TSTP Solution File: NUM396+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM396+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:47:34 EDT 2023
% Result : Theorem 98.48s 13.90s
% Output : Proof 100.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM396+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 07:34:20 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.55/1.16 Prover 1: Preprocessing ...
% 2.55/1.16 Prover 4: Preprocessing ...
% 3.26/1.20 Prover 6: Preprocessing ...
% 3.26/1.20 Prover 0: Preprocessing ...
% 3.26/1.20 Prover 5: Preprocessing ...
% 3.26/1.20 Prover 2: Preprocessing ...
% 3.26/1.20 Prover 3: Preprocessing ...
% 6.64/1.75 Prover 1: Warning: ignoring some quantifiers
% 6.64/1.78 Prover 5: Proving ...
% 7.23/1.79 Prover 2: Proving ...
% 7.23/1.80 Prover 1: Constructing countermodel ...
% 7.23/1.82 Prover 3: Warning: ignoring some quantifiers
% 7.23/1.84 Prover 3: Constructing countermodel ...
% 7.23/1.85 Prover 6: Proving ...
% 8.09/1.89 Prover 4: Warning: ignoring some quantifiers
% 8.09/1.91 Prover 0: Proving ...
% 8.31/1.93 Prover 4: Constructing countermodel ...
% 10.99/2.38 Prover 3: gave up
% 10.99/2.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.72/2.46 Prover 7: Preprocessing ...
% 11.72/2.46 Prover 1: gave up
% 11.72/2.48 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.36/2.51 Prover 8: Preprocessing ...
% 12.36/2.55 Prover 7: Warning: ignoring some quantifiers
% 12.36/2.56 Prover 7: Constructing countermodel ...
% 13.16/2.68 Prover 8: Warning: ignoring some quantifiers
% 13.81/2.71 Prover 8: Constructing countermodel ...
% 18.30/3.29 Prover 8: gave up
% 18.34/3.30 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 18.34/3.37 Prover 7: gave up
% 18.34/3.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 18.34/3.38 Prover 9: Preprocessing ...
% 19.06/3.44 Prover 10: Preprocessing ...
% 19.80/3.56 Prover 10: Warning: ignoring some quantifiers
% 19.80/3.57 Prover 10: Constructing countermodel ...
% 19.80/3.58 Prover 9: Warning: ignoring some quantifiers
% 20.38/3.60 Prover 9: Constructing countermodel ...
% 20.38/3.63 Prover 10: gave up
% 20.38/3.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 21.15/3.70 Prover 11: Preprocessing ...
% 22.01/3.88 Prover 11: Warning: ignoring some quantifiers
% 22.69/3.90 Prover 11: Constructing countermodel ...
% 57.55/8.51 Prover 2: stopped
% 58.22/8.54 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 58.75/8.58 Prover 12: Preprocessing ...
% 58.75/8.71 Prover 12: Proving ...
% 72.34/10.40 Prover 12: stopped
% 72.34/10.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 72.34/10.45 Prover 13: Preprocessing ...
% 73.14/10.49 Prover 13: Warning: ignoring some quantifiers
% 73.14/10.50 Prover 13: Constructing countermodel ...
% 75.49/10.84 Prover 13: gave up
% 75.49/10.85 Prover 14: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379
% 75.49/10.88 Prover 14: Preprocessing ...
% 76.35/10.98 Prover 14: Proving ...
% 98.48/13.90 Prover 11: Found proof (size 422)
% 98.48/13.90 Prover 11: proved (10255ms)
% 98.48/13.90 Prover 14: stopped
% 98.48/13.90 Prover 9: stopped
% 98.48/13.90 Prover 5: stopped
% 98.48/13.90 Prover 6: stopped
% 98.48/13.90 Prover 0: stopped
% 98.48/13.90 Prover 4: stopped
% 98.48/13.90
% 98.48/13.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 98.48/13.90
% 99.05/13.92 % SZS output start Proof for theBenchmark
% 99.05/13.93 Assumptions after simplification:
% 99.05/13.93 ---------------------------------
% 99.05/13.93
% 99.05/13.93 (antisymmetry_r2_hidden)
% 99.05/13.96 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 99.05/13.96 [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : (
% 99.05/13.96 ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 99.05/13.96 in(v1, v0) = v2))
% 99.05/13.96
% 99.05/13.96 (cc3_ordinal1)
% 99.05/13.97 ! [v0: $i] : ! [v1: any] : ( ~ (epsilon_transitive(v0) = v1) | ~ $i(v0) |
% 99.05/13.97 ? [v2: int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & v3 = 0 & v1 = 0 &
% 99.05/13.97 ordinal(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0)
% 99.05/13.97 = v2))) & ! [v0: $i] : ! [v1: any] : ( ~ (ordinal(v0) = v1) | ~
% 99.05/13.97 $i(v0) | ? [v2: int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & v3 = 0 & v1
% 99.05/13.97 = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2
% 99.05/13.97 = 0) & empty(v0) = v2))) & ! [v0: $i] : ! [v1: any] : ( ~
% 99.05/13.97 (epsilon_connected(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ?
% 99.05/13.97 [v4: int] : ((v4 = 0 & v3 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 &
% 99.05/13.97 ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0: $i] : ( ~
% 99.05/13.97 (empty(v0) = 0) | ~ $i(v0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0
% 99.05/13.97 & epsilon_connected(v0) = 0))
% 99.05/13.97
% 99.05/13.97 (commutativity_k2_xboole_0)
% 99.05/13.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 99.05/13.98 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 99.05/13.98 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 99.05/13.98 | (set_union2(v1, v0) = v2 & $i(v2)))
% 99.05/13.98
% 99.05/13.98 (d1_ordinal1)
% 99.33/13.98 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 99.33/13.98 (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & $i(v1))) & ! [v0:
% 99.33/13.98 $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 99.33/13.98 (succ(v0) = v2 & set_union2(v0, v1) = v2 & $i(v2)))
% 99.33/13.98
% 99.33/13.98 (d1_tarski)
% 99.33/13.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 99.33/13.98 ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : !
% 99.33/13.98 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) =
% 99.33/13.98 v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 99.33/13.98 (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 99.33/13.98 [v4: int] : ($i(v3) & ( ~ (v3 = v1) | ( ~ (v4 = 0) & in(v1, v0) = v4)) & (v3
% 99.33/13.98 = v1 | (v4 = 0 & in(v3, v0) = 0))))
% 99.33/13.98
% 99.33/13.98 (d2_ordinal1)
% 99.33/13.99 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v1, v0) = v2)
% 99.33/13.99 | ~ (epsilon_transitive(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : (
% 99.33/13.99 ~ (v3 = 0) & in(v1, v0) = v3)) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 99.33/13.99 (epsilon_transitive(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~
% 99.33/13.99 (v3 = 0) & subset(v2, v0) = v3 & in(v2, v0) = 0 & $i(v2))) & ! [v0: $i] :
% 99.33/13.99 ! [v1: $i] : ( ~ (epsilon_transitive(v0) = 0) | ~ (in(v1, v0) = 0) | ~
% 99.33/13.99 $i(v1) | ~ $i(v0) | subset(v1, v0) = 0)
% 99.33/13.99
% 99.33/13.99 (d2_xboole_0)
% 99.33/14.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 99.33/14.00 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~
% 99.33/14.00 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0)
% 99.33/14.00 & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0: $i] : !
% 99.33/14.00 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 99.33/14.00 (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) |
% 99.33/14.00 ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 = 0 & in(v3, v0) =
% 99.33/14.00 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0: $i] : ! [v1: $i] : !
% 99.33/14.00 [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (set_union2(v0, v1) = v2)
% 99.33/14.00 | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 99.33/14.00 [v5: int] : ? [v6: int] : ((v6 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) &
% 99.33/14.00 in(v3, v2) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 99.33/14.00 $i] : ! [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) |
% 99.33/14.00 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] :
% 99.33/14.00 ((v6 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v0) = v5)))
% 99.33/14.00 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 99.33/14.00 (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) |
% 99.33/14.00 ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 = 0 & in(v3, v2) =
% 99.33/14.00 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v1) = v5))) & ! [v0: $i] : !
% 99.33/14.00 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~
% 99.33/14.00 (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 99.33/14.00 int] : ? [v5: int] : ((v5 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) =
% 99.33/14.00 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0
% 99.33/14.00 | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 99.33/14.00 $i] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ($i(v4) & ((v7 = 0 &
% 99.33/14.00 in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) =
% 99.33/14.00 0)) & (( ~ (v7 = 0) & ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6)
% 99.33/14.00 | ( ~ (v5 = 0) & in(v4, v0) = v5))))
% 99.33/14.00
% 99.33/14.00 (d3_ordinal1)
% 99.33/14.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 = v1 |
% 99.33/14.01 ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 99.33/14.01 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ((v6 = 0 & in(v1,
% 99.33/14.01 v2) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4 = 0) & in(v1, v0)
% 99.33/14.01 = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 =
% 99.33/14.01 0 | v2 = v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v1, v2) = v3) | ~
% 99.33/14.01 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int]
% 99.33/14.01 : ((v6 = 0 & in(v2, v1) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4 =
% 99.33/14.01 0) & in(v1, v0) = v4))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 99.33/14.01 (epsilon_connected(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ?
% 99.33/14.01 [v4: int] : ? [v5: int] : ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) &
% 99.33/14.01 in(v3, v2) = v5 & in(v3, v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 &
% 99.33/14.01 $i(v3) & $i(v2)))
% 99.33/14.01
% 99.33/14.01 (d4_ordinal1)
% 99.33/14.02 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (ordinal(v0) = v1) | ~ $i(v0) | ?
% 99.33/14.02 [v2: int] : ? [v3: int] : (( ~ (v3 = 0) & epsilon_connected(v0) = v3) | ( ~
% 99.33/14.02 (v2 = 0) & epsilon_transitive(v0) = v2))) & ! [v0: $i] : ! [v1: any] :
% 99.33/14.02 ( ~ (epsilon_transitive(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] :
% 99.33/14.02 ((v3 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0)
% 99.33/14.02 = v2))) & ! [v0: $i] : ! [v1: any] : ( ~ (epsilon_connected(v0) = v1)
% 99.33/14.02 | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & v1 = 0 &
% 99.33/14.02 epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & !
% 99.33/14.02 [v0: $i] : ( ~ (epsilon_transitive(v0) = 0) | ~ $i(v0) | ? [v1: int] : ?
% 99.33/14.02 [v2: int] : ((v2 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) &
% 99.33/14.02 epsilon_connected(v0) = v1))) & ! [v0: $i] : ( ~ (ordinal(v0) = 0) | ~
% 99.33/14.02 $i(v0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) & ! [v0:
% 99.33/14.02 $i] : ( ~ (epsilon_connected(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2:
% 99.33/14.02 int] : ((v2 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0)
% 99.33/14.02 = v1)))
% 99.33/14.02
% 99.33/14.02 (t1_xboole_1)
% 99.33/14.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 99.33/14.02 (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 99.33/14.02 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] :
% 99.33/14.02 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (subset(v0, v2) = v3)
% 99.33/14.02 | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int]
% 99.33/14.02 : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 99.33/14.02 $i] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~
% 99.33/14.02 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0)
% 99.33/14.02
% 99.33/14.02 (t29_ordinal1)
% 99.33/14.02 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & succ(v0) = v1 &
% 99.33/14.02 ordinal(v1) = v2 & ordinal(v0) = 0 & $i(v1) & $i(v0))
% 99.33/14.02
% 99.33/14.02 (t2_subset)
% 99.33/14.03 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~
% 99.33/14.03 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & empty(v1) = 0)
% 99.33/14.03 | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 99.33/14.03 (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int]
% 99.33/14.03 : ((v3 = 0 & in(v0, v1) = 0) | (v2 = 0 & empty(v1) = 0)))
% 99.33/14.03
% 99.33/14.03 (t3_subset)
% 99.33/14.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 99.33/14.03 (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 99.33/14.03 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i]
% 99.33/14.03 : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 99.33/14.03 ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0,
% 99.33/14.03 v3) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 99.33/14.03 (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) |
% 99.33/14.03 subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) |
% 99.33/14.03 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) =
% 99.33/14.03 0 & $i(v2)))
% 99.33/14.03
% 99.33/14.03 (t6_boole)
% 99.33/14.03 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~
% 99.33/14.03 $i(v0))
% 99.33/14.03
% 99.33/14.03 (t7_boole)
% 99.33/14.03 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 99.33/14.03 [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 99.33/14.03
% 99.33/14.03 (t7_xboole_1)
% 99.33/14.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~
% 99.33/14.04 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0)
% 99.33/14.04
% 99.33/14.04 (function-axioms)
% 99.33/14.04 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 99.33/14.04 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 99.33/14.04 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 99.33/14.04 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 99.33/14.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 99.33/14.04 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0:
% 99.33/14.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 99.33/14.04 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 99.33/14.04 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 99.33/14.04 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 99.33/14.04 $i] : (v1 = v0 | ~ (relation_non_empty(v2) = v1) | ~
% 99.33/14.04 (relation_non_empty(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 99.33/14.04 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 99.33/14.04 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 99.33/14.04 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~
% 99.33/14.04 (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 99.33/14.04 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: MultipleValueBool]
% 99.33/14.04 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) =
% 99.33/14.04 v1) | ~ (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 99.33/14.04 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 99.33/14.04 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 99.33/14.04 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_transitive(v2) =
% 99.33/14.04 v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 99.33/14.04 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~
% 99.33/14.04 (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 99.33/14.04 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_connected(v2) =
% 99.33/14.04 v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 99.33/14.04 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~
% 99.33/14.04 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 99.33/14.04 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 99.33/14.04 (empty(v2) = v0))
% 99.33/14.04
% 99.33/14.04 Further assumptions not needed in the proof:
% 99.33/14.04 --------------------------------------------
% 99.33/14.05 cc1_funct_1, cc1_ordinal1, cc1_relat_1, cc2_funct_1, cc2_ordinal1,
% 99.33/14.05 existence_m1_subset_1, fc12_relat_1, fc1_ordinal1, fc1_xboole_0, fc2_ordinal1,
% 99.33/14.05 fc2_relat_1, fc2_xboole_0, fc3_xboole_0, fc4_relat_1, idempotence_k2_xboole_0,
% 99.33/14.05 rc1_funct_1, rc1_ordinal1, rc1_relat_1, rc1_xboole_0, rc2_funct_1, rc2_ordinal1,
% 99.33/14.05 rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, rc4_funct_1, rc5_funct_1,
% 99.33/14.05 reflexivity_r1_tarski, t1_boole, t1_subset, t4_subset, t5_subset, t8_boole
% 99.33/14.05
% 99.33/14.05 Those formulas are unsatisfiable:
% 99.33/14.05 ---------------------------------
% 99.33/14.05
% 99.33/14.05 Begin of proof
% 99.33/14.05 |
% 99.33/14.05 | ALPHA: (antisymmetry_r2_hidden) implies:
% 99.33/14.05 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~
% 99.33/14.05 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 99.33/14.05 |
% 99.33/14.05 | ALPHA: (cc3_ordinal1) implies:
% 99.33/14.05 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (ordinal(v0) = v1) | ~ $i(v0) | ?
