TSTP Solution File: SEU232+3 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU232+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n014.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 17:43:31 EDT 2023
% Result : Theorem 23.37s 4.00s
% Output : Proof 175.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU232+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n014.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 : Wed Aug 23 14:14:34 EDT 2023
% 0.14/0.35 % 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/sandbox/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
% 2.87/1.12 Prover 4: Preprocessing ...
% 2.87/1.12 Prover 1: Preprocessing ...
% 2.87/1.16 Prover 3: Preprocessing ...
% 2.87/1.16 Prover 2: Preprocessing ...
% 2.87/1.16 Prover 0: Preprocessing ...
% 2.87/1.16 Prover 6: Preprocessing ...
% 2.87/1.16 Prover 5: Preprocessing ...
% 5.35/1.64 Prover 1: Warning: ignoring some quantifiers
% 5.35/1.68 Prover 5: Proving ...
% 5.35/1.70 Prover 1: Constructing countermodel ...
% 5.35/1.70 Prover 2: Proving ...
% 6.92/1.73 Prover 6: Proving ...
% 7.10/1.76 Prover 3: Warning: ignoring some quantifiers
% 7.10/1.78 Prover 3: Constructing countermodel ...
% 7.10/1.82 Prover 4: Warning: ignoring some quantifiers
% 7.57/1.86 Prover 0: Proving ...
% 7.57/1.86 Prover 4: Constructing countermodel ...
% 12.06/2.53 Prover 3: gave up
% 12.06/2.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.71/2.58 Prover 7: Preprocessing ...
% 13.34/2.65 Prover 7: Warning: ignoring some quantifiers
% 13.34/2.66 Prover 7: Constructing countermodel ...
% 23.37/4.00 Prover 0: proved (3347ms)
% 23.37/4.00
% 23.37/4.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.37/4.00
% 23.37/4.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 23.37/4.00 Prover 6: stopped
% 23.37/4.01 Prover 5: stopped
% 23.37/4.01 Prover 2: stopped
% 23.37/4.02 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 23.37/4.02 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 23.37/4.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 23.95/4.04 Prover 8: Preprocessing ...
% 23.95/4.05 Prover 10: Preprocessing ...
% 23.95/4.06 Prover 13: Preprocessing ...
% 23.95/4.06 Prover 11: Preprocessing ...
% 24.22/4.11 Prover 10: Warning: ignoring some quantifiers
% 24.22/4.13 Prover 10: Constructing countermodel ...
% 24.63/4.14 Prover 13: Warning: ignoring some quantifiers
% 24.63/4.14 Prover 13: Constructing countermodel ...
% 24.82/4.16 Prover 8: Warning: ignoring some quantifiers
% 24.82/4.17 Prover 8: Constructing countermodel ...
% 24.82/4.20 Prover 11: Warning: ignoring some quantifiers
% 24.82/4.21 Prover 11: Constructing countermodel ...
% 66.10/9.61 Prover 13: stopped
% 66.10/9.61 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 66.64/9.65 Prover 16: Preprocessing ...
% 66.64/9.70 Prover 16: Warning: ignoring some quantifiers
% 67.14/9.72 Prover 16: Constructing countermodel ...
% 108.25/15.24 Prover 16: stopped
% 108.25/15.24 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 108.25/15.30 Prover 19: Preprocessing ...
% 108.25/15.39 Prover 19: Warning: ignoring some quantifiers
% 108.25/15.40 Prover 19: Constructing countermodel ...
% 113.99/15.99 Prover 1: stopped
% 132.92/18.99 Prover 19: stopped
% 174.67/25.54 Prover 11: Found proof (size 300)
% 174.67/25.54 Prover 11: proved (21519ms)
% 174.67/25.54 Prover 4: stopped
% 174.67/25.54 Prover 10: stopped
% 174.67/25.54 Prover 7: stopped
% 174.67/25.54 Prover 8: stopped
% 174.67/25.54
% 174.67/25.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 174.67/25.54
% 174.67/25.56 % SZS output start Proof for theBenchmark
% 174.67/25.56 Assumptions after simplification:
% 174.67/25.56 ---------------------------------
% 174.67/25.56
% 174.67/25.56 (antisymmetry_r2_hidden)
% 175.03/25.59 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 175.03/25.59 [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : (
% 175.03/25.59 ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 175.03/25.59 in(v1, v0) = v2))
% 175.03/25.59
% 175.03/25.59 (d2_ordinal1)
% 175.03/25.59 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v1, v0) = v2)
% 175.03/25.59 | ~ (epsilon_transitive(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : (
% 175.03/25.59 ~ (v3 = 0) & in(v1, v0) = v3)) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 175.03/25.59 (epsilon_transitive(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~
% 175.03/25.59 (v3 = 0) & subset(v2, v0) = v3 & in(v2, v0) = 0 & $i(v2))) & ! [v0: $i] :
% 175.03/25.59 ! [v1: $i] : ( ~ (epsilon_transitive(v0) = 0) | ~ (in(v1, v0) = 0) | ~
% 175.03/25.59 $i(v1) | ~ $i(v0) | subset(v1, v0) = 0)
% 175.03/25.59
% 175.03/25.59 (d3_ordinal1)
% 175.03/25.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 = v1 |
% 175.03/25.60 ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 175.03/25.60 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ((v6 = 0 & in(v1,
% 175.03/25.60 v2) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4 = 0) & in(v1, v0)
% 175.03/25.60 = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 =
% 175.03/25.60 0 | v2 = v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v1, v2) = v3) | ~
% 175.03/25.60 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int]
% 175.03/25.60 : ((v6 = 0 & in(v2, v1) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4 =
% 175.03/25.60 0) & in(v1, v0) = v4))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 175.03/25.60 (epsilon_connected(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ?
% 175.03/25.60 [v4: int] : ? [v5: int] : ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) &
% 175.03/25.60 in(v3, v2) = v5 & in(v3, v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 &
% 175.03/25.60 $i(v3) & $i(v2)))
% 175.03/25.60
% 175.03/25.60 (d3_tarski)
% 175.03/25.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 175.03/25.61 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 175.03/25.61 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 175.03/25.61 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 175.03/25.61 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 175.03/25.61 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 175.03/25.61 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 175.03/25.61 $i(v0) | in(v2, v1) = 0)
% 175.03/25.61
% 175.03/25.61 (d4_ordinal1)
% 175.03/25.61 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (ordinal(v0) = v1) | ~ $i(v0) | ?
% 175.03/25.61 [v2: int] : ? [v3: int] : (( ~ (v3 = 0) & epsilon_connected(v0) = v3) | ( ~
% 175.03/25.61 (v2 = 0) & epsilon_transitive(v0) = v2))) & ! [v0: $i] : ! [v1: any] :
% 175.03/25.61 ( ~ (epsilon_transitive(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] :
% 175.03/25.61 ((v3 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0)
% 175.03/25.61 = v2))) & ! [v0: $i] : ! [v1: any] : ( ~ (epsilon_connected(v0) = v1)
% 175.03/25.61 | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & v1 = 0 &
% 175.03/25.61 epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & !
% 175.03/25.61 [v0: $i] : ( ~ (epsilon_transitive(v0) = 0) | ~ $i(v0) | ? [v1: int] : ?
% 175.03/25.61 [v2: int] : ((v2 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) &
% 175.03/25.61 epsilon_connected(v0) = v1))) & ! [v0: $i] : ( ~ (ordinal(v0) = 0) | ~
% 175.03/25.61 $i(v0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) & ! [v0:
% 175.03/25.61 $i] : ( ~ (epsilon_connected(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2:
% 175.03/25.61 int] : ((v2 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0)
% 175.03/25.61 = v1)))
% 175.03/25.61
% 175.03/25.61 (fc4_relat_1)
% 175.03/25.61 relation(empty_set) = 0 & empty(empty_set) = 0 & $i(empty_set)
% 175.03/25.61
% 175.03/25.61 (rc1_ordinal1)
% 175.03/25.61 ? [v0: $i] : (epsilon_transitive(v0) = 0 & ordinal(v0) = 0 &
% 175.03/25.61 epsilon_connected(v0) = 0 & $i(v0))
% 175.03/25.61
% 175.03/25.61 (rc1_relat_1)
% 175.03/25.61 ? [v0: $i] : (relation(v0) = 0 & empty(v0) = 0 & $i(v0))
% 175.03/25.61
% 175.03/25.61 (rc1_xboole_0)
% 175.03/25.61 ? [v0: $i] : (empty(v0) = 0 & $i(v0))
% 175.03/25.61
% 175.03/25.61 (rc2_funct_1)
% 175.03/25.62 ? [v0: $i] : (relation(v0) = 0 & function(v0) = 0 & empty(v0) = 0 & $i(v0))
% 175.03/25.62
% 175.03/25.62 (t1_subset)
% 175.03/25.62 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (element(v0, v1) = v2)
% 175.03/25.62 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v0, v1) = v3)) &
% 175.03/25.62 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 175.03/25.62 element(v0, v1) = 0)
% 175.03/25.62
% 175.03/25.62 (t23_ordinal1)
% 175.03/25.62 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & ordinal(v1) = 0 &
% 175.03/25.62 ordinal(v0) = v2 & in(v0, v1) = 0 & $i(v1) & $i(v0))
% 175.03/25.62
% 175.03/25.62 (t2_subset)
% 175.03/25.62 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~
% 175.03/25.62 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & empty(v1) = 0)
% 175.03/25.62 | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 175.03/25.62 (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int]
% 175.03/25.62 : ((v3 = 0 & in(v0, v1) = 0) | (v2 = 0 & empty(v1) = 0)))
% 175.03/25.62
% 175.03/25.62 (t3_ordinal1)
% 175.03/25.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ (in(v1,
% 175.03/25.62 v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 =
% 175.03/25.62 0) & in(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 175.03/25.62 (in(v2, v0) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 175.03/25.62 ? [v3: int] : ( ~ (v3 = 0) & in(v1, v2) = v3)) & ! [v0: $i] : ! [v1: $i]
% 175.03/25.62 : ! [v2: $i] : ( ~ (in(v1, v2) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~
% 175.03/25.62 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v2, v0) = v3))
% 175.03/25.62
% 175.03/25.62 (t3_subset)
% 175.03/25.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 175.03/25.63 (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 175.03/25.63 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i]
% 175.03/25.63 : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 175.03/25.63 ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0,
% 175.03/25.63 v3) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 175.03/25.63 (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) |
% 175.03/25.63 subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) |
% 175.03/25.63 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) =
% 175.03/25.63 0 & $i(v2)))
% 175.03/25.63
% 175.03/25.63 (t5_subset)
% 175.03/25.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) =
% 175.03/25.63 v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~
% 175.03/25.63 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & empty(v2) = v4)) & !
