TSTP Solution File: SEU173+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU173+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 17:43:02 EDT 2023
% Result : Theorem 27.99s 4.61s
% Output : Proof 140.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU173+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 19:16:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.17/1.35 Prover 1: Preprocessing ...
% 4.17/1.35 Prover 4: Preprocessing ...
% 4.17/1.39 Prover 2: Preprocessing ...
% 4.17/1.39 Prover 5: Preprocessing ...
% 4.81/1.39 Prover 6: Preprocessing ...
% 4.81/1.39 Prover 3: Preprocessing ...
% 4.81/1.39 Prover 0: Preprocessing ...
% 10.99/2.29 Prover 1: Warning: ignoring some quantifiers
% 11.72/2.38 Prover 5: Proving ...
% 11.72/2.40 Prover 6: Proving ...
% 11.72/2.41 Prover 4: Warning: ignoring some quantifiers
% 11.72/2.42 Prover 3: Warning: ignoring some quantifiers
% 12.25/2.46 Prover 1: Constructing countermodel ...
% 12.25/2.47 Prover 3: Constructing countermodel ...
% 12.94/2.53 Prover 4: Constructing countermodel ...
% 12.94/2.54 Prover 2: Proving ...
% 13.60/2.64 Prover 0: Proving ...
% 27.99/4.61 Prover 0: proved (3962ms)
% 27.99/4.61
% 27.99/4.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.99/4.61
% 28.43/4.62 Prover 2: stopped
% 28.43/4.62 Prover 5: stopped
% 28.43/4.65 Prover 3: stopped
% 28.68/4.66 Prover 6: stopped
% 28.68/4.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 28.68/4.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 28.68/4.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 28.68/4.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 28.68/4.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 29.28/4.80 Prover 7: Preprocessing ...
% 29.28/4.81 Prover 8: Preprocessing ...
% 29.28/4.88 Prover 11: Preprocessing ...
% 29.28/4.90 Prover 10: Preprocessing ...
% 29.28/4.93 Prover 13: Preprocessing ...
% 31.35/5.07 Prover 7: Warning: ignoring some quantifiers
% 31.98/5.10 Prover 7: Constructing countermodel ...
% 31.98/5.17 Prover 10: Warning: ignoring some quantifiers
% 32.56/5.19 Prover 8: Warning: ignoring some quantifiers
% 32.56/5.19 Prover 10: Constructing countermodel ...
% 32.56/5.23 Prover 8: Constructing countermodel ...
% 32.56/5.23 Prover 13: Warning: ignoring some quantifiers
% 32.56/5.25 Prover 13: Constructing countermodel ...
% 34.28/5.50 Prover 11: Warning: ignoring some quantifiers
% 34.28/5.53 Prover 11: Constructing countermodel ...
% 46.87/7.18 Prover 8: gave up
% 46.87/7.18 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 48.41/7.25 Prover 16: Preprocessing ...
% 49.65/7.44 Prover 16: Warning: ignoring some quantifiers
% 49.65/7.45 Prover 16: Constructing countermodel ...
% 55.99/8.27 Prover 1: gave up
% 55.99/8.28 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 55.99/8.32 Prover 19: Preprocessing ...
% 57.00/8.54 Prover 19: Warning: ignoring some quantifiers
% 57.89/8.60 Prover 19: Constructing countermodel ...
% 68.27/9.87 Prover 13: stopped
% 87.57/12.42 Prover 19: stopped
% 95.81/13.68 Prover 16: stopped
% 139.94/22.63 Prover 11: Found proof (size 170)
% 139.94/22.63 Prover 11: proved (17965ms)
% 139.94/22.63 Prover 10: stopped
% 139.94/22.63 Prover 7: stopped
% 139.94/22.64 Prover 4: stopped
% 139.94/22.64
% 139.94/22.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 139.94/22.64
% 139.94/22.65 % SZS output start Proof for theBenchmark
% 139.94/22.65 Assumptions after simplification:
% 139.94/22.65 ---------------------------------
% 139.94/22.65
% 139.94/22.65 (d1_zfmisc_1)
% 140.45/22.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 140.45/22.68 (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 140.45/22.68 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0: $i] : !
% 140.45/22.68 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (powerset(v0) = v1) | ~
% 140.45/22.68 (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~
% 140.45/22.68 (v4 = 0) & subset(v2, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 140.45/22.69 : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 140.45/22.69 ~ $i(v0) | in(v2, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 140.45/22.69 (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 140.45/22.69 $i(v0) | subset(v2, v0) = 0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2
% 140.45/22.69 = v0 | ~ (powerset(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 140.45/22.69 [v4: int] : ? [v5: int] : ($i(v3) & ((v5 = 0 & subset(v3, v1) = 0) | (v4 =
% 140.45/22.69 0 & in(v3, v0) = 0)) & (( ~ (v5 = 0) & subset(v3, v1) = v5) | ( ~ (v4
% 140.45/22.69 = 0) & in(v3, v0) = v4))))
% 140.45/22.69
% 140.45/22.69 (d2_subset_1)
% 140.45/22.69 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) | ~
% 140.45/22.69 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v3 = 0 & empty(v0) = 0)
% 140.45/22.69 | (( ~ (v2 = 0) | (v4 = 0 & in(v1, v0) = 0)) & (v2 = 0 | ( ~ (v4 = 0) &
% 140.45/22.69 in(v1, v0) = v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : (
% 140.45/22.69 ~ (element(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4:
% 140.45/22.69 int] : (( ~ (v3 = 0) & empty(v0) = v3) | (( ~ (v2 = 0) | (v4 = 0 &
% 140.45/22.69 empty(v1) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & empty(v1) = v4))))) & !
% 140.45/22.69 [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (in(v1, v0) = v2) | ~ $i(v1) | ~
% 140.45/22.69 $i(v0) | ? [v3: int] : ? [v4: int] : ((v3 = 0 & empty(v0) = 0) | (( ~ (v2
% 140.45/22.69 = 0) | (v4 = 0 & element(v1, v0) = 0)) & (v2 = 0 | ( ~ (v4 = 0) &
% 140.45/22.69 element(v1, v0) = v4)))))
% 140.45/22.69
% 140.45/22.69 (d2_xboole_0)
% 140.63/22.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 140.63/22.70 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~
% 140.63/22.70 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0)
% 140.63/22.70 & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0: $i] : !
% 140.63/22.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 140.63/22.70 (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) |
% 140.63/22.70 ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 = 0 & in(v3, v0) =
% 140.63/22.70 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0: $i] : ! [v1: $i] : !
% 140.63/22.70 [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (set_union2(v0, v1) = v2)
% 140.63/22.70 | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 140.63/22.70 [v5: int] : ? [v6: int] : ((v6 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) &
% 140.63/22.70 in(v3, v2) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 140.63/22.70 $i] : ! [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) |
% 140.63/22.70 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] :
% 140.63/22.70 ((v6 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v0) = v5)))
% 140.63/22.70 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 140.63/22.70 (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) |
% 140.63/22.70 ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 = 0 & in(v3, v2) =
% 140.63/22.70 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v1) = v5))) & ! [v0: $i] : !
% 140.63/22.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~
% 140.63/22.71 (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 140.63/22.71 int] : ? [v5: int] : ((v5 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) =
% 140.63/22.71 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0
% 140.63/22.71 | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 140.63/22.71 $i] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ($i(v4) & ((v7 = 0 &
% 140.63/22.71 in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) =
% 140.63/22.71 0)) & (( ~ (v7 = 0) & ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6)
% 140.63/22.71 | ( ~ (v5 = 0) & in(v4, v0) = v5))))
% 140.63/22.71
% 140.63/22.71 (d3_tarski)
% 140.63/22.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 140.63/22.71 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 140.63/22.71 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 140.63/22.71 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 140.63/22.71 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 140.63/22.71 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 140.63/22.71 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 140.63/22.71 $i(v0) | in(v2, v1) = 0)
% 140.63/22.71
% 140.63/22.71 (d4_tarski)
% 140.63/22.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0
% 140.63/22.72 | ~ (union(v0) = v1) | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ~
% 140.63/22.72 $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 140.63/22.72 in(v2, v4) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int]
% 140.63/22.72 : ! [v4: $i] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~
% 140.63/22.72 (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 140.63/22.72 int] : ( ~ (v5 = 0) & in(v4, v0) = v5)) & ! [v0: $i] : ! [v1: $i] : !