% 99.33/14.05 | [v2: int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & v3 = 0 & v1 = 0
% 99.33/14.05 | & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0) | ( ~
% 99.33/14.05 | (v2 = 0) & empty(v0) = v2)))
% 99.33/14.05 |
% 99.33/14.05 | ALPHA: (commutativity_k2_xboole_0) implies:
% 99.33/14.05 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 99.33/14.05 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 99.33/14.05 |
% 99.33/14.05 | ALPHA: (d1_ordinal1) implies:
% 99.33/14.05 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2:
% 99.33/14.05 | $i] : (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) &
% 99.33/14.05 | $i(v1)))
% 99.33/14.05 |
% 99.33/14.05 | ALPHA: (d1_tarski) implies:
% 99.33/14.06 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0)
% 99.33/14.06 | = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 99.33/14.06 |
% 99.33/14.06 | ALPHA: (d2_ordinal1) implies:
% 99.33/14.06 | (6) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1)
% 99.33/14.06 | | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & subset(v2,
% 99.33/14.06 | v0) = v3 & in(v2, v0) = 0 & $i(v2)))
% 99.33/14.06 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v1, v0)
% 99.33/14.06 | = v2) | ~ (epsilon_transitive(v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 99.33/14.06 | ? [v3: int] : ( ~ (v3 = 0) & in(v1, v0) = v3))
% 99.33/14.06 |
% 99.33/14.06 | ALPHA: (d2_xboole_0) implies:
% 99.33/14.06 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 99.33/14.06 | (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 99.33/14.06 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ((v5 =
% 99.33/14.06 | 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)))
% 99.33/14.06 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 99.33/14.06 | ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~
% 99.33/14.06 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 =
% 99.33/14.06 | 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v1) =
% 99.33/14.06 | v5)))
% 99.75/14.06 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 99.75/14.06 | (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~
% 99.75/14.06 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 99.75/14.06 | int] : ((v6 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) =
% 99.75/14.06 | v5)))
% 99.75/14.07 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 99.75/14.07 | (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~
% 99.75/14.07 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 99.75/14.07 | int] : ((v6 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) =
% 99.75/14.07 | v5)))
% 99.75/14.07 |
% 99.75/14.07 | ALPHA: (d3_ordinal1) implies:
% 99.75/14.07 | (12) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_connected(v0) = v1)
% 99.75/14.07 | | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5:
% 99.75/14.07 | int] : ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) & in(v3, v2) = v5
% 99.75/14.07 | & in(v3, v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 & $i(v3) &
% 99.75/14.07 | $i(v2)))
% 99.75/14.07 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2
% 99.75/14.07 | = v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v1, v2) = v3) | ~
% 99.75/14.07 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ?
% 99.75/14.07 | [v6: int] : ((v6 = 0 & in(v2, v1) = 0) | ( ~ (v5 = 0) & in(v2, v0) =
% 99.75/14.07 | v5) | ( ~ (v4 = 0) & in(v1, v0) = v4)))
% 99.75/14.07 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2
% 99.75/14.07 | = v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~
% 99.75/14.07 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ?
% 99.75/14.07 | [v6: int] : ((v6 = 0 & in(v1, v2) = 0) | ( ~ (v5 = 0) & in(v2, v0) =
% 99.75/14.07 | v5) | ( ~ (v4 = 0) & in(v1, v0) = v4)))
% 99.75/14.07 |
% 99.75/14.07 | ALPHA: (d4_ordinal1) implies:
% 99.75/14.07 | (15) ! [v0: $i] : ( ~ (ordinal(v0) = 0) | ~ $i(v0) |
% 99.75/14.07 | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0))
% 99.75/14.07 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (ordinal(v0) = v1) | ~
% 99.75/14.07 | $i(v0) | ? [v2: int] : ? [v3: int] : (( ~ (v3 = 0) &
% 99.75/14.07 | epsilon_connected(v0) = v3) | ( ~ (v2 = 0) &
% 99.75/14.07 | epsilon_transitive(v0) = v2)))
% 99.75/14.07 |
% 99.75/14.08 | ALPHA: (t1_xboole_1) implies:
% 99.75/14.08 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 99.75/14.08 | (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ~ $i(v2) | ~
% 99.75/14.08 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) =
% 99.75/14.08 | v4))
% 99.75/14.08 |
% 99.75/14.08 | ALPHA: (t2_subset) implies:
% 99.75/14.08 | (18) ! [v0: $i] : ! [v1: $i] : ( ~ (element(v0, v1) = 0) | ~ $i(v1) | ~
% 99.75/14.08 | $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & in(v0, v1) = 0) |
% 99.75/14.08 | (v2 = 0 & empty(v1) = 0)))
% 99.75/14.08 |
% 99.75/14.08 | ALPHA: (t3_subset) implies:
% 99.75/14.08 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 99.75/14.08 | $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) = 0 &
% 99.75/14.08 | $i(v2)))
% 99.75/14.08 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0,
% 99.75/14.08 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 99.75/14.08 | ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4 & $i(v3)))
% 99.75/14.08 |
% 99.75/14.08 | ALPHA: (t6_boole) implies:
% 99.75/14.08 | (21) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 99.75/14.08 |
% 99.75/14.08 | ALPHA: (function-axioms) implies:
% 99.85/14.08 | (22) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 99.85/14.08 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 99.85/14.08 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2)
% 99.85/14.08 | = v1) | ~ (powerset(v2) = v0))
% 99.85/14.08 | (24) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 99.85/14.08 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 99.85/14.08 | v0))
% 99.85/14.08 | (25) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 99.85/14.08 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3,
% 99.85/14.08 | v2) = v0))
% 99.85/14.08 |
% 99.85/14.09 | DELTA: instantiating (t29_ordinal1) with fresh symbols all_58_0, all_58_1,
% 99.85/14.09 | all_58_2 gives:
% 99.85/14.09 | (26) ~ (all_58_0 = 0) & succ(all_58_2) = all_58_1 & ordinal(all_58_1) =
% 99.85/14.09 | all_58_0 & ordinal(all_58_2) = 0 & $i(all_58_1) & $i(all_58_2)
% 99.85/14.09 |
% 99.85/14.09 | ALPHA: (26) implies:
% 99.85/14.09 | (27) ~ (all_58_0 = 0)
% 99.85/14.09 | (28) $i(all_58_2)
% 99.85/14.09 | (29) $i(all_58_1)
% 99.85/14.09 | (30) ordinal(all_58_2) = 0
% 99.85/14.09 | (31) ordinal(all_58_1) = all_58_0
% 99.85/14.09 | (32) succ(all_58_2) = all_58_1
% 99.85/14.09 |
% 99.85/14.09 | GROUND_INST: instantiating (15) with all_58_2, simplifying with (28), (30)
% 99.85/14.09 | gives:
% 99.85/14.09 | (33) epsilon_transitive(all_58_2) = 0 & epsilon_connected(all_58_2) = 0
% 99.85/14.09 |
% 99.85/14.09 | ALPHA: (33) implies:
% 99.85/14.09 | (34) epsilon_connected(all_58_2) = 0
% 99.85/14.09 | (35) epsilon_transitive(all_58_2) = 0
% 99.85/14.09 |
% 99.85/14.09 | GROUND_INST: instantiating (16) with all_58_1, all_58_0, simplifying with
% 99.85/14.09 | (29), (31) gives:
% 99.85/14.09 | (36) all_58_0 = 0 | ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 99.85/14.09 | epsilon_connected(all_58_1) = v1) | ( ~ (v0 = 0) &
% 99.85/14.09 | epsilon_transitive(all_58_1) = v0))
% 99.85/14.09 |
% 99.85/14.09 | GROUND_INST: instantiating (2) with all_58_1, all_58_0, simplifying with (29),
% 99.85/14.09 | (31) gives:
% 99.85/14.09 | (37) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & v1 = 0 &
% 99.85/14.09 | all_58_0 = 0 & epsilon_transitive(all_58_1) = 0 &
% 99.85/14.09 | epsilon_connected(all_58_1) = 0) | ( ~ (v0 = 0) & empty(all_58_1)
% 99.85/14.09 | = v0))
% 99.85/14.09 |
% 99.85/14.09 | GROUND_INST: instantiating (4) with all_58_2, all_58_1, simplifying with (28),
% 99.85/14.09 | (32) gives:
% 99.85/14.09 | (38) ? [v0: $i] : (singleton(all_58_2) = v0 & set_union2(all_58_2, v0) =
% 99.85/14.09 | all_58_1 & $i(v0) & $i(all_58_1))
% 99.85/14.09 |
% 99.85/14.09 | DELTA: instantiating (38) with fresh symbol all_74_0 gives:
% 99.85/14.09 | (39) singleton(all_58_2) = all_74_0 & set_union2(all_58_2, all_74_0) =
% 99.85/14.09 | all_58_1 & $i(all_74_0) & $i(all_58_1)
% 99.85/14.09 |
% 99.85/14.09 | ALPHA: (39) implies:
% 99.85/14.09 | (40) $i(all_74_0)
% 99.85/14.09 | (41) set_union2(all_58_2, all_74_0) = all_58_1
% 99.85/14.09 | (42) singleton(all_58_2) = all_74_0
% 99.85/14.09 |
% 99.85/14.09 | DELTA: instantiating (37) with fresh symbols all_80_0, all_80_1, all_80_2
% 99.85/14.09 | gives:
% 99.85/14.10 | (43) (all_80_0 = 0 & all_80_1 = 0 & all_58_0 = 0 &
% 99.85/14.10 | epsilon_transitive(all_58_1) = 0 & epsilon_connected(all_58_1) = 0)
% 99.85/14.10 | | ( ~ (all_80_2 = 0) & empty(all_58_1) = all_80_2)
% 99.85/14.10 |
% 99.85/14.10 | BETA: splitting (36) gives:
% 99.85/14.10 |
% 99.85/14.10 | Case 1:
% 99.85/14.10 | |
% 99.85/14.10 | | (44) all_58_0 = 0
% 99.85/14.10 | |
% 99.85/14.10 | | REDUCE: (27), (44) imply:
% 99.85/14.10 | | (45) $false
% 99.85/14.10 | |
% 99.85/14.10 | | CLOSE: (45) is inconsistent.
% 99.85/14.10 | |
% 99.85/14.10 | Case 2:
% 99.85/14.10 | |
% 99.85/14.10 | | (46) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 99.85/14.10 | | epsilon_connected(all_58_1) = v1) | ( ~ (v0 = 0) &
% 99.85/14.10 | | epsilon_transitive(all_58_1) = v0))
% 99.85/14.10 | |
% 99.85/14.10 | | DELTA: instantiating (46) with fresh symbols all_105_0, all_105_1 gives:
% 99.85/14.10 | | (47) ( ~ (all_105_0 = 0) & epsilon_connected(all_58_1) = all_105_0) | ( ~
% 99.85/14.10 | | (all_105_1 = 0) & epsilon_transitive(all_58_1) = all_105_1)
% 99.85/14.10 | |
% 99.85/14.10 | | BETA: splitting (43) gives:
% 99.85/14.10 | |
% 99.85/14.10 | | Case 1:
% 99.85/14.10 | | |
% 99.85/14.10 | | | (48) all_80_0 = 0 & all_80_1 = 0 & all_58_0 = 0 &
% 99.85/14.10 | | | epsilon_transitive(all_58_1) = 0 & epsilon_connected(all_58_1) = 0
% 99.85/14.10 | | |
% 99.85/14.10 | | | ALPHA: (48) implies:
% 99.85/14.10 | | | (49) all_58_0 = 0
% 99.85/14.10 | | |
% 99.85/14.10 | | | REDUCE: (27), (49) imply:
% 99.85/14.10 | | | (50) $false
% 99.85/14.10 | | |
% 99.85/14.10 | | | CLOSE: (50) is inconsistent.
% 99.85/14.10 | | |
% 99.85/14.10 | | Case 2:
% 99.85/14.10 | | |
% 99.85/14.10 | | |
% 99.85/14.10 | | | GROUND_INST: instantiating (3) with all_74_0, all_58_2, all_58_1,
% 99.85/14.10 | | | simplifying with (28), (40), (41) gives:
% 99.85/14.10 | | | (51) set_union2(all_74_0, all_58_2) = all_58_1 & $i(all_58_1)
% 99.85/14.10 | | |
% 99.85/14.10 | | | ALPHA: (51) implies:
% 99.85/14.10 | | | (52) set_union2(all_74_0, all_58_2) = all_58_1
% 99.85/14.10 | | |
% 99.85/14.10 | | | GROUND_INST: instantiating (t7_xboole_1) with all_58_2, all_74_0,
% 99.85/14.10 | | | all_58_1, simplifying with (28), (40), (41) gives:
% 99.85/14.10 | | | (53) subset(all_58_2, all_58_1) = 0
% 99.85/14.10 | | |
% 99.85/14.10 | | | GROUND_INST: instantiating (t7_xboole_1) with all_74_0, all_58_2,
% 99.85/14.10 | | | all_58_1, simplifying with (28), (40), (52) gives:
% 99.85/14.10 | | | (54) subset(all_74_0, all_58_1) = 0
% 99.85/14.10 | | |
% 99.85/14.10 | | | GROUND_INST: instantiating (19) with all_58_2, all_58_1, simplifying with
% 99.85/14.10 | | | (28), (29), (53) gives:
% 99.85/14.10 | | | (55) ? [v0: $i] : (powerset(all_58_1) = v0 & element(all_58_2, v0) = 0
% 99.85/14.10 | | | & $i(v0))
% 99.85/14.10 | | |
% 99.85/14.10 | | | DELTA: instantiating (55) with fresh symbol all_159_0 gives:
% 99.85/14.10 | | | (56) powerset(all_58_1) = all_159_0 & element(all_58_2, all_159_0) = 0
% 99.85/14.10 | | | & $i(all_159_0)
% 99.85/14.10 | | |
% 99.85/14.10 | | | ALPHA: (56) implies:
% 99.85/14.10 | | | (57) $i(all_159_0)
% 99.85/14.10 | | | (58) element(all_58_2, all_159_0) = 0
% 99.85/14.10 | | | (59) powerset(all_58_1) = all_159_0
% 99.85/14.10 | | |
% 99.85/14.10 | | | GROUND_INST: instantiating (19) with all_74_0, all_58_1, simplifying with
% 99.85/14.10 | | | (29), (40), (54) gives:
% 99.85/14.10 | | | (60) ? [v0: $i] : (powerset(all_58_1) = v0 & element(all_74_0, v0) = 0
% 99.85/14.10 | | | & $i(v0))
% 99.85/14.11 | | |
% 99.85/14.11 | | | GROUND_INST: instantiating (18) with all_58_2, all_159_0, simplifying with
% 99.85/14.11 | | | (28), (57), (58) gives:
% 99.85/14.11 | | | (61) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_58_2, all_159_0) =
% 99.85/14.11 | | | 0) | (v0 = 0 & empty(all_159_0) = 0))
% 99.85/14.11 | | |
% 99.85/14.11 | | | DELTA: instantiating (60) with fresh symbol all_170_0 gives:
% 99.85/14.11 | | | (62) powerset(all_58_1) = all_170_0 & element(all_74_0, all_170_0) = 0
% 99.85/14.11 | | | & $i(all_170_0)
% 99.85/14.11 | | |
% 99.85/14.11 | | | ALPHA: (62) implies:
% 99.85/14.11 | | | (63) $i(all_170_0)
% 99.85/14.11 | | | (64) element(all_74_0, all_170_0) = 0
% 99.85/14.11 | | | (65) powerset(all_58_1) = all_170_0
% 99.85/14.11 | | |
% 99.85/14.11 | | | DELTA: instantiating (61) with fresh symbols all_172_0, all_172_1 gives:
% 99.85/14.11 | | | (66) (all_172_0 = 0 & in(all_58_2, all_159_0) = 0) | (all_172_1 = 0 &
% 99.85/14.11 | | | empty(all_159_0) = 0)
% 99.85/14.11 | | |
% 99.85/14.11 | | | GROUND_INST: instantiating (23) with all_159_0, all_170_0, all_58_1,
% 99.85/14.11 | | | simplifying with (59), (65) gives:
% 99.85/14.11 | | | (67) all_170_0 = all_159_0
% 99.85/14.11 | | |
% 99.85/14.11 | | | REDUCE: (64), (67) imply:
% 99.85/14.11 | | | (68) element(all_74_0, all_159_0) = 0
% 99.85/14.11 | | |
% 99.85/14.11 | | | GROUND_INST: instantiating (18) with all_74_0, all_159_0, simplifying with
% 99.85/14.11 | | | (40), (57), (68) gives:
% 99.85/14.11 | | | (69) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_74_0, all_159_0) =
% 99.85/14.11 | | | 0) | (v0 = 0 & empty(all_159_0) = 0))
% 99.85/14.11 | | |
% 99.85/14.11 | | | DELTA: instantiating (69) with fresh symbols all_182_0, all_182_1 gives:
% 99.85/14.11 | | | (70) (all_182_0 = 0 & in(all_74_0, all_159_0) = 0) | (all_182_1 = 0 &
% 99.85/14.11 | | | empty(all_159_0) = 0)
% 99.85/14.11 | | |
% 99.85/14.11 | | | BETA: splitting (47) gives:
% 99.85/14.11 | | |
% 99.85/14.11 | | | Case 1:
% 99.85/14.11 | | | |
% 99.85/14.11 | | | | (71) ~ (all_105_0 = 0) & epsilon_connected(all_58_1) = all_105_0
% 99.85/14.11 | | | |
% 99.85/14.11 | | | | ALPHA: (71) implies:
% 99.85/14.11 | | | | (72) ~ (all_105_0 = 0)
% 99.85/14.11 | | | | (73) epsilon_connected(all_58_1) = all_105_0
% 99.85/14.11 | | | |
% 99.85/14.11 | | | | GROUND_INST: instantiating (12) with all_58_1, all_105_0, simplifying
% 99.85/14.11 | | | | with (29), (73) gives:
% 99.85/14.11 | | | | (74) all_105_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ?
