TSTP Solution File: SEU236+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU236+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 : n027.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 17:43:33 EDT 2023
% Result : Theorem 85.94s 12.24s
% Output : Proof 87.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU236+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n027.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 16:27:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 ________ _____
% 0.19/0.58 ___ __ \_________(_)________________________________
% 0.19/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.58 (2023-06-19)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2023
% 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.58 Amanda Stjerna.
% 0.19/0.58 Free software under BSD-3-Clause.
% 0.19/0.58
% 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.59 Running up to 7 provers in parallel.
% 0.19/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.07/1.09 Prover 1: Preprocessing ...
% 3.07/1.10 Prover 4: Preprocessing ...
% 3.07/1.12 Prover 2: Preprocessing ...
% 3.07/1.12 Prover 0: Preprocessing ...
% 3.07/1.12 Prover 3: Preprocessing ...
% 3.07/1.12 Prover 6: Preprocessing ...
% 3.07/1.13 Prover 5: Preprocessing ...
% 5.25/1.58 Prover 5: Proving ...
% 5.25/1.61 Prover 1: Warning: ignoring some quantifiers
% 7.21/1.64 Prover 2: Proving ...
% 7.21/1.67 Prover 1: Constructing countermodel ...
% 7.41/1.71 Prover 4: Warning: ignoring some quantifiers
% 7.41/1.72 Prover 3: Warning: ignoring some quantifiers
% 7.80/1.75 Prover 6: Proving ...
% 7.96/1.75 Prover 3: Constructing countermodel ...
% 7.96/1.77 Prover 4: Constructing countermodel ...
% 8.51/1.86 Prover 0: Proving ...
% 11.93/2.32 Prover 3: gave up
% 11.93/2.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.93/2.35 Prover 1: gave up
% 11.93/2.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.50/2.39 Prover 8: Preprocessing ...
% 12.50/2.41 Prover 7: Preprocessing ...
% 13.24/2.50 Prover 7: Warning: ignoring some quantifiers
% 13.42/2.52 Prover 7: Constructing countermodel ...
% 13.53/2.56 Prover 8: Warning: ignoring some quantifiers
% 13.53/2.57 Prover 8: Constructing countermodel ...
% 16.91/3.05 Prover 8: gave up
% 16.91/3.06 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 17.71/3.09 Prover 9: Preprocessing ...
% 19.90/3.39 Prover 9: Warning: ignoring some quantifiers
% 19.99/3.39 Prover 9: Constructing countermodel ...
% 22.41/3.75 Prover 7: gave up
% 22.41/3.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.90/3.83 Prover 10: Preprocessing ...
% 23.74/3.91 Prover 10: Warning: ignoring some quantifiers
% 23.98/3.92 Prover 10: Constructing countermodel ...
% 27.34/4.39 Prover 10: gave up
% 27.34/4.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 27.96/4.45 Prover 11: Preprocessing ...
% 29.05/4.59 Prover 11: Warning: ignoring some quantifiers
% 29.05/4.60 Prover 11: Constructing countermodel ...
% 58.09/8.41 Prover 2: stopped
% 58.09/8.43 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 58.98/8.51 Prover 12: Preprocessing ...
% 58.98/8.62 Prover 12: Proving ...
% 72.05/10.28 Prover 12: stopped
% 72.05/10.29 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 72.67/10.33 Prover 13: Preprocessing ...
% 73.19/10.40 Prover 13: Warning: ignoring some quantifiers
% 73.19/10.41 Prover 13: Constructing countermodel ...
% 85.94/12.23 Prover 4: Found proof (size 271)
% 85.94/12.23 Prover 4: proved (11628ms)
% 85.94/12.23 Prover 0: stopped
% 85.94/12.23 Prover 9: stopped
% 85.94/12.23 Prover 6: stopped
% 85.94/12.23 Prover 5: stopped
% 85.94/12.23 Prover 13: stopped
% 85.94/12.24 Prover 11: stopped
% 85.94/12.24
% 85.94/12.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 85.94/12.24
% 85.94/12.28 % SZS output start Proof for theBenchmark
% 86.62/12.28 Assumptions after simplification:
% 86.62/12.28 ---------------------------------
% 86.62/12.28
% 86.62/12.28 (antisymmetry_r2_hidden)
% 86.62/12.31 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 86.62/12.31 [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : (
% 86.62/12.31 ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 86.62/12.31 in(v1, v0) = v2))
% 86.62/12.31
% 86.62/12.31 (cc1_ordinal1)
% 86.62/12.31 ! [v0: $i] : ! [v1: any] : ( ~ (epsilon_transitive(v0) = v1) | ~ $i(v0) |
% 86.62/12.31 ? [v2: any] : ? [v3: any] : (ordinal(v0) = v2 & epsilon_connected(v0) = v3
% 86.62/12.31 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: $i] : ! [v1: any] : ( ~
% 86.62/12.31 (epsilon_connected(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 86.62/12.31 (epsilon_transitive(v0) = v3 & ordinal(v0) = v2 & ( ~ (v2 = 0) | (v3 = 0 &
% 86.62/12.31 v1 = 0)))) & ! [v0: $i] : ( ~ (ordinal(v0) = 0) | ~ $i(v0) |
% 86.62/12.31 (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0))
% 86.62/12.31
% 86.62/12.31 (cc2_funct_1)
% 87.47/12.31 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 87.47/12.31 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) =
% 87.47/12.31 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 87.47/12.31 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 87.47/12.31 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0)
% 87.47/12.31 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 87.47/12.31 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any]
% 87.47/12.31 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) |
% 87.47/12.31 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0)
% 87.47/12.31 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 &
% 87.47/12.31 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 =
% 87.47/12.32 0)))
% 87.47/12.32
% 87.47/12.32 (cc3_ordinal1)
% 87.47/12.32 ! [v0: $i] : ! [v1: any] : ( ~ (epsilon_transitive(v0) = v1) | ~ $i(v0) |
% 87.47/12.32 ? [v2: any] : ? [v3: any] : ? [v4: any] : (ordinal(v0) = v4 &
% 87.47/12.32 epsilon_connected(v0) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3
% 87.47/12.32 = 0 & v1 = 0)))) & ! [v0: $i] : ! [v1: any] : ( ~ (ordinal(v0) = v1)
% 87.47/12.32 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 87.47/12.32 (epsilon_transitive(v0) = v3 & epsilon_connected(v0) = v4 & empty(v0) = v2 &
% 87.47/12.32 ( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0)))) & ! [v0: $i] : ! [v1: any]
% 87.47/12.32 : ( ~ (epsilon_connected(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 87.47/12.32 ? [v4: any] : (epsilon_transitive(v0) = v3 & ordinal(v0) = v4 & empty(v0) =
% 87.47/12.32 v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0)))) & ! [v0: $i] : ( ~
% 87.47/12.32 (empty(v0) = 0) | ~ $i(v0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0
% 87.47/12.32 & epsilon_connected(v0) = 0))
% 87.47/12.32
% 87.47/12.32 (commutativity_k2_xboole_0)
% 87.47/12.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 87.47/12.32 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 87.47/12.32 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 87.47/12.32 | (set_union2(v1, v0) = v2 & $i(v2)))
% 87.47/12.32
% 87.47/12.32 (d1_ordinal1)
% 87.47/12.32 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 87.47/12.32 (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & $i(v1))) & ! [v0:
% 87.47/12.32 $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 87.47/12.32 (succ(v0) = v2 & set_union2(v0, v1) = v2 & $i(v2)))
% 87.47/12.32
% 87.47/12.32 (d1_tarski)
% 87.47/12.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 87.47/12.32 ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : !
% 87.47/12.32 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) =
% 87.47/12.32 v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 87.47/12.32 (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 87.47/12.32 [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 =
% 87.47/12.32 0 | v3 = v1)))
% 87.47/12.32
% 87.47/12.32 (d2_ordinal1)
% 87.47/12.32 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v1, v0) = v2)
% 87.47/12.32 | ~ (epsilon_transitive(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : (
% 87.47/12.32 ~ (v3 = 0) & in(v1, v0) = v3)) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 87.47/12.32 (epsilon_transitive(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~
% 87.47/12.32 (v3 = 0) & subset(v2, v0) = v3 & in(v2, v0) = 0 & $i(v2))) & ! [v0: $i] :
% 87.47/12.32 ! [v1: $i] : ( ~ (epsilon_transitive(v0) = 0) | ~ (in(v1, v0) = 0) | ~
% 87.47/12.32 $i(v1) | ~ $i(v0) | subset(v1, v0) = 0)
% 87.47/12.32
% 87.47/12.32 (d3_tarski)
% 87.47/12.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 87.47/12.33 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 87.47/12.33 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 87.47/12.33 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 87.47/12.33 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 87.47/12.33 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 87.47/12.33 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 87.47/12.33 $i(v0) | in(v2, v1) = 0)
% 87.47/12.33
% 87.47/12.33 (fc3_ordinal1)
% 87.47/12.33 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 87.47/12.33 ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 87.47/12.33 (epsilon_transitive(v1) = v4 & ordinal(v1) = v6 & ordinal(v0) = v2 &
% 87.47/12.33 epsilon_connected(v1) = v5 & empty(v1) = v3 & ( ~ (v2 = 0) | (v6 = 0 & v5
% 87.47/12.33 = 0 & v4 = 0 & ~ (v3 = 0))))) & ! [v0: $i] : ( ~ (ordinal(v0) = 0) |
% 87.47/12.33 ~ $i(v0) | ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & succ(v0) = v1 &
% 87.47/12.33 epsilon_transitive(v1) = 0 & ordinal(v1) = 0 & epsilon_connected(v1) = 0 &
% 87.47/12.33 empty(v1) = v2 & $i(v1)))
% 87.47/12.33
% 87.47/12.33 (fc3_xboole_0)
% 87.47/12.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 87.47/12.33 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v2) = v4 &
% 87.47/12.33 empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 87.47/12.33
% 87.47/12.33 (rc1_relat_1)
% 87.47/12.33 ? [v0: $i] : (relation(v0) = 0 & empty(v0) = 0 & $i(v0))
% 87.47/12.33
% 87.47/12.33 (rc1_xboole_0)
% 87.47/12.33 ? [v0: $i] : (empty(v0) = 0 & $i(v0))
% 87.47/12.33
% 87.47/12.33 (rc2_funct_1)
% 87.47/12.33 ? [v0: $i] : (relation(v0) = 0 & function(v0) = 0 & empty(v0) = 0 & $i(v0))
% 87.47/12.33
% 87.47/12.33 (rc2_ordinal1)
% 87.47/12.33 ? [v0: $i] : (one_to_one(v0) = 0 & relation(v0) = 0 & epsilon_transitive(v0)
% 87.47/12.33 = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0 & function(v0) = 0 &
% 87.47/12.33 empty(v0) = 0 & $i(v0))
% 87.47/12.33
% 87.47/12.33 (rc4_funct_1)
% 87.47/12.33 ? [v0: $i] : (relation_empty_yielding(v0) = 0 & relation(v0) = 0 &
% 87.47/12.33 function(v0) = 0 & $i(v0))
% 87.47/12.33
% 87.47/12.33 (rc5_funct_1)
% 87.47/12.33 ? [v0: $i] : (relation_non_empty(v0) = 0 & relation(v0) = 0 & function(v0) =
% 87.47/12.33 0 & $i(v0))
% 87.47/12.33
% 87.47/12.33 (redefinition_r1_ordinal1)
% 87.47/12.33 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | ~
% 87.47/12.33 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 87.47/12.33 (ordinal_subset(v0, v1) = v5 & ordinal(v1) = v4 & ordinal(v0) = v3 & ( ~ (v4
% 87.47/12.33 = 0) | ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 =
% 87.47/12.33 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 87.47/12.33 (ordinal_subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ?