% 140.63/22.72 [v2: $i] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1)
% 140.63/22.72 | ~ $i(v0) | ? [v3: $i] : (in(v3, v0) = 0 & in(v2, v3) = 0 & $i(v3))) & ?
% 140.63/22.72 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (union(v1) = v2) | ~
% 140.63/22.72 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ? [v6: int]
% 140.63/22.72 : ? [v7: int] : ($i(v5) & $i(v3) & ((v7 = 0 & v6 = 0 & in(v5, v1) = 0 &
% 140.63/22.72 in(v3, v5) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v4 = 0) & in(v3,
% 140.63/22.72 v0) = v4) | ( ! [v8: $i] : ( ~ (in(v8, v1) = 0) | ~ $i(v8) | ?
% 140.63/22.72 [v9: int] : ( ~ (v9 = 0) & in(v3, v8) = v9)) & ! [v8: $i] : ( ~
% 140.63/22.72 (in(v3, v8) = 0) | ~ $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & in(v8,
% 140.63/22.72 v1) = v9))))))
% 140.63/22.72
% 140.63/22.72 (d5_subset_1)
% 140.63/22.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2)
% 140.63/22.72 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ((v5 =
% 140.63/22.72 v2 & set_difference(v0, v1) = v2 & $i(v2)) | ( ~ (v4 = 0) & element(v1,
% 140.63/22.72 v3) = v4 & powerset(v0) = v3 & $i(v3)))) & ! [v0: $i] : ! [v1: $i] :
% 140.63/22.72 ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 140.63/22.72 [v3: $i] : ? [v4: int] : ? [v5: $i] : ((v5 = v2 & subset_complement(v0,
% 140.63/22.72 v1) = v2 & $i(v2)) | ( ~ (v4 = 0) & element(v1, v3) = v4 &
% 140.63/22.72 powerset(v0) = v3 & $i(v3)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 140.63/22.72 : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) |
% 140.63/22.72 ? [v3: $i] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3
% 140.63/22.72 & $i(v3)))
% 140.63/22.72
% 140.63/22.72 (dt_k3_subset_1)
% 140.63/22.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2)
% 140.63/22.72 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: int] :
% 140.63/22.72 (powerset(v0) = v3 & $i(v3) & ((v5 = 0 & element(v2, v3) = 0) | ( ~ (v4 = 0)
% 140.63/22.72 & element(v1, v3) = v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 140.63/22.72 ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) |
% 140.63/22.72 ? [v3: $i] : (subset_complement(v0, v1) = v3 & element(v3, v2) = 0 &
% 140.63/22.72 $i(v3)))
% 140.63/22.72
% 140.63/22.72 (fc1_subset_1)
% 140.63/22.72 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int]
% 140.63/22.72 : ( ~ (v2 = 0) & empty(v1) = v2))
% 140.63/22.72
% 140.63/22.72 (involutiveness_k3_subset_1)
% 140.63/22.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2)
% 140.63/22.73 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ((v5 =
% 140.63/22.73 v1 & subset_complement(v0, v2) = v1) | ( ~ (v4 = 0) & element(v1, v3) =
% 140.63/22.73 v4 & powerset(v0) = v3 & $i(v3)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 140.63/22.73 $i] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ $i(v1) | ~
% 140.63/22.73 $i(v0) | ? [v3: $i] : (subset_complement(v0, v3) = v1 &
% 140.63/22.73 subset_complement(v0, v1) = v3 & $i(v3)))
% 140.63/22.73
% 140.63/22.73 (l71_subset_1)
% 140.63/22.73 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 140.63/22.73 element(v0, v2) = v3 & powerset(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & !
% 140.63/22.73 [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v1) = v5) | ~ $i(v4) | ?
% 140.63/22.73 [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = v6)) & ! [v4: $i] : ( ~ (in(v4,
% 140.63/22.73 v0) = 0) | ~ $i(v4) | in(v4, v1) = 0))
% 140.63/22.73
% 140.63/22.73 (rc1_xboole_0)
% 140.63/22.73 ? [v0: $i] : (empty(v0) = 0 & $i(v0))
% 140.63/22.73
% 140.63/22.73 (rc2_subset_1)
% 140.63/22.73 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i]
% 140.63/22.73 : (empty(v2) = 0 & element(v2, v1) = 0 & $i(v2)))
% 140.63/22.73
% 140.63/22.73 (t1_zfmisc_1)
% 140.63/22.73 $i(empty_set) & ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set)
% 140.63/22.73 = v0 & $i(v0))
% 140.63/22.73
% 140.63/22.73 (t3_boole)
% 140.63/22.73 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (set_difference(v0,
% 140.63/22.73 empty_set) = v1) | ~ $i(v0))
% 140.63/22.73
% 140.63/22.73 (t40_xboole_1)
% 140.63/22.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) |
% 140.63/22.73 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (set_difference(v3, v1) = v2 &
% 140.63/22.73 set_union2(v0, v1) = v3 & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] :
% 140.63/22.73 ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 140.63/22.73 $i] : (set_difference(v2, v1) = v3 & set_difference(v0, v1) = v3 &
% 140.63/22.73 $i(v3)))
% 140.63/22.73
% 140.63/22.73 (t45_xboole_1)
% 140.63/22.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v1, v0) = v2) |
% 140.63/22.73 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ((v4 = v1 &
% 140.63/22.73 set_union2(v0, v2) = v1) | ( ~ (v3 = 0) & subset(v0, v1) = v3))) & !
% 140.63/22.73 [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 140.63/22.73 [v2: $i] : (set_difference(v1, v0) = v2 & set_union2(v0, v2) = v1 & $i(v2)))
% 140.63/22.73
% 140.63/22.73 (t69_enumset1)
% 140.63/22.73 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 140.63/22.73 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 140.63/22.73 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1)))
% 140.63/22.73
% 140.63/22.73 (t6_boole)
% 140.63/22.73 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~
% 140.63/22.73 $i(v0))
% 140.63/22.73
% 140.63/22.73 (t8_boole)
% 140.63/22.73 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)
% 140.63/22.73 | ~ $i(v1) | ~ $i(v0))
% 140.63/22.73
% 140.63/22.73 (t99_zfmisc_1)
% 140.81/22.74 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | union(v1) =
% 140.81/22.74 v0)
% 140.81/22.74
% 140.81/22.74 (function-axioms)
% 140.81/22.74 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 140.81/22.74 [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~
% 140.81/22.74 (are_equipotent(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 140.81/22.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3,
% 140.81/22.74 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 140.81/22.74 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~
% 140.81/22.74 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 140.81/22.74 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~
% 140.81/22.74 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 140.81/22.74 ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~
% 140.81/22.74 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 140.81/22.74 : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~
% 140.81/22.74 (ordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 140.81/22.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3,
% 140.81/22.74 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 140.81/22.74 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.81/22.74 (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 140.81/22.74 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) =
% 140.81/22.74 v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 140.81/22.74 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~
% 140.81/22.74 (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 140.81/22.74 [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~
% 140.81/22.74 (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 140.81/22.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.81/22.74 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0:
