
% 233.37/32.39 | | (16), (21), (313), (377), (655) gives:
% 233.37/32.39 | | (706) ? [v0: $i] : (addition(all_112_0, v0) = all_116_0 &
% 233.37/32.39 | | addition(all_20_3, all_20_10) = v0 & $i(v0) & $i(all_116_0))
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (additive_associativity) with all_20_12,
% 233.37/32.39 | | all_20_3, all_112_0, all_64_0, all_20_0, simplifying with (14),
% 233.37/32.39 | | (21), (313), (377), (546) gives:
% 233.37/32.39 | | (707) ? [v0: $i] : (addition(all_112_0, v0) = all_20_0 &
% 233.37/32.39 | | addition(all_20_3, all_20_12) = v0 & $i(v0) & $i(all_20_0))
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (additive_associativity) with all_20_8, all_20_1,
% 233.37/32.39 | | all_50_0, all_116_0, all_20_0, simplifying with (18), (22),
% 233.37/32.39 | | (140), (652), (657) gives:
% 233.37/32.39 | | (708) ? [v0: $i] : (addition(all_50_0, v0) = all_20_0 &
% 233.37/32.39 | | addition(all_20_1, all_20_8) = v0 & $i(v0) & $i(all_20_0))
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_1,
% 233.37/32.39 | | all_20_10, all_142_0, all_270_0, simplifying with (16), (21),
% 233.37/32.39 | | (22), (279), (524) gives:
% 233.37/32.39 | | (709) ? [v0: $i] : (addition(all_20_1, all_20_3) = v0 &
% 233.37/32.39 | | addition(all_20_10, v0) = all_270_0 & $i(v0) & $i(all_270_0))
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (additive_associativity) with all_20_3,
% 233.37/32.39 | | all_20_10, all_20_1, all_142_0, all_270_0, simplifying with
% 233.37/32.39 | | (16), (21), (22), (336), (524) gives:
% 233.37/32.39 | | (710) ? [v0: $i] : (addition(all_20_1, v0) = all_270_0 &
% 233.37/32.39 | | addition(all_20_10, all_20_3) = v0 & $i(v0) & $i(all_270_0))
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (multiplicative_associativity) with one,
% 233.37/32.39 | | all_20_12, all_20_11, all_20_12, all_20_6, simplifying with
% 233.37/32.39 | | (14), (15), (27), (545), (681) gives:
% 233.37/32.39 | | (711) ? [v0: $i] : (multiplication(all_20_12, all_20_11) = v0 &
% 233.37/32.39 | | multiplication(one, v0) = all_20_6 & $i(v0) & $i(all_20_6))
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (2) with all_20_11, all_36_0, simplifying with
% 233.37/32.39 | | (15), (543) gives:
% 233.37/32.39 | | (712) all_36_0 = all_20_11
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.37/32.39 | | one, all_20_9, all_20_4, all_20_1, simplifying with (17), (20),
% 233.37/32.39 | | (31), (544), (681) gives:
% 233.37/32.39 | | (713) ? [v0: $i] : (multiplication(all_20_4, v0) = all_20_1 &
% 233.37/32.39 | | multiplication(one, all_20_9) = v0 & $i(v0) & $i(all_20_1))
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.37/32.39 | | one, all_20_11, all_20_4, all_20_3, simplifying with (15),
% 233.37/32.39 | | (20), (30), (544), (681) gives:
% 233.37/32.39 | | (714) ? [v0: $i] : (multiplication(all_20_4, v0) = all_20_3 &
% 233.37/32.39 | | multiplication(one, all_20_11) = v0 & $i(v0) & $i(all_20_3))
% 233.37/32.39 | |
% 233.37/32.39 | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.37/32.39 | | one, one, all_20_4, all_20_4, simplifying with (20), (544),
% 233.37/32.39 | | (681) gives:
% 233.37/32.39 | | (715) ? [v0: $i] : (multiplication(all_20_4, v0) = all_20_4 &
% 233.37/32.39 | | multiplication(one, one) = v0 & $i(v0))
% 233.37/32.39 | |
% 233.37/32.39 | | DELTA: instantiating (715) with fresh symbol all_316_0 gives:
% 233.37/32.39 | | (716) multiplication(all_20_4, all_316_0) = all_20_4 &
% 233.37/32.39 | | multiplication(one, one) = all_316_0 & $i(all_316_0)
% 233.37/32.39 | |
% 233.37/32.39 | | ALPHA: (716) implies:
% 233.37/32.39 | | (717) $i(all_316_0)
% 233.37/32.39 | | (718) multiplication(one, one) = all_316_0
% 233.37/32.39 | | (719) multiplication(all_20_4, all_316_0) = all_20_4
% 233.37/32.39 | |
% 233.37/32.39 | | DELTA: instantiating (688) with fresh symbol all_322_0 gives:
% 233.37/32.39 | | (720) addition(all_94_0, all_186_0) = all_322_0 & addition(all_20_6,
% 233.37/32.39 | | all_322_0) = all_20_0 & $i(all_322_0) & $i(all_20_0)
% 233.37/32.39 | |
% 233.37/32.39 | | ALPHA: (720) implies:
% 233.37/32.39 | | (721) addition(all_94_0, all_186_0) = all_322_0
% 233.37/32.39 | |
% 233.37/32.39 | | DELTA: instantiating (665) with fresh symbol all_326_0 gives:
% 233.37/32.39 | | (722) addition(all_20_9, all_20_6) = all_326_0 & addition(all_20_11,
% 233.37/32.39 | | all_326_0) = all_20_0 & $i(all_326_0) & $i(all_20_0)
% 233.37/32.39 | |
% 233.37/32.39 | | ALPHA: (722) implies:
% 233.37/32.39 | | (723) addition(all_20_11, all_326_0) = all_20_0
% 233.37/32.39 | | (724) addition(all_20_9, all_20_6) = all_326_0
% 233.37/32.39 | |
% 233.37/32.39 | | DELTA: instantiating (685) with fresh symbol all_332_0 gives:
% 233.37/32.39 | | (725) addition(all_20_1, all_332_0) = all_132_0 & addition(all_20_3,
% 233.37/32.39 | | all_20_10) = all_332_0 & $i(all_332_0) & $i(all_132_0)
% 233.37/32.39 | |
% 233.37/32.39 | | ALPHA: (725) implies:
% 233.37/32.39 | | (726) $i(all_332_0)
% 233.37/32.39 | | (727) addition(all_20_3, all_20_10) = all_332_0
% 233.37/32.39 | |
% 233.37/32.39 | | DELTA: instantiating (664) with fresh symbol all_338_0 gives:
% 233.37/32.39 | | (728) addition(all_20_9, all_338_0) = all_20_0 & addition(all_20_11,
% 233.37/32.39 | | all_20_6) = all_338_0 & $i(all_338_0) & $i(all_20_0)
% 233.37/32.39 | |
% 233.37/32.39 | | ALPHA: (728) implies:
% 233.37/32.39 | | (729) addition(all_20_11, all_20_6) = all_338_0
% 233.37/32.39 | | (730) addition(all_20_9, all_338_0) = all_20_0
% 233.37/32.39 | |
% 233.37/32.39 | | DELTA: instantiating (708) with fresh symbol all_344_0 gives:
% 233.37/32.39 | | (731) addition(all_50_0, all_344_0) = all_20_0 & addition(all_20_1,
% 233.37/32.39 | | all_20_8) = all_344_0 & $i(all_344_0) & $i(all_20_0)
% 233.37/32.39 | |
% 233.37/32.39 | | ALPHA: (731) implies:
% 233.37/32.39 | | (732) $i(all_344_0)
% 233.37/32.39 | | (733) addition(all_20_1, all_20_8) = all_344_0
% 233.37/32.39 | |
% 233.37/32.39 | | DELTA: instantiating (706) with fresh symbol all_346_0 gives:
% 233.37/32.39 | | (734) addition(all_112_0, all_346_0) = all_116_0 & addition(all_20_3,
% 233.37/32.39 | | all_20_10) = all_346_0 & $i(all_346_0) & $i(all_116_0)
% 233.37/32.39 | |
% 233.37/32.39 | | ALPHA: (734) implies:
% 233.37/32.39 | | (735) addition(all_20_3, all_20_10) = all_346_0
% 233.37/32.39 | |
% 233.37/32.39 | | DELTA: instantiating (707) with fresh symbol all_350_0 gives:
% 233.37/32.39 | | (736) addition(all_112_0, all_350_0) = all_20_0 & addition(all_20_3,
% 233.37/32.39 | | all_20_12) = all_350_0 & $i(all_350_0) & $i(all_20_0)
% 233.37/32.39 | |
% 233.37/32.39 | | ALPHA: (736) implies:
% 233.37/32.39 | | (737) $i(all_350_0)
% 233.37/32.39 | | (738) addition(all_20_3, all_20_12) = all_350_0
% 233.37/32.39 | |
% 233.37/32.39 | | DELTA: instantiating (679) with fresh symbol all_372_0 gives:
% 233.37/32.39 | | (739) addition(all_20_1, all_20_8) = all_372_0 & addition(all_20_3,
% 233.37/32.39 | | all_372_0) = all_102_0 & $i(all_372_0) & $i(all_102_0)
% 233.37/32.39 | |
% 233.37/32.39 | | ALPHA: (739) implies:
% 233.37/32.39 | | (740) addition(all_20_1, all_20_8) = all_372_0
% 233.37/32.39 | |
% 233.37/32.39 | | DELTA: instantiating (714) with fresh symbol all_384_0 gives:
% 233.37/32.39 | | (741) multiplication(all_20_4, all_384_0) = all_20_3 &
% 233.37/32.39 | | multiplication(one, all_20_11) = all_384_0 & $i(all_384_0) &
% 233.37/32.39 | | $i(all_20_3)
% 233.37/32.39 | |
% 233.37/32.39 | | ALPHA: (741) implies:
% 233.37/32.39 | | (742) $i(all_384_0)
% 233.37/32.39 | | (743) multiplication(one, all_20_11) = all_384_0
% 233.37/32.39 | | (744) multiplication(all_20_4, all_384_0) = all_20_3
% 233.37/32.39 | |
% 233.37/32.39 | | DELTA: instantiating (713) with fresh symbol all_386_0 gives:
% 233.37/32.39 | | (745) multiplication(all_20_4, all_386_0) = all_20_1 &
% 233.37/32.39 | | multiplication(one, all_20_9) = all_386_0 & $i(all_386_0) &
% 233.37/32.39 | | $i(all_20_1)
% 233.37/32.39 | |
% 233.37/32.39 | | ALPHA: (745) implies:
% 233.37/32.39 | | (746) $i(all_386_0)
% 233.37/32.39 | | (747) multiplication(one, all_20_9) = all_386_0
% 233.37/32.39 | | (748) multiplication(all_20_4, all_386_0) = all_20_1
% 233.37/32.39 | |
% 233.37/32.39 | | DELTA: instantiating (709) with fresh symbol all_388_0 gives:
% 233.37/32.39 | | (749) addition(all_20_1, all_20_3) = all_388_0 & addition(all_20_10,
% 233.37/32.39 | | all_388_0) = all_270_0 & $i(all_388_0) & $i(all_270_0)
% 233.37/32.39 | |
% 233.37/32.39 | | ALPHA: (749) implies:
% 233.37/32.39 | | (750) $i(all_388_0)
% 233.37/32.39 | | (751) addition(all_20_1, all_20_3) = all_388_0
% 233.37/32.39 | |
% 233.37/32.39 | | DELTA: instantiating (696) with fresh symbol all_390_0 gives:
% 233.37/32.39 | | (752) addition(all_60_0, all_390_0) = all_48_0 & addition(all_20_1,
% 233.37/32.39 | | all_20_8) = all_390_0 & $i(all_390_0) & $i(all_48_0)
% 233.37/32.39 | |
% 233.37/32.39 | | ALPHA: (752) implies:
% 233.37/32.39 | | (753) addition(all_20_1, all_20_8) = all_390_0
% 233.37/32.39 | |
% 233.37/32.39 | | DELTA: instantiating (698) with fresh symbol all_400_0 gives:
% 233.37/32.39 | | (754) addition(all_60_0, all_400_0) = all_260_0 & addition(all_20_1,
% 233.37/32.39 | | all_20_3) = all_400_0 & $i(all_400_0) & $i(all_260_0)
% 233.37/32.39 | |
% 233.37/32.39 | | ALPHA: (754) implies:
% 233.37/32.39 | | (755) addition(all_20_1, all_20_3) = all_400_0
% 233.37/32.39 | |
% 233.37/32.39 | | DELTA: instantiating (704) with fresh symbol all_406_0 gives:
% 233.37/32.39 | | (756) addition(all_38_0, all_406_0) = all_276_0 & addition(all_20_1,
% 233.37/32.39 | | all_20_3) = all_406_0 & $i(all_406_0) & $i(all_276_0)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (756) implies:
% 233.37/32.40 | | (757) addition(all_20_1, all_20_3) = all_406_0
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (702) with fresh symbol all_408_0 gives:
% 233.37/32.40 | | (758) addition(all_110_0, all_408_0) = all_20_0 & addition(all_20_10,
% 233.37/32.40 | | all_20_3) = all_408_0 & $i(all_408_0) & $i(all_20_0)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (758) implies:
% 233.37/32.40 | | (759) addition(all_20_10, all_20_3) = all_408_0
% 233.37/32.40 | | (760) addition(all_110_0, all_408_0) = all_20_0
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (690) with fresh symbol all_414_0 gives:
% 233.37/32.40 | | (761) addition(all_186_0, all_20_3) = all_414_0 & addition(all_60_0,
% 233.37/32.40 | | all_414_0) = all_20_0 & $i(all_414_0) & $i(all_20_0)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (761) implies:
% 233.37/32.40 | | (762) addition(all_186_0, all_20_3) = all_414_0
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (703) with fresh symbol all_420_0 gives:
% 233.37/32.40 | | (763) addition(all_186_0, all_20_10) = all_420_0 & addition(all_20_6,
% 233.37/32.40 | | all_420_0) = all_48_0 & $i(all_420_0) & $i(all_48_0)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (763) implies:
% 233.37/32.40 | | (764) addition(all_186_0, all_20_10) = all_420_0
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (687) with fresh symbol all_426_0 gives:
% 233.37/32.40 | | (765) addition(all_186_0, all_20_10) = all_426_0 & addition(all_36_0,
% 233.37/32.40 | | all_426_0) = all_20_0 & $i(all_426_0) & $i(all_20_0)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (765) implies:
% 233.37/32.40 | | (766) addition(all_186_0, all_20_10) = all_426_0
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (695) with fresh symbol all_430_0 gives:
% 233.37/32.40 | | (767) addition(all_20_3, all_20_6) = all_430_0 & addition(all_20_10,
% 233.37/32.40 | | all_430_0) = all_216_0 & $i(all_430_0) & $i(all_216_0)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (767) implies:
% 233.37/32.40 | | (768) addition(all_20_3, all_20_6) = all_430_0
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (692) with fresh symbol all_432_0 gives:
% 233.37/32.40 | | (769) addition(all_112_0, all_20_8) = all_432_0 & addition(all_20_3,
% 233.37/32.40 | | all_432_0) = all_66_0 & $i(all_432_0) & $i(all_66_0)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (769) implies:
% 233.37/32.40 | | (770) $i(all_432_0)
% 233.37/32.40 | | (771) addition(all_112_0, all_20_8) = all_432_0
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (694) with fresh symbol all_434_0 gives:
% 233.37/32.40 | | (772) addition(all_94_0, all_434_0) = one & addition(all_20_8, all_20_1)
% 233.37/32.40 | | = all_434_0 & $i(all_434_0) & $i(one)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (772) implies:
% 233.37/32.40 | | (773) addition(all_20_8, all_20_1) = all_434_0
% 233.37/32.40 | | (774) addition(all_94_0, all_434_0) = one
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (691) with fresh symbol all_436_0 gives:
% 233.37/32.40 | | (775) addition(all_36_0, all_436_0) = all_66_0 & addition(all_20_1,
% 233.37/32.40 | | all_20_8) = all_436_0 & $i(all_436_0) & $i(all_66_0)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (775) implies:
% 233.37/32.40 | | (776) addition(all_20_1, all_20_8) = all_436_0
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (697) with fresh symbol all_438_0 gives:
% 233.37/32.40 | | (777) addition(all_112_0, all_20_8) = all_438_0 & addition(all_20_10,
% 233.37/32.40 | | all_438_0) = all_48_0 & $i(all_438_0) & $i(all_48_0)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (777) implies:
% 233.37/32.40 | | (778) addition(all_112_0, all_20_8) = all_438_0
