TSTP Solution File: SET677+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET677+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n026.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 15:25:57 EDT 2023
% Result : Theorem 43.49s 6.59s
% Output : Proof 142.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET677+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 10:23:03 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.56/1.21 Prover 4: Preprocessing ...
% 3.56/1.21 Prover 1: Preprocessing ...
% 3.74/1.25 Prover 3: Preprocessing ...
% 3.74/1.25 Prover 6: Preprocessing ...
% 3.74/1.25 Prover 2: Preprocessing ...
% 3.74/1.25 Prover 5: Preprocessing ...
% 3.74/1.26 Prover 0: Preprocessing ...
% 9.26/2.08 Prover 1: Constructing countermodel ...
% 9.26/2.09 Prover 3: Constructing countermodel ...
% 9.26/2.10 Prover 6: Proving ...
% 9.26/2.13 Prover 5: Proving ...
% 9.26/2.15 Prover 2: Proving ...
% 12.72/2.55 Prover 4: Constructing countermodel ...
% 14.43/2.77 Prover 0: Proving ...
% 43.49/6.59 Prover 0: proved (5959ms)
% 43.49/6.59
% 43.49/6.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.49/6.59
% 43.49/6.60 Prover 3: stopped
% 43.49/6.61 Prover 5: stopped
% 43.49/6.62 Prover 2: stopped
% 43.49/6.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 43.49/6.63 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 43.49/6.63 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 43.49/6.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 43.49/6.64 Prover 6: stopped
% 44.19/6.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 44.19/6.69 Prover 7: Preprocessing ...
% 44.53/6.71 Prover 10: Preprocessing ...
% 44.53/6.72 Prover 8: Preprocessing ...
% 45.37/6.81 Prover 11: Preprocessing ...
% 45.37/6.82 Prover 13: Preprocessing ...
% 45.69/6.85 Prover 10: Warning: ignoring some quantifiers
% 45.69/6.86 Prover 10: Constructing countermodel ...
% 45.69/6.88 Prover 7: Warning: ignoring some quantifiers
% 45.69/6.90 Prover 7: Constructing countermodel ...
% 45.69/6.94 Prover 8: Warning: ignoring some quantifiers
% 46.37/6.95 Prover 8: Constructing countermodel ...
% 46.74/7.00 Prover 13: Warning: ignoring some quantifiers
% 46.74/7.02 Prover 13: Constructing countermodel ...
% 49.21/7.35 Prover 11: Constructing countermodel ...
% 50.16/7.46 Prover 10: gave up
% 50.16/7.47 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 50.91/7.55 Prover 16: Preprocessing ...
% 51.52/7.62 Prover 16: Warning: ignoring some quantifiers
% 51.52/7.63 Prover 16: Constructing countermodel ...
% 79.52/11.35 Prover 13: stopped
% 79.89/11.42 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 80.56/11.47 Prover 19: Preprocessing ...
% 82.20/11.70 Prover 19: Warning: ignoring some quantifiers
% 82.20/11.71 Prover 19: Constructing countermodel ...
% 95.57/13.49 Prover 16: stopped
% 108.97/15.32 Prover 19: stopped
% 113.87/15.97 Prover 1: stopped
% 139.90/20.78 Prover 4: Found proof (size 330)
% 139.90/20.78 Prover 4: proved (20146ms)
% 139.90/20.78 Prover 8: stopped
% 139.90/20.78 Prover 7: stopped
% 139.90/20.79 Prover 11: stopped
% 139.90/20.79
% 139.90/20.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 139.90/20.79
% 140.76/20.83 % SZS output start Proof for theBenchmark
% 140.76/20.84 Assumptions after simplification:
% 140.76/20.84 ---------------------------------
% 140.76/20.84
% 140.76/20.84 (p1)
% 140.76/20.89 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 140.76/20.89 (identity_relation_of(v1) = v2) | ~ (ilf_type(v0, set_type) = 0) | ~
% 140.76/20.89 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : (relation_type(v1, v0) =
% 140.76/20.89 v4 & ilf_type(v1, set_type) = v3 & $i(v4) & ( ~ (v3 = 0) | ( ! [v5: $i] :
% 140.76/20.89 ! [v6: $i] : ( ~ (domain(v1, v0, v5) = v6) | ~ $i(v5) | ? [v7: any]
% 140.76/20.89 : ? [v8: any] : ? [v9: $i] : ? [v10: any] : (ilf_type(v5, v4) =
% 140.76/20.89 v7 & range(v1, v0, v5) = v9 & subset(v2, v5) = v8 & subset(v1, v9)
% 140.76/20.89 = v10 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = 0 & v6 =
% 140.76/20.89 v1)))) & ! [v5: $i] : ! [v6: $i] : ( ~ (range(v1, v0, v5) =
% 140.76/20.89 v6) | ~ $i(v5) | ? [v7: any] : ? [v8: any] : ? [v9: $i] : ?