% 140.81/22.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 140.81/22.74 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 140.81/22.74 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 140.81/22.74 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 140.81/22.74 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1:
% 140.81/22.74 $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) =
% 140.81/22.74 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 140.81/22.74 (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 140.81/22.74
% 140.81/22.74 Further assumptions not needed in the proof:
% 140.81/22.74 --------------------------------------------
% 140.81/22.74 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski,
% 140.81/22.74 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_tarski,
% 140.81/22.74 d1_xboole_0, d2_tarski, d2_zfmisc_1, d3_xboole_0, d4_xboole_0, d5_tarski,
% 140.81/22.74 d7_xboole_0, d8_xboole_0, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1,
% 140.81/22.74 dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_tarski, dt_k3_xboole_0,
% 140.81/22.74 dt_k4_tarski, dt_k4_xboole_0, dt_m1_subset_1, existence_m1_subset_1,
% 140.81/22.74 fc1_xboole_0, fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0,
% 140.81/22.74 idempotence_k3_xboole_0, irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1,
% 140.81/22.74 l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_subset_1, l3_zfmisc_1,
% 140.81/22.74 l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, rc1_subset_1, rc2_xboole_0,
% 140.81/22.74 reflexivity_r1_tarski, symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1,
% 140.81/22.74 t118_zfmisc_1, t119_zfmisc_1, t12_xboole_1, t136_zfmisc_1, t17_xboole_1,
% 140.81/22.74 t19_xboole_1, t1_boole, t1_xboole_1, t26_xboole_1, t28_xboole_1, t2_boole,
% 140.81/22.74 t2_tarski, t2_xboole_1, t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_xboole_1,
% 140.81/22.74 t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_xboole_0,
% 140.81/22.74 t3_xboole_1, t43_subset_1, t46_zfmisc_1, t48_xboole_1, t4_boole, t4_xboole_0,
% 140.81/22.74 t50_subset_1, t54_subset_1, t60_xboole_1, t63_xboole_1, t65_zfmisc_1,
% 140.81/22.74 t6_zfmisc_1, t7_boole, t7_xboole_1, t83_xboole_1, t8_xboole_1, t8_zfmisc_1,
% 140.81/22.74 t92_zfmisc_1, t9_tarski, t9_zfmisc_1
% 140.81/22.74
% 140.81/22.74 Those formulas are unsatisfiable:
% 140.81/22.74 ---------------------------------
% 140.81/22.74
% 140.81/22.74 Begin of proof
% 140.81/22.74 |
% 140.81/22.74 | ALPHA: (d1_zfmisc_1) implies:
% 140.81/22.75 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v1) | ~
% 140.81/22.75 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | subset(v2, v0)
% 140.81/22.75 | = 0)
% 140.81/22.75 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 140.81/22.75 | (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 140.81/22.75 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v2, v0) = v4))
% 140.81/22.75 |
% 140.81/22.75 | ALPHA: (d2_subset_1) implies:
% 140.81/22.75 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) |
% 140.81/22.75 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v3 = 0 &
% 140.81/22.75 | empty(v0) = 0) | (( ~ (v2 = 0) | (v4 = 0 & in(v1, v0) = 0)) & (v2
% 140.81/22.75 | = 0 | ( ~ (v4 = 0) & in(v1, v0) = v4)))))
% 140.81/22.75 |
% 140.81/22.75 | ALPHA: (d2_xboole_0) implies:
% 140.81/22.75 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 140.81/22.75 | (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~
% 140.81/22.75 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 140.81/22.75 | int] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) =
% 140.81/22.75 | v5))
% 140.81/22.75 |
% 140.81/22.75 | ALPHA: (d3_tarski) implies:
% 140.81/22.75 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 140.81/22.75 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 140.81/22.75 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 140.81/22.75 |
% 140.81/22.75 | ALPHA: (d4_tarski) implies:
% 140.81/22.75 | (6) ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (union(v1) =
% 140.81/22.75 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5:
% 140.81/22.75 | $i] : ? [v6: int] : ? [v7: int] : ($i(v5) & $i(v3) & ((v7 = 0 &
% 140.81/22.75 | v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0) | (v4 = 0 & in(v3,
% 140.81/22.75 | v0) = 0)) & (( ~ (v4 = 0) & in(v3, v0) = v4) | ( ! [v8: $i] :
% 140.81/22.75 | ( ~ (in(v8, v1) = 0) | ~ $i(v8) | ? [v9: int] : ( ~ (v9 = 0)
% 140.81/22.75 | & in(v3, v8) = v9)) & ! [v8: $i] : ( ~ (in(v3, v8) = 0) |
% 140.81/22.75 | ~ $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & in(v8, v1) =
% 140.81/22.75 | v9))))))
% 140.81/22.75 |
% 140.81/22.75 | ALPHA: (d5_subset_1) implies:
% 140.81/22.75 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (element(v1, v2) = 0) |
% 140.81/22.75 | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 140.81/22.75 | (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3 &
% 140.81/22.75 | $i(v3)))
% 140.81/22.75 |
% 140.81/22.75 | ALPHA: (dt_k3_subset_1) implies:
% 140.81/22.75 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (element(v1, v2) = 0) |
% 140.81/22.75 | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 140.81/22.75 | (subset_complement(v0, v1) = v3 & element(v3, v2) = 0 & $i(v3)))
% 140.81/22.75 |
% 140.81/22.75 | ALPHA: (involutiveness_k3_subset_1) implies:
% 140.81/22.75 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (element(v1, v2) = 0) |
% 140.81/22.75 | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 140.81/22.75 | (subset_complement(v0, v3) = v1 & subset_complement(v0, v1) = v3 &
% 140.81/22.75 | $i(v3)))
% 140.81/22.75 |
% 140.81/22.76 | ALPHA: (t1_zfmisc_1) implies:
% 140.81/22.76 | (10) ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) = v0 &
% 140.81/22.76 | $i(v0))
% 140.81/22.76 |
% 140.81/22.76 | ALPHA: (t3_boole) implies:
% 140.81/22.76 | (11) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (set_difference(v0,
% 140.81/22.76 | empty_set) = v1) | ~ $i(v0))
% 140.81/22.76 |
% 140.81/22.76 | ALPHA: (t40_xboole_1) implies:
% 140.81/22.76 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1)
% 140.81/22.76 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (set_difference(v3,
% 140.81/22.76 | v1) = v2 & set_union2(v0, v1) = v3 & $i(v3) & $i(v2)))
% 140.81/22.76 |
% 140.81/22.76 | ALPHA: (t45_xboole_1) implies:
% 140.81/22.76 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v1, v0)
% 140.81/22.76 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ((v4
% 140.81/22.76 | = v1 & set_union2(v0, v2) = v1) | ( ~ (v3 = 0) & subset(v0, v1)
% 140.81/22.76 | = v3)))
% 140.81/22.76 |
% 140.81/22.76 | ALPHA: (t69_enumset1) implies:
% 140.81/22.76 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 140.81/22.76 | (unordered_pair(v0, v0) = v1 & $i(v1)))
% 140.81/22.76 |
% 140.81/22.76 | ALPHA: (t6_boole) implies:
% 140.81/22.76 | (15) $i(empty_set)
% 140.81/22.76 | (16) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 140.81/22.76 |
% 140.81/22.76 | ALPHA: (function-axioms) implies:
% 140.81/22.76 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 140.81/22.76 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 140.81/22.76 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 140.81/22.76 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 140.81/22.76 | v0))