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (710) with fresh symbol all_446_0 gives:
% 233.37/32.40 | | (779) addition(all_20_1, all_446_0) = all_270_0 & addition(all_20_10,
% 233.37/32.40 | | all_20_3) = all_446_0 & $i(all_446_0) & $i(all_270_0)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (779) implies:
% 233.37/32.40 | | (780) addition(all_20_10, all_20_3) = all_446_0
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (701) with fresh symbol all_448_0 gives:
% 233.37/32.40 | | (781) addition(all_20_1, all_20_3) = all_448_0 & addition(all_20_12,
% 233.37/32.40 | | all_448_0) = all_262_0 & $i(all_448_0) & $i(all_262_0)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (781) implies:
% 233.37/32.40 | | (782) addition(all_20_1, all_20_3) = all_448_0
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (700) with fresh symbol all_450_0 gives:
% 233.37/32.40 | | (783) addition(all_186_0, all_20_3) = all_450_0 & addition(all_20_10,
% 233.37/32.40 | | all_450_0) = all_262_0 & $i(all_450_0) & $i(all_262_0)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (783) implies:
% 233.37/32.40 | | (784) $i(all_450_0)
% 233.37/32.40 | | (785) addition(all_20_10, all_450_0) = all_262_0
% 233.37/32.40 | | (786) addition(all_186_0, all_20_3) = all_450_0
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (699) with fresh symbol all_452_0 gives:
% 233.37/32.40 | | (787) addition(all_20_1, all_452_0) = all_262_0 & addition(all_20_12,
% 233.37/32.40 | | all_20_3) = all_452_0 & $i(all_452_0) & $i(all_262_0)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (787) implies:
% 233.37/32.40 | | (788) addition(all_20_12, all_20_3) = all_452_0
% 233.37/32.40 | | (789) addition(all_20_1, all_452_0) = all_262_0
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (693) with fresh symbol all_472_0 gives:
% 233.37/32.40 | | (790) addition(all_20_3, all_472_0) = all_226_0 & addition(all_20_8,
% 233.37/32.40 | | all_20_1) = all_472_0 & $i(all_472_0) & $i(all_226_0)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (790) implies:
% 233.37/32.40 | | (791) addition(all_20_8, all_20_1) = all_472_0
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (705) with fresh symbol all_480_0 gives:
% 233.37/32.40 | | (792) addition(all_186_0, all_20_3) = all_480_0 & addition(all_20_6,
% 233.37/32.40 | | all_480_0) = all_276_0 & $i(all_480_0) & $i(all_276_0)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (792) implies:
% 233.37/32.40 | | (793) addition(all_20_6, all_480_0) = all_276_0
% 233.37/32.40 | | (794) addition(all_186_0, all_20_3) = all_480_0
% 233.37/32.40 | |
% 233.37/32.40 | | DELTA: instantiating (711) with fresh symbol all_486_0 gives:
% 233.37/32.40 | | (795) multiplication(all_20_12, all_20_11) = all_486_0 &
% 233.37/32.40 | | multiplication(one, all_486_0) = all_20_6 & $i(all_486_0) &
% 233.37/32.40 | | $i(all_20_6)
% 233.37/32.40 | |
% 233.37/32.40 | | ALPHA: (795) implies:
% 233.37/32.40 | | (796) $i(all_486_0)
% 233.37/32.40 | | (797) multiplication(one, all_486_0) = all_20_6
% 233.37/32.40 | | (798) multiplication(all_20_12, all_20_11) = all_486_0
% 233.37/32.40 | |
% 233.37/32.40 | | REDUCE: (543), (712) imply:
% 233.37/32.40 | | (799) multiplication(one, all_20_11) = all_20_11
% 233.37/32.40 | |
% 233.37/32.40 | | REDUCE: (80), (712) imply:
% 233.37/32.40 | | (800) addition(all_20_3, all_20_6) = all_20_11
% 233.37/32.40 | |
% 233.37/32.40 | | REDUCE: (58), (712) imply:
% 233.37/32.40 | | (801) addition(all_20_6, all_20_3) = all_20_11
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_58_0, all_452_0, all_20_3,
% 233.37/32.40 | | all_20_12, simplifying with (565), (788) gives:
% 233.37/32.40 | | (802) all_452_0 = all_58_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_94_0, all_446_0, all_20_3,
% 233.37/32.40 | | all_20_10, simplifying with (215), (780) gives:
% 233.37/32.40 | | (803) all_446_0 = all_94_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_408_0, all_446_0, all_20_3,
% 233.37/32.40 | | all_20_10, simplifying with (759), (780) gives:
% 233.37/32.40 | | (804) all_446_0 = all_408_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_186_0, all_472_0, all_20_1,
% 233.37/32.40 | | all_20_8, simplifying with (442), (791) gives:
% 233.37/32.40 | | (805) all_472_0 = all_186_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_434_0, all_472_0, all_20_1,
% 233.37/32.40 | | all_20_8, simplifying with (773), (791) gives:
% 233.37/32.40 | | (806) all_472_0 = all_434_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_58_0, all_350_0, all_20_12,
% 233.37/32.40 | | all_20_3, simplifying with (558), (738) gives:
% 233.37/32.40 | | (807) all_350_0 = all_58_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_94_0, all_346_0, all_20_10,
% 233.37/32.40 | | all_20_3, simplifying with (333), (735) gives:
% 233.37/32.40 | | (808) all_346_0 = all_94_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_332_0, all_346_0, all_20_10,
% 233.37/32.40 | | all_20_3, simplifying with (727), (735) gives:
% 233.37/32.40 | | (809) all_346_0 = all_332_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_20_11, all_430_0, all_20_6,
% 233.37/32.40 | | all_20_3, simplifying with (768), (800) gives:
% 233.37/32.40 | | (810) all_430_0 = all_20_11
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_344_0, all_372_0, all_20_8,
% 233.37/32.40 | | all_20_1, simplifying with (733), (740) gives:
% 233.37/32.40 | | (811) all_372_0 = all_344_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_372_0, all_390_0, all_20_8,
% 233.37/32.40 | | all_20_1, simplifying with (740), (753) gives:
% 233.37/32.40 | | (812) all_390_0 = all_372_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_390_0, all_436_0, all_20_8,
% 233.37/32.40 | | all_20_1, simplifying with (753), (776) gives:
% 233.37/32.40 | | (813) all_436_0 = all_390_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_186_0, all_436_0, all_20_8,
% 233.37/32.40 | | all_20_1, simplifying with (671), (776) gives:
% 233.37/32.40 | | (814) all_436_0 = all_186_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_400_0, all_406_0, all_20_3,
% 233.37/32.40 | | all_20_1, simplifying with (755), (757) gives:
% 233.37/32.40 | | (815) all_406_0 = all_400_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_388_0, all_406_0, all_20_3,
% 233.37/32.40 | | all_20_1, simplifying with (751), (757) gives:
% 233.37/32.40 | | (816) all_406_0 = all_388_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_20_4, all_448_0, all_20_3, all_20_1,
% 233.37/32.40 | | simplifying with (552), (782) gives:
% 233.37/32.40 | | (817) all_448_0 = all_20_4
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_400_0, all_448_0, all_20_3,
% 233.37/32.40 | | all_20_1, simplifying with (755), (782) gives:
% 233.37/32.40 | | (818) all_448_0 = all_400_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_262_0, one, all_20_3, all_100_0,
% 233.37/32.40 | | simplifying with (514), (682) gives:
% 233.37/32.40 | | (819) all_262_0 = one
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_276_0, all_66_0, all_20_3,
% 233.37/32.40 | | all_110_0, simplifying with (533), (684) gives:
% 233.37/32.40 | | (820) all_276_0 = all_66_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_432_0, all_438_0, all_20_8,
% 233.37/32.40 | | all_112_0, simplifying with (771), (778) gives:
% 233.37/32.40 | | (821) all_438_0 = all_432_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_110_0, all_438_0, all_20_8,
% 233.37/32.40 | | all_112_0, simplifying with (673), (778) gives:
% 233.37/32.40 | | (822) all_438_0 = all_110_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_420_0, all_426_0, all_20_10,
% 233.37/32.40 | | all_186_0, simplifying with (764), (766) gives:
% 233.37/32.40 | | (823) all_426_0 = all_420_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_100_0, all_426_0, all_20_10,
% 233.37/32.40 | | all_186_0, simplifying with (667), (766) gives:
% 233.37/32.40 | | (824) all_426_0 = all_100_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_450_0, all_480_0, all_20_3,
% 233.37/32.40 | | all_186_0, simplifying with (786), (794) gives:
% 233.37/32.40 | | (825) all_480_0 = all_450_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (9) with all_414_0, all_480_0, all_20_3,
% 233.37/32.40 | | all_186_0, simplifying with (762), (794) gives:
% 233.37/32.40 | | (826) all_480_0 = all_414_0
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (10) with all_20_11, all_384_0, all_20_11, one,
% 233.37/32.40 | | simplifying with (743), (799) gives:
% 233.37/32.40 | | (827) all_384_0 = all_20_11
% 233.37/32.40 | |
% 233.37/32.40 | | GROUND_INST: instantiating (10) with all_20_6, all_486_0, all_20_11,
% 233.37/32.40 | | all_20_12, simplifying with (27), (798) gives:
% 233.37/32.40 | | (828) all_486_0 = all_20_6
% 233.37/32.40 | |
% 233.37/32.40 | | COMBINE_EQS: (825), (826) imply:
% 233.37/32.40 | | (829) all_450_0 = all_414_0
% 233.37/32.40 | |
% 233.37/32.40 | | COMBINE_EQS: (805), (806) imply:
% 233.37/32.40 | | (830) all_434_0 = all_186_0
% 233.37/32.40 | |
% 233.37/32.40 | | COMBINE_EQS: (817), (818) imply:
% 233.37/32.40 | | (831) all_400_0 = all_20_4
% 233.37/32.40 | |
% 233.37/32.40 | | SIMP: (831) implies:
% 233.37/32.40 | | (832) all_400_0 = all_20_4
% 233.37/32.40 | |
% 233.37/32.40 | | COMBINE_EQS: (803), (804) imply:
% 233.37/32.40 | | (833) all_408_0 = all_94_0
% 233.37/32.40 | |
% 233.37/32.40 | | SIMP: (833) implies:
% 233.37/32.40 | | (834) all_408_0 = all_94_0
% 233.37/32.40 | |
% 233.37/32.40 | | COMBINE_EQS: (821), (822) imply:
% 233.37/32.40 | | (835) all_432_0 = all_110_0
% 233.37/32.40 | |
% 233.37/32.40 | | SIMP: (835) implies:
% 233.37/32.40 | | (836) all_432_0 = all_110_0
% 233.37/32.40 | |
% 233.37/32.40 | | COMBINE_EQS: (813), (814) imply:
% 233.37/32.40 | | (837) all_390_0 = all_186_0
% 233.37/32.40 | |
% 233.37/32.40 | | SIMP: (837) implies:
% 233.37/32.40 | | (838) all_390_0 = all_186_0
% 233.37/32.40 | |
% 233.37/32.40 | | COMBINE_EQS: (823), (824) imply:
% 233.37/32.40 | | (839) all_420_0 = all_100_0
% 233.37/32.40 | |
% 233.37/32.40 | | SIMP: (839) implies:
% 233.37/32.40 | | (840) all_420_0 = all_100_0
% 233.37/32.40 | |
% 233.37/32.40 | | COMBINE_EQS: (815), (816) imply:
% 233.37/32.40 | | (841) all_400_0 = all_388_0
% 233.37/32.40 | |
% 233.37/32.40 | | SIMP: (841) implies:
% 233.37/32.40 | | (842) all_400_0 = all_388_0
% 233.37/32.40 | |
% 233.37/32.40 | | COMBINE_EQS: (832), (842) imply:
% 233.37/32.40 | | (843) all_388_0 = all_20_4
% 233.37/32.40 | |
% 233.37/32.40 | | SIMP: (843) implies:
% 233.37/32.40 | | (844) all_388_0 = all_20_4
% 233.37/32.40 | |
% 233.37/32.40 | | COMBINE_EQS: (812), (838) imply:
% 233.37/32.40 | | (845) all_372_0 = all_186_0
% 233.37/32.40 | |
% 233.37/32.40 | | SIMP: (845) implies:
% 233.37/32.40 | | (846) all_372_0 = all_186_0
% 233.37/32.40 | |
% 233.37/32.40 | | COMBINE_EQS: (811), (846) imply:
% 233.37/32.40 | | (847) all_344_0 = all_186_0
% 233.37/32.40 | |
% 233.37/32.40 | | SIMP: (847) implies:
% 233.37/32.40 | | (848) all_344_0 = all_186_0
% 233.37/32.40 | |
% 233.37/32.40 | | COMBINE_EQS: (808), (809) imply:
% 233.37/32.40 | | (849) all_332_0 = all_94_0
% 233.37/32.40 | |
% 233.37/32.40 | | SIMP: (849) implies:
% 233.37/32.40 | | (850) all_332_0 = all_94_0
% 233.37/32.40 | |
% 233.37/32.40 | | REDUCE: (797), (828) imply:
% 233.37/32.40 | | (851) multiplication(one, all_20_6) = all_20_6
% 233.37/32.40 | |
% 233.37/32.40 | | REDUCE: (760), (834) imply:
% 233.37/32.40 | | (852) addition(all_110_0, all_94_0) = all_20_0
% 233.37/32.40 | |
% 233.37/32.40 | | REDUCE: (774), (830) imply:
% 233.37/32.41 | | (853) addition(all_94_0, all_186_0) = one
% 233.37/32.41 | |
% 233.37/32.41 | | REDUCE: (793), (820), (826) imply:
% 233.37/32.41 | | (854) addition(all_20_6, all_414_0) = all_66_0
% 233.37/32.41 | |
% 233.37/32.41 | | REDUCE: (785), (819), (829) imply:
% 233.37/32.41 | | (855) addition(all_20_10, all_414_0) = one
% 233.37/32.41 | |
% 233.37/32.41 | | REDUCE: (784), (829) imply:
% 233.37/32.41 | | (856) $i(all_414_0)
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (9) with all_322_0, one, all_186_0, all_94_0,
% 233.37/32.41 | | simplifying with (721), (853) gives:
% 233.37/32.41 | | (857) all_322_0 = one
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (additive_commutativity) with all_20_11,
% 233.37/32.41 | | all_20_6, all_338_0, simplifying with (15), (19), (729) gives:
% 233.37/32.41 | | (858) addition(all_20_6, all_20_11) = all_338_0 & $i(all_338_0)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (858) implies:
% 233.37/32.41 | | (859) $i(all_338_0)
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (additive_associativity) with all_20_6,
% 233.37/32.41 | | all_414_0, all_20_10, one, all_20_0, simplifying with (16),
% 233.37/32.41 | | (19), (653), (855), (856) gives:
% 233.37/32.41 | | (860) ? [v0: $i] : (addition(all_414_0, all_20_6) = v0 &
% 233.37/32.41 | | addition(all_20_10, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (additive_commutativity) with all_20_9, all_20_6,
% 233.37/32.41 | | all_326_0, simplifying with (17), (19), (724) gives:
% 233.37/32.41 | | (861) addition(all_20_6, all_20_9) = all_326_0 & $i(all_326_0)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (861) implies:
% 233.37/32.41 | | (862) $i(all_326_0)
% 233.37/32.41 | | (863) addition(all_20_6, all_20_9) = all_326_0