% 99.85/14.11 | | | | [v3: int] : ( ~ (v3 = 0) & ~ (v2 = 0) & ~ (v1 = v0) & in(v1,
% 99.85/14.11 | | | | v0) = v3 & in(v1, all_58_1) = 0 & in(v0, v1) = v2 & in(v0,
% 99.85/14.11 | | | | all_58_1) = 0 & $i(v1) & $i(v0))
% 99.85/14.11 | | | |
% 99.85/14.11 | | | | BETA: splitting (74) gives:
% 99.85/14.11 | | | |
% 99.85/14.11 | | | | Case 1:
% 99.85/14.11 | | | | |
% 99.85/14.11 | | | | | (75) all_105_0 = 0
% 99.85/14.11 | | | | |
% 99.85/14.11 | | | | | REDUCE: (72), (75) imply:
% 99.85/14.11 | | | | | (76) $false
% 99.85/14.11 | | | | |
% 99.85/14.11 | | | | | CLOSE: (76) is inconsistent.
% 99.85/14.11 | | | | |
% 99.85/14.11 | | | | Case 2:
% 99.85/14.11 | | | | |
% 99.85/14.11 | | | | | (77) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ( ~
% 99.85/14.11 | | | | | (v3 = 0) & ~ (v2 = 0) & ~ (v1 = v0) & in(v1, v0) = v3 &
% 99.85/14.11 | | | | | in(v1, all_58_1) = 0 & in(v0, v1) = v2 & in(v0, all_58_1) =
% 99.85/14.11 | | | | | 0 & $i(v1) & $i(v0))
% 99.85/14.11 | | | | |
% 99.85/14.11 | | | | | DELTA: instantiating (77) with fresh symbols all_299_0, all_299_1,
% 99.85/14.11 | | | | | all_299_2, all_299_3 gives:
% 99.85/14.11 | | | | | (78) ~ (all_299_0 = 0) & ~ (all_299_1 = 0) & ~ (all_299_2 =
% 99.85/14.11 | | | | | all_299_3) & in(all_299_2, all_299_3) = all_299_0 &
% 99.85/14.11 | | | | | in(all_299_2, all_58_1) = 0 & in(all_299_3, all_299_2) =
% 99.85/14.11 | | | | | all_299_1 & in(all_299_3, all_58_1) = 0 & $i(all_299_2) &
% 99.85/14.11 | | | | | $i(all_299_3)
% 99.85/14.11 | | | | |
% 99.85/14.11 | | | | | ALPHA: (78) implies:
% 99.85/14.11 | | | | | (79) ~ (all_299_2 = all_299_3)
% 99.85/14.11 | | | | | (80) ~ (all_299_1 = 0)
% 99.85/14.11 | | | | | (81) ~ (all_299_0 = 0)
% 99.85/14.11 | | | | | (82) $i(all_299_3)
% 99.85/14.11 | | | | | (83) $i(all_299_2)
% 99.85/14.11 | | | | | (84) in(all_299_3, all_58_1) = 0
% 99.85/14.11 | | | | | (85) in(all_299_3, all_299_2) = all_299_1
% 99.85/14.11 | | | | | (86) in(all_299_2, all_58_1) = 0
% 99.85/14.11 | | | | | (87) in(all_299_2, all_299_3) = all_299_0
% 99.85/14.11 | | | | |
% 99.85/14.11 | | | | | BETA: splitting (66) gives:
% 99.85/14.11 | | | | |
% 99.85/14.11 | | | | | Case 1:
% 99.85/14.11 | | | | | |
% 99.85/14.11 | | | | | | (88) all_172_0 = 0 & in(all_58_2, all_159_0) = 0
% 99.85/14.12 | | | | | |
% 99.85/14.12 | | | | | | ALPHA: (88) implies:
% 99.85/14.12 | | | | | | (89) in(all_58_2, all_159_0) = 0
% 99.85/14.12 | | | | | |
% 99.85/14.12 | | | | | | BETA: splitting (70) gives:
% 99.85/14.12 | | | | | |
% 99.85/14.12 | | | | | | Case 1:
% 99.85/14.12 | | | | | | |
% 99.85/14.12 | | | | | | |
% 100.01/14.12 | | | | | | | GROUND_INST: instantiating (8) with all_74_0, all_58_2, all_58_1,
% 100.01/14.12 | | | | | | | all_299_3, simplifying with (28), (29), (40), (52),
% 100.01/14.12 | | | | | | | (82), (84) gives:
% 100.01/14.12 | | | | | | | (90) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_299_3,
% 100.01/14.12 | | | | | | | all_58_2) = 0) | (v0 = 0 & in(all_299_3, all_74_0) =
% 100.01/14.12 | | | | | | | 0))
% 100.01/14.12 | | | | | | |
% 100.01/14.12 | | | | | | | GROUND_INST: instantiating (8) with all_58_2, all_74_0, all_58_1,
% 100.01/14.12 | | | | | | | all_299_3, simplifying with (28), (29), (40), (41),
% 100.01/14.12 | | | | | | | (82), (84) gives:
% 100.01/14.12 | | | | | | | (91) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_299_3,
% 100.01/14.12 | | | | | | | all_74_0) = 0) | (v0 = 0 & in(all_299_3, all_58_2) =
% 100.01/14.12 | | | | | | | 0))
% 100.01/14.12 | | | | | | |
% 100.01/14.12 | | | | | | | GROUND_INST: instantiating (14) with all_58_2, all_299_2,
% 100.01/14.12 | | | | | | | all_299_3, all_299_1, simplifying with (28), (34),
% 100.01/14.12 | | | | | | | (82), (83), (85) gives:
% 100.01/14.12 | | | | | | | (92) all_299_1 = 0 | all_299_2 = all_299_3 | ? [v0: int] : ?
% 100.01/14.12 | | | | | | | [v1: int] : ? [v2: int] : ((v2 = 0 & in(all_299_2,
% 100.01/14.12 | | | | | | | all_299_3) = 0) | ( ~ (v1 = 0) & in(all_299_3,
% 100.01/14.12 | | | | | | | all_58_2) = v1) | ( ~ (v0 = 0) & in(all_299_2,
% 100.01/14.12 | | | | | | | all_58_2) = v0))
% 100.01/14.12 | | | | | | |
% 100.01/14.12 | | | | | | | GROUND_INST: instantiating (13) with all_58_2, all_299_3,
% 100.01/14.12 | | | | | | | all_299_2, all_299_1, simplifying with (28), (34),
% 100.01/14.12 | | | | | | | (82), (83), (85) gives:
% 100.01/14.12 | | | | | | | (93) all_299_1 = 0 | all_299_2 = all_299_3 | ? [v0: int] : ?
% 100.01/14.12 | | | | | | | [v1: int] : ? [v2: int] : ((v2 = 0 & in(all_299_2,
% 100.01/14.12 | | | | | | | all_299_3) = 0) | ( ~ (v1 = 0) & in(all_299_2,
% 100.01/14.12 | | | | | | | all_58_2) = v1) | ( ~ (v0 = 0) & in(all_299_3,
% 100.01/14.12 | | | | | | | all_58_2) = v0))
% 100.01/14.12 | | | | | | |
% 100.01/14.12 | | | | | | | GROUND_INST: instantiating (8) with all_74_0, all_58_2, all_58_1,
% 100.01/14.12 | | | | | | | all_299_2, simplifying with (28), (29), (40), (52),
% 100.01/14.12 | | | | | | | (83), (86) gives:
% 100.01/14.12 | | | | | | | (94) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_299_2,
% 100.01/14.12 | | | | | | | all_58_2) = 0) | (v0 = 0 & in(all_299_2, all_74_0) =
% 100.01/14.12 | | | | | | | 0))
% 100.01/14.12 | | | | | | |
% 100.01/14.12 | | | | | | | GROUND_INST: instantiating (8) with all_58_2, all_74_0, all_58_1,
% 100.01/14.12 | | | | | | | all_299_2, simplifying with (28), (29), (40), (41),
% 100.01/14.12 | | | | | | | (83), (86) gives:
% 100.01/14.12 | | | | | | | (95) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_299_2,
% 100.01/14.12 | | | | | | | all_74_0) = 0) | (v0 = 0 & in(all_299_2, all_58_2) =
% 100.01/14.12 | | | | | | | 0))
% 100.01/14.12 | | | | | | |
% 100.01/14.12 | | | | | | | GROUND_INST: instantiating (13) with all_58_2, all_299_2,
% 100.01/14.12 | | | | | | | all_299_3, all_299_0, simplifying with (28), (34),
% 100.01/14.12 | | | | | | | (82), (83), (87) gives:
% 100.01/14.12 | | | | | | | (96) all_299_0 = 0 | all_299_2 = all_299_3 | ? [v0: int] : ?
% 100.01/14.12 | | | | | | | [v1: int] : ? [v2: int] : ((v2 = 0 & in(all_299_3,
% 100.01/14.12 | | | | | | | all_299_2) = 0) | ( ~ (v1 = 0) & in(all_299_3,
% 100.01/14.12 | | | | | | | all_58_2) = v1) | ( ~ (v0 = 0) & in(all_299_2,
% 100.01/14.12 | | | | | | | all_58_2) = v0))
% 100.01/14.12 | | | | | | |
% 100.01/14.12 | | | | | | | DELTA: instantiating (90) with fresh symbols all_409_0, all_409_1
% 100.01/14.12 | | | | | | | gives:
% 100.01/14.13 | | | | | | | (97) (all_409_0 = 0 & in(all_299_3, all_58_2) = 0) | (all_409_1
% 100.01/14.13 | | | | | | | = 0 & in(all_299_3, all_74_0) = 0)
% 100.01/14.13 | | | | | | |
% 100.01/14.13 | | | | | | | DELTA: instantiating (94) with fresh symbols all_410_0, all_410_1
% 100.01/14.13 | | | | | | | gives:
% 100.01/14.13 | | | | | | | (98) (all_410_0 = 0 & in(all_299_2, all_58_2) = 0) | (all_410_1
% 100.01/14.13 | | | | | | | = 0 & in(all_299_2, all_74_0) = 0)
% 100.01/14.13 | | | | | | |
% 100.01/14.13 | | | | | | | DELTA: instantiating (95) with fresh symbols all_415_0, all_415_1
% 100.01/14.13 | | | | | | | gives:
% 100.01/14.13 | | | | | | | (99) (all_415_0 = 0 & in(all_299_2, all_74_0) = 0) | (all_415_1
% 100.01/14.13 | | | | | | | = 0 & in(all_299_2, all_58_2) = 0)
% 100.01/14.13 | | | | | | |
% 100.01/14.13 | | | | | | | DELTA: instantiating (91) with fresh symbols all_416_0, all_416_1
% 100.01/14.13 | | | | | | | gives:
% 100.01/14.13 | | | | | | | (100) (all_416_0 = 0 & in(all_299_3, all_74_0) = 0) |
% 100.01/14.13 | | | | | | | (all_416_1 = 0 & in(all_299_3, all_58_2) = 0)
% 100.01/14.13 | | | | | | |
% 100.01/14.13 | | | | | | | BETA: splitting (96) gives:
% 100.01/14.13 | | | | | | |
% 100.01/14.13 | | | | | | | Case 1:
% 100.01/14.13 | | | | | | | |
% 100.01/14.13 | | | | | | | | (101) all_299_0 = 0
% 100.01/14.13 | | | | | | | |
% 100.01/14.13 | | | | | | | | REDUCE: (81), (101) imply:
% 100.01/14.13 | | | | | | | | (102) $false
% 100.01/14.13 | | | | | | | |
% 100.01/14.13 | | | | | | | | CLOSE: (102) is inconsistent.
% 100.01/14.13 | | | | | | | |
% 100.01/14.13 | | | | | | | Case 2:
% 100.01/14.13 | | | | | | | |
% 100.01/14.13 | | | | | | | | (103) all_299_2 = all_299_3 | ? [v0: int] : ? [v1: int] :
% 100.01/14.13 | | | | | | | | ? [v2: int] : ((v2 = 0 & in(all_299_3, all_299_2) = 0)
% 100.01/14.13 | | | | | | | | | ( ~ (v1 = 0) & in(all_299_3, all_58_2) = v1) | ( ~
% 100.01/14.13 | | | | | | | | (v0 = 0) & in(all_299_2, all_58_2) = v0))
% 100.01/14.13 | | | | | | | |
% 100.01/14.13 | | | | | | | | BETA: splitting (93) gives:
% 100.01/14.13 | | | | | | | |
% 100.01/14.13 | | | | | | | | Case 1:
% 100.01/14.13 | | | | | | | | |
% 100.01/14.13 | | | | | | | | | (104) all_299_1 = 0
% 100.01/14.13 | | | | | | | | |
% 100.01/14.13 | | | | | | | | | REDUCE: (80), (104) imply:
% 100.01/14.13 | | | | | | | | | (105) $false
% 100.01/14.13 | | | | | | | | |
% 100.01/14.13 | | | | | | | | | CLOSE: (105) is inconsistent.
% 100.01/14.13 | | | | | | | | |
% 100.01/14.13 | | | | | | | | Case 2:
% 100.01/14.13 | | | | | | | | |
% 100.01/14.13 | | | | | | | | | (106) all_299_2 = all_299_3 | ? [v0: int] : ? [v1: int] :
% 100.01/14.13 | | | | | | | | | ? [v2: int] : ((v2 = 0 & in(all_299_2, all_299_3) =
% 100.01/14.13 | | | | | | | | | 0) | ( ~ (v1 = 0) & in(all_299_2, all_58_2) = v1)
% 100.01/14.13 | | | | | | | | | | ( ~ (v0 = 0) & in(all_299_3, all_58_2) = v0))
% 100.01/14.13 | | | | | | | | |
% 100.01/14.13 | | | | | | | | | BETA: splitting (92) gives:
% 100.01/14.13 | | | | | | | | |
% 100.01/14.13 | | | | | | | | | Case 1:
% 100.01/14.13 | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | (107) all_299_1 = 0
% 100.01/14.13 | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | REDUCE: (80), (107) imply:
% 100.01/14.13 | | | | | | | | | | (108) $false
% 100.01/14.13 | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | CLOSE: (108) is inconsistent.
% 100.01/14.13 | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | Case 2:
% 100.01/14.13 | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | (109) all_299_2 = all_299_3 | ? [v0: int] : ? [v1: int]
% 100.01/14.13 | | | | | | | | | | : ? [v2: int] : ((v2 = 0 & in(all_299_2,
% 100.01/14.13 | | | | | | | | | | all_299_3) = 0) | ( ~ (v1 = 0) &
% 100.01/14.13 | | | | | | | | | | in(all_299_3, all_58_2) = v1) | ( ~ (v0 = 0) &
% 100.01/14.13 | | | | | | | | | | in(all_299_2, all_58_2) = v0))
% 100.01/14.13 | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | BETA: splitting (103) gives:
% 100.01/14.13 | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | Case 1:
% 100.01/14.13 | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | (110) all_299_2 = all_299_3
% 100.01/14.13 | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | REDUCE: (79), (110) imply:
% 100.01/14.13 | | | | | | | | | | | (111) $false
% 100.01/14.13 | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | CLOSE: (111) is inconsistent.