% 140.76/20.89 [v10: any] : (ilf_type(v5, v4) = v7 & domain(v1, v0, v5) = v9 &
% 140.76/20.89 subset(v2, v5) = v8 & subset(v1, v6) = v10 & $i(v9) & ( ~ (v8 = 0)
% 140.76/20.89 | ~ (v7 = 0) | (v10 = 0 & v9 = v1)))) & ! [v5: $i] : ( ~
% 140.76/20.89 (ilf_type(v5, v4) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: $i] : ?
% 140.76/20.89 [v8: $i] : ? [v9: any] : (domain(v1, v0, v5) = v7 & range(v1, v0,
% 140.76/20.89 v5) = v8 & subset(v2, v5) = v6 & subset(v1, v8) = v9 & $i(v8) &
% 140.76/20.89 $i(v7) & ( ~ (v6 = 0) | (v9 = 0 & v7 = v1)))) & ! [v5: $i] : ( ~
% 140.76/20.89 (subset(v2, v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: $i] : ?
% 140.76/20.89 [v8: $i] : ? [v9: any] : (ilf_type(v5, v4) = v6 & domain(v1, v0,
% 140.76/20.89 v5) = v7 & range(v1, v0, v5) = v8 & subset(v1, v8) = v9 & $i(v8)
% 140.76/20.89 & $i(v7) & ( ~ (v6 = 0) | (v9 = 0 & v7 = v1)))))))) & ! [v0: $i]
% 140.76/20.89 : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_type(v1, v0) = v2) | ~
% 140.76/20.89 (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ?
% 140.76/20.89 [v4: $i] : (identity_relation_of(v1) = v4 & ilf_type(v1, set_type) = v3 &
% 140.76/20.89 $i(v4) & ( ~ (v3 = 0) | ( ! [v5: $i] : ! [v6: $i] : ( ~ (domain(v1, v0,
% 140.76/20.89 v5) = v6) | ~ $i(v5) | ? [v7: any] : ? [v8: any] : ? [v9:
% 140.76/20.89 $i] : ? [v10: any] : (ilf_type(v5, v2) = v7 & range(v1, v0, v5) =
% 140.76/20.89 v9 & subset(v4, v5) = v8 & subset(v1, v9) = v10 & $i(v9) & ( ~ (v8
% 140.76/20.89 = 0) | ~ (v7 = 0) | (v10 = 0 & v6 = v1)))) & ! [v5: $i] : !
% 140.76/20.89 [v6: $i] : ( ~ (range(v1, v0, v5) = v6) | ~ $i(v5) | ? [v7: any] :
% 140.76/20.89 ? [v8: any] : ? [v9: $i] : ? [v10: any] : (ilf_type(v5, v2) = v7 &
% 140.76/20.89 domain(v1, v0, v5) = v9 & subset(v4, v5) = v8 & subset(v1, v6) =
% 140.76/20.89 v10 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = 0 & v9 = v1))))
% 140.76/20.89 & ! [v5: $i] : ( ~ (ilf_type(v5, v2) = 0) | ~ $i(v5) | ? [v6: any]
% 140.76/20.89 : ? [v7: $i] : ? [v8: $i] : ? [v9: any] : (domain(v1, v0, v5) =
% 140.76/20.89 v7 & range(v1, v0, v5) = v8 & subset(v4, v5) = v6 & subset(v1, v8)
% 140.76/20.89 = v9 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | (v9 = 0 & v7 = v1)))) & !
% 140.76/20.89 [v5: $i] : ( ~ (subset(v4, v5) = 0) | ~ $i(v5) | ? [v6: any] : ?