% 175.03/25.63 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) =
% 175.03/25.63 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 175.03/25.63 (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4 & $i(v3)))
% 175.03/25.63
% 175.03/25.63 (t6_boole)
% 175.03/25.63 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~
% 175.03/25.63 $i(v0))
% 175.03/25.63
% 175.03/25.63 (t8_boole)
% 175.03/25.63 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)
% 175.03/25.63 | ~ $i(v1) | ~ $i(v0))
% 175.03/25.63
% 175.03/25.63 (function-axioms)
% 175.03/25.63 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 175.03/25.63 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 175.03/25.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 175.03/25.63 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 175.03/25.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 175.03/25.63 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 175.03/25.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 175.03/25.63 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 175.03/25.63 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 175.03/25.63 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 175.03/25.63 $i] : (v1 = v0 | ~ (relation_non_empty(v2) = v1) | ~
% 175.03/25.63 (relation_non_empty(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 175.03/25.63 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 175.03/25.63 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 175.03/25.63 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 175.03/25.63 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0:
% 175.03/25.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 175.03/25.63 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool]
% 175.03/25.64 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 175.03/25.64 (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0:
% 175.03/25.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 175.03/25.64 ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] :
% 175.03/25.64 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 175.03/25.64 (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0:
% 175.03/25.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 175.03/25.64 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool]
% 175.03/25.64 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) |
% 175.03/25.64 ~ (empty(v2) = v0))
% 175.03/25.64
% 175.03/25.64 Further assumptions not needed in the proof:
% 175.03/25.64 --------------------------------------------
% 175.03/25.64 cc1_funct_1, cc1_ordinal1, cc1_relat_1, cc2_funct_1, cc2_ordinal1, d4_xboole_0,
% 175.03/25.64 existence_m1_subset_1, fc12_relat_1, fc1_xboole_0, fc3_relat_1, rc1_funct_1,
% 175.03/25.64 rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, rc4_funct_1, rc5_funct_1,
% 175.03/25.64 reflexivity_r1_tarski, t3_boole, t4_boole, t4_subset, t7_boole, t7_tarski
% 175.03/25.64
% 175.03/25.64 Those formulas are unsatisfiable:
% 175.03/25.64 ---------------------------------
% 175.03/25.64
% 175.03/25.64 Begin of proof
% 175.03/25.64 |
% 175.03/25.64 | ALPHA: (antisymmetry_r2_hidden) implies:
% 175.03/25.64 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~
% 175.03/25.64 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 175.03/25.64 |
% 175.03/25.64 | ALPHA: (d2_ordinal1) implies:
% 175.03/25.64 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (epsilon_transitive(v0) = 0) | ~
% 175.03/25.64 | (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | subset(v1, v0) = 0)
% 175.03/25.64 | (3) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1)
% 175.03/25.64 | | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & subset(v2,
% 175.03/25.64 | v0) = v3 & in(v2, v0) = 0 & $i(v2)))
% 175.03/25.64 |
% 175.03/25.64 | ALPHA: (d3_ordinal1) implies:
% 175.03/25.64 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_connected(v0) = v1)
% 175.03/25.64 | | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: int]
% 175.03/25.64 | : ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) & in(v3, v2) = v5 &
% 175.03/25.64 | in(v3, v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 & $i(v3) &
% 175.03/25.64 | $i(v2)))
% 175.03/25.64 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 175.03/25.64 | v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v1, v2) = v3) | ~
% 175.03/25.64 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ?
% 175.03/25.64 | [v6: int] : ((v6 = 0 & in(v2, v1) = 0) | ( ~ (v5 = 0) & in(v2, v0) =
% 175.03/25.64 | v5) | ( ~ (v4 = 0) & in(v1, v0) = v4)))
% 175.03/25.64 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 175.03/25.64 | v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~
% 175.03/25.64 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ?
% 175.03/25.64 | [v6: int] : ((v6 = 0 & in(v1, v2) = 0) | ( ~ (v5 = 0) & in(v2, v0) =
% 175.03/25.64 | v5) | ( ~ (v4 = 0) & in(v1, v0) = v4)))
% 175.03/25.65 |
% 175.03/25.65 | ALPHA: (d3_tarski) implies:
% 175.03/25.65 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 175.03/25.65 | (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) =
% 175.03/25.65 | 0)
% 175.03/25.65 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 175.03/25.65 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 175.03/25.65 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 175.03/25.65 |
% 175.03/25.65 | ALPHA: (d4_ordinal1) implies:
% 175.03/25.65 | (9) ! [v0: $i] : ( ~ (ordinal(v0) = 0) | ~ $i(v0) |
% 175.03/25.65 | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0))
% 175.03/25.65 | (10) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (ordinal(v0) = v1) | ~
% 175.03/25.65 | $i(v0) | ? [v2: int] : ? [v3: int] : (( ~ (v3 = 0) &
% 175.03/25.65 | epsilon_connected(v0) = v3) | ( ~ (v2 = 0) &
% 175.03/25.65 | epsilon_transitive(v0) = v2)))
% 175.03/25.65 |
% 175.03/25.65 | ALPHA: (fc4_relat_1) implies:
% 175.03/25.65 | (11) empty(empty_set) = 0
% 175.03/25.65 |
% 175.03/25.65 | ALPHA: (t1_subset) implies:
% 175.03/25.65 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (element(v0,
% 175.03/25.65 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0)
% 175.03/25.65 | & in(v0, v1) = v3))
% 175.03/25.65 |
% 175.03/25.65 | ALPHA: (t2_subset) implies:
% 175.03/25.65 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 175.03/25.65 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 =
% 175.03/25.65 | 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 175.03/25.65 |
% 175.03/25.65 | ALPHA: (t3_ordinal1) implies:
% 175.03/25.65 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~
% 175.03/25.65 | (in(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 175.03/25.65 | : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 175.03/25.65 |
% 175.03/25.65 | ALPHA: (t3_subset) implies:
% 175.03/25.65 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 175.03/25.65 | (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~
% 175.03/25.65 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 175.03/25.65 |
% 175.03/25.65 | ALPHA: (t5_subset) implies:
% 175.03/25.65 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (empty(v2) = 0) | ~
% 175.03/25.65 | (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 175.03/25.65 | ? [v4: int] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) =
% 175.03/25.65 | v4 & $i(v3)))
% 175.03/25.65 |
% 175.03/25.65 | ALPHA: (t6_boole) implies:
% 175.03/25.65 | (17) $i(empty_set)
% 175.03/25.65 | (18) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 175.03/25.65 |
% 175.03/25.65 | ALPHA: (function-axioms) implies:
% 175.03/25.66 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 175.03/25.66 | : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 175.03/25.66 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2)
% 175.03/25.66 | = v1) | ~ (powerset(v2) = v0))
% 175.03/25.66 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 175.03/25.66 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 175.03/25.66 | v0))
% 175.03/25.66 | (22) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 175.03/25.66 | : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 175.03/25.66 | v2) = v0))
% 175.03/25.66 |
% 175.03/25.66 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_29_0 gives:
% 175.03/25.66 | (23) empty(all_29_0) = 0 & $i(all_29_0)
% 175.03/25.66 |
% 175.03/25.66 | ALPHA: (23) implies:
% 175.03/25.66 | (24) $i(all_29_0)
% 175.03/25.66 | (25) empty(all_29_0) = 0
% 175.03/25.66 |
% 175.03/25.66 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_38_0 gives:
% 175.03/25.66 | (26) relation(all_38_0) = 0 & empty(all_38_0) = 0 & $i(all_38_0)
% 175.03/25.66 |
% 175.03/25.66 | ALPHA: (26) implies:
% 175.03/25.66 | (27) $i(all_38_0)
% 175.03/25.66 | (28) empty(all_38_0) = 0
% 175.03/25.66 |
% 175.03/25.66 | DELTA: instantiating (rc2_funct_1) with fresh symbol all_46_0 gives:
% 175.03/25.66 | (29) relation(all_46_0) = 0 & function(all_46_0) = 0 & empty(all_46_0) = 0
% 175.03/25.66 | & $i(all_46_0)
% 175.03/25.66 |
% 175.03/25.66 | ALPHA: (29) implies:
% 175.03/25.66 | (30) $i(all_46_0)
% 175.03/25.66 | (31) empty(all_46_0) = 0
% 175.03/25.66 |
% 175.03/25.66 | DELTA: instantiating (rc1_ordinal1) with fresh symbol all_50_0 gives:
% 175.03/25.66 | (32) epsilon_transitive(all_50_0) = 0 & ordinal(all_50_0) = 0 &
% 175.03/25.66 | epsilon_connected(all_50_0) = 0 & $i(all_50_0)
% 175.03/25.66 |
% 175.03/25.66 | ALPHA: (32) implies:
% 175.03/25.66 | (33) $i(all_50_0)
% 175.03/25.66 | (34) epsilon_connected(all_50_0) = 0
% 175.03/25.66 |
% 175.03/25.66 | DELTA: instantiating (t23_ordinal1) with fresh symbols all_52_0, all_52_1,
% 175.03/25.66 | all_52_2 gives:
% 175.03/25.66 | (35) ~ (all_52_0 = 0) & ordinal(all_52_1) = 0 & ordinal(all_52_2) =
% 175.03/25.66 | all_52_0 & in(all_52_2, all_52_1) = 0 & $i(all_52_1) & $i(all_52_2)
% 175.03/25.66 |
% 175.03/25.66 | ALPHA: (35) implies:
% 175.03/25.66 | (36) ~ (all_52_0 = 0)
% 175.03/25.66 | (37) $i(all_52_2)
% 175.03/25.66 | (38) $i(all_52_1)
% 175.03/25.66 | (39) in(all_52_2, all_52_1) = 0
% 175.03/25.66 | (40) ordinal(all_52_2) = all_52_0
% 175.03/25.66 | (41) ordinal(all_52_1) = 0
% 175.03/25.66 |
% 175.03/25.66 | GROUND_INST: instantiating (1) with all_52_1, all_52_2, simplifying with (37),
% 175.03/25.66 | (38), (39) gives:
% 175.03/25.66 | (42) ? [v0: int] : ( ~ (v0 = 0) & in(all_52_1, all_52_2) = v0)
% 175.03/25.66 |
% 175.03/25.66 | GROUND_INST: instantiating (16) with all_52_2, all_52_1, empty_set,
% 175.03/25.66 | simplifying with (11), (17), (37), (38), (39) gives:
% 175.03/25.66 | (43) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & powerset(empty_set) = v0 &
% 175.03/25.66 | element(all_52_1, v0) = v1 & $i(v0))
% 175.03/25.66 |
% 175.03/25.67 | GROUND_INST: instantiating (16) with all_52_2, all_52_1, all_29_0, simplifying
% 175.03/25.67 | with (24), (25), (37), (38), (39) gives:
% 175.03/25.67 | (44) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & powerset(all_29_0) = v0 &