% 87.47/12.33 [v4: any] : ? [v5: any] : (subset(v0, v1) = v5 & ordinal(v1) = v4 &
% 87.47/12.33 ordinal(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) &
% 87.47/12.33 ( ~ (v2 = 0) | v5 = 0)))))
% 87.47/12.33
% 87.47/12.33 (reflexivity_r1_ordinal1)
% 87.47/12.33 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (ordinal_subset(v0,
% 87.47/12.33 v0) = v2) | ~ (ordinal(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 87.47/12.33 : ( ~ (v3 = 0) & ordinal(v0) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 87.47/12.33 (ordinal(v1) = 0) | ~ (ordinal(v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 87.47/12.33 ordinal_subset(v0, v0) = 0)
% 87.47/12.33
% 87.47/12.33 (t10_ordinal1)
% 87.47/12.33 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | in(v0, v1) = 0)
% 87.47/12.33
% 87.47/12.33 (t2_subset)
% 87.47/12.33 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~
% 87.47/12.33 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (element(v0, v1) = v3 &
% 87.47/12.34 empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : (
% 87.47/12.34 ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 87.47/12.34 any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 87.47/12.34
% 87.47/12.34 (t33_ordinal1)
% 87.47/12.34 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 87.47/12.34 (succ(v0) = v1 & ordinal_subset(v1, v2) = v4 & ordinal(v2) = 0 & ordinal(v0) =
% 87.47/12.34 0 & in(v0, v2) = v3 & $i(v2) & $i(v1) & $i(v0) & ((v4 = 0 & ~ (v3 = 0)) |
% 87.47/12.34 (v3 = 0 & ~ (v4 = 0))))
% 87.47/12.34
% 87.47/12.34 (t6_boole)
% 87.47/12.34 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~
% 87.47/12.34 $i(v0))
% 87.47/12.34
% 87.47/12.34 (t8_boole)
% 87.47/12.34 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)
% 87.47/12.34 | ~ $i(v1) | ~ $i(v0))
% 87.47/12.34
% 87.47/12.34 (t8_xboole_1)
% 87.47/12.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 87.47/12.34 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ~ $i(v2) | ~
% 87.47/12.34 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (subset(v2, v1) = v6 &
% 87.47/12.34 subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 87.47/12.34
% 87.47/12.34 (function-axioms)
% 87.47/12.34 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 87.47/12.34 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 87.47/12.34 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 87.47/12.34 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 87.47/12.34 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 87.47/12.34 $i] : (v1 = v0 | ~ (ordinal_subset(v3, v2) = v1) | ~ (ordinal_subset(v3,
% 87.47/12.34 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 87.47/12.34 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & !
% 87.47/12.34 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 87.47/12.34 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i]
% 87.47/12.34 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 87.47/12.34 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 87.47/12.34 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation_non_empty(v2) =
% 87.47/12.34 v1) | ~ (relation_non_empty(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 87.47/12.34 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 87.47/12.34 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 87.47/12.34 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~
% 87.47/12.34 (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 87.47/12.34 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: MultipleValueBool]
% 87.47/12.34 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) =
% 87.47/12.34 v1) | ~ (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 87.47/12.34 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 87.47/12.34 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 87.47/12.34 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_transitive(v2) =
% 87.47/12.34 v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 87.47/12.34 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~
% 87.47/12.34 (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 87.47/12.34 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_connected(v2) =
% 87.47/12.34 v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 87.47/12.34 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~
% 87.47/12.34 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 87.47/12.34 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 87.47/12.34 (empty(v2) = v0))
% 87.47/12.34
% 87.47/12.34 Further assumptions not needed in the proof:
% 87.47/12.34 --------------------------------------------
% 87.47/12.34 cc1_funct_1, cc1_relat_1, cc2_ordinal1, connectedness_r1_ordinal1,
% 87.47/12.34 existence_m1_subset_1, fc12_relat_1, fc1_ordinal1, fc1_xboole_0, fc2_ordinal1,
% 87.47/12.34 fc2_relat_1, fc2_xboole_0, fc4_relat_1, idempotence_k2_xboole_0, rc1_funct_1,
% 87.47/12.34 rc1_ordinal1, rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_ordinal1, rc3_relat_1,
% 87.47/12.34 reflexivity_r1_tarski, t1_boole, t1_subset, t3_subset, t4_subset, t5_subset,
% 87.47/12.34 t7_boole
% 87.47/12.34
% 87.47/12.34 Those formulas are unsatisfiable:
% 87.47/12.34 ---------------------------------
% 87.47/12.34
% 87.47/12.34 Begin of proof
% 87.47/12.34 |
% 87.47/12.34 | ALPHA: (antisymmetry_r2_hidden) implies:
% 87.47/12.34 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~
% 87.47/12.34 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 87.47/12.34 |
% 87.47/12.34 | ALPHA: (cc1_ordinal1) implies:
% 87.47/12.35 | (2) ! [v0: $i] : ( ~ (ordinal(v0) = 0) | ~ $i(v0) |
% 87.47/12.35 | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0))
% 87.47/12.35 |
% 87.47/12.35 | ALPHA: (cc2_funct_1) implies:
% 87.47/12.35 | (3) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 87.47/12.35 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & relation(v0) = v1 &
% 87.47/12.35 | empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 87.47/12.35 | (4) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 87.47/12.35 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 &
% 87.47/12.35 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 87.47/12.35 | (5) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ?
% 87.47/12.35 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 &
% 87.47/12.35 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 87.47/12.35 | ~ (v2 = 0) | v1 = 0)))
% 87.47/12.35 |
% 87.47/12.35 | ALPHA: (cc3_ordinal1) implies:
% 87.47/12.35 | (6) ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | (epsilon_transitive(v0)
% 87.47/12.35 | = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0))
% 87.47/12.35 | (7) ! [v0: $i] : ! [v1: any] : ( ~ (epsilon_connected(v0) = v1) | ~
% 87.47/12.35 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 87.47/12.35 | (epsilon_transitive(v0) = v3 & ordinal(v0) = v4 & empty(v0) = v2 & (
% 87.47/12.35 | ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0))))
% 87.47/12.35 | (8) ! [v0: $i] : ! [v1: any] : ( ~ (ordinal(v0) = v1) | ~ $i(v0) | ?
% 87.47/12.35 | [v2: any] : ? [v3: any] : ? [v4: any] : (epsilon_transitive(v0) =
% 87.47/12.35 | v3 & epsilon_connected(v0) = v4 & empty(v0) = v2 & ( ~ (v2 = 0) |
% 87.47/12.35 | (v4 = 0 & v3 = 0 & v1 = 0))))
% 87.47/12.35 |
% 87.47/12.35 | ALPHA: (commutativity_k2_xboole_0) implies:
% 87.47/12.35 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 87.47/12.35 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 87.47/12.35 |
% 87.47/12.35 | ALPHA: (d1_ordinal1) implies:
% 87.47/12.35 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2:
% 87.47/12.35 | $i] : (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) &
% 87.47/12.35 | $i(v1)))
% 87.47/12.35 |
% 87.47/12.35 | ALPHA: (d1_tarski) implies:
% 87.47/12.35 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0)
% 87.47/12.35 | = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 87.47/12.35 |
% 87.47/12.35 | ALPHA: (d2_ordinal1) implies:
% 87.47/12.35 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (epsilon_transitive(v0) = 0) | ~
% 87.47/12.35 | (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | subset(v1, v0) = 0)
% 87.47/12.35 |
% 87.47/12.35 | ALPHA: (d3_tarski) implies:
% 87.47/12.35 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) |
% 87.47/12.35 | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1)
% 87.47/12.35 | = 0)
% 87.47/12.35 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0,
% 87.47/12.35 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 87.47/12.35 | ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 87.47/12.35 |
% 87.47/12.35 | ALPHA: (fc3_ordinal1) implies:
% 87.47/12.35 | (15) ! [v0: $i] : ( ~ (ordinal(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 87.47/12.35 | [v2: int] : ( ~ (v2 = 0) & succ(v0) = v1 & epsilon_transitive(v1) =
% 87.47/12.35 | 0 & ordinal(v1) = 0 & epsilon_connected(v1) = 0 & empty(v1) = v2 &
% 87.47/12.35 | $i(v1)))
% 87.47/12.35 | (16) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2:
% 87.47/12.35 | any] : ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 87.47/12.35 | (epsilon_transitive(v1) = v4 & ordinal(v1) = v6 & ordinal(v0) = v2 &
% 87.47/12.35 | epsilon_connected(v1) = v5 & empty(v1) = v3 & ( ~ (v2 = 0) | (v6 =
% 87.47/12.35 | 0 & v5 = 0 & v4 = 0 & ~ (v3 = 0)))))
% 87.47/12.35 |
% 87.47/12.35 | ALPHA: (redefinition_r1_ordinal1) implies:
% 87.47/12.36 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (ordinal_subset(v0, v1)
% 87.47/12.36 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 87.47/12.36 | [v5: any] : (subset(v0, v1) = v5 & ordinal(v1) = v4 & ordinal(v0) =
% 87.47/12.36 | v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~
% 87.47/12.36 | (v2 = 0) | v5 = 0)))))
% 87.47/12.36 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) |
