TSTP Solution File: GEO535+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO535+1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n019.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 : Wed Aug 30 23:23:38 EDT 2023
% Result : Theorem 54.51s 7.90s
% Output : Proof 131.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO535+1 : TPTP v8.1.2. Released v7.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 23:57:57 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 8.83/1.99 Prover 1: Preprocessing ...
% 8.83/2.00 Prover 4: Preprocessing ...
% 9.52/2.02 Prover 2: Preprocessing ...
% 9.52/2.02 Prover 5: Preprocessing ...
% 9.52/2.02 Prover 3: Preprocessing ...
% 9.52/2.02 Prover 0: Preprocessing ...
% 9.52/2.02 Prover 6: Preprocessing ...
% 22.12/3.75 Prover 1: Warning: ignoring some quantifiers
% 22.12/3.76 Prover 5: Proving ...
% 22.67/3.78 Prover 2: Proving ...
% 24.61/4.03 Prover 6: Proving ...
% 24.61/4.03 Prover 3: Warning: ignoring some quantifiers
% 25.24/4.18 Prover 1: Constructing countermodel ...
% 25.80/4.20 Prover 3: Constructing countermodel ...
% 36.18/5.57 Prover 4: Constructing countermodel ...
% 39.00/5.90 Prover 0: Proving ...
% 54.51/7.90 Prover 2: proved (7180ms)
% 54.51/7.90
% 54.51/7.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 54.51/7.90
% 54.51/7.90 Prover 3: stopped
% 54.51/7.90 Prover 5: stopped
% 54.51/7.90 Prover 6: stopped
% 54.51/7.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 54.51/7.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 54.51/7.91 Prover 0: stopped
% 54.51/7.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 54.51/7.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 54.51/7.91 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 57.53/8.31 Prover 13: Preprocessing ...
% 57.53/8.31 Prover 7: Preprocessing ...
% 57.53/8.34 Prover 8: Preprocessing ...
% 57.53/8.36 Prover 10: Preprocessing ...
% 57.53/8.41 Prover 11: Preprocessing ...
% 60.70/8.72 Prover 10: Warning: ignoring some quantifiers
% 60.80/8.75 Prover 7: Warning: ignoring some quantifiers
% 60.80/8.78 Prover 10: Constructing countermodel ...
% 60.80/8.80 Prover 7: Constructing countermodel ...
% 62.00/8.90 Prover 13: Warning: ignoring some quantifiers
% 62.81/8.99 Prover 13: Constructing countermodel ...
% 62.81/9.00 Prover 8: Warning: ignoring some quantifiers
% 63.06/9.06 Prover 8: Constructing countermodel ...
% 69.07/9.82 Prover 11: Constructing countermodel ...
% 71.43/10.15 Prover 10: gave up
% 71.90/10.16 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 72.88/10.40 Prover 16: Preprocessing ...
% 76.08/10.76 Prover 16: Warning: ignoring some quantifiers
% 76.53/10.82 Prover 16: Constructing countermodel ...
% 82.57/11.56 Prover 7: gave up
% 82.57/11.58 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 85.19/11.90 Prover 19: Preprocessing ...
% 87.54/12.28 Prover 19: Warning: ignoring some quantifiers
% 87.54/12.35 Prover 19: Constructing countermodel ...
% 89.15/12.41 Prover 13: stopped
% 112.74/15.57 Prover 19: stopped
% 114.56/15.81 Prover 16: stopped
% 115.90/15.97 Prover 1: stopped
% 130.11/19.29 Prover 4: Found proof (size 489)
% 130.11/19.29 Prover 4: proved (18665ms)
% 130.54/19.30 Prover 8: stopped
% 130.54/19.30 Prover 11: stopped
% 130.54/19.31
% 130.54/19.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 130.54/19.31
% 130.71/19.33 % SZS output start Proof for theBenchmark
% 130.71/19.34 Assumptions after simplification:
% 130.71/19.34 ---------------------------------
% 130.71/19.34
% 130.71/19.34 (aA8)
% 130.71/19.36 $i(gamma) & $i(beta) & $i(alpha) & ? [v0: int] : ? [v1: int] : ? [v2: int]
% 130.71/19.36 : ( ~ (v2 = 0) & ~ (v1 = 0) & ~ (v0 = 0) & s_t(gamma, alpha, beta) = v2 &
% 130.71/19.36 s_t(beta, gamma, alpha) = v1 & s_t(alpha, beta, gamma) = v0)
% 130.71/19.36
% 130.71/19.37 (aSatz11_3a)
% 130.71/19.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 130.71/19.38 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: int]
% 130.71/19.38 : (v10 = 0 | ~ (s_e3(v6, v1, v7, v8, v4, v9) = v10) | ~ (ext(v4, v5, v1, v2)
% 130.71/19.38 = v9) | ~ (ext(v4, v3, v1, v0) = v8) | ~ (ext(v1, v2, v4, v5) = v7) | ~
% 130.71/19.38 (ext(v1, v0, v4, v3) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 130.71/19.38 ~ $i(v1) | ~ $i(v0) | ? [v11: int] : ( ~ (v11 = 0) & congruent(v0, v1,
% 130.71/19.38 v2, v3, v4, v5) = v11)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 130.71/19.38 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (congruent(v0, v1, v2, v3, v4, v5)
% 130.71/19.38 = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 130.71/19.38 $i(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (s_e3(v6,
% 130.71/19.38 v1, v7, v8, v4, v9) = 0 & ext(v4, v5, v1, v2) = v9 & ext(v4, v3, v1, v0)
% 130.71/19.38 = v8 & ext(v1, v2, v4, v5) = v7 & ext(v1, v0, v4, v3) = v6 & $i(v9) &
% 130.71/19.38 $i(v8) & $i(v7) & $i(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 130.71/19.38 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (congruent(v0, v1, v2, v3, v4, v5)
% 130.71/19.38 = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 130.71/19.38 $i(v0) | ? [v6: $i] : (sameside(v6, v4, v5) = 0 & ext(v4, v5, v1, v2) = v6
% 130.71/19.38 & $i(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 130.71/19.38 [v4: $i] : ! [v5: $i] : ( ~ (congruent(v0, v1, v2, v3, v4, v5) = 0) | ~
% 130.71/19.38 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 130.71/19.38 $i] : (sameside(v6, v4, v3) = 0 & ext(v4, v3, v1, v0) = v6 & $i(v6))) & !
% 130.71/19.38 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 130.71/19.38 : ( ~ (congruent(v0, v1, v2, v3, v4, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 130.71/19.38 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : (sameside(v6, v1,
% 130.71/19.38 v2) = 0 & ext(v1, v2, v4, v5) = v6 & $i(v6))) & ! [v0: $i] : ! [v1:
% 130.71/19.38 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 130.71/19.38 (congruent(v0, v1, v2, v3, v4, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3)
% 130.71/19.38 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : (sameside(v6, v1, v0) =
% 130.71/19.38 0 & ext(v1, v0, v4, v3) = v6 & $i(v6)))
% 130.71/19.38
% 130.71/19.38 (aSatz11_4)
% 130.98/19.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 130.98/19.40 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: int]
% 130.98/19.40 : (v10 = 0 | ~ (congruent(v0, v1, v2, v3, v4, v5) = 0) | ~ (s_e(v6, v7, v8,
% 130.98/19.40 v9) = v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) |
% 130.98/19.40 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v11: any] :
% 130.98/19.40 ? [v12: any] : ? [v13: any] : ? [v14: any] : ? [v15: any] : ? [v16: any]
% 130.98/19.40 : (sameside(v9, v4, v5) = v14 & sameside(v8, v4, v3) = v13 & sameside(v7,
% 130.98/19.40 v1, v2) = v12 & sameside(v6, v1, v0) = v11 & s_e(v1, v7, v4, v9) = v16 &
% 130.98/19.40 s_e(v1, v6, v4, v8) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) |
% 130.98/19.40 ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v0: $i] : ! [v1: $i]
% 130.98/19.40 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 130.98/19.40 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (congruent(v0, v1, v2, v3, v4, v5)
% 130.98/19.40 = 0) | ~ (sameside(v9, v4, v5) = 0) | ~ (sameside(v7, v1, v2) = 0) | ~
% 130.98/19.40 (s_e(v1, v6, v4, v8) = 0) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) |
% 130.98/19.40 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 130.98/19.40 [v10: any] : ? [v11: any] : ? [v12: any] : ? [v13: any] : (sameside(v8,
% 130.98/19.40 v4, v3) = v11 & sameside(v6, v1, v0) = v10 & s_e(v6, v7, v8, v9) = v13 &
% 130.98/19.40 s_e(v1, v7, v4, v9) = v12 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) |
% 130.98/19.40 v13 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 130.98/19.40 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i]
% 130.98/19.40 : ( ~ (congruent(v0, v1, v2, v3, v4, v5) = 0) | ~ (sameside(v8, v4, v3) = 0)
% 130.98/19.40 | ~ (sameside(v6, v1, v0) = 0) | ~ (s_e(v1, v7, v4, v9) = 0) | ~ $i(v9) |
% 130.98/19.40 ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 130.98/19.40 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ? [v12:
% 130.98/19.40 any] : ? [v13: any] : (sameside(v9, v4, v5) = v11 & sameside(v7, v1, v2)
% 130.98/19.40 = v10 & s_e(v6, v7, v8, v9) = v13 & s_e(v1, v6, v4, v8) = v12 & ( ~ (v12 =
% 130.98/19.40 0) | ~ (v11 = 0) | ~ (v10 = 0) | v13 = 0))) & ! [v0: $i] : ! [v1:
% 130.98/19.40 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 130.98/19.40 ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (congruent(v0, v1, v2, v3, v4,
% 130.98/19.40 v5) = 0) | ~ (s_e(v1, v7, v4, v9) = 0) | ~ (s_e(v1, v6, v4, v8) = 0) |
% 130.98/19.40 ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~
% 130.98/19.40 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] :
% 130.98/19.40 ? [v12: any] : ? [v13: any] : ? [v14: any] : (sameside(v9, v4, v5) = v13
% 130.98/19.40 & sameside(v8, v4, v3) = v12 & sameside(v7, v1, v2) = v11 & sameside(v6,
% 130.98/19.40 v1, v0) = v10 & s_e(v6, v7, v8, v9) = v14 & ( ~ (v13 = 0) | ~ (v12 = 0)
% 130.98/19.40 | ~ (v11 = 0) | ~ (v10 = 0) | v14 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 130.98/19.40 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 130.98/19.40 $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (sameside(v9, v4, v5) = 0) | ~
% 130.98/19.40 (sameside(v8, v4, v3) = 0) | ~ (sameside(v7, v1, v2) = 0) | ~
% 130.98/19.40 (sameside(v6, v1, v0) = 0) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) |
% 130.98/19.40 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 130.98/19.40 [v10: any] : ? [v11: any] : ? [v12: any] : ? [v13: any] : (congruent(v0,
% 130.98/19.40 v1, v2, v3, v4, v5) = v10 & s_e(v6, v7, v8, v9) = v13 & s_e(v1, v7, v4,
% 130.98/19.40 v9) = v12 & s_e(v1, v6, v4, v8) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) |
% 130.98/19.40 ~ (v10 = 0) | v13 = 0)))
% 130.98/19.40
% 130.98/19.40 (aSatz11_49a)
% 130.98/19.40 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 130.98/19.40 $i] : ? [v6: int] : ( ~ (v6 = 0) & congruent(v0, v1, v2, v3, v4, v5) = 0 &
% 130.98/19.40 s_e(v1, v2, v4, v5) = 0 & s_e(v1, v0, v4, v3) = 0 & s_e(v0, v2, v3, v5) = v6
% 130.98/19.40 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 130.98/19.40
% 130.98/19.40 (aSatz3_13b)
% 130.98/19.41 ~ (gamma = beta) & $i(gamma) & $i(beta)
% 130.98/19.41
% 130.98/19.41 (aSatz3_2)
% 130.98/19.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (s_t(v2,
% 130.98/19.41 v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~
% 130.98/19.41 (v4 = 0) & s_t(v0, v1, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 130.98/19.41 $i] : ( ~ (s_t(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 130.98/19.41 s_t(v2, v1, v0) = 0)
% 130.98/19.41
% 130.98/19.41 (aSatz5_12b)
% 130.98/19.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (s_t(v0,
% 130.98/19.41 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ?
% 130.98/19.41 [v5: any] : ? [v6: any] : (le(v1, v2, v0, v2) = v6 & le(v0, v1, v0, v2) =
% 130.98/19.41 v5 & s_col(v0, v1, v2) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 130.98/19.41 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (le(v1, v2, v0, v2) = 0) | ~
% 130.98/19.41 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any]
% 130.98/19.41 : (le(v0, v1, v0, v2) = v5 & s_col(v0, v1, v2) = v3 & s_t(v0, v1, v2) = v4 &
% 130.98/19.41 ( ~ (v5 = 0) | ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : !
% 130.98/19.41 [v2: $i] : ( ~ (le(v0, v1, v0, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 130.98/19.41 ? [v3: any] : ? [v4: any] : ? [v5: any] : (le(v1, v2, v0, v2) = v5 &
% 130.98/19.42 s_col(v0, v1, v2) = v3 & s_t(v0, v1, v2) = v4 & ( ~ (v5 = 0) | ~ (v3 = 0)
% 130.98/19.42 | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (s_col(v0,
% 130.98/19.42 v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ?