% 140.76/20.89 [v7: $i] : ? [v8: $i] : ? [v9: any] : (ilf_type(v5, v2) = v6 &
% 140.76/20.89 domain(v1, v0, v5) = v7 & range(v1, v0, v5) = v8 & subset(v1, v8)
% 140.76/20.89 = v9 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | (v9 = 0 & v7 = v1))))))))
% 140.76/20.89 & ! [v0: $i] : ! [v1: $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~
% 140.76/20.89 (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3:
% 140.76/20.89 $i] : (identity_relation_of(v1) = v3 & relation_type(v1, v0) = v2 & $i(v3)
% 140.76/20.89 & $i(v2) & ! [v4: $i] : ! [v5: $i] : ( ~ (domain(v1, v0, v4) = v5) | ~
% 140.76/20.89 $i(v4) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] :
% 140.76/20.89 (ilf_type(v4, v2) = v6 & range(v1, v0, v4) = v8 & subset(v3, v4) = v7 &
% 140.76/20.89 subset(v1, v8) = v9 & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | (v9 = 0 &
% 140.76/20.89 v5 = v1)))) & ! [v4: $i] : ! [v5: $i] : ( ~ (range(v1, v0, v4) =
% 141.09/20.89 v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9:
% 141.09/20.89 any] : (ilf_type(v4, v2) = v6 & domain(v1, v0, v4) = v8 & subset(v3,
% 141.09/20.89 v4) = v7 & subset(v1, v5) = v9 & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0)
% 141.09/20.89 | (v9 = 0 & v8 = v1)))) & ! [v4: $i] : ( ~ (ilf_type(v4, v2) = 0) |
% 141.09/20.89 ~ $i(v4) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] :
% 141.09/20.89 (domain(v1, v0, v4) = v6 & range(v1, v0, v4) = v7 & subset(v3, v4) = v5
% 141.09/20.89 & subset(v1, v7) = v8 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | (v8 = 0 & v6
% 141.09/20.89 = v1)))) & ! [v4: $i] : ( ~ (subset(v3, v4) = 0) | ~ $i(v4) | ?
% 141.09/20.89 [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : (ilf_type(v4, v2)
% 141.09/20.89 = v5 & domain(v1, v0, v4) = v6 & range(v1, v0, v4) = v7 & subset(v1,
% 141.09/20.89 v7) = v8 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | (v8 = 0 & v6 = v1))))))
% 141.09/20.89
% 141.09/20.89 (p14)
% 141.09/20.90 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 141.09/20.90 (cross_product(v0, v1) = v2) | ~ (ilf_type(v0, set_type) = 0) | ~ $i(v1) |
% 141.09/20.90 ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : (subset_type(v2) = v4
% 141.09/20.90 & relation_type(v0, v1) = v5 & ilf_type(v1, set_type) = v3 & $i(v5) &
% 141.09/20.90 $i(v4) & ( ~ (v3 = 0) | ( ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~
% 141.09/20.90 (ilf_type(v6, v5) = v7) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) &
% 141.09/20.90 ilf_type(v6, v4) = v8)) & ! [v6: $i] : ! [v7: int] : (v7 = 0 |
% 141.09/20.90 ~ (ilf_type(v6, v4) = v7) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0)
% 141.09/20.90 & ilf_type(v6, v5) = v8)) & ! [v6: $i] : ( ~ (ilf_type(v6, v5) =
% 141.09/20.90 0) | ~ $i(v6) | ilf_type(v6, v4) = 0) & ! [v6: $i] : ( ~
% 141.09/20.90 (ilf_type(v6, v4) = 0) | ~ $i(v6) | ilf_type(v6, v5) = 0))))) & !
% 141.09/20.90 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_type(v0, v1) = v2) | ~
% 141.09/20.90 (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ?
% 141.09/20.90 [v4: $i] : ? [v5: $i] : (cross_product(v0, v1) = v4 & subset_type(v4) = v5
% 141.09/20.90 & ilf_type(v1, set_type) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | ( ! [v6:
% 141.09/20.90 $i] : ! [v7: int] : (v7 = 0 | ~ (ilf_type(v6, v5) = v7) | ~
% 141.09/20.90 $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & ilf_type(v6, v2) = v8)) & !
% 141.09/20.90 [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (ilf_type(v6, v2) = v7) | ~
% 141.09/20.90 $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & ilf_type(v6, v5) = v8)) & !