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (additive_commutativity) with all_20_9,
% 233.37/32.41 | | all_338_0, all_20_0, simplifying with (17), (730), (859) gives:
% 233.37/32.41 | | (864) addition(all_338_0, all_20_9) = all_20_0 & $i(all_20_0)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (864) implies:
% 233.37/32.41 | | (865) addition(all_338_0, all_20_9) = all_20_0
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (additive_associativity) with all_326_0,
% 233.37/32.41 | | all_20_3, all_20_6, all_20_11, all_20_0, simplifying with (19),
% 233.37/32.41 | | (21), (723), (801), (862) gives:
% 233.37/32.41 | | (866) ? [v0: $i] : (addition(all_20_3, all_326_0) = v0 &
% 233.37/32.41 | | addition(all_20_6, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (additive_commutativity) with all_20_6,
% 233.37/32.41 | | all_414_0, all_66_0, simplifying with (19), (854), (856) gives:
% 233.37/32.41 | | (867) addition(all_414_0, all_20_6) = all_66_0 & $i(all_66_0)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (867) implies:
% 233.37/32.41 | | (868) addition(all_414_0, all_20_6) = all_66_0
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (additive_associativity) with all_20_9, all_20_6,
% 233.37/32.41 | | all_20_3, all_20_11, one, simplifying with (17), (19), (21),
% 233.37/32.41 | | (292), (800) gives:
% 233.37/32.41 | | (869) ? [v0: $i] : (addition(all_20_3, v0) = one & addition(all_20_6,
% 233.37/32.41 | | all_20_9) = v0 & $i(v0) & $i(one))
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (additive_associativity) with all_20_6, all_20_6,
% 233.37/32.41 | | all_20_3, all_20_11, all_338_0, simplifying with (19), (21),
% 233.37/32.41 | | (729), (800) gives:
% 233.37/32.41 | | (870) ? [v0: $i] : (addition(all_20_3, v0) = all_338_0 &
% 233.37/32.41 | | addition(all_20_6, all_20_6) = v0 & $i(v0) & $i(all_338_0))
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (additive_commutativity) with all_94_0,
% 233.37/32.41 | | all_186_0, one, simplifying with (332), (637), (853) gives:
% 233.37/32.41 | | (871) addition(all_186_0, all_94_0) = one & $i(one)
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (additive_associativity) with all_20_3,
% 233.37/32.41 | | all_20_10, all_186_0, all_100_0, one, simplifying with (16),
% 233.37/32.41 | | (21), (637), (667), (682) gives:
% 233.37/32.41 | | (872) ? [v0: $i] : (addition(all_186_0, v0) = one & addition(all_20_10,
% 233.37/32.41 | | all_20_3) = v0 & $i(v0) & $i(one))
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (1) with one, all_316_0, simplifying with (681),
% 233.37/32.41 | | (718) gives:
% 233.37/32.41 | | (873) all_316_0 = one
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (multiplicative_associativity) with one,
% 233.37/32.41 | | all_20_11, all_20_12, all_20_11, all_20_10, simplifying with
% 233.37/32.41 | | (14), (15), (28), (681), (799) gives:
% 233.37/32.41 | | (874) ? [v0: $i] : (multiplication(all_20_11, all_20_12) = v0 &
% 233.37/32.41 | | multiplication(one, v0) = all_20_10 & $i(v0) & $i(all_20_10))
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (2) with all_20_9, all_386_0, simplifying with
% 233.37/32.41 | | (17), (747) gives:
% 233.37/32.41 | | (875) all_386_0 = all_20_9
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (right_distributivity) with one, all_20_11,
% 233.37/32.41 | | all_20_6, all_20_11, all_20_6, all_338_0, simplifying with
% 233.37/32.41 | | (15), (19), (681), (729), (799), (851) gives:
% 233.37/32.41 | | (876) ? [v0: $i] : (multiplication(one, v0) = all_338_0 &
% 233.37/32.41 | | addition(all_20_11, all_20_6) = v0 & $i(v0) & $i(all_338_0))
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.37/32.41 | | all_316_0, all_20_9, all_20_4, all_20_1, simplifying with (17),
% 233.37/32.41 | | (20), (31), (717), (719) gives:
% 233.37/32.41 | | (877) ? [v0: $i] : (multiplication(all_316_0, all_20_9) = v0 &
% 233.37/32.41 | | multiplication(all_20_4, v0) = all_20_1 & $i(v0) & $i(all_20_1))
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.37/32.41 | | all_316_0, all_20_11, all_20_4, all_20_3, simplifying with
% 233.37/32.41 | | (15), (20), (30), (717), (719) gives:
% 233.37/32.41 | | (878) ? [v0: $i] : (multiplication(all_316_0, all_20_11) = v0 &
% 233.37/32.41 | | multiplication(all_20_4, v0) = all_20_3 & $i(v0) & $i(all_20_3))
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.37/32.41 | | one, all_316_0, all_20_4, all_20_4, simplifying with (20),
% 233.37/32.41 | | (544), (681), (717), (719) gives:
% 233.37/32.41 | | (879) ? [v0: $i] : (multiplication(all_20_4, v0) = all_20_4 &
% 233.37/32.41 | | multiplication(one, all_316_0) = v0 & $i(v0))
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.37/32.41 | | all_316_0, one, all_20_4, all_20_4, simplifying with (20),
% 233.37/32.41 | | (544), (681), (717), (719) gives:
% 233.37/32.41 | | (880) ? [v0: $i] : (multiplication(all_316_0, one) = v0 &
% 233.37/32.41 | | multiplication(all_20_4, v0) = all_20_4 & $i(v0))
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.37/32.41 | | all_316_0, all_316_0, all_20_4, all_20_4, simplifying with
% 233.37/32.41 | | (20), (717), (719) gives:
% 233.37/32.41 | | (881) ? [v0: $i] : (multiplication(all_316_0, all_316_0) = v0 &
% 233.37/32.41 | | multiplication(all_20_4, v0) = all_20_4 & $i(v0))
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.37/32.41 | | one, all_386_0, all_20_4, all_20_1, simplifying with (20),
% 233.37/32.41 | | (544), (681), (746), (748) gives:
% 233.37/32.41 | | (882) ? [v0: $i] : (multiplication(all_20_4, v0) = all_20_1 &
% 233.37/32.41 | | multiplication(one, all_386_0) = v0 & $i(v0) & $i(all_20_1))
% 233.37/32.41 | |
% 233.37/32.41 | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.37/32.41 | | all_316_0, all_386_0, all_20_4, all_20_1, simplifying with
% 233.37/32.41 | | (20), (717), (719), (746), (748) gives:
% 233.37/32.41 | | (883) ? [v0: $i] : (multiplication(all_316_0, all_386_0) = v0 &
% 233.37/32.41 | | multiplication(all_20_4, v0) = all_20_1 & $i(v0) & $i(all_20_1))
% 233.37/32.41 | |
% 233.37/32.41 | | DELTA: instantiating (879) with fresh symbol all_516_0 gives:
% 233.37/32.41 | | (884) multiplication(all_20_4, all_516_0) = all_20_4 &
% 233.37/32.41 | | multiplication(one, all_316_0) = all_516_0 & $i(all_516_0)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (884) implies:
% 233.37/32.41 | | (885) multiplication(one, all_316_0) = all_516_0
% 233.37/32.41 | |
% 233.37/32.41 | | DELTA: instantiating (881) with fresh symbol all_522_0 gives:
% 233.37/32.41 | | (886) multiplication(all_316_0, all_316_0) = all_522_0 &
% 233.37/32.41 | | multiplication(all_20_4, all_522_0) = all_20_4 & $i(all_522_0)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (886) implies:
% 233.37/32.41 | | (887) multiplication(all_316_0, all_316_0) = all_522_0
% 233.37/32.41 | |
% 233.37/32.41 | | DELTA: instantiating (880) with fresh symbol all_524_0 gives:
% 233.37/32.41 | | (888) multiplication(all_316_0, one) = all_524_0 &
% 233.37/32.41 | | multiplication(all_20_4, all_524_0) = all_20_4 & $i(all_524_0)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (888) implies:
% 233.37/32.41 | | (889) multiplication(all_316_0, one) = all_524_0
% 233.37/32.41 | |
% 233.37/32.41 | | DELTA: instantiating (860) with fresh symbol all_540_0 gives:
% 233.37/32.41 | | (890) addition(all_414_0, all_20_6) = all_540_0 & addition(all_20_10,
% 233.37/32.41 | | all_540_0) = all_20_0 & $i(all_540_0) & $i(all_20_0)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (890) implies:
% 233.37/32.41 | | (891) $i(all_540_0)
% 233.37/32.41 | | (892) addition(all_414_0, all_20_6) = all_540_0
% 233.37/32.41 | |
% 233.37/32.41 | | DELTA: instantiating (869) with fresh symbol all_542_0 gives:
% 233.37/32.41 | | (893) addition(all_20_3, all_542_0) = one & addition(all_20_6, all_20_9)
% 233.37/32.41 | | = all_542_0 & $i(all_542_0) & $i(one)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (893) implies:
% 233.37/32.41 | | (894) $i(all_542_0)
% 233.37/32.41 | | (895) addition(all_20_6, all_20_9) = all_542_0
% 233.37/32.41 | | (896) addition(all_20_3, all_542_0) = one
% 233.37/32.41 | |
% 233.37/32.41 | | DELTA: instantiating (883) with fresh symbol all_548_0 gives:
% 233.37/32.41 | | (897) multiplication(all_316_0, all_386_0) = all_548_0 &
% 233.37/32.41 | | multiplication(all_20_4, all_548_0) = all_20_1 & $i(all_548_0) &
% 233.37/32.41 | | $i(all_20_1)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (897) implies:
% 233.37/32.41 | | (898) $i(all_548_0)
% 233.37/32.41 | | (899) multiplication(all_316_0, all_386_0) = all_548_0
% 233.37/32.41 | |
% 233.37/32.41 | | DELTA: instantiating (866) with fresh symbol all_550_0 gives:
% 233.37/32.41 | | (900) addition(all_20_3, all_326_0) = all_550_0 & addition(all_20_6,
% 233.37/32.41 | | all_550_0) = all_20_0 & $i(all_550_0) & $i(all_20_0)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (900) implies:
% 233.37/32.41 | | (901) $i(all_550_0)
% 233.37/32.41 | | (902) addition(all_20_6, all_550_0) = all_20_0
% 233.37/32.41 | | (903) addition(all_20_3, all_326_0) = all_550_0
% 233.37/32.41 | |
% 233.37/32.41 | | DELTA: instantiating (878) with fresh symbol all_552_0 gives:
% 233.37/32.41 | | (904) multiplication(all_316_0, all_20_11) = all_552_0 &
% 233.37/32.41 | | multiplication(all_20_4, all_552_0) = all_20_3 & $i(all_552_0) &
% 233.37/32.41 | | $i(all_20_3)
% 233.37/32.41 | |
% 233.37/32.41 | | DELTA: instantiating (877) with fresh symbol all_558_0 gives:
% 233.37/32.41 | | (905) multiplication(all_316_0, all_20_9) = all_558_0 &
% 233.37/32.41 | | multiplication(all_20_4, all_558_0) = all_20_1 & $i(all_558_0) &
% 233.37/32.41 | | $i(all_20_1)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (905) implies:
% 233.37/32.41 | | (906) multiplication(all_316_0, all_20_9) = all_558_0
% 233.37/32.41 | |
% 233.37/32.41 | | DELTA: instantiating (876) with fresh symbol all_560_0 gives:
% 233.37/32.41 | | (907) multiplication(one, all_560_0) = all_338_0 & addition(all_20_11,
% 233.37/32.41 | | all_20_6) = all_560_0 & $i(all_560_0) & $i(all_338_0)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (907) implies:
% 233.37/32.41 | | (908) addition(all_20_11, all_20_6) = all_560_0
% 233.37/32.41 | | (909) multiplication(one, all_560_0) = all_338_0
% 233.37/32.41 | |
% 233.37/32.41 | | DELTA: instantiating (874) with fresh symbol all_564_0 gives:
% 233.37/32.41 | | (910) multiplication(all_20_11, all_20_12) = all_564_0 &
% 233.37/32.41 | | multiplication(one, all_564_0) = all_20_10 & $i(all_564_0) &
% 233.37/32.41 | | $i(all_20_10)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (910) implies:
% 233.37/32.41 | | (911) $i(all_564_0)
% 233.37/32.41 | | (912) multiplication(all_20_11, all_20_12) = all_564_0
% 233.37/32.41 | |
% 233.37/32.41 | | DELTA: instantiating (870) with fresh symbol all_568_0 gives:
% 233.37/32.41 | | (913) addition(all_20_3, all_568_0) = all_338_0 & addition(all_20_6,
% 233.37/32.41 | | all_20_6) = all_568_0 & $i(all_568_0) & $i(all_338_0)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (913) implies:
% 233.37/32.41 | | (914) $i(all_568_0)
% 233.37/32.41 | | (915) addition(all_20_6, all_20_6) = all_568_0
% 233.37/32.41 | | (916) addition(all_20_3, all_568_0) = all_338_0
% 233.37/32.41 | |
% 233.37/32.41 | | DELTA: instantiating (882) with fresh symbol all_572_0 gives:
% 233.37/32.41 | | (917) multiplication(all_20_4, all_572_0) = all_20_1 &
% 233.37/32.41 | | multiplication(one, all_386_0) = all_572_0 & $i(all_572_0) &
% 233.37/32.41 | | $i(all_20_1)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (917) implies:
% 233.37/32.41 | | (918) multiplication(one, all_386_0) = all_572_0
% 233.37/32.41 | |
% 233.37/32.41 | | DELTA: instantiating (872) with fresh symbol all_578_0 gives:
% 233.37/32.41 | | (919) addition(all_186_0, all_578_0) = one & addition(all_20_10,
% 233.37/32.41 | | all_20_3) = all_578_0 & $i(all_578_0) & $i(one)
% 233.37/32.41 | |
% 233.37/32.41 | | ALPHA: (919) implies:
% 233.37/32.41 | | (920) $i(all_578_0)
% 233.37/32.41 | | (921) addition(all_20_10, all_20_3) = all_578_0
% 233.37/32.41 | |
% 233.37/32.41 | | REDUCE: (873), (875), (899) imply:
% 233.37/32.41 | | (922) multiplication(one, all_20_9) = all_548_0
% 233.37/32.41 | |
% 233.37/32.41 | | REDUCE: (873), (887) imply:
% 233.37/32.41 | | (923) multiplication(one, one) = all_522_0
% 233.37/32.41 | |
% 233.37/32.41 | | REDUCE: (873), (906) imply:
% 233.37/32.41 | | (924) multiplication(one, all_20_9) = all_558_0
% 233.67/32.41 | |
% 233.67/32.41 | | REDUCE: (873), (889) imply:
% 233.67/32.41 | | (925) multiplication(one, one) = all_524_0
% 233.67/32.41 | |
% 233.67/32.41 | | REDUCE: (875), (918) imply:
% 233.67/32.41 | | (926) multiplication(one, all_20_9) = all_572_0
% 233.67/32.41 | |
% 233.67/32.41 | | REDUCE: (873), (885) imply:
% 233.67/32.41 | | (927) multiplication(one, one) = all_516_0
% 233.67/32.41 | |
% 233.67/32.41 | | REDUCE: (747), (875) imply:
% 233.67/32.41 | | (928) multiplication(one, all_20_9) = all_20_9
% 233.67/32.41 | |
% 233.67/32.41 | | REDUCE: (718), (873) imply:
% 233.67/32.41 | | (929) multiplication(one, one) = one
% 233.67/32.41 | |
% 233.67/32.41 | | GROUND_INST: instantiating (9) with all_338_0, all_560_0, all_20_6,
% 233.67/32.41 | | all_20_11, simplifying with (729), (908) gives:
% 233.67/32.41 | | (930) all_560_0 = all_338_0
% 233.67/32.41 | |