% 100.01/14.13 | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | Case 2:
% 100.01/14.13 | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | (112) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2
% 100.01/14.13 | | | | | | | | | | | = 0 & in(all_299_3, all_299_2) = 0) | ( ~ (v1
% 100.01/14.13 | | | | | | | | | | | = 0) & in(all_299_3, all_58_2) = v1) | ( ~
% 100.01/14.13 | | | | | | | | | | | (v0 = 0) & in(all_299_2, all_58_2) = v0))
% 100.01/14.13 | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | DELTA: instantiating (112) with fresh symbols all_491_0,
% 100.01/14.13 | | | | | | | | | | | all_491_1, all_491_2 gives:
% 100.01/14.13 | | | | | | | | | | | (113) (all_491_0 = 0 & in(all_299_3, all_299_2) = 0) | (
% 100.01/14.13 | | | | | | | | | | | ~ (all_491_1 = 0) & in(all_299_3, all_58_2) =
% 100.01/14.13 | | | | | | | | | | | all_491_1) | ( ~ (all_491_2 = 0) & in(all_299_2,
% 100.01/14.13 | | | | | | | | | | | all_58_2) = all_491_2)
% 100.01/14.13 | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | BETA: splitting (106) gives:
% 100.01/14.13 | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | Case 1:
% 100.01/14.13 | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | (114) all_299_2 = all_299_3
% 100.01/14.13 | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | REDUCE: (79), (114) imply:
% 100.01/14.13 | | | | | | | | | | | | (115) $false
% 100.01/14.13 | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | CLOSE: (115) is inconsistent.
% 100.01/14.13 | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | Case 2:
% 100.01/14.13 | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | (116) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2
% 100.01/14.13 | | | | | | | | | | | | = 0 & in(all_299_2, all_299_3) = 0) | ( ~ (v1
% 100.01/14.13 | | | | | | | | | | | | = 0) & in(all_299_2, all_58_2) = v1) | ( ~
% 100.01/14.13 | | | | | | | | | | | | (v0 = 0) & in(all_299_3, all_58_2) = v0))
% 100.01/14.13 | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | DELTA: instantiating (116) with fresh symbols all_499_0,
% 100.01/14.13 | | | | | | | | | | | | all_499_1, all_499_2 gives:
% 100.01/14.13 | | | | | | | | | | | | (117) (all_499_0 = 0 & in(all_299_2, all_299_3) = 0) | (
% 100.01/14.13 | | | | | | | | | | | | ~ (all_499_1 = 0) & in(all_299_2, all_58_2) =
% 100.01/14.13 | | | | | | | | | | | | all_499_1) | ( ~ (all_499_2 = 0) & in(all_299_3,
% 100.01/14.13 | | | | | | | | | | | | all_58_2) = all_499_2)
% 100.01/14.13 | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | BETA: splitting (109) gives:
% 100.01/14.13 | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | Case 1:
% 100.01/14.13 | | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | | (118) all_299_2 = all_299_3
% 100.01/14.13 | | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | | REDUCE: (79), (118) imply:
% 100.01/14.13 | | | | | | | | | | | | | (119) $false
% 100.01/14.13 | | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | | CLOSE: (119) is inconsistent.
% 100.01/14.13 | | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | Case 2:
% 100.01/14.13 | | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | | (120) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2
% 100.01/14.13 | | | | | | | | | | | | | = 0 & in(all_299_2, all_299_3) = 0) | ( ~ (v1
% 100.01/14.13 | | | | | | | | | | | | | = 0) & in(all_299_3, all_58_2) = v1) | ( ~
% 100.01/14.13 | | | | | | | | | | | | | (v0 = 0) & in(all_299_2, all_58_2) = v0))
% 100.01/14.13 | | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | | DELTA: instantiating (120) with fresh symbols all_507_0,
% 100.01/14.13 | | | | | | | | | | | | | all_507_1, all_507_2 gives:
% 100.01/14.13 | | | | | | | | | | | | | (121) (all_507_0 = 0 & in(all_299_2, all_299_3) = 0) | (
% 100.01/14.13 | | | | | | | | | | | | | ~ (all_507_1 = 0) & in(all_299_3, all_58_2) =
% 100.01/14.13 | | | | | | | | | | | | | all_507_1) | ( ~ (all_507_2 = 0) & in(all_299_2,
% 100.01/14.13 | | | | | | | | | | | | | all_58_2) = all_507_2)
% 100.01/14.13 | | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | | BETA: splitting (97) gives:
% 100.01/14.13 | | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | | Case 1:
% 100.01/14.13 | | | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | | | (122) all_409_0 = 0 & in(all_299_3, all_58_2) = 0
% 100.01/14.13 | | | | | | | | | | | | | |
% 100.01/14.13 | | | | | | | | | | | | | | ALPHA: (122) implies:
% 100.01/14.14 | | | | | | | | | | | | | | (123) in(all_299_3, all_58_2) = 0
% 100.01/14.14 | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 100.01/14.14 | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | Case 1:
% 100.01/14.14 | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | (124) all_507_0 = 0 & in(all_299_2, all_299_3) = 0
% 100.01/14.14 | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 100.01/14.14 | | | | | | | | | | | | | | | (125) in(all_299_2, all_299_3) = 0
% 100.01/14.14 | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | REF_CLOSE: (24), (81), (87), (125) are inconsistent by
% 100.01/14.14 | | | | | | | | | | | | | | | sub-proof #5.
% 100.01/14.14 | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | Case 2:
% 100.01/14.14 | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | (126) ( ~ (all_507_1 = 0) & in(all_299_3, all_58_2) =
% 100.01/14.14 | | | | | | | | | | | | | | | all_507_1) | ( ~ (all_507_2 = 0) & in(all_299_2,
% 100.01/14.14 | | | | | | | | | | | | | | | all_58_2) = all_507_2)
% 100.01/14.14 | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 100.01/14.14 | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | Case 1:
% 100.01/14.14 | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | (127) ~ (all_507_1 = 0) & in(all_299_3, all_58_2) =
% 100.01/14.14 | | | | | | | | | | | | | | | | all_507_1
% 100.01/14.14 | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 100.01/14.14 | | | | | | | | | | | | | | | | (128) ~ (all_507_1 = 0)
% 100.01/14.14 | | | | | | | | | | | | | | | | (129) in(all_299_3, all_58_2) = all_507_1
% 100.01/14.14 | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_507_1, all_58_2,
% 100.01/14.14 | | | | | | | | | | | | | | | | all_299_3, simplifying with (123), (129) gives:
% 100.01/14.14 | | | | | | | | | | | | | | | | (130) all_507_1 = 0
% 100.01/14.14 | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | REDUCE: (128), (130) imply:
% 100.01/14.14 | | | | | | | | | | | | | | | | (131) $false
% 100.01/14.14 | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | CLOSE: (131) is inconsistent.
% 100.01/14.14 | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | Case 2:
% 100.01/14.14 | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | (132) ~ (all_507_2 = 0) & in(all_299_2, all_58_2) =
% 100.01/14.14 | | | | | | | | | | | | | | | | all_507_2
% 100.01/14.14 | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 100.01/14.14 | | | | | | | | | | | | | | | | (133) in(all_299_2, all_58_2) = all_507_2
% 100.01/14.14 | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 100.01/14.14 | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | Case 1:
% 100.01/14.14 | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | (134) all_410_0 = 0 & in(all_299_2, all_58_2) = 0
% 100.01/14.14 | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 100.01/14.14 | | | | | | | | | | | | | | | | | (135) in(all_299_2, all_58_2) = 0
% 100.01/14.14 | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 100.01/14.14 | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | Case 1:
% 100.01/14.14 | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | (136) all_499_0 = 0 & in(all_299_2, all_299_3) = 0
% 100.01/14.14 | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | (137) in(all_299_2, all_299_3) = 0
% 100.01/14.14 | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (81), (87), (137) are inconsistent by
% 100.01/14.14 | | | | | | | | | | | | | | | | | | sub-proof #5.
% 100.01/14.14 | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | Case 2:
% 100.01/14.14 | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | (138) ( ~ (all_499_1 = 0) & in(all_299_2, all_58_2) =
% 100.01/14.14 | | | | | | | | | | | | | | | | | | all_499_1) | ( ~ (all_499_2 = 0) & in(all_299_3,
% 100.01/14.14 | | | | | | | | | | | | | | | | | | all_58_2) = all_499_2)
% 100.01/14.14 | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 100.01/14.14 | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | Case 1:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | (139) ~ (all_499_1 = 0) & in(all_299_2, all_58_2) =
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | all_499_1
% 100.01/14.14 | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | (140) in(all_299_2, all_58_2) = all_499_1
% 100.01/14.14 | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | Case 1:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | (141) all_491_0 = 0 & in(all_299_3, all_299_2) = 0
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | (142) in(all_299_3, all_299_2) = 0
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_299_1, 0, all_299_2,
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | all_299_3, simplifying with (85), (142) gives:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | (143) all_299_1 = 0
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (143) imply:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | (144) $false
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | CLOSE: (144) is inconsistent.
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | Case 2:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | (145) ( ~ (all_491_1 = 0) & in(all_299_3, all_58_2) =
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | all_491_1) | ( ~ (all_491_2 = 0) & in(all_299_2,
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | all_58_2) = all_491_2)
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | Case 1:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | (146) ~ (all_491_1 = 0) & in(all_299_3, all_58_2) =
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | all_491_1
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | (147) ~ (all_491_1 = 0)
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | (148) in(all_299_3, all_58_2) = all_491_1
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_491_1, all_58_2,
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | all_299_3, simplifying with (123), (148) gives:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | (149) all_491_1 = 0
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (149) imply:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | (150) $false
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | CLOSE: (150) is inconsistent.
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | Case 2:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | (151) ~ (all_491_2 = 0) & in(all_299_2, all_58_2) =
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | all_491_2
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | (152) ~ (all_491_2 = 0)
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | (153) in(all_299_2, all_58_2) = all_491_2
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_491_2, all_499_1,
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | all_58_2, all_299_2, simplifying with (140), (153)
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | gives:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | (154) all_499_1 = all_491_2
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_499_1, all_507_2,
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | all_58_2, all_299_2, simplifying with (133), (140)
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | gives:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | (155) all_507_2 = all_499_1
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_507_2, all_58_2,
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | all_299_2, simplifying with (133), (135) gives:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | (156) all_507_2 = 0
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (155), (156) imply:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | (157) all_499_1 = 0
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | SIMP: (157) implies:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | (158) all_499_1 = 0
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (154), (158) imply:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | (159) all_491_2 = 0
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | REDUCE: (152), (159) imply:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | (160) $false
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | | CLOSE: (160) is inconsistent.
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | | End of split
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | End of split
% 100.01/14.14 | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | Case 2:
% 100.01/14.14 | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | (161) ~ (all_499_2 = 0) & in(all_299_3, all_58_2) =
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | all_499_2
% 100.01/14.14 | | | | | | | | | | | | | | | | | | |
% 100.01/14.14 | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 100.01/14.15 | | | | | | | | | | | | | | | | | | | (162) ~ (all_499_2 = 0)
% 100.01/14.15 | | | | | | | | | | | | | | | | | | | (163) in(all_299_3, all_58_2) = all_499_2
% 100.01/14.15 | | | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_499_2, all_58_2,
% 100.01/14.15 | | | | | | | | | | | | | | | | | | | all_299_3, simplifying with (123), (163) gives:
% 100.01/14.15 | | | | | | | | | | | | | | | | | | | (164) all_499_2 = 0
% 100.01/14.15 | | | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | | | REDUCE: (162), (164) imply:
% 100.01/14.15 | | | | | | | | | | | | | | | | | | | (165) $false
% 100.01/14.15 | | | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | | | CLOSE: (165) is inconsistent.
% 100.01/14.15 | | | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | | End of split
% 100.01/14.15 | | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | End of split
% 100.01/14.15 | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | Case 2:
% 100.01/14.15 | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | (166) all_410_1 = 0 & in(all_299_2, all_74_0) = 0
% 100.01/14.15 | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 100.01/14.15 | | | | | | | | | | | | | | | | | (167) in(all_299_2, all_74_0) = 0
% 100.01/14.15 | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 100.01/14.15 | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | Case 1:
% 100.01/14.15 | | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | | (168) all_416_0 = 0 & in(all_299_3, all_74_0) = 0
% 100.01/14.15 | | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 100.01/14.15 | | | | | | | | | | | | | | | | | | (169) in(all_299_3, all_74_0) = 0
% 100.01/14.15 | | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (28), (40), (42), (79), (82), (83), (167),
% 100.01/14.15 | | | | | | | | | | | | | | | | | | (169) are inconsistent by sub-proof #4.
% 100.01/14.15 | | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | Case 2:
% 100.01/14.15 | | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | | (170) all_416_1 = 0 & in(all_299_3, all_58_2) = 0
% 100.01/14.15 | | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_58_2, all_74_0,
% 100.01/14.15 | | | | | | | | | | | | | | | | | | all_299_2, simplifying with (28), (40), (42),
% 100.01/14.15 | | | | | | | | | | | | | | | | | | (83), (167) gives:
% 100.01/14.15 | | | | | | | | | | | | | | | | | | (171) all_299_2 = all_58_2
% 100.01/14.15 | | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | | REDUCE: (85), (171) imply:
% 100.01/14.15 | | | | | | | | | | | | | | | | | | (172) in(all_299_3, all_58_2) = all_299_1
% 100.01/14.15 | | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (80), (123), (172) are inconsistent by
% 100.01/14.15 | | | | | | | | | | | | | | | | | | sub-proof #3.
% 100.01/14.15 | | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | | End of split
% 100.01/14.15 | | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | | End of split
% 100.01/14.15 | | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | End of split
% 100.01/14.15 | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | End of split
% 100.01/14.15 | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | Case 2:
% 100.01/14.15 | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | (173) all_409_1 = 0 & in(all_299_3, all_74_0) = 0
% 100.01/14.15 | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | ALPHA: (173) implies:
% 100.01/14.15 | | | | | | | | | | | | | | (174) in(all_299_3, all_74_0) = 0
% 100.01/14.15 | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 100.01/14.15 | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | Case 1:
% 100.01/14.15 | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | (175) all_415_0 = 0 & in(all_299_2, all_74_0) = 0
% 100.01/14.15 | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 100.01/14.15 | | | | | | | | | | | | | | | (176) in(all_299_2, all_74_0) = 0
% 100.01/14.15 | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | REF_CLOSE: (5), (28), (40), (42), (79), (82), (83), (174),
% 100.01/14.15 | | | | | | | | | | | | | | | (176) are inconsistent by sub-proof #4.
% 100.01/14.15 | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | Case 2:
% 100.01/14.15 | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | (177) all_415_1 = 0 & in(all_299_2, all_58_2) = 0
% 100.01/14.15 | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 100.01/14.15 | | | | | | | | | | | | | | | (178) in(all_299_2, all_58_2) = 0
% 100.01/14.15 | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_58_2, all_74_0,
% 100.01/14.15 | | | | | | | | | | | | | | | all_299_3, simplifying with (28), (40), (42),
% 100.01/14.15 | | | | | | | | | | | | | | | (82), (174) gives:
% 100.01/14.15 | | | | | | | | | | | | | | | (179) all_299_3 = all_58_2
% 100.01/14.15 | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | REDUCE: (87), (179) imply:
% 100.01/14.15 | | | | | | | | | | | | | | | (180) in(all_299_2, all_58_2) = all_299_0
% 100.01/14.15 | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | | REF_CLOSE: (24), (81), (178), (180) are inconsistent by
% 100.01/14.15 | | | | | | | | | | | | | | | sub-proof #2.