% 141.09/20.90 [v6: $i] : ( ~ (ilf_type(v6, v5) = 0) | ~ $i(v6) | ilf_type(v6, v2) =
% 141.09/20.90 0) & ! [v6: $i] : ( ~ (ilf_type(v6, v2) = 0) | ~ $i(v6) |
% 141.09/20.90 ilf_type(v6, v5) = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 141.09/20.90 (ilf_type(v1, set_type) = 0) | ~ (ilf_type(v0, set_type) = 0) | ~ $i(v1) |
% 141.09/20.90 ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (cross_product(v0, v1)
% 141.09/20.90 = v2 & subset_type(v2) = v3 & relation_type(v0, v1) = v4 & $i(v4) & $i(v3)
% 141.09/20.90 & $i(v2) & ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (ilf_type(v5, v4) =
% 141.09/20.90 v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & ilf_type(v5, v3) =
% 141.09/20.90 v7)) & ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (ilf_type(v5, v3) =
% 141.09/20.90 v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & ilf_type(v5, v4) =
% 141.09/20.90 v7)) & ! [v5: $i] : ( ~ (ilf_type(v5, v4) = 0) | ~ $i(v5) |
% 141.09/20.90 ilf_type(v5, v3) = 0) & ! [v5: $i] : ( ~ (ilf_type(v5, v3) = 0) | ~
% 141.09/20.90 $i(v5) | ilf_type(v5, v4) = 0)))
% 141.09/20.90
% 141.09/20.90 (p15)
% 141.09/20.91 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 141.09/20.91 (relation_type(v1, v0) = v2) | ~ (ilf_type(v0, set_type) = 0) | ~ $i(v1) |
% 141.09/20.91 ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ($i(v4) & ((v5 = 0 &
% 141.09/20.91 ilf_type(v4, v2) = 0) | ( ~ (v3 = 0) & ilf_type(v1, set_type) = v3))))
% 141.09/20.91 & ! [v0: $i] : ! [v1: $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~
% 141.09/20.91 (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3:
% 141.09/20.91 $i] : (relation_type(v1, v0) = v2 & ilf_type(v3, v2) = 0 & $i(v3) &
% 141.09/20.91 $i(v2)))
% 141.09/20.91
% 141.09/20.91 (p18)
% 141.09/20.92 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 =
% 141.09/20.92 0 | ~ (member(v2, v1) = v3) | ~ (ilf_type(v0, set_type) = 0) | ~
% 141.09/20.92 (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ?
% 141.09/20.92 [v5: any] : (( ~ (v4 = 0) & ilf_type(v1, set_type) = v4) | (member(v2, v0) =
% 141.09/20.92 v5 & ilf_type(v2, set_type) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & !
% 141.09/20.92 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (ilf_type(v0, set_type) =
% 141.09/20.92 0) | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ?
% 141.09/20.92 [v4: $i] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ($i(v4) & ((v6 = 0 &
% 141.09/20.92 v5 = 0 & ~ (v7 = 0) & member(v4, v1) = v7 & member(v4, v0) = 0 &
% 141.09/20.92 ilf_type(v4, set_type) = 0) | ( ~ (v3 = 0) & ilf_type(v1, set_type) =
% 141.09/20.92 v3)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (member(v2, v0)
% 141.09/20.92 = 0) | ~ (ilf_type(v0, set_type) = 0) | ~ (subset(v0, v1) = 0) | ~
% 141.09/20.92 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: any] : (( ~ (v3 = 0)
% 141.09/20.92 & ilf_type(v1, set_type) = v3) | (member(v2, v1) = v4 & ilf_type(v2,
% 141.09/20.92 set_type) = v3 & ( ~ (v3 = 0) | v4 = 0)))) & ! [v0: $i] : ! [v1: $i]
% 141.09/20.92 : ! [v2: $i] : ( ~ (ilf_type(v2, set_type) = 0) | ~ (ilf_type(v0, set_type)
% 141.09/20.92 = 0) | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 141.09/20.92 [v3: int] : ? [v4: any] : (( ~ (v3 = 0) & ilf_type(v1, set_type) = v3) |
% 141.09/20.92 (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))) &
% 141.09/20.92 ! [v0: $i] : ! [v1: $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~ (ilf_type(v0,
% 141.09/20.92 set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ?