% 233.67/32.41 | | GROUND_INST: instantiating (9) with all_94_0, all_578_0, all_20_3,
% 233.67/32.41 | | all_20_10, simplifying with (215), (921) gives:
% 233.67/32.41 | | (931) all_578_0 = all_94_0
% 233.67/32.41 | |
% 233.67/32.41 | | GROUND_INST: instantiating (9) with all_326_0, all_542_0, all_20_9,
% 233.67/32.41 | | all_20_6, simplifying with (863), (895) gives:
% 233.67/32.42 | | (932) all_542_0 = all_326_0
% 233.67/32.42 | |
% 233.67/32.42 | | GROUND_INST: instantiating (9) with all_66_0, all_540_0, all_20_6,
% 233.67/32.42 | | all_414_0, simplifying with (868), (892) gives:
% 233.67/32.42 | | (933) all_540_0 = all_66_0
% 233.67/32.42 | |
% 233.67/32.42 | | GROUND_INST: instantiating (10) with all_522_0, all_524_0, one, one,
% 233.67/32.42 | | simplifying with (923), (925) gives:
% 233.67/32.42 | | (934) all_524_0 = all_522_0
% 233.67/32.42 | |
% 233.67/32.42 | | GROUND_INST: instantiating (10) with all_516_0, all_524_0, one, one,
% 233.67/32.42 | | simplifying with (925), (927) gives:
% 233.67/32.42 | | (935) all_524_0 = all_516_0
% 233.67/32.42 | |
% 233.67/32.42 | | GROUND_INST: instantiating (10) with one, all_524_0, one, one, simplifying
% 233.67/32.42 | | with (925), (929) gives:
% 233.67/32.42 | | (936) all_524_0 = one
% 233.67/32.42 | |
% 233.67/32.42 | | GROUND_INST: instantiating (10) with all_20_9, all_558_0, all_20_9, one,
% 233.67/32.42 | | simplifying with (924), (928) gives:
% 233.67/32.42 | | (937) all_558_0 = all_20_9
% 233.67/32.42 | |
% 233.67/32.42 | | GROUND_INST: instantiating (10) with all_558_0, all_572_0, all_20_9, one,
% 233.67/32.42 | | simplifying with (924), (926) gives:
% 233.67/32.42 | | (938) all_572_0 = all_558_0
% 233.67/32.42 | |
% 233.67/32.42 | | GROUND_INST: instantiating (10) with all_548_0, all_572_0, all_20_9, one,
% 233.67/32.42 | | simplifying with (922), (926) gives:
% 233.67/32.42 | | (939) all_572_0 = all_548_0
% 233.67/32.42 | |
% 233.67/32.42 | | GROUND_INST: instantiating (10) with all_20_10, all_564_0, all_20_12,
% 233.67/32.42 | | all_20_11, simplifying with (28), (912) gives:
% 233.67/32.42 | | (940) all_564_0 = all_20_10
% 233.67/32.42 | |
% 233.67/32.42 | | COMBINE_EQS: (938), (939) imply:
% 233.67/32.42 | | (941) all_558_0 = all_548_0
% 233.67/32.42 | |
% 233.67/32.42 | | SIMP: (941) implies:
% 233.67/32.42 | | (942) all_558_0 = all_548_0
% 233.67/32.42 | |
% 233.67/32.42 | | COMBINE_EQS: (937), (942) imply:
% 233.67/32.42 | | (943) all_548_0 = all_20_9
% 233.67/32.42 | |
% 233.67/32.42 | | COMBINE_EQS: (934), (936) imply:
% 233.67/32.42 | | (944) all_522_0 = one
% 233.67/32.42 | |
% 233.67/32.42 | | COMBINE_EQS: (934), (935) imply:
% 233.67/32.42 | | (945) all_522_0 = all_516_0
% 233.67/32.42 | |
% 233.67/32.42 | | COMBINE_EQS: (944), (945) imply:
% 233.67/32.42 | | (946) all_516_0 = one
% 233.67/32.42 | |
% 233.67/32.42 | | SIMP: (946) implies:
% 233.67/32.42 | | (947) all_516_0 = one
% 233.67/32.42 | |
% 233.67/32.42 | | REDUCE: (909), (930) imply:
% 233.67/32.42 | | (948) multiplication(one, all_338_0) = all_338_0
% 233.67/32.42 | |
% 233.67/32.42 | | REDUCE: (896), (932) imply:
% 233.67/32.42 | | (949) addition(all_20_3, all_326_0) = one
% 233.67/32.42 | |
% 233.67/32.42 | | GROUND_INST: instantiating (9) with all_550_0, one, all_326_0, all_20_3,
% 233.67/32.42 | | simplifying with (903), (949) gives:
% 233.67/32.42 | | (950) all_550_0 = one
% 233.67/32.42 | |
% 233.67/32.42 | | REDUCE: (902), (950) imply:
% 233.67/32.42 | | (951) addition(all_20_6, one) = all_20_0
% 233.67/32.42 | |
% 233.67/32.42 | | BETA: splitting (689) gives:
% 233.67/32.42 | |
% 233.67/32.42 | | Case 1:
% 233.67/32.42 | | |
% 233.67/32.42 | | | (952) complement(all_20_1, all_58_0)
% 233.67/32.42 | | |
% 233.67/32.42 | | | BETA: splitting (686) gives:
% 233.67/32.42 | | |
% 233.67/32.42 | | | Case 1:
% 233.67/32.42 | | | |
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | GROUND_INST: instantiating (left_distributivity) with one, one,
% 233.67/32.42 | | | | all_20_6, all_20_6, all_20_6, all_568_0, simplifying with
% 233.67/32.42 | | | | (19), (681), (851), (915) gives:
% 233.67/32.42 | | | | (953) ? [v0: $i] : (multiplication(v0, all_20_6) = all_568_0 &
% 233.67/32.42 | | | | addition(one, one) = v0 & $i(v0) & $i(all_568_0))
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | GROUND_INST: instantiating (additive_idempotence) with all_20_6,
% 233.67/32.42 | | | | all_568_0, simplifying with (19), (915) gives:
% 233.67/32.42 | | | | (954) all_568_0 = all_20_6
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | GROUND_INST: instantiating (additive_commutativity) with all_20_3,
% 233.67/32.42 | | | | all_326_0, one, simplifying with (21), (862), (949) gives:
% 233.67/32.42 | | | | (955) addition(all_326_0, all_20_3) = one & $i(one)
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | GROUND_INST: instantiating (additive_associativity) with all_20_9,
% 233.67/32.42 | | | | all_568_0, all_20_3, all_338_0, all_20_0, simplifying with
% 233.67/32.42 | | | | (17), (21), (865), (914), (916) gives:
% 233.67/32.42 | | | | (956) ? [v0: $i] : (addition(all_568_0, all_20_9) = v0 &
% 233.67/32.42 | | | | addition(all_20_3, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | GROUND_INST: instantiating (right_distributivity) with one, all_20_6,
% 233.67/32.42 | | | | one, all_20_6, one, all_20_0, simplifying with (19), (681),
% 233.67/32.42 | | | | (851), (929), (951) gives:
% 233.67/32.42 | | | | (957) ? [v0: $i] : (multiplication(one, v0) = all_20_0 &
% 233.67/32.42 | | | | addition(all_20_6, one) = v0 & $i(v0) & $i(all_20_0))
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | GROUND_INST: instantiating (right_distributivity) with one, all_20_6,
% 233.67/32.42 | | | | all_20_9, all_20_6, all_20_9, all_326_0, simplifying with
% 233.67/32.42 | | | | (17), (19), (681), (851), (863), (928) gives:
% 233.67/32.42 | | | | (958) ? [v0: $i] : (multiplication(one, v0) = all_326_0 &
% 233.67/32.42 | | | | addition(all_20_6, all_20_9) = v0 & $i(v0) & $i(all_326_0))
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | DELTA: instantiating (953) with fresh symbol all_693_0 gives:
% 233.67/32.42 | | | | (959) multiplication(all_693_0, all_20_6) = all_568_0 & addition(one,
% 233.67/32.42 | | | | one) = all_693_0 & $i(all_693_0) & $i(all_568_0)
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | ALPHA: (959) implies:
% 233.67/32.42 | | | | (960) addition(one, one) = all_693_0
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | DELTA: instantiating (957) with fresh symbol all_707_0 gives:
% 233.67/32.42 | | | | (961) multiplication(one, all_707_0) = all_20_0 & addition(all_20_6,
% 233.67/32.42 | | | | one) = all_707_0 & $i(all_707_0) & $i(all_20_0)
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | ALPHA: (961) implies:
% 233.67/32.42 | | | | (962) addition(all_20_6, one) = all_707_0
% 233.67/32.42 | | | | (963) $i(all_707_0)
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | DELTA: instantiating (956) with fresh symbol all_709_0 gives:
% 233.67/32.42 | | | | (964) addition(all_568_0, all_20_9) = all_709_0 & addition(all_20_3,
% 233.67/32.42 | | | | all_709_0) = all_20_0 & $i(all_709_0) & $i(all_20_0)
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | ALPHA: (964) implies:
% 233.67/32.42 | | | | (965) addition(all_568_0, all_20_9) = all_709_0
% 233.67/32.42 | | | | (966) addition(all_20_3, all_709_0) = all_20_0
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | DELTA: instantiating (958) with fresh symbol all_727_0 gives:
% 233.67/32.42 | | | | (967) multiplication(one, all_727_0) = all_326_0 & addition(all_20_6,
% 233.67/32.42 | | | | all_20_9) = all_727_0 & $i(all_727_0) & $i(all_326_0)
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | ALPHA: (967) implies:
% 233.67/32.42 | | | | (968) addition(all_20_6, all_20_9) = all_727_0
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | REDUCE: (954), (965) imply:
% 233.67/32.42 | | | | (969) addition(all_20_6, all_20_9) = all_709_0
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | GROUND_INST: instantiating (9) with all_20_0, all_707_0, one, all_20_6,
% 233.67/32.42 | | | | simplifying with (951), (962) gives:
% 233.67/32.42 | | | | (970) all_707_0 = all_20_0
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | GROUND_INST: instantiating (9) with all_326_0, all_727_0, all_20_9,
% 233.67/32.42 | | | | all_20_6, simplifying with (863), (968) gives:
% 233.67/32.42 | | | | (971) all_727_0 = all_326_0
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | GROUND_INST: instantiating (9) with all_709_0, all_727_0, all_20_9,
% 233.67/32.42 | | | | all_20_6, simplifying with (968), (969) gives:
% 233.67/32.42 | | | | (972) all_727_0 = all_709_0
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | COMBINE_EQS: (971), (972) imply:
% 233.67/32.42 | | | | (973) all_709_0 = all_326_0
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | REDUCE: (966), (973) imply:
% 233.67/32.42 | | | | (974) addition(all_20_3, all_326_0) = all_20_0
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | REDUCE: (963), (970) imply:
% 233.67/32.42 | | | | (975) $i(all_20_0)
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | GROUND_INST: instantiating (9) with one, all_20_0, all_326_0, all_20_3,
% 233.67/32.42 | | | | simplifying with (949), (974) gives:
% 233.67/32.42 | | | | (976) all_20_0 = one
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | REDUCE: (852), (976) imply:
% 233.67/32.42 | | | | (977) addition(all_110_0, all_94_0) = one
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | REDUCE: (663), (976) imply:
% 233.67/32.42 | | | | (978) ~ leq(one, one)
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | GROUND_INST: instantiating (additive_idempotence) with one, all_693_0,
% 233.67/32.42 | | | | simplifying with (681), (960) gives:
% 233.67/32.42 | | | | (979) all_693_0 = one
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | GROUND_INST: instantiating (additive_associativity) with one, all_94_0,
% 233.67/32.42 | | | | all_110_0, one, all_693_0, simplifying with (236), (332),
% 233.67/32.42 | | | | (681), (960), (977) gives:
% 233.67/32.42 | | | | (980) ? [v0: $i] : (addition(all_110_0, v0) = all_693_0 &
% 233.67/32.42 | | | | addition(all_94_0, one) = v0 & $i(v0) & $i(all_693_0))
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | DELTA: instantiating (980) with fresh symbol all_1292_0 gives:
% 233.67/32.42 | | | | (981) addition(all_110_0, all_1292_0) = all_693_0 &
% 233.67/32.42 | | | | addition(all_94_0, one) = all_1292_0 & $i(all_1292_0) &
% 233.67/32.42 | | | | $i(all_693_0)
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | ALPHA: (981) implies:
% 233.67/32.42 | | | | (982) $i(all_693_0)
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | REDUCE: (960), (979) imply:
% 233.67/32.42 | | | | (983) addition(one, one) = one
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | GROUND_INST: instantiating (3) with one, one, simplifying with (681),
% 233.67/32.42 | | | | (978), (983) gives:
% 233.67/32.42 | | | | (984) $false
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | CLOSE: (984) is inconsistent.
% 233.67/32.42 | | | |
% 233.67/32.42 | | | Case 2:
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | (985) ? [v0: $i] : ? [v1: $i] : (( ~ (v1 = zero) &
% 233.67/32.42 | | | | multiplication(all_58_0, all_20_1) = v1 & $i(v1)) | ( ~ (v0
% 233.67/32.42 | | | | = zero) & multiplication(all_20_1, all_58_0) = v0 &
% 233.67/32.42 | | | | $i(v0)))
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | DELTA: instantiating (985) with fresh symbols all_653_0, all_653_1
% 233.67/32.42 | | | | gives:
% 233.67/32.42 | | | | (986) ( ~ (all_653_0 = zero) & multiplication(all_58_0, all_20_1) =
% 233.67/32.42 | | | | all_653_0 & $i(all_653_0)) | ( ~ (all_653_1 = zero) &
% 233.67/32.42 | | | | multiplication(all_20_1, all_58_0) = all_653_1 &
% 233.67/32.42 | | | | $i(all_653_1))
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | GROUND_INST: instantiating (5) with all_58_0, all_20_1, one, simplifying
% 233.67/32.42 | | | | with (22), (161), (656), (952) gives:
% 233.67/32.42 | | | | (987) multiplication(all_58_0, all_20_1) = zero &
% 233.67/32.42 | | | | multiplication(all_20_1, all_58_0) = zero
% 233.67/32.42 | | | |
% 233.67/32.42 | | | | ALPHA: (987) implies:
% 233.67/32.43 | | | | (988) multiplication(all_20_1, all_58_0) = zero
% 233.67/32.43 | | | | (989) multiplication(all_58_0, all_20_1) = zero
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | BETA: splitting (986) gives:
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | Case 1:
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | (990) ~ (all_653_0 = zero) & multiplication(all_58_0, all_20_1) =
% 233.67/32.43 | | | | | all_653_0 & $i(all_653_0)
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | ALPHA: (990) implies:
% 233.67/32.43 | | | | | (991) ~ (all_653_0 = zero)
% 233.67/32.43 | | | | | (992) multiplication(all_58_0, all_20_1) = all_653_0
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | GROUND_INST: instantiating (10) with zero, all_653_0, all_20_1,
% 233.67/32.43 | | | | | all_58_0, simplifying with (989), (992) gives:
% 233.67/32.43 | | | | | (993) all_653_0 = zero
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | REDUCE: (991), (993) imply:
% 233.67/32.43 | | | | | (994) $false
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | CLOSE: (994) is inconsistent.