% 130.98/19.42 [v4: any] : ? [v5: any] : (le(v1, v2, v0, v2) = v5 & le(v0, v1, v0, v2) =
% 130.98/19.42 v4 & s_t(v0, v1, v2) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | v3 = 0)))
% 130.98/19.42
% 130.98/19.42 (aSatz6_28)
% 130.98/19.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 130.98/19.42 $i] : ! [v6: int] : (v6 = 0 | ~ (s_e(v1, v2, v4, v5) = 0) | ~ (s_e(v0,
% 130.98/19.42 v2, v3, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 130.98/19.42 $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : ? [v9: any] :
% 130.98/19.43 (sameside(v3, v4, v5) = v8 & sameside(v0, v1, v2) = v7 & s_e(v1, v0, v4, v3)
% 130.98/19.43 = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1:
% 130.98/19.43 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] :
% 130.98/19.43 (v6 = 0 | ~ (s_e(v1, v0, v4, v3) = 0) | ~ (s_e(v0, v2, v3, v5) = v6) | ~
% 130.98/19.43 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7:
% 130.98/19.43 any] : ? [v8: any] : ? [v9: any] : (sameside(v3, v4, v5) = v8 &
% 130.98/19.43 sameside(v0, v1, v2) = v7 & s_e(v1, v2, v4, v5) = v9 & ( ~ (v9 = 0) | ~
% 130.98/19.43 (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 130.98/19.43 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sameside(v3, v4, v5) = 0) | ~
% 130.98/19.43 (sameside(v0, v1, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 130.98/19.43 ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 130.98/19.43 (s_e(v1, v2, v4, v5) = v7 & s_e(v1, v0, v4, v3) = v6 & s_e(v0, v2, v3, v5) =
% 130.98/19.43 v8 & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 130.98/19.43 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (s_e(v1, v2, v4,
% 130.98/19.43 v5) = 0) | ~ (s_e(v1, v0, v4, v3) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 130.98/19.43 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 130.98/19.43 ? [v8: any] : (sameside(v3, v4, v5) = v7 & sameside(v0, v1, v2) = v6 &
% 130.98/19.43 s_e(v0, v2, v3, v5) = v8 & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0)))
% 130.98/19.43
% 130.98/19.43 (aSatz6_4b)
% 130.98/19.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 130.98/19.43 (sameside(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 130.98/19.43 any] : ? [v5: any] : (s_col(v0, v1, v2) = v4 & s_t(v0, v1, v2) = v5 & ( ~
% 130.98/19.43 (v4 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 130.98/19.43 int] : (v3 = 0 | ~ (s_t(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 130.98/19.43 $i(v0) | ? [v4: any] : ? [v5: any] : (sameside(v0, v1, v2) = v4 &
% 130.98/19.43 s_col(v0, v1, v2) = v5 & ( ~ (v5 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1:
% 130.98/19.43 $i] : ! [v2: $i] : ( ~ (s_col(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 130.98/19.43 $i(v0) | ? [v3: any] : ? [v4: any] : (sameside(v0, v1, v2) = v3 & s_t(v0,
% 130.98/19.43 v1, v2) = v4 & (v4 = 0 | v3 = 0)))
% 130.98/19.43
% 130.98/19.43 (aSatz6_5)
% 130.98/19.43 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~
% 130.98/19.43 (sameside(v0, v1, v0) = v2) | ~ $i(v1) | ~ $i(v0))
% 130.98/19.43
% 130.98/19.43 (aSatz6_6)
% 130.98/19.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 130.98/19.43 (sameside(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 130.98/19.43 int] : ( ~ (v4 = 0) & sameside(v0, v1, v2) = v4)) & ! [v0: $i] : ! [v1:
% 130.98/19.43 $i] : ! [v2: $i] : ( ~ (sameside(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) |
% 130.98/19.43 ~ $i(v0) | sameside(v2, v1, v0) = 0)
% 130.98/19.43
% 130.98/19.43 (aSatz6_7)
% 130.98/19.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 130.98/19.44 | ~ (sameside(v2, v1, v3) = 0) | ~ (sameside(v0, v1, v3) = v4) | ~ $i(v3)
% 130.98/19.44 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 130.98/19.44 sameside(v0, v1, v2) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 130.98/19.44 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (sameside(v0, v1, v3) = v4) | ~
% 130.98/19.44 (sameside(v0, v1, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 130.98/19.44 ? [v5: int] : ( ~ (v5 = 0) & sameside(v2, v1, v3) = v5)) & ! [v0: $i] : !
% 130.98/19.44 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sameside(v2, v1, v3) = 0) | ~
% 130.98/19.44 (sameside(v0, v1, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 130.98/19.44 sameside(v0, v1, v3) = 0)
% 130.98/19.44
% 130.98/19.44 (d_Defn6_1)
% 130.98/19.44 $i(xb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2
% 130.98/19.44 = v1 | v1 = v0 | ~ (sameside(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 130.98/19.44 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & s_t(v1, v2, v0) = v4)) & ! [v0: $i]
% 130.98/19.44 : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v1 = v0 | v1 = xb | ~
% 130.98/19.44 (sameside(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 130.98/19.44 int] : ( ~ (v4 = 0) & s_t(v1, v0, v2) = v4)) & ! [v0: $i] : ! [v1: $i] :
% 130.98/19.44 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (s_t(v1, v2, v0) = v3) | ~ $i(v2) |
% 130.98/19.44 ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (sameside(v0, v1, v2)
% 130.98/19.44 = v4 & s_t(v1, v0, v2) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] : !
% 130.98/19.44 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (s_t(v1, v0, v2) = v3) |
% 130.98/19.44 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 130.98/19.44 (sameside(v0, v1, v2) = v4 & s_t(v1, v2, v0) = v5 & ( ~ (v4 = 0) | v5 = 0)))
% 130.98/19.44 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | v1 = v0 | ~ (s_t(v1,
% 130.98/19.44 v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | sameside(v0, v1, v2)
% 130.98/19.44 = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | v1 = xb | ~
% 130.98/19.44 (s_t(v1, v0, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | sameside(v0, v1,
% 130.98/19.44 v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sameside(v0, v1,
% 130.98/19.44 v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 130.98/19.44 any] : (s_t(v1, v2, v0) = v4 & s_t(v1, v0, v2) = v3 & (v4 = 0 | v3 = 0)))
% 130.98/19.44 & ! [v0: $i] : ! [v1: $i] : ( ~ (sameside(v0, v1, v1) = 0) | ~ $i(v1) | ~
% 130.98/19.44 $i(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sameside(v0, v0, v1) = 0) | ~
% 130.98/19.44 $i(v1) | ~ $i(v0))
% 130.98/19.44
% 130.98/19.44 (d_insert)
% 130.98/19.45 $i(gamma) & $i(alpha) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 130.98/19.45 : ! [v4: $i] : ! [v5: $i] : ( ~ (ext(v4, v2, v0, v1) = v5) | ~ (ext(v3, v2,
% 130.98/19.45 alpha, gamma) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 130.98/19.45 (insert(v0, v1, v2, v3) = v5 & $i(v5))) & ! [v0: $i] : ! [v1: $i] : !
% 130.98/19.45 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (insert(v0, v1, v2, v3) = v4) | ~
% 130.98/19.45 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (ext(v5, v2, v0,
% 130.98/19.45 v1) = v4 & ext(v3, v2, alpha, gamma) = v5 & $i(v5) & $i(v4)))
% 130.98/19.45
% 130.98/19.45 (function-axioms)
% 131.43/19.47 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 131.43/19.47 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 131.43/19.47 : ! [v9: $i] : (v1 = v0 | ~ (s_afs(v9, v8, v7, v6, v5, v4, v3, v2) = v1) |
% 131.43/19.47 ~ (s_afs(v9, v8, v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 131.43/19.47 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 131.43/19.47 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v1 = v0 |
% 131.43/19.47 ~ (s_fs(v9, v8, v7, v6, v5, v4, v3, v2) = v1) | ~ (s_fs(v9, v8, v7, v6, v5,
% 131.43/19.47 v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 131.43/19.47 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 131.43/19.47 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v1 = v0 | ~
% 131.43/19.47 (s_ifs(v9, v8, v7, v6, v5, v4, v3, v2) = v1) | ~ (s_ifs(v9, v8, v7, v6, v5,
% 131.43/19.47 v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 131.43/19.47 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 131.43/19.47 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v1 = v0 | ~ (s_kf(v8, v7, v6, v5,
% 131.43/19.47 v4, v3, v2) = v1) | ~ (s_kf(v8, v7, v6, v5, v4, v3, v2) = v0)) & !
% 131.43/19.47 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 131.43/19.47 : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ (constructAngle(v7, v6, v5, v4,
% 131.43/19.47 v3, v2) = v1) | ~ (constructAngle(v7, v6, v5, v4, v3, v2) = v0)) & !
% 131.43/19.47 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 131.43/19.47 : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ (f113f(v7, v6, v5, v4, v3, v2) =
% 131.43/19.47 v1) | ~ (f113f(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 131.43/19.47 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 131.43/19.47 [v7: $i] : (v1 = v0 | ~ (f113d(v7, v6, v5, v4, v3, v2) = v1) | ~ (f113d(v7,
% 131.43/19.47 v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 131.43/19.47 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0
% 131.43/19.47 | ~ (f113c(v7, v6, v5, v4, v3, v2) = v1) | ~ (f113c(v7, v6, v5, v4, v3,
% 131.43/19.47 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 131.43/19.47 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ (f113a(v7,
% 131.43/19.47 v6, v5, v4, v3, v2) = v1) | ~ (f113a(v7, v6, v5, v4, v3, v2) = v0)) &
% 131.43/19.47 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 131.43/19.47 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~
% 131.43/19.47 (congruent(v7, v6, v5, v4, v3, v2) = v1) | ~ (congruent(v7, v6, v5, v4, v3,
% 131.43/19.47 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 131.43/19.47 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~
% 131.43/19.47 (triangle(v7, v6, v5, v4, v3, v2) = v1) | ~ (triangle(v7, v6, v5, v4, v3,
% 131.43/19.47 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 131.43/19.47 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 131.43/19.47 $i] : (v1 = v0 | ~ (s_e3(v7, v6, v5, v4, v3, v2) = v1) | ~ (s_e3(v7, v6,
% 131.43/19.47 v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 131.43/19.47 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 131.43/19.47 ~ (crossbar(v7, v6, v5, v4, v3, v2) = v1) | ~ (crossbar(v7, v6, v5, v4, v3,
% 131.43/19.47 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 131.43/19.47 [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (g811(v6, v5, v4, v3, v2)
% 131.43/19.47 = v1) | ~ (g811(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 131.43/19.47 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0
% 131.43/19.47 | ~ (f811(v6, v5, v4, v3, v2) = v1) | ~ (f811(v6, v5, v4, v3, v2) = v0)) &
% 131.43/19.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 131.43/19.47 $i] : ! [v6: $i] : (v1 = v0 | ~ (op(v6, v5, v4, v3, v2) = v1) | ~ (op(v6,
% 131.43/19.47 v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 131.43/19.47 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~
% 131.43/19.47 (midpointAux(v6, v5, v4, v3, v2) = v1) | ~ (midpointAux(v6, v5, v4, v3, v2)
% 131.43/19.47 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 131.43/19.47 $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (g813(v6, v5, v4, v3, v2) =
% 131.43/19.47 v1) | ~ (g813(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 131.43/19.47 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 |
% 131.43/19.47 ~ (f813(v6, v5, v4, v3, v2) = v1) | ~ (f813(v6, v5, v4, v3, v2) = v0)) & !
% 131.43/19.47 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 131.43/19.47 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (perpAt(v6,
% 131.43/19.47 v5, v4, v3, v2) = v1) | ~ (perpAt(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 131.43/19.47 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 131.43/19.47 ! [v6: $i] : (v1 = v0 | ~ (insert5(v6, v5, v4, v3, v2) = v1) | ~
% 131.43/19.47 (insert5(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 131.43/19.47 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~
% 131.43/19.47 (ip(v6, v5, v4, v3, v2) = v1) | ~ (ip(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 131.43/19.47 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 131.43/19.47 (v1 = v0 | ~ (ss3(v5, v4, v3, v2) = v1) | ~ (ss3(v5, v4, v3, v2) = v0)) & !
% 131.43/19.47 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 131.43/19.47 : (v1 = v0 | ~ (ss2(v5, v4, v3, v2) = v1) | ~ (ss2(v5, v4, v3, v2) = v0)) &
% 131.43/19.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 131.43/19.47 $i] : (v1 = v0 | ~ (ss1(v5, v4, v3, v2) = v1) | ~ (ss1(v5, v4, v3, v2) =
% 131.43/19.48 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 131.43/19.48 : ! [v5: $i] : (v1 = v0 | ~ (erectsameside(v5, v4, v3, v2) = v1) | ~
% 131.43/19.48 (erectsameside(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 131.43/19.48 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 131.43/19.48 (v1 = v0 | ~ (opposite(v5, v4, v3, v2) = v1) | ~ (opposite(v5, v4, v3, v2) =
% 131.43/19.48 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 131.43/19.48 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~
% 131.43/19.48 (samesideline(v5, v4, v3, v2) = v1) | ~ (samesideline(v5, v4, v3, v2) =
% 131.43/19.48 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 131.43/19.48 : ! [v5: $i] : (v1 = v0 | ~ (il(v5, v4, v3, v2) = v1) | ~ (il(v5, v4, v3,
% 131.43/19.48 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 131.43/19.48 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (perp(v5,
% 131.43/19.48 v4, v3, v2) = v1) | ~ (perp(v5, v4, v3, v2) = v0)) & ! [v0: $i] : !