% 100.01/14.15 | | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | | End of split
% 100.01/14.15 | | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | | End of split
% 100.01/14.15 | | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | | End of split
% 100.01/14.15 | | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | | End of split
% 100.01/14.15 | | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | | End of split
% 100.01/14.15 | | | | | | | | | |
% 100.01/14.15 | | | | | | | | | End of split
% 100.01/14.15 | | | | | | | | |
% 100.01/14.15 | | | | | | | | End of split
% 100.01/14.15 | | | | | | | |
% 100.01/14.15 | | | | | | | End of split
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | Case 2:
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | (181) all_182_1 = 0 & empty(all_159_0) = 0
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | ALPHA: (181) implies:
% 100.01/14.15 | | | | | | | (182) empty(all_159_0) = 0
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | GROUND_INST: instantiating (t7_boole) with all_58_2, all_159_0,
% 100.01/14.15 | | | | | | | simplifying with (28), (57), (89) gives:
% 100.01/14.15 | | | | | | | (183) ? [v0: int] : ( ~ (v0 = 0) & empty(all_159_0) = v0)
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | GROUND_INST: instantiating (21) with all_159_0, simplifying with
% 100.01/14.15 | | | | | | | (57), (182) gives:
% 100.01/14.15 | | | | | | | (184) all_159_0 = empty_set
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | DELTA: instantiating (183) with fresh symbol all_401_0 gives:
% 100.01/14.15 | | | | | | | (185) ~ (all_401_0 = 0) & empty(all_159_0) = all_401_0
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | ALPHA: (185) implies:
% 100.01/14.15 | | | | | | | (186) ~ (all_401_0 = 0)
% 100.01/14.15 | | | | | | | (187) empty(all_159_0) = all_401_0
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | REDUCE: (184), (187) imply:
% 100.01/14.15 | | | | | | | (188) empty(empty_set) = all_401_0
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | REDUCE: (182), (184) imply:
% 100.01/14.15 | | | | | | | (189) empty(empty_set) = 0
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | GROUND_INST: instantiating (22) with 0, all_401_0, empty_set,
% 100.01/14.15 | | | | | | | simplifying with (188), (189) gives:
% 100.01/14.15 | | | | | | | (190) all_401_0 = 0
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | REDUCE: (186), (190) imply:
% 100.01/14.15 | | | | | | | (191) $false
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | CLOSE: (191) is inconsistent.
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | End of split
% 100.01/14.15 | | | | | |
% 100.01/14.15 | | | | | Case 2:
% 100.01/14.15 | | | | | |
% 100.01/14.15 | | | | | | (192) all_172_1 = 0 & empty(all_159_0) = 0
% 100.01/14.15 | | | | | |
% 100.01/14.15 | | | | | | ALPHA: (192) implies:
% 100.01/14.15 | | | | | | (193) empty(all_159_0) = 0
% 100.01/14.15 | | | | | |
% 100.01/14.15 | | | | | | BETA: splitting (70) gives:
% 100.01/14.15 | | | | | |
% 100.01/14.15 | | | | | | Case 1:
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | (194) all_182_0 = 0 & in(all_74_0, all_159_0) = 0
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | ALPHA: (194) implies:
% 100.01/14.15 | | | | | | | (195) in(all_74_0, all_159_0) = 0
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | GROUND_INST: instantiating (t7_boole) with all_74_0, all_159_0,
% 100.01/14.15 | | | | | | | simplifying with (40), (57), (195) gives:
% 100.01/14.15 | | | | | | | (196) ? [v0: int] : ( ~ (v0 = 0) & empty(all_159_0) = v0)
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | GROUND_INST: instantiating (21) with all_159_0, simplifying with
% 100.01/14.15 | | | | | | | (57), (193) gives:
% 100.01/14.15 | | | | | | | (197) all_159_0 = empty_set
% 100.01/14.15 | | | | | | |
% 100.01/14.15 | | | | | | | DELTA: instantiating (196) with fresh symbol all_401_0 gives:
% 100.01/14.16 | | | | | | | (198) ~ (all_401_0 = 0) & empty(all_159_0) = all_401_0
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | ALPHA: (198) implies:
% 100.01/14.16 | | | | | | | (199) ~ (all_401_0 = 0)
% 100.01/14.16 | | | | | | | (200) empty(all_159_0) = all_401_0
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | REDUCE: (197), (200) imply:
% 100.01/14.16 | | | | | | | (201) empty(empty_set) = all_401_0
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | REDUCE: (193), (197) imply:
% 100.01/14.16 | | | | | | | (202) empty(empty_set) = 0
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | GROUND_INST: instantiating (22) with 0, all_401_0, empty_set,
% 100.01/14.16 | | | | | | | simplifying with (201), (202) gives:
% 100.01/14.16 | | | | | | | (203) all_401_0 = 0
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | REDUCE: (199), (203) imply:
% 100.01/14.16 | | | | | | | (204) $false
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | CLOSE: (204) is inconsistent.
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | Case 2:
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | GROUND_INST: instantiating (8) with all_74_0, all_58_2, all_58_1,
% 100.01/14.16 | | | | | | | all_299_3, simplifying with (28), (29), (40), (52),
% 100.01/14.16 | | | | | | | (82), (84) gives:
% 100.01/14.16 | | | | | | | (205) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_299_3,
% 100.01/14.16 | | | | | | | all_58_2) = 0) | (v0 = 0 & in(all_299_3, all_74_0)
% 100.01/14.16 | | | | | | | = 0))
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | GROUND_INST: instantiating (8) with all_58_2, all_74_0, all_58_1,
% 100.01/14.16 | | | | | | | all_299_3, simplifying with (28), (29), (40), (41),
% 100.01/14.16 | | | | | | | (82), (84) gives:
% 100.01/14.16 | | | | | | | (206) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_299_3,
% 100.01/14.16 | | | | | | | all_74_0) = 0) | (v0 = 0 & in(all_299_3, all_58_2)
% 100.01/14.16 | | | | | | | = 0))
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | GROUND_INST: instantiating (14) with all_58_2, all_299_2,
% 100.01/14.16 | | | | | | | all_299_3, all_299_1, simplifying with (28), (34),
% 100.01/14.16 | | | | | | | (82), (83), (85) gives:
% 100.01/14.16 | | | | | | | (207) all_299_1 = 0 | all_299_2 = all_299_3 | ? [v0: int] : ?
% 100.01/14.16 | | | | | | | [v1: int] : ? [v2: int] : ((v2 = 0 & in(all_299_2,
% 100.01/14.16 | | | | | | | all_299_3) = 0) | ( ~ (v1 = 0) & in(all_299_3,
% 100.01/14.16 | | | | | | | all_58_2) = v1) | ( ~ (v0 = 0) & in(all_299_2,
% 100.01/14.16 | | | | | | | all_58_2) = v0))
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | GROUND_INST: instantiating (8) with all_74_0, all_58_2, all_58_1,
% 100.01/14.16 | | | | | | | all_299_2, simplifying with (28), (29), (40), (52),
% 100.01/14.16 | | | | | | | (83), (86) gives:
% 100.01/14.16 | | | | | | | (208) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_299_2,
% 100.01/14.16 | | | | | | | all_58_2) = 0) | (v0 = 0 & in(all_299_2, all_74_0)
% 100.01/14.16 | | | | | | | = 0))
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | GROUND_INST: instantiating (8) with all_58_2, all_74_0, all_58_1,
% 100.01/14.16 | | | | | | | all_299_2, simplifying with (28), (29), (40), (41),
% 100.01/14.16 | | | | | | | (83), (86) gives:
% 100.01/14.16 | | | | | | | (209) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_299_2,
% 100.01/14.16 | | | | | | | all_74_0) = 0) | (v0 = 0 & in(all_299_2, all_58_2)
% 100.01/14.16 | | | | | | | = 0))
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | DELTA: instantiating (205) with fresh symbols all_401_0, all_401_1
% 100.01/14.16 | | | | | | | gives:
% 100.01/14.16 | | | | | | | (210) (all_401_0 = 0 & in(all_299_3, all_58_2) = 0) |
% 100.01/14.16 | | | | | | | (all_401_1 = 0 & in(all_299_3, all_74_0) = 0)
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | DELTA: instantiating (209) with fresh symbols all_406_0, all_406_1
% 100.01/14.16 | | | | | | | gives:
% 100.01/14.16 | | | | | | | (211) (all_406_0 = 0 & in(all_299_2, all_74_0) = 0) |
% 100.01/14.16 | | | | | | | (all_406_1 = 0 & in(all_299_2, all_58_2) = 0)
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | DELTA: instantiating (206) with fresh symbols all_407_0, all_407_1
% 100.01/14.16 | | | | | | | gives:
% 100.01/14.16 | | | | | | | (212) (all_407_0 = 0 & in(all_299_3, all_74_0) = 0) |
% 100.01/14.16 | | | | | | | (all_407_1 = 0 & in(all_299_3, all_58_2) = 0)
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | DELTA: instantiating (208) with fresh symbols all_408_0, all_408_1
% 100.01/14.16 | | | | | | | gives:
% 100.01/14.16 | | | | | | | (213) (all_408_0 = 0 & in(all_299_2, all_58_2) = 0) |
% 100.01/14.16 | | | | | | | (all_408_1 = 0 & in(all_299_2, all_74_0) = 0)
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | BETA: splitting (207) gives:
% 100.01/14.16 | | | | | | |
% 100.01/14.16 | | | | | | | Case 1:
% 100.01/14.16 | | | | | | | |
% 100.01/14.16 | | | | | | | | (214) all_299_1 = 0
% 100.01/14.16 | | | | | | | |
% 100.01/14.16 | | | | | | | | REDUCE: (80), (214) imply:
% 100.01/14.16 | | | | | | | | (215) $false
% 100.01/14.16 | | | | | | | |
% 100.01/14.16 | | | | | | | | CLOSE: (215) is inconsistent.
% 100.01/14.16 | | | | | | | |
% 100.01/14.16 | | | | | | | Case 2:
% 100.01/14.16 | | | | | | | |
% 100.01/14.16 | | | | | | | | (216) all_299_2 = all_299_3 | ? [v0: int] : ? [v1: int] :
% 100.01/14.16 | | | | | | | | ? [v2: int] : ((v2 = 0 & in(all_299_2, all_299_3) = 0)
% 100.01/14.16 | | | | | | | | | ( ~ (v1 = 0) & in(all_299_3, all_58_2) = v1) | ( ~
% 100.01/14.16 | | | | | | | | (v0 = 0) & in(all_299_2, all_58_2) = v0))
% 100.01/14.16 | | | | | | | |
% 100.01/14.16 | | | | | | | | BETA: splitting (216) gives:
% 100.01/14.16 | | | | | | | |
% 100.01/14.16 | | | | | | | | Case 1:
% 100.01/14.16 | | | | | | | | |
% 100.01/14.16 | | | | | | | | | (217) all_299_2 = all_299_3
% 100.01/14.16 | | | | | | | | |
% 100.01/14.16 | | | | | | | | | REDUCE: (79), (217) imply:
% 100.01/14.16 | | | | | | | | | (218) $false
% 100.01/14.16 | | | | | | | | |
% 100.01/14.16 | | | | | | | | | CLOSE: (218) is inconsistent.
% 100.01/14.16 | | | | | | | | |
% 100.01/14.16 | | | | | | | | Case 2:
% 100.01/14.16 | | | | | | | | |
% 100.01/14.16 | | | | | | | | | (219) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0
% 100.01/14.16 | | | | | | | | | & in(all_299_2, all_299_3) = 0) | ( ~ (v1 = 0) &
% 100.01/14.16 | | | | | | | | | in(all_299_3, all_58_2) = v1) | ( ~ (v0 = 0) &
% 100.01/14.16 | | | | | | | | | in(all_299_2, all_58_2) = v0))
% 100.01/14.16 | | | | | | | | |
% 100.01/14.16 | | | | | | | | | DELTA: instantiating (219) with fresh symbols all_491_0,
% 100.01/14.16 | | | | | | | | | all_491_1, all_491_2 gives:
% 100.01/14.16 | | | | | | | | | (220) (all_491_0 = 0 & in(all_299_2, all_299_3) = 0) | ( ~
% 100.01/14.16 | | | | | | | | | (all_491_1 = 0) & in(all_299_3, all_58_2) =
% 100.01/14.16 | | | | | | | | | all_491_1) | ( ~ (all_491_2 = 0) & in(all_299_2,
% 100.01/14.16 | | | | | | | | | all_58_2) = all_491_2)
% 100.01/14.16 | | | | | | | | |
% 100.01/14.16 | | | | | | | | | BETA: splitting (210) gives:
% 100.01/14.16 | | | | | | | | |
% 100.01/14.16 | | | | | | | | | Case 1:
% 100.01/14.16 | | | | | | | | | |
% 100.01/14.16 | | | | | | | | | | (221) all_401_0 = 0 & in(all_299_3, all_58_2) = 0
% 100.01/14.16 | | | | | | | | | |
% 100.01/14.16 | | | | | | | | | | ALPHA: (221) implies:
% 100.01/14.16 | | | | | | | | | | (222) in(all_299_3, all_58_2) = 0
% 100.01/14.16 | | | | | | | | | |
% 100.01/14.16 | | | | | | | | | | BETA: splitting (220) gives:
% 100.01/14.16 | | | | | | | | | |
% 100.01/14.16 | | | | | | | | | | Case 1:
% 100.01/14.16 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | (223) all_491_0 = 0 & in(all_299_2, all_299_3) = 0
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | ALPHA: (223) implies:
% 100.01/14.17 | | | | | | | | | | | (224) in(all_299_2, all_299_3) = 0
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | REF_CLOSE: (24), (81), (87), (224) are inconsistent by
% 100.01/14.17 | | | | | | | | | | | sub-proof #5.
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | Case 2:
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | (225) ( ~ (all_491_1 = 0) & in(all_299_3, all_58_2) =
% 100.01/14.17 | | | | | | | | | | | all_491_1) | ( ~ (all_491_2 = 0) & in(all_299_2,
% 100.01/14.17 | | | | | | | | | | | all_58_2) = all_491_2)
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | BETA: splitting (225) gives:
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | Case 1:
% 100.01/14.17 | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | (226) ~ (all_491_1 = 0) & in(all_299_3, all_58_2) =
% 100.01/14.17 | | | | | | | | | | | | all_491_1
% 100.01/14.17 | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | ALPHA: (226) implies:
% 100.01/14.17 | | | | | | | | | | | | (227) ~ (all_491_1 = 0)
% 100.01/14.17 | | | | | | | | | | | | (228) in(all_299_3, all_58_2) = all_491_1
% 100.01/14.17 | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_491_1, all_58_2,
% 100.01/14.17 | | | | | | | | | | | | all_299_3, simplifying with (222), (228) gives:
% 100.01/14.17 | | | | | | | | | | | | (229) all_491_1 = 0
% 100.01/14.17 | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | REDUCE: (227), (229) imply:
% 100.01/14.17 | | | | | | | | | | | | (230) $false
% 100.01/14.17 | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | CLOSE: (230) is inconsistent.
% 100.01/14.17 | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | Case 2:
% 100.01/14.17 | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | (231) ~ (all_491_2 = 0) & in(all_299_2, all_58_2) =
% 100.01/14.17 | | | | | | | | | | | | all_491_2
% 100.01/14.17 | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | ALPHA: (231) implies:
% 100.01/14.17 | | | | | | | | | | | | (232) ~ (all_491_2 = 0)
% 100.01/14.17 | | | | | | | | | | | | (233) in(all_299_2, all_58_2) = all_491_2
% 100.01/14.17 | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | BETA: splitting (211) gives:
% 100.01/14.17 | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | Case 1:
% 100.01/14.17 | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | (234) all_406_0 = 0 & in(all_299_2, all_74_0) = 0
% 100.01/14.17 | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | ALPHA: (234) implies:
% 100.01/14.17 | | | | | | | | | | | | | (235) in(all_299_2, all_74_0) = 0
% 100.01/14.17 | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | BETA: splitting (212) gives:
% 100.01/14.17 | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | Case 1:
% 100.01/14.17 | | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | | (236) all_407_0 = 0 & in(all_299_3, all_74_0) = 0
% 100.01/14.17 | | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | | ALPHA: (236) implies:
% 100.01/14.17 | | | | | | | | | | | | | | (237) in(all_299_3, all_74_0) = 0
% 100.01/14.17 | | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | | REF_CLOSE: (5), (28), (40), (42), (79), (82), (83), (235),
% 100.01/14.17 | | | | | | | | | | | | | | (237) are inconsistent by sub-proof #4.