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | Case 2:
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | (995) ~ (all_653_1 = zero) & multiplication(all_20_1, all_58_0) =
% 233.67/32.43 | | | | | all_653_1 & $i(all_653_1)
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | ALPHA: (995) implies:
% 233.67/32.43 | | | | | (996) ~ (all_653_1 = zero)
% 233.67/32.43 | | | | | (997) multiplication(all_20_1, all_58_0) = all_653_1
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | GROUND_INST: instantiating (10) with zero, all_653_1, all_58_0,
% 233.67/32.43 | | | | | all_20_1, simplifying with (988), (997) gives:
% 233.67/32.43 | | | | | (998) all_653_1 = zero
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | REDUCE: (996), (998) imply:
% 233.67/32.43 | | | | | (999) $false
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | CLOSE: (999) is inconsistent.
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | End of split
% 233.67/32.43 | | | |
% 233.67/32.43 | | | End of split
% 233.67/32.43 | | |
% 233.67/32.43 | | Case 2:
% 233.67/32.43 | | |
% 233.67/32.43 | | | (1000) ? [v0: $i] : ? [v1: $i] : (( ~ (v1 = zero) &
% 233.67/32.43 | | | multiplication(all_20_1, all_58_0) = v1 & $i(v1)) | ( ~ (v0
% 233.67/32.43 | | | = zero) & multiplication(all_58_0, all_20_1) = v0 &
% 233.67/32.43 | | | $i(v0)))
% 233.67/32.43 | | |
% 233.67/32.43 | | | DELTA: instantiating (1000) with fresh symbols all_598_0, all_598_1 gives:
% 233.67/32.43 | | | (1001) ( ~ (all_598_0 = zero) & multiplication(all_20_1, all_58_0) =
% 233.67/32.43 | | | all_598_0 & $i(all_598_0)) | ( ~ (all_598_1 = zero) &
% 233.67/32.43 | | | multiplication(all_58_0, all_20_1) = all_598_1 &
% 233.67/32.43 | | | $i(all_598_1))
% 233.67/32.43 | | |
% 233.67/32.43 | | | BETA: splitting (686) gives:
% 233.67/32.43 | | |
% 233.67/32.43 | | | Case 1:
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | (1002) complement(all_58_0, all_20_1)
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | GROUND_INST: instantiating (5) with all_20_1, all_58_0, one, simplifying
% 233.67/32.43 | | | | with (22), (161), (659), (1002) gives:
% 233.67/32.43 | | | | (1003) multiplication(all_58_0, all_20_1) = zero &
% 233.67/32.43 | | | | multiplication(all_20_1, all_58_0) = zero
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | ALPHA: (1003) implies:
% 233.67/32.43 | | | | (1004) multiplication(all_20_1, all_58_0) = zero
% 233.67/32.43 | | | | (1005) multiplication(all_58_0, all_20_1) = zero
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | BETA: splitting (1001) gives:
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | Case 1:
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | (1006) ~ (all_598_0 = zero) & multiplication(all_20_1, all_58_0) =
% 233.67/32.43 | | | | | all_598_0 & $i(all_598_0)
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | ALPHA: (1006) implies:
% 233.67/32.43 | | | | | (1007) ~ (all_598_0 = zero)
% 233.67/32.43 | | | | | (1008) multiplication(all_20_1, all_58_0) = all_598_0
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | GROUND_INST: instantiating (10) with zero, all_598_0, all_58_0,
% 233.67/32.43 | | | | | all_20_1, simplifying with (1004), (1008) gives:
% 233.67/32.43 | | | | | (1009) all_598_0 = zero
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | REDUCE: (1007), (1009) imply:
% 233.67/32.43 | | | | | (1010) $false
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | CLOSE: (1010) is inconsistent.
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | Case 2:
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | (1011) ~ (all_598_1 = zero) & multiplication(all_58_0, all_20_1) =
% 233.67/32.43 | | | | | all_598_1 & $i(all_598_1)
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | ALPHA: (1011) implies:
% 233.67/32.43 | | | | | (1012) ~ (all_598_1 = zero)
% 233.67/32.43 | | | | | (1013) multiplication(all_58_0, all_20_1) = all_598_1
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | GROUND_INST: instantiating (10) with zero, all_598_1, all_20_1,
% 233.67/32.43 | | | | | all_58_0, simplifying with (1005), (1013) gives:
% 233.67/32.43 | | | | | (1014) all_598_1 = zero
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | REDUCE: (1012), (1014) imply:
% 233.67/32.43 | | | | | (1015) $false
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | | CLOSE: (1015) is inconsistent.
% 233.67/32.43 | | | | |
% 233.67/32.43 | | | | End of split
% 233.67/32.43 | | | |
% 233.67/32.43 | | | Case 2:
% 233.67/32.43 | | | |
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | GROUND_INST: instantiating (left_distributivity) with one, one,
% 233.67/32.43 | | | | all_20_6, all_20_6, all_20_6, all_568_0, simplifying with
% 233.67/32.43 | | | | (19), (681), (851), (915) gives:
% 233.67/32.43 | | | | (1016) ? [v0: $i] : (multiplication(v0, all_20_6) = all_568_0 &
% 233.67/32.43 | | | | addition(one, one) = v0 & $i(v0) & $i(all_568_0))
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | GROUND_INST: instantiating (additive_idempotence) with all_20_6,
% 233.67/32.43 | | | | all_568_0, simplifying with (19), (915) gives:
% 233.67/32.43 | | | | (1017) all_568_0 = all_20_6
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | GROUND_INST: instantiating (additive_commutativity) with all_20_3,
% 233.67/32.43 | | | | all_326_0, one, simplifying with (21), (862), (949) gives:
% 233.67/32.43 | | | | (1018) addition(all_326_0, all_20_3) = one & $i(one)
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | GROUND_INST: instantiating (additive_commutativity) with all_20_3,
% 233.67/32.43 | | | | all_568_0, all_338_0, simplifying with (21), (914), (916)
% 233.67/32.43 | | | | gives:
% 233.67/32.43 | | | | (1019) addition(all_568_0, all_20_3) = all_338_0 & $i(all_338_0)
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | GROUND_INST: instantiating (additive_associativity) with all_20_9,
% 233.67/32.43 | | | | all_568_0, all_20_3, all_338_0, all_20_0, simplifying with
% 233.67/32.43 | | | | (17), (21), (865), (914), (916) gives:
% 233.67/32.43 | | | | (1020) ? [v0: $i] : (addition(all_568_0, all_20_9) = v0 &
% 233.67/32.43 | | | | addition(all_20_3, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | GROUND_INST: instantiating (right_distributivity) with one, all_20_6,
% 233.67/32.43 | | | | all_20_9, all_20_6, all_20_9, all_326_0, simplifying with
% 233.67/32.43 | | | | (17), (19), (681), (851), (863), (928) gives:
% 233.67/32.43 | | | | (1021) ? [v0: $i] : (multiplication(one, v0) = all_326_0 &
% 233.67/32.43 | | | | addition(all_20_6, all_20_9) = v0 & $i(v0) & $i(all_326_0))
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | GROUND_INST: instantiating (right_distributivity) with one, all_338_0,
% 233.67/32.43 | | | | all_20_9, all_338_0, all_20_9, all_20_0, simplifying with
% 233.67/32.43 | | | | (17), (681), (859), (865), (928), (948) gives:
% 233.67/32.43 | | | | (1022) ? [v0: $i] : (multiplication(one, v0) = all_20_0 &
% 233.67/32.43 | | | | addition(all_338_0, all_20_9) = v0 & $i(v0) & $i(all_20_0))
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | DELTA: instantiating (1022) with fresh symbol all_667_0 gives:
% 233.67/32.43 | | | | (1023) multiplication(one, all_667_0) = all_20_0 &
% 233.67/32.43 | | | | addition(all_338_0, all_20_9) = all_667_0 & $i(all_667_0) &
% 233.67/32.43 | | | | $i(all_20_0)
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | ALPHA: (1023) implies:
% 233.67/32.43 | | | | (1024) addition(all_338_0, all_20_9) = all_667_0
% 233.67/32.43 | | | | (1025) $i(all_667_0)
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | DELTA: instantiating (1021) with fresh symbol all_681_0 gives:
% 233.67/32.43 | | | | (1026) multiplication(one, all_681_0) = all_326_0 &
% 233.67/32.43 | | | | addition(all_20_6, all_20_9) = all_681_0 & $i(all_681_0) &
% 233.67/32.43 | | | | $i(all_326_0)
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | ALPHA: (1026) implies:
% 233.67/32.43 | | | | (1027) addition(all_20_6, all_20_9) = all_681_0
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | DELTA: instantiating (1020) with fresh symbol all_687_0 gives:
% 233.67/32.43 | | | | (1028) addition(all_568_0, all_20_9) = all_687_0 & addition(all_20_3,
% 233.67/32.43 | | | | all_687_0) = all_20_0 & $i(all_687_0) & $i(all_20_0)
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | ALPHA: (1028) implies:
% 233.67/32.43 | | | | (1029) addition(all_568_0, all_20_9) = all_687_0
% 233.67/32.43 | | | | (1030) addition(all_20_3, all_687_0) = all_20_0
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | DELTA: instantiating (1016) with fresh symbol all_693_0 gives:
% 233.67/32.43 | | | | (1031) multiplication(all_693_0, all_20_6) = all_568_0 &
% 233.67/32.43 | | | | addition(one, one) = all_693_0 & $i(all_693_0) & $i(all_568_0)
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | ALPHA: (1031) implies:
% 233.67/32.43 | | | | (1032) addition(one, one) = all_693_0
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | REDUCE: (1017), (1029) imply:
% 233.67/32.43 | | | | (1033) addition(all_20_6, all_20_9) = all_687_0
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | GROUND_INST: instantiating (9) with all_326_0, all_687_0, all_20_9,
% 233.67/32.43 | | | | all_20_6, simplifying with (863), (1033) gives:
% 233.67/32.43 | | | | (1034) all_687_0 = all_326_0
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | GROUND_INST: instantiating (9) with all_681_0, all_687_0, all_20_9,
% 233.67/32.43 | | | | all_20_6, simplifying with (1027), (1033) gives:
% 233.67/32.43 | | | | (1035) all_687_0 = all_681_0
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | GROUND_INST: instantiating (9) with all_20_0, all_667_0, all_20_9,
% 233.67/32.43 | | | | all_338_0, simplifying with (865), (1024) gives:
% 233.67/32.43 | | | | (1036) all_667_0 = all_20_0
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | COMBINE_EQS: (1034), (1035) imply:
% 233.67/32.43 | | | | (1037) all_681_0 = all_326_0
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | REDUCE: (1030), (1034) imply:
% 233.67/32.43 | | | | (1038) addition(all_20_3, all_326_0) = all_20_0
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | REDUCE: (1025), (1036) imply:
% 233.67/32.43 | | | | (1039) $i(all_20_0)
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | GROUND_INST: instantiating (9) with one, all_20_0, all_326_0, all_20_3,
% 233.67/32.43 | | | | simplifying with (949), (1038) gives:
% 233.67/32.43 | | | | (1040) all_20_0 = one
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | REDUCE: (147), (1040) imply:
% 233.67/32.43 | | | | (1041) addition(all_66_0, all_20_10) = one
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | REDUCE: (663), (1040) imply:
% 233.67/32.43 | | | | (1042) ~ leq(one, one)
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | GROUND_INST: instantiating (additive_idempotence) with one, all_693_0,
% 233.67/32.43 | | | | simplifying with (681), (1032) gives:
% 233.67/32.43 | | | | (1043) all_693_0 = one
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | GROUND_INST: instantiating (additive_associativity) with one, all_20_10,
% 233.67/32.43 | | | | all_66_0, one, all_693_0, simplifying with (16), (120),
% 233.67/32.43 | | | | (681), (1032), (1041) gives:
% 233.67/32.43 | | | | (1044) ? [v0: $i] : (addition(all_66_0, v0) = all_693_0 &
% 233.67/32.43 | | | | addition(all_20_10, one) = v0 & $i(v0) & $i(all_693_0))
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | DELTA: instantiating (1044) with fresh symbol all_1298_0 gives:
% 233.67/32.43 | | | | (1045) addition(all_66_0, all_1298_0) = all_693_0 &
% 233.67/32.43 | | | | addition(all_20_10, one) = all_1298_0 & $i(all_1298_0) &
% 233.67/32.43 | | | | $i(all_693_0)
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | ALPHA: (1045) implies:
% 233.67/32.43 | | | | (1046) $i(all_693_0)
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | REDUCE: (1032), (1043) imply:
% 233.67/32.43 | | | | (1047) addition(one, one) = one
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | GROUND_INST: instantiating (3) with one, one, simplifying with (681),
% 233.67/32.43 | | | | (1042), (1047) gives:
% 233.67/32.43 | | | | (1048) $false
% 233.67/32.43 | | | |
% 233.67/32.43 | | | | CLOSE: (1048) is inconsistent.