% 87.47/12.36 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 87.47/12.36 | (ordinal_subset(v0, v1) = v5 & ordinal(v1) = v4 & ordinal(v0) = v3 &
% 87.47/12.36 | ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 =
% 87.47/12.36 | 0) | v5 = 0)))))
% 87.47/12.36 |
% 87.47/12.36 | ALPHA: (reflexivity_r1_ordinal1) implies:
% 87.47/12.36 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (ordinal(v1) = 0) | ~ (ordinal(v0) =
% 87.47/12.36 | 0) | ~ $i(v1) | ~ $i(v0) | ordinal_subset(v0, v0) = 0)
% 87.47/12.36 |
% 87.47/12.36 | ALPHA: (t2_subset) implies:
% 87.47/12.36 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 87.47/12.36 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 87.47/12.36 | (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 87.47/12.36 |
% 87.47/12.36 | ALPHA: (t6_boole) implies:
% 87.47/12.36 | (21) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 87.47/12.36 |
% 87.47/12.36 | ALPHA: (function-axioms) implies:
% 87.47/12.36 | (22) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 87.47/12.36 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 87.47/12.36 | (23) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 87.47/12.36 | : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 87.47/12.36 | (24) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 87.47/12.36 | : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~
% 87.47/12.36 | (epsilon_connected(v2) = v0))
% 87.47/12.36 | (25) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 87.47/12.36 | : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 87.47/12.36 | (26) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 87.47/12.36 | : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~
% 87.47/12.36 | (epsilon_transitive(v2) = v0))
% 87.47/12.36 | (27) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 87.47/12.36 | : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 87.47/12.36 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) =
% 87.47/12.36 | v1) | ~ (succ(v2) = v0))
% 87.47/12.36 | (29) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 87.47/12.36 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 87.47/12.36 | v0))
% 87.47/12.36 | (30) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 87.47/12.36 | : ! [v3: $i] : (v1 = v0 | ~ (ordinal_subset(v3, v2) = v1) | ~
% 87.47/12.36 | (ordinal_subset(v3, v2) = v0))
% 87.47/12.36 | (31) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 87.47/12.36 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3,
% 87.47/12.36 | v2) = v0))
% 87.47/12.36 |
% 87.47/12.36 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_37_0 gives:
% 87.47/12.36 | (32) empty(all_37_0) = 0 & $i(all_37_0)
% 87.47/12.36 |
% 87.47/12.36 | ALPHA: (32) implies:
% 87.47/12.36 | (33) $i(all_37_0)
% 87.47/12.36 | (34) empty(all_37_0) = 0
% 87.47/12.36 |
% 87.47/12.36 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_42_0 gives:
% 87.47/12.36 | (35) relation(all_42_0) = 0 & empty(all_42_0) = 0 & $i(all_42_0)
% 87.47/12.36 |
% 87.47/12.36 | ALPHA: (35) implies:
% 87.47/12.36 | (36) $i(all_42_0)
% 87.47/12.36 | (37) empty(all_42_0) = 0
% 87.47/12.36 |
% 87.47/12.36 | DELTA: instantiating (rc2_funct_1) with fresh symbol all_48_0 gives:
% 87.47/12.37 | (38) relation(all_48_0) = 0 & function(all_48_0) = 0 & empty(all_48_0) = 0
% 87.47/12.37 | & $i(all_48_0)
% 87.47/12.37 |
% 87.47/12.37 | ALPHA: (38) implies:
% 87.74/12.37 | (39) $i(all_48_0)
% 87.74/12.37 | (40) empty(all_48_0) = 0
% 87.74/12.37 |
% 87.74/12.37 | DELTA: instantiating (rc4_funct_1) with fresh symbol all_50_0 gives:
% 87.74/12.37 | (41) relation_empty_yielding(all_50_0) = 0 & relation(all_50_0) = 0 &
% 87.74/12.37 | function(all_50_0) = 0 & $i(all_50_0)
% 87.74/12.37 |
% 87.74/12.37 | ALPHA: (41) implies:
% 87.74/12.37 | (42) $i(all_50_0)
% 87.74/12.37 | (43) function(all_50_0) = 0
% 87.74/12.37 | (44) relation(all_50_0) = 0
% 87.74/12.37 |
% 87.74/12.37 | DELTA: instantiating (rc5_funct_1) with fresh symbol all_54_0 gives:
% 87.74/12.37 | (45) relation_non_empty(all_54_0) = 0 & relation(all_54_0) = 0 &
% 87.74/12.37 | function(all_54_0) = 0 & $i(all_54_0)
% 87.74/12.37 |
% 87.74/12.37 | ALPHA: (45) implies:
% 87.74/12.37 | (46) $i(all_54_0)
% 87.74/12.37 | (47) function(all_54_0) = 0
% 87.74/12.37 | (48) relation(all_54_0) = 0
% 87.74/12.37 |
% 87.74/12.37 | DELTA: instantiating (rc2_ordinal1) with fresh symbol all_62_0 gives:
% 87.74/12.37 | (49) one_to_one(all_62_0) = 0 & relation(all_62_0) = 0 &
% 87.74/12.37 | epsilon_transitive(all_62_0) = 0 & ordinal(all_62_0) = 0 &
% 87.74/12.37 | epsilon_connected(all_62_0) = 0 & function(all_62_0) = 0 &
% 87.74/12.37 | empty(all_62_0) = 0 & $i(all_62_0)
% 87.74/12.37 |
% 87.74/12.37 | ALPHA: (49) implies:
% 87.74/12.37 | (50) $i(all_62_0)
% 87.74/12.37 | (51) empty(all_62_0) = 0
% 87.74/12.37 | (52) ordinal(all_62_0) = 0
% 87.74/12.37 |
% 87.74/12.37 | DELTA: instantiating (t33_ordinal1) with fresh symbols all_66_0, all_66_1,
% 87.74/12.37 | all_66_2, all_66_3, all_66_4 gives:
% 87.74/12.37 | (53) succ(all_66_4) = all_66_3 & ordinal_subset(all_66_3, all_66_2) =
% 87.74/12.37 | all_66_0 & ordinal(all_66_2) = 0 & ordinal(all_66_4) = 0 &
% 87.74/12.37 | in(all_66_4, all_66_2) = all_66_1 & $i(all_66_2) & $i(all_66_3) &
% 87.74/12.37 | $i(all_66_4) & ((all_66_0 = 0 & ~ (all_66_1 = 0)) | (all_66_1 = 0 &
% 87.74/12.37 | ~ (all_66_0 = 0)))
% 87.74/12.37 |
% 87.74/12.37 | ALPHA: (53) implies:
% 87.74/12.37 | (54) $i(all_66_4)
% 87.74/12.37 | (55) $i(all_66_3)
% 87.74/12.37 | (56) $i(all_66_2)
% 87.74/12.37 | (57) in(all_66_4, all_66_2) = all_66_1
% 87.74/12.37 | (58) ordinal(all_66_4) = 0
% 87.74/12.37 | (59) ordinal(all_66_2) = 0
% 87.74/12.37 | (60) ordinal_subset(all_66_3, all_66_2) = all_66_0
% 87.74/12.37 | (61) succ(all_66_4) = all_66_3
% 87.74/12.37 | (62) (all_66_0 = 0 & ~ (all_66_1 = 0)) | (all_66_1 = 0 & ~ (all_66_0 =
% 87.74/12.37 | 0))
% 87.74/12.37 |
% 87.74/12.37 | GROUND_INST: instantiating (6) with all_37_0, simplifying with (33), (34)
% 87.74/12.37 | gives:
% 87.74/12.37 | (63) epsilon_transitive(all_37_0) = 0 & ordinal(all_37_0) = 0 &
% 87.74/12.37 | epsilon_connected(all_37_0) = 0
% 87.74/12.37 |
% 87.74/12.37 | ALPHA: (63) implies:
% 87.74/12.37 | (64) ordinal(all_37_0) = 0
% 87.74/12.37 |
% 87.74/12.37 | GROUND_INST: instantiating (t8_boole) with all_42_0, all_48_0, simplifying
% 87.74/12.37 | with (36), (37), (39), (40) gives:
% 87.74/12.37 | (65) all_48_0 = all_42_0
% 87.74/12.37 |
% 87.74/12.37 | GROUND_INST: instantiating (t8_boole) with all_37_0, all_48_0, simplifying
% 87.74/12.37 | with (33), (34), (39), (40) gives:
% 87.74/12.37 | (66) all_48_0 = all_37_0
% 87.74/12.37 |
% 87.74/12.37 | GROUND_INST: instantiating (t8_boole) with all_48_0, all_62_0, simplifying
% 87.74/12.37 | with (39), (40), (50), (51) gives:
% 87.74/12.37 | (67) all_62_0 = all_48_0
% 87.74/12.37 |
% 87.74/12.37 | GROUND_INST: instantiating (21) with all_62_0, simplifying with (50), (51)
% 87.74/12.37 | gives:
% 87.74/12.37 | (68) all_62_0 = empty_set
% 87.74/12.37 |
% 87.74/12.37 | GROUND_INST: instantiating (3) with all_50_0, simplifying with (42), (43)
% 87.74/12.37 | gives:
% 87.74/12.37 | (69) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_50_0) =
% 87.74/12.37 | v2 & relation(all_50_0) = v0 & empty(all_50_0) = v1 & ( ~ (v1 = 0) |
% 87.74/12.37 | ~ (v0 = 0) | v2 = 0))
% 87.74/12.37 |
% 87.74/12.37 | GROUND_INST: instantiating (3) with all_54_0, simplifying with (46), (47)
% 87.74/12.37 | gives:
% 87.74/12.37 | (70) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_54_0) =
% 87.74/12.37 | v2 & relation(all_54_0) = v0 & empty(all_54_0) = v1 & ( ~ (v1 = 0) |
% 87.74/12.37 | ~ (v0 = 0) | v2 = 0))
% 87.74/12.37 |
% 87.74/12.37 | GROUND_INST: instantiating (15) with all_66_4, simplifying with (54), (58)
% 87.74/12.37 | gives:
% 87.74/12.38 | (71) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & succ(all_66_4) = v0 &
% 87.74/12.38 | epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & epsilon_connected(v0)
% 87.74/12.38 | = 0 & empty(v0) = v1 & $i(v0))
% 87.74/12.38 |
% 87.74/12.38 | GROUND_INST: instantiating (19) with all_62_0, all_66_2, simplifying with
% 87.74/12.38 | (50), (52), (56), (59) gives:
% 87.74/12.38 | (72) ordinal_subset(all_62_0, all_62_0) = 0
% 87.74/12.38 |
% 87.74/12.38 | GROUND_INST: instantiating (2) with all_66_2, simplifying with (56), (59)
% 87.74/12.38 | gives:
% 87.74/12.38 | (73) epsilon_transitive(all_66_2) = 0 & epsilon_connected(all_66_2) = 0
% 87.74/12.38 |
% 87.74/12.38 | ALPHA: (73) implies:
% 87.74/12.38 | (74) epsilon_connected(all_66_2) = 0
% 87.74/12.38 | (75) epsilon_transitive(all_66_2) = 0
% 87.74/12.38 |
% 87.74/12.38 | GROUND_INST: instantiating (8) with all_66_2, 0, simplifying with (56), (59)
% 87.74/12.38 | gives:
% 87.74/12.38 | (76) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 87.74/12.38 | (epsilon_transitive(all_66_2) = v1 & epsilon_connected(all_66_2) = v2
% 87.74/12.38 | & empty(all_66_2) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 87.74/12.38 |
% 87.74/12.38 | GROUND_INST: instantiating (4) with all_50_0, simplifying with (42), (44)
% 87.74/12.38 | gives:
% 87.74/12.38 | (77) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_50_0) =
% 87.74/12.38 | v2 & function(all_50_0) = v1 & empty(all_50_0) = v0 & ( ~ (v1 = 0) |
% 87.74/12.38 | ~ (v0 = 0) | v2 = 0))
% 87.74/12.38 |
% 87.74/12.38 | GROUND_INST: instantiating (4) with all_54_0, simplifying with (46), (48)
% 87.74/12.38 | gives:
% 87.74/12.38 | (78) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_54_0) =
% 87.74/12.38 | v2 & function(all_54_0) = v1 & empty(all_54_0) = v0 & ( ~ (v1 = 0) |
% 87.74/12.38 | ~ (v0 = 0) | v2 = 0))
% 87.74/12.38 |
% 87.74/12.38 | GROUND_INST: instantiating (17) with all_66_3, all_66_2, all_66_0, simplifying