% 175.03/25.67 | element(all_52_1, v0) = v1 & $i(v0))
% 175.03/25.67 |
% 175.42/25.67 | GROUND_INST: instantiating (16) with all_52_2, all_52_1, all_38_0, simplifying
% 175.42/25.67 | with (27), (28), (37), (38), (39) gives:
% 175.42/25.67 | (45) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & powerset(all_38_0) = v0 &
% 175.42/25.67 | element(all_52_1, v0) = v1 & $i(v0))
% 175.42/25.67 |
% 175.42/25.67 | GROUND_INST: instantiating (t8_boole) with all_29_0, all_38_0, simplifying
% 175.42/25.67 | with (24), (25), (27), (28) gives:
% 175.42/25.67 | (46) all_38_0 = all_29_0
% 175.42/25.67 |
% 175.42/25.67 | GROUND_INST: instantiating (16) with all_52_2, all_52_1, all_46_0, simplifying
% 175.42/25.67 | with (30), (31), (37), (38), (39) gives:
% 175.42/25.67 | (47) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & powerset(all_46_0) = v0 &
% 175.42/25.67 | element(all_52_1, v0) = v1 & $i(v0))
% 175.42/25.67 |
% 175.42/25.67 | GROUND_INST: instantiating (t8_boole) with all_38_0, all_46_0, simplifying
% 175.42/25.67 | with (27), (28), (30), (31) gives:
% 175.42/25.67 | (48) all_46_0 = all_38_0
% 175.42/25.67 |
% 175.42/25.67 | GROUND_INST: instantiating (18) with all_46_0, simplifying with (30), (31)
% 175.42/25.67 | gives:
% 175.42/25.67 | (49) all_46_0 = empty_set
% 175.42/25.67 |
% 175.42/25.67 | GROUND_INST: instantiating (10) with all_52_2, all_52_0, simplifying with
% 175.42/25.67 | (37), (40) gives:
% 175.42/25.67 | (50) all_52_0 = 0 | ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 175.42/25.67 | epsilon_connected(all_52_2) = v1) | ( ~ (v0 = 0) &
% 175.42/25.67 | epsilon_transitive(all_52_2) = v0))
% 175.42/25.67 |
% 175.42/25.67 | GROUND_INST: instantiating (9) with all_52_1, simplifying with (38), (41)
% 175.42/25.67 | gives:
% 175.42/25.67 | (51) epsilon_transitive(all_52_1) = 0 & epsilon_connected(all_52_1) = 0
% 175.42/25.67 |
% 175.42/25.67 | ALPHA: (51) implies:
% 175.42/25.67 | (52) epsilon_connected(all_52_1) = 0
% 175.42/25.67 | (53) epsilon_transitive(all_52_1) = 0
% 175.42/25.67 |
% 175.42/25.67 | COMBINE_EQS: (48), (49) imply:
% 175.42/25.67 | (54) all_38_0 = empty_set
% 175.42/25.67 |
% 175.42/25.67 | SIMP: (54) implies:
% 175.42/25.67 | (55) all_38_0 = empty_set
% 175.42/25.67 |
% 175.42/25.67 | COMBINE_EQS: (46), (55) imply:
% 175.42/25.67 | (56) all_29_0 = empty_set
% 175.42/25.67 |
% 175.42/25.67 | SIMP: (56) implies:
% 175.42/25.67 | (57) all_29_0 = empty_set
% 175.42/25.67 |
% 175.42/25.67 | DELTA: instantiating (42) with fresh symbol all_62_0 gives:
% 175.42/25.67 | (58) ~ (all_62_0 = 0) & in(all_52_1, all_52_2) = all_62_0
% 175.42/25.67 |
% 175.42/25.67 | ALPHA: (58) implies:
% 175.42/25.67 | (59) ~ (all_62_0 = 0)
% 175.42/25.67 | (60) in(all_52_1, all_52_2) = all_62_0
% 175.42/25.67 |
% 175.42/25.67 | DELTA: instantiating (44) with fresh symbols all_66_0, all_66_1 gives:
% 175.42/25.67 | (61) ~ (all_66_0 = 0) & powerset(all_29_0) = all_66_1 & element(all_52_1,
% 175.42/25.67 | all_66_1) = all_66_0 & $i(all_66_1)
% 175.42/25.67 |
% 175.42/25.67 | ALPHA: (61) implies:
% 175.42/25.67 | (62) element(all_52_1, all_66_1) = all_66_0
% 175.42/25.68 | (63) powerset(all_29_0) = all_66_1
% 175.42/25.68 |
% 175.42/25.68 | DELTA: instantiating (45) with fresh symbols all_68_0, all_68_1 gives:
% 175.42/25.68 | (64) ~ (all_68_0 = 0) & powerset(all_38_0) = all_68_1 & element(all_52_1,
% 175.42/25.68 | all_68_1) = all_68_0 & $i(all_68_1)
% 175.42/25.68 |
% 175.42/25.68 | ALPHA: (64) implies:
% 175.42/25.68 | (65) ~ (all_68_0 = 0)
% 175.42/25.68 | (66) $i(all_68_1)
% 175.42/25.68 | (67) element(all_52_1, all_68_1) = all_68_0
% 175.42/25.68 | (68) powerset(all_38_0) = all_68_1
% 175.42/25.68 |
% 175.42/25.68 | DELTA: instantiating (43) with fresh symbols all_70_0, all_70_1 gives:
% 175.42/25.68 | (69) ~ (all_70_0 = 0) & powerset(empty_set) = all_70_1 & element(all_52_1,
% 175.42/25.68 | all_70_1) = all_70_0 & $i(all_70_1)
% 175.42/25.68 |
% 175.42/25.68 | ALPHA: (69) implies:
% 175.42/25.68 | (70) element(all_52_1, all_70_1) = all_70_0
% 175.42/25.68 | (71) powerset(empty_set) = all_70_1
% 175.42/25.68 |
% 175.42/25.68 | DELTA: instantiating (47) with fresh symbols all_72_0, all_72_1 gives:
% 175.42/25.68 | (72) ~ (all_72_0 = 0) & powerset(all_46_0) = all_72_1 & element(all_52_1,
% 175.42/25.68 | all_72_1) = all_72_0 & $i(all_72_1)
% 175.42/25.68 |
% 175.42/25.68 | ALPHA: (72) implies:
% 175.42/25.68 | (73) element(all_52_1, all_72_1) = all_72_0
% 175.42/25.68 | (74) powerset(all_46_0) = all_72_1
% 175.42/25.68 |
% 175.42/25.68 | REDUCE: (49), (74) imply:
% 175.42/25.68 | (75) powerset(empty_set) = all_72_1
% 175.42/25.68 |
% 175.42/25.68 | REDUCE: (55), (68) imply:
% 175.42/25.68 | (76) powerset(empty_set) = all_68_1
% 175.42/25.68 |
% 175.42/25.68 | REDUCE: (57), (63) imply:
% 175.42/25.68 | (77) powerset(empty_set) = all_66_1
% 175.42/25.68 |
% 175.42/25.68 | BETA: splitting (50) gives:
% 175.42/25.68 |
% 175.42/25.68 | Case 1:
% 175.42/25.68 | |
% 175.42/25.68 | | (78) all_52_0 = 0
% 175.42/25.68 | |
% 175.42/25.68 | | REDUCE: (36), (78) imply:
% 175.42/25.68 | | (79) $false
% 175.42/25.68 | |
% 175.42/25.68 | | CLOSE: (79) is inconsistent.
% 175.42/25.68 | |
% 175.42/25.68 | Case 2:
% 175.42/25.68 | |
% 175.42/25.68 | | (80) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 175.42/25.68 | | epsilon_connected(all_52_2) = v1) | ( ~ (v0 = 0) &
% 175.42/25.68 | | epsilon_transitive(all_52_2) = v0))
% 175.42/25.68 | |
% 175.42/25.68 | | DELTA: instantiating (80) with fresh symbols all_105_0, all_105_1 gives:
% 175.42/25.68 | | (81) ( ~ (all_105_0 = 0) & epsilon_connected(all_52_2) = all_105_0) | ( ~
% 175.42/25.68 | | (all_105_1 = 0) & epsilon_transitive(all_52_2) = all_105_1)
% 175.42/25.68 | |
% 175.42/25.68 | | GROUND_INST: instantiating (20) with all_68_1, all_70_1, empty_set,
% 175.42/25.68 | | simplifying with (71), (76) gives:
% 175.42/25.68 | | (82) all_70_1 = all_68_1
% 175.42/25.68 | |
% 175.42/25.68 | | GROUND_INST: instantiating (20) with all_70_1, all_72_1, empty_set,
% 175.42/25.68 | | simplifying with (71), (75) gives:
% 175.42/25.68 | | (83) all_72_1 = all_70_1
% 175.42/25.68 | |
% 175.42/25.68 | | GROUND_INST: instantiating (20) with all_66_1, all_72_1, empty_set,
% 175.42/25.68 | | simplifying with (75), (77) gives:
% 175.42/25.68 | | (84) all_72_1 = all_66_1
% 175.42/25.68 | |
% 175.42/25.68 | | COMBINE_EQS: (83), (84) imply:
% 175.42/25.68 | | (85) all_70_1 = all_66_1
% 175.42/25.68 | |
% 175.42/25.68 | | SIMP: (85) implies:
% 175.42/25.68 | | (86) all_70_1 = all_66_1
% 175.42/25.68 | |
% 175.42/25.68 | | COMBINE_EQS: (82), (86) imply:
% 175.42/25.68 | | (87) all_68_1 = all_66_1
% 175.42/25.68 | |
% 175.42/25.68 | | SIMP: (87) implies:
% 175.42/25.69 | | (88) all_68_1 = all_66_1
% 175.42/25.69 | |
% 175.42/25.69 | | REDUCE: (73), (84) imply:
% 175.42/25.69 | | (89) element(all_52_1, all_66_1) = all_72_0
% 175.42/25.69 | |
% 175.42/25.69 | | REDUCE: (70), (86) imply:
% 175.42/25.69 | | (90) element(all_52_1, all_66_1) = all_70_0
% 175.42/25.69 | |
% 175.42/25.69 | | REDUCE: (67), (88) imply:
% 175.42/25.69 | | (91) element(all_52_1, all_66_1) = all_68_0
% 175.42/25.69 | |
% 175.42/25.69 | | REDUCE: (66), (88) imply:
% 175.42/25.69 | | (92) $i(all_66_1)
% 175.42/25.69 | |
% 175.42/25.69 | | GROUND_INST: instantiating (22) with all_66_0, all_72_0, all_66_1, all_52_1,
% 175.42/25.69 | | simplifying with (62), (89) gives:
% 175.42/25.69 | | (93) all_72_0 = all_66_0
% 175.42/25.69 | |
% 175.42/25.69 | | GROUND_INST: instantiating (22) with all_70_0, all_72_0, all_66_1, all_52_1,
% 175.42/25.69 | | simplifying with (89), (90) gives:
% 175.42/25.69 | | (94) all_72_0 = all_70_0
% 175.42/25.69 | |
% 175.42/25.69 | | GROUND_INST: instantiating (22) with all_68_0, all_72_0, all_66_1, all_52_1,
% 175.42/25.69 | | simplifying with (89), (91) gives:
% 175.42/25.69 | | (95) all_72_0 = all_68_0
% 175.42/25.69 | |
% 175.42/25.69 | | COMBINE_EQS: (94), (95) imply:
% 175.42/25.69 | | (96) all_70_0 = all_68_0
% 175.42/25.69 | |
% 175.42/25.69 | | COMBINE_EQS: (93), (94) imply:
% 175.42/25.69 | | (97) all_70_0 = all_66_0
% 175.42/25.69 | |
% 175.42/25.69 | | COMBINE_EQS: (96), (97) imply:
% 175.42/25.69 | | (98) all_68_0 = all_66_0
% 175.42/25.69 | |
% 175.42/25.69 | | SIMP: (98) implies:
% 175.42/25.69 | | (99) all_68_0 = all_66_0
% 175.42/25.69 | |
% 175.42/25.69 | | REDUCE: (65), (99) imply:
% 175.42/25.69 | | (100) ~ (all_66_0 = 0)
% 175.42/25.69 | |
% 175.53/25.69 | | GROUND_INST: instantiating (5) with all_50_0, all_52_1, all_52_2, all_62_0,
% 175.53/25.69 | | simplifying with (33), (34), (37), (38), (60) gives:
% 175.53/25.69 | | (101) all_62_0 = 0 | all_52_1 = all_52_2 | ? [v0: int] : ? [v1: int] :
% 175.53/25.69 | | ? [v2: int] : ((v2 = 0 & in(all_52_2, all_52_1) = 0) | ( ~ (v1 = 0)
% 175.53/25.69 | | & in(all_52_2, all_50_0) = v1) | ( ~ (v0 = 0) & in(all_52_1,
% 175.53/25.69 | | all_50_0) = v0))
% 175.53/25.69 | |
% 175.53/25.69 | | GROUND_INST: instantiating (13) with all_52_1, all_52_2, all_62_0,
% 175.53/25.69 | | simplifying with (37), (38), (60) gives:
% 175.53/25.69 | | (102) all_62_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 175.53/25.69 | | empty(all_52_2) = 0) | ( ~ (v0 = 0) & element(all_52_1,
% 175.53/25.69 | | all_52_2) = v0))
% 175.53/25.69 | |
% 175.53/25.69 | | GROUND_INST: instantiating (6) with all_52_1, all_52_2, all_52_1, all_62_0,
% 175.53/25.69 | | simplifying with (37), (38), (52), (60) gives:
% 175.53/25.69 | | (103) all_62_0 = 0 | all_52_1 = all_52_2 | ? [v0: int] : ? [v1: int] :
% 175.53/25.69 | | ? [v2: int] : ((v2 = 0 & in(all_52_2, all_52_1) = 0) | ( ~ (v1 = 0)
% 175.53/25.69 | | & in(all_52_1, all_52_1) = v1) | ( ~ (v0 = 0) & in(all_52_2,
% 175.53/25.70 | | all_52_1) = v0))
% 175.53/25.70 | |
% 175.53/25.70 | | GROUND_INST: instantiating (2) with all_52_1, all_52_2, simplifying with
% 175.53/25.70 | | (37), (38), (39), (53) gives:
% 175.53/25.70 | | (104) subset(all_52_2, all_52_1) = 0
% 175.53/25.70 | |
% 175.53/25.70 | | GROUND_INST: instantiating (12) with all_52_1, all_66_1, all_66_0,
% 175.53/25.70 | | simplifying with (38), (62), (92) gives:
% 175.53/25.70 | | (105) all_66_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_52_1, all_66_1)
% 175.53/25.70 | | = v0)
% 175.53/25.70 | |
% 175.53/25.70 | | GROUND_INST: instantiating (15) with all_52_1, empty_set, all_66_1,
% 175.53/25.70 | | all_66_0, simplifying with (17), (38), (62), (77) gives:
% 175.53/25.70 | | (106) all_66_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_52_1,
% 175.53/25.70 | | empty_set) = v0)
% 175.53/25.70 | |
% 175.53/25.70 | | BETA: splitting (106) gives:
% 175.53/25.70 | |
% 175.53/25.70 | | Case 1:
% 175.53/25.70 | | |
% 175.53/25.70 | | | (107) all_66_0 = 0
% 175.53/25.70 | | |
% 175.53/25.70 | | | REDUCE: (100), (107) imply:
% 175.53/25.70 | | | (108) $false
% 175.53/25.70 | | |
% 175.53/25.70 | | | CLOSE: (108) is inconsistent.