% 131.43/19.48 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 |
% 131.43/19.48 ~ (ins(v5, v4, v3, v2) = v1) | ~ (ins(v5, v4, v3, v2) = v0)) & ! [v0:
% 131.43/19.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 131.43/19.48 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (le(v5, v4, v3, v2) = v1) | ~
% 131.43/19.48 (le(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 131.43/19.48 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (insert(v5, v4, v3, v2) =
% 131.43/19.48 v1) | ~ (insert(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 131.43/19.48 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (ext(v5,
% 131.43/19.48 v4, v3, v2) = v1) | ~ (ext(v5, v4, v3, v2) = v0)) & ! [v0:
% 131.43/19.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 131.43/19.48 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (s_e(v5, v4, v3, v2) = v1) | ~
% 131.43/19.48 (s_e(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 131.43/19.48 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (reflect(v4, v3, v2) = v1) | ~
% 131.43/19.48 (reflect(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 131.43/19.48 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (erectAux(v4, v3, v2) = v1) | ~
% 131.43/19.48 (erectAux(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 131.43/19.48 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (erect(v4, v3, v2) = v1) | ~
% 131.43/19.48 (erect(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 131.43/19.48 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (erectAux21a(v4, v3, v2) = v1) | ~
% 131.43/19.48 (erectAux21a(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 131.43/19.48 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (erect21a(v4, v3, v2) = v1) | ~
% 131.43/19.48 (erect21a(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 131.43/19.48 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (foot(v4, v3, v2) = v1) | ~ (foot(v4,
% 131.43/19.48 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 131.43/19.48 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (s_r(v4, v3, v2) =
% 131.43/19.48 v1) | ~ (s_r(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 131.43/19.48 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (isomidpoint(v4, v3, v2) = v1) |
% 131.43/19.48 ~ (isomidpoint(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 131.43/19.48 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 131.43/19.48 (s_m(v4, v3, v2) = v1) | ~ (s_m(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 131.43/19.48 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c63(v4, v3,
% 131.43/19.48 v2) = v1) | ~ (c63(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 131.43/19.48 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 131.43/19.48 ~ (sameside(v4, v3, v2) = v1) | ~ (sameside(v4, v3, v2) = v0)) & ! [v0:
% 131.43/19.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 131.43/19.48 : ! [v4: $i] : (v1 = v0 | ~ (s_col(v4, v3, v2) = v1) | ~ (s_col(v4, v3, v2)
% 131.43/19.48 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 131.43/19.48 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (s_t(v4, v3, v2) = v1) | ~
% 131.43/19.48 (s_t(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 131.43/19.48 $i] : (v1 = v0 | ~ (midpoint(v3, v2) = v1) | ~ (midpoint(v3, v2) = v0)) &
% 131.43/19.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (s(v3,
% 131.43/19.48 v2) = v1) | ~ (s(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 131.43/19.48 $i] : ! [v3: $i] : (v1 = v0 | ~ (pointOffLine(v3, v2) = v1) | ~
% 131.43/19.48 (pointOffLine(v3, v2) = v0))
% 131.43/19.48
% 131.43/19.48 Further assumptions not needed in the proof:
% 131.43/19.48 --------------------------------------------
% 131.43/19.48 aA1, aA2, aA3, aA4, aA5, aA6, aA7, aExtCol2, aExtPerp, aExtPerp2, aExtPerp3,
% 131.43/19.48 aExtPerp4, aExtPerp5, aExtPerp6, aExtSameSide1, aExtSameSide2, aLemma9_13a,
% 131.43/19.48 aLemma9_13b, aLemma9_13c, aLemma9_13d, aLemma9_13e, aLemma9_13f,
% 131.43/19.48 aLemma9_13f_case1, aLemma9_13f_case2, aLemma9_13g, aNarbouxLemma1, aSatz10_10,
% 131.43/19.48 aSatz10_10a, aSatz10_12, aSatz10_12a, aSatz10_12b, aSatz10_12c, aSatz10_14,
% 131.43/19.48 aSatz10_15, aSatz10_16a, aSatz10_16b, aSatz10_2a, aSatz10_2b, aSatz10_4,
% 131.43/19.48 aSatz10_5, aSatz10_6, aSatz10_7, aSatz10_8a, aSatz10_8b, aSatz11_15a,
% 131.43/19.48 aSatz11_15b, aSatz11_3d, aSatz11_4b, aSatz11_4d, aSatz11_6, aSatz11_7,
% 131.43/19.48 aSatz11_8, aSatz11_9, aSatz2_1, aSatz2_11, aSatz2_12, aSatz2_13, aSatz2_14,
% 131.43/19.48 aSatz2_15, aSatz2_2, aSatz2_3, aSatz2_4, aSatz2_5, aSatz2_8, aSatz3_1,
% 131.43/19.48 aSatz3_13a, aSatz3_13c, aSatz3_14a, aSatz3_14b, aSatz3_17, aSatz3_3, aSatz3_4,
% 131.43/19.48 aSatz3_5a, aSatz3_5b, aSatz3_6a, aSatz3_6b, aSatz3_7a, aSatz3_7b, aSatz4_11a,
% 131.43/19.48 aSatz4_11b, aSatz4_11c, aSatz4_11d, aSatz4_11e, aSatz4_12, aSatz4_12b,
% 131.43/19.48 aSatz4_13, aSatz4_14, aSatz4_16, aSatz4_17, aSatz4_18, aSatz4_19, aSatz4_2,
% 131.43/19.48 aSatz4_3, aSatz4_5, aSatz4_6, aSatz5_1, aSatz5_10, aSatz5_11, aSatz5_12a1,
% 131.43/19.48 aSatz5_12a2, aSatz5_2, aSatz5_3, aSatz5_5a, aSatz5_5b, aSatz5_6, aSatz5_7,
% 131.43/19.48 aSatz5_8, aSatz5_9, aSatz6_11a, aSatz6_11b, aSatz6_13a, aSatz6_13b, aSatz6_15a,
% 131.43/19.48 aSatz6_15b, aSatz6_15c, aSatz6_15d, aSatz6_16a, aSatz6_16b, aSatz6_17a,
% 131.43/19.48 aSatz6_17b, aSatz6_18, aSatz6_21, aSatz6_25, aSatz6_2a, aSatz6_2b, aSatz6_3a,
% 131.43/19.48 aSatz6_3b, aSatz6_4a, aSatz7_10a, aSatz7_10b, aSatz7_13, aSatz7_15a, aSatz7_15b,
% 131.43/19.48 aSatz7_16a, aSatz7_16b, aSatz7_17, aSatz7_18, aSatz7_19, aSatz7_2, aSatz7_20,
% 131.43/19.48 aSatz7_21, aSatz7_22, aSatz7_22a, aSatz7_22b, aSatz7_25, aSatz7_3a, aSatz7_3b,
% 131.43/19.48 aSatz7_4a, aSatz7_4b, aSatz7_6, aSatz7_7, aSatz7_8, aSatz7_9, aSatz8_10,
% 131.43/19.48 aSatz8_12a, aSatz8_12b, aSatz8_13a, aSatz8_13b, aSatz8_14a, aSatz8_14b,
% 131.43/19.48 aSatz8_14c, aSatz8_15, aSatz8_16a, aSatz8_16b, aSatz8_18, aSatz8_18a, aSatz8_2,
% 131.43/19.48 aSatz8_20a, aSatz8_20b, aSatz8_21, aSatz8_21a, aSatz8_22, aSatz8_22b, aSatz8_24,
% 131.43/19.48 aSatz8_24a, aSatz8_24b, aSatz8_3, aSatz8_4, aSatz8_5, aSatz8_6, aSatz8_7,
% 131.43/19.48 aSatz8_8, aSatz8_9, aSatz9_13, aSatz9_16, aSatz9_19b, aSatz9_2, aSatz9_3,
% 131.43/19.48 aSatz9_3a, aSatz9_4, aSatz9_4a, aSatz9_4a2, aSatz9_4b, aSatz9_4c, aSatz9_5,
% 131.43/19.48 aSatz9_6, aSatz9_8, aSatz9_9, aSideReflect, aext1, aperp1, d_Defn2_10,
% 131.43/19.48 d_Defn4_1, d_Defn4_10, d_Defn4_15, d_Defn4_4, d_Defn5_4, d_Defn7_1, d_Defn7_23,
% 131.43/19.48 d_Defn8_1, d_Defn8_11a, d_Defn8_11b, d_Defn9_1, d_Defn9_7
% 131.43/19.48
% 131.43/19.48 Those formulas are unsatisfiable:
% 131.43/19.48 ---------------------------------
% 131.43/19.48
% 131.43/19.48 Begin of proof
% 131.43/19.48 |
% 131.43/19.48 | ALPHA: (aA8) implies:
% 131.43/19.48 | (1) ? [v0: int] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = 0) & ~ (v1 = 0)
% 131.43/19.48 | & ~ (v0 = 0) & s_t(gamma, alpha, beta) = v2 & s_t(beta, gamma,
% 131.43/19.48 | alpha) = v1 & s_t(alpha, beta, gamma) = v0)
% 131.43/19.48 |
% 131.43/19.48 | ALPHA: (aSatz3_2) implies:
% 131.43/19.48 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 131.43/19.48 | (s_t(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 131.43/19.48 | int] : ( ~ (v4 = 0) & s_t(v0, v1, v2) = v4))
% 131.43/19.48 |
% 131.43/19.48 | ALPHA: (aSatz3_13b) implies:
% 131.43/19.48 | (3) $i(beta)
% 131.43/19.48 |
% 131.43/19.48 | ALPHA: (aSatz5_12b) implies:
% 131.43/19.48 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 131.43/19.48 | (s_t(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 131.43/19.48 | any] : ? [v5: any] : ? [v6: any] : (le(v1, v2, v0, v2) = v6 &
% 131.43/19.48 | le(v0, v1, v0, v2) = v5 & s_col(v0, v1, v2) = v4 & ( ~ (v6 = 0) |
% 131.43/19.48 | ~ (v5 = 0) | ~ (v4 = 0))))
% 131.43/19.49 |
% 131.43/19.49 | ALPHA: (aSatz6_4b) implies:
% 131.43/19.49 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 131.43/19.49 | (s_t(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 131.43/19.49 | any] : ? [v5: any] : (sameside(v0, v1, v2) = v4 & s_col(v0, v1,
% 131.43/19.49 | v2) = v5 & ( ~ (v5 = 0) | v4 = 0)))
% 131.43/19.49 |
% 131.43/19.49 | ALPHA: (aSatz6_6) implies:
% 131.43/19.49 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sameside(v0, v1, v2) =
% 131.43/19.49 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | sameside(v2, v1, v0) = 0)
% 131.43/19.49 |
% 131.43/19.49 | ALPHA: (aSatz6_7) implies:
% 131.43/19.49 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 131.43/19.49 | (v4 = 0 | ~ (sameside(v2, v1, v3) = 0) | ~ (sameside(v0, v1, v3) =
% 131.43/19.49 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int]
% 131.43/19.49 | : ( ~ (v5 = 0) & sameside(v0, v1, v2) = v5))
% 131.43/19.49 |
% 131.43/19.49 | ALPHA: (aSatz6_28) implies:
% 131.43/19.49 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 131.43/19.49 | ! [v5: $i] : ( ~ (s_e(v1, v2, v4, v5) = 0) | ~ (s_e(v1, v0, v4, v3) =
% 131.43/19.49 | 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 131.43/19.49 | $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (sameside(v3,
% 131.43/19.49 | v4, v5) = v7 & sameside(v0, v1, v2) = v6 & s_e(v0, v2, v3, v5) =
% 131.43/19.49 | v8 & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0)))
% 131.43/19.49 |
% 131.43/19.49 | ALPHA: (aSatz11_3a) implies:
% 131.43/19.49 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 131.43/19.49 | ! [v5: $i] : ( ~ (congruent(v0, v1, v2, v3, v4, v5) = 0) | ~ $i(v5) |
% 131.43/19.49 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 131.43/19.49 | $i] : (sameside(v6, v1, v0) = 0 & ext(v1, v0, v4, v3) = v6 &
% 131.43/19.49 | $i(v6)))
% 131.43/19.49 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 131.43/19.49 | ! [v5: $i] : ( ~ (congruent(v0, v1, v2, v3, v4, v5) = 0) | ~ $i(v5) |
% 131.43/19.49 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 131.43/19.49 | $i] : (sameside(v6, v1, v2) = 0 & ext(v1, v2, v4, v5) = v6 &
% 131.43/19.49 | $i(v6)))
% 131.43/19.50 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 131.43/19.50 | ! [v5: $i] : ( ~ (congruent(v0, v1, v2, v3, v4, v5) = 0) | ~ $i(v5) |
% 131.43/19.50 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 131.43/19.50 | $i] : (sameside(v6, v4, v3) = 0 & ext(v4, v3, v1, v0) = v6 &
% 131.43/19.50 | $i(v6)))
% 131.43/19.50 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 131.43/19.50 | ! [v5: $i] : ( ~ (congruent(v0, v1, v2, v3, v4, v5) = 0) | ~ $i(v5) |
% 131.43/19.50 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 131.43/19.50 | $i] : (sameside(v6, v4, v5) = 0 & ext(v4, v5, v1, v2) = v6 &
% 131.43/19.50 | $i(v6)))