% 100.01/14.17 | | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | Case 2:
% 100.01/14.17 | | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | | (238) all_407_1 = 0 & in(all_299_3, all_58_2) = 0
% 100.01/14.17 | | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_58_2, all_74_0,
% 100.01/14.17 | | | | | | | | | | | | | | all_299_2, simplifying with (28), (40), (42),
% 100.01/14.17 | | | | | | | | | | | | | | (83), (235) gives:
% 100.01/14.17 | | | | | | | | | | | | | | (239) all_299_2 = all_58_2
% 100.01/14.17 | | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | | REDUCE: (85), (239) imply:
% 100.01/14.17 | | | | | | | | | | | | | | (240) in(all_299_3, all_58_2) = all_299_1
% 100.01/14.17 | | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | | REF_CLOSE: (24), (80), (222), (240) are inconsistent by
% 100.01/14.17 | | | | | | | | | | | | | | sub-proof #3.
% 100.01/14.17 | | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | End of split
% 100.01/14.17 | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | Case 2:
% 100.01/14.17 | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | (241) all_406_1 = 0 & in(all_299_2, all_58_2) = 0
% 100.01/14.17 | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | ALPHA: (241) implies:
% 100.01/14.17 | | | | | | | | | | | | | (242) in(all_299_2, all_58_2) = 0
% 100.01/14.17 | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_491_2, all_58_2,
% 100.01/14.17 | | | | | | | | | | | | | all_299_2, simplifying with (233), (242) gives:
% 100.01/14.17 | | | | | | | | | | | | | (243) all_491_2 = 0
% 100.01/14.17 | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | REDUCE: (232), (243) imply:
% 100.01/14.17 | | | | | | | | | | | | | (244) $false
% 100.01/14.17 | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | | CLOSE: (244) is inconsistent.
% 100.01/14.17 | | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | | End of split
% 100.01/14.17 | | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | End of split
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | End of split
% 100.01/14.17 | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | Case 2:
% 100.01/14.17 | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | (245) all_401_1 = 0 & in(all_299_3, all_74_0) = 0
% 100.01/14.17 | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | ALPHA: (245) implies:
% 100.01/14.17 | | | | | | | | | | (246) in(all_299_3, all_74_0) = 0
% 100.01/14.17 | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | BETA: splitting (213) gives:
% 100.01/14.17 | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | Case 1:
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | (247) all_408_0 = 0 & in(all_299_2, all_58_2) = 0
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | ALPHA: (247) implies:
% 100.01/14.17 | | | | | | | | | | | (248) in(all_299_2, all_58_2) = 0
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | GROUND_INST: instantiating (5) with all_58_2, all_74_0,
% 100.01/14.17 | | | | | | | | | | | all_299_3, simplifying with (28), (40), (42),
% 100.01/14.17 | | | | | | | | | | | (82), (246) gives:
% 100.01/14.17 | | | | | | | | | | | (249) all_299_3 = all_58_2
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | REDUCE: (87), (249) imply:
% 100.01/14.17 | | | | | | | | | | | (250) in(all_299_2, all_58_2) = all_299_0
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | REF_CLOSE: (24), (81), (248), (250) are inconsistent by
% 100.01/14.17 | | | | | | | | | | | sub-proof #2.
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | Case 2:
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | (251) all_408_1 = 0 & in(all_299_2, all_74_0) = 0
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | ALPHA: (251) implies:
% 100.01/14.17 | | | | | | | | | | | (252) in(all_299_2, all_74_0) = 0
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | | REF_CLOSE: (5), (28), (40), (42), (79), (82), (83), (246),
% 100.01/14.17 | | | | | | | | | | | (252) are inconsistent by sub-proof #4.
% 100.01/14.17 | | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | | End of split
% 100.01/14.17 | | | | | | | | | |
% 100.01/14.17 | | | | | | | | | End of split
% 100.01/14.17 | | | | | | | | |
% 100.01/14.17 | | | | | | | | End of split
% 100.01/14.17 | | | | | | | |
% 100.01/14.17 | | | | | | | End of split
% 100.01/14.17 | | | | | | |
% 100.01/14.17 | | | | | | End of split
% 100.01/14.17 | | | | | |
% 100.01/14.17 | | | | | End of split
% 100.01/14.17 | | | | |
% 100.01/14.17 | | | | End of split
% 100.01/14.17 | | | |
% 100.01/14.17 | | | Case 2:
% 100.01/14.17 | | | |
% 100.01/14.17 | | | | (253) ~ (all_105_1 = 0) & epsilon_transitive(all_58_1) = all_105_1
% 100.01/14.17 | | | |
% 100.01/14.17 | | | | ALPHA: (253) implies:
% 100.01/14.17 | | | | (254) ~ (all_105_1 = 0)
% 100.01/14.17 | | | | (255) epsilon_transitive(all_58_1) = all_105_1
% 100.01/14.17 | | | |
% 100.01/14.17 | | | | GROUND_INST: instantiating (6) with all_58_1, all_105_1, simplifying
% 100.01/14.17 | | | | with (29), (255) gives:
% 100.01/14.17 | | | | (256) all_105_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 100.01/14.17 | | | | subset(v0, all_58_1) = v1 & in(v0, all_58_1) = 0 & $i(v0))
% 100.01/14.17 | | | |
% 100.01/14.17 | | | | BETA: splitting (256) gives:
% 100.01/14.17 | | | |
% 100.01/14.17 | | | | Case 1:
% 100.01/14.17 | | | | |
% 100.01/14.17 | | | | | (257) all_105_1 = 0
% 100.01/14.17 | | | | |
% 100.01/14.17 | | | | | REDUCE: (254), (257) imply:
% 100.01/14.17 | | | | | (258) $false
% 100.01/14.17 | | | | |
% 100.01/14.17 | | | | | CLOSE: (258) is inconsistent.
% 100.01/14.17 | | | | |
% 100.01/14.17 | | | | Case 2:
% 100.01/14.17 | | | | |
% 100.01/14.17 | | | | | (259) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0,
% 100.01/14.17 | | | | | all_58_1) = v1 & in(v0, all_58_1) = 0 & $i(v0))
% 100.01/14.18 | | | | |
% 100.01/14.18 | | | | | DELTA: instantiating (259) with fresh symbols all_299_0, all_299_1
% 100.01/14.18 | | | | | gives:
% 100.01/14.18 | | | | | (260) ~ (all_299_0 = 0) & subset(all_299_1, all_58_1) = all_299_0
% 100.01/14.18 | | | | | & in(all_299_1, all_58_1) = 0 & $i(all_299_1)
% 100.01/14.18 | | | | |
% 100.01/14.18 | | | | | ALPHA: (260) implies:
% 100.01/14.18 | | | | | (261) ~ (all_299_0 = 0)
% 100.01/14.18 | | | | | (262) $i(all_299_1)
% 100.01/14.18 | | | | | (263) in(all_299_1, all_58_1) = 0
% 100.01/14.18 | | | | | (264) subset(all_299_1, all_58_1) = all_299_0
% 100.01/14.18 | | | | |
% 100.01/14.18 | | | | | BETA: splitting (66) gives:
% 100.01/14.18 | | | | |
% 100.01/14.18 | | | | | Case 1:
% 100.01/14.18 | | | | | |
% 100.01/14.18 | | | | | | (265) all_172_0 = 0 & in(all_58_2, all_159_0) = 0
% 100.01/14.18 | | | | | |
% 100.01/14.18 | | | | | | ALPHA: (265) implies:
% 100.01/14.18 | | | | | | (266) in(all_58_2, all_159_0) = 0
% 100.01/14.18 | | | | | |
% 100.01/14.18 | | | | | | BETA: splitting (70) gives:
% 100.01/14.18 | | | | | |
% 100.01/14.18 | | | | | | Case 1:
% 100.01/14.18 | | | | | | |
% 100.01/14.18 | | | | | | | (267) all_182_0 = 0 & in(all_74_0, all_159_0) = 0
% 100.01/14.18 | | | | | | |
% 100.01/14.18 | | | | | | | ALPHA: (267) implies:
% 100.01/14.18 | | | | | | | (268) in(all_74_0, all_159_0) = 0
% 100.01/14.18 | | | | | | |
% 100.01/14.18 | | | | | | | GROUND_INST: instantiating (1) with all_159_0, all_58_2,
% 100.01/14.18 | | | | | | | simplifying with (28), (57), (266) gives:
% 100.01/14.18 | | | | | | | (269) ? [v0: int] : ( ~ (v0 = 0) & in(all_159_0, all_58_2) =
% 100.01/14.18 | | | | | | | v0)
% 100.01/14.18 | | | | | | |
% 100.01/14.18 | | | | | | | GROUND_INST: instantiating (1) with all_159_0, all_74_0,
% 100.01/14.18 | | | | | | | simplifying with (40), (57), (268) gives:
% 100.01/14.18 | | | | | | | (270) ? [v0: int] : ( ~ (v0 = 0) & in(all_159_0, all_74_0) =
% 100.01/14.18 | | | | | | | v0)
% 100.01/14.18 | | | | | | |
% 100.01/14.18 | | | | | | | GROUND_INST: instantiating (8) with all_74_0, all_58_2, all_58_1,
% 100.01/14.18 | | | | | | | all_299_1, simplifying with (28), (29), (40), (52),
% 100.01/14.18 | | | | | | | (262), (263) gives:
% 100.01/14.18 | | | | | | | (271) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_299_1,
% 100.01/14.18 | | | | | | | all_58_2) = 0) | (v0 = 0 & in(all_299_1, all_74_0)
% 100.01/14.18 | | | | | | | = 0))
% 100.01/14.18 | | | | | | |
% 100.01/14.18 | | | | | | | GROUND_INST: instantiating (17) with all_299_1, all_74_0,
% 100.01/14.18 | | | | | | | all_58_1, all_299_0, simplifying with (29), (40),
% 100.01/14.18 | | | | | | | (54), (262), (264) gives:
% 100.01/14.18 | | | | | | | (272) all_299_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 100.01/14.18 | | | | | | | subset(all_299_1, all_74_0) = v0)
% 100.01/14.18 | | | | | | |
% 100.01/14.18 | | | | | | | GROUND_INST: instantiating (17) with all_299_1, all_58_2,
% 100.01/14.18 | | | | | | | all_58_1, all_299_0, simplifying with (28), (29),
% 100.01/14.18 | | | | | | | (53), (262), (264) gives:
% 100.01/14.18 | | | | | | | (273) all_299_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 100.01/14.18 | | | | | | | subset(all_299_1, all_58_2) = v0)
% 100.01/14.18 | | | | | | |
% 100.01/14.18 | | | | | | | GROUND_INST: instantiating (20) with all_299_1, all_58_1,
% 100.01/14.18 | | | | | | | all_299_0, simplifying with (29), (262), (264) gives:
% 100.01/14.18 | | | | | | | (274) all_299_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0)
% 100.01/14.18 | | | | | | | & powerset(all_58_1) = v0 & element(all_299_1, v0) = v1
% 100.01/14.18 | | | | | | | & $i(v0))
% 100.01/14.18 | | | | | | |
% 100.01/14.18 | | | | | | | DELTA: instantiating (270) with fresh symbol all_397_0 gives:
% 100.01/14.18 | | | | | | | (275) ~ (all_397_0 = 0) & in(all_159_0, all_74_0) = all_397_0
% 100.01/14.18 | | | | | | |
% 100.01/14.18 | | | | | | | ALPHA: (275) implies:
% 100.01/14.18 | | | | | | | (276) ~ (all_397_0 = 0)
% 100.01/14.18 | | | | | | | (277) in(all_159_0, all_74_0) = all_397_0
% 100.01/14.18 | | | | | | |
% 100.01/14.18 | | | | | | | DELTA: instantiating (269) with fresh symbol all_399_0 gives:
% 100.01/14.18 | | | | | | | (278) ~ (all_399_0 = 0) & in(all_159_0, all_58_2) = all_399_0
% 100.01/14.18 | | | | | | |
% 100.01/14.18 | | | | | | | ALPHA: (278) implies:
% 100.01/14.18 | | | | | | | (279) ~ (all_399_0 = 0)
% 100.01/14.18 | | | | | | | (280) in(all_159_0, all_58_2) = all_399_0
% 100.01/14.18 | | | | | | |
% 100.01/14.18 | | | | | | | DELTA: instantiating (271) with fresh symbols all_407_0, all_407_1
% 100.01/14.18 | | | | | | | gives:
% 100.01/14.18 | | | | | | | (281) (all_407_0 = 0 & in(all_299_1, all_58_2) = 0) |
% 100.01/14.18 | | | | | | | (all_407_1 = 0 & in(all_299_1, all_74_0) = 0)
% 100.01/14.18 | | | | | | |
% 100.01/14.18 | | | | | | | BETA: splitting (274) gives:
% 100.01/14.18 | | | | | | |
% 100.01/14.18 | | | | | | | Case 1:
% 100.01/14.18 | | | | | | | |
% 100.01/14.18 | | | | | | | | (282) all_299_0 = 0
% 100.01/14.18 | | | | | | | |
% 100.01/14.18 | | | | | | | | REDUCE: (261), (282) imply:
% 100.01/14.18 | | | | | | | | (283) $false
% 100.01/14.18 | | | | | | | |
% 100.01/14.18 | | | | | | | | CLOSE: (283) is inconsistent.
% 100.01/14.18 | | | | | | | |
% 100.01/14.18 | | | | | | | Case 2:
% 100.01/14.18 | | | | | | | |
% 100.01/14.18 | | | | | | | | (284) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 100.01/14.18 | | | | | | | | powerset(all_58_1) = v0 & element(all_299_1, v0) = v1
% 100.01/14.18 | | | | | | | | & $i(v0))
% 100.01/14.18 | | | | | | | |
% 100.01/14.18 | | | | | | | | DELTA: instantiating (284) with fresh symbols all_418_0,
% 100.01/14.18 | | | | | | | | all_418_1 gives:
% 100.01/14.18 | | | | | | | | (285) ~ (all_418_0 = 0) & powerset(all_58_1) = all_418_1 &
% 100.01/14.18 | | | | | | | | element(all_299_1, all_418_1) = all_418_0 &
% 100.01/14.18 | | | | | | | | $i(all_418_1)
% 100.01/14.18 | | | | | | | |
% 100.01/14.18 | | | | | | | | ALPHA: (285) implies:
% 100.01/14.18 | | | | | | | | (286) $i(all_418_1)
% 100.01/14.18 | | | | | | | | (287) powerset(all_58_1) = all_418_1
% 100.01/14.18 | | | | | | | |
% 100.01/14.18 | | | | | | | | BETA: splitting (273) gives:
% 100.01/14.18 | | | | | | | |
% 100.01/14.18 | | | | | | | | Case 1:
% 100.01/14.18 | | | | | | | | |
% 100.01/14.18 | | | | | | | | | (288) all_299_0 = 0
% 100.01/14.18 | | | | | | | | |
% 100.01/14.18 | | | | | | | | | REDUCE: (261), (288) imply:
% 100.01/14.18 | | | | | | | | | (289) $false
% 100.01/14.18 | | | | | | | | |
% 100.01/14.18 | | | | | | | | | CLOSE: (289) is inconsistent.
% 100.01/14.18 | | | | | | | | |
% 100.01/14.18 | | | | | | | | Case 2:
% 100.01/14.18 | | | | | | | | |
% 100.01/14.18 | | | | | | | | | (290) ? [v0: int] : ( ~ (v0 = 0) & subset(all_299_1,
% 100.01/14.18 | | | | | | | | | all_58_2) = v0)
% 100.01/14.18 | | | | | | | | |
% 100.01/14.18 | | | | | | | | | DELTA: instantiating (290) with fresh symbol all_423_0 gives:
% 100.01/14.18 | | | | | | | | | (291) ~ (all_423_0 = 0) & subset(all_299_1, all_58_2) =
% 100.01/14.18 | | | | | | | | | all_423_0
% 100.01/14.18 | | | | | | | | |
% 100.01/14.18 | | | | | | | | | ALPHA: (291) implies:
% 100.01/14.18 | | | | | | | | | (292) ~ (all_423_0 = 0)
% 100.01/14.18 | | | | | | | | | (293) subset(all_299_1, all_58_2) = all_423_0
% 100.01/14.18 | | | | | | | | |
% 100.01/14.18 | | | | | | | | | BETA: splitting (272) gives:
% 100.01/14.18 | | | | | | | | |
% 100.01/14.18 | | | | | | | | | Case 1:
% 100.01/14.18 | | | | | | | | | |
% 100.01/14.18 | | | | | | | | | | (294) all_299_0 = 0
% 100.01/14.18 | | | | | | | | | |
% 100.01/14.18 | | | | | | | | | | REDUCE: (261), (294) imply:
% 100.01/14.18 | | | | | | | | | | (295) $false
% 100.01/14.18 | | | | | | | | | |
% 100.01/14.18 | | | | | | | | | | CLOSE: (295) is inconsistent.