% 141.09/20.92 [v4: int] : ? [v5: int] : ? [v6: int] : (subset(v0, v1) = v2 & $i(v3) & (
% 141.09/20.92 ~ (v2 = 0) | ( ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ (member(v7, v1)
% 141.09/20.92 = v8) | ~ $i(v7) | ? [v9: any] : ? [v10: any] : (member(v7, v0)
% 141.09/20.92 = v10 & ilf_type(v7, set_type) = v9 & ( ~ (v10 = 0) | ~ (v9 =
% 141.09/20.92 0)))) & ! [v7: $i] : ( ~ (member(v7, v0) = 0) | ~ $i(v7) |
% 141.09/20.92 ? [v8: any] : ? [v9: any] : (member(v7, v1) = v9 & ilf_type(v7,
% 141.09/20.92 set_type) = v8 & ( ~ (v8 = 0) | v9 = 0))) & ! [v7: $i] : ( ~
% 141.09/20.92 (ilf_type(v7, set_type) = 0) | ~ $i(v7) | ? [v8: any] : ? [v9:
% 141.09/20.92 any] : (member(v7, v1) = v9 & member(v7, v0) = v8 & ( ~ (v8 = 0) |
% 141.09/20.92 v9 = 0))))) & (v2 = 0 | (v5 = 0 & v4 = 0 & ~ (v6 = 0) &
% 141.09/20.92 member(v3, v1) = v6 & member(v3, v0) = 0 & ilf_type(v3, set_type) =
% 141.09/20.92 0))))
% 141.09/20.92
% 141.09/20.92 (p2)
% 141.09/20.93 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 141.09/20.93 (identity_relation_of(v1) = v2) | ~ (ilf_type(v0, set_type) = 0) | ~
% 141.09/20.93 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : (relation_type(v0, v1) =
% 141.09/20.93 v4 & ilf_type(v1, set_type) = v3 & $i(v4) & ( ~ (v3 = 0) | ( ! [v5: $i] :
% 141.09/20.93 ! [v6: $i] : ( ~ (domain(v0, v1, v5) = v6) | ~ $i(v5) | ? [v7: any]
% 141.09/20.93 : ? [v8: any] : ? [v9: any] : ? [v10: $i] : (ilf_type(v5, v4) =
% 141.09/20.93 v7 & range(v0, v1, v5) = v10 & subset(v2, v5) = v8 & subset(v1,
% 141.09/20.93 v6) = v9 & $i(v10) & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = v1 & v9
% 141.09/20.93 = 0)))) & ! [v5: $i] : ! [v6: $i] : ( ~ (range(v0, v1, v5) =
% 141.09/20.93 v6) | ~ $i(v5) | ? [v7: any] : ? [v8: any] : ? [v9: $i] : ?
% 141.09/20.93 [v10: any] : (ilf_type(v5, v4) = v7 & domain(v0, v1, v5) = v9 &
% 141.09/20.93 subset(v2, v5) = v8 & subset(v1, v9) = v10 & $i(v9) & ( ~ (v8 = 0)
% 141.09/20.93 | ~ (v7 = 0) | (v10 = 0 & v6 = v1)))) & ! [v5: $i] : ( ~
% 141.09/20.93 (ilf_type(v5, v4) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: $i] : ?
% 141.09/20.93 [v8: any] : ? [v9: $i] : (domain(v0, v1, v5) = v7 & range(v0, v1,
% 141.09/20.93 v5) = v9 & subset(v2, v5) = v6 & subset(v1, v7) = v8 & $i(v9) &
% 141.09/20.93 $i(v7) & ( ~ (v6 = 0) | (v9 = v1 & v8 = 0)))) & ! [v5: $i] : ( ~
% 141.09/20.93 (subset(v2, v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: $i] : ?
% 141.09/20.93 [v8: any] : ? [v9: $i] : (ilf_type(v5, v4) = v6 & domain(v0, v1,
% 141.09/20.93 v5) = v7 & range(v0, v1, v5) = v9 & subset(v1, v7) = v8 & $i(v9)
% 141.09/20.93 & $i(v7) & ( ~ (v6 = 0) | (v9 = v1 & v8 = 0)))))))) & ! [v0: $i]
% 141.09/20.93 : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_type(v0, v1) = v2) | ~
% 141.09/20.93 (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ?
% 141.09/20.93 [v4: $i] : (identity_relation_of(v1) = v4 & ilf_type(v1, set_type) = v3 &
% 141.09/20.93 $i(v4) & ( ~ (v3 