% 131.43/19.50 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 131.43/19.50 | ! [v5: $i] : ( ~ (congruent(v0, v1, v2, v3, v4, v5) = 0) | ~ $i(v5) |
% 131.43/19.50 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 131.43/19.50 | $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (s_e3(v6, v1, v7,
% 131.43/19.50 | v8, v4, v9) = 0 & ext(v4, v5, v1, v2) = v9 & ext(v4, v3, v1, v0)
% 131.43/19.50 | = v8 & ext(v1, v2, v4, v5) = v7 & ext(v1, v0, v4, v3) = v6 &
% 131.43/19.50 | $i(v9) & $i(v8) & $i(v7) & $i(v6)))
% 131.43/19.50 |
% 131.43/19.50 | ALPHA: (aSatz11_4) implies:
% 131.43/19.50 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 131.43/19.50 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (
% 131.43/19.50 | ~ (congruent(v0, v1, v2, v3, v4, v5) = 0) | ~ (s_e(v1, v7, v4, v9)
% 131.43/19.50 | = 0) | ~ (s_e(v1, v6, v4, v8) = 0) | ~ $i(v9) | ~ $i(v8) | ~
% 131.43/19.50 | $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 131.43/19.50 | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ? [v12:
% 131.43/19.50 | any] : ? [v13: any] : ? [v14: any] : (sameside(v9, v4, v5) = v13
% 131.43/19.50 | & sameside(v8, v4, v3) = v12 & sameside(v7, v1, v2) = v11 &
% 131.43/19.50 | sameside(v6, v1, v0) = v10 & s_e(v6, v7, v8, v9) = v14 & ( ~ (v13
% 131.43/19.50 | = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v14 = 0)))
% 131.43/19.50 |
% 131.43/19.50 | ALPHA: (d_insert) implies:
% 131.43/19.50 | (15) $i(alpha)
% 131.43/19.50 | (16) $i(gamma)
% 131.43/19.50 |
% 131.43/19.50 | ALPHA: (d_Defn6_1) implies:
% 131.43/19.51 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 131.43/19.51 | (s_t(v1, v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 131.43/19.51 | any] : ? [v5: any] : (sameside(v0, v1, v2) = v4 & s_t(v1, v2, v0)
% 131.43/19.51 | = v5 & ( ~ (v4 = 0) | v5 = 0)))
% 131.43/19.51 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 131.43/19.51 | (s_t(v1, v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 131.43/19.51 | any] : ? [v5: any] : (sameside(v0, v1, v2) = v4 & s_t(v1, v0, v2)
% 131.43/19.51 | = v5 & ( ~ (v4 = 0) | v5 = 0)))
% 131.43/19.51 |
% 131.43/19.51 | ALPHA: (function-axioms) implies:
% 131.43/19.51 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 131.43/19.51 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (s_t(v4, v3, v2) = v1) |
% 131.43/19.51 | ~ (s_t(v4, v3, v2) = v0))
% 131.43/19.51 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 131.43/19.51 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sameside(v4, v3, v2) =
% 131.43/19.51 | v1) | ~ (sameside(v4, v3, v2) = v0))
% 131.43/19.51 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 131.43/19.51 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (s_e(v5, v4,
% 131.43/19.51 | v3, v2) = v1) | ~ (s_e(v5, v4, v3, v2) = v0))
% 131.43/19.51 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 131.43/19.51 | ! [v5: $i] : (v1 = v0 | ~ (ext(v5, v4, v3, v2) = v1) | ~ (ext(v5,
% 131.43/19.51 | v4, v3, v2) = v0))
% 131.43/19.51 |
% 131.43/19.51 | DELTA: instantiating (1) with fresh symbols all_226_0, all_226_1, all_226_2
% 131.43/19.51 | gives:
% 131.43/19.51 | (23) ~ (all_226_0 = 0) & ~ (all_226_1 = 0) & ~ (all_226_2 = 0) &
% 131.43/19.51 | s_t(gamma, alpha, beta) = all_226_0 & s_t(beta, gamma, alpha) =
% 131.43/19.51 | all_226_1 & s_t(alpha, beta, gamma) = all_226_2
% 131.43/19.51 |
% 131.43/19.51 | ALPHA: (23) implies:
% 131.43/19.51 | (24) ~ (all_226_2 = 0)
% 131.43/19.51 | (25) ~ (all_226_1 = 0)
% 131.43/19.51 | (26) ~ (all_226_0 = 0)
% 131.43/19.51 | (27) s_t(alpha, beta, gamma) = all_226_2
% 131.43/19.51 | (28) s_t(beta, gamma, alpha) = all_226_1
% 131.43/19.51 | (29) s_t(gamma, alpha, beta) = all_226_0
% 131.43/19.51 |
% 131.43/19.51 | DELTA: instantiating (aSatz11_49a) with fresh symbols all_230_0, all_230_1,
% 131.43/19.51 | all_230_2, all_230_3, all_230_4, all_230_5, all_230_6 gives:
% 131.43/19.51 | (30) ~ (all_230_0 = 0) & congruent(all_230_6, all_230_5, all_230_4,
% 131.43/19.51 | all_230_3, all_230_2, all_230_1) = 0 & s_e(all_230_5, all_230_4,
% 131.43/19.51 | all_230_2, all_230_1) = 0 & s_e(all_230_5, all_230_6, all_230_2,
% 131.43/19.51 | all_230_3) = 0 & s_e(all_230_6, all_230_4, all_230_3, all_230_1) =
% 131.43/19.51 | all_230_0 & $i(all_230_1) & $i(all_230_2) & $i(all_230_3) &
% 131.43/19.51 | $i(all_230_4) & $i(all_230_5) & $i(all_230_6)
% 131.43/19.51 |
% 131.43/19.51 | ALPHA: (30) implies:
% 131.43/19.51 | (31) ~ (all_230_0 = 0)
% 131.43/19.51 | (32) $i(all_230_6)
% 131.43/19.51 | (33) $i(all_230_5)
% 131.43/19.51 | (34) $i(all_230_4)
% 131.43/19.51 | (35) $i(all_230_3)
% 131.43/19.51 | (36) $i(all_230_2)
% 131.43/19.51 | (37) $i(all_230_1)
% 131.43/19.51 | (38) s_e(all_230_6, all_230_4, all_230_3, all_230_1) = all_230_0
% 131.43/19.51 | (39) s_e(all_230_5, all_230_6, all_230_2, all_230_3) = 0
% 131.43/19.51 | (40) s_e(all_230_5, all_230_4, all_230_2, all_230_1) = 0
% 131.43/19.51 | (41) congruent(all_230_6, all_230_5, all_230_4, all_230_3, all_230_2,
% 131.43/19.51 | all_230_1) = 0
% 131.43/19.51 |
% 131.43/19.52 | GROUND_INST: instantiating (8) with all_230_6, all_230_5, all_230_6,
% 131.43/19.52 | all_230_3, all_230_2, all_230_3, simplifying with (32), (33),
% 131.43/19.52 | (35), (36), (39) gives:
% 131.65/19.52 | (42) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sameside(all_230_3,
% 131.65/19.52 | all_230_2, all_230_3) = v1 & sameside(all_230_6, all_230_5,
% 131.65/19.52 | all_230_6) = v0 & s_e(all_230_6, all_230_6, all_230_3, all_230_3)
% 131.65/19.52 | = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 131.65/19.52 |
% 131.65/19.52 | GROUND_INST: instantiating (8) with all_230_4, all_230_5, all_230_4,
% 131.65/19.52 | all_230_1, all_230_2, all_230_1, simplifying with (33), (34),
% 131.65/19.52 | (36), (37), (40) gives:
% 131.65/19.52 | (43) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sameside(all_230_1,
% 131.65/19.52 | all_230_2, all_230_1) = v1 & sameside(all_230_4, all_230_5,
% 131.65/19.52 | all_230_4) = v0 & s_e(all_230_4, all_230_4, all_230_1, all_230_1)
% 131.65/19.52 | = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 131.65/19.52 |
% 131.65/19.52 | GROUND_INST: instantiating (18) with gamma, alpha, beta, all_226_2,
% 131.65/19.52 | simplifying with (3), (15), (16), (27) gives:
% 131.65/19.52 | (44) all_226_2 = 0 | ? [v0: any] : ? [v1: any] : (sameside(gamma, alpha,
% 131.65/19.52 | beta) = v0 & s_t(alpha, gamma, beta) = v1 & ( ~ (v0 = 0) | v1 =
% 131.65/19.52 | 0))
% 131.65/19.52 |
% 131.65/19.52 | GROUND_INST: instantiating (17) with beta, alpha, gamma, all_226_2,
% 131.65/19.52 | simplifying with (3), (15), (16), (27) gives:
% 131.65/19.52 | (45) all_226_2 = 0 | ? [v0: any] : ? [v1: any] : (sameside(beta, alpha,
% 131.65/19.52 | gamma) = v0 & s_t(alpha, gamma, beta) = v1 & ( ~ (v0 = 0) | v1 =
% 131.65/19.52 | 0))
% 131.65/19.52 |
% 131.65/19.52 | GROUND_INST: instantiating (2) with alpha, gamma, beta, all_226_1, simplifying
% 131.65/19.52 | with (3), (15), (16), (28) gives:
% 131.65/19.52 | (46) all_226_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & s_t(alpha, gamma, beta)
% 131.65/19.52 | = v0)
% 131.65/19.52 |
% 131.65/19.52 | GROUND_INST: instantiating (4) with beta, gamma, alpha, all_226_1, simplifying
% 131.65/19.52 | with (3), (15), (16), (28) gives:
% 131.65/19.52 | (47) all_226_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 131.65/19.52 | (le(gamma, alpha, beta, alpha) = v2 & le(beta, gamma, beta, alpha) =
% 131.65/19.52 | v1 & s_col(beta, gamma, alpha) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) |
% 131.65/19.52 | ~ (v0 = 0)))
% 131.65/19.52 |
% 131.65/19.52 | GROUND_INST: instantiating (5) with gamma, alpha, beta, all_226_0, simplifying
% 131.65/19.52 | with (3), (15), (16), (29) gives:
% 131.65/19.52 | (48) all_226_0 = 0 | ? [v0: any] : ? [v1: any] : (sameside(gamma, alpha,
% 131.65/19.52 | beta) = v0 & s_col(gamma, alpha, beta) = v1 & ( ~ (v1 = 0) | v0 =
% 131.65/19.52 | 0))
% 131.65/19.52 |
% 131.65/19.52 | GROUND_INST: instantiating (14) with all_230_6, all_230_5, all_230_4,
% 131.65/19.52 | all_230_3, all_230_2, all_230_1, all_230_4, all_230_4, all_230_1,
% 131.65/19.52 | all_230_1, simplifying with (32), (33), (34), (35), (36), (37),
% 131.65/19.52 | (40), (41) gives:
% 131.65/19.52 | (49) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 131.65/19.52 | any] : (sameside(all_230_1, all_230_2, all_230_1) = v3 &
% 131.65/19.52 | sameside(all_230_1, all_230_2, all_230_3) = v2 & sameside(all_230_4,
% 131.65/19.52 | all_230_5, all_230_4) = v1 & sameside(all_230_4, all_230_5,
% 131.65/19.52 | all_230_6) = v0 & s_e(all_230_4, all_230_4, all_230_1, all_230_1)
% 131.65/19.52 | = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 =
% 131.65/19.52 | 0))
% 131.65/19.52 |
% 131.65/19.52 | GROUND_INST: instantiating (14) with all_230_6, all_230_5, all_230_4,
% 131.65/19.52 | all_230_3, all_230_2, all_230_1, all_230_6, all_230_4, all_230_3,
% 131.65/19.52 | all_230_1, simplifying with (32), (33), (34), (35), (36), (37),
% 131.65/19.52 | (39), (40), (41) gives:
% 131.65/19.52 | (50) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 131.65/19.52 | any] : (sameside(all_230_1, all_230_2, all_230_1) = v3 &
% 131.65/19.52 | sameside(all_230_3, all_230_2, all_230_3) = v2 & sameside(all_230_4,
% 131.65/19.52 | all_230_5, all_230_4) = v1 & sameside(all_230_6, all_230_5,
% 131.65/19.52 | all_230_6) = v0 & s_e(all_230_6, all_230_4, all_230_3, all_230_1)
% 131.65/19.52 | = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 =
% 131.65/19.52 | 0))
% 131.65/19.52 |
% 131.65/19.53 | GROUND_INST: instantiating (14) with all_230_6, all_230_5, all_230_4,
% 131.65/19.53 | all_230_3, all_230_2, all_230_1, all_230_6, all_230_6, all_230_3,
% 131.65/19.53 | all_230_3, simplifying with (32), (33), (34), (35), (36), (37),
% 131.65/19.53 | (39), (41) gives:
% 131.65/19.53 | (51) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 131.65/19.53 | any] : (sameside(all_230_3, all_230_2, all_230_1) = v3 &
% 131.65/19.53 | sameside(all_230_3, all_230_2, all_230_3) = v2 & sameside(all_230_6,
% 131.65/19.53 | all_230_5, all_230_4) = v1 & sameside(all_230_6, all_230_5,
% 131.65/19.53 | all_230_6) = v0 & s_e(all_230_6, all_230_6, all_230_3, all_230_3)
% 131.65/19.53 | = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 =
% 131.65/19.53 | 0))
% 131.65/19.53 |
% 131.65/19.53 | GROUND_INST: instantiating (13) with all_230_6, all_230_5, all_230_4,
% 131.65/19.53 | all_230_3, all_230_2, all_230_1, simplifying with (32), (33),
% 131.65/19.53 | (34), (35), (36), (37), (41) gives:
% 131.65/19.53 | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (s_e3(v0,