% 87.74/12.38 | with (55), (56), (60) gives:
% 87.74/12.38 | (79) ? [v0: any] : ? [v1: any] : ? [v2: any] : (subset(all_66_3,
% 87.74/12.38 | all_66_2) = v2 & ordinal(all_66_2) = v1 & ordinal(all_66_3) = v0 &
% 87.74/12.38 | ( ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v2 = 0) | all_66_0 = 0) & ( ~
% 87.74/12.38 | (all_66_0 = 0) | v2 = 0))))
% 87.74/12.38 |
% 87.74/12.38 | GROUND_INST: instantiating (t10_ordinal1) with all_66_4, all_66_3, simplifying
% 87.74/12.38 | with (54), (61) gives:
% 87.74/12.38 | (80) in(all_66_4, all_66_3) = 0
% 87.74/12.38 |
% 87.74/12.38 | GROUND_INST: instantiating (16) with all_66_4, all_66_3, simplifying with
% 87.74/12.38 | (54), (61) gives:
% 87.74/12.38 | (81) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 87.74/12.38 | any] : (epsilon_transitive(all_66_3) = v2 & ordinal(all_66_3) = v4 &
% 87.74/12.38 | ordinal(all_66_4) = v0 & epsilon_connected(all_66_3) = v3 &
% 87.74/12.38 | empty(all_66_3) = v1 & ( ~ (v0 = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & ~
% 87.74/12.38 | (v1 = 0))))
% 87.74/12.38 |
% 87.74/12.38 | GROUND_INST: instantiating (10) with all_66_4, all_66_3, simplifying with
% 87.74/12.38 | (54), (61) gives:
% 87.74/12.38 | (82) ? [v0: $i] : (singleton(all_66_4) = v0 & set_union2(all_66_4, v0) =
% 87.74/12.38 | all_66_3 & $i(v0) & $i(all_66_3))
% 87.74/12.38 |
% 87.74/12.38 | COMBINE_EQS: (67), (68) imply:
% 87.74/12.38 | (83) all_48_0 = empty_set
% 87.74/12.38 |
% 87.74/12.38 | SIMP: (83) implies:
% 87.74/12.38 | (84) all_48_0 = empty_set
% 87.74/12.38 |
% 87.74/12.38 | COMBINE_EQS: (65), (66) imply:
% 87.74/12.38 | (85) all_42_0 = all_37_0
% 87.74/12.38 |
% 87.74/12.38 | COMBINE_EQS: (65), (84) imply:
% 87.74/12.38 | (86) all_42_0 = empty_set
% 87.74/12.38 |
% 87.74/12.38 | COMBINE_EQS: (85), (86) imply:
% 87.74/12.38 | (87) all_37_0 = empty_set
% 87.74/12.38 |
% 87.74/12.38 | SIMP: (87) implies:
% 87.74/12.38 | (88) all_37_0 = empty_set
% 87.74/12.38 |
% 87.74/12.38 | DELTA: instantiating (82) with fresh symbol all_78_0 gives:
% 87.74/12.38 | (89) singleton(all_66_4) = all_78_0 & set_union2(all_66_4, all_78_0) =
% 87.74/12.38 | all_66_3 & $i(all_78_0) & $i(all_66_3)
% 87.74/12.38 |
% 87.74/12.38 | ALPHA: (89) implies:
% 87.74/12.38 | (90) $i(all_78_0)
% 87.74/12.38 | (91) set_union2(all_66_4, all_78_0) = all_66_3
% 87.74/12.38 | (92) singleton(all_66_4) = all_78_0
% 87.74/12.38 |
% 87.74/12.38 | DELTA: instantiating (76) with fresh symbols all_88_0, all_88_1, all_88_2
% 87.74/12.38 | gives:
% 87.74/12.38 | (93) epsilon_transitive(all_66_2) = all_88_1 & epsilon_connected(all_66_2)
% 87.74/12.38 | = all_88_0 & empty(all_66_2) = all_88_2 & ( ~ (all_88_2 = 0) |
% 87.74/12.38 | (all_88_0 = 0 & all_88_1 = 0))
% 87.74/12.38 |
% 87.74/12.38 | ALPHA: (93) implies:
% 87.74/12.38 | (94) epsilon_connected(all_66_2) = all_88_0
% 87.74/12.38 | (95) epsilon_transitive(all_66_2) = all_88_1
% 87.74/12.38 |
% 87.74/12.38 | DELTA: instantiating (78) with fresh symbols all_90_0, all_90_1, all_90_2
% 87.74/12.38 | gives:
% 87.74/12.38 | (96) one_to_one(all_54_0) = all_90_0 & function(all_54_0) = all_90_1 &
% 87.74/12.38 | empty(all_54_0) = all_90_2 & ( ~ (all_90_1 = 0) | ~ (all_90_2 = 0) |
% 87.74/12.38 | all_90_0 = 0)
% 87.74/12.38 |
% 87.74/12.38 | ALPHA: (96) implies:
% 87.74/12.38 | (97) empty(all_54_0) = all_90_2
% 87.74/12.38 | (98) function(all_54_0) = all_90_1
% 87.74/12.38 | (99) one_to_one(all_54_0) = all_90_0
% 87.74/12.38 |
% 87.74/12.38 | DELTA: instantiating (70) with fresh symbols all_106_0, all_106_1, all_106_2
% 87.74/12.38 | gives:
% 87.74/12.38 | (100) one_to_one(all_54_0) = all_106_0 & relation(all_54_0) = all_106_2 &
% 87.74/12.38 | empty(all_54_0) = all_106_1 & ( ~ (all_106_1 = 0) | ~ (all_106_2 =
% 87.74/12.38 | 0) | all_106_0 = 0)
% 87.74/12.38 |
% 87.74/12.38 | ALPHA: (100) implies:
% 87.74/12.38 | (101) empty(all_54_0) = all_106_1
% 87.74/12.38 | (102) one_to_one(all_54_0) = all_106_0
% 87.74/12.38 | (103) ~ (all_106_1 = 0) | ~ (all_106_2 = 0) | all_106_0 = 0
% 87.74/12.38 |
% 87.74/12.38 | DELTA: instantiating (69) with fresh symbols all_108_0, all_108_1, all_108_2
% 87.74/12.38 | gives:
% 87.74/12.38 | (104) one_to_one(all_50_0) = all_108_0 & relation(all_50_0) = all_108_2 &
% 87.74/12.38 | empty(all_50_0) = all_108_1 & ( ~ (all_108_1 = 0) | ~ (all_108_2 =
% 87.74/12.38 | 0) | all_108_0 = 0)
% 87.74/12.38 |
% 87.74/12.38 | ALPHA: (104) implies:
% 87.74/12.38 | (105) one_to_one(all_50_0) = all_108_0
% 87.74/12.38 |
% 87.74/12.38 | DELTA: instantiating (77) with fresh symbols all_112_0, all_112_1, all_112_2
% 87.74/12.38 | gives:
% 87.74/12.38 | (106) one_to_one(all_50_0) = all_112_0 & function(all_50_0) = all_112_1 &
% 87.74/12.38 | empty(all_50_0) = all_112_2 & ( ~ (all_112_1 = 0) | ~ (all_112_2 =
% 87.74/12.38 | 0) | all_112_0 = 0)
% 87.74/12.38 |
% 87.74/12.38 | ALPHA: (106) implies:
% 87.74/12.38 | (107) function(all_50_0) = all_112_1
% 87.74/12.38 | (108) one_to_one(all_50_0) = all_112_0
% 87.74/12.38 |
% 87.74/12.38 | DELTA: instantiating (71) with fresh symbols all_122_0, all_122_1 gives:
% 87.74/12.38 | (109) ~ (all_122_0 = 0) & succ(all_66_4) = all_122_1 &
% 87.74/12.38 | epsilon_transitive(all_122_1) = 0 & ordinal(all_122_1) = 0 &
% 87.74/12.38 | epsilon_connected(all_122_1) = 0 & empty(all_122_1) = all_122_0 &
% 87.74/12.38 | $i(all_122_1)
% 87.74/12.38 |
% 87.74/12.38 | ALPHA: (109) implies:
% 87.74/12.38 | (110) $i(all_122_1)
% 87.74/12.38 | (111) succ(all_66_4) = all_122_1
% 87.74/12.38 |
% 87.74/12.38 | DELTA: instantiating (79) with fresh symbols all_134_0, all_134_1, all_134_2
% 87.74/12.38 | gives:
% 87.74/12.39 | (112) subset(all_66_3, all_66_2) = all_134_0 & ordinal(all_66_2) =
% 87.74/12.39 | all_134_1 & ordinal(all_66_3) = all_134_2 & ( ~ (all_134_1 = 0) | ~
% 87.74/12.39 | (all_134_2 = 0) | (( ~ (all_134_0 = 0) | all_66_0 = 0) & ( ~
% 87.74/12.39 | (all_66_0 = 0) | all_134_0 = 0)))
% 87.74/12.39 |
% 87.74/12.39 | ALPHA: (112) implies:
% 87.74/12.39 | (113) ordinal(all_66_3) = all_134_2
% 87.74/12.39 | (114) ordinal(all_66_2) = all_134_1
% 87.74/12.39 | (115) subset(all_66_3, all_66_2) = all_134_0
% 87.74/12.39 | (116) ~ (all_134_1 = 0) | ~ (all_134_2 = 0) | (( ~ (all_134_0 = 0) |
% 87.74/12.39 | all_66_0 = 0) & ( ~ (all_66_0 = 0) | all_134_0 = 0))
% 87.74/12.39 |
% 87.74/12.39 | DELTA: instantiating (81) with fresh symbols all_136_0, all_136_1, all_136_2,
% 87.74/12.39 | all_136_3, all_136_4 gives:
% 87.74/12.39 | (117) epsilon_transitive(all_66_3) = all_136_2 & ordinal(all_66_3) =
% 87.74/12.39 | all_136_0 & ordinal(all_66_4) = all_136_4 &
% 87.74/12.39 | epsilon_connected(all_66_3) = all_136_1 & empty(all_66_3) = all_136_3
% 87.74/12.39 | & ( ~ (all_136_4 = 0) | (all_136_0 = 0 & all_136_1 = 0 & all_136_2 =
% 87.74/12.39 | 0 & ~ (all_136_3 = 0)))
% 87.74/12.39 |
% 87.74/12.39 | ALPHA: (117) implies:
% 87.74/12.39 | (118) ordinal(all_66_4) = all_136_4
% 87.74/12.39 | (119) ordinal(all_66_3) = all_136_0
% 87.74/12.39 | (120) ~ (all_136_4 = 0) | (all_136_0 = 0 & all_136_1 = 0 & all_136_2 = 0 &
% 87.74/12.39 | ~ (all_136_3 = 0))
% 87.74/12.39 |
% 87.74/12.39 | REDUCE: (68), (72) imply:
% 87.74/12.39 | (121) ordinal_subset(empty_set, empty_set) = 0
% 87.74/12.39 |
% 87.74/12.39 | REDUCE: (64), (88) imply:
% 87.74/12.39 | (122) ordinal(empty_set) = 0
% 87.74/12.39 |
% 87.74/12.39 | REDUCE: (33), (88) imply:
% 87.74/12.39 | (123) $i(empty_set)
% 87.74/12.39 |
% 87.74/12.39 | GROUND_INST: instantiating (22) with all_90_2, all_106_1, all_54_0,
% 87.74/12.39 | simplifying with (97), (101) gives:
% 87.74/12.39 | (124) all_106_1 = all_90_2
% 87.74/12.39 |
% 87.74/12.39 | GROUND_INST: instantiating (23) with 0, all_112_1, all_50_0, simplifying with
% 87.74/12.39 | (43), (107) gives:
% 87.74/12.39 | (125) all_112_1 = 0
% 87.74/12.39 |
% 87.74/12.39 | GROUND_INST: instantiating (23) with 0, all_90_1, all_54_0, simplifying with
% 87.74/12.39 | (47), (98) gives:
% 87.74/12.39 | (126) all_90_1 = 0
% 87.74/12.39 |
% 87.74/12.39 | GROUND_INST: instantiating (24) with 0, all_88_0, all_66_2, simplifying with
% 87.74/12.39 | (74), (94) gives:
% 87.74/12.39 | (127) all_88_0 = 0
% 87.74/12.39 |
% 87.74/12.39 | GROUND_INST: instantiating (25) with 0, all_136_4, all_66_4, simplifying with
% 87.74/12.39 | (58), (118) gives:
% 87.74/12.39 | (128) all_136_4 = 0
% 87.74/12.39 |
% 87.74/12.39 | GROUND_INST: instantiating (25) with all_134_2, all_136_0, all_66_3,
% 87.74/12.39 | simplifying with (113), (119) gives:
% 87.74/12.39 | (129) all_136_0 = all_134_2
% 87.74/12.39 |
% 87.74/12.39 | GROUND_INST: instantiating (25) with 0, all_134_1, all_66_2, simplifying with
% 87.74/12.39 | (59), (114) gives:
% 87.74/12.39 | (130) all_134_1 = 0
% 87.74/12.39 |
% 87.74/12.39 | GROUND_INST: instantiating (26) with 0, all_88_1, all_66_2, simplifying with
% 87.74/12.39 | (75), (95) gives:
% 87.74/12.39 | (131) all_88_1 = 0
% 87.74/12.39 |
% 87.74/12.39 | GROUND_INST: instantiating (27) with all_108_0, all_112_0, all_50_0,
% 87.74/12.39 | simplifying with (105), (108) gives:
% 87.74/12.39 | (132) all_112_0 = all_108_0
% 87.74/12.39 |
% 87.74/12.39 | GROUND_INST: instantiating (27) with all_90_0, all_106_0, all_54_0,
% 87.74/12.39 | simplifying with (99), (102) gives:
% 87.74/12.39 | (133) all_106_0 = all_90_0
% 87.74/12.39 |
% 87.74/12.39 | GROUND_INST: instantiating (28) with all_66_3, all_122_1, all_66_4,
% 87.74/12.39 | simplifying with (61), (111) gives:
% 87.74/12.39 | (134) all_122_1 = all_66_3
% 87.74/12.39 |
% 87.74/12.39 | BETA: splitting (120) gives:
% 87.74/12.39 |
% 87.74/12.39 | Case 1:
% 87.74/12.39 | |
% 87.74/12.39 | | (135) ~ (all_136_4 = 0)
% 87.74/12.39 | |
% 87.74/12.39 | | REDUCE: (128), (135) imply:
% 87.74/12.39 | | (136) $false
% 87.74/12.39 | |
% 87.74/12.39 | | CLOSE: (136) is inconsistent.