% 140.81/22.76 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 140.81/22.76 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3,
% 140.81/22.76 | v2) = v0))
% 140.81/22.76 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.81/22.76 | (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) =
% 140.81/22.76 | v0))
% 140.81/22.76 |
% 140.81/22.76 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_97_0 gives:
% 140.81/22.76 | (21) empty(all_97_0) = 0 & $i(all_97_0)
% 140.81/22.76 |
% 140.81/22.76 | ALPHA: (21) implies:
% 140.81/22.76 | (22) $i(all_97_0)
% 140.81/22.76 | (23) empty(all_97_0) = 0
% 140.81/22.76 |
% 140.81/22.76 | DELTA: instantiating (10) with fresh symbol all_99_0 gives:
% 140.81/22.76 | (24) powerset(empty_set) = all_99_0 & singleton(empty_set) = all_99_0 &
% 140.81/22.76 | $i(all_99_0)
% 140.81/22.76 |
% 140.81/22.76 | ALPHA: (24) implies:
% 140.81/22.76 | (25) singleton(empty_set) = all_99_0
% 140.81/22.76 | (26) powerset(empty_set) = all_99_0
% 140.81/22.76 |
% 140.81/22.76 | DELTA: instantiating (l71_subset_1) with fresh symbols all_112_0, all_112_1,
% 140.81/22.76 | all_112_2, all_112_3 gives:
% 140.81/22.76 | (27) ~ (all_112_0 = 0) & element(all_112_3, all_112_1) = all_112_0 &
% 140.81/22.76 | powerset(all_112_2) = all_112_1 & $i(all_112_1) & $i(all_112_2) &
% 140.81/22.76 | $i(all_112_3) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 140.81/22.76 | all_112_2) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 140.81/22.76 | in(v0, all_112_3) = v2)) & ! [v0: $i] : ( ~ (in(v0, all_112_3) =
% 140.81/22.76 | 0) | ~ $i(v0) | in(v0, all_112_2) = 0)
% 140.81/22.76 |
% 140.81/22.76 | ALPHA: (27) implies:
% 140.81/22.77 | (28) ~ (all_112_0 = 0)
% 140.81/22.77 | (29) $i(all_112_3)
% 140.81/22.77 | (30) $i(all_112_2)
% 140.81/22.77 | (31) $i(all_112_1)
% 140.81/22.77 | (32) powerset(all_112_2) = all_112_1
% 140.81/22.77 | (33) element(all_112_3, all_112_1) = all_112_0
% 140.81/22.77 | (34) ! [v0: $i] : ( ~ (in(v0, all_112_3) = 0) | ~ $i(v0) | in(v0,
% 140.81/22.77 | all_112_2) = 0)
% 140.81/22.77 |
% 140.81/22.77 | DELTA: instantiating (6) with fresh symbol all_121_0 gives:
% 140.81/22.77 | (35) ! [v0: $i] : ! [v1: int] : (v1 = all_121_0 | ~ (union(v0) = v1) |
% 140.81/22.77 | ~ $i(v0) | ~ $i(all_121_0) | ? [v2: $i] : ? [v3: int] : ? [v4:
% 140.81/22.77 | $i] : ? [v5: int] : ? [v6: int] : ($i(v4) & $i(v2) & ((v6 = 0 &
% 140.81/22.77 | v5 = 0 & in(v4, v0) = 0 & in(v2, v4) = 0) | (v3 = 0 & in(v2,
% 140.81/22.77 | all_121_0) = 0)) & (( ~ (v3 = 0) & in(v2, all_121_0) = v3) |
% 140.81/22.77 | ( ! [v7: $i] : ( ~ (in(v7, v0) = 0) | ~ $i(v7) | ? [v8: int] :
% 140.81/22.77 | ( ~ (v8 = 0) & in(v2, v7) = v8)) & ! [v7: $i] : ( ~ (in(v2,
% 140.81/22.77 | v7) = 0) | ~ $i(v7) | ? [v8: int] : ( ~ (v8 = 0) &
% 140.81/22.77 | in(v7, v0) = v8))))))
% 140.81/22.77 |
% 140.81/22.77 | GROUND_INST: instantiating (14) with empty_set, all_99_0, simplifying with
% 140.81/22.77 | (15), (25) gives:
% 140.81/22.77 | (36) unordered_pair(empty_set, empty_set) = all_99_0 & $i(all_99_0)
% 140.81/22.77 |
% 140.81/22.77 | ALPHA: (36) implies:
% 140.81/22.77 | (37) $i(all_99_0)
% 140.81/22.77 |
% 140.81/22.77 | GROUND_INST: instantiating (t99_zfmisc_1) with empty_set, all_99_0,
% 140.81/22.77 | simplifying with (15), (26) gives:
% 140.81/22.77 | (38) union(all_99_0) = empty_set
% 140.81/22.77 |
% 140.81/22.77 | GROUND_INST: instantiating (rc2_subset_1) with empty_set, all_99_0,
% 140.81/22.77 | simplifying with (15), (26) gives:
% 140.81/22.77 | (39) ? [v0: $i] : (empty(v0) = 0 & element(v0, all_99_0) = 0 & $i(v0))
% 140.81/22.77 |
% 140.81/22.77 | GROUND_INST: instantiating (t99_zfmisc_1) with all_112_2, all_112_1,
% 140.81/22.77 | simplifying with (30), (32) gives:
% 140.81/22.77 | (40) union(all_112_1) = all_112_2
% 140.81/22.77 |
% 140.81/22.77 | GROUND_INST: instantiating (fc1_subset_1) with all_112_2, all_112_1,
% 140.81/22.77 | simplifying with (30), (32) gives:
% 140.81/22.77 | (41) ? [v0: int] : ( ~ (v0 = 0) & empty(all_112_1) = v0)
% 140.81/22.77 |
% 140.81/22.77 | GROUND_INST: instantiating (rc2_subset_1) with all_112_2, all_112_1,
% 140.81/22.77 | simplifying with (30), (32) gives:
% 140.81/22.77 | (42) ? [v0: $i] : (empty(v0) = 0 & element(v0, all_112_1) = 0 & $i(v0))
% 140.81/22.77 |
% 140.81/22.77 | GROUND_INST: instantiating (3) with all_112_1, all_112_3, all_112_0,
% 140.81/22.77 | simplifying with (29), (31), (33) gives:
% 140.81/22.77 | (43) ? [v0: int] : ? [v1: int] : ((v0 = 0 & empty(all_112_1) = 0) | (( ~
% 140.81/22.77 | (all_112_0 = 0) | (v1 = 0 & in(all_112_3, all_112_1) = 0)) &
% 140.81/22.77 | (all_112_0 = 0 | ( ~ (v1 = 0) & in(all_112_3, all_112_1) = v1))))
% 140.81/22.77 |
% 140.81/22.77 | GROUND_INST: instantiating (16) with all_97_0, simplifying with (22), (23)
% 140.81/22.77 | gives:
% 140.81/22.77 | (44) all_97_0 = empty_set
% 140.81/22.77 |
% 140.81/22.77 | DELTA: instantiating (41) with fresh symbol all_135_0 gives:
% 140.81/22.77 | (45) ~ (all_135_0 = 0) & empty(all_112_1) = all_135_0
% 140.81/22.77 |
% 140.81/22.77 | ALPHA: (45) implies:
% 140.81/22.77 | (46) ~ (all_135_0 = 0)
% 140.81/22.77 | (47) empty(all_112_1) = all_135_0
% 140.81/22.77 |
% 140.81/22.77 | DELTA: instantiating (39) with fresh symbol all_137_0 gives:
% 140.81/22.77 | (48) empty(all_137_0) = 0 & element(all_137_0, all_99_0) = 0 &
% 140.81/22.77 | $i(all_137_0)
% 140.81/22.77 |
% 140.81/22.77 | ALPHA: (48) implies:
% 140.81/22.77 | (49) $i(all_137_0)
% 140.81/22.77 | (50) element(all_137_0, all_99_0) = 0
% 140.81/22.78 | (51) empty(all_137_0) = 0
% 140.81/22.78 |
% 140.81/22.78 | DELTA: instantiating (42) with fresh symbol all_139_0 gives:
% 140.81/22.78 | (52) empty(all_139_0) = 0 & element(all_139_0, all_112_1) = 0 &
% 140.81/22.78 | $i(all_139_0)
% 140.81/22.78 |
% 140.81/22.78 | ALPHA: (52) implies:
% 140.81/22.78 | (53) $i(all_139_0)
% 140.81/22.78 | (54) element(all_139_0, all_112_1) = 0
% 140.81/22.78 | (55) empty(all_139_0) = 0
% 140.81/22.78 |
% 140.81/22.78 | DELTA: instantiating (43) with fresh symbols all_146_0, all_146_1 gives:
% 140.81/22.78 | (56) (all_146_1 = 0 & empty(all_112_1) = 0) | (( ~ (all_112_0 = 0) |
% 140.81/22.78 | (all_146_0 = 0 & in(all_112_3, all_112_1) = 0)) & (all_112_0 = 0 |
% 140.81/22.78 | ( ~ (all_146_0 = 0) & in(all_112_3, all_112_1) = all_146_0)))
% 140.81/22.78 |
% 140.81/22.78 | BETA: splitting (56) gives:
% 140.81/22.78 |
% 140.81/22.78 | Case 1:
% 140.81/22.78 | |
% 140.81/22.78 | | (57) all_146_1 = 0 & empty(all_112_1) = 0
% 140.81/22.78 | |
% 140.81/22.78 | | ALPHA: (57) implies:
% 140.81/22.78 | | (58) empty(all_112_1) = 0
% 140.81/22.78 | |
% 140.81/22.78 | | REF_CLOSE: (17), (46), (47), (58) are inconsistent by sub-proof #2.
% 140.81/22.78 | |
% 140.81/22.78 | Case 2:
% 140.81/22.78 | |
% 140.81/22.78 | | (59) ( ~ (all_112_0 = 0) | (all_146_0 = 0 & in(all_112_3, all_112_1) =
% 140.81/22.78 | | 0)) & (all_112_0 = 0 | ( ~ (all_146_0 = 0) & in(all_112_3,
% 140.81/22.78 | | all_112_1) = all_146_0))
% 140.81/22.78 | |
% 140.81/22.78 | | ALPHA: (59) implies:
% 140.81/22.78 | | (60) all_112_0 = 0 | ( ~ (all_146_0 = 0) & in(all_112_3, all_112_1) =
% 140.81/22.78 | | all_146_0)
% 140.81/22.78 | |
% 140.81/22.78 | | BETA: splitting (60) gives:
% 140.81/22.78 | |
% 140.81/22.78 | | Case 1:
% 140.81/22.78 | | |
% 140.81/22.78 | | | (61) all_112_0 = 0
% 140.81/22.78 | | |
% 140.81/22.78 | | | REDUCE: (28), (61) imply:
% 140.81/22.78 | | | (62) $false
% 140.81/22.78 | | |
% 140.81/22.78 | | | CLOSE: (62) is inconsistent.