% 100.01/14.18 | | | | | | | | | |
% 100.01/14.18 | | | | | | | | | Case 2:
% 100.01/14.18 | | | | | | | | | |
% 100.01/14.18 | | | | | | | | | |
% 100.01/14.18 | | | | | | | | | | GROUND_INST: instantiating (23) with all_159_0, all_418_1,
% 100.01/14.18 | | | | | | | | | | all_58_1, simplifying with (59), (287) gives:
% 100.01/14.18 | | | | | | | | | | (296) all_418_1 = all_159_0
% 100.01/14.18 | | | | | | | | | |
% 100.01/14.18 | | | | | | | | | | GROUND_INST: instantiating (10) with all_58_2, all_74_0,
% 100.01/14.18 | | | | | | | | | | all_58_1, all_159_0, all_399_0, simplifying with
% 100.01/14.18 | | | | | | | | | | (28), (29), (40), (41), (57), (280) gives:
% 100.01/14.18 | | | | | | | | | | (297) all_399_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1
% 100.01/14.18 | | | | | | | | | | = 0 & in(all_159_0, all_74_0) = 0) | ( ~ (v0 =
% 100.01/14.18 | | | | | | | | | | 0) & in(all_159_0, all_58_1) = v0))
% 100.01/14.19 | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | GROUND_INST: instantiating (9) with all_58_2, all_74_0,
% 100.01/14.19 | | | | | | | | | | all_58_1, all_159_0, all_399_0, simplifying with
% 100.01/14.19 | | | | | | | | | | (28), (29), (40), (41), (57), (280) gives:
% 100.01/14.19 | | | | | | | | | | (298) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 100.01/14.19 | | | | | | | | | | in(all_159_0, all_58_1) = 0) | ( ~ (v0 = 0) &
% 100.01/14.19 | | | | | | | | | | ~ (all_399_0 = 0) & in(all_159_0, all_74_0) =
% 100.01/14.19 | | | | | | | | | | v0))
% 100.01/14.19 | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | GROUND_INST: instantiating (11) with all_58_2, all_74_0,
% 100.01/14.19 | | | | | | | | | | all_58_1, all_159_0, all_397_0, simplifying with
% 100.01/14.19 | | | | | | | | | | (28), (29), (40), (41), (57), (277) gives:
% 100.01/14.19 | | | | | | | | | | (299) all_397_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1
% 100.01/14.19 | | | | | | | | | | = 0 & in(all_159_0, all_58_2) = 0) | ( ~ (v0 =
% 100.01/14.19 | | | | | | | | | | 0) & in(all_159_0, all_58_1) = v0))
% 100.01/14.19 | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | GROUND_INST: instantiating (7) with all_58_2, all_299_1,
% 100.01/14.19 | | | | | | | | | | all_423_0, simplifying with (28), (35), (262),
% 100.01/14.19 | | | | | | | | | | (293) gives:
% 100.01/14.19 | | | | | | | | | | (300) all_423_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 100.01/14.19 | | | | | | | | | | in(all_299_1, all_58_2) = v0)
% 100.01/14.19 | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | DELTA: instantiating (298) with fresh symbols all_445_0,
% 100.01/14.19 | | | | | | | | | | all_445_1 gives:
% 100.01/14.19 | | | | | | | | | | (301) (all_445_0 = 0 & in(all_159_0, all_58_1) = 0) | ( ~
% 100.01/14.19 | | | | | | | | | | (all_445_1 = 0) & ~ (all_399_0 = 0) &
% 100.01/14.19 | | | | | | | | | | in(all_159_0, all_74_0) = all_445_1)
% 100.01/14.19 | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | BETA: splitting (300) gives:
% 100.01/14.19 | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | Case 1:
% 100.01/14.19 | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | (302) all_423_0 = 0
% 100.01/14.19 | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | REDUCE: (292), (302) imply:
% 100.01/14.19 | | | | | | | | | | | (303) $false
% 100.01/14.19 | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | CLOSE: (303) is inconsistent.
% 100.01/14.19 | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | Case 2:
% 100.01/14.19 | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | (304) ? [v0: int] : ( ~ (v0 = 0) & in(all_299_1,
% 100.01/14.19 | | | | | | | | | | | all_58_2) = v0)
% 100.01/14.19 | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | DELTA: instantiating (304) with fresh symbol all_482_0
% 100.01/14.19 | | | | | | | | | | | gives:
% 100.01/14.19 | | | | | | | | | | | (305) ~ (all_482_0 = 0) & in(all_299_1, all_58_2) =
% 100.01/14.19 | | | | | | | | | | | all_482_0
% 100.01/14.19 | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | ALPHA: (305) implies:
% 100.01/14.19 | | | | | | | | | | | (306) ~ (all_482_0 = 0)
% 100.01/14.19 | | | | | | | | | | | (307) in(all_299_1, all_58_2) = all_482_0
% 100.01/14.19 | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | BETA: splitting (297) gives:
% 100.01/14.19 | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | Case 1:
% 100.01/14.19 | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | (308) all_399_0 = 0
% 100.01/14.19 | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | REDUCE: (279), (308) imply:
% 100.01/14.19 | | | | | | | | | | | | (309) $false
% 100.01/14.19 | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | CLOSE: (309) is inconsistent.
% 100.01/14.19 | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | Case 2:
% 100.01/14.19 | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | (310) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 100.01/14.19 | | | | | | | | | | | | in(all_159_0, all_74_0) = 0) | ( ~ (v0 = 0) &
% 100.01/14.19 | | | | | | | | | | | | in(all_159_0, all_58_1) = v0))
% 100.01/14.19 | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | DELTA: instantiating (310) with fresh symbols all_506_0,
% 100.01/14.19 | | | | | | | | | | | | all_506_1 gives:
% 100.01/14.19 | | | | | | | | | | | | (311) (all_506_0 = 0 & in(all_159_0, all_74_0) = 0) | (
% 100.01/14.19 | | | | | | | | | | | | ~ (all_506_1 = 0) & in(all_159_0, all_58_1) =
% 100.01/14.19 | | | | | | | | | | | | all_506_1)
% 100.01/14.19 | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | BETA: splitting (299) gives:
% 100.01/14.19 | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | Case 1:
% 100.01/14.19 | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | (312) all_397_0 = 0
% 100.01/14.19 | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | REDUCE: (276), (312) imply:
% 100.01/14.19 | | | | | | | | | | | | | (313) $false
% 100.01/14.19 | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | CLOSE: (313) is inconsistent.
% 100.01/14.19 | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | Case 2:
% 100.01/14.19 | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | (314) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 100.01/14.19 | | | | | | | | | | | | | in(all_159_0, all_58_2) = 0) | ( ~ (v0 = 0) &
% 100.01/14.19 | | | | | | | | | | | | | in(all_159_0, all_58_1) = v0))
% 100.01/14.19 | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | DELTA: instantiating (314) with fresh symbols all_510_0,
% 100.01/14.19 | | | | | | | | | | | | | all_510_1 gives:
% 100.01/14.19 | | | | | | | | | | | | | (315) (all_510_0 = 0 & in(all_159_0, all_58_2) = 0) | (
% 100.01/14.19 | | | | | | | | | | | | | ~ (all_510_1 = 0) & in(all_159_0, all_58_1) =
% 100.01/14.19 | | | | | | | | | | | | | all_510_1)
% 100.01/14.19 | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | BETA: splitting (281) gives:
% 100.01/14.19 | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | Case 1:
% 100.01/14.19 | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | (316) all_407_0 = 0 & in(all_299_1, all_58_2) = 0
% 100.01/14.19 | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | ALPHA: (316) implies:
% 100.01/14.19 | | | | | | | | | | | | | | (317) in(all_299_1, all_58_2) = 0
% 100.01/14.19 | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_482_0, all_58_2,
% 100.01/14.19 | | | | | | | | | | | | | | all_299_1, simplifying with (307), (317) gives:
% 100.01/14.19 | | | | | | | | | | | | | | (318) all_482_0 = 0
% 100.01/14.19 | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | REDUCE: (306), (318) imply:
% 100.01/14.19 | | | | | | | | | | | | | | (319) $false
% 100.01/14.19 | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | CLOSE: (319) is inconsistent.
% 100.01/14.19 | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | Case 2:
% 100.01/14.19 | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | (320) all_407_1 = 0 & in(all_299_1, all_74_0) = 0
% 100.01/14.19 | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | ALPHA: (320) implies:
% 100.01/14.19 | | | | | | | | | | | | | | (321) in(all_299_1, all_74_0) = 0
% 100.01/14.19 | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 100.01/14.19 | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | Case 1:
% 100.01/14.19 | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | (322) all_510_0 = 0 & in(all_159_0, all_58_2) = 0
% 100.01/14.19 | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | ALPHA: (322) implies:
% 100.01/14.19 | | | | | | | | | | | | | | | (323) in(all_159_0, all_58_2) = 0
% 100.01/14.19 | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_399_0, 0, all_58_2,
% 100.01/14.19 | | | | | | | | | | | | | | | all_159_0, simplifying with (280), (323) gives:
% 100.01/14.19 | | | | | | | | | | | | | | | (324) all_399_0 = 0
% 100.01/14.19 | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | REDUCE: (279), (324) imply:
% 100.01/14.19 | | | | | | | | | | | | | | | (325) $false
% 100.01/14.19 | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | CLOSE: (325) is inconsistent.
% 100.01/14.19 | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | Case 2:
% 100.01/14.19 | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | (326) ~ (all_510_1 = 0) & in(all_159_0, all_58_1) =
% 100.01/14.19 | | | | | | | | | | | | | | | all_510_1
% 100.01/14.19 | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | ALPHA: (326) implies:
% 100.01/14.19 | | | | | | | | | | | | | | | (327) in(all_159_0, all_58_1) = all_510_1
% 100.01/14.19 | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 100.01/14.19 | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | Case 1:
% 100.01/14.19 | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | | (328) all_506_0 = 0 & in(all_159_0, all_74_0) = 0
% 100.01/14.19 | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | | ALPHA: (328) implies:
% 100.01/14.19 | | | | | | | | | | | | | | | | (329) in(all_159_0, all_74_0) = 0
% 100.01/14.19 | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_397_0, 0, all_74_0,
% 100.01/14.19 | | | | | | | | | | | | | | | | all_159_0, simplifying with (277), (329) gives:
% 100.01/14.19 | | | | | | | | | | | | | | | | (330) all_397_0 = 0
% 100.01/14.19 | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | | REDUCE: (276), (330) imply:
% 100.01/14.19 | | | | | | | | | | | | | | | | (331) $false
% 100.01/14.19 | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | | CLOSE: (331) is inconsistent.
% 100.01/14.19 | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | Case 2:
% 100.01/14.19 | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | | (332) ~ (all_506_1 = 0) & in(all_159_0, all_58_1) =
% 100.01/14.19 | | | | | | | | | | | | | | | | all_506_1
% 100.01/14.19 | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | | ALPHA: (332) implies:
% 100.01/14.19 | | | | | | | | | | | | | | | | (333) ~ (all_506_1 = 0)
% 100.01/14.19 | | | | | | | | | | | | | | | | (334) in(all_159_0, all_58_1) = all_506_1
% 100.01/14.19 | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 100.01/14.19 | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | | Case 1:
% 100.01/14.19 | | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | | | (335) all_445_0 = 0 & in(all_159_0, all_58_1) = 0
% 100.01/14.19 | | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | | | ALPHA: (335) implies:
% 100.01/14.19 | | | | | | | | | | | | | | | | | (336) in(all_159_0, all_58_1) = 0
% 100.01/14.19 | | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_506_1, all_510_1,
% 100.01/14.19 | | | | | | | | | | | | | | | | | all_58_1, all_159_0, simplifying with (327), (334)
% 100.01/14.19 | | | | | | | | | | | | | | | | | gives:
% 100.01/14.19 | | | | | | | | | | | | | | | | | (337) all_510_1 = all_506_1
% 100.01/14.19 | | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_510_1, all_58_1,
% 100.01/14.19 | | | | | | | | | | | | | | | | | all_159_0, simplifying with (327), (336) gives:
% 100.01/14.19 | | | | | | | | | | | | | | | | | (338) all_510_1 = 0
% 100.01/14.19 | | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | | | COMBINE_EQS: (337), (338) imply:
% 100.01/14.19 | | | | | | | | | | | | | | | | | (339) all_506_1 = 0
% 100.01/14.19 | | | | | | | | | | | | | | | | |
% 100.01/14.19 | | | | | | | | | | | | | | | | | SIMP: (339) implies:
% 100.01/14.20 | | | | | | | | | | | | | | | | | (340) all_506_1 = 0
% 100.01/14.20 | | | | | | | | | | | | | | | | |
% 100.01/14.20 | | | | | | | | | | | | | | | | | REDUCE: (333), (340) imply:
% 100.01/14.20 | | | | | | | | | | | | | | | | | (341) $false
% 100.01/14.20 | | | | | | | | | | | | | | | | |
% 100.01/14.20 | | | | | | | | | | | | | | | | | CLOSE: (341) is inconsistent.
% 100.01/14.20 | | | | | | | | | | | | | | | | |
% 100.01/14.20 | | | | | | | | | | | | | | | | Case 2:
% 100.01/14.20 | | | | | | | | | | | | | | | | |
% 100.01/14.20 | | | | | | | | | | | | | | | | |
% 100.01/14.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_58_2, all_74_0,
% 100.01/14.20 | | | | | | | | | | | | | | | | | all_299_1, simplifying with (28), (40), (42),
% 100.01/14.20 | | | | | | | | | | | | | | | | | (262), (321) gives:
% 100.01/14.20 | | | | | | | | | | | | | | | | | (342) all_299_1 = all_58_2
% 100.01/14.20 | | | | | | | | | | | | | | | | |
% 100.01/14.20 | | | | | | | | | | | | | | | | | REDUCE: (264), (342) imply:
% 100.01/14.20 | | | | | | | | | | | | | | | | | (343) subset(all_58_2, all_58_1) = all_299_0
% 100.01/14.20 | | | | | | | | | | | | | | | | |
% 100.01/14.20 | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (53), (261), (343) are inconsistent by
% 100.01/14.20 | | | | | | | | | | | | | | | | | sub-proof #1.