% 87.74/12.39 | |
% 87.74/12.39 | Case 2:
% 87.74/12.39 | |
% 87.74/12.39 | | (137) all_136_0 = 0 & all_136_1 = 0 & all_136_2 = 0 & ~ (all_136_3 = 0)
% 87.74/12.39 | |
% 87.74/12.39 | | ALPHA: (137) implies:
% 87.74/12.39 | | (138) all_136_0 = 0
% 87.74/12.39 | |
% 87.74/12.39 | | COMBINE_EQS: (129), (138) imply:
% 87.74/12.39 | | (139) all_134_2 = 0
% 87.74/12.39 | |
% 87.74/12.39 | | REDUCE: (113), (139) imply:
% 87.74/12.39 | | (140) ordinal(all_66_3) = 0
% 87.74/12.39 | |
% 87.74/12.39 | | GROUND_INST: instantiating (1) with all_66_3, all_66_4, simplifying with
% 87.74/12.39 | | (54), (55), (80) gives:
% 87.74/12.39 | | (141) ? [v0: int] : ( ~ (v0 = 0) & in(all_66_3, all_66_4) = v0)
% 87.74/12.39 | |
% 87.74/12.39 | | GROUND_INST: instantiating (7) with all_66_2, 0, simplifying with (56), (74)
% 87.74/12.39 | | gives:
% 87.74/12.39 | | (142) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 87.74/12.39 | | (epsilon_transitive(all_66_2) = v1 & ordinal(all_66_2) = v2 &
% 87.74/12.39 | | empty(all_66_2) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 87.74/12.39 | |
% 87.74/12.39 | | GROUND_INST: instantiating (5) with all_50_0, all_108_0, simplifying with
% 87.74/12.39 | | (42), (105) gives:
% 87.74/12.39 | | (143) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_50_0) =
% 87.74/12.39 | | v0 & function(all_50_0) = v2 & empty(all_50_0) = v1 & ( ~ (v2 =
% 87.74/12.39 | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | all_108_0 = 0))
% 87.74/12.39 | |
% 87.74/12.39 | | GROUND_INST: instantiating (5) with all_54_0, all_90_0, simplifying with
% 87.74/12.39 | | (46), (99) gives:
% 87.74/12.39 | | (144) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_54_0) =
% 87.74/12.39 | | v0 & function(all_54_0) = v2 & empty(all_54_0) = v1 & ( ~ (v2 =
% 87.74/12.39 | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | all_90_0 = 0))
% 87.74/12.39 | |
% 87.74/12.39 | | GROUND_INST: instantiating (9) with all_78_0, all_66_4, all_66_3,
% 87.74/12.39 | | simplifying with (54), (90), (91) gives:
% 87.74/12.39 | | (145) set_union2(all_78_0, all_66_4) = all_66_3 & $i(all_66_3)
% 87.74/12.39 | |
% 87.74/12.39 | | ALPHA: (145) implies:
% 87.74/12.39 | | (146) set_union2(all_78_0, all_66_4) = all_66_3
% 87.74/12.39 | |
% 87.74/12.39 | | GROUND_INST: instantiating (17) with empty_set, empty_set, 0, simplifying
% 87.74/12.39 | | with (121), (123) gives:
% 87.74/12.39 | | (147) ? [v0: any] : ? [v1: any] : ? [v2: any] : (subset(empty_set,
% 87.74/12.39 | | empty_set) = v2 & ordinal(empty_set) = v1 & ordinal(empty_set)
% 87.74/12.39 | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 87.74/12.39 | |
% 87.74/12.39 | | GROUND_INST: instantiating (t8_xboole_1) with all_66_4, all_66_2, all_78_0,
% 87.74/12.39 | | all_66_3, all_134_0, simplifying with (54), (56), (90), (91),
% 87.74/12.39 | | (115) gives:
% 87.74/12.39 | | (148) all_134_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_78_0,
% 87.74/12.39 | | all_66_2) = v1 & subset(all_66_4, all_66_2) = v0 & ( ~ (v1 = 0)
% 87.74/12.39 | | | ~ (v0 = 0)))
% 87.74/12.39 | |
% 87.74/12.39 | | GROUND_INST: instantiating (14) with all_66_3, all_66_2, all_134_0,
% 87.74/12.39 | | simplifying with (55), (56), (115) gives:
% 87.74/12.40 | | (149) all_134_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 87.74/12.40 | | all_66_2) = v1 & in(v0, all_66_3) = 0 & $i(v0))
% 87.74/12.40 | |
% 87.74/12.40 | | GROUND_INST: instantiating (18) with all_66_3, all_66_2, all_134_0,
% 87.74/12.40 | | simplifying with (55), (56), (115) gives:
% 87.74/12.40 | | (150) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 87.74/12.40 | | (ordinal_subset(all_66_3, all_66_2) = v2 & ordinal(all_66_2) = v1 &
% 87.74/12.40 | | ordinal(all_66_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v2 =
% 87.74/12.40 | | 0) | all_134_0 = 0) & ( ~ (all_134_0 = 0) | v2 = 0))))
% 87.74/12.40 | |
% 87.74/12.40 | | DELTA: instantiating (141) with fresh symbol all_156_0 gives:
% 87.74/12.40 | | (151) ~ (all_156_0 = 0) & in(all_66_3, all_66_4) = all_156_0
% 87.74/12.40 | |
% 87.74/12.40 | | ALPHA: (151) implies:
% 87.74/12.40 | | (152) ~ (all_156_0 = 0)
% 87.74/12.40 | | (153) in(all_66_3, all_66_4) = all_156_0
% 87.74/12.40 | |
% 87.74/12.40 | | DELTA: instantiating (147) with fresh symbols all_184_0, all_184_1,
% 87.74/12.40 | | all_184_2 gives:
% 87.74/12.40 | | (154) subset(empty_set, empty_set) = all_184_0 & ordinal(empty_set) =
% 87.74/12.40 | | all_184_1 & ordinal(empty_set) = all_184_2 & ( ~ (all_184_1 = 0) |
% 87.74/12.40 | | ~ (all_184_2 = 0) | all_184_0 = 0)
% 87.74/12.40 | |
% 87.74/12.40 | | ALPHA: (154) implies:
% 87.74/12.40 | | (155) ordinal(empty_set) = all_184_2
% 87.74/12.40 | | (156) ordinal(empty_set) = all_184_1
% 87.74/12.40 | | (157) ~ (all_184_1 = 0) | ~ (all_184_2 = 0) | all_184_0 = 0
% 87.74/12.40 | |
% 87.74/12.40 | | DELTA: instantiating (142) with fresh symbols all_188_0, all_188_1,
% 87.74/12.40 | | all_188_2 gives:
% 87.74/12.40 | | (158) epsilon_transitive(all_66_2) = all_188_1 & ordinal(all_66_2) =
% 87.74/12.40 | | all_188_0 & empty(all_66_2) = all_188_2 & ( ~ (all_188_2 = 0) |
% 87.74/12.40 | | (all_188_0 = 0 & all_188_1 = 0))
% 87.74/12.40 | |
% 87.74/12.40 | | ALPHA: (158) implies:
% 87.74/12.40 | | (159) epsilon_transitive(all_66_2) = all_188_1
% 87.74/12.40 | |
% 87.74/12.40 | | DELTA: instantiating (144) with fresh symbols all_200_0, all_200_1,
% 87.74/12.40 | | all_200_2 gives:
% 87.74/12.40 | | (160) relation(all_54_0) = all_200_2 & function(all_54_0) = all_200_0 &
% 87.74/12.40 | | empty(all_54_0) = all_200_1 & ( ~ (all_200_0 = 0) | ~ (all_200_1 =
% 87.74/12.40 | | 0) | ~ (all_200_2 = 0) | all_90_0 = 0)
% 87.74/12.40 | |
% 87.74/12.40 | | ALPHA: (160) implies:
% 87.74/12.40 | | (161) empty(all_54_0) = all_200_1
% 87.74/12.40 | | (162) function(all_54_0) = all_200_0
% 87.74/12.40 | | (163) ~ (all_200_0 = 0) | ~ (all_200_1 = 0) | ~ (all_200_2 = 0) |
% 87.74/12.40 | | all_90_0 = 0
% 87.74/12.40 | |
% 87.74/12.40 | | DELTA: instantiating (143) with fresh symbols all_204_0, all_204_1,
% 87.74/12.40 | | all_204_2 gives:
% 87.74/12.40 | | (164) relation(all_50_0) = all_204_2 & function(all_50_0) = all_204_0 &
% 87.74/12.40 | | empty(all_50_0) = all_204_1 & ( ~ (all_204_0 = 0) | ~ (all_204_1 =
% 87.74/12.40 | | 0) | ~ (all_204_2 = 0) | all_108_0 = 0)
% 87.74/12.40 | |
% 87.74/12.40 | | ALPHA: (164) implies:
% 87.74/12.40 | | (165) function(all_50_0) = all_204_0
% 87.74/12.40 | | (166) ~ (all_204_0 = 0) | ~ (all_204_1 = 0) | ~ (all_204_2 = 0) |
% 87.74/12.40 | | all_108_0 = 0
% 87.74/12.40 | |
% 87.74/12.40 | | DELTA: instantiating (150) with fresh symbols all_210_0, all_210_1,
% 87.74/12.40 | | all_210_2 gives:
% 87.74/12.40 | | (167) ordinal_subset(all_66_3, all_66_2) = all_210_0 & ordinal(all_66_2)
% 87.74/12.40 | | = all_210_1 & ordinal(all_66_3) = all_210_2 & ( ~ (all_210_1 = 0) |
% 87.74/12.40 | | ~ (all_210_2 = 0) | (( ~ (all_210_0 = 0) | all_134_0 = 0) & ( ~
% 87.74/12.40 | | (all_134_0 = 0) | all_210_0 = 0)))
% 87.74/12.40 | |
% 87.74/12.40 | | ALPHA: (167) implies:
% 87.74/12.40 | | (168) ordinal(all_66_3) = all_210_2
% 87.74/12.40 | | (169) ordinal(all_66_2) = all_210_1
% 87.74/12.40 | | (170) ordinal_subset(all_66_3, all_66_2) = all_210_0
% 87.74/12.40 | | (171) ~ (all_210_1 = 0) | ~ (all_210_2 = 0) | (( ~ (all_210_0 = 0) |
% 87.74/12.40 | | all_134_0 = 0) & ( ~ (all_134_0 = 0) | all_210_0 = 0))