% 140.81/22.78 | | |
% 140.81/22.78 | | Case 2:
% 140.81/22.78 | | |
% 140.81/22.78 | | | (63) ~ (all_146_0 = 0) & in(all_112_3, all_112_1) = all_146_0
% 140.81/22.78 | | |
% 140.81/22.78 | | | ALPHA: (63) implies:
% 140.81/22.78 | | | (64) ~ (all_146_0 = 0)
% 140.81/22.78 | | | (65) in(all_112_3, all_112_1) = all_146_0
% 140.81/22.78 | | |
% 140.81/22.78 | | | GROUND_INST: instantiating (2) with all_112_2, all_112_1, all_112_3,
% 140.81/22.78 | | | all_146_0, simplifying with (29), (30), (31), (32), (65)
% 140.81/22.78 | | | gives:
% 140.81/22.78 | | | (66) all_146_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_112_3,
% 140.81/22.78 | | | all_112_2) = v0)
% 140.81/22.78 | | |
% 140.81/22.79 | | | GROUND_INST: instantiating (9) with empty_set, all_137_0, all_99_0,
% 140.81/22.79 | | | simplifying with (15), (26), (49), (50) gives:
% 140.81/22.79 | | | (67) ? [v0: $i] : (subset_complement(empty_set, v0) = all_137_0 &
% 140.81/22.79 | | | subset_complement(empty_set, all_137_0) = v0 & $i(v0))
% 140.81/22.79 | | |
% 140.81/22.79 | | | GROUND_INST: instantiating (7) with empty_set, all_137_0, all_99_0,
% 140.81/22.79 | | | simplifying with (15), (26), (49), (50) gives:
% 140.81/22.79 | | | (68) ? [v0: $i] : (subset_complement(empty_set, all_137_0) = v0 &
% 140.81/22.79 | | | set_difference(empty_set, all_137_0) = v0 & $i(v0))
% 140.81/22.79 | | |
% 140.81/22.79 | | | GROUND_INST: instantiating (8) with empty_set, all_137_0, all_99_0,
% 140.81/22.79 | | | simplifying with (15), (26), (49), (50) gives:
% 140.81/22.79 | | | (69) ? [v0: $i] : (subset_complement(empty_set, all_137_0) = v0 &
% 140.81/22.79 | | | element(v0, all_99_0) = 0 & $i(v0))
% 140.81/22.79 | | |
% 140.81/22.79 | | | GROUND_INST: instantiating (9) with all_112_2, all_139_0, all_112_1,
% 140.81/22.79 | | | simplifying with (30), (32), (53), (54) gives:
% 140.81/22.79 | | | (70) ? [v0: $i] : (subset_complement(all_112_2, v0) = all_139_0 &
% 140.81/22.79 | | | subset_complement(all_112_2, all_139_0) = v0 & $i(v0))
% 140.81/22.79 | | |
% 140.81/22.79 | | | GROUND_INST: instantiating (7) with all_112_2, all_139_0, all_112_1,
% 140.81/22.79 | | | simplifying with (30), (32), (53), (54) gives:
% 140.81/22.79 | | | (71) ? [v0: $i] : (subset_complement(all_112_2, all_139_0) = v0 &
% 140.81/22.79 | | | set_difference(all_112_2, all_139_0) = v0 & $i(v0))
% 140.81/22.79 | | |
% 140.81/22.79 | | | GROUND_INST: instantiating (8) with all_112_2, all_139_0, all_112_1,
% 140.81/22.79 | | | simplifying with (30), (32), (53), (54) gives:
% 140.81/22.79 | | | (72) ? [v0: $i] : (subset_complement(all_112_2, all_139_0) = v0 &
% 140.81/22.79 | | | element(v0, all_112_1) = 0 & $i(v0))
% 140.81/22.79 | | |
% 140.81/22.79 | | | GROUND_INST: instantiating (3) with all_112_1, all_139_0, 0, simplifying
% 140.81/22.79 | | | with (31), (53), (54) gives:
% 140.81/22.79 | | | (73) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_139_0, all_112_1)
% 140.81/22.79 | | | = 0) | (v0 = 0 & empty(all_112_1) = 0))
% 140.81/22.79 | | |
% 140.81/22.79 | | | GROUND_INST: instantiating (t8_boole) with all_137_0, all_139_0,
% 140.81/22.79 | | | simplifying with (49), (51), (53), (55) gives:
% 140.81/22.79 | | | (74) all_139_0 = all_137_0
% 140.81/22.79 | | |
% 140.81/22.79 | | | GROUND_INST: instantiating (16) with all_139_0, simplifying with (53),
% 140.81/22.79 | | | (55) gives:
% 140.81/22.79 | | | (75) all_139_0 = empty_set
% 140.81/22.79 | | |
% 140.81/22.79 | | | GROUND_INST: instantiating (35) with all_99_0, empty_set, simplifying with
% 140.81/22.79 | | | (37), (38) gives:
% 140.81/22.79 | | | (76) all_121_0 = empty_set | ~ $i(all_121_0) | ? [v0: $i] : ? [v1:
% 140.81/22.79 | | | int] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ($i(v2) &
% 140.81/22.79 | | | $i(v0) & ((v4 = 0 & v3 = 0 & in(v2, all_99_0) = 0 & in(v0, v2) =
% 140.81/22.79 | | | 0) | (v1 = 0 & in(v0, all_121_0) = 0)) & (( ~ (v1 = 0) &
% 140.81/22.79 | | | in(v0, all_121_0) = v1) | ( ! [v5: $i] : ( ~ (in(v5,
% 140.81/22.79 | | | all_99_0) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 =
% 140.81/22.79 | | | 0) & in(v0, v5) = v6)) & ! [v5: $i] : ( ~ (in(v0, v5)
% 140.81/22.79 | | | = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & in(v5,
% 140.81/22.79 | | | all_99_0) = v6)))))
% 140.81/22.79 | | |
% 140.81/22.79 | | | GROUND_INST: instantiating (35) with all_112_1, all_112_2, simplifying
% 140.81/22.79 | | | with (31), (40) gives:
% 140.81/22.80 | | | (77) all_121_0 = all_112_2 | ~ $i(all_121_0) | ? [v0: $i] : ? [v1:
% 140.81/22.80 | | | int] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ($i(v2) &
% 140.81/22.80 | | | $i(v0) & ((v4 = 0 & v3 = 0 & in(v2, all_112_1) = 0 & in(v0, v2)
% 140.81/22.80 | | | = 0) | (v1 = 0 & in(v0, all_121_0) = 0)) & (( ~ (v1 = 0) &
% 140.81/22.80 | | | in(v0, all_121_0) = v1) | ( ! [v5: $i] : ( ~ (in(v5,
% 140.81/22.80 | | | all_112_1) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 =
% 140.81/22.80 | | | 0) & in(v0, v5) = v6)) & ! [v5: $i] : ( ~ (in(v0, v5)
% 140.81/22.80 | | | = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & in(v5,
% 140.81/22.80 | | | all_112_1) = v6)))))
% 140.81/22.80 | | |
% 140.81/22.80 | | | COMBINE_EQS: (74), (75) imply:
% 140.81/22.80 | | | (78) all_137_0 = empty_set
% 140.81/22.80 | | |
% 140.81/22.80 | | | DELTA: instantiating (69) with fresh symbol all_166_0 gives:
% 140.81/22.80 | | | (79) subset_complement(empty_set, all_137_0) = all_166_0 &
% 140.81/22.80 | | | element(all_166_0, all_99_0) = 0 & $i(all_166_0)
% 140.81/22.80 | | |
% 140.81/22.80 | | | ALPHA: (79) implies:
% 140.81/22.80 | | | (80) subset_complement(empty_set, all_137_0) = all_166_0
% 140.81/22.80 | | |
% 140.81/22.80 | | | DELTA: instantiating (72) with fresh symbol all_172_0 gives:
% 140.81/22.80 | | | (81) subset_complement(all_112_2, all_139_0) = all_172_0 &
% 140.81/22.80 | | | element(all_172_0, all_112_1) = 0 & $i(all_172_0)
% 140.81/22.80 | | |
% 140.81/22.80 | | | ALPHA: (81) implies:
% 140.81/22.80 | | | (82) subset_complement(all_112_2, all_139_0) = all_172_0
% 140.81/22.80 | | |
% 140.81/22.80 | | | DELTA: instantiating (71) with fresh symbol all_176_0 gives:
% 140.81/22.80 | | | (83) subset_complement(all_112_2, all_139_0) = all_176_0 &
% 140.81/22.80 | | | set_difference(all_112_2, all_139_0) = all_176_0 & $i(all_176_0)
% 140.81/22.80 | | |