% 175.53/25.70 | | |
% 175.53/25.70 | | Case 2:
% 175.53/25.70 | | |
% 175.53/25.70 | | | (109) ? [v0: int] : ( ~ (v0 = 0) & subset(all_52_1, empty_set) = v0)
% 175.53/25.70 | | |
% 175.53/25.70 | | | DELTA: instantiating (109) with fresh symbol all_163_0 gives:
% 175.53/25.70 | | | (110) ~ (all_163_0 = 0) & subset(all_52_1, empty_set) = all_163_0
% 175.53/25.70 | | |
% 175.53/25.70 | | | ALPHA: (110) implies:
% 175.53/25.70 | | | (111) ~ (all_163_0 = 0)
% 175.53/25.70 | | | (112) subset(all_52_1, empty_set) = all_163_0
% 175.53/25.70 | | |
% 175.53/25.70 | | | BETA: splitting (105) gives:
% 175.53/25.70 | | |
% 175.53/25.70 | | | Case 1:
% 175.53/25.70 | | | |
% 175.53/25.70 | | | | (113) all_66_0 = 0
% 175.53/25.70 | | | |
% 175.53/25.70 | | | | REDUCE: (100), (113) imply:
% 175.53/25.70 | | | | (114) $false
% 175.53/25.70 | | | |
% 175.53/25.70 | | | | CLOSE: (114) is inconsistent.
% 175.53/25.70 | | | |
% 175.53/25.70 | | | Case 2:
% 175.53/25.70 | | | |
% 175.53/25.70 | | | | (115) ? [v0: int] : ( ~ (v0 = 0) & in(all_52_1, all_66_1) = v0)
% 175.53/25.70 | | | |
% 175.53/25.70 | | | | DELTA: instantiating (115) with fresh symbol all_168_0 gives:
% 175.53/25.70 | | | | (116) ~ (all_168_0 = 0) & in(all_52_1, all_66_1) = all_168_0
% 175.53/25.70 | | | |
% 175.53/25.70 | | | | ALPHA: (116) implies:
% 175.53/25.70 | | | | (117) ~ (all_168_0 = 0)
% 175.53/25.70 | | | | (118) in(all_52_1, all_66_1) = all_168_0
% 175.53/25.70 | | | |
% 175.53/25.70 | | | | BETA: splitting (102) gives:
% 175.53/25.70 | | | |
% 175.53/25.70 | | | | Case 1:
% 175.53/25.70 | | | | |
% 175.53/25.70 | | | | | (119) all_62_0 = 0
% 175.53/25.70 | | | | |
% 175.53/25.70 | | | | | REDUCE: (59), (119) imply:
% 175.53/25.70 | | | | | (120) $false
% 175.53/25.70 | | | | |
% 175.53/25.70 | | | | | CLOSE: (120) is inconsistent.
% 175.53/25.70 | | | | |
% 175.53/25.70 | | | | Case 2:
% 175.53/25.70 | | | | |
% 175.53/25.70 | | | | |
% 175.53/25.70 | | | | | GROUND_INST: instantiating (5) with all_52_1, all_52_1, all_66_1,
% 175.53/25.70 | | | | | all_168_0, simplifying with (38), (52), (92), (118)
% 175.53/25.70 | | | | | gives:
% 175.53/25.70 | | | | | (121) all_168_0 = 0 | all_66_1 = all_52_1 | ? [v0: int] : ? [v1:
% 175.53/25.70 | | | | | int] : ? [v2: int] : ((v2 = 0 & in(all_66_1, all_52_1) =
% 175.53/25.70 | | | | | 0) | ( ~ (v1 = 0) & in(all_66_1, all_52_1) = v1) | ( ~
% 175.53/25.70 | | | | | (v0 = 0) & in(all_52_1, all_52_1) = v0))
% 175.53/25.70 | | | | |
% 175.53/25.70 | | | | | GROUND_INST: instantiating (13) with all_52_1, all_66_1, all_168_0,
% 175.53/25.70 | | | | | simplifying with (38), (92), (118) gives:
% 175.53/25.70 | | | | | (122) all_168_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 175.53/25.70 | | | | | empty(all_66_1) = 0) | ( ~ (v0 = 0) & element(all_52_1,
% 175.53/25.70 | | | | | all_66_1) = v0))
% 175.53/25.70 | | | | |
% 175.53/25.70 | | | | | GROUND_INST: instantiating (8) with all_52_1, empty_set, all_163_0,
% 175.53/25.70 | | | | | simplifying with (17), (38), (112) gives:
% 175.53/25.70 | | | | | (123) all_163_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 175.53/25.70 | | | | | in(v0, all_52_1) = 0 & in(v0, empty_set) = v1 & $i(v0))
% 175.53/25.70 | | | | |
% 175.53/25.70 | | | | | BETA: splitting (123) gives:
% 175.53/25.70 | | | | |
% 175.53/25.70 | | | | | Case 1:
% 175.53/25.70 | | | | | |
% 175.53/25.70 | | | | | | (124) all_163_0 = 0
% 175.53/25.70 | | | | | |
% 175.53/25.71 | | | | | | REDUCE: (111), (124) imply:
% 175.53/25.71 | | | | | | (125) $false
% 175.53/25.71 | | | | | |
% 175.53/25.71 | | | | | | CLOSE: (125) is inconsistent.
% 175.53/25.71 | | | | | |
% 175.53/25.71 | | | | | Case 2:
% 175.53/25.71 | | | | | |
% 175.53/25.71 | | | | | | (126) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 175.53/25.71 | | | | | | all_52_1) = 0 & in(v0, empty_set) = v1 & $i(v0))
% 175.53/25.71 | | | | | |
% 175.53/25.71 | | | | | | DELTA: instantiating (126) with fresh symbols all_227_0, all_227_1
% 175.53/25.71 | | | | | | gives:
% 175.53/25.71 | | | | | | (127) ~ (all_227_0 = 0) & in(all_227_1, all_52_1) = 0 &
% 175.53/25.71 | | | | | | in(all_227_1, empty_set) = all_227_0 & $i(all_227_1)
% 175.53/25.71 | | | | | |
% 175.53/25.71 | | | | | | ALPHA: (127) implies:
% 175.53/25.71 | | | | | | (128) $i(all_227_1)
% 175.53/25.71 | | | | | | (129) in(all_227_1, all_52_1) = 0
% 175.53/25.71 | | | | | |
% 175.53/25.71 | | | | | | BETA: splitting (122) gives:
% 175.53/25.71 | | | | | |
% 175.53/25.71 | | | | | | Case 1:
% 175.53/25.71 | | | | | | |
% 175.53/25.71 | | | | | | | (130) all_168_0 = 0
% 175.53/25.71 | | | | | | |
% 175.53/25.71 | | | | | | | REDUCE: (117), (130) imply:
% 175.53/25.71 | | | | | | | (131) $false
% 175.53/25.71 | | | | | | |
% 175.53/25.71 | | | | | | | CLOSE: (131) is inconsistent.
% 175.53/25.71 | | | | | | |
% 175.53/25.71 | | | | | | Case 2:
% 175.53/25.71 | | | | | | |
% 175.53/25.71 | | | | | | |
% 175.53/25.71 | | | | | | | GROUND_INST: instantiating (1) with all_52_1, all_227_1,
% 175.53/25.71 | | | | | | | simplifying with (38), (128), (129) gives:
% 175.53/25.71 | | | | | | | (132) ? [v0: int] : ( ~ (v0 = 0) & in(all_52_1, all_227_1) =
% 175.53/25.71 | | | | | | | v0)
% 175.53/25.71 | | | | | | |
% 175.53/25.71 | | | | | | | DELTA: instantiating (132) with fresh symbol all_305_0 gives:
% 175.53/25.71 | | | | | | | (133) ~ (all_305_0 = 0) & in(all_52_1, all_227_1) = all_305_0
% 175.53/25.71 | | | | | | |
% 175.53/25.71 | | | | | | | ALPHA: (133) implies:
% 175.53/25.71 | | | | | | | (134) ~ (all_305_0 = 0)
% 175.53/25.71 | | | | | | | (135) in(all_52_1, all_227_1) = all_305_0
% 175.53/25.71 | | | | | | |
% 175.53/25.71 | | | | | | | BETA: splitting (81) gives:
% 175.53/25.71 | | | | | | |
% 175.53/25.71 | | | | | | | Case 1:
% 175.53/25.71 | | | | | | | |
% 175.53/25.71 | | | | | | | | (136) ~ (all_105_0 = 0) & epsilon_connected(all_52_2) =
% 175.53/25.71 | | | | | | | | all_105_0
% 175.53/25.71 | | | | | | | |
% 175.53/25.71 | | | | | | | | ALPHA: (136) implies:
% 175.53/25.71 | | | | | | | | (137) ~ (all_105_0 = 0)
% 175.53/25.71 | | | | | | | | (138) epsilon_connected(all_52_2) = all_105_0
% 175.53/25.71 | | | | | | | |
% 175.53/25.71 | | | | | | | | BETA: splitting (101) gives:
% 175.53/25.71 | | | | | | | |
% 175.53/25.71 | | | | | | | | Case 1:
% 175.53/25.71 | | | | | | | | |
% 175.53/25.71 | | | | | | | | | (139) all_62_0 = 0
% 175.53/25.71 | | | | | | | | |
% 175.53/25.71 | | | | | | | | | REDUCE: (59), (139) imply:
% 175.53/25.71 | | | | | | | | | (140) $false
% 175.53/25.71 | | | | | | | | |
% 175.53/25.71 | | | | | | | | | CLOSE: (140) is inconsistent.