% 131.65/19.53 | all_230_5, v1, v2, all_230_2, v3) = 0 & ext(all_230_2, all_230_1,
% 131.65/19.53 | all_230_5, all_230_4) = v3 & ext(all_230_2, all_230_3, all_230_5,
% 131.65/19.53 | all_230_6) = v2 & ext(all_230_5, all_230_4, all_230_2, all_230_1)
% 131.65/19.53 | = v1 & ext(all_230_5, all_230_6, all_230_2, all_230_3) = v0 & $i(v3)
% 131.65/19.53 | & $i(v2) & $i(v1) & $i(v0))
% 131.65/19.53 |
% 131.65/19.53 | GROUND_INST: instantiating (12) with all_230_6, all_230_5, all_230_4,
% 131.65/19.53 | all_230_3, all_230_2, all_230_1, simplifying with (32), (33),
% 131.65/19.53 | (34), (35), (36), (37), (41) gives:
% 131.65/19.53 | (53) ? [v0: $i] : (sameside(v0, all_230_2, all_230_1) = 0 & ext(all_230_2,
% 131.65/19.53 | all_230_1, all_230_5, all_230_4) = v0 & $i(v0))
% 131.65/19.53 |
% 131.65/19.53 | GROUND_INST: instantiating (11) with all_230_6, all_230_5, all_230_4,
% 131.65/19.53 | all_230_3, all_230_2, all_230_1, simplifying with (32), (33),
% 131.65/19.53 | (34), (35), (36), (37), (41) gives:
% 131.65/19.53 | (54) ? [v0: $i] : (sameside(v0, all_230_2, all_230_3) = 0 & ext(all_230_2,
% 131.65/19.53 | all_230_3, all_230_5, all_230_6) = v0 & $i(v0))
% 131.65/19.53 |
% 131.65/19.53 | GROUND_INST: instantiating (10) with all_230_6, all_230_5, all_230_4,
% 131.65/19.53 | all_230_3, all_230_2, all_230_1, simplifying with (32), (33),
% 131.65/19.53 | (34), (35), (36), (37), (41) gives:
% 131.65/19.53 | (55) ? [v0: $i] : (sameside(v0, all_230_5, all_230_4) = 0 & ext(all_230_5,
% 131.65/19.53 | all_230_4, all_230_2, all_230_1) = v0 & $i(v0))
% 131.65/19.53 |
% 131.65/19.53 | GROUND_INST: instantiating (9) with all_230_6, all_230_5, all_230_4,
% 131.65/19.53 | all_230_3, all_230_2, all_230_1, simplifying with (32), (33),
% 131.65/19.53 | (34), (35), (36), (37), (41) gives:
% 131.65/19.53 | (56) ? [v0: $i] : (sameside(v0, all_230_5, all_230_6) = 0 & ext(all_230_5,
% 131.65/19.53 | all_230_6, all_230_2, all_230_3) = v0 & $i(v0))
% 131.65/19.53 |
% 131.65/19.53 | DELTA: instantiating (53) with fresh symbol all_238_0 gives:
% 131.65/19.53 | (57) sameside(all_238_0, all_230_2, all_230_1) = 0 & ext(all_230_2,
% 131.65/19.53 | all_230_1, all_230_5, all_230_4) = all_238_0 & $i(all_238_0)
% 131.65/19.53 |
% 131.65/19.53 | ALPHA: (57) implies:
% 131.65/19.53 | (58) ext(all_230_2, all_230_1, all_230_5, all_230_4) = all_238_0
% 131.65/19.53 | (59) sameside(all_238_0, all_230_2, all_230_1) = 0
% 131.65/19.53 |
% 131.65/19.53 | DELTA: instantiating (56) with fresh symbol all_240_0 gives:
% 131.65/19.53 | (60) sameside(all_240_0, all_230_5, all_230_6) = 0 & ext(all_230_5,
% 131.65/19.53 | all_230_6, all_230_2, all_230_3) = all_240_0 & $i(all_240_0)
% 131.65/19.53 |
% 131.65/19.53 | ALPHA: (60) implies:
% 131.65/19.53 | (61) ext(all_230_5, all_230_6, all_230_2, all_230_3) = all_240_0
% 131.65/19.53 | (62) sameside(all_240_0, all_230_5, all_230_6) = 0
% 131.65/19.53 |
% 131.65/19.53 | DELTA: instantiating (55) with fresh symbol all_242_0 gives:
% 131.65/19.53 | (63) sameside(all_242_0, all_230_5, all_230_4) = 0 & ext(all_230_5,
% 131.65/19.53 | all_230_4, all_230_2, all_230_1) = all_242_0 & $i(all_242_0)
% 131.65/19.53 |
% 131.65/19.53 | ALPHA: (63) implies:
% 131.65/19.53 | (64) ext(all_230_5, all_230_4, all_230_2, all_230_1) = all_242_0
% 131.65/19.53 | (65) sameside(all_242_0, all_230_5, all_230_4) = 0
% 131.65/19.53 |
% 131.65/19.53 | DELTA: instantiating (54) with fresh symbol all_244_0 gives:
% 131.65/19.53 | (66) sameside(all_244_0, all_230_2, all_230_3) = 0 & ext(all_230_2,
% 131.65/19.53 | all_230_3, all_230_5, all_230_6) = all_244_0 & $i(all_244_0)
% 131.65/19.53 |
% 131.65/19.53 | ALPHA: (66) implies:
% 131.65/19.53 | (67) ext(all_230_2, all_230_3, all_230_5, all_230_6) = all_244_0
% 131.65/19.53 | (68) sameside(all_244_0, all_230_2, all_230_3) = 0
% 131.65/19.53 |
% 131.65/19.53 | DELTA: instantiating (43) with fresh symbols all_254_0, all_254_1, all_254_2
% 131.65/19.53 | gives:
% 131.65/19.53 | (69) sameside(all_230_1, all_230_2, all_230_1) = all_254_1 &
% 131.65/19.53 | sameside(all_230_4, all_230_5, all_230_4) = all_254_2 & s_e(all_230_4,
% 131.65/19.53 | all_230_4, all_230_1, all_230_1) = all_254_0 & ( ~ (all_254_1 = 0) |
% 131.65/19.53 | ~ (all_254_2 = 0) | all_254_0 = 0)
% 131.65/19.53 |
% 131.65/19.53 | ALPHA: (69) implies:
% 131.65/19.53 | (70) sameside(all_230_4, all_230_5, all_230_4) = all_254_2
% 131.65/19.53 | (71) sameside(all_230_1, all_230_2, all_230_1) = all_254_1
% 131.65/19.53 |
% 131.65/19.53 | DELTA: instantiating (42) with fresh symbols all_260_0, all_260_1, all_260_2
% 131.65/19.53 | gives:
% 131.65/19.54 | (72) sameside(all_230_3, all_230_2, all_230_3) = all_260_1 &
% 131.65/19.54 | sameside(all_230_6, all_230_5, all_230_6) = all_260_2 & s_e(all_230_6,
% 131.65/19.54 | all_230_6, all_230_3, all_230_3) = all_260_0 & ( ~ (all_260_1 = 0) |
% 131.65/19.54 | ~ (all_260_2 = 0) | all_260_0 = 0)
% 131.65/19.54 |
% 131.65/19.54 | ALPHA: (72) implies:
% 131.65/19.54 | (73) sameside(all_230_6, all_230_5, all_230_6) = all_260_2
% 131.65/19.54 | (74) sameside(all_230_3, all_230_2, all_230_3) = all_260_1
% 131.65/19.54 |
% 131.65/19.54 | DELTA: instantiating (52) with fresh symbols all_266_0, all_266_1, all_266_2,
% 131.65/19.54 | all_266_3 gives:
% 131.65/19.54 | (75) s_e3(all_266_3, all_230_5, all_266_2, all_266_1, all_230_2, all_266_0)
% 131.65/19.54 | = 0 & ext(all_230_2, all_230_1, all_230_5, all_230_4) = all_266_0 &
% 131.65/19.54 | ext(all_230_2, all_230_3, all_230_5, all_230_6) = all_266_1 &
% 131.65/19.54 | ext(all_230_5, all_230_4, all_230_2, all_230_1) = all_266_2 &
% 131.65/19.54 | ext(all_230_5, all_230_6, all_230_2, all_230_3) = all_266_3 &
% 131.65/19.54 | $i(all_266_0) & $i(all_266_1) & $i(all_266_2) & $i(all_266_3)
% 131.65/19.54 |
% 131.65/19.54 | ALPHA: (75) implies:
% 131.65/19.54 | (76) $i(all_266_3)
% 131.65/19.54 | (77) $i(all_266_2)
% 131.65/19.54 | (78) $i(all_266_1)
% 131.65/19.54 | (79) $i(all_266_0)
% 131.65/19.54 | (80) ext(all_230_5, all_230_6, all_230_2, all_230_3) = all_266_3
% 131.65/19.54 | (81) ext(all_230_5, all_230_4, all_230_2, all_230_1) = all_266_2
% 131.65/19.54 | (82) ext(all_230_2, all_230_3, all_230_5, all_230_6) = all_266_1
% 131.65/19.54 | (83) ext(all_230_2, all_230_1, all_230_5, all_230_4) = all_266_0
% 131.65/19.54 |
% 131.65/19.54 | DELTA: instantiating (51) with fresh symbols all_268_0, all_268_1, all_268_2,
% 131.65/19.54 | all_268_3, all_268_4 gives:
% 131.65/19.54 | (84) sameside(all_230_3, all_230_2, all_230_1) = all_268_1 &
% 131.65/19.54 | sameside(all_230_3, all_230_2, all_230_3) = all_268_2 &
% 131.65/19.54 | sameside(all_230_6, all_230_5, all_230_4) = all_268_3 &
% 131.65/19.54 | sameside(all_230_6, all_230_5, all_230_6) = all_268_4 & s_e(all_230_6,
% 131.65/19.54 | all_230_6, all_230_3, all_230_3) = all_268_0 & ( ~ (all_268_1 = 0) |
% 131.65/19.54 | ~ (all_268_2 = 0) | ~ (all_268_3 = 0) | ~ (all_268_4 = 0) |
% 131.65/19.54 | all_268_0 = 0)
% 131.65/19.54 |
% 131.65/19.54 | ALPHA: (84) implies:
% 131.65/19.54 | (85) sameside(all_230_6, all_230_5, all_230_6) = all_268_4
% 131.65/19.54 | (86) sameside(all_230_3, all_230_2, all_230_3) = all_268_2
% 131.65/19.54 |
% 131.65/19.54 | DELTA: instantiating (50) with fresh symbols all_272_0, all_272_1, all_272_2,
% 131.65/19.54 | all_272_3, all_272_4 gives:
% 131.65/19.54 | (87) sameside(all_230_1, all_230_2, all_230_1) = all_272_1 &
% 131.65/19.54 | sameside(all_230_3, all_230_2, all_230_3) = all_272_2 &
% 131.65/19.54 | sameside(all_230_4, all_230_5, all_230_4) = all_272_3 &
% 131.65/19.54 | sameside(all_230_6, all_230_5, all_230_6) = all_272_4 & s_e(all_230_6,
% 131.65/19.54 | all_230_4, all_230_3, all_230_1) = all_272_0 & ( ~ (all_272_1 = 0) |
% 131.65/19.54 | ~ (all_272_2 = 0) | ~ (all_272_3 = 0) | ~ (all_272_4 = 0) |
% 131.65/19.54 | all_272_0 = 0)
% 131.65/19.54 |
% 131.65/19.54 | ALPHA: (87) implies:
% 131.65/19.54 | (88) s_e(all_230_6, all_230_4, all_230_3, all_230_1) = all_272_0
% 131.65/19.54 | (89) sameside(all_230_6, all_230_5, all_230_6) = all_272_4
% 131.65/19.54 | (90) sameside(all_230_4, all_230_5, all_230_4) = all_272_3
% 131.65/19.54 | (91) sameside(all_230_3, all_230_2, all_230_3) = all_272_2
% 131.65/19.54 | (92) sameside(all_230_1, all_230_2, all_230_1) = all_272_1
% 131.65/19.54 | (93) ~ (all_272_1 = 0) | ~ (all_272_2 = 0) | ~ (all_272_3 = 0) | ~
% 131.65/19.54 | (all_272_4 = 0) | all_272_0 = 0
% 131.65/19.54 |
% 131.65/19.54 | DELTA: instantiating (49) with fresh symbols all_274_0, all_274_1, all_274_2,
% 131.65/19.54 | all_274_3, all_274_4 gives:
% 131.65/19.54 | (94) sameside(all_230_1, all_230_2, all_230_1) = all_274_1 &
% 131.65/19.54 | sameside(all_230_1, all_230_2, all_230_3) = all_274_2 &
% 131.65/19.54 | sameside(all_230_4, all_230_5, all_230_4) = all_274_3 &
% 131.65/19.54 | sameside(all_230_4, all_230_5, all_230_6) = all_274_4 & s_e(all_230_4,
% 131.65/19.54 | all_230_4, all_230_1, all_230_1) = all_274_0 & ( ~ (all_274_1 = 0) |
% 131.65/19.54 | ~ (all_274_2 = 0) | ~ (all_274_3 = 0) | ~ (all_274_4 = 0) |
% 131.65/19.54 | all_274_0 = 0)
% 131.65/19.54 |
% 131.65/19.54 | ALPHA: (94) implies:
% 131.65/19.54 | (95) sameside(all_230_4, all_230_5, all_230_4) = all_274_3
% 131.65/19.54 | (96) sameside(all_230_1, all_230_2, all_230_1) = all_274_1
% 131.65/19.54 |
% 131.65/19.54 | BETA: splitting (44) gives:
% 131.65/19.54 |
% 131.65/19.54 | Case 1:
% 131.65/19.54 | |
% 131.65/19.54 | | (97) all_226_2 = 0
% 131.65/19.54 | |
% 131.65/19.54 | | REDUCE: (24), (97) imply:
% 131.65/19.54 | | (98) $false
% 131.78/19.54 | |
% 131.78/19.54 | | CLOSE: (98) is inconsistent.
% 131.78/19.54 | |
% 131.78/19.54 | Case 2:
% 131.78/19.54 | |
% 131.78/19.54 | | (99) ? [v0: any] : ? [v1: any] : (sameside(gamma, alpha, beta) = v0 &
% 131.78/19.54 | | s_t(alpha, gamma, beta) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 131.78/19.54 | |
% 131.78/19.54 | | DELTA: instantiating (99) with fresh symbols all_346_0, all_346_1 gives:
% 131.78/19.54 | | (100) sameside(gamma, alpha, beta) = all_346_1 & s_t(alpha, gamma, beta)
% 131.78/19.54 | | = all_346_0 & ( ~ (all_346_1 = 0) | all_346_0 = 0)
% 131.78/19.54 | |
% 131.78/19.54 | | ALPHA: (100) implies:
% 131.78/19.54 | | (101) s_t(alpha, gamma, beta) = all_346_0
% 131.78/19.54 | | (102) sameside(gamma, alpha, beta) = all_346_1
% 131.78/19.54 | | (103) ~ (all_346_1 = 0) | all_346_0 = 0
% 131.78/19.54 | |
% 131.78/19.54 | | BETA: splitting (48) gives:
% 131.78/19.54 | |
% 131.78/19.54 | | Case 1:
% 131.78/19.54 | | |
% 131.78/19.54 | | | (104) all_226_0 = 0
% 131.78/19.54 | | |
% 131.78/19.54 | | | REDUCE: (26), (104) imply:
% 131.78/19.54 | | | (105) $false
% 131.78/19.54 | | |
% 131.78/19.54 | | | CLOSE: (105) is inconsistent.