% 140.81/22.80 | | | ALPHA: (83) implies:
% 140.81/22.80 | | | (84) set_difference(all_112_2, all_139_0) = all_176_0
% 140.81/22.80 | | | (85) subset_complement(all_112_2, all_139_0) = all_176_0
% 140.81/22.80 | | |
% 140.81/22.80 | | | DELTA: instantiating (70) with fresh symbol all_178_0 gives:
% 140.81/22.80 | | | (86) subset_complement(all_112_2, all_178_0) = all_139_0 &
% 140.81/22.80 | | | subset_complement(all_112_2, all_139_0) = all_178_0 &
% 140.81/22.80 | | | $i(all_178_0)
% 140.81/22.80 | | |
% 140.81/22.80 | | | ALPHA: (86) implies:
% 140.81/22.80 | | | (87) subset_complement(all_112_2, all_139_0) = all_178_0
% 140.81/22.80 | | |
% 140.81/22.80 | | | DELTA: instantiating (68) with fresh symbol all_180_0 gives:
% 140.81/22.80 | | | (88) subset_complement(empty_set, all_137_0) = all_180_0 &
% 140.81/22.80 | | | set_difference(empty_set, all_137_0) = all_180_0 & $i(all_180_0)
% 140.81/22.80 | | |
% 140.81/22.80 | | | ALPHA: (88) implies:
% 140.81/22.80 | | | (89) set_difference(empty_set, all_137_0) = all_180_0
% 140.81/22.80 | | | (90) subset_complement(empty_set, all_137_0) = all_180_0
% 140.81/22.80 | | |
% 140.81/22.80 | | | DELTA: instantiating (67) with fresh symbol all_182_0 gives:
% 140.81/22.80 | | | (91) subset_complement(empty_set, all_182_0) = all_137_0 &
% 140.81/22.80 | | | subset_complement(empty_set, all_137_0) = all_182_0 &
% 140.81/22.80 | | | $i(all_182_0)
% 140.81/22.80 | | |
% 140.81/22.80 | | | ALPHA: (91) implies:
% 140.81/22.80 | | | (92) subset_complement(empty_set, all_137_0) = all_182_0
% 140.81/22.80 | | |
% 140.81/22.80 | | | DELTA: instantiating (73) with fresh symbols all_188_0, all_188_1 gives:
% 140.81/22.80 | | | (93) (all_188_0 = 0 & in(all_139_0, all_112_1) = 0) | (all_188_1 = 0 &
% 140.81/22.80 | | | empty(all_112_1) = 0)
% 140.81/22.80 | | |
% 140.81/22.80 | | | REDUCE: (75), (87) imply:
% 140.81/22.80 | | | (94) subset_complement(all_112_2, empty_set) = all_178_0
% 140.81/22.80 | | |
% 140.81/22.80 | | | REDUCE: (75), (85) imply:
% 140.81/22.80 | | | (95) subset_complement(all_112_2, empty_set) = all_176_0
% 140.81/22.80 | | |
% 140.81/22.80 | | | REDUCE: (75), (82) imply:
% 140.81/22.80 | | | (96) subset_complement(all_112_2, empty_set) = all_172_0
% 140.81/22.80 | | |
% 140.81/22.80 | | | REDUCE: (78), (92) imply:
% 140.81/22.80 | | | (97) subset_complement(empty_set, empty_set) = all_182_0
% 140.81/22.80 | | |
% 140.81/22.80 | | | REDUCE: (78), (90) imply:
% 140.81/22.80 | | | (98) subset_complement(empty_set, empty_set) = all_180_0
% 140.81/22.80 | | |
% 140.81/22.80 | | | REDUCE: (78), (80) imply:
% 140.81/22.80 | | | (99) subset_complement(empty_set, empty_set) = all_166_0
% 140.81/22.80 | | |
% 140.81/22.80 | | | REDUCE: (75), (84) imply:
% 140.81/22.80 | | | (100) set_difference(all_112_2, empty_set) = all_176_0
% 140.81/22.80 | | |
% 140.81/22.80 | | | REDUCE: (78), (89) imply:
% 140.81/22.80 | | | (101) set_difference(empty_set, empty_set) = all_180_0
% 140.81/22.80 | | |
% 140.81/22.80 | | | BETA: splitting (66) gives:
% 140.81/22.80 | | |
% 140.81/22.80 | | | Case 1:
% 140.81/22.80 | | | |
% 140.81/22.80 | | | | (102) all_146_0 = 0
% 140.81/22.80 | | | |
% 140.81/22.80 | | | | REDUCE: (64), (102) imply:
% 140.81/22.80 | | | | (103) $false
% 140.81/22.80 | | | |
% 140.81/22.80 | | | | CLOSE: (103) is inconsistent.
% 140.81/22.80 | | | |
% 140.81/22.80 | | | Case 2:
% 140.81/22.80 | | | |
% 140.81/22.80 | | | | (104) ? [v0: int] : ( ~ (v0 = 0) & subset(all_112_3, all_112_2) =
% 140.81/22.80 | | | | v0)
% 140.81/22.80 | | | |
% 140.81/22.80 | | | | DELTA: instantiating (104) with fresh symbol all_244_0 gives:
% 140.81/22.80 | | | | (105) ~ (all_244_0 = 0) & subset(all_112_3, all_112_2) = all_244_0
% 140.81/22.80 | | | |
% 140.81/22.80 | | | | ALPHA: (105) implies:
% 140.81/22.80 | | | | (106) ~ (all_244_0 = 0)
% 140.81/22.80 | | | | (107) subset(all_112_3, all_112_2) = all_244_0
% 140.81/22.80 | | | |
% 140.81/22.80 | | | | BETA: splitting (93) gives:
% 140.81/22.80 | | | |
% 140.81/22.80 | | | | Case 1:
% 140.81/22.80 | | | | |
% 140.81/22.80 | | | | | (108) all_188_0 = 0 & in(all_139_0, all_112_1) = 0
% 140.81/22.80 | | | | |
% 140.81/22.80 | | | | | ALPHA: (108) implies:
% 140.81/22.80 | | | | | (109) in(all_139_0, all_112_1) = 0
% 140.81/22.80 | | | | |
% 140.81/22.80 | | | | | REDUCE: (75), (109) imply:
% 140.81/22.80 | | | | | (110) in(empty_set, all_112_1) = 0
% 140.81/22.80 | | | | |
% 140.81/22.80 | | | | | GROUND_INST: instantiating (20) with all_180_0, all_182_0, empty_set,
% 140.81/22.80 | | | | | empty_set, simplifying with (97), (98) gives:
% 140.81/22.80 | | | | | (111) all_182_0 = all_180_0
% 140.81/22.80 | | | | |
% 140.81/22.80 | | | | | GROUND_INST: instantiating (20) with all_166_0, all_182_0, empty_set,
% 140.81/22.80 | | | | | empty_set, simplifying with (97), (99) gives:
% 140.81/22.80 | | | | | (112) all_182_0 = all_166_0
% 140.81/22.80 | | | | |
% 140.81/22.80 | | | | | GROUND_INST: instantiating (20) with all_176_0, all_178_0, empty_set,
% 140.81/22.80 | | | | | all_112_2, simplifying with (94), (95) gives:
% 140.81/22.80 | | | | | (113) all_178_0 = all_176_0
% 140.81/22.80 | | | | |
% 140.81/22.80 | | | | | GROUND_INST: instantiating (20) with all_172_0, all_178_0, empty_set,
% 140.81/22.80 | | | | | all_112_2, simplifying with (94), (96) gives:
% 140.81/22.80 | | | | | (114) all_178_0 = all_172_0
% 140.81/22.80 | | | | |
% 140.81/22.80 | | | | | COMBINE_EQS: (111), (112) imply:
% 140.81/22.80 | | | | | (115) all_180_0 = all_166_0
% 140.81/22.80 | | | | |
% 140.81/22.80 | | | | | COMBINE_EQS: (113), (114) imply:
% 140.81/22.80 | | | | | (116) all_176_0 = all_172_0
% 140.81/22.80 | | | | |
% 140.81/22.80 | | | | | REDUCE: (100), (116) imply:
% 140.81/22.80 | | | | | (117) set_difference(all_112_2, empty_set) = all_172_0
% 140.81/22.80 | | | | |
% 140.81/22.80 | | | | | REDUCE: (101), (115) imply:
% 140.81/22.81 | | | | | (118) set_difference(empty_set, empty_set) = all_166_0
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | GROUND_INST: instantiating (1) with all_112_2, all_112_1, empty_set,
% 140.81/22.81 | | | | | simplifying with (15), (30), (31), (32), (110) gives:
% 140.81/22.81 | | | | | (119) subset(empty_set, all_112_2) = 0
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | GROUND_INST: instantiating (5) with all_112_3, all_112_2, all_244_0,