% 175.53/25.71 | | | | | | | | |
% 175.53/25.71 | | | | | | | | Case 2:
% 175.53/25.71 | | | | | | | | |
% 175.53/25.71 | | | | | | | | | (141) all_52_1 = all_52_2 | ? [v0: int] : ? [v1: int] :
% 175.53/25.71 | | | | | | | | | ? [v2: int] : ((v2 = 0 & in(all_52_2, all_52_1) = 0)
% 175.53/25.71 | | | | | | | | | | ( ~ (v1 = 0) & in(all_52_2, all_50_0) = v1) | ( ~
% 175.53/25.71 | | | | | | | | | (v0 = 0) & in(all_52_1, all_50_0) = v0))
% 175.53/25.71 | | | | | | | | |
% 175.53/25.71 | | | | | | | | | BETA: splitting (103) gives:
% 175.53/25.71 | | | | | | | | |
% 175.53/25.71 | | | | | | | | | Case 1:
% 175.53/25.71 | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | (142) all_62_0 = 0
% 175.53/25.71 | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | REDUCE: (59), (142) imply:
% 175.53/25.71 | | | | | | | | | | (143) $false
% 175.53/25.71 | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | CLOSE: (143) is inconsistent.
% 175.53/25.71 | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | Case 2:
% 175.53/25.71 | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | (144) all_52_1 = all_52_2 | ? [v0: int] : ? [v1: int] :
% 175.53/25.71 | | | | | | | | | | ? [v2: int] : ((v2 = 0 & in(all_52_2, all_52_1) =
% 175.53/25.71 | | | | | | | | | | 0) | ( ~ (v1 = 0) & in(all_52_1, all_52_1) =
% 175.53/25.71 | | | | | | | | | | v1) | ( ~ (v0 = 0) & in(all_52_2, all_52_1) =
% 175.53/25.71 | | | | | | | | | | v0))
% 175.53/25.71 | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | BETA: splitting (121) gives:
% 175.53/25.71 | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | Case 1:
% 175.53/25.71 | | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | | (145) all_168_0 = 0
% 175.53/25.71 | | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | | REDUCE: (117), (145) imply:
% 175.53/25.71 | | | | | | | | | | | (146) $false
% 175.53/25.71 | | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 175.53/25.71 | | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | Case 2:
% 175.53/25.71 | | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_2, all_105_0,
% 175.53/25.71 | | | | | | | | | | | simplifying with (37), (138) gives:
% 175.53/25.71 | | | | | | | | | | | (147) all_105_0 = 0 | ? [v0: $i] : ? [v1: $i] : ?
% 175.53/25.71 | | | | | | | | | | | [v2: int] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v2 =
% 175.53/25.71 | | | | | | | | | | | 0) & ~ (v1 = v0) & in(v1, v0) = v3 & in(v1,
% 175.53/25.71 | | | | | | | | | | | all_52_2) = 0 & in(v0, v1) = v2 & in(v0,
% 175.53/25.71 | | | | | | | | | | | all_52_2) = 0 & $i(v1) & $i(v0))
% 175.53/25.71 | | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | | BETA: splitting (147) gives:
% 175.53/25.71 | | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | | Case 1:
% 175.53/25.71 | | | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | | | (148) all_105_0 = 0
% 175.53/25.71 | | | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | | | REDUCE: (137), (148) imply:
% 175.53/25.71 | | | | | | | | | | | | (149) $false
% 175.53/25.71 | | | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | | | CLOSE: (149) is inconsistent.
% 175.53/25.71 | | | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | | Case 2:
% 175.53/25.71 | | | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | | | (150) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3:
% 175.53/25.71 | | | | | | | | | | | | int] : ( ~ (v3 = 0) & ~ (v2 = 0) & ~ (v1 = v0)
% 175.53/25.71 | | | | | | | | | | | | & in(v1, v0) = v3 & in(v1, all_52_2) = 0 &
% 175.53/25.71 | | | | | | | | | | | | in(v0, v1) = v2 & in(v0, all_52_2) = 0 & $i(v1)
% 175.53/25.71 | | | | | | | | | | | | & $i(v0))
% 175.53/25.71 | | | | | | | | | | | |
% 175.53/25.71 | | | | | | | | | | | | DELTA: instantiating (150) with fresh symbols all_597_0,
% 175.53/25.71 | | | | | | | | | | | | all_597_1, all_597_2, all_597_3 gives:
% 175.53/25.72 | | | | | | | | | | | | (151) ~ (all_597_0 = 0) & ~ (all_597_1 = 0) & ~
% 175.53/25.72 | | | | | | | | | | | | (all_597_2 = all_597_3) & in(all_597_2, all_597_3)
% 175.53/25.72 | | | | | | | | | | | | = all_597_0 & in(all_597_2, all_52_2) = 0 &
% 175.53/25.72 | | | | | | | | | | | | in(all_597_3, all_597_2) = all_597_1 &
% 175.53/25.72 | | | | | | | | | | | | in(all_597_3, all_52_2) = 0 & $i(all_597_2) &
% 175.53/25.72 | | | | | | | | | | | | $i(all_597_3)
% 175.53/25.72 | | | | | | | | | | | |
% 175.53/25.72 | | | | | | | | | | | | ALPHA: (151) implies:
% 175.53/25.72 | | | | | | | | | | | | (152) ~ (all_597_2 = all_597_3)
% 175.53/25.72 | | | | | | | | | | | | (153) ~ (all_597_1 = 0)
% 175.53/25.72 | | | | | | | | | | | | (154) ~ (all_597_0 = 0)
% 175.53/25.72 | | | | | | | | | | | | (155) $i(all_597_3)
% 175.53/25.72 | | | | | | | | | | | | (156) $i(all_597_2)
% 175.53/25.72 | | | | | | | | | | | | (157) in(all_597_3, all_52_2) = 0
% 175.53/25.72 | | | | | | | | | | | | (158) in(all_597_3, all_597_2) = all_597_1
% 175.53/25.72 | | | | | | | | | | | | (159) in(all_597_2, all_52_2) = 0
% 175.53/25.72 | | | | | | | | | | | | (160) in(all_597_2, all_597_3) = all_597_0
% 175.53/25.72 | | | | | | | | | | | |
% 175.53/25.72 | | | | | | | | | | | | BETA: splitting (141) gives:
% 175.53/25.72 | | | | | | | | | | | |
% 175.53/25.72 | | | | | | | | | | | | Case 1:
% 175.53/25.72 | | | | | | | | | | | | |
% 175.53/25.72 | | | | | | | | | | | | | (161) all_52_1 = all_52_2
% 175.53/25.72 | | | | | | | | | | | | |
% 175.53/25.72 | | | | | | | | | | | | | REDUCE: (41), (161) imply:
% 175.53/25.72 | | | | | | | | | | | | | (162) ordinal(all_52_2) = 0
% 175.53/25.72 | | | | | | | | | | | | |
% 175.53/25.72 | | | | | | | | | | | | | REF_CLOSE: (19), (36), (40), (162) are inconsistent by
% 175.53/25.72 | | | | | | | | | | | | | sub-proof #2.
% 175.53/25.72 | | | | | | | | | | | | |
% 175.53/25.72 | | | | | | | | | | | | Case 2:
% 175.53/25.72 | | | | | | | | | | | | |
% 175.53/25.72 | | | | | | | | | | | | | (163) ~ (all_52_1 = all_52_2)
% 175.53/25.72 | | | | | | | | | | | | |
% 175.53/25.72 | | | | | | | | | | | | | BETA: splitting (144) gives:
% 175.53/25.72 | | | | | | | | | | | | |
% 175.53/25.72 | | | | | | | | | | | | | Case 1:
% 175.53/25.72 | | | | | | | | | | | | | |
% 175.53/25.72 | | | | | | | | | | | | | | (164) all_52_1 = all_52_2
% 175.53/25.72 | | | | | | | | | | | | | |
% 175.53/25.72 | | | | | | | | | | | | | | REDUCE: (163), (164) imply:
% 175.53/25.72 | | | | | | | | | | | | | | (165) $false
% 175.53/25.72 | | | | | | | | | | | | | |
% 175.53/25.72 | | | | | | | | | | | | | | CLOSE: (165) is inconsistent.
% 175.53/25.72 | | | | | | | | | | | | | |
% 175.53/25.72 | | | | | | | | | | | | | Case 2:
% 175.53/25.72 | | | | | | | | | | | | | |
% 175.53/25.72 | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_2, all_52_1,
% 175.68/25.72 | | | | | | | | | | | | | | all_597_3, simplifying with (37), (38), (104),
% 175.68/25.72 | | | | | | | | | | | | | | (155), (157) gives:
% 175.68/25.72 | | | | | | | | | | | | | | (166) in(all_597_3, all_52_1) = 0
% 175.68/25.72 | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_2, all_52_1,
% 175.68/25.72 | | | | | | | | | | | | | | all_597_2, simplifying with (37), (38), (104),
% 175.68/25.72 | | | | | | | | | | | | | | (156), (159) gives:
% 175.68/25.72 | | | | | | | | | | | | | | (167) in(all_597_2, all_52_1) = 0
% 175.68/25.72 | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_52_1, all_597_2,
% 175.68/25.72 | | | | | | | | | | | | | | all_597_3, all_597_0, simplifying with (38), (52),
% 175.68/25.72 | | | | | | | | | | | | | | (155), (156), (160) gives:
% 175.68/25.72 | | | | | | | | | | | | | | (168) all_597_0 = 0 | all_597_2 = all_597_3 | ? [v0:
% 175.68/25.72 | | | | | | | | | | | | | | int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 175.68/25.72 | | | | | | | | | | | | | | in(all_597_3, all_597_2) = 0) | ( ~ (v1 = 0) &
% 175.68/25.72 | | | | | | | | | | | | | | in(all_597_3, all_52_1) = v1) | ( ~ (v0 = 0) &
% 175.68/25.72 | | | | | | | | | | | | | | in(all_597_2, all_52_1) = v0))
% 175.68/25.72 | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 175.68/25.72 | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | Case 1:
% 175.68/25.72 | | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | | (169) all_597_0 = 0
% 175.68/25.72 | | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | | REDUCE: (154), (169) imply:
% 175.68/25.72 | | | | | | | | | | | | | | | (170) $false
% 175.68/25.72 | | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | | CLOSE: (170) is inconsistent.
% 175.68/25.72 | | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | Case 2:
% 175.68/25.72 | | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | | (171) all_597_2 = all_597_3 | ? [v0: int] : ? [v1:
% 175.68/25.72 | | | | | | | | | | | | | | | int] : ? [v2: int] : ((v2 = 0 & in(all_597_3,
% 175.68/25.72 | | | | | | | | | | | | | | | all_597_2) = 0) | ( ~ (v1 = 0) &
% 175.68/25.72 | | | | | | | | | | | | | | | in(all_597_3, all_52_1) = v1) | ( ~ (v0 = 0) &
% 175.68/25.72 | | | | | | | | | | | | | | | in(all_597_2, all_52_1) = v0))
% 175.68/25.72 | | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 175.68/25.72 | | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | | Case 1:
% 175.68/25.72 | | | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | | | (172) all_597_2 = all_597_3
% 175.68/25.72 | | | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | | | REDUCE: (152), (172) imply:
% 175.68/25.72 | | | | | | | | | | | | | | | | (173) $false
% 175.68/25.72 | | | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | | | CLOSE: (173) is inconsistent.