% 233.67/32.43 | | | |
% 233.67/32.44 | | | End of split
% 233.67/32.44 | | |
% 233.67/32.44 | | End of split
% 233.67/32.44 | |
% 233.67/32.44 | Case 2:
% 233.67/32.44 | |
% 233.67/32.44 | | (1049) ~ leq(one, all_20_0)
% 233.67/32.44 | | (1050) leq(all_20_0, one)
% 233.67/32.44 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_20_6,
% 233.67/32.45 | | all_20_11, all_20_9, one, all_20_0, simplifying with (15),
% 233.67/32.45 | | (17), (19), (291), (653) gives:
% 233.67/32.45 | | (1051) ? [v0: $i] : (addition(all_20_9, v0) = all_20_0 &
% 233.67/32.45 | | addition(all_20_11, all_20_6) = v0 & $i(v0) & $i(all_20_0))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_20_6, all_20_9,
% 233.67/32.45 | | all_20_11, one, all_20_0, simplifying with (15), (17), (19),
% 233.67/32.45 | | (292), (653) gives:
% 233.67/32.45 | | (1052) ? [v0: $i] : (addition(all_20_9, all_20_6) = v0 &
% 233.67/32.45 | | addition(all_20_11, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (4) with all_20_12, all_20_4, simplifying with
% 233.67/32.45 | | (14), (20), (661) gives:
% 233.67/32.45 | | (1053) complement(all_20_4, all_20_12) | ? [v0: $i] : ? [v1: $i] : (( ~
% 233.67/32.45 | | (v1 = zero) & multiplication(all_20_4, all_20_12) = v1 &
% 233.67/32.45 | | $i(v1)) | ( ~ (v0 = zero) & multiplication(all_20_12,
% 233.67/32.45 | | all_20_4) = v0 & $i(v0)))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_commutativity) with all_20_8, all_20_1,
% 233.67/32.45 | | all_186_0, simplifying with (18), (22), (442) gives:
% 233.67/32.45 | | (1054) addition(all_20_1, all_20_8) = all_186_0 & $i(all_186_0)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1054) implies:
% 233.67/32.45 | | (1055) addition(all_20_1, all_20_8) = all_186_0
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_commutativity) with all_20_8,
% 233.67/32.45 | | all_142_0, all_100_0, simplifying with (18), (335), (630)
% 233.67/32.45 | | gives:
% 233.67/32.45 | | (1056) addition(all_142_0, all_20_8) = all_100_0 & $i(all_100_0)
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_commutativity) with all_20_6, all_94_0,
% 233.67/32.45 | | all_50_0, simplifying with (19), (332), (628) gives:
% 233.67/32.45 | | (1057) addition(all_94_0, all_20_6) = all_50_0 & $i(all_50_0)
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_20_8, all_20_1,
% 233.67/32.45 | | all_20_3, all_20_4, all_102_0, simplifying with (18), (21),
% 233.67/32.45 | | (22), (549), (556) gives:
% 233.67/32.45 | | (1058) ? [v0: $i] : (addition(all_20_1, all_20_8) = v0 &
% 233.67/32.45 | | addition(all_20_3, v0) = all_102_0 & $i(v0) & $i(all_102_0))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_commutativity) with all_20_3,
% 233.67/32.45 | | all_100_0, one, simplifying with (21), (363), (626) gives:
% 233.67/32.45 | | (1059) addition(all_100_0, all_20_3) = one & $i(one)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1059) implies:
% 233.67/32.45 | | (1060) $i(one)
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_20_10,
% 233.67/32.45 | | all_20_3, all_20_1, all_20_4, all_132_0, simplifying with (16),
% 233.67/32.45 | | (21), (22), (551), (552) gives:
% 233.67/32.45 | | (1061) ? [v0: $i] : (addition(all_20_1, v0) = all_132_0 &
% 233.67/32.45 | | addition(all_20_3, all_20_10) = v0 & $i(v0) & $i(all_132_0))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_186_0,
% 233.67/32.45 | | all_94_0, all_20_6, all_50_0, all_20_0, simplifying with (19),
% 233.67/32.45 | | (332), (622), (628), (637) gives:
% 233.67/32.45 | | (1062) ? [v0: $i] : (addition(all_94_0, all_186_0) = v0 &
% 233.67/32.45 | | addition(all_20_6, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_20_8, all_20_1,
% 233.67/32.45 | | all_36_0, all_64_0, all_66_0, simplifying with (18), (22),
% 233.67/32.45 | | (56), (118), (352) gives:
% 233.67/32.45 | | (1063) ? [v0: $i] : (addition(all_36_0, v0) = all_66_0 &
% 233.67/32.45 | | addition(all_20_1, all_20_8) = v0 & $i(v0) & $i(all_66_0))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_8,
% 233.67/32.45 | | all_20_3, all_86_0, all_226_0, simplifying with (18), (21),
% 233.67/32.45 | | (22), (348), (475) gives:
% 233.67/32.45 | | (1064) ? [v0: $i] : (addition(all_20_3, v0) = all_226_0 &
% 233.67/32.45 | | addition(all_20_8, all_20_1) = v0 & $i(v0) & $i(all_226_0))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_20_1, all_20_8,
% 233.67/32.45 | | all_94_0, all_58_0, one, simplifying with (18), (22), (332),
% 233.67/32.45 | | (355), (656) gives:
% 233.67/32.45 | | (1065) ? [v0: $i] : (addition(all_94_0, v0) = one & addition(all_20_8,
% 233.67/32.45 | | all_20_1) = v0 & $i(v0) & $i(one))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_20_6, all_20_3,
% 233.67/32.45 | | all_20_10, all_94_0, all_216_0, simplifying with (16), (19),
% 233.67/32.45 | | (21), (215), (465) gives:
% 233.67/32.45 | | (1066) ? [v0: $i] : (addition(all_20_3, all_20_6) = v0 &
% 233.67/32.45 | | addition(all_20_10, v0) = all_216_0 & $i(v0) & $i(all_216_0))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_20_8, all_20_1,
% 233.67/32.45 | | all_60_0, all_98_0, all_48_0, simplifying with (18), (22),
% 233.67/32.45 | | (137), (222), (357) gives:
% 233.67/32.45 | | (1067) ? [v0: $i] : (addition(all_60_0, v0) = all_48_0 &
% 233.67/32.45 | | addition(all_20_1, all_20_8) = v0 & $i(v0) & $i(all_48_0))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_1,
% 233.67/32.45 | | all_60_0, all_98_0, all_260_0, simplifying with (21), (22),
% 233.67/32.45 | | (137), (222), (510) gives:
% 233.67/32.45 | | (1068) ? [v0: $i] : (addition(all_60_0, v0) = all_260_0 &
% 233.67/32.45 | | addition(all_20_1, all_20_3) = v0 & $i(v0) & $i(all_260_0))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_1,
% 233.67/32.45 | | all_20_12, all_100_0, all_262_0, simplifying with (14), (21),
% 233.67/32.45 | | (22), (514), (564) gives:
% 233.67/32.45 | | (1069) ? [v0: $i] : (addition(all_20_1, all_20_3) = v0 &
% 233.67/32.45 | | addition(all_20_12, v0) = all_262_0 & $i(v0) & $i(all_262_0))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_1,
% 233.67/32.45 | | all_38_0, all_110_0, all_276_0, simplifying with (21), (22),
% 233.67/32.45 | | (60), (238), (533) gives:
% 233.67/32.45 | | (1070) ? [v0: $i] : (addition(all_38_0, v0) = all_276_0 &
% 233.67/32.45 | | addition(all_20_1, all_20_3) = v0 & $i(v0) & $i(all_276_0))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_20_10,
% 233.67/32.45 | | all_20_3, all_112_0, all_64_0, all_116_0, simplifying with
% 233.67/32.45 | | (16), (21), (313), (377), (655) gives:
% 233.67/32.45 | | (1071) ? [v0: $i] : (addition(all_112_0, v0) = all_116_0 &
% 233.67/32.45 | | addition(all_20_3, all_20_10) = v0 & $i(v0) & $i(all_116_0))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_20_8, all_20_1,
% 233.67/32.45 | | all_50_0, all_116_0, all_20_0, simplifying with (18), (22),
% 233.67/32.45 | | (140), (652), (657) gives:
% 233.67/32.45 | | (1072) ? [v0: $i] : (addition(all_50_0, v0) = all_20_0 &
% 233.67/32.45 | | addition(all_20_1, all_20_8) = v0 & $i(v0) & $i(all_20_0))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (additive_associativity) with all_20_3, all_20_1,
% 233.67/32.45 | | all_20_10, all_142_0, all_270_0, simplifying with (16), (21),
% 233.67/32.45 | | (22), (279), (524) gives:
% 233.67/32.45 | | (1073) ? [v0: $i] : (addition(all_20_1, all_20_3) = v0 &
% 233.67/32.45 | | addition(all_20_10, v0) = all_270_0 & $i(v0) & $i(all_270_0))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (multiplicative_associativity) with one,
% 233.67/32.45 | | all_20_12, all_20_11, all_20_12, all_20_6, simplifying with
% 233.67/32.45 | | (14), (15), (27), (545), (1060) gives:
% 233.67/32.45 | | (1074) ? [v0: $i] : (multiplication(all_20_12, all_20_11) = v0 &
% 233.67/32.45 | | multiplication(one, v0) = all_20_6 & $i(v0) & $i(all_20_6))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (2) with all_20_11, all_36_0, simplifying with
% 233.67/32.45 | | (15), (543) gives:
% 233.67/32.45 | | (1075) all_36_0 = all_20_11
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (multiplicative_associativity) with one,
% 233.67/32.45 | | all_20_12, all_20_4, all_20_12, zero, simplifying with (14),
% 233.67/32.45 | | (20), (374), (545), (1060) gives:
% 233.67/32.45 | | (1076) ? [v0: $i] : (multiplication(all_20_12, all_20_4) = v0 &
% 233.67/32.45 | | multiplication(one, v0) = zero & $i(v0) & $i(zero))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.67/32.45 | | one, all_20_9, all_20_4, all_20_1, simplifying with (17), (20),
% 233.67/32.45 | | (31), (544), (1060) gives:
% 233.67/32.45 | | (1077) ? [v0: $i] : (multiplication(all_20_4, v0) = all_20_1 &
% 233.67/32.45 | | multiplication(one, all_20_9) = v0 & $i(v0) & $i(all_20_1))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.67/32.45 | | one, all_20_11, all_20_4, all_20_3, simplifying with (15),
% 233.67/32.45 | | (20), (30), (544), (1060) gives:
% 233.67/32.45 | | (1078) ? [v0: $i] : (multiplication(all_20_4, v0) = all_20_3 &
% 233.67/32.45 | | multiplication(one, all_20_11) = v0 & $i(v0) & $i(all_20_3))
% 233.67/32.45 | |
% 233.67/32.45 | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.67/32.45 | | one, one, all_20_4, all_20_4, simplifying with (20), (544),
% 233.67/32.45 | | (1060) gives:
% 233.67/32.45 | | (1079) ? [v0: $i] : (multiplication(all_20_4, v0) = all_20_4 &
% 233.67/32.45 | | multiplication(one, one) = v0 & $i(v0))
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1079) with fresh symbol all_316_0 gives:
% 233.67/32.45 | | (1080) multiplication(all_20_4, all_316_0) = all_20_4 &
% 233.67/32.45 | | multiplication(one, one) = all_316_0 & $i(all_316_0)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1080) implies:
% 233.67/32.45 | | (1081) $i(all_316_0)
% 233.67/32.45 | | (1082) multiplication(one, one) = all_316_0
% 233.67/32.45 | | (1083) multiplication(all_20_4, all_316_0) = all_20_4
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1062) with fresh symbol all_322_0 gives:
% 233.67/32.45 | | (1084) addition(all_94_0, all_186_0) = all_322_0 & addition(all_20_6,
% 233.67/32.45 | | all_322_0) = all_20_0 & $i(all_322_0) & $i(all_20_0)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1084) implies:
% 233.67/32.45 | | (1085) addition(all_94_0, all_186_0) = all_322_0
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1052) with fresh symbol all_326_0 gives:
% 233.67/32.45 | | (1086) addition(all_20_9, all_20_6) = all_326_0 & addition(all_20_11,
% 233.67/32.45 | | all_326_0) = all_20_0 & $i(all_326_0) & $i(all_20_0)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1086) implies:
% 233.67/32.45 | | (1087) addition(all_20_11, all_326_0) = all_20_0
% 233.67/32.45 | | (1088) addition(all_20_9, all_20_6) = all_326_0
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1061) with fresh symbol all_332_0 gives:
% 233.67/32.45 | | (1089) addition(all_20_1, all_332_0) = all_132_0 & addition(all_20_3,
% 233.67/32.45 | | all_20_10) = all_332_0 & $i(all_332_0) & $i(all_132_0)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1089) implies:
% 233.67/32.45 | | (1090) $i(all_332_0)
% 233.67/32.45 | | (1091) addition(all_20_3, all_20_10) = all_332_0
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1051) with fresh symbol all_338_0 gives:
% 233.67/32.45 | | (1092) addition(all_20_9, all_338_0) = all_20_0 & addition(all_20_11,
% 233.67/32.45 | | all_20_6) = all_338_0 & $i(all_338_0) & $i(all_20_0)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1092) implies:
% 233.67/32.45 | | (1093) addition(all_20_11, all_20_6) = all_338_0
% 233.67/32.45 | | (1094) addition(all_20_9, all_338_0) = all_20_0
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1072) with fresh symbol all_344_0 gives:
% 233.67/32.45 | | (1095) addition(all_50_0, all_344_0) = all_20_0 & addition(all_20_1,
% 233.67/32.45 | | all_20_8) = all_344_0 & $i(all_344_0) & $i(all_20_0)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1095) implies:
% 233.67/32.45 | | (1096) $i(all_344_0)
% 233.67/32.45 | | (1097) addition(all_20_1, all_20_8) = all_344_0
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1071) with fresh symbol all_346_0 gives:
% 233.67/32.45 | | (1098) addition(all_112_0, all_346_0) = all_116_0 & addition(all_20_3,
% 233.67/32.45 | | all_20_10) = all_346_0 & $i(all_346_0) & $i(all_116_0)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1098) implies:
% 233.67/32.45 | | (1099) addition(all_20_3, all_20_10) = all_346_0
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1058) with fresh symbol all_372_0 gives:
% 233.67/32.45 | | (1100) addition(all_20_1, all_20_8) = all_372_0 & addition(all_20_3,
% 233.67/32.45 | | all_372_0) = all_102_0 & $i(all_372_0) & $i(all_102_0)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1100) implies:
% 233.67/32.45 | | (1101) addition(all_20_1, all_20_8) = all_372_0
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1078) with fresh symbol all_384_0 gives:
% 233.67/32.45 | | (1102) multiplication(all_20_4, all_384_0) = all_20_3 &
% 233.67/32.45 | | multiplication(one, all_20_11) = all_384_0 & $i(all_384_0) &
% 233.67/32.45 | | $i(all_20_3)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1102) implies:
% 233.67/32.45 | | (1103) $i(all_384_0)
% 233.67/32.45 | | (1104) multiplication(one, all_20_11) = all_384_0
% 233.67/32.45 | | (1105) multiplication(all_20_4, all_384_0) = all_20_3
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1077) with fresh symbol all_386_0 gives:
% 233.67/32.45 | | (1106) multiplication(all_20_4, all_386_0) = all_20_1 &
% 233.67/32.45 | | multiplication(one, all_20_9) = all_386_0 & $i(all_386_0) &