% 87.74/12.40 | |
% 87.74/12.40 | | GROUND_INST: instantiating (22) with all_90_2, all_200_1, all_54_0,
% 87.74/12.40 | | simplifying with (97), (161) gives:
% 87.74/12.40 | | (172) all_200_1 = all_90_2
% 87.74/12.40 | |
% 87.74/12.40 | | GROUND_INST: instantiating (23) with 0, all_204_0, all_50_0, simplifying
% 87.74/12.40 | | with (43), (165) gives:
% 87.74/12.40 | | (173) all_204_0 = 0
% 87.74/12.40 | |
% 87.74/12.40 | | GROUND_INST: instantiating (23) with 0, all_200_0, all_54_0, simplifying
% 87.74/12.40 | | with (47), (162) gives:
% 87.74/12.40 | | (174) all_200_0 = 0
% 87.74/12.40 | |
% 87.74/12.40 | | GROUND_INST: instantiating (25) with 0, all_184_1, empty_set, simplifying
% 87.74/12.40 | | with (122), (156) gives:
% 87.74/12.40 | | (175) all_184_1 = 0
% 87.74/12.40 | |
% 87.74/12.40 | | GROUND_INST: instantiating (25) with all_184_2, all_184_1, empty_set,
% 87.74/12.40 | | simplifying with (155), (156) gives:
% 87.74/12.40 | | (176) all_184_1 = all_184_2
% 87.74/12.40 | |
% 87.74/12.40 | | GROUND_INST: instantiating (25) with 0, all_210_2, all_66_3, simplifying
% 87.74/12.40 | | with (140), (168) gives:
% 87.74/12.40 | | (177) all_210_2 = 0
% 87.74/12.40 | |
% 87.74/12.40 | | GROUND_INST: instantiating (25) with 0, all_210_1, all_66_2, simplifying
% 87.74/12.40 | | with (59), (169) gives:
% 87.74/12.40 | | (178) all_210_1 = 0
% 87.74/12.40 | |
% 87.74/12.40 | | GROUND_INST: instantiating (26) with 0, all_188_1, all_66_2, simplifying
% 87.74/12.40 | | with (75), (159) gives:
% 87.74/12.40 | | (179) all_188_1 = 0
% 87.74/12.40 | |
% 87.74/12.40 | | GROUND_INST: instantiating (30) with all_66_0, all_210_0, all_66_2,
% 87.74/12.40 | | all_66_3, simplifying with (60), (170) gives:
% 87.74/12.40 | | (180) all_210_0 = all_66_0
% 87.74/12.40 | |
% 87.74/12.40 | | COMBINE_EQS: (175), (176) imply:
% 87.74/12.40 | | (181) all_184_2 = 0
% 87.74/12.40 | |
% 87.74/12.40 | | SIMP: (181) implies:
% 87.74/12.40 | | (182) all_184_2 = 0
% 87.74/12.40 | |
% 87.74/12.40 | | BETA: splitting (157) gives:
% 87.74/12.40 | |
% 87.74/12.40 | | Case 1:
% 87.74/12.40 | | |
% 87.74/12.40 | | | (183) ~ (all_184_1 = 0)
% 87.74/12.40 | | |
% 87.74/12.40 | | | REDUCE: (175), (183) imply:
% 87.74/12.40 | | | (184) $false
% 87.74/12.40 | | |
% 87.74/12.40 | | | CLOSE: (184) is inconsistent.
% 87.74/12.40 | | |
% 87.74/12.40 | | Case 2:
% 87.74/12.40 | | |
% 87.74/12.40 | | | (185) ~ (all_184_2 = 0) | all_184_0 = 0
% 87.74/12.40 | | |
% 87.74/12.40 | | | BETA: splitting (185) gives:
% 87.74/12.40 | | |
% 87.74/12.40 | | | Case 1:
% 87.74/12.40 | | | |
% 87.74/12.40 | | | | (186) ~ (all_184_2 = 0)
% 87.74/12.40 | | | |
% 87.74/12.40 | | | | REDUCE: (182), (186) imply:
% 87.74/12.40 | | | | (187) $false
% 87.74/12.40 | | | |
% 87.74/12.40 | | | | CLOSE: (187) is inconsistent.
% 87.74/12.40 | | | |
% 87.74/12.40 | | | Case 2:
% 87.74/12.40 | | | |
% 87.74/12.40 | | | |
% 87.74/12.40 | | | | GROUND_INST: instantiating (20) with all_66_3, all_66_4, all_156_0,
% 87.74/12.40 | | | | simplifying with (54), (55), (153) gives:
% 87.74/12.40 | | | | (188) all_156_0 = 0 | ? [v0: any] : ? [v1: any] :
% 87.74/12.40 | | | | (element(all_66_3, all_66_4) = v0 & empty(all_66_4) = v1 & ( ~
% 87.74/12.40 | | | | (v0 = 0) | v1 = 0))
% 87.74/12.40 | | | |
% 87.74/12.40 | | | | GROUND_INST: instantiating (t8_xboole_1) with all_78_0, all_66_2,
% 87.74/12.40 | | | | all_66_4, all_66_3, all_134_0, simplifying with (54), (56),
% 87.74/12.40 | | | | (90), (115), (146) gives:
% 87.74/12.40 | | | | (189) all_134_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_78_0,
% 87.74/12.40 | | | | all_66_2) = v0 & subset(all_66_4, all_66_2) = v1 & ( ~ (v1
% 87.74/12.40 | | | | = 0) | ~ (v0 = 0)))
% 87.74/12.40 | | | |
% 87.74/12.40 | | | | GROUND_INST: instantiating (fc3_xboole_0) with all_66_4, all_78_0,
% 87.74/12.40 | | | | all_66_3, simplifying with (54), (90), (146) gives:
% 87.74/12.40 | | | | (190) ? [v0: any] : ? [v1: any] : (empty(all_66_3) = v1 &
% 87.74/12.40 | | | | empty(all_66_4) = v0 & ( ~ (v1 = 0) | v0 = 0))
% 87.74/12.40 | | | |
% 87.74/12.40 | | | | DELTA: instantiating (190) with fresh symbols all_298_0, all_298_1
% 87.74/12.40 | | | | gives:
% 87.74/12.40 | | | | (191) empty(all_66_3) = all_298_0 & empty(all_66_4) = all_298_1 & ( ~
% 87.74/12.40 | | | | (all_298_0 = 0) | all_298_1 = 0)
% 87.74/12.40 | | | |
% 87.74/12.40 | | | | ALPHA: (191) implies:
% 87.74/12.40 | | | | (192) empty(all_66_4) = all_298_1
% 87.74/12.40 | | | |
% 87.74/12.40 | | | | BETA: splitting (188) gives:
% 87.74/12.40 | | | |
% 87.74/12.40 | | | | Case 1:
% 87.74/12.40 | | | | |
% 87.74/12.40 | | | | | (193) all_156_0 = 0
% 87.74/12.40 | | | | |
% 87.74/12.40 | | | | | REDUCE: (152), (193) imply:
% 87.74/12.40 | | | | | (194) $false
% 87.74/12.40 | | | | |
% 87.74/12.40 | | | | | CLOSE: (194) is inconsistent.
% 87.74/12.40 | | | | |
% 87.74/12.40 | | | | Case 2:
% 87.74/12.40 | | | | |
% 87.74/12.40 | | | | | (195) ? [v0: any] : ? [v1: any] : (element(all_66_3, all_66_4) =
% 87.74/12.40 | | | | | v0 & empty(all_66_4) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 87.74/12.40 | | | | |
% 87.74/12.40 | | | | | DELTA: instantiating (195) with fresh symbols all_372_0, all_372_1
% 87.74/12.40 | | | | | gives:
% 87.74/12.40 | | | | | (196) element(all_66_3, all_66_4) = all_372_1 & empty(all_66_4) =
% 87.74/12.40 | | | | | all_372_0 & ( ~ (all_372_1 = 0) | all_372_0 = 0)
% 87.74/12.40 | | | | |
% 87.74/12.40 | | | | | ALPHA: (196) implies:
% 87.74/12.40 | | | | | (197) empty(all_66_4) = all_372_0
% 87.74/12.40 | | | | | (198) ~ (all_372_1 = 0) | all_372_0 = 0
% 87.74/12.40 | | | | |
% 87.74/12.40 | | | | | GROUND_INST: instantiating (22) with all_298_1, all_372_0, all_66_4,
% 87.74/12.40 | | | | | simplifying with (192), (197) gives:
% 87.74/12.40 | | | | | (199) all_372_0 = all_298_1
% 87.74/12.40 | | | | |
% 87.74/12.40 | | | | | BETA: splitting (62) gives:
% 87.74/12.40 | | | | |
% 87.74/12.40 | | | | | Case 1:
% 87.74/12.40 | | | | | |
% 87.74/12.40 | | | | | | (200) all_66_0 = 0 & ~ (all_66_1 = 0)
% 87.74/12.40 | | | | | |
% 87.74/12.40 | | | | | | ALPHA: (200) implies:
% 87.74/12.40 | | | | | | (201) all_66_0 = 0
% 87.74/12.40 | | | | | | (202) ~ (all_66_1 = 0)
% 87.74/12.40 | | | | | |
% 87.74/12.41 | | | | | | BETA: splitting (116) gives:
% 87.74/12.41 | | | | | |
% 87.74/12.41 | | | | | | Case 1:
% 87.74/12.41 | | | | | | |
% 87.74/12.41 | | | | | | | (203) ~ (all_134_1 = 0)
% 87.74/12.41 | | | | | | |
% 87.74/12.41 | | | | | | | REDUCE: (130), (203) imply:
% 87.74/12.41 | | | | | | | (204) $false
% 87.74/12.41 | | | | | | |
% 87.74/12.41 | | | | | | | CLOSE: (204) is inconsistent.
% 87.74/12.41 | | | | | | |
% 87.74/12.41 | | | | | | Case 2:
% 87.74/12.41 | | | | | | |
% 87.74/12.41 | | | | | | | (205) ~ (all_134_2 = 0) | (( ~ (all_134_0 = 0) | all_66_0 = 0)
% 87.74/12.41 | | | | | | | & ( ~ (all_66_0 = 0) | all_134_0 = 0))
% 87.74/12.41 | | | | | | |
% 87.74/12.41 | | | | | | | BETA: splitting (205) gives:
% 87.74/12.41 | | | | | | |
% 87.74/12.41 | | | | | | | Case 1:
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | | (206) ~ (all_134_2 = 0)
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | | REDUCE: (139), (206) imply:
% 87.74/12.41 | | | | | | | | (207) $false
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | | CLOSE: (207) is inconsistent.