% 175.68/25.72 | | | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | | Case 2:
% 175.68/25.72 | | | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | | | (174) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2
% 175.68/25.72 | | | | | | | | | | | | | | | | = 0 & in(all_597_3, all_597_2) = 0) | ( ~ (v1
% 175.68/25.72 | | | | | | | | | | | | | | | | = 0) & in(all_597_3, all_52_1) = v1) | ( ~
% 175.68/25.72 | | | | | | | | | | | | | | | | (v0 = 0) & in(all_597_2, all_52_1) = v0))
% 175.68/25.72 | | | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | | | DELTA: instantiating (174) with fresh symbols all_936_0,
% 175.68/25.72 | | | | | | | | | | | | | | | | all_936_1, all_936_2 gives:
% 175.68/25.72 | | | | | | | | | | | | | | | | (175) (all_936_0 = 0 & in(all_597_3, all_597_2) = 0) | (
% 175.68/25.72 | | | | | | | | | | | | | | | | ~ (all_936_1 = 0) & in(all_597_3, all_52_1) =
% 175.68/25.72 | | | | | | | | | | | | | | | | all_936_1) | ( ~ (all_936_2 = 0) & in(all_597_2,
% 175.68/25.72 | | | | | | | | | | | | | | | | all_52_1) = all_936_2)
% 175.68/25.72 | | | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 175.68/25.72 | | | | | | | | | | | | | | | |
% 175.68/25.72 | | | | | | | | | | | | | | | | Case 1:
% 175.68/25.73 | | | | | | | | | | | | | | | | |
% 175.68/25.73 | | | | | | | | | | | | | | | | | (176) all_936_0 = 0 & in(all_597_3, all_597_2) = 0
% 175.68/25.73 | | | | | | | | | | | | | | | | |
% 175.68/25.73 | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 175.68/25.73 | | | | | | | | | | | | | | | | | (177) in(all_597_3, all_597_2) = 0
% 175.68/25.73 | | | | | | | | | | | | | | | | |
% 175.68/25.73 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_597_1, 0, all_597_2,
% 175.68/25.73 | | | | | | | | | | | | | | | | | all_597_3, simplifying with (158), (177) gives:
% 175.71/25.73 | | | | | | | | | | | | | | | | | (178) all_597_1 = 0
% 175.71/25.73 | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | REDUCE: (153), (178) imply:
% 175.71/25.73 | | | | | | | | | | | | | | | | | (179) $false
% 175.71/25.73 | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | CLOSE: (179) is inconsistent.
% 175.71/25.73 | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | Case 2:
% 175.71/25.73 | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | (180) ( ~ (all_936_1 = 0) & in(all_597_3, all_52_1) =
% 175.71/25.73 | | | | | | | | | | | | | | | | | all_936_1) | ( ~ (all_936_2 = 0) & in(all_597_2,
% 175.71/25.73 | | | | | | | | | | | | | | | | | all_52_1) = all_936_2)
% 175.71/25.73 | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 175.71/25.73 | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | Case 1:
% 175.71/25.73 | | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | | (181) ~ (all_936_1 = 0) & in(all_597_3, all_52_1) =
% 175.71/25.73 | | | | | | | | | | | | | | | | | | all_936_1
% 175.71/25.73 | | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 175.71/25.73 | | | | | | | | | | | | | | | | | | (182) ~ (all_936_1 = 0)
% 175.71/25.73 | | | | | | | | | | | | | | | | | | (183) in(all_597_3, all_52_1) = all_936_1
% 175.71/25.73 | | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_936_1, all_52_1,
% 175.71/25.73 | | | | | | | | | | | | | | | | | | all_597_3, simplifying with (166), (183) gives:
% 175.71/25.73 | | | | | | | | | | | | | | | | | | (184) all_936_1 = 0
% 175.71/25.73 | | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | | REDUCE: (182), (184) imply:
% 175.71/25.73 | | | | | | | | | | | | | | | | | | (185) $false
% 175.71/25.73 | | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | | CLOSE: (185) is inconsistent.
% 175.71/25.73 | | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | Case 2:
% 175.71/25.73 | | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | | (186) ~ (all_936_2 = 0) & in(all_597_2, all_52_1) =
% 175.71/25.73 | | | | | | | | | | | | | | | | | | all_936_2
% 175.71/25.73 | | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 175.71/25.73 | | | | | | | | | | | | | | | | | | (187) ~ (all_936_2 = 0)
% 175.71/25.73 | | | | | | | | | | | | | | | | | | (188) in(all_597_2, all_52_1) = all_936_2
% 175.71/25.73 | | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_936_2, all_52_1,
% 175.71/25.73 | | | | | | | | | | | | | | | | | | all_597_2, simplifying with (167), (188) gives:
% 175.71/25.73 | | | | | | | | | | | | | | | | | | (189) all_936_2 = 0
% 175.71/25.73 | | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | | REDUCE: (187), (189) imply:
% 175.71/25.73 | | | | | | | | | | | | | | | | | | (190) $false
% 175.71/25.73 | | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | | CLOSE: (190) is inconsistent.
% 175.71/25.73 | | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | | End of split
% 175.71/25.73 | | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | | End of split
% 175.71/25.73 | | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | | End of split
% 175.71/25.73 | | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | | End of split
% 175.71/25.73 | | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | | End of split
% 175.71/25.73 | | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | End of split
% 175.71/25.73 | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | End of split
% 175.71/25.73 | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | End of split
% 175.71/25.73 | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | End of split
% 175.71/25.73 | | | | | | | | |
% 175.71/25.73 | | | | | | | | End of split
% 175.71/25.73 | | | | | | | |
% 175.71/25.73 | | | | | | | Case 2:
% 175.71/25.73 | | | | | | | |
% 175.71/25.73 | | | | | | | | (191) ~ (all_105_1 = 0) & epsilon_transitive(all_52_2) =
% 175.71/25.73 | | | | | | | | all_105_1
% 175.71/25.73 | | | | | | | |
% 175.71/25.73 | | | | | | | | ALPHA: (191) implies:
% 175.71/25.73 | | | | | | | | (192) ~ (all_105_1 = 0)
% 175.71/25.73 | | | | | | | | (193) epsilon_transitive(all_52_2) = all_105_1
% 175.71/25.73 | | | | | | | |
% 175.71/25.73 | | | | | | | | BETA: splitting (101) gives:
% 175.71/25.73 | | | | | | | |
% 175.71/25.73 | | | | | | | | Case 1:
% 175.71/25.73 | | | | | | | | |
% 175.71/25.73 | | | | | | | | | (194) all_62_0 = 0
% 175.71/25.73 | | | | | | | | |
% 175.71/25.73 | | | | | | | | | REDUCE: (59), (194) imply:
% 175.71/25.73 | | | | | | | | | (195) $false
% 175.71/25.73 | | | | | | | | |
% 175.71/25.73 | | | | | | | | | CLOSE: (195) is inconsistent.
% 175.71/25.73 | | | | | | | | |
% 175.71/25.73 | | | | | | | | Case 2:
% 175.71/25.73 | | | | | | | | |
% 175.71/25.73 | | | | | | | | | (196) all_52_1 = all_52_2 | ? [v0: int] : ? [v1: int] :
% 175.71/25.73 | | | | | | | | | ? [v2: int] : ((v2 = 0 & in(all_52_2, all_52_1) = 0)
% 175.71/25.73 | | | | | | | | | | ( ~ (v1 = 0) & in(all_52_2, all_50_0) = v1) | ( ~
% 175.71/25.73 | | | | | | | | | (v0 = 0) & in(all_52_1, all_50_0) = v0))
% 175.71/25.73 | | | | | | | | |
% 175.71/25.73 | | | | | | | | | BETA: splitting (103) gives:
% 175.71/25.73 | | | | | | | | |
% 175.71/25.73 | | | | | | | | | Case 1:
% 175.71/25.73 | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | (197) all_62_0 = 0
% 175.71/25.73 | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | REDUCE: (59), (197) imply:
% 175.71/25.73 | | | | | | | | | | (198) $false
% 175.71/25.73 | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | CLOSE: (198) is inconsistent.
% 175.71/25.73 | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | Case 2:
% 175.71/25.73 | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | (199) all_52_1 = all_52_2 | ? [v0: int] : ? [v1: int] :
% 175.71/25.73 | | | | | | | | | | ? [v2: int] : ((v2 = 0 & in(all_52_2, all_52_1) =
% 175.71/25.73 | | | | | | | | | | 0) | ( ~ (v1 = 0) & in(all_52_1, all_52_1) =
% 175.71/25.73 | | | | | | | | | | v1) | ( ~ (v0 = 0) & in(all_52_2, all_52_1) =
% 175.71/25.73 | | | | | | | | | | v0))
% 175.71/25.73 | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | BETA: splitting (121) gives:
% 175.71/25.73 | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | Case 1:
% 175.71/25.73 | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | (200) all_168_0 = 0
% 175.71/25.73 | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | REDUCE: (117), (200) imply:
% 175.71/25.73 | | | | | | | | | | | (201) $false
% 175.71/25.73 | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | CLOSE: (201) is inconsistent.
% 175.71/25.73 | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | Case 2:
% 175.71/25.73 | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | GROUND_INST: instantiating (5) with all_52_1, all_52_1,
% 175.71/25.73 | | | | | | | | | | | all_227_1, all_305_0, simplifying with (38), (52),
% 175.71/25.73 | | | | | | | | | | | (128), (135) gives:
% 175.71/25.73 | | | | | | | | | | | (202) all_305_0 = 0 | all_227_1 = all_52_1 | ? [v0:
% 175.71/25.73 | | | | | | | | | | | int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 175.71/25.73 | | | | | | | | | | | in(all_227_1, all_52_1) = 0) | ( ~ (v1 = 0) &
% 175.71/25.73 | | | | | | | | | | | in(all_227_1, all_52_1) = v1) | ( ~ (v0 = 0) &
% 175.71/25.73 | | | | | | | | | | | in(all_52_1, all_52_1) = v0))
% 175.71/25.73 | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_2, all_105_1,
% 175.71/25.73 | | | | | | | | | | | simplifying with (37), (193) gives:
% 175.71/25.73 | | | | | | | | | | | (203) all_105_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~
% 175.71/25.73 | | | | | | | | | | | (v1 = 0) & subset(v0, all_52_2) = v1 & in(v0,
% 175.71/25.73 | | | | | | | | | | | all_52_2) = 0 & $i(v0))
% 175.71/25.73 | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | BETA: splitting (203) gives:
% 175.71/25.73 | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | Case 1:
% 175.71/25.73 | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | (204) all_105_1 = 0
% 175.71/25.73 | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | REDUCE: (192), (204) imply:
% 175.71/25.73 | | | | | | | | | | | | (205) $false
% 175.71/25.73 | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | CLOSE: (205) is inconsistent.
% 175.71/25.73 | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | Case 2:
% 175.71/25.73 | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | (206) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 175.71/25.73 | | | | | | | | | | | | subset(v0, all_52_2) = v1 & in(v0, all_52_2) = 0
% 175.71/25.73 | | | | | | | | | | | | & $i(v0))
% 175.71/25.73 | | | | | | | | | | | |
% 175.71/25.73 | | | | | | | | | | | | DELTA: instantiating (206) with fresh symbols all_570_0,
% 175.71/25.73 | | | | | | | | | | | | all_570_1 gives:
% 175.71/25.74 | | | | | | | | | | | | (207) ~ (all_570_0 = 0) & subset(all_570_1, all_52_2) =
% 175.71/25.74 | | | | | | | | | | | | all_570_0 & in(all_570_1, all_52_2) = 0 &
% 175.71/25.74 | | | | | | | | | | | | $i(all_570_1)
% 175.71/25.74 | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | ALPHA: (207) implies:
% 175.71/25.74 | | | | | | | | | | | | (208) ~ (all_570_0 = 0)
% 175.71/25.74 | | | | | | | | | | | | (209) $i(all_570_1)
% 175.71/25.74 | | | | | | | | | | | | (210) in(all_570_1, all_52_2) = 0
% 175.71/25.74 | | | | | | | | | | | | (211) subset(all_570_1, all_52_2) = all_570_0
% 175.71/25.74 | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | BETA: splitting (196) gives:
% 175.71/25.74 | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | Case 1:
% 175.71/25.74 | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | (212) all_52_1 = all_52_2
% 175.71/25.74 | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | REDUCE: (41), (212) imply:
% 175.71/25.74 | | | | | | | | | | | | | (213) ordinal(all_52_2) = 0
% 175.71/25.74 | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | REF_CLOSE: (19), (36), (40), (213) are inconsistent by
% 175.71/25.74 | | | | | | | | | | | | | sub-proof #2.