% 233.67/32.45 | | $i(all_20_1)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1106) implies:
% 233.67/32.45 | | (1107) $i(all_386_0)
% 233.67/32.45 | | (1108) multiplication(one, all_20_9) = all_386_0
% 233.67/32.45 | | (1109) multiplication(all_20_4, all_386_0) = all_20_1
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1073) with fresh symbol all_388_0 gives:
% 233.67/32.45 | | (1110) addition(all_20_1, all_20_3) = all_388_0 & addition(all_20_10,
% 233.67/32.45 | | all_388_0) = all_270_0 & $i(all_388_0) & $i(all_270_0)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1110) implies:
% 233.67/32.45 | | (1111) $i(all_388_0)
% 233.67/32.45 | | (1112) addition(all_20_1, all_20_3) = all_388_0
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1067) with fresh symbol all_390_0 gives:
% 233.67/32.45 | | (1113) addition(all_60_0, all_390_0) = all_48_0 & addition(all_20_1,
% 233.67/32.45 | | all_20_8) = all_390_0 & $i(all_390_0) & $i(all_48_0)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1113) implies:
% 233.67/32.45 | | (1114) addition(all_20_1, all_20_8) = all_390_0
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1068) with fresh symbol all_400_0 gives:
% 233.67/32.45 | | (1115) addition(all_60_0, all_400_0) = all_260_0 & addition(all_20_1,
% 233.67/32.45 | | all_20_3) = all_400_0 & $i(all_400_0) & $i(all_260_0)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1115) implies:
% 233.67/32.45 | | (1116) addition(all_20_1, all_20_3) = all_400_0
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1070) with fresh symbol all_406_0 gives:
% 233.67/32.45 | | (1117) addition(all_38_0, all_406_0) = all_276_0 & addition(all_20_1,
% 233.67/32.45 | | all_20_3) = all_406_0 & $i(all_406_0) & $i(all_276_0)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1117) implies:
% 233.67/32.45 | | (1118) addition(all_20_1, all_20_3) = all_406_0
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1066) with fresh symbol all_430_0 gives:
% 233.67/32.45 | | (1119) addition(all_20_3, all_20_6) = all_430_0 & addition(all_20_10,
% 233.67/32.45 | | all_430_0) = all_216_0 & $i(all_430_0) & $i(all_216_0)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1119) implies:
% 233.67/32.45 | | (1120) addition(all_20_3, all_20_6) = all_430_0
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1065) with fresh symbol all_434_0 gives:
% 233.67/32.45 | | (1121) addition(all_94_0, all_434_0) = one & addition(all_20_8, all_20_1)
% 233.67/32.45 | | = all_434_0 & $i(all_434_0) & $i(one)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1121) implies:
% 233.67/32.45 | | (1122) addition(all_20_8, all_20_1) = all_434_0
% 233.67/32.45 | | (1123) addition(all_94_0, all_434_0) = one
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1063) with fresh symbol all_436_0 gives:
% 233.67/32.45 | | (1124) addition(all_36_0, all_436_0) = all_66_0 & addition(all_20_1,
% 233.67/32.45 | | all_20_8) = all_436_0 & $i(all_436_0) & $i(all_66_0)
% 233.67/32.45 | |
% 233.67/32.45 | | ALPHA: (1124) implies:
% 233.67/32.45 | | (1125) addition(all_20_1, all_20_8) = all_436_0
% 233.67/32.45 | |
% 233.67/32.45 | | DELTA: instantiating (1069) with fresh symbol all_448_0 gives:
% 233.67/32.46 | | (1126) addition(all_20_1, all_20_3) = all_448_0 & addition(all_20_12,
% 233.67/32.46 | | all_448_0) = all_262_0 & $i(all_448_0) & $i(all_262_0)
% 233.67/32.46 | |
% 233.67/32.46 | | ALPHA: (1126) implies:
% 233.67/32.46 | | (1127) addition(all_20_1, all_20_3) = all_448_0
% 233.67/32.46 | |
% 233.67/32.46 | | DELTA: instantiating (1064) with fresh symbol all_472_0 gives:
% 233.67/32.46 | | (1128) addition(all_20_3, all_472_0) = all_226_0 & addition(all_20_8,
% 233.67/32.46 | | all_20_1) = all_472_0 & $i(all_472_0) & $i(all_226_0)
% 233.67/32.46 | |
% 233.67/32.46 | | ALPHA: (1128) implies:
% 233.67/32.46 | | (1129) addition(all_20_8, all_20_1) = all_472_0
% 233.67/32.46 | |
% 233.67/32.46 | | DELTA: instantiating (1076) with fresh symbol all_476_0 gives:
% 233.67/32.46 | | (1130) multiplication(all_20_12, all_20_4) = all_476_0 &
% 233.67/32.46 | | multiplication(one, all_476_0) = zero & $i(all_476_0) & $i(zero)
% 233.67/32.46 | |
% 233.67/32.46 | | ALPHA: (1130) implies:
% 233.67/32.46 | | (1131) multiplication(all_20_12, all_20_4) = all_476_0
% 233.67/32.46 | |
% 233.67/32.46 | | DELTA: instantiating (1074) with fresh symbol all_486_0 gives:
% 233.67/32.46 | | (1132) multiplication(all_20_12, all_20_11) = all_486_0 &
% 233.67/32.46 | | multiplication(one, all_486_0) = all_20_6 & $i(all_486_0) &
% 233.67/32.46 | | $i(all_20_6)
% 233.67/32.46 | |
% 233.67/32.46 | | ALPHA: (1132) implies:
% 233.67/32.46 | | (1133) $i(all_486_0)
% 233.67/32.46 | | (1134) multiplication(one, all_486_0) = all_20_6
% 233.67/32.46 | | (1135) multiplication(all_20_12, all_20_11) = all_486_0
% 233.67/32.46 | |
% 233.67/32.46 | | REDUCE: (543), (1075) imply:
% 233.67/32.46 | | (1136) multiplication(one, all_20_11) = all_20_11
% 233.67/32.46 | |
% 233.67/32.46 | | REDUCE: (80), (1075) imply:
% 233.67/32.46 | | (1137) addition(all_20_3, all_20_6) = all_20_11
% 233.67/32.46 | |
% 233.67/32.46 | | REDUCE: (58), (1075) imply:
% 233.67/32.46 | | (1138) addition(all_20_6, all_20_3) = all_20_11
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (9) with all_186_0, all_472_0, all_20_1,
% 233.67/32.46 | | all_20_8, simplifying with (442), (1129) gives:
% 233.67/32.46 | | (1139) all_472_0 = all_186_0
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (9) with all_434_0, all_472_0, all_20_1,
% 233.67/32.46 | | all_20_8, simplifying with (1122), (1129) gives:
% 233.67/32.46 | | (1140) all_472_0 = all_434_0
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (9) with all_94_0, all_346_0, all_20_10,
% 233.67/32.46 | | all_20_3, simplifying with (333), (1099) gives:
% 233.67/32.46 | | (1141) all_346_0 = all_94_0
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (9) with all_332_0, all_346_0, all_20_10,
% 233.67/32.46 | | all_20_3, simplifying with (1091), (1099) gives:
% 233.67/32.46 | | (1142) all_346_0 = all_332_0
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (9) with all_20_11, all_430_0, all_20_6,
% 233.67/32.46 | | all_20_3, simplifying with (1120), (1137) gives:
% 233.67/32.46 | | (1143) all_430_0 = all_20_11
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (9) with all_344_0, all_372_0, all_20_8,
% 233.67/32.46 | | all_20_1, simplifying with (1097), (1101) gives:
% 233.67/32.46 | | (1144) all_372_0 = all_344_0
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (9) with all_372_0, all_390_0, all_20_8,
% 233.67/32.46 | | all_20_1, simplifying with (1101), (1114) gives:
% 233.67/32.46 | | (1145) all_390_0 = all_372_0
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (9) with all_390_0, all_436_0, all_20_8,
% 233.67/32.46 | | all_20_1, simplifying with (1114), (1125) gives:
% 233.67/32.46 | | (1146) all_436_0 = all_390_0
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (9) with all_186_0, all_436_0, all_20_8,
% 233.67/32.46 | | all_20_1, simplifying with (1055), (1125) gives:
% 233.67/32.46 | | (1147) all_436_0 = all_186_0
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (9) with all_400_0, all_406_0, all_20_3,
% 233.67/32.46 | | all_20_1, simplifying with (1116), (1118) gives:
% 233.67/32.46 | | (1148) all_406_0 = all_400_0
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (9) with all_388_0, all_406_0, all_20_3,
% 233.67/32.46 | | all_20_1, simplifying with (1112), (1118) gives:
% 233.67/32.46 | | (1149) all_406_0 = all_388_0
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (9) with all_20_4, all_448_0, all_20_3, all_20_1,
% 233.67/32.46 | | simplifying with (552), (1127) gives:
% 233.67/32.46 | | (1150) all_448_0 = all_20_4
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (9) with all_400_0, all_448_0, all_20_3,
% 233.67/32.46 | | all_20_1, simplifying with (1116), (1127) gives:
% 233.67/32.46 | | (1151) all_448_0 = all_400_0
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (10) with all_20_11, all_384_0, all_20_11, one,
% 233.67/32.46 | | simplifying with (1104), (1136) gives:
% 233.67/32.46 | | (1152) all_384_0 = all_20_11
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (10) with all_20_6, all_486_0, all_20_11,
% 233.67/32.46 | | all_20_12, simplifying with (27), (1135) gives:
% 233.67/32.46 | | (1153) all_486_0 = all_20_6
% 233.67/32.46 | |
% 233.67/32.46 | | GROUND_INST: instantiating (10) with zero, all_476_0, all_20_4, all_20_12,
% 233.67/32.46 | | simplifying with (374), (1131) gives:
% 233.67/32.46 | | (1154) all_476_0 = zero
% 233.67/32.46 | |
% 233.67/32.46 | | COMBINE_EQS: (1139), (1140) imply:
% 233.67/32.46 | | (1155) all_434_0 = all_186_0
% 233.67/32.46 | |
% 233.67/32.46 | | COMBINE_EQS: (1150), (1151) imply:
% 233.67/32.46 | | (1156) all_400_0 = all_20_4
% 233.67/32.46 | |
% 233.67/32.46 | | SIMP: (1156) implies:
% 233.67/32.46 | | (1157) all_400_0 = all_20_4
% 233.67/32.46 | |
% 233.67/32.46 | | COMBINE_EQS: (1146), (1147) imply:
% 233.67/32.46 | | (1158) all_390_0 = all_186_0
% 233.67/32.46 | |
% 233.67/32.46 | | SIMP: (1158) implies:
% 233.67/32.46 | | (1159) all_390_0 = all_186_0
% 233.67/32.46 | |
% 233.67/32.46 | | COMBINE_EQS: (1148), (1149) imply:
% 233.67/32.46 | | (1160) all_400_0 = all_388_0
% 233.67/32.46 | |
% 233.67/32.46 | | SIMP: (1160) implies:
% 233.67/32.46 | | (1161) all_400_0 = all_388_0
% 233.67/32.46 | |
% 233.67/32.46 | | COMBINE_EQS: (1157), (1161) imply:
% 233.67/32.46 | | (1162) all_388_0 = all_20_4
% 233.67/32.46 | |
% 233.67/32.46 | | SIMP: (1162) implies:
% 233.67/32.46 | | (1163) all_388_0 = all_20_4
% 233.67/32.46 | |
% 233.67/32.46 | | COMBINE_EQS: (1145), (1159) imply:
% 233.67/32.46 | | (1164) all_372_0 = all_186_0
% 233.67/32.46 | |
% 233.67/32.46 | | SIMP: (1164) implies:
% 233.87/32.46 | | (1165) all_372_0 = all_186_0
% 233.87/32.46 | |
% 233.87/32.46 | | COMBINE_EQS: (1144), (1165) imply:
% 233.87/32.46 | | (1166) all_344_0 = all_186_0
% 233.87/32.46 | |
% 233.87/32.46 | | SIMP: (1166) implies:
% 233.87/32.46 | | (1167) all_344_0 = all_186_0
% 233.87/32.46 | |
% 233.87/32.46 | | COMBINE_EQS: (1141), (1142) imply:
% 233.87/32.46 | | (1168) all_332_0 = all_94_0
% 233.87/32.46 | |
% 233.87/32.46 | | SIMP: (1168) implies:
% 233.87/32.46 | | (1169) all_332_0 = all_94_0
% 233.87/32.46 | |
% 233.87/32.46 | | REDUCE: (1134), (1153) imply:
% 233.87/32.46 | | (1170) multiplication(one, all_20_6) = all_20_6
% 233.87/32.46 | |
% 233.87/32.46 | | REDUCE: (1123), (1155) imply:
% 233.87/32.46 | | (1171) addition(all_94_0, all_186_0) = one
% 233.87/32.46 | |
% 233.87/32.46 | | BETA: splitting (1053) gives:
% 233.87/32.46 | |
% 233.87/32.46 | | Case 1:
% 233.87/32.46 | | |
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (9) with all_322_0, one, all_186_0, all_94_0,
% 233.87/32.46 | | | simplifying with (1085), (1171) gives:
% 233.87/32.46 | | | (1172) all_322_0 = one
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (additive_commutativity) with all_20_11,
% 233.87/32.46 | | | all_20_6, all_338_0, simplifying with (15), (19), (1093)
% 233.87/32.46 | | | gives:
% 233.87/32.46 | | | (1173) addition(all_20_6, all_20_11) = all_338_0 & $i(all_338_0)
% 233.87/32.46 | | |
% 233.87/32.46 | | | ALPHA: (1173) implies:
% 233.87/32.46 | | | (1174) $i(all_338_0)
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (additive_commutativity) with all_20_9,
% 233.87/32.46 | | | all_20_6, all_326_0, simplifying with (17), (19), (1088)
% 233.87/32.46 | | | gives:
% 233.87/32.46 | | | (1175) addition(all_20_6, all_20_9) = all_326_0 & $i(all_326_0)
% 233.87/32.46 | | |
% 233.87/32.46 | | | ALPHA: (1175) implies:
% 233.87/32.46 | | | (1176) $i(all_326_0)
% 233.87/32.46 | | | (1177) addition(all_20_6, all_20_9) = all_326_0
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (additive_commutativity) with all_20_9,
% 233.87/32.46 | | | all_338_0, all_20_0, simplifying with (17), (1094), (1174)
% 233.87/32.46 | | | gives:
% 233.87/32.46 | | | (1178) addition(all_338_0, all_20_9) = all_20_0 & $i(all_20_0)
% 233.87/32.46 | | |
% 233.87/32.46 | | | ALPHA: (1178) implies:
% 233.87/32.46 | | | (1179) addition(all_338_0, all_20_9) = all_20_0
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (additive_associativity) with all_326_0,
% 233.87/32.46 | | | all_20_3, all_20_6, all_20_11, all_20_0, simplifying with
% 233.87/32.46 | | | (19), (21), (1087), (1138), (1176) gives:
% 233.87/32.46 | | | (1180) ? [v0: $i] : (addition(all_20_3, all_326_0) = v0 &
% 233.87/32.46 | | | addition(all_20_6, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (additive_associativity) with all_20_9,
% 233.87/32.46 | | | all_20_6, all_20_3, all_20_11, one, simplifying with (17),
% 233.87/32.46 | | | (19), (21), (292), (1137) gives:
% 233.87/32.46 | | | (1181) ? [v0: $i] : (addition(all_20_3, v0) = one & addition(all_20_6,
% 233.87/32.46 | | | all_20_9) = v0 & $i(v0) & $i(one))
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (additive_associativity) with all_20_6,
% 233.87/32.46 | | | all_20_6, all_20_3, all_20_11, all_338_0, simplifying with
% 233.87/32.46 | | | (19), (21), (1093), (1137) gives:
% 233.87/32.46 | | | (1182) ? [v0: $i] : (addition(all_20_3, v0) = all_338_0 &
% 233.87/32.46 | | | addition(all_20_6, all_20_6) = v0 & $i(v0) & $i(all_338_0))
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (additive_commutativity) with all_94_0,
% 233.87/32.46 | | | all_186_0, one, simplifying with (332), (637), (1171) gives:
% 233.87/32.46 | | | (1183) addition(all_186_0, all_94_0) = one & $i(one)
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (1) with one, all_316_0, simplifying with