% 140.81/22.81 | | | | | simplifying with (29), (30), (107) gives:
% 140.81/22.81 | | | | | (120) all_244_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 140.81/22.81 | | | | | in(v0, all_112_2) = v1 & in(v0, all_112_3) = 0 & $i(v0))
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | GROUND_INST: instantiating (11) with empty_set, all_166_0, simplifying
% 140.81/22.81 | | | | | with (15), (118) gives:
% 140.81/22.81 | | | | | (121) all_166_0 = empty_set
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | GROUND_INST: instantiating (12) with empty_set, empty_set, all_166_0,
% 140.81/22.81 | | | | | simplifying with (15), (118) gives:
% 140.81/22.81 | | | | | (122) ? [v0: $i] : (set_difference(v0, empty_set) = all_166_0 &
% 140.81/22.81 | | | | | set_union2(empty_set, empty_set) = v0 & $i(v0) &
% 140.81/22.81 | | | | | $i(all_166_0))
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | GROUND_INST: instantiating (11) with all_112_2, all_172_0, simplifying
% 140.81/22.81 | | | | | with (30), (117) gives:
% 140.81/22.81 | | | | | (123) all_172_0 = all_112_2
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | GROUND_INST: instantiating (13) with empty_set, all_112_2, all_172_0,
% 140.81/22.81 | | | | | simplifying with (15), (30), (117) gives:
% 140.81/22.81 | | | | | (124) ? [v0: int] : ? [v1: int] : ((v1 = all_112_2 &
% 140.81/22.81 | | | | | set_union2(empty_set, all_172_0) = all_112_2) | ( ~ (v0 =
% 140.81/22.81 | | | | | 0) & subset(empty_set, all_112_2) = v0))
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | GROUND_INST: instantiating (12) with all_112_2, empty_set, all_172_0,
% 140.81/22.81 | | | | | simplifying with (15), (30), (117) gives:
% 140.81/22.81 | | | | | (125) ? [v0: $i] : (set_difference(v0, empty_set) = all_172_0 &
% 140.81/22.81 | | | | | set_union2(all_112_2, empty_set) = v0 & $i(v0) &
% 140.81/22.81 | | | | | $i(all_172_0))
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | DELTA: instantiating (122) with fresh symbol all_365_0 gives:
% 140.81/22.81 | | | | | (126) set_difference(all_365_0, empty_set) = all_166_0 &
% 140.81/22.81 | | | | | set_union2(empty_set, empty_set) = all_365_0 & $i(all_365_0)
% 140.81/22.81 | | | | | & $i(all_166_0)
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | ALPHA: (126) implies:
% 140.81/22.81 | | | | | (127) $i(all_166_0)
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | DELTA: instantiating (125) with fresh symbol all_373_0 gives:
% 140.81/22.81 | | | | | (128) set_difference(all_373_0, empty_set) = all_172_0 &
% 140.81/22.81 | | | | | set_union2(all_112_2, empty_set) = all_373_0 & $i(all_373_0)
% 140.81/22.81 | | | | | & $i(all_172_0)
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | ALPHA: (128) implies:
% 140.81/22.81 | | | | | (129) $i(all_172_0)
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | DELTA: instantiating (124) with fresh symbols all_390_0, all_390_1
% 140.81/22.81 | | | | | gives:
% 140.81/22.81 | | | | | (130) (all_390_0 = all_112_2 & set_union2(empty_set, all_172_0) =
% 140.81/22.81 | | | | | all_112_2) | ( ~ (all_390_1 = 0) & subset(empty_set,
% 140.81/22.81 | | | | | all_112_2) = all_390_1)
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | BETA: splitting (120) gives:
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | Case 1:
% 140.81/22.81 | | | | | |
% 140.81/22.81 | | | | | | (131) all_244_0 = 0
% 140.81/22.81 | | | | | |
% 140.81/22.81 | | | | | | REDUCE: (106), (131) imply:
% 140.81/22.81 | | | | | | (132) $false
% 140.81/22.81 | | | | | |
% 140.81/22.81 | | | | | | CLOSE: (132) is inconsistent.
% 140.81/22.81 | | | | | |
% 140.81/22.81 | | | | | Case 2:
% 140.81/22.81 | | | | | |
% 140.81/22.81 | | | | | | (133) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 140.81/22.81 | | | | | | all_112_2) = v1 & in(v0, all_112_3) = 0 & $i(v0))
% 140.81/22.81 | | | | | |
% 140.81/22.81 | | | | | | DELTA: instantiating (133) with fresh symbols all_504_0, all_504_1
% 140.81/22.81 | | | | | | gives:
% 140.81/22.81 | | | | | | (134) ~ (all_504_0 = 0) & in(all_504_1, all_112_2) = all_504_0 &
% 140.81/22.81 | | | | | | in(all_504_1, all_112_3) = 0 & $i(all_504_1)
% 140.81/22.81 | | | | | |
% 140.81/22.81 | | | | | | ALPHA: (134) implies:
% 140.81/22.81 | | | | | | (135) ~ (all_504_0 = 0)
% 140.81/22.81 | | | | | | (136) $i(all_504_1)
% 140.81/22.81 | | | | | | (137) in(all_504_1, all_112_3) = 0
% 140.81/22.81 | | | | | | (138) in(all_504_1, all_112_2) = all_504_0
% 140.81/22.81 | | | | | |
% 140.81/22.81 | | | | | | BETA: splitting (130) gives:
% 140.81/22.81 | | | | | |
% 140.81/22.81 | | | | | | Case 1:
% 140.81/22.81 | | | | | | |
% 140.81/22.81 | | | | | | | (139) all_390_0 = all_112_2 & set_union2(empty_set, all_172_0)
% 140.81/22.81 | | | | | | | = all_112_2
% 140.81/22.81 | | | | | | |
% 140.81/22.81 | | | | | | | ALPHA: (139) implies:
% 140.81/22.81 | | | | | | | (140) set_union2(empty_set, all_172_0) = all_112_2
% 140.81/22.81 | | | | | | |
% 140.81/22.81 | | | | | | | REDUCE: (123), (140) imply:
% 140.81/22.81 | | | | | | | (141) set_union2(empty_set, all_112_2) = all_112_2
% 140.81/22.81 | | | | | | |
% 140.81/22.81 | | | | | | | BETA: splitting (77) gives:
% 140.81/22.81 | | | | | | |
% 140.81/22.81 | | | | | | | Case 1:
% 140.81/22.81 | | | | | | | |
% 140.81/22.81 | | | | | | | |
% 140.81/22.81 | | | | | | | | GROUND_INST: instantiating (34) with all_504_1, simplifying with
% 140.81/22.81 | | | | | | | | (136), (137) gives:
% 140.81/22.81 | | | | | | | | (142) in(all_504_1, all_112_2) = 0
% 140.81/22.81 | | | | | | | |
% 140.81/22.81 | | | | | | | | REF_CLOSE: (4), (15), (18), (30), (135), (136), (138), (141),
% 140.81/22.81 | | | | | | | | (142) are inconsistent by sub-proof #1.
% 140.81/22.81 | | | | | | | |
% 140.81/22.81 | | | | | | | Case 2:
% 140.81/22.81 | | | | | | | |
% 140.81/22.81 | | | | | | | | (143) $i(all_121_0)
% 140.81/22.81 | | | | | | | |
% 140.81/22.81 | | | | | | | | BETA: splitting (76) gives:
% 140.81/22.81 | | | | | | | |
% 140.81/22.81 | | | | | | | | Case 1:
% 140.81/22.81 | | | | | | | | |
% 140.81/22.81 | | | | | | | | | (144) ~ $i(all_121_0)
% 140.81/22.81 | | | | | | | | |
% 140.81/22.81 | | | | | | | | | PRED_UNIFY: (143), (144) imply:
% 140.81/22.81 | | | | | | | | | (145) $false
% 140.81/22.81 | | | | | | | | |
% 140.81/22.81 | | | | | | | | | CLOSE: (145) is inconsistent.