% 175.71/25.74 | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | Case 2:
% 175.71/25.74 | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | (214) ~ (all_52_1 = all_52_2)
% 175.71/25.74 | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | BETA: splitting (199) gives:
% 175.71/25.74 | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | Case 1:
% 175.71/25.74 | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | (215) all_52_1 = all_52_2
% 175.71/25.74 | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | REDUCE: (214), (215) imply:
% 175.71/25.74 | | | | | | | | | | | | | | (216) $false
% 175.71/25.74 | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | CLOSE: (216) is inconsistent.
% 175.71/25.74 | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | Case 2:
% 175.71/25.74 | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | (217) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2
% 175.71/25.74 | | | | | | | | | | | | | | = 0 & in(all_52_2, all_52_1) = 0) | ( ~ (v1 =
% 175.71/25.74 | | | | | | | | | | | | | | 0) & in(all_52_1, all_52_1) = v1) | ( ~ (v0
% 175.71/25.74 | | | | | | | | | | | | | | = 0) & in(all_52_2, all_52_1) = v0))
% 175.71/25.74 | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | DELTA: instantiating (217) with fresh symbols all_878_0,
% 175.71/25.74 | | | | | | | | | | | | | | all_878_1, all_878_2 gives:
% 175.71/25.74 | | | | | | | | | | | | | | (218) (all_878_0 = 0 & in(all_52_2, all_52_1) = 0) | ( ~
% 175.71/25.74 | | | | | | | | | | | | | | (all_878_1 = 0) & in(all_52_1, all_52_1) =
% 175.71/25.74 | | | | | | | | | | | | | | all_878_1) | ( ~ (all_878_2 = 0) & in(all_52_2,
% 175.71/25.74 | | | | | | | | | | | | | | all_52_1) = all_878_2)
% 175.71/25.74 | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_2, all_52_1,
% 175.71/25.74 | | | | | | | | | | | | | | all_570_1, simplifying with (37), (38), (104),
% 175.71/25.74 | | | | | | | | | | | | | | (209), (210) gives:
% 175.71/25.74 | | | | | | | | | | | | | | (219) in(all_570_1, all_52_1) = 0
% 175.71/25.74 | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_52_2, all_570_1,
% 175.71/25.74 | | | | | | | | | | | | | | simplifying with (37), (209), (210) gives:
% 175.71/25.74 | | | | | | | | | | | | | | (220) ? [v0: int] : ( ~ (v0 = 0) & in(all_52_2,
% 175.71/25.74 | | | | | | | | | | | | | | all_570_1) = v0)
% 175.71/25.74 | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_570_1, all_52_2,
% 175.71/25.74 | | | | | | | | | | | | | | all_570_0, simplifying with (37), (209), (211)
% 175.71/25.74 | | | | | | | | | | | | | | gives:
% 175.71/25.74 | | | | | | | | | | | | | | (221) all_570_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~
% 175.71/25.74 | | | | | | | | | | | | | | (v1 = 0) & in(v0, all_570_1) = 0 & in(v0,
% 175.71/25.74 | | | | | | | | | | | | | | all_52_2) = v1 & $i(v0))
% 175.71/25.74 | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | DELTA: instantiating (220) with fresh symbol all_885_0
% 175.71/25.74 | | | | | | | | | | | | | | gives:
% 175.71/25.74 | | | | | | | | | | | | | | (222) ~ (all_885_0 = 0) & in(all_52_2, all_570_1) =
% 175.71/25.74 | | | | | | | | | | | | | | all_885_0
% 175.71/25.74 | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | ALPHA: (222) implies:
% 175.71/25.74 | | | | | | | | | | | | | | (223) ~ (all_885_0 = 0)
% 175.71/25.74 | | | | | | | | | | | | | | (224) in(all_52_2, all_570_1) = all_885_0
% 175.71/25.74 | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 175.71/25.74 | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | Case 1:
% 175.71/25.74 | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | (225) all_570_0 = 0
% 175.71/25.74 | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | REDUCE: (208), (225) imply:
% 175.71/25.74 | | | | | | | | | | | | | | | (226) $false
% 175.71/25.74 | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | CLOSE: (226) is inconsistent.
% 175.71/25.74 | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | Case 2:
% 175.71/25.74 | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | (227) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 175.71/25.74 | | | | | | | | | | | | | | | all_570_1) = 0 & in(v0, all_52_2) = v1 &
% 175.71/25.74 | | | | | | | | | | | | | | | $i(v0))
% 175.71/25.74 | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | DELTA: instantiating (227) with fresh symbols all_999_0,
% 175.71/25.74 | | | | | | | | | | | | | | | all_999_1 gives:
% 175.71/25.74 | | | | | | | | | | | | | | | (228) ~ (all_999_0 = 0) & in(all_999_1, all_570_1) = 0
% 175.71/25.74 | | | | | | | | | | | | | | | & in(all_999_1, all_52_2) = all_999_0 &
% 175.71/25.74 | | | | | | | | | | | | | | | $i(all_999_1)
% 175.71/25.74 | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | ALPHA: (228) implies:
% 175.71/25.74 | | | | | | | | | | | | | | | (229) ~ (all_999_0 = 0)
% 175.71/25.74 | | | | | | | | | | | | | | | (230) $i(all_999_1)
% 175.71/25.74 | | | | | | | | | | | | | | | (231) in(all_999_1, all_52_2) = all_999_0
% 175.71/25.74 | | | | | | | | | | | | | | | (232) in(all_999_1, all_570_1) = 0
% 175.71/25.74 | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 175.71/25.74 | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | Case 1:
% 175.71/25.74 | | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | | (233) all_305_0 = 0
% 175.71/25.74 | | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | | REDUCE: (134), (233) imply:
% 175.71/25.74 | | | | | | | | | | | | | | | | (234) $false
% 175.71/25.74 | | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | | CLOSE: (234) is inconsistent.
% 175.71/25.74 | | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | Case 2:
% 175.71/25.74 | | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_52_1, all_570_1,
% 175.71/25.74 | | | | | | | | | | | | | | | | simplifying with (38), (53), (209), (219) gives:
% 175.71/25.74 | | | | | | | | | | | | | | | | (235) subset(all_570_1, all_52_1) = 0
% 175.71/25.74 | | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_52_2, all_999_1,
% 175.71/25.74 | | | | | | | | | | | | | | | | all_570_1, simplifying with (37), (209), (210),
% 175.71/25.74 | | | | | | | | | | | | | | | | (230), (232) gives:
% 175.71/25.74 | | | | | | | | | | | | | | | | (236) ? [v0: int] : ( ~ (v0 = 0) & in(all_52_2,
% 175.71/25.74 | | | | | | | | | | | | | | | | all_999_1) = v0)
% 175.71/25.74 | | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | | DELTA: instantiating (236) with fresh symbol all_1237_0
% 175.71/25.74 | | | | | | | | | | | | | | | | gives:
% 175.71/25.74 | | | | | | | | | | | | | | | | (237) ~ (all_1237_0 = 0) & in(all_52_2, all_999_1) =
% 175.71/25.74 | | | | | | | | | | | | | | | | all_1237_0
% 175.71/25.74 | | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | | ALPHA: (237) implies:
% 175.71/25.74 | | | | | | | | | | | | | | | | (238) ~ (all_1237_0 = 0)
% 175.71/25.74 | | | | | | | | | | | | | | | | (239) in(all_52_2, all_999_1) = all_1237_0
% 175.71/25.74 | | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 175.71/25.74 | | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | | Case 1:
% 175.71/25.74 | | | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | | | (240) all_878_0 = 0 & in(all_52_2, all_52_1) = 0
% 175.71/25.74 | | | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_52_1, all_52_2,
% 175.71/25.74 | | | | | | | | | | | | | | | | | all_999_1, all_1237_0, simplifying with (37),
% 175.71/25.74 | | | | | | | | | | | | | | | | | (38), (52), (230), (239) gives:
% 175.71/25.74 | | | | | | | | | | | | | | | | | (241) all_1237_0 = 0 | all_999_1 = all_52_2 | ? [v0:
% 175.71/25.74 | | | | | | | | | | | | | | | | | int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 175.71/25.74 | | | | | | | | | | | | | | | | | in(all_999_1, all_52_2) = 0) | ( ~ (v1 = 0) &
% 175.71/25.74 | | | | | | | | | | | | | | | | | in(all_999_1, all_52_1) = v1) | ( ~ (v0 = 0) &
% 175.71/25.74 | | | | | | | | | | | | | | | | | in(all_52_2, all_52_1) = v0))
% 175.71/25.74 | | | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (21), (38), (39), (209), (223), (224), (229),
% 175.71/25.74 | | | | | | | | | | | | | | | | | (230), (231), (232), (235), (238), (241) are
% 175.71/25.74 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1.
% 175.71/25.74 | | | | | | | | | | | | | | | | |
% 175.71/25.74 | | | | | | | | | | | | | | | | Case 2:
% 175.71/25.74 | | | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | | | | (242) ( ~ (all_878_1 = 0) & in(all_52_1, all_52_1) =
% 175.71/25.75 | | | | | | | | | | | | | | | | | all_878_1) | ( ~ (all_878_2 = 0) & in(all_52_2,
% 175.71/25.75 | | | | | | | | | | | | | | | | | all_52_1) = all_878_2)
% 175.71/25.75 | | | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 175.71/25.75 | | | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | | | | Case 1:
% 175.71/25.75 | | | | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_52_1, all_52_2,
% 175.71/25.75 | | | | | | | | | | | | | | | | | | all_999_1, all_1237_0, simplifying with (37),
% 175.71/25.75 | | | | | | | | | | | | | | | | | | (38), (52), (230), (239) gives:
% 175.71/25.75 | | | | | | | | | | | | | | | | | | (243) all_1237_0 = 0 | all_999_1 = all_52_2 | ? [v0:
% 175.71/25.75 | | | | | | | | | | | | | | | | | | int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 175.71/25.75 | | | | | | | | | | | | | | | | | | in(all_999_1, all_52_2) = 0) | ( ~ (v1 = 0) &
% 175.71/25.75 | | | | | | | | | | | | | | | | | | in(all_999_1, all_52_1) = v1) | ( ~ (v0 = 0) &
% 175.71/25.75 | | | | | | | | | | | | | | | | | | in(all_52_2, all_52_1) = v0))
% 175.71/25.75 | | | | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (21), (38), (39), (209), (223), (224), (229),
% 175.71/25.75 | | | | | | | | | | | | | | | | | | (230), (231), (232), (235), (238), (243) are
% 175.71/25.75 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1.
% 175.71/25.75 | | | | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | | | | Case 2:
% 175.71/25.75 | | | | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | | | | | (244) ~ (all_878_2 = 0) & in(all_52_2, all_52_1) =
% 175.71/25.75 | | | | | | | | | | | | | | | | | | all_878_2
% 175.71/25.75 | | | | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 175.71/25.75 | | | | | | | | | | | | | | | | | | (245) ~ (all_878_2 = 0)
% 175.71/25.75 | | | | | | | | | | | | | | | | | | (246) in(all_52_2, all_52_1) = all_878_2
% 175.71/25.75 | | | | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_878_2, all_52_1,
% 175.71/25.75 | | | | | | | | | | | | | | | | | | all_52_2, simplifying with (39), (246) gives:
% 175.71/25.75 | | | | | | | | | | | | | | | | | | (247) all_878_2 = 0
% 175.71/25.75 | | | | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | | | | | REDUCE: (245), (247) imply:
% 175.71/25.75 | | | | | | | | | | | | | | | | | | (248) $false
% 175.71/25.75 | | | | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | | | | | CLOSE: (248) is inconsistent.