% 100.01/14.20 | | | | | | | | | | | | | | | | |
% 100.01/14.20 | | | | | | | | | | | | | | | | End of split
% 100.01/14.20 | | | | | | | | | | | | | | | |
% 100.01/14.20 | | | | | | | | | | | | | | | End of split
% 100.01/14.20 | | | | | | | | | | | | | | |
% 100.01/14.20 | | | | | | | | | | | | | | End of split
% 100.01/14.20 | | | | | | | | | | | | | |
% 100.01/14.20 | | | | | | | | | | | | | End of split
% 100.01/14.20 | | | | | | | | | | | | |
% 100.01/14.20 | | | | | | | | | | | | End of split
% 100.01/14.20 | | | | | | | | | | | |
% 100.01/14.20 | | | | | | | | | | | End of split
% 100.01/14.20 | | | | | | | | | | |
% 100.01/14.20 | | | | | | | | | | End of split
% 100.01/14.20 | | | | | | | | | |
% 100.01/14.20 | | | | | | | | | End of split
% 100.01/14.20 | | | | | | | | |
% 100.01/14.20 | | | | | | | | End of split
% 100.01/14.20 | | | | | | | |
% 100.01/14.20 | | | | | | | End of split
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | Case 2:
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | (344) all_182_1 = 0 & empty(all_159_0) = 0
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | ALPHA: (344) implies:
% 100.01/14.20 | | | | | | | (345) empty(all_159_0) = 0
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | GROUND_INST: instantiating (t7_boole) with all_58_2, all_159_0,
% 100.01/14.20 | | | | | | | simplifying with (28), (57), (266) gives:
% 100.01/14.20 | | | | | | | (346) ? [v0: int] : ( ~ (v0 = 0) & empty(all_159_0) = v0)
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | GROUND_INST: instantiating (21) with all_159_0, simplifying with
% 100.01/14.20 | | | | | | | (57), (345) gives:
% 100.01/14.20 | | | | | | | (347) all_159_0 = empty_set
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | DELTA: instantiating (346) with fresh symbol all_395_0 gives:
% 100.01/14.20 | | | | | | | (348) ~ (all_395_0 = 0) & empty(all_159_0) = all_395_0
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | ALPHA: (348) implies:
% 100.01/14.20 | | | | | | | (349) ~ (all_395_0 = 0)
% 100.01/14.20 | | | | | | | (350) empty(all_159_0) = all_395_0
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | REDUCE: (347), (350) imply:
% 100.01/14.20 | | | | | | | (351) empty(empty_set) = all_395_0
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | REDUCE: (345), (347) imply:
% 100.01/14.20 | | | | | | | (352) empty(empty_set) = 0
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | GROUND_INST: instantiating (22) with 0, all_395_0, empty_set,
% 100.01/14.20 | | | | | | | simplifying with (351), (352) gives:
% 100.01/14.20 | | | | | | | (353) all_395_0 = 0
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | REDUCE: (349), (353) imply:
% 100.01/14.20 | | | | | | | (354) $false
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | CLOSE: (354) is inconsistent.
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | End of split
% 100.01/14.20 | | | | | |
% 100.01/14.20 | | | | | Case 2:
% 100.01/14.20 | | | | | |
% 100.01/14.20 | | | | | |
% 100.01/14.20 | | | | | | GROUND_INST: instantiating (8) with all_58_2, all_74_0, all_58_1,
% 100.01/14.20 | | | | | | all_299_1, simplifying with (28), (29), (40), (41),
% 100.01/14.20 | | | | | | (262), (263) gives:
% 100.01/14.20 | | | | | | (355) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_299_1,
% 100.01/14.20 | | | | | | all_74_0) = 0) | (v0 = 0 & in(all_299_1, all_58_2) =
% 100.01/14.20 | | | | | | 0))
% 100.01/14.20 | | | | | |
% 100.01/14.20 | | | | | | GROUND_INST: instantiating (17) with all_299_1, all_58_2, all_58_1,
% 100.01/14.20 | | | | | | all_299_0, simplifying with (28), (29), (53), (262),
% 100.01/14.20 | | | | | | (264) gives:
% 100.01/14.20 | | | | | | (356) all_299_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 100.01/14.20 | | | | | | subset(all_299_1, all_58_2) = v0)
% 100.01/14.20 | | | | | |
% 100.01/14.20 | | | | | | DELTA: instantiating (355) with fresh symbols all_408_0, all_408_1
% 100.01/14.20 | | | | | | gives:
% 100.01/14.20 | | | | | | (357) (all_408_0 = 0 & in(all_299_1, all_74_0) = 0) | (all_408_1
% 100.01/14.20 | | | | | | = 0 & in(all_299_1, all_58_2) = 0)
% 100.01/14.20 | | | | | |
% 100.01/14.20 | | | | | | BETA: splitting (356) gives:
% 100.01/14.20 | | | | | |
% 100.01/14.20 | | | | | | Case 1:
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | (358) all_299_0 = 0
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | REDUCE: (261), (358) imply:
% 100.01/14.20 | | | | | | | (359) $false
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | CLOSE: (359) is inconsistent.
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | Case 2:
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | (360) ? [v0: int] : ( ~ (v0 = 0) & subset(all_299_1, all_58_2)
% 100.01/14.20 | | | | | | | = v0)
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | DELTA: instantiating (360) with fresh symbol all_434_0 gives:
% 100.01/14.20 | | | | | | | (361) ~ (all_434_0 = 0) & subset(all_299_1, all_58_2) =
% 100.01/14.20 | | | | | | | all_434_0
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | ALPHA: (361) implies:
% 100.01/14.20 | | | | | | | (362) ~ (all_434_0 = 0)
% 100.01/14.20 | | | | | | | (363) subset(all_299_1, all_58_2) = all_434_0
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | GROUND_INST: instantiating (7) with all_58_2, all_299_1,
% 100.01/14.20 | | | | | | | all_434_0, simplifying with (28), (35), (262), (363)
% 100.01/14.20 | | | | | | | gives:
% 100.01/14.20 | | | | | | | (364) all_434_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 100.01/14.20 | | | | | | | in(all_299_1, all_58_2) = v0)
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | BETA: splitting (364) gives:
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | | Case 1:
% 100.01/14.20 | | | | | | | |
% 100.01/14.20 | | | | | | | | (365) all_434_0 = 0
% 100.01/14.20 | | | | | | | |
% 100.01/14.20 | | | | | | | | REDUCE: (362), (365) imply:
% 100.01/14.20 | | | | | | | | (366) $false
% 100.01/14.20 | | | | | | | |
% 100.01/14.20 | | | | | | | | CLOSE: (366) is inconsistent.
% 100.01/14.20 | | | | | | | |
% 100.01/14.20 | | | | | | | Case 2:
% 100.01/14.20 | | | | | | | |
% 100.01/14.20 | | | | | | | | (367) ? [v0: int] : ( ~ (v0 = 0) & in(all_299_1, all_58_2) =
% 100.01/14.20 | | | | | | | | v0)
% 100.01/14.20 | | | | | | | |
% 100.01/14.20 | | | | | | | | DELTA: instantiating (367) with fresh symbol all_482_0 gives:
% 100.01/14.20 | | | | | | | | (368) ~ (all_482_0 = 0) & in(all_299_1, all_58_2) =
% 100.01/14.20 | | | | | | | | all_482_0
% 100.01/14.20 | | | | | | | |
% 100.01/14.20 | | | | | | | | ALPHA: (368) implies:
% 100.01/14.20 | | | | | | | | (369) ~ (all_482_0 = 0)
% 100.01/14.20 | | | | | | | | (370) in(all_299_1, all_58_2) = all_482_0
% 100.01/14.20 | | | | | | | |
% 100.01/14.20 | | | | | | | | BETA: splitting (357) gives:
% 100.01/14.20 | | | | | | | |
% 100.01/14.20 | | | | | | | | Case 1:
% 100.01/14.20 | | | | | | | | |
% 100.01/14.20 | | | | | | | | | (371) all_408_0 = 0 & in(all_299_1, all_74_0) = 0
% 100.01/14.20 | | | | | | | | |
% 100.01/14.20 | | | | | | | | | ALPHA: (371) implies:
% 100.01/14.20 | | | | | | | | | (372) in(all_299_1, all_74_0) = 0
% 100.01/14.20 | | | | | | | | |
% 100.01/14.20 | | | | | | | | | GROUND_INST: instantiating (5) with all_58_2, all_74_0,
% 100.01/14.20 | | | | | | | | | all_299_1, simplifying with (28), (40), (42),
% 100.01/14.20 | | | | | | | | | (262), (372) gives:
% 100.01/14.20 | | | | | | | | | (373) all_299_1 = all_58_2
% 100.01/14.20 | | | | | | | | |
% 100.01/14.20 | | | | | | | | | REDUCE: (264), (373) imply:
% 100.01/14.20 | | | | | | | | | (374) subset(all_58_2, all_58_1) = all_299_0
% 100.01/14.20 | | | | | | | | |
% 100.01/14.20 | | | | | | | | | REF_CLOSE: (25), (53), (261), (374) are inconsistent by
% 100.01/14.20 | | | | | | | | | sub-proof #1.
% 100.01/14.20 | | | | | | | | |
% 100.01/14.20 | | | | | | | | Case 2:
% 100.01/14.20 | | | | | | | | |
% 100.01/14.20 | | | | | | | | | (375) all_408_1 = 0 & in(all_299_1, all_58_2) = 0
% 100.01/14.20 | | | | | | | | |
% 100.01/14.20 | | | | | | | | | ALPHA: (375) implies:
% 100.01/14.20 | | | | | | | | | (376) in(all_299_1, all_58_2) = 0
% 100.01/14.20 | | | | | | | | |
% 100.01/14.20 | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_482_0, all_58_2,
% 100.01/14.20 | | | | | | | | | all_299_1, simplifying with (370), (376) gives:
% 100.01/14.20 | | | | | | | | | (377) all_482_0 = 0
% 100.01/14.20 | | | | | | | | |
% 100.01/14.20 | | | | | | | | | REDUCE: (369), (377) imply:
% 100.01/14.20 | | | | | | | | | (378) $false
% 100.01/14.20 | | | | | | | | |
% 100.01/14.20 | | | | | | | | | CLOSE: (378) is inconsistent.
% 100.01/14.20 | | | | | | | | |
% 100.01/14.20 | | | | | | | | End of split
% 100.01/14.20 | | | | | | | |
% 100.01/14.20 | | | | | | | End of split
% 100.01/14.20 | | | | | | |
% 100.01/14.20 | | | | | | End of split
% 100.01/14.20 | | | | | |
% 100.01/14.20 | | | | | End of split
% 100.01/14.20 | | | | |
% 100.01/14.20 | | | | End of split
% 100.01/14.20 | | | |
% 100.01/14.20 | | | End of split
% 100.01/14.20 | | |
% 100.01/14.20 | | End of split
% 100.01/14.20 | |
% 100.01/14.20 | End of split
% 100.01/14.20 |
% 100.01/14.20 End of proof
% 100.01/14.20
% 100.01/14.20 Sub-proof #1 shows that the following formulas are inconsistent:
% 100.01/14.20 ----------------------------------------------------------------
% 100.01/14.20 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 100.01/14.20 ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) =
% 100.01/14.20 v0))
% 100.01/14.21 (2) subset(all_58_2, all_58_1) = all_299_0
% 100.01/14.21 (3) subset(all_58_2, all_58_1) = 0
% 100.01/14.21 (4) ~ (all_299_0 = 0)
% 100.01/14.21
% 100.01/14.21 Begin of proof
% 100.01/14.21 |
% 100.01/14.21 | GROUND_INST: instantiating (1) with 0, all_299_0, all_58_1, all_58_2,
% 100.01/14.21 | simplifying with (2), (3) gives:
% 100.01/14.21 | (5) all_299_0 = 0
% 100.01/14.21 |
% 100.01/14.21 | REDUCE: (4), (5) imply:
% 100.01/14.21 | (6) $false
% 100.01/14.21 |
% 100.01/14.21 | CLOSE: (6) is inconsistent.
% 100.01/14.21 |
% 100.01/14.21 End of proof
% 100.01/14.21
% 100.01/14.21 Sub-proof #2 shows that the following formulas are inconsistent:
% 100.01/14.21 ----------------------------------------------------------------
% 100.01/14.21 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 100.01/14.21 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 100.01/14.21 (2) in(all_299_2, all_58_2) = all_299_0
% 100.01/14.21 (3) in(all_299_2, all_58_2) = 0
% 100.01/14.21 (4) ~ (all_299_0 = 0)
% 100.01/14.21
% 100.01/14.21 Begin of proof
% 100.01/14.21 |
% 100.01/14.21 | GROUND_INST: instantiating (1) with 0, all_299_0, all_58_2, all_299_2,
% 100.01/14.21 | simplifying with (2), (3) gives:
% 100.01/14.21 | (5) all_299_0 = 0
% 100.01/14.21 |
% 100.01/14.21 | REDUCE: (4), (5) imply:
% 100.01/14.21 | (6) $false
% 100.01/14.21 |
% 100.01/14.21 | CLOSE: (6) is inconsistent.
% 100.01/14.21 |
% 100.01/14.21 End of proof
% 100.01/14.21
% 100.01/14.21 Sub-proof #3 shows that the following formulas are inconsistent:
% 100.01/14.21 ----------------------------------------------------------------
% 100.01/14.21 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 100.01/14.21 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 100.01/14.21 (2) in(all_299_3, all_58_2) = all_299_1
% 100.01/14.21 (3) in(all_299_3, all_58_2) = 0
% 100.01/14.21 (4) ~ (all_299_1 = 0)
% 100.01/14.21
% 100.01/14.21 Begin of proof
% 100.01/14.21 |
% 100.01/14.21 | GROUND_INST: instantiating (1) with 0, all_299_1, all_58_2, all_299_3,
% 100.01/14.21 | simplifying with (2), (3) gives:
% 100.01/14.21 | (5) all_299_1 = 0
% 100.01/14.21 |
% 100.01/14.21 | REDUCE: (4), (5) imply:
% 100.01/14.21 | (6) $false
% 100.01/14.21 |
% 100.01/14.21 | CLOSE: (6) is inconsistent.
% 100.01/14.21 |
% 100.01/14.21 End of proof
% 100.01/14.21
% 100.01/14.21 Sub-proof #4 shows that the following formulas are inconsistent:
% 100.01/14.21 ----------------------------------------------------------------
% 100.01/14.21 (1) $i(all_74_0)
% 100.01/14.21 (2) $i(all_58_2)
% 100.01/14.21 (3) singleton(all_58_2) = all_74_0
% 100.01/14.21 (4) $i(all_299_2)
% 100.01/14.21 (5) in(all_299_3, all_74_0) = 0
% 100.01/14.21 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) =
% 100.01/14.21 v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 100.01/14.21 (7) in(all_299_2, all_74_0) = 0
% 100.01/14.21 (8) ~ (all_299_2 = all_299_3)
% 100.01/14.21 (9) $i(all_299_3)
% 100.01/14.21
% 100.01/14.21 Begin of proof
% 100.01/14.21 |
% 100.01/14.21 | GROUND_INST: instantiating (6) with all_58_2, all_74_0, all_299_3, simplifying
% 100.01/14.21 | with (1), (2), (3), (5), (9) gives:
% 100.01/14.21 | (10) all_299_3 = all_58_2
% 100.01/14.21 |
% 100.01/14.21 | GROUND_INST: instantiating (6) with all_58_2, all_74_0, all_299_2, simplifying
% 100.01/14.21 | with (1), (2), (3), (4), (7) gives:
% 100.01/14.21 | (11) all_299_2 = all_58_2
% 100.01/14.21 |
% 100.01/14.21 | REDUCE: (8), (10), (11) imply:
% 100.01/14.21 | (12) $false
% 100.01/14.21 |
% 100.01/14.21 | CLOSE: (12) is inconsistent.
% 100.01/14.21 |
% 100.01/14.21 End of proof
% 100.01/14.21
% 100.01/14.21 Sub-proof #5 shows that the following formulas are inconsistent:
% 100.01/14.21 ----------------------------------------------------------------
% 100.01/14.21 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 100.01/14.21 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 100.01/14.21 (2) in(all_299_2, all_299_3) = all_299_0
% 100.01/14.21 (3) in(all_299_2, all_299_3) = 0
% 100.01/14.21 (4) ~ (all_299_0 = 0)
% 100.01/14.21
% 100.01/14.21 Begin of proof
% 100.01/14.21 |
% 100.01/14.21 | GROUND_INST: instantiating (1) with all_299_0, 0, all_299_3, all_299_2,
% 100.01/14.21 | simplifying with (2), (3) gives:
% 100.01/14.21 | (5) all_299_0 = 0
% 100.01/14.21 |
% 100.01/14.21 | REDUCE: (4), (5) imply:
% 100.01/14.21 | (6) $false
% 100.01/14.21 |
% 100.01/14.21 | CLOSE: (6) is inconsistent.
% 100.01/14.21 |
% 100.01/14.21 End of proof
% 100.01/14.21 % SZS output end Proof for theBenchmark
% 100.01/14.21
% 100.01/14.21 13582ms
%------------------------------------------------------------------------------