% 131.78/19.54 | | |
% 131.78/19.54 | | Case 2:
% 131.78/19.54 | | |
% 131.78/19.55 | | | (106) ? [v0: any] : ? [v1: any] : (sameside(gamma, alpha, beta) = v0
% 131.78/19.55 | | | & s_col(gamma, alpha, beta) = v1 & ( ~ (v1 = 0) | v0 = 0))
% 131.78/19.55 | | |
% 131.78/19.55 | | | DELTA: instantiating (106) with fresh symbols all_356_0, all_356_1 gives:
% 131.78/19.55 | | | (107) sameside(gamma, alpha, beta) = all_356_1 & s_col(gamma, alpha,
% 131.78/19.55 | | | beta) = all_356_0 & ( ~ (all_356_0 = 0) | all_356_1 = 0)
% 131.78/19.55 | | |
% 131.78/19.55 | | | ALPHA: (107) implies:
% 131.78/19.55 | | | (108) sameside(gamma, alpha, beta) = all_356_1
% 131.78/19.55 | | | (109) ~ (all_356_0 = 0) | all_356_1 = 0
% 131.78/19.55 | | |
% 131.78/19.55 | | | BETA: splitting (46) gives:
% 131.78/19.55 | | |
% 131.78/19.55 | | | Case 1:
% 131.78/19.55 | | | |
% 131.78/19.55 | | | | (110) all_226_1 = 0
% 131.78/19.55 | | | |
% 131.78/19.55 | | | | REDUCE: (25), (110) imply:
% 131.78/19.55 | | | | (111) $false
% 131.78/19.55 | | | |
% 131.78/19.55 | | | | CLOSE: (111) is inconsistent.
% 131.78/19.55 | | | |
% 131.78/19.55 | | | Case 2:
% 131.78/19.55 | | | |
% 131.78/19.55 | | | | (112) ? [v0: int] : ( ~ (v0 = 0) & s_t(alpha, gamma, beta) = v0)
% 131.78/19.55 | | | |
% 131.78/19.55 | | | | DELTA: instantiating (112) with fresh symbol all_367_0 gives:
% 131.78/19.55 | | | | (113) ~ (all_367_0 = 0) & s_t(alpha, gamma, beta) = all_367_0
% 131.78/19.55 | | | |
% 131.78/19.55 | | | | ALPHA: (113) implies:
% 131.78/19.55 | | | | (114) ~ (all_367_0 = 0)
% 131.78/19.55 | | | | (115) s_t(alpha, gamma, beta) = all_367_0
% 131.78/19.55 | | | |
% 131.78/19.55 | | | | BETA: splitting (45) gives:
% 131.78/19.55 | | | |
% 131.78/19.55 | | | | Case 1:
% 131.78/19.55 | | | | |
% 131.78/19.55 | | | | | (116) all_226_2 = 0
% 131.78/19.55 | | | | |
% 131.78/19.55 | | | | | REDUCE: (24), (116) imply:
% 131.78/19.55 | | | | | (117) $false
% 131.78/19.55 | | | | |
% 131.78/19.55 | | | | | CLOSE: (117) is inconsistent.
% 131.78/19.55 | | | | |
% 131.78/19.55 | | | | Case 2:
% 131.78/19.55 | | | | |
% 131.78/19.55 | | | | | (118) ? [v0: any] : ? [v1: any] : (sameside(beta, alpha, gamma) =
% 131.78/19.55 | | | | | v0 & s_t(alpha, gamma, beta) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 131.78/19.55 | | | | |
% 131.78/19.55 | | | | | DELTA: instantiating (118) with fresh symbols all_387_0, all_387_1
% 131.78/19.55 | | | | | gives:
% 131.78/19.55 | | | | | (119) sameside(beta, alpha, gamma) = all_387_1 & s_t(alpha, gamma,
% 131.78/19.55 | | | | | beta) = all_387_0 & ( ~ (all_387_1 = 0) | all_387_0 = 0)
% 131.78/19.55 | | | | |
% 131.78/19.55 | | | | | ALPHA: (119) implies:
% 131.78/19.55 | | | | | (120) s_t(alpha, gamma, beta) = all_387_0
% 131.78/19.55 | | | | |
% 131.78/19.55 | | | | | BETA: splitting (47) gives:
% 131.78/19.55 | | | | |
% 131.78/19.55 | | | | | Case 1:
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | (121) all_226_1 = 0
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | REDUCE: (25), (121) imply:
% 131.78/19.55 | | | | | | (122) $false
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | CLOSE: (122) is inconsistent.
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | Case 2:
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (21) with all_230_0, all_272_0,
% 131.78/19.55 | | | | | | all_230_1, all_230_3, all_230_4, all_230_6, simplifying
% 131.78/19.55 | | | | | | with (38), (88) gives:
% 131.78/19.55 | | | | | | (123) all_272_0 = all_230_0
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (19) with all_367_0, all_387_0, beta,
% 131.78/19.55 | | | | | | gamma, alpha, simplifying with (115), (120) gives:
% 131.78/19.55 | | | | | | (124) all_387_0 = all_367_0
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (19) with all_346_0, all_387_0, beta,
% 131.78/19.55 | | | | | | gamma, alpha, simplifying with (101), (120) gives:
% 131.78/19.55 | | | | | | (125) all_387_0 = all_346_0
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (22) with all_240_0, all_266_3,
% 131.78/19.55 | | | | | | all_230_3, all_230_2, all_230_6, all_230_5, simplifying
% 131.78/19.55 | | | | | | with (61), (80) gives:
% 131.78/19.55 | | | | | | (126) all_266_3 = all_240_0
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (22) with all_242_0, all_266_2,
% 131.78/19.55 | | | | | | all_230_1, all_230_2, all_230_4, all_230_5, simplifying
% 131.78/19.55 | | | | | | with (64), (81) gives:
% 131.78/19.55 | | | | | | (127) all_266_2 = all_242_0
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (22) with all_244_0, all_266_1,
% 131.78/19.55 | | | | | | all_230_6, all_230_5, all_230_3, all_230_2, simplifying
% 131.78/19.55 | | | | | | with (67), (82) gives:
% 131.78/19.55 | | | | | | (128) all_266_1 = all_244_0
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (22) with all_238_0, all_266_0,
% 131.78/19.55 | | | | | | all_230_4, all_230_5, all_230_1, all_230_2, simplifying
% 131.78/19.55 | | | | | | with (58), (83) gives:
% 131.78/19.55 | | | | | | (129) all_266_0 = all_238_0
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (20) with all_346_1, all_356_1, beta,
% 131.78/19.55 | | | | | | alpha, gamma, simplifying with (102), (108) gives:
% 131.78/19.55 | | | | | | (130) all_356_1 = all_346_1
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (20) with all_268_4, all_272_4,
% 131.78/19.55 | | | | | | all_230_6, all_230_5, all_230_6, simplifying with (85),
% 131.78/19.55 | | | | | | (89) gives:
% 131.78/19.55 | | | | | | (131) all_272_4 = all_268_4
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (20) with all_260_2, all_272_4,
% 131.78/19.55 | | | | | | all_230_6, all_230_5, all_230_6, simplifying with (73),
% 131.78/19.55 | | | | | | (89) gives:
% 131.78/19.55 | | | | | | (132) all_272_4 = all_260_2
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (20) with all_272_3, all_274_3,
% 131.78/19.55 | | | | | | all_230_4, all_230_5, all_230_4, simplifying with (90),
% 131.78/19.55 | | | | | | (95) gives:
% 131.78/19.55 | | | | | | (133) all_274_3 = all_272_3
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (20) with all_254_2, all_274_3,
% 131.78/19.55 | | | | | | all_230_4, all_230_5, all_230_4, simplifying with (70),
% 131.78/19.55 | | | | | | (95) gives:
% 131.78/19.55 | | | | | | (134) all_274_3 = all_254_2
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (20) with all_268_2, all_272_2,
% 131.78/19.55 | | | | | | all_230_3, all_230_2, all_230_3, simplifying with (86),
% 131.78/19.55 | | | | | | (91) gives:
% 131.78/19.55 | | | | | | (135) all_272_2 = all_268_2
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (20) with all_260_1, all_272_2,
% 131.78/19.55 | | | | | | all_230_3, all_230_2, all_230_3, simplifying with (74),
% 131.78/19.55 | | | | | | (91) gives:
% 131.78/19.55 | | | | | | (136) all_272_2 = all_260_1
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (20) with all_272_1, all_274_1,
% 131.78/19.55 | | | | | | all_230_1, all_230_2, all_230_1, simplifying with (92),
% 131.78/19.55 | | | | | | (96) gives:
% 131.78/19.55 | | | | | | (137) all_274_1 = all_272_1
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | GROUND_INST: instantiating (20) with all_254_1, all_274_1,
% 131.78/19.55 | | | | | | all_230_1, all_230_2, all_230_1, simplifying with (71),
% 131.78/19.55 | | | | | | (96) gives:
% 131.78/19.55 | | | | | | (138) all_274_1 = all_254_1
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | COMBINE_EQS: (124), (125) imply:
% 131.78/19.55 | | | | | | (139) all_367_0 = all_346_0
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | SIMP: (139) implies:
% 131.78/19.55 | | | | | | (140) all_367_0 = all_346_0
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | COMBINE_EQS: (137), (138) imply:
% 131.78/19.55 | | | | | | (141) all_272_1 = all_254_1
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | COMBINE_EQS: (133), (134) imply:
% 131.78/19.55 | | | | | | (142) all_272_3 = all_254_2
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | SIMP: (142) implies:
% 131.78/19.55 | | | | | | (143) all_272_3 = all_254_2
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | COMBINE_EQS: (135), (136) imply:
% 131.78/19.55 | | | | | | (144) all_268_2 = all_260_1
% 131.78/19.55 | | | | | |
% 131.78/19.55 | | | | | | SIMP: (144) implies:
% 131.78/19.55 | | | | | | (145) all_268_2 = all_260_1
% 131.78/19.56 | | | | | |
% 131.78/19.56 | | | | | | COMBINE_EQS: (131), (132) imply:
% 131.78/19.56 | | | | | | (146) all_268_4 = all_260_2
% 131.78/19.56 | | | | | |
% 131.78/19.56 | | | | | | SIMP: (146) implies:
% 131.78/19.56 | | | | | | (147) all_268_4 = all_260_2
% 131.78/19.56 | | | | | |
% 131.78/19.56 | | | | | | REDUCE: (114), (140) imply:
% 131.78/19.56 | | | | | | (148) ~ (all_346_0 = 0)
% 131.78/19.56 | | | | | |
% 131.78/19.56 | | | | | | REDUCE: (79), (129) imply:
% 131.78/19.56 | | | | | | (149) $i(all_238_0)
% 131.78/19.56 | | | | | |
% 131.78/19.56 | | | | | | REDUCE: (78), (128) imply:
% 131.78/19.56 | | | | | | (150) $i(all_244_0)
% 131.78/19.56 | | | | | |
% 131.78/19.56 | | | | | | REDUCE: (77), (127) imply:
% 131.78/19.56 | | | | | | (151) $i(all_242_0)
% 131.78/19.56 | | | | | |
% 131.78/19.56 | | | | | | REDUCE: (76), (126) imply:
% 131.78/19.56 | | | | | | (152) $i(all_240_0)
% 131.78/19.56 | | | | | |
% 131.78/19.56 | | | | | | BETA: splitting (103) gives:
% 131.78/19.56 | | | | | |
% 131.78/19.56 | | | | | | Case 1:
% 131.78/19.56 | | | | | | |
% 131.78/19.56 | | | | | | | (153) ~ (all_346_1 = 0)
% 131.78/19.56 | | | | | | |
% 131.78/19.56 | | | | | | | BETA: splitting (109) gives:
% 131.78/19.56 | | | | | | |
% 131.78/19.56 | | | | | | | Case 1:
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | | GROUND_INST: instantiating (aSatz6_5) with all_230_6, all_230_5,
% 131.78/19.56 | | | | | | | | all_260_2, simplifying with (32), (33), (73) gives:
% 131.78/19.56 | | | | | | | | (154) all_260_2 = 0 | all_230_5 = all_230_6
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | | GROUND_INST: instantiating (aSatz6_5) with all_230_4, all_230_5,
% 131.78/19.56 | | | | | | | | all_254_2, simplifying with (33), (34), (70) gives:
% 131.78/19.56 | | | | | | | | (155) all_254_2 = 0 | all_230_4 = all_230_5
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | | GROUND_INST: instantiating (aSatz6_5) with all_230_3, all_230_2,
% 131.78/19.56 | | | | | | | | all_260_1, simplifying with (35), (36), (74) gives:
% 131.78/19.56 | | | | | | | | (156) all_260_1 = 0 | all_230_2 = all_230_3
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | | GROUND_INST: instantiating (aSatz6_5) with all_230_1, all_230_2,
% 131.78/19.56 | | | | | | | | all_254_1, simplifying with (36), (37), (71) gives:
% 131.78/19.56 | | | | | | | | (157) all_254_1 = 0 | all_230_1 = all_230_2
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | | GROUND_INST: instantiating (7) with all_230_1, all_230_2,
% 131.78/19.56 | | | | | | | | all_238_0, all_230_1, all_254_1, simplifying with
% 131.78/19.56 | | | | | | | | (36), (37), (59), (71), (149) gives:
% 131.78/19.56 | | | | | | | | (158) all_254_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 131.78/19.56 | | | | | | | | sameside(all_230_1, all_230_2, all_238_0) = v0)
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | | GROUND_INST: instantiating (6) with all_238_0, all_230_2,
% 131.78/19.56 | | | | | | | | all_230_1, simplifying with (36), (37), (59), (149)
% 131.78/19.56 | | | | | | | | gives:
% 131.78/19.56 | | | | | | | | (159) sameside(all_230_1, all_230_2, all_238_0) = 0
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | | GROUND_INST: instantiating (7) with all_230_6, all_230_5,
% 131.78/19.56 | | | | | | | | all_240_0, all_230_6, all_260_2, simplifying with
% 131.78/19.56 | | | | | | | | (32), (33), (62), (73), (152) gives:
% 131.78/19.56 | | | | | | | | (160) all_260_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 131.78/19.56 | | | | | | | | sameside(all_230_6, all_230_5, all_240_0) = v0)
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | | GROUND_INST: instantiating (6) with all_240_0, all_230_5,
% 131.78/19.56 | | | | | | | | all_230_6, simplifying with (32), (33), (62), (152)
% 131.78/19.56 | | | | | | | | gives:
% 131.78/19.56 | | | | | | | | (161) sameside(all_230_6, all_230_5, all_240_0) = 0
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | | GROUND_INST: instantiating (7) with all_230_4, all_230_5,
% 131.78/19.56 | | | | | | | | all_242_0, all_230_4, all_254_2, simplifying with
% 131.78/19.56 | | | | | | | | (33), (34), (65), (70), (151) gives:
% 131.78/19.56 | | | | | | | | (162) all_254_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 131.78/19.56 | | | | | | | | sameside(all_230_4, all_230_5, all_242_0) = v0)
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | | GROUND_INST: instantiating (6) with all_242_0, all_230_5,
% 131.78/19.56 | | | | | | | | all_230_4, simplifying with (33), (34), (65), (151)
% 131.78/19.56 | | | | | | | | gives:
% 131.78/19.56 | | | | | | | | (163) sameside(all_230_4, all_230_5, all_242_0) = 0
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | | GROUND_INST: instantiating (7) with all_230_3, all_230_2,
% 131.78/19.56 | | | | | | | | all_244_0, all_230_3, all_260_1, simplifying with
% 131.78/19.56 | | | | | | | | (35), (36), (68), (74), (150) gives:
% 131.78/19.56 | | | | | | | | (164) all_260_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 131.78/19.56 | | | | | | | | sameside(all_230_3, all_230_2, all_244_0) = v0)
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | | GROUND_INST: instantiating (6) with all_244_0, all_230_2,
% 131.78/19.56 | | | | | | | | all_230_3, simplifying with (35), (36), (68), (150)
% 131.78/19.56 | | | | | | | | gives:
% 131.78/19.56 | | | | | | | | (165) sameside(all_230_3, all_230_2, all_244_0) = 0
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | | BETA: splitting (160) gives:
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | | Case 1:
% 131.78/19.56 | | | | | | | | |
% 131.78/19.56 | | | | | | | | | (166) all_260_2 = 0
% 131.78/19.56 | | | | | | | | |
% 131.78/19.56 | | | | | | | | | COMBINE_EQS: (132), (166) imply:
% 131.78/19.56 | | | | | | | | | (167) all_272_4 = 0
% 131.78/19.56 | | | | | | | | |
% 131.78/19.56 | | | | | | | | | REF_CLOSE: (20), (31), (93), (123), (136), (141), (143),
% 131.78/19.56 | | | | | | | | | (155), (156), (157), (158), (159), (162), (163),
% 131.78/19.56 | | | | | | | | | (164), (165), (167) are inconsistent by sub-proof
% 131.78/19.56 | | | | | | | | | #1.