% 175.71/25.75 | | | | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | | | | End of split
% 175.71/25.75 | | | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | | | End of split
% 175.71/25.75 | | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | | End of split
% 175.71/25.75 | | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | | End of split
% 175.71/25.75 | | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | | End of split
% 175.71/25.75 | | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | | End of split
% 175.71/25.75 | | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | | End of split
% 175.71/25.75 | | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | | End of split
% 175.71/25.75 | | | | | | | | | |
% 175.71/25.75 | | | | | | | | | End of split
% 175.71/25.75 | | | | | | | | |
% 175.71/25.75 | | | | | | | | End of split
% 175.71/25.75 | | | | | | | |
% 175.71/25.75 | | | | | | | End of split
% 175.71/25.75 | | | | | | |
% 175.71/25.75 | | | | | | End of split
% 175.71/25.75 | | | | | |
% 175.71/25.75 | | | | | End of split
% 175.71/25.75 | | | | |
% 175.71/25.75 | | | | End of split
% 175.71/25.75 | | | |
% 175.71/25.75 | | | End of split
% 175.71/25.75 | | |
% 175.71/25.75 | | End of split
% 175.71/25.75 | |
% 175.71/25.75 | End of split
% 175.71/25.75 |
% 175.71/25.75 End of proof
% 175.71/25.75
% 175.71/25.75 Sub-proof #1 shows that the following formulas are inconsistent:
% 175.71/25.75 ----------------------------------------------------------------
% 175.71/25.75 (1) ~ (all_999_0 = 0)
% 175.71/25.75 (2) in(all_999_1, all_570_1) = 0
% 175.71/25.75 (3) in(all_52_2, all_570_1) = all_885_0
% 175.71/25.75 (4) subset(all_570_1, all_52_1) = 0
% 175.71/25.75 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 175.71/25.75 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 175.71/25.75 (6) ~ (all_1237_0 = 0)
% 175.71/25.75 (7) in(all_52_2, all_52_1) = 0
% 175.71/25.75 (8) $i(all_570_1)
% 175.71/25.75 (9) ~ (all_885_0 = 0)
% 175.71/25.75 (10) all_1237_0 = 0 | all_999_1 = all_52_2 | ? [v0: int] : ? [v1: int] : ?
% 175.71/25.75 [v2: int] : ((v2 = 0 & in(all_999_1, all_52_2) = 0) | ( ~ (v1 = 0) &
% 175.71/25.75 in(all_999_1, all_52_1) = v1) | ( ~ (v0 = 0) & in(all_52_2,
% 175.71/25.75 all_52_1) = v0))
% 175.71/25.75 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 175.71/25.75 (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) = 0)
% 175.71/25.75 (12) $i(all_999_1)
% 175.71/25.75 (13) in(all_999_1, all_52_2) = all_999_0
% 175.71/25.75 (14) $i(all_52_1)
% 175.71/25.75
% 175.71/25.75 Begin of proof
% 175.71/25.75 |
% 175.71/25.75 | GROUND_INST: instantiating (11) with all_570_1, all_52_1, all_999_1,
% 175.71/25.75 | simplifying with (2), (4), (8), (12), (14) gives:
% 175.71/25.75 | (15) in(all_999_1, all_52_1) = 0
% 175.71/25.75 |
% 175.71/25.75 | BETA: splitting (10) gives:
% 175.71/25.75 |
% 175.71/25.75 | Case 1:
% 175.71/25.75 | |
% 175.71/25.75 | | (16) all_1237_0 = 0
% 175.71/25.75 | |
% 175.71/25.75 | | REDUCE: (6), (16) imply:
% 175.71/25.75 | | (17) $false
% 175.71/25.75 | |
% 175.71/25.75 | | CLOSE: (17) is inconsistent.
% 175.71/25.75 | |
% 175.71/25.75 | Case 2:
% 175.71/25.75 | |
% 175.71/25.75 | | (18) all_999_1 = all_52_2 | ? [v0: int] : ? [v1: int] : ? [v2: int] :
% 175.71/25.75 | | ((v2 = 0 & in(all_999_1, all_52_2) = 0) | ( ~ (v1 = 0) &
% 175.71/25.75 | | in(all_999_1, all_52_1) = v1) | ( ~ (v0 = 0) & in(all_52_2,
% 175.71/25.75 | | all_52_1) = v0))
% 175.71/25.75 | |
% 175.71/25.75 | | BETA: splitting (18) gives:
% 175.71/25.75 | |
% 175.71/25.75 | | Case 1:
% 175.71/25.75 | | |
% 175.71/25.75 | | | (19) all_999_1 = all_52_2
% 175.71/25.75 | | |
% 175.71/25.75 | | | REDUCE: (2), (19) imply:
% 175.71/25.75 | | | (20) in(all_52_2, all_570_1) = 0
% 175.71/25.75 | | |
% 175.71/25.75 | | | GROUND_INST: instantiating (5) with all_885_0, 0, all_570_1, all_52_2,
% 175.71/25.75 | | | simplifying with (3), (20) gives:
% 175.71/25.75 | | | (21) all_885_0 = 0
% 175.71/25.75 | | |
% 175.71/25.75 | | | REDUCE: (9), (21) imply:
% 175.71/25.75 | | | (22) $false
% 175.71/25.75 | | |
% 175.71/25.75 | | | CLOSE: (22) is inconsistent.
% 175.71/25.75 | | |
% 175.71/25.75 | | Case 2:
% 175.71/25.75 | | |
% 175.71/25.75 | | | (23) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 175.71/25.75 | | | in(all_999_1, all_52_2) = 0) | ( ~ (v1 = 0) & in(all_999_1,
% 175.71/25.75 | | | all_52_1) = v1) | ( ~ (v0 = 0) & in(all_52_2, all_52_1) =
% 175.71/25.75 | | | v0))
% 175.71/25.75 | | |
% 175.71/25.75 | | | DELTA: instantiating (23) with fresh symbols all_1936_0, all_1936_1,
% 175.71/25.75 | | | all_1936_2 gives:
% 175.71/25.75 | | | (24) (all_1936_0 = 0 & in(all_999_1, all_52_2) = 0) | ( ~ (all_1936_1 =
% 175.71/25.75 | | | 0) & in(all_999_1, all_52_1) = all_1936_1) | ( ~ (all_1936_2 =
% 175.71/25.75 | | | 0) & in(all_52_2, all_52_1) = all_1936_2)
% 175.71/25.75 | | |
% 175.71/25.75 | | | BETA: splitting (24) gives:
% 175.71/25.75 | | |
% 175.71/25.75 | | | Case 1:
% 175.71/25.75 | | | |
% 175.71/25.75 | | | | (25) all_1936_0 = 0 & in(all_999_1, all_52_2) = 0
% 175.71/25.75 | | | |
% 175.71/25.75 | | | | ALPHA: (25) implies:
% 175.71/25.75 | | | | (26) in(all_999_1, all_52_2) = 0
% 175.71/25.75 | | | |
% 175.71/25.76 | | | | GROUND_INST: instantiating (5) with all_999_0, 0, all_52_2, all_999_1,
% 175.71/25.76 | | | | simplifying with (13), (26) gives:
% 175.71/25.76 | | | | (27) all_999_0 = 0
% 175.71/25.76 | | | |
% 175.71/25.76 | | | | REDUCE: (1), (27) imply:
% 175.71/25.76 | | | | (28) $false
% 175.71/25.76 | | | |
% 175.71/25.76 | | | | CLOSE: (28) is inconsistent.
% 175.71/25.76 | | | |
% 175.71/25.76 | | | Case 2:
% 175.71/25.76 | | | |
% 175.71/25.76 | | | | (29) ( ~ (all_1936_1 = 0) & in(all_999_1, all_52_1) = all_1936_1) | (
% 175.71/25.76 | | | | ~ (all_1936_2 = 0) & in(all_52_2, all_52_1) = all_1936_2)
% 175.71/25.76 | | | |
% 175.71/25.76 | | | | BETA: splitting (29) gives:
% 175.71/25.76 | | | |
% 175.71/25.76 | | | | Case 1:
% 175.71/25.76 | | | | |
% 175.71/25.76 | | | | | (30) ~ (all_1936_1 = 0) & in(all_999_1, all_52_1) = all_1936_1
% 175.71/25.76 | | | | |
% 175.71/25.76 | | | | | ALPHA: (30) implies:
% 175.71/25.76 | | | | | (31) ~ (all_1936_1 = 0)
% 175.71/25.76 | | | | | (32) in(all_999_1, all_52_1) = all_1936_1
% 175.71/25.76 | | | | |
% 175.71/25.76 | | | | | GROUND_INST: instantiating (5) with 0, all_1936_1, all_52_1,
% 175.71/25.76 | | | | | all_999_1, simplifying with (15), (32) gives:
% 175.71/25.76 | | | | | (33) all_1936_1 = 0
% 175.71/25.76 | | | | |
% 175.71/25.76 | | | | | REDUCE: (31), (33) imply:
% 175.71/25.76 | | | | | (34) $false
% 175.71/25.76 | | | | |
% 175.71/25.76 | | | | | CLOSE: (34) is inconsistent.
% 175.71/25.76 | | | | |
% 175.71/25.76 | | | | Case 2:
% 175.71/25.76 | | | | |
% 175.71/25.76 | | | | | (35) ~ (all_1936_2 = 0) & in(all_52_2, all_52_1) = all_1936_2
% 175.71/25.76 | | | | |
% 175.71/25.76 | | | | | ALPHA: (35) implies:
% 175.71/25.76 | | | | | (36) ~ (all_1936_2 = 0)
% 175.71/25.76 | | | | | (37) in(all_52_2, all_52_1) = all_1936_2
% 175.71/25.76 | | | | |
% 175.71/25.76 | | | | | GROUND_INST: instantiating (5) with 0, all_1936_2, all_52_1, all_52_2,
% 175.71/25.76 | | | | | simplifying with (7), (37) gives:
% 175.71/25.76 | | | | | (38) all_1936_2 = 0
% 175.71/25.76 | | | | |
% 175.71/25.76 | | | | | REDUCE: (36), (38) imply:
% 175.71/25.76 | | | | | (39) $false
% 175.71/25.76 | | | | |
% 175.71/25.76 | | | | | CLOSE: (39) is inconsistent.
% 175.71/25.76 | | | | |
% 175.71/25.76 | | | | End of split
% 175.71/25.76 | | | |
% 175.71/25.76 | | | End of split
% 175.71/25.76 | | |
% 175.71/25.76 | | End of split
% 175.71/25.76 | |
% 175.71/25.76 | End of split
% 175.71/25.76 |
% 175.71/25.76 End of proof
% 175.71/25.76
% 175.71/25.76 Sub-proof #2 shows that the following formulas are inconsistent:
% 175.71/25.76 ----------------------------------------------------------------
% 175.71/25.76 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 175.71/25.76 (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 175.71/25.76 (2) ordinal(all_52_2) = all_52_0
% 175.71/25.76 (3) ordinal(all_52_2) = 0
% 175.71/25.76 (4) ~ (all_52_0 = 0)
% 175.71/25.76
% 175.71/25.76 Begin of proof
% 175.71/25.76 |
% 175.71/25.76 | GROUND_INST: instantiating (1) with all_52_0, 0, all_52_2, simplifying with
% 175.71/25.76 | (2), (3) gives:
% 175.71/25.76 | (5) all_52_0 = 0
% 175.71/25.76 |
% 175.71/25.76 | REDUCE: (4), (5) imply:
% 175.71/25.76 | (6) $false
% 175.71/25.76 |
% 175.71/25.76 | CLOSE: (6) is inconsistent.
% 175.71/25.76 |
% 175.71/25.76 End of proof
% 175.71/25.76 % SZS output end Proof for theBenchmark
% 175.71/25.76
% 175.71/25.76 25129ms
%------------------------------------------------------------------------------