% 140.81/22.81 | | | | | | | | |
% 140.81/22.81 | | | | | | | | Case 2:
% 140.81/22.81 | | | | | | | | |
% 140.81/22.81 | | | | | | | | |
% 140.81/22.81 | | | | | | | | | GROUND_INST: instantiating (34) with all_504_1, simplifying
% 140.81/22.81 | | | | | | | | | with (136), (137) gives:
% 140.81/22.81 | | | | | | | | | (146) in(all_504_1, all_112_2) = 0
% 140.81/22.81 | | | | | | | | |
% 140.81/22.81 | | | | | | | | | REF_CLOSE: (4), (15), (18), (30), (135), (136), (138), (141),
% 140.81/22.81 | | | | | | | | | (146) are inconsistent by sub-proof #1.
% 140.81/22.81 | | | | | | | | |
% 140.81/22.81 | | | | | | | | End of split
% 140.81/22.81 | | | | | | | |
% 140.81/22.81 | | | | | | | End of split
% 140.81/22.81 | | | | | | |
% 140.81/22.81 | | | | | | Case 2:
% 140.81/22.81 | | | | | | |
% 140.81/22.81 | | | | | | | (147) ~ (all_390_1 = 0) & subset(empty_set, all_112_2) =
% 140.81/22.81 | | | | | | | all_390_1
% 140.81/22.81 | | | | | | |
% 140.81/22.81 | | | | | | | ALPHA: (147) implies:
% 140.81/22.81 | | | | | | | (148) ~ (all_390_1 = 0)
% 140.81/22.81 | | | | | | | (149) subset(empty_set, all_112_2) = all_390_1
% 140.81/22.81 | | | | | | |
% 140.81/22.81 | | | | | | | GROUND_INST: instantiating (19) with 0, all_390_1, all_112_2,
% 140.81/22.81 | | | | | | | empty_set, simplifying with (119), (149) gives:
% 140.81/22.81 | | | | | | | (150) all_390_1 = 0
% 140.81/22.81 | | | | | | |
% 140.81/22.81 | | | | | | | REDUCE: (148), (150) imply:
% 140.81/22.81 | | | | | | | (151) $false
% 140.81/22.81 | | | | | | |
% 140.81/22.81 | | | | | | | CLOSE: (151) is inconsistent.
% 140.81/22.81 | | | | | | |
% 140.81/22.81 | | | | | | End of split
% 140.81/22.81 | | | | | |
% 140.81/22.81 | | | | | End of split
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | Case 2:
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | (152) all_188_1 = 0 & empty(all_112_1) = 0
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | ALPHA: (152) implies:
% 140.81/22.81 | | | | | (153) empty(all_112_1) = 0
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | | REF_CLOSE: (17), (46), (47), (153) are inconsistent by sub-proof #2.
% 140.81/22.81 | | | | |
% 140.81/22.81 | | | | End of split
% 140.81/22.81 | | | |
% 140.81/22.82 | | | End of split
% 140.81/22.82 | | |
% 140.81/22.82 | | End of split
% 140.81/22.82 | |
% 140.81/22.82 | End of split
% 140.81/22.82 |
% 140.81/22.82 End of proof
% 140.81/22.82
% 140.81/22.82 Sub-proof #1 shows that the following formulas are inconsistent:
% 140.81/22.82 ----------------------------------------------------------------
% 140.81/22.82 (1) ~ (all_504_0 = 0)
% 140.81/22.82 (2) set_union2(empty_set, all_112_2) = all_112_2
% 140.81/22.82 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 140.81/22.82 (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3)
% 140.81/22.82 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~
% 140.81/22.82 (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5))
% 140.81/22.82 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 140.81/22.82 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 140.81/22.82 (5) in(all_504_1, all_112_2) = all_504_0
% 140.81/22.82 (6) $i(all_504_1)
% 140.81/22.82 (7) $i(all_112_2)
% 140.81/22.82 (8) in(all_504_1, all_112_2) = 0
% 140.81/22.82 (9) $i(empty_set)
% 140.81/22.82
% 140.81/22.82 Begin of proof
% 140.81/22.82 |
% 140.81/22.82 | GROUND_INST: instantiating (3) with empty_set, all_112_2, all_112_2,
% 140.81/22.82 | all_504_1, all_504_0, simplifying with (2), (5), (6), (7), (9)
% 140.81/22.82 | gives:
% 140.81/22.82 | (10) all_504_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 =
% 140.81/22.82 | 0) & in(all_504_1, all_112_2) = v1 & in(all_504_1, empty_set) =
% 140.81/22.82 | v0)
% 140.81/22.82 |
% 140.81/22.82 | BETA: splitting (10) gives:
% 140.81/22.82 |
% 140.81/22.82 | Case 1:
% 140.81/22.82 | |
% 140.81/22.82 | | (11) all_504_0 = 0
% 140.81/22.82 | |
% 140.81/22.82 | | REDUCE: (1), (11) imply:
% 140.81/22.82 | | (12) $false
% 140.81/22.82 | |
% 140.81/22.82 | | CLOSE: (12) is inconsistent.
% 140.81/22.82 | |
% 140.81/22.82 | Case 2:
% 140.81/22.82 | |
% 140.81/22.82 | | (13) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 140.81/22.82 | | in(all_504_1, all_112_2) = v1 & in(all_504_1, empty_set) = v0)
% 140.81/22.82 | |
% 140.81/22.82 | | DELTA: instantiating (13) with fresh symbols all_1670_0, all_1670_1 gives:
% 140.81/22.82 | | (14) ~ (all_1670_0 = 0) & ~ (all_1670_1 = 0) & in(all_504_1, all_112_2)
% 140.81/22.82 | | = all_1670_0 & in(all_504_1, empty_set) = all_1670_1
% 140.81/22.82 | |
% 140.81/22.82 | | ALPHA: (14) implies:
% 140.81/22.82 | | (15) in(all_504_1, all_112_2) = all_1670_0
% 140.81/22.82 | |
% 140.81/22.82 | | GROUND_INST: instantiating (4) with all_504_0, all_1670_0, all_112_2,
% 140.81/22.82 | | all_504_1, simplifying with (5), (15) gives:
% 140.81/22.82 | | (16) all_1670_0 = all_504_0
% 140.81/22.82 | |
% 140.81/22.82 | | GROUND_INST: instantiating (4) with 0, all_1670_0, all_112_2, all_504_1,
% 140.81/22.82 | | simplifying with (8), (15) gives:
% 140.81/22.82 | | (17) all_1670_0 = 0
% 140.81/22.82 | |
% 140.81/22.82 | | COMBINE_EQS: (16), (17) imply:
% 140.81/22.82 | | (18) all_504_0 = 0
% 140.81/22.82 | |
% 140.81/22.82 | | REDUCE: (1), (18) imply:
% 140.81/22.82 | | (19) $false
% 140.81/22.82 | |
% 140.81/22.82 | | CLOSE: (19) is inconsistent.
% 140.81/22.82 | |
% 140.81/22.82 | End of split
% 140.81/22.82 |
% 140.81/22.82 End of proof
% 140.81/22.82
% 140.81/22.82 Sub-proof #2 shows that the following formulas are inconsistent:
% 140.81/22.82 ----------------------------------------------------------------
% 140.81/22.82 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 140.81/22.82 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 140.81/22.82 (2) empty(all_112_1) = all_135_0
% 140.81/22.82 (3) empty(all_112_1) = 0
% 140.81/22.82 (4) ~ (all_135_0 = 0)
% 140.81/22.82
% 140.81/22.82 Begin of proof
% 140.81/22.82 |
% 140.81/22.82 | GROUND_INST: instantiating (1) with 0, all_135_0, all_112_1, simplifying with
% 140.81/22.82 | (2), (3) gives:
% 140.81/22.82 | (5) all_135_0 = 0
% 140.81/22.82 |
% 140.81/22.82 | REDUCE: (4), (5) imply:
% 140.81/22.82 | (6) $false
% 140.81/22.82 |
% 140.81/22.82 | CLOSE: (6) is inconsistent.
% 140.81/22.82 |
% 140.81/22.82 End of proof
% 140.81/22.82 % SZS output end Proof for theBenchmark
% 140.81/22.82
% 140.81/22.82 22205ms
%------------------------------------------------------------------------------