% 233.87/32.46 | | | (1060), (1082) gives:
% 233.87/32.46 | | | (1184) all_316_0 = one
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (2) with all_20_9, all_386_0, simplifying with
% 233.87/32.46 | | | (17), (1108) gives:
% 233.87/32.46 | | | (1185) all_386_0 = all_20_9
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.87/32.46 | | | all_316_0, all_20_9, all_20_4, all_20_1, simplifying with
% 233.87/32.46 | | | (17), (20), (31), (1081), (1083) gives:
% 233.87/32.46 | | | (1186) ? [v0: $i] : (multiplication(all_316_0, all_20_9) = v0 &
% 233.87/32.46 | | | multiplication(all_20_4, v0) = all_20_1 & $i(v0) &
% 233.87/32.46 | | | $i(all_20_1))
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.87/32.46 | | | all_316_0, all_20_11, all_20_4, all_20_3, simplifying with
% 233.87/32.46 | | | (15), (20), (30), (1081), (1083) gives:
% 233.87/32.46 | | | (1187) ? [v0: $i] : (multiplication(all_316_0, all_20_11) = v0 &
% 233.87/32.46 | | | multiplication(all_20_4, v0) = all_20_3 & $i(v0) &
% 233.87/32.46 | | | $i(all_20_3))
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.87/32.46 | | | one, all_386_0, all_20_4, all_20_1, simplifying with (20),
% 233.87/32.46 | | | (544), (1060), (1107), (1109) gives:
% 233.87/32.46 | | | (1188) ? [v0: $i] : (multiplication(all_20_4, v0) = all_20_1 &
% 233.87/32.46 | | | multiplication(one, all_386_0) = v0 & $i(v0) & $i(all_20_1))
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (multiplicative_associativity) with all_20_4,
% 233.87/32.46 | | | all_316_0, all_386_0, all_20_4, all_20_1, simplifying with
% 233.87/32.46 | | | (20), (1081), (1083), (1107), (1109) gives:
% 233.87/32.46 | | | (1189) ? [v0: $i] : (multiplication(all_316_0, all_386_0) = v0 &
% 233.87/32.46 | | | multiplication(all_20_4, v0) = all_20_1 & $i(v0) &
% 233.87/32.46 | | | $i(all_20_1))
% 233.87/32.46 | | |
% 233.87/32.46 | | | DELTA: instantiating (1181) with fresh symbol all_542_0 gives:
% 233.87/32.46 | | | (1190) addition(all_20_3, all_542_0) = one & addition(all_20_6,
% 233.87/32.46 | | | all_20_9) = all_542_0 & $i(all_542_0) & $i(one)
% 233.87/32.46 | | |
% 233.87/32.46 | | | ALPHA: (1190) implies:
% 233.87/32.46 | | | (1191) $i(all_542_0)
% 233.87/32.46 | | | (1192) addition(all_20_6, all_20_9) = all_542_0
% 233.87/32.46 | | | (1193) addition(all_20_3, all_542_0) = one
% 233.87/32.46 | | |
% 233.87/32.46 | | | DELTA: instantiating (1189) with fresh symbol all_548_0 gives:
% 233.87/32.46 | | | (1194) multiplication(all_316_0, all_386_0) = all_548_0 &
% 233.87/32.46 | | | multiplication(all_20_4, all_548_0) = all_20_1 & $i(all_548_0) &
% 233.87/32.46 | | | $i(all_20_1)
% 233.87/32.46 | | |
% 233.87/32.46 | | | ALPHA: (1194) implies:
% 233.87/32.46 | | | (1195) $i(all_548_0)
% 233.87/32.46 | | | (1196) multiplication(all_316_0, all_386_0) = all_548_0
% 233.87/32.46 | | |
% 233.87/32.46 | | | DELTA: instantiating (1180) with fresh symbol all_550_0 gives:
% 233.87/32.46 | | | (1197) addition(all_20_3, all_326_0) = all_550_0 & addition(all_20_6,
% 233.87/32.46 | | | all_550_0) = all_20_0 & $i(all_550_0) & $i(all_20_0)
% 233.87/32.46 | | |
% 233.87/32.46 | | | ALPHA: (1197) implies:
% 233.87/32.46 | | | (1198) addition(all_20_3, all_326_0) = all_550_0
% 233.87/32.46 | | |
% 233.87/32.46 | | | DELTA: instantiating (1187) with fresh symbol all_552_0 gives:
% 233.87/32.46 | | | (1199) multiplication(all_316_0, all_20_11) = all_552_0 &
% 233.87/32.46 | | | multiplication(all_20_4, all_552_0) = all_20_3 & $i(all_552_0) &
% 233.87/32.46 | | | $i(all_20_3)
% 233.87/32.46 | | |
% 233.87/32.46 | | | DELTA: instantiating (1186) with fresh symbol all_558_0 gives:
% 233.87/32.46 | | | (1200) multiplication(all_316_0, all_20_9) = all_558_0 &
% 233.87/32.46 | | | multiplication(all_20_4, all_558_0) = all_20_1 & $i(all_558_0) &
% 233.87/32.46 | | | $i(all_20_1)
% 233.87/32.46 | | |
% 233.87/32.46 | | | ALPHA: (1200) implies:
% 233.87/32.46 | | | (1201) multiplication(all_316_0, all_20_9) = all_558_0
% 233.87/32.46 | | |
% 233.87/32.46 | | | DELTA: instantiating (1182) with fresh symbol all_568_0 gives:
% 233.87/32.46 | | | (1202) addition(all_20_3, all_568_0) = all_338_0 & addition(all_20_6,
% 233.87/32.46 | | | all_20_6) = all_568_0 & $i(all_568_0) & $i(all_338_0)
% 233.87/32.46 | | |
% 233.87/32.46 | | | ALPHA: (1202) implies:
% 233.87/32.46 | | | (1203) $i(all_568_0)
% 233.87/32.46 | | | (1204) addition(all_20_6, all_20_6) = all_568_0
% 233.87/32.46 | | | (1205) addition(all_20_3, all_568_0) = all_338_0
% 233.87/32.46 | | |
% 233.87/32.46 | | | DELTA: instantiating (1188) with fresh symbol all_572_0 gives:
% 233.87/32.46 | | | (1206) multiplication(all_20_4, all_572_0) = all_20_1 &
% 233.87/32.46 | | | multiplication(one, all_386_0) = all_572_0 & $i(all_572_0) &
% 233.87/32.46 | | | $i(all_20_1)
% 233.87/32.46 | | |
% 233.87/32.46 | | | ALPHA: (1206) implies:
% 233.87/32.46 | | | (1207) multiplication(one, all_386_0) = all_572_0
% 233.87/32.46 | | |
% 233.87/32.46 | | | REDUCE: (1184), (1185), (1196) imply:
% 233.87/32.46 | | | (1208) multiplication(one, all_20_9) = all_548_0
% 233.87/32.46 | | |
% 233.87/32.46 | | | REDUCE: (1184), (1201) imply:
% 233.87/32.46 | | | (1209) multiplication(one, all_20_9) = all_558_0
% 233.87/32.46 | | |
% 233.87/32.46 | | | REDUCE: (1185), (1207) imply:
% 233.87/32.46 | | | (1210) multiplication(one, all_20_9) = all_572_0
% 233.87/32.46 | | |
% 233.87/32.46 | | | REDUCE: (1108), (1185) imply:
% 233.87/32.46 | | | (1211) multiplication(one, all_20_9) = all_20_9
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (9) with all_326_0, all_542_0, all_20_9,
% 233.87/32.46 | | | all_20_6, simplifying with (1177), (1192) gives:
% 233.87/32.46 | | | (1212) all_542_0 = all_326_0
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (10) with all_20_9, all_558_0, all_20_9, one,
% 233.87/32.46 | | | simplifying with (1209), (1211) gives:
% 233.87/32.46 | | | (1213) all_558_0 = all_20_9
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (10) with all_558_0, all_572_0, all_20_9, one,
% 233.87/32.46 | | | simplifying with (1209), (1210) gives:
% 233.87/32.46 | | | (1214) all_572_0 = all_558_0
% 233.87/32.46 | | |
% 233.87/32.46 | | | GROUND_INST: instantiating (10) with all_548_0, all_572_0, all_20_9, one,
% 233.87/32.46 | | | simplifying with (1208), (1210) gives:
% 233.87/32.46 | | | (1215) all_572_0 = all_548_0
% 233.87/32.46 | | |
% 233.87/32.46 | | | COMBINE_EQS: (1214), (1215) imply:
% 233.87/32.46 | | | (1216) all_558_0 = all_548_0
% 233.87/32.46 | | |
% 233.87/32.46 | | | SIMP: (1216) implies:
% 233.87/32.46 | | | (1217) all_558_0 = all_548_0
% 233.87/32.46 | | |
% 233.87/32.46 | | | COMBINE_EQS: (1213), (1217) imply:
% 233.87/32.46 | | | (1218) all_548_0 = all_20_9
% 233.87/32.46 | | |
% 233.87/32.46 | | | REDUCE: (1193), (1212) imply:
% 233.87/32.47 | | | (1219) addition(all_20_3, all_326_0) = one
% 233.87/32.47 | | |
% 233.87/32.47 | | | GROUND_INST: instantiating (9) with all_550_0, one, all_326_0, all_20_3,
% 233.87/32.47 | | | simplifying with (1198), (1219) gives:
% 233.87/32.47 | | | (1220) all_550_0 = one
% 233.87/32.47 | | |
% 233.87/32.47 | | | GROUND_INST: instantiating (additive_idempotence) with all_20_6,
% 233.87/32.47 | | | all_568_0, simplifying with (19), (1204) gives:
% 233.87/32.47 | | | (1221) all_568_0 = all_20_6
% 233.87/32.47 | | |
% 233.87/32.47 | | | GROUND_INST: instantiating (additive_commutativity) with all_20_3,
% 233.87/32.47 | | | all_326_0, one, simplifying with (21), (1176), (1219) gives:
% 233.87/32.47 | | | (1222) addition(all_326_0, all_20_3) = one & $i(one)
% 233.87/32.47 | | |
% 233.87/32.47 | | | GROUND_INST: instantiating (additive_associativity) with all_20_9,
% 233.87/32.47 | | | all_568_0, all_20_3, all_338_0, all_20_0, simplifying with
% 233.87/32.47 | | | (17), (21), (1179), (1203), (1205) gives:
% 233.87/32.47 | | | (1223) ? [v0: $i] : (addition(all_568_0, all_20_9) = v0 &
% 233.87/32.47 | | | addition(all_20_3, v0) = all_20_0 & $i(v0) & $i(all_20_0))
% 233.87/32.47 | | |
% 233.87/32.47 | | | GROUND_INST: instantiating (right_distributivity) with one, all_20_6,
% 233.87/32.47 | | | all_20_9, all_20_6, all_20_9, all_326_0, simplifying with
% 233.87/32.47 | | | (17), (19), (1060), (1170), (1177), (1211) gives:
% 233.87/32.47 | | | (1224) ? [v0: $i] : (multiplication(one, v0) = all_326_0 &
% 233.87/32.47 | | | addition(all_20_6, all_20_9) = v0 & $i(v0) & $i(all_326_0))
% 233.87/32.47 | | |
% 233.87/32.47 | | | DELTA: instantiating (1223) with fresh symbol all_704_0 gives:
% 233.87/32.47 | | | (1225) addition(all_568_0, all_20_9) = all_704_0 & addition(all_20_3,
% 233.87/32.47 | | | all_704_0) = all_20_0 & $i(all_704_0) & $i(all_20_0)
% 233.87/32.47 | | |
% 233.87/32.47 | | | ALPHA: (1225) implies:
% 233.87/32.47 | | | (1226) addition(all_20_3, all_704_0) = all_20_0
% 233.87/32.47 | | | (1227) addition(all_568_0, all_20_9) = all_704_0
% 233.87/32.47 | | |
% 233.87/32.47 | | | DELTA: instantiating (1224) with fresh symbol all_722_0 gives:
% 233.87/32.47 | | | (1228) multiplication(one, all_722_0) = all_326_0 & addition(all_20_6,
% 233.87/32.47 | | | all_20_9) = all_722_0 & $i(all_722_0) & $i(all_326_0)
% 233.87/32.47 | | |
% 233.87/32.47 | | | ALPHA: (1228) implies:
% 233.87/32.47 | | | (1229) addition(all_20_6, all_20_9) = all_722_0
% 233.87/32.47 | | |
% 233.87/32.47 | | | REDUCE: (1221), (1227) imply:
% 233.87/32.47 | | | (1230) addition(all_20_6, all_20_9) = all_704_0
% 233.87/32.47 | | |
% 233.87/32.47 | | | GROUND_INST: instantiating (9) with all_326_0, all_722_0, all_20_9,
% 233.87/32.47 | | | all_20_6, simplifying with (1177), (1229) gives:
% 233.87/32.47 | | | (1231) all_722_0 = all_326_0
% 233.87/32.47 | | |
% 233.87/32.47 | | | GROUND_INST: instantiating (9) with all_704_0, all_722_0, all_20_9,
% 233.87/32.47 | | | all_20_6, simplifying with (1229), (1230) gives:
% 233.87/32.47 | | | (1232) all_722_0 = all_704_0
% 233.87/32.47 | | |
% 233.87/32.47 | | | COMBINE_EQS: (1231), (1232) imply:
% 233.87/32.47 | | | (1233) all_704_0 = all_326_0
% 233.87/32.47 | | |
% 233.87/32.47 | | | REDUCE: (1226), (1233) imply:
% 233.87/32.47 | | | (1234) addition(all_20_3, all_326_0) = all_20_0
% 233.87/32.47 | | |
% 233.87/32.47 | | | GROUND_INST: instantiating (9) with one, all_20_0, all_326_0, all_20_3,
% 233.87/32.47 | | | simplifying with (1219), (1234) gives:
% 233.87/32.47 | | | (1235) all_20_0 = one
% 233.87/32.47 | | |
% 233.87/32.47 | | | REDUCE: (1050), (1235) imply:
% 233.87/32.47 | | | (1236) leq(one, one)
% 233.87/32.47 | | |
% 233.87/32.47 | | | REDUCE: (1049), (1235) imply:
% 233.87/32.47 | | | (1237) ~ leq(one, one)
% 233.87/32.47 | | |
% 233.87/32.47 | | | PRED_UNIFY: (1236), (1237) imply:
% 233.87/32.47 | | | (1238) $false
% 233.87/32.47 | | |
% 233.87/32.47 | | | CLOSE: (1238) is inconsistent.
% 233.87/32.47 | | |
% 233.87/32.47 | | Case 2:
% 233.87/32.47 | | |
% 233.87/32.47 | | | (1239) ? [v0: $i] : ? [v1: $i] : (( ~ (v1 = zero) &
% 233.87/32.47 | | | multiplication(all_20_4, all_20_12) = v1 & $i(v1)) | ( ~ (v0
% 233.87/32.47 | | | = zero) & multiplication(all_20_12, all_20_4) = v0 &
% 233.87/32.47 | | | $i(v0)))
% 233.87/32.47 | | |
% 233.87/32.47 | | | DELTA: instantiating (1239) with fresh symbols all_502_0, all_502_1 gives:
% 233.87/32.47 | | | (1240) ( ~ (all_502_0 = zero) & multiplication(all_20_4, all_20_12) =
% 233.87/32.47 | | | all_502_0 & $i(all_502_0)) | ( ~ (all_502_1 = zero) &
% 233.87/32.47 | | | multiplication(all_20_12, all_20_4) = all_502_1 &
% 233.87/32.47 | | | $i(all_502_1))
% 233.87/32.47 | | |
% 233.87/32.47 | | | BETA: splitting (1240) gives:
% 233.87/32.47 | | |
% 233.87/32.47 | | | Case 1:
% 233.87/32.47 | | | |
% 233.87/32.47 | | | | (1241) ~ (all_502_0 = zero) & multiplication(all_20_4, all_20_12) =
% 233.87/32.47 | | | | all_502_0 & $i(all_502_0)
% 233.87/32.47 | | | |
% 233.87/32.47 | | | | ALPHA: (1241) implies:
% 233.87/32.47 | | | | (1242) ~ (all_502_0 = zero)
% 233.87/32.47 | | | | (1243) multiplication(all_20_4, all_20_12) = all_502_0
% 233.87/32.47 | | | |
% 233.87/32.47 | | | | GROUND_INST: instantiating (10) with zero, all_502_0, all_20_12,
% 233.87/32.47 | | | | all_20_4, simplifying with (375), (1243) gives:
% 233.87/32.47 | | | | (1244) all_502_0 = zero
% 233.87/32.47 | | | |
% 233.87/32.47 | | | | REDUCE: (1242), (1244) imply:
% 233.87/32.47 | | | | (1245) $false
% 233.87/32.47 | | | |
% 233.87/32.47 | | | | CLOSE: (1245) is inconsistent.
% 233.87/32.47 | | | |
% 233.87/32.47 | | | Case 2:
% 233.87/32.47 | | | |
% 233.87/32.47 | | | | (1246) ~ (all_502_1 = zero) & multiplication(all_20_12, all_20_4) =
% 233.87/32.47 | | | | all_502_1 & $i(all_502_1)
% 233.87/32.47 | | | |
% 233.87/32.47 | | | | ALPHA: (1246) implies:
% 233.87/32.47 | | | | (1247) ~ (all_502_1 = zero)
% 233.87/32.47 | | | | (1248) multiplication(all_20_12, all_20_4) = all_502_1
% 233.87/32.47 | | | |
% 233.87/32.47 | | | | GROUND_INST: instantiating (10) with zero, all_502_1, all_20_4,
% 233.87/32.47 | | | | all_20_12, simplifying with (374), (1248) gives:
% 233.87/32.47 | | | | (1249) all_502_1 = zero
% 233.87/32.47 | | | |
% 233.87/32.47 | | | | REDUCE: (1247), (1249) imply:
% 233.87/32.47 | | | | (1250) $false
% 233.87/32.47 | | | |
% 233.87/32.47 | | | | CLOSE: (1250) is inconsistent.
% 233.87/32.47 | | | |
% 233.87/32.47 | | | End of split
% 233.87/32.47 | | |
% 233.87/32.47 | | End of split
% 233.87/32.47 | |
% 233.87/32.47 | End of split
% 233.87/32.47 |
% 233.87/32.47 End of proof
% 233.87/32.47 % SZS output end Proof for theBenchmark
% 233.87/32.47
% 233.87/32.47 31866ms
%------------------------------------------------------------------------------