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | Case 2:
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | | (208) ( ~ (all_134_0 = 0) | all_66_0 = 0) & ( ~ (all_66_0 =
% 87.74/12.41 | | | | | | | | 0) | all_134_0 = 0)
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | | ALPHA: (208) implies:
% 87.74/12.41 | | | | | | | | (209) ~ (all_66_0 = 0) | all_134_0 = 0
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | | BETA: splitting (209) gives:
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | | Case 1:
% 87.74/12.41 | | | | | | | | |
% 87.74/12.41 | | | | | | | | | (210) ~ (all_66_0 = 0)
% 87.74/12.41 | | | | | | | | |
% 87.74/12.41 | | | | | | | | | REDUCE: (201), (210) imply:
% 87.74/12.41 | | | | | | | | | (211) $false
% 87.74/12.41 | | | | | | | | |
% 87.74/12.41 | | | | | | | | | CLOSE: (211) is inconsistent.
% 87.74/12.41 | | | | | | | | |
% 87.74/12.41 | | | | | | | | Case 2:
% 87.74/12.41 | | | | | | | | |
% 87.74/12.41 | | | | | | | | | (212) all_134_0 = 0
% 87.74/12.41 | | | | | | | | |
% 87.74/12.41 | | | | | | | | | REDUCE: (115), (212) imply:
% 87.74/12.41 | | | | | | | | | (213) subset(all_66_3, all_66_2) = 0
% 87.74/12.41 | | | | | | | | |
% 87.74/12.41 | | | | | | | | | BETA: splitting (103) gives:
% 87.74/12.41 | | | | | | | | |
% 87.74/12.41 | | | | | | | | | Case 1:
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | REF_CLOSE: (13), (29), (54), (55), (56), (57), (80), (202),
% 87.74/12.41 | | | | | | | | | | (213) are inconsistent by sub-proof #1.
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | Case 2:
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | (214) all_106_1 = 0
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | COMBINE_EQS: (124), (214) imply:
% 87.74/12.41 | | | | | | | | | | (215) all_90_2 = 0
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | COMBINE_EQS: (172), (215) imply:
% 87.74/12.41 | | | | | | | | | | (216) all_200_1 = 0
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | BETA: splitting (163) gives:
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | Case 1:
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | (217) ~ (all_200_0 = 0)
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | REDUCE: (174), (217) imply:
% 87.74/12.41 | | | | | | | | | | | (218) $false
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | CLOSE: (218) is inconsistent.
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | Case 2:
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | (219) ~ (all_200_1 = 0) | ~ (all_200_2 = 0) | all_90_0
% 87.74/12.41 | | | | | | | | | | | = 0
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | BETA: splitting (219) gives:
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | Case 1:
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | (220) ~ (all_200_1 = 0)
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | REDUCE: (216), (220) imply:
% 87.74/12.41 | | | | | | | | | | | | (221) $false
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | CLOSE: (221) is inconsistent.
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | Case 2:
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | REF_CLOSE: (13), (29), (54), (55), (56), (57), (80), (202),
% 87.74/12.41 | | | | | | | | | | | | (213) are inconsistent by sub-proof #1.
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | End of split
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | End of split
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | End of split
% 87.74/12.41 | | | | | | | | |
% 87.74/12.41 | | | | | | | | End of split
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | End of split
% 87.74/12.41 | | | | | | |
% 87.74/12.41 | | | | | | End of split
% 87.74/12.41 | | | | | |
% 87.74/12.41 | | | | | Case 2:
% 87.74/12.41 | | | | | |
% 87.74/12.41 | | | | | | (222) all_66_1 = 0 & ~ (all_66_0 = 0)
% 87.74/12.41 | | | | | |
% 87.74/12.41 | | | | | | ALPHA: (222) implies:
% 87.74/12.41 | | | | | | (223) all_66_1 = 0
% 87.74/12.41 | | | | | | (224) ~ (all_66_0 = 0)
% 87.74/12.41 | | | | | |
% 87.74/12.41 | | | | | | REDUCE: (57), (223) imply:
% 87.74/12.41 | | | | | | (225) in(all_66_4, all_66_2) = 0
% 87.74/12.41 | | | | | |
% 87.74/12.41 | | | | | | BETA: splitting (171) gives:
% 87.74/12.41 | | | | | |
% 87.74/12.41 | | | | | | Case 1:
% 87.74/12.41 | | | | | | |
% 87.74/12.41 | | | | | | | (226) ~ (all_210_1 = 0)
% 87.74/12.41 | | | | | | |
% 87.74/12.41 | | | | | | | REDUCE: (178), (226) imply:
% 87.74/12.41 | | | | | | | (227) $false
% 87.74/12.41 | | | | | | |
% 87.74/12.41 | | | | | | | CLOSE: (227) is inconsistent.
% 87.74/12.41 | | | | | | |
% 87.74/12.41 | | | | | | Case 2:
% 87.74/12.41 | | | | | | |
% 87.74/12.41 | | | | | | | (228) ~ (all_210_2 = 0) | (( ~ (all_210_0 = 0) | all_134_0 =
% 87.74/12.41 | | | | | | | 0) & ( ~ (all_134_0 = 0) | all_210_0 = 0))
% 87.74/12.41 | | | | | | |
% 87.74/12.41 | | | | | | | BETA: splitting (228) gives:
% 87.74/12.41 | | | | | | |
% 87.74/12.41 | | | | | | | Case 1:
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | | (229) ~ (all_210_2 = 0)
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | | REDUCE: (177), (229) imply:
% 87.74/12.41 | | | | | | | | (230) $false
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | | CLOSE: (230) is inconsistent.
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | Case 2:
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | | (231) ( ~ (all_210_0 = 0) | all_134_0 = 0) & ( ~ (all_134_0 =
% 87.74/12.41 | | | | | | | | 0) | all_210_0 = 0)
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | | ALPHA: (231) implies:
% 87.74/12.41 | | | | | | | | (232) ~ (all_134_0 = 0) | all_210_0 = 0
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | | BETA: splitting (232) gives:
% 87.74/12.41 | | | | | | | |
% 87.74/12.41 | | | | | | | | Case 1:
% 87.74/12.41 | | | | | | | | |
% 87.74/12.41 | | | | | | | | | (233) ~ (all_134_0 = 0)
% 87.74/12.41 | | | | | | | | |
% 87.74/12.41 | | | | | | | | | BETA: splitting (149) gives:
% 87.74/12.41 | | | | | | | | |
% 87.74/12.41 | | | | | | | | | Case 1:
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | (234) all_134_0 = 0
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | REDUCE: (233), (234) imply:
% 87.74/12.41 | | | | | | | | | | (235) $false
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | CLOSE: (235) is inconsistent.
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | Case 2:
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | (236) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 87.74/12.41 | | | | | | | | | | all_66_2) = v1 & in(v0, all_66_3) = 0 & $i(v0))
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | DELTA: instantiating (236) with fresh symbols all_465_0,
% 87.74/12.41 | | | | | | | | | | all_465_1 gives:
% 87.74/12.41 | | | | | | | | | | (237) ~ (all_465_0 = 0) & in(all_465_1, all_66_2) =
% 87.74/12.41 | | | | | | | | | | all_465_0 & in(all_465_1, all_66_3) = 0 &
% 87.74/12.41 | | | | | | | | | | $i(all_465_1)
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | ALPHA: (237) implies:
% 87.74/12.41 | | | | | | | | | | (238) ~ (all_465_0 = 0)
% 87.74/12.41 | | | | | | | | | | (239) $i(all_465_1)
% 87.74/12.41 | | | | | | | | | | (240) in(all_465_1, all_66_2) = all_465_0
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | BETA: splitting (148) gives:
% 87.74/12.41 | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | Case 1:
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | (241) all_134_0 = 0
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | REDUCE: (233), (241) imply:
% 87.74/12.41 | | | | | | | | | | | (242) $false
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | CLOSE: (242) is inconsistent.
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | Case 2:
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | (243) ? [v0: any] : ? [v1: any] : (subset(all_78_0,
% 87.74/12.41 | | | | | | | | | | | all_66_2) = v1 & subset(all_66_4, all_66_2) =
% 87.74/12.41 | | | | | | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | DELTA: instantiating (243) with fresh symbols all_475_0,
% 87.74/12.41 | | | | | | | | | | | all_475_1 gives:
% 87.74/12.41 | | | | | | | | | | | (244) subset(all_78_0, all_66_2) = all_475_0 &
% 87.74/12.41 | | | | | | | | | | | subset(all_66_4, all_66_2) = all_475_1 & ( ~
% 87.74/12.41 | | | | | | | | | | | (all_475_0 = 0) | ~ (all_475_1 = 0))
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | ALPHA: (244) implies:
% 87.74/12.41 | | | | | | | | | | | (245) subset(all_66_4, all_66_2) = all_475_1
% 87.74/12.41 | | | | | | | | | | | (246) subset(all_78_0, all_66_2) = all_475_0
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | BETA: splitting (189) gives:
% 87.74/12.41 | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | Case 1:
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | (247) all_134_0 = 0
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | REDUCE: (233), (247) imply:
% 87.74/12.41 | | | | | | | | | | | | (248) $false
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | CLOSE: (248) is inconsistent.
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | Case 2:
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | (249) ? [v0: any] : ? [v1: any] : (subset(all_78_0,
% 87.74/12.41 | | | | | | | | | | | | all_66_2) = v0 & subset(all_66_4, all_66_2) =
% 87.74/12.41 | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | DELTA: instantiating (249) with fresh symbols all_480_0,
% 87.74/12.41 | | | | | | | | | | | | all_480_1 gives:
% 87.74/12.41 | | | | | | | | | | | | (250) subset(all_78_0, all_66_2) = all_480_1 &
% 87.74/12.41 | | | | | | | | | | | | subset(all_66_4, all_66_2) = all_480_0 & ( ~
% 87.74/12.41 | | | | | | | | | | | | (all_480_0 = 0) | ~ (all_480_1 = 0))
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | ALPHA: (250) implies:
% 87.74/12.41 | | | | | | | | | | | | (251) subset(all_66_4, all_66_2) = all_480_0
% 87.74/12.41 | | | | | | | | | | | | (252) subset(all_78_0, all_66_2) = all_480_1
% 87.74/12.41 | | | | | | | | | | | | (253) ~ (all_480_0 = 0) | ~ (all_480_1 = 0)
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_475_1, all_480_0,
% 87.74/12.41 | | | | | | | | | | | | all_66_2, all_66_4, simplifying with (245), (251)
% 87.74/12.41 | | | | | | | | | | | | gives:
% 87.74/12.41 | | | | | | | | | | | | (254) all_480_0 = all_475_1
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_475_0, all_480_1,
% 87.74/12.41 | | | | | | | | | | | | all_66_2, all_78_0, simplifying with (246), (252)
% 87.74/12.41 | | | | | | | | | | | | gives:
% 87.74/12.41 | | | | | | | | | | | | (255) all_480_1 = all_475_0
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | BETA: splitting (166) gives:
% 87.74/12.41 | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | Case 1:
% 87.74/12.41 | | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | | (256) ~ (all_204_0 = 0)
% 87.74/12.41 | | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | | REDUCE: (173), (256) imply:
% 87.74/12.41 | | | | | | | | | | | | | (257) $false
% 87.74/12.41 | | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | | CLOSE: (257) is inconsistent.