% 131.78/19.56 | | | | | | | | |
% 131.78/19.56 | | | | | | | | Case 2:
% 131.78/19.56 | | | | | | | | |
% 131.78/19.56 | | | | | | | | | (168) ? [v0: int] : ( ~ (v0 = 0) & sameside(all_230_6,
% 131.78/19.56 | | | | | | | | | all_230_5, all_240_0) = v0)
% 131.78/19.56 | | | | | | | | |
% 131.78/19.56 | | | | | | | | | DELTA: instantiating (168) with fresh symbol all_1329_0 gives:
% 131.78/19.56 | | | | | | | | | (169) ~ (all_1329_0 = 0) & sameside(all_230_6, all_230_5,
% 131.78/19.56 | | | | | | | | | all_240_0) = all_1329_0
% 131.78/19.56 | | | | | | | | |
% 131.78/19.56 | | | | | | | | | ALPHA: (169) implies:
% 131.78/19.56 | | | | | | | | | (170) ~ (all_1329_0 = 0)
% 131.78/19.56 | | | | | | | | | (171) sameside(all_230_6, all_230_5, all_240_0) =
% 131.78/19.56 | | | | | | | | | all_1329_0
% 131.78/19.56 | | | | | | | | |
% 131.78/19.56 | | | | | | | | | BETA: splitting (154) gives:
% 131.78/19.56 | | | | | | | | |
% 131.78/19.56 | | | | | | | | | Case 1:
% 131.78/19.56 | | | | | | | | | |
% 131.78/19.56 | | | | | | | | | | (172) all_260_2 = 0
% 131.78/19.56 | | | | | | | | | |
% 131.78/19.56 | | | | | | | | | | COMBINE_EQS: (132), (172) imply:
% 131.78/19.56 | | | | | | | | | | (173) all_272_4 = 0
% 131.78/19.56 | | | | | | | | | |
% 131.78/19.56 | | | | | | | | | | REF_CLOSE: (20), (31), (93), (123), (136), (141), (143),
% 131.78/19.56 | | | | | | | | | | (155), (156), (157), (158), (159), (162), (163),
% 131.78/19.56 | | | | | | | | | | (164), (165), (173) are inconsistent by sub-proof
% 131.78/19.56 | | | | | | | | | | #1.
% 131.78/19.56 | | | | | | | | | |
% 131.78/19.56 | | | | | | | | | Case 2:
% 131.78/19.56 | | | | | | | | | |
% 131.78/19.56 | | | | | | | | | | (174) all_230_5 = all_230_6
% 131.78/19.56 | | | | | | | | | |
% 131.78/19.56 | | | | | | | | | | REDUCE: (171), (174) imply:
% 131.78/19.56 | | | | | | | | | | (175) sameside(all_230_6, all_230_6, all_240_0) =
% 131.78/19.56 | | | | | | | | | | all_1329_0
% 131.78/19.56 | | | | | | | | | |
% 131.78/19.56 | | | | | | | | | | REDUCE: (161), (174) imply:
% 131.78/19.56 | | | | | | | | | | (176) sameside(all_230_6, all_230_6, all_240_0) = 0
% 131.78/19.56 | | | | | | | | | |
% 131.78/19.56 | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1329_0, all_240_0,
% 131.78/19.56 | | | | | | | | | | all_230_6, all_230_6, simplifying with (175),
% 131.78/19.56 | | | | | | | | | | (176) gives:
% 131.78/19.56 | | | | | | | | | | (177) all_1329_0 = 0
% 131.78/19.56 | | | | | | | | | |
% 131.78/19.56 | | | | | | | | | | REDUCE: (170), (177) imply:
% 131.78/19.56 | | | | | | | | | | (178) $false
% 131.78/19.56 | | | | | | | | | |
% 131.78/19.56 | | | | | | | | | | CLOSE: (178) is inconsistent.
% 131.78/19.56 | | | | | | | | | |
% 131.78/19.56 | | | | | | | | | End of split
% 131.78/19.56 | | | | | | | | |
% 131.78/19.56 | | | | | | | | End of split
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | Case 2:
% 131.78/19.56 | | | | | | | |
% 131.78/19.56 | | | | | | | | (179) all_356_1 = 0
% 131.78/19.56 | | | | | | | |
% 131.78/19.57 | | | | | | | | COMBINE_EQS: (130), (179) imply:
% 131.78/19.57 | | | | | | | | (180) all_346_1 = 0
% 131.78/19.57 | | | | | | | |
% 131.78/19.57 | | | | | | | | SIMP: (180) implies:
% 131.78/19.57 | | | | | | | | (181) all_346_1 = 0
% 131.78/19.57 | | | | | | | |
% 131.78/19.57 | | | | | | | | REDUCE: (153), (181) imply:
% 131.78/19.57 | | | | | | | | (182) $false
% 131.78/19.57 | | | | | | | |
% 131.78/19.57 | | | | | | | | CLOSE: (182) is inconsistent.
% 131.78/19.57 | | | | | | | |
% 131.78/19.57 | | | | | | | End of split
% 131.78/19.57 | | | | | | |
% 131.78/19.57 | | | | | | Case 2:
% 131.78/19.57 | | | | | | |
% 131.78/19.57 | | | | | | | (183) all_346_0 = 0
% 131.78/19.57 | | | | | | |
% 131.78/19.57 | | | | | | | REDUCE: (148), (183) imply:
% 131.78/19.57 | | | | | | | (184) $false
% 131.78/19.57 | | | | | | |
% 131.78/19.57 | | | | | | | CLOSE: (184) is inconsistent.
% 131.78/19.57 | | | | | | |
% 131.78/19.57 | | | | | | End of split
% 131.78/19.57 | | | | | |
% 131.78/19.57 | | | | | End of split
% 131.78/19.57 | | | | |
% 131.78/19.57 | | | | End of split
% 131.78/19.57 | | | |
% 131.78/19.57 | | | End of split
% 131.78/19.57 | | |
% 131.78/19.57 | | End of split
% 131.78/19.57 | |
% 131.78/19.57 | End of split
% 131.78/19.57 |
% 131.78/19.57 End of proof
% 131.78/19.57
% 131.78/19.57 Sub-proof #1 shows that the following formulas are inconsistent:
% 131.78/19.57 ----------------------------------------------------------------
% 131.78/19.57 (1) all_272_1 = all_254_1
% 131.78/19.57 (2) all_254_2 = 0 | all_230_4 = all_230_5
% 131.78/19.57 (3) all_254_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) & sameside(all_230_4,
% 131.78/19.57 all_230_5, all_242_0) = v0)
% 131.78/19.57 (4) ~ (all_230_0 = 0)
% 131.78/19.57 (5) all_272_3 = all_254_2
% 131.78/19.57 (6) all_272_4 = 0
% 131.78/19.57 (7) all_260_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & sameside(all_230_3,
% 131.78/19.57 all_230_2, all_244_0) = v0)
% 131.78/19.57 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 131.78/19.57 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sameside(v4, v3, v2) = v1) | ~
% 131.78/19.57 (sameside(v4, v3, v2) = v0))
% 131.78/19.57 (9) sameside(all_230_4, all_230_5, all_242_0) = 0
% 131.78/19.57 (10) sameside(all_230_3, all_230_2, all_244_0) = 0
% 131.78/19.57 (11) all_272_2 = all_260_1
% 131.78/19.57 (12) all_272_0 = all_230_0
% 131.78/19.57 (13) sameside(all_230_1, all_230_2, all_238_0) = 0
% 131.78/19.57 (14) all_254_1 = 0 | all_230_1 = all_230_2
% 131.78/19.57 (15) all_254_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & sameside(all_230_1,
% 131.78/19.57 all_230_2, all_238_0) = v0)
% 131.78/19.57 (16) all_260_1 = 0 | all_230_2 = all_230_3
% 131.78/19.57 (17) ~ (all_272_1 = 0) | ~ (all_272_2 = 0) | ~ (all_272_3 = 0) | ~
% 131.78/19.57 (all_272_4 = 0) | all_272_0 = 0
% 131.78/19.57
% 131.78/19.57 Begin of proof
% 131.78/19.57 |
% 131.78/19.57 | BETA: splitting (15) gives:
% 131.78/19.57 |
% 131.78/19.57 | Case 1:
% 131.78/19.57 | |
% 131.78/19.57 | | (18) all_254_1 = 0
% 131.78/19.57 | |
% 131.78/19.57 | | COMBINE_EQS: (1), (18) imply:
% 131.78/19.57 | | (19) all_272_1 = 0
% 131.78/19.57 | |
% 131.78/19.57 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (16),
% 131.78/19.57 | | (17), (19) are inconsistent by sub-proof #2.
% 131.78/19.57 | |
% 131.78/19.57 | Case 2:
% 131.78/19.57 | |
% 131.78/19.57 | | (20) ? [v0: int] : ( ~ (v0 = 0) & sameside(all_230_1, all_230_2,
% 131.78/19.57 | | all_238_0) = v0)
% 131.78/19.57 | |
% 131.78/19.57 | | DELTA: instantiating (20) with fresh symbol all_1446_0 gives:
% 131.78/19.57 | | (21) ~ (all_1446_0 = 0) & sameside(all_230_1, all_230_2, all_238_0) =
% 131.78/19.57 | | all_1446_0
% 131.78/19.57 | |
% 131.78/19.57 | | ALPHA: (21) implies:
% 131.78/19.57 | | (22) ~ (all_1446_0 = 0)
% 131.78/19.57 | | (23) sameside(all_230_1, all_230_2, all_238_0) = all_1446_0
% 131.78/19.57 | |
% 131.78/19.57 | | BETA: splitting (14) gives:
% 131.78/19.57 | |
% 131.78/19.57 | | Case 1:
% 131.78/19.57 | | |
% 131.78/19.57 | | | (24) all_254_1 = 0
% 131.78/19.57 | | |
% 131.78/19.57 | | | COMBINE_EQS: (1), (24) imply:
% 131.78/19.57 | | | (25) all_272_1 = 0
% 131.78/19.57 | | |
% 131.78/19.57 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (16),
% 131.78/19.57 | | | (17), (25) are inconsistent by sub-proof #2.
% 131.78/19.57 | | |
% 131.78/19.57 | | Case 2:
% 131.78/19.57 | | |
% 131.78/19.57 | | | (26) all_230_1 = all_230_2
% 131.78/19.57 | | |
% 131.78/19.57 | | | REDUCE: (23), (26) imply:
% 131.78/19.57 | | | (27) sameside(all_230_2, all_230_2, all_238_0) = all_1446_0
% 131.78/19.57 | | |
% 131.78/19.57 | | | REDUCE: (13), (26) imply:
% 131.78/19.57 | | | (28) sameside(all_230_2, all_230_2, all_238_0) = 0
% 131.78/19.57 | | |
% 131.78/19.57 | | | GROUND_INST: instantiating (8) with 0, all_1446_0, all_238_0, all_230_2,
% 131.78/19.57 | | | all_230_2, simplifying with (27), (28) gives:
% 131.78/19.57 | | | (29) all_1446_0 = 0
% 131.78/19.57 | | |
% 131.78/19.57 | | | REDUCE: (22), (29) imply:
% 131.78/19.57 | | | (30) $false
% 131.78/19.57 | | |
% 131.78/19.57 | | | CLOSE: (30) is inconsistent.
% 131.78/19.57 | | |
% 131.78/19.57 | | End of split
% 131.78/19.57 | |
% 131.78/19.57 | End of split
% 131.78/19.57 |
% 131.78/19.57 End of proof
% 131.78/19.57
% 131.78/19.57 Sub-proof #2 shows that the following formulas are inconsistent:
% 131.78/19.57 ----------------------------------------------------------------
% 131.78/19.57 (1) all_254_2 = 0 | all_230_4 = all_230_5
% 131.78/19.57 (2) all_254_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) & sameside(all_230_4,
% 131.78/19.57 all_230_5, all_242_0) = v0)
% 131.78/19.57 (3) ~ (all_230_0 = 0)
% 131.78/19.57 (4) all_272_1 = 0
% 131.78/19.57 (5) all_272_3 = all_254_2
% 131.78/19.57 (6) all_272_4 = 0
% 131.78/19.57 (7) all_260_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & sameside(all_230_3,
% 131.78/19.57 all_230_2, all_244_0) = v0)
% 131.78/19.57 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 131.78/19.57 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sameside(v4, v3, v2) = v1) | ~
% 131.78/19.57 (sameside(v4, v3, v2) = v0))
% 131.78/19.57 (9) sameside(all_230_4, all_230_5, all_242_0) = 0
% 131.78/19.57 (10) sameside(all_230_3, all_230_2, all_244_0) = 0
% 131.78/19.57 (11) all_272_2 = all_260_1
% 131.78/19.57 (12) all_272_0 = all_230_0
% 131.78/19.57 (13) all_260_1 = 0 | all_230_2 = all_230_3
% 131.78/19.57 (14) ~ (all_272_1 = 0) | ~ (all_272_2 = 0) | ~ (all_272_3 = 0) | ~
% 131.78/19.57 (all_272_4 = 0) | all_272_0 = 0
% 131.78/19.57
% 131.78/19.57 Begin of proof
% 131.78/19.57 |
% 131.78/19.57 | BETA: splitting (2) gives:
% 131.78/19.57 |
% 131.78/19.57 | Case 1:
% 131.78/19.57 | |
% 131.78/19.57 | | (15) all_254_2 = 0
% 131.78/19.57 | |
% 131.78/19.57 | | COMBINE_EQS: (5), (15) imply:
% 131.78/19.57 | | (16) all_272_3 = 0
% 131.78/19.57 | |
% 131.78/19.57 | | REF_CLOSE: (3), (4), (6), (7), (8), (10), (11), (12), (13), (14), (16) are
% 131.78/19.57 | | inconsistent by sub-proof #3.
% 131.78/19.57 | |
% 131.78/19.57 | Case 2:
% 131.78/19.57 | |
% 131.78/19.57 | | (17) ? [v0: int] : ( ~ (v0 = 0) & sameside(all_230_4, all_230_5,
% 131.78/19.57 | | all_242_0) = v0)
% 131.78/19.57 | |
% 131.78/19.57 | | DELTA: instantiating (17) with fresh symbol all_1506_0 gives:
% 131.78/19.57 | | (18) ~ (all_1506_0 = 0) & sameside(all_230_4, all_230_5, all_242_0) =
% 131.78/19.57 | | all_1506_0
% 131.78/19.57 | |
% 131.78/19.57 | | ALPHA: (18) implies:
% 131.78/19.57 | | (19) ~ (all_1506_0 = 0)
% 131.78/19.57 | | (20) sameside(all_230_4, all_230_5, all_242_0) = all_1506_0
% 131.78/19.57 | |
% 131.78/19.57 | | BETA: splitting (1) gives:
% 131.78/19.57 | |
% 131.78/19.57 | | Case 1:
% 131.78/19.57 | | |
% 131.78/19.57 | | | (21) all_254_2 = 0
% 131.78/19.57 | | |
% 131.78/19.57 | | | COMBINE_EQS: (5), (21) imply:
% 131.78/19.57 | | | (22) all_272_3 = 0
% 131.78/19.57 | | |
% 131.78/19.58 | | | REF_CLOSE: (3), (4), (6), (7), (8), (10), (11), (12), (13), (14), (22) are
% 131.78/19.58 | | | inconsistent by sub-proof #3.
% 131.78/19.58 | | |
% 131.78/19.58 | | Case 2:
% 131.78/19.58 | | |
% 131.78/19.58 | | | (23) all_230_4 = all_230_5
% 131.78/19.58 | | |
% 131.78/19.58 | | | REDUCE: (20), (23) imply:
% 131.78/19.58 | | | (24) sameside(all_230_5, all_230_5, all_242_0) = all_1506_0
% 131.78/19.58 | | |
% 131.78/19.58 | | | REDUCE: (9), (23) imply:
% 131.78/19.58 | | | (25) sameside(all_230_5, all_230_5, all_242_0) = 0
% 131.78/19.58 | | |
% 131.78/19.58 | | | GROUND_INST: instantiating (8) with 0, all_1506_0, all_242_0, all_230_5,
% 131.78/19.58 | | | all_230_5, simplifying with (24), (25) gives:
% 131.78/19.58 | | | (26) all_1506_0 = 0
% 131.78/19.58 | | |
% 131.78/19.58 | | | REDUCE: (19), (26) imply:
% 131.78/19.58 | | | (27) $false
% 131.78/19.58 | | |
% 131.78/19.58 | | | CLOSE: (27) is inconsistent.
% 131.78/19.58 | | |
% 131.78/19.58 | | End of split
% 131.78/19.58 | |
% 131.78/19.58 | End of split
% 131.78/19.58 |
% 131.78/19.58 End of proof
% 131.78/19.58
% 131.78/19.58 Sub-proof #3 shows that the following formulas are inconsistent:
% 131.78/19.58 ----------------------------------------------------------------
% 131.78/19.58 (1) ~ (all_230_0 = 0)
% 131.78/19.58 (2) all_272_1 = 0
% 131.78/19.58 (3) all_272_4 = 0
% 131.78/19.58 (4) all_260_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & sameside(all_230_3,
% 131.78/19.58 all_230_2, all_244_0) = v0)
% 131.78/19.58 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 131.78/19.58 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sameside(v4, v3, v2) = v1) | ~
% 131.78/19.58 (sameside(v4, v3, v2) = v0))
% 131.78/19.58 (6) sameside(all_230_3, all_230_2, all_244_0) = 0
% 131.78/19.58 (7) all_272_2 = all_260_1
% 131.78/19.58 (8) all_272_0 = all_230_0
% 131.78/19.58 (9) all_260_1 = 0 | all_230_2 = all_230_3
% 131.78/19.58 (10) ~ (all_272_1 = 0) | ~ (all_272_2 = 0) | ~ (all_272_3 = 0) | ~
% 131.78/19.58 (all_272_4 = 0) | all_272_0 = 0
% 131.78/19.58 (11) all_272_3 = 0
% 131.78/19.58
% 131.78/19.58 Begin of proof
% 131.78/19.58 |
% 131.78/19.58 | BETA: splitting (10) gives:
% 131.78/19.58 |
% 131.78/19.58 | Case 1:
% 131.78/19.58 | |
% 131.78/19.58 | | (12) ~ (all_272_1 = 0)
% 131.78/19.58 | |
% 131.78/19.58 | | REDUCE: (2), (12) imply:
% 131.78/19.58 | | (13) $false
% 131.78/19.58 | |
% 131.78/19.58 | | CLOSE: (13) is inconsistent.
% 131.78/19.58 | |
% 131.78/19.58 | Case 2:
% 131.78/19.58 | |
% 131.78/19.58 | | (14) ~ (all_272_2 = 0) | ~ (all_272_3 = 0) | ~ (all_272_4 = 0) |
% 131.78/19.58 | | all_272_0 = 0
% 131.78/19.58 | |
% 131.78/19.58 | | BETA: splitting (4) gives:
% 131.78/19.58 | |
% 131.78/19.58 | | Case 1:
% 131.78/19.58 | | |
% 131.78/19.58 | | | (15) all_260_1 = 0
% 131.78/19.58 | | |
% 131.78/19.58 | | | COMBINE_EQS: (7), (15) imply:
% 131.78/19.58 | | | (16) all_272_2 = 0
% 131.78/19.58 | | |
% 131.78/19.58 | | | BETA: splitting (14) gives:
% 131.78/19.58 | | |
% 131.78/19.58 | | | Case 1:
% 131.78/19.58 | | | |
% 131.78/19.58 | | | | (17) ~ (all_272_2 = 0)
% 131.78/19.58 | | | |
% 131.78/19.58 | | | | REDUCE: (16), (17) imply:
% 131.78/19.58 | | | | (18) $false
% 131.78/19.58 | | | |
% 131.78/19.58 | | | | CLOSE: (18) is inconsistent.
% 131.78/19.58 | | | |
% 131.78/19.58 | | | Case 2:
% 131.78/19.58 | | | |
% 131.78/19.58 | | | | (19) ~ (all_272_3 = 0) | ~ (all_272_4 = 0) | all_272_0 = 0
% 131.78/19.58 | | | |
% 131.78/19.58 | | | | BETA: splitting (19) gives:
% 131.78/19.58 | | | |
% 131.78/19.58 | | | | Case 1:
% 131.78/19.58 | | | | |
% 131.78/19.58 | | | | | (20) ~ (all_272_3 = 0)
% 131.78/19.58 | | | | |
% 131.78/19.58 | | | | | REDUCE: (11), (20) imply:
% 131.78/19.58 | | | | | (21) $false
% 131.78/19.58 | | | | |
% 131.78/19.58 | | | | | CLOSE: (21) is inconsistent.
% 131.78/19.58 | | | | |
% 131.78/19.58 | | | | Case 2:
% 131.78/19.58 | | | | |
% 131.78/19.58 | | | | | (22) ~ (all_272_4 = 0) | all_272_0 = 0
% 131.78/19.58 | | | | |
% 131.78/19.58 | | | | | BETA: splitting (22) gives:
% 131.78/19.58 | | | | |
% 131.78/19.58 | | | | | Case 1:
% 131.78/19.58 | | | | | |
% 131.78/19.58 | | | | | | (23) ~ (all_272_4 = 0)
% 131.78/19.58 | | | | | |
% 131.78/19.58 | | | | | | REDUCE: (3), (23) imply:
% 131.78/19.58 | | | | | | (24) $false
% 131.78/19.58 | | | | | |
% 131.78/19.58 | | | | | | CLOSE: (24) is inconsistent.
% 131.78/19.58 | | | | | |
% 131.78/19.58 | | | | | Case 2:
% 131.78/19.58 | | | | | |
% 131.78/19.58 | | | | | | (25) all_272_0 = 0
% 131.78/19.58 | | | | | |
% 131.78/19.58 | | | | | | COMBINE_EQS: (8), (25) imply:
% 131.78/19.58 | | | | | | (26) all_230_0 = 0
% 131.78/19.58 | | | | | |
% 131.78/19.58 | | | | | | REDUCE: (1), (26) imply:
% 131.78/19.58 | | | | | | (27) $false
% 131.78/19.58 | | | | | |
% 131.78/19.58 | | | | | | CLOSE: (27) is inconsistent.
% 131.78/19.58 | | | | | |
% 131.78/19.58 | | | | | End of split
% 131.78/19.58 | | | | |
% 131.78/19.58 | | | | End of split
% 131.78/19.58 | | | |
% 131.78/19.58 | | | End of split
% 131.78/19.58 | | |
% 131.78/19.58 | | Case 2:
% 131.78/19.58 | | |
% 131.78/19.58 | | | (28) ~ (all_260_1 = 0)
% 131.78/19.58 | | | (29) ? [v0: int] : ( ~ (v0 = 0) & sameside(all_230_3, all_230_2,
% 131.78/19.58 | | | all_244_0) = v0)
% 131.78/19.58 | | |
% 131.78/19.58 | | | DELTA: instantiating (29) with fresh symbol all_1556_0 gives:
% 131.78/19.58 | | | (30) ~ (all_1556_0 = 0) & sameside(all_230_3, all_230_2, all_244_0) =
% 131.78/19.58 | | | all_1556_0
% 131.78/19.58 | | |
% 131.78/19.58 | | | ALPHA: (30) implies:
% 131.78/19.58 | | | (31) ~ (all_1556_0 = 0)
% 131.78/19.58 | | | (32) sameside(all_230_3, all_230_2, all_244_0) = all_1556_0
% 131.78/19.58 | | |
% 131.78/19.58 | | | BETA: splitting (9) gives:
% 131.78/19.58 | | |
% 131.78/19.58 | | | Case 1:
% 131.78/19.58 | | | |
% 131.78/19.58 | | | | (33) all_260_1 = 0
% 131.78/19.58 | | | |
% 131.78/19.58 | | | | REDUCE: (28), (33) imply:
% 131.78/19.58 | | | | (34) $false
% 131.78/19.58 | | | |
% 131.78/19.58 | | | | CLOSE: (34) is inconsistent.
% 131.78/19.58 | | | |
% 131.78/19.58 | | | Case 2:
% 131.78/19.58 | | | |
% 131.78/19.58 | | | | (35) all_230_2 = all_230_3
% 131.78/19.58 | | | |
% 131.78/19.58 | | | | REDUCE: (32), (35) imply:
% 131.78/19.58 | | | | (36) sameside(all_230_3, all_230_3, all_244_0) = all_1556_0
% 131.78/19.58 | | | |
% 131.78/19.58 | | | | REDUCE: (6), (35) imply:
% 131.78/19.58 | | | | (37) sameside(all_230_3, all_230_3, all_244_0) = 0
% 131.78/19.58 | | | |
% 131.78/19.58 | | | | GROUND_INST: instantiating (5) with 0, all_1556_0, all_244_0, all_230_3,
% 131.78/19.58 | | | | all_230_3, simplifying with (36), (37) gives:
% 131.78/19.58 | | | | (38) all_1556_0 = 0
% 131.78/19.58 | | | |
% 131.78/19.58 | | | | REDUCE: (31), (38) imply:
% 131.78/19.58 | | | | (39) $false
% 131.78/19.58 | | | |
% 131.78/19.58 | | | | CLOSE: (39) is inconsistent.
% 131.78/19.58 | | | |
% 131.78/19.58 | | | End of split
% 131.78/19.58 | | |
% 131.78/19.58 | | End of split
% 131.78/19.58 | |
% 131.78/19.58 | End of split
% 131.78/19.58 |
% 131.78/19.58 End of proof
% 131.78/19.58 % SZS output end Proof for theBenchmark
% 131.78/19.58
% 131.78/19.58 18976ms
%------------------------------------------------------------------------------