% 87.74/12.41 | | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | Case 2:
% 87.74/12.41 | | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_66_2, all_66_4,
% 87.74/12.41 | | | | | | | | | | | | | simplifying with (54), (56), (75), (225) gives:
% 87.74/12.41 | | | | | | | | | | | | | (258) subset(all_66_4, all_66_2) = 0
% 87.74/12.41 | | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_465_1, all_66_2,
% 87.74/12.41 | | | | | | | | | | | | | all_465_0, simplifying with (56), (239), (240)
% 87.74/12.41 | | | | | | | | | | | | | gives:
% 87.74/12.41 | | | | | | | | | | | | | (259) all_465_0 = 0 | ? [v0: any] : ? [v1: any] :
% 87.74/12.41 | | | | | | | | | | | | | (element(all_465_1, all_66_2) = v0 &
% 87.74/12.41 | | | | | | | | | | | | | empty(all_66_2) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 87.74/12.41 | | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_78_0, all_66_2,
% 87.74/12.41 | | | | | | | | | | | | | all_475_0, simplifying with (56), (90), (246)
% 87.74/12.41 | | | | | | | | | | | | | gives:
% 87.74/12.41 | | | | | | | | | | | | | (260) all_475_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~
% 87.74/12.41 | | | | | | | | | | | | | (v1 = 0) & in(v0, all_78_0) = 0 & in(v0,
% 87.74/12.41 | | | | | | | | | | | | | all_66_2) = v1 & $i(v0))
% 87.74/12.41 | | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | | BETA: splitting (259) gives:
% 87.74/12.41 | | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | | Case 1:
% 87.74/12.41 | | | | | | | | | | | | | |
% 87.74/12.41 | | | | | | | | | | | | | | (261) all_465_0 = 0
% 87.74/12.41 | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | REDUCE: (238), (261) imply:
% 87.74/12.42 | | | | | | | | | | | | | | (262) $false
% 87.74/12.42 | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | CLOSE: (262) is inconsistent.
% 87.74/12.42 | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | Case 2:
% 87.74/12.42 | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_475_1, 0, all_66_2,
% 87.74/12.42 | | | | | | | | | | | | | | all_66_4, simplifying with (245), (258) gives:
% 87.74/12.42 | | | | | | | | | | | | | | (263) all_475_1 = 0
% 87.74/12.42 | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | COMBINE_EQS: (254), (263) imply:
% 87.74/12.42 | | | | | | | | | | | | | | (264) all_480_0 = 0
% 87.74/12.42 | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 87.74/12.42 | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | Case 1:
% 87.74/12.42 | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | (265) ~ (all_480_0 = 0)
% 87.74/12.42 | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | REDUCE: (264), (265) imply:
% 87.74/12.42 | | | | | | | | | | | | | | | (266) $false
% 87.74/12.42 | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | CLOSE: (266) is inconsistent.
% 87.74/12.42 | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | Case 2:
% 87.74/12.42 | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | (267) ~ (all_480_1 = 0)
% 87.74/12.42 | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | REDUCE: (255), (267) imply:
% 87.74/12.42 | | | | | | | | | | | | | | | (268) ~ (all_475_0 = 0)
% 87.74/12.42 | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 87.74/12.42 | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | Case 1:
% 87.74/12.42 | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | (269) all_475_0 = 0
% 87.74/12.42 | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | REDUCE: (268), (269) imply:
% 87.74/12.42 | | | | | | | | | | | | | | | | (270) $false
% 87.74/12.42 | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | CLOSE: (270) is inconsistent.
% 87.74/12.42 | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | Case 2:
% 87.74/12.42 | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | (271) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 87.74/12.42 | | | | | | | | | | | | | | | | all_78_0) = 0 & in(v0, all_66_2) = v1 &
% 87.74/12.42 | | | | | | | | | | | | | | | | $i(v0))
% 87.74/12.42 | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | DELTA: instantiating (271) with fresh symbols all_857_0,
% 87.74/12.42 | | | | | | | | | | | | | | | | all_857_1 gives:
% 87.74/12.42 | | | | | | | | | | | | | | | | (272) ~ (all_857_0 = 0) & in(all_857_1, all_78_0) = 0 &
% 87.74/12.42 | | | | | | | | | | | | | | | | in(all_857_1, all_66_2) = all_857_0 &
% 87.74/12.42 | | | | | | | | | | | | | | | | $i(all_857_1)
% 87.74/12.42 | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | ALPHA: (272) implies:
% 87.74/12.42 | | | | | | | | | | | | | | | | (273) ~ (all_857_0 = 0)
% 87.74/12.42 | | | | | | | | | | | | | | | | (274) $i(all_857_1)
% 87.74/12.42 | | | | | | | | | | | | | | | | (275) in(all_857_1, all_66_2) = all_857_0
% 87.74/12.42 | | | | | | | | | | | | | | | | (276) in(all_857_1, all_78_0) = 0
% 87.74/12.42 | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 87.74/12.42 | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | Case 1:
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_66_4, all_78_0,
% 87.74/12.42 | | | | | | | | | | | | | | | | | all_857_1, simplifying with (54), (90), (92),
% 87.74/12.42 | | | | | | | | | | | | | | | | | (274), (276) gives:
% 87.74/12.42 | | | | | | | | | | | | | | | | | (277) all_857_1 = all_66_4
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | REDUCE: (275), (277) imply:
% 87.74/12.42 | | | | | | | | | | | | | | | | | (278) in(all_66_4, all_66_2) = all_857_0
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_857_0, all_66_2,
% 87.74/12.42 | | | | | | | | | | | | | | | | | all_66_4, simplifying with (225), (278) gives:
% 87.74/12.42 | | | | | | | | | | | | | | | | | (279) all_857_0 = 0
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | REDUCE: (273), (279) imply:
% 87.74/12.42 | | | | | | | | | | | | | | | | | (280) $false
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | CLOSE: (280) is inconsistent.
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | Case 2:
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | (281) all_372_0 = 0
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | COMBINE_EQS: (199), (281) imply:
% 87.74/12.42 | | | | | | | | | | | | | | | | | (282) all_298_1 = 0
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | SIMP: (282) implies:
% 87.74/12.42 | | | | | | | | | | | | | | | | | (283) all_298_1 = 0
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | REDUCE: (192), (283) imply:
% 87.74/12.42 | | | | | | | | | | | | | | | | | (284) empty(all_66_4) = 0
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_66_4, all_78_0,
% 87.74/12.42 | | | | | | | | | | | | | | | | | all_857_1, simplifying with (54), (90), (92),
% 87.74/12.42 | | | | | | | | | | | | | | | | | (274), (276) gives:
% 87.74/12.42 | | | | | | | | | | | | | | | | | (285) all_857_1 = all_66_4
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_66_4, simplifying with
% 87.74/12.42 | | | | | | | | | | | | | | | | | (54), (284) gives:
% 87.74/12.42 | | | | | | | | | | | | | | | | | (286) all_66_4 = empty_set
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | COMBINE_EQS: (285), (286) imply:
% 87.74/12.42 | | | | | | | | | | | | | | | | | (287) all_857_1 = empty_set
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | REDUCE: (275), (287) imply:
% 87.74/12.42 | | | | | | | | | | | | | | | | | (288) in(empty_set, all_66_2) = all_857_0
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | REDUCE: (225), (286) imply:
% 87.74/12.42 | | | | | | | | | | | | | | | | | (289) in(empty_set, all_66_2) = 0
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with 0, all_857_0, all_66_2,
% 87.74/12.42 | | | | | | | | | | | | | | | | | empty_set, simplifying with (288), (289) gives:
% 87.74/12.42 | | | | | | | | | | | | | | | | | (290) all_857_0 = 0
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | REDUCE: (273), (290) imply:
% 87.74/12.42 | | | | | | | | | | | | | | | | | (291) $false
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | | CLOSE: (291) is inconsistent.
% 87.74/12.42 | | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | | End of split
% 87.74/12.42 | | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | | End of split
% 87.74/12.42 | | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | | End of split
% 87.74/12.42 | | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | | End of split
% 87.74/12.42 | | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | | End of split
% 87.74/12.42 | | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | | End of split
% 87.74/12.42 | | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | | End of split
% 87.74/12.42 | | | | | | | | | |
% 87.74/12.42 | | | | | | | | | End of split
% 87.74/12.42 | | | | | | | | |
% 87.74/12.42 | | | | | | | | Case 2:
% 87.74/12.42 | | | | | | | | |
% 87.74/12.42 | | | | | | | | | (292) all_210_0 = 0
% 87.74/12.42 | | | | | | | | |
% 87.74/12.42 | | | | | | | | | COMBINE_EQS: (180), (292) imply:
% 87.74/12.42 | | | | | | | | | (293) all_66_0 = 0
% 87.74/12.42 | | | | | | | | |
% 87.74/12.42 | | | | | | | | | SIMP: (293) implies:
% 87.74/12.42 | | | | | | | | | (294) all_66_0 = 0
% 87.74/12.42 | | | | | | | | |
% 87.74/12.42 | | | | | | | | | REDUCE: (224), (294) imply:
% 87.74/12.42 | | | | | | | | | (295) $false
% 87.74/12.42 | | | | | | | | |
% 87.74/12.42 | | | | | | | | | CLOSE: (295) is inconsistent.
% 87.74/12.42 | | | | | | | | |
% 87.74/12.42 | | | | | | | | End of split
% 87.74/12.42 | | | | | | | |
% 87.74/12.42 | | | | | | | End of split
% 87.74/12.42 | | | | | | |
% 87.74/12.42 | | | | | | End of split
% 87.74/12.42 | | | | | |
% 87.74/12.42 | | | | | End of split
% 87.74/12.42 | | | | |
% 87.74/12.42 | | | | End of split
% 87.74/12.42 | | | |
% 87.74/12.42 | | | End of split
% 87.74/12.42 | | |
% 87.74/12.42 | | End of split
% 87.74/12.42 | |
% 87.74/12.42 | End of split
% 87.74/12.42 |
% 87.74/12.42 End of proof
% 87.74/12.42
% 87.74/12.42 Sub-proof #1 shows that the following formulas are inconsistent:
% 87.74/12.42 ----------------------------------------------------------------
% 87.74/12.42 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 87.74/12.42 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 87.74/12.42 (2) subset(all_66_3, all_66_2) = 0
% 87.74/12.42 (3) ~ (all_66_1 = 0)
% 87.74/12.42 (4) in(all_66_4, all_66_3) = 0
% 87.74/12.42 (5) $i(all_66_3)
% 87.74/12.42 (6) $i(all_66_2)
% 87.74/12.42 (7) in(all_66_4, all_66_2) = all_66_1
% 87.74/12.42 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 87.74/12.42 (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) = 0)
% 87.74/12.42 (9) $i(all_66_4)
% 87.74/12.42
% 87.74/12.42 Begin of proof
% 87.74/12.42 |
% 87.74/12.42 | GROUND_INST: instantiating (8) with all_66_3, all_66_2, all_66_4, simplifying
% 87.74/12.42 | with (2), (4), (5), (6), (9) gives:
% 87.74/12.42 | (10) in(all_66_4, all_66_2) = 0
% 87.74/12.42 |
% 87.74/12.42 | GROUND_INST: instantiating (1) with all_66_1, 0, all_66_2, all_66_4,
% 87.74/12.42 | simplifying with (7), (10) gives:
% 87.74/12.42 | (11) all_66_1 = 0
% 87.74/12.42 |
% 87.74/12.42 | REDUCE: (3), (11) imply:
% 87.74/12.42 | (12) $false
% 87.74/12.42 |
% 87.74/12.42 | CLOSE: (12) is inconsistent.
% 87.74/12.42 |
% 87.74/12.42 End of proof
% 87.74/12.42 % SZS output end Proof for theBenchmark
% 87.74/12.42
% 87.74/12.42 11841ms
%------------------------------------------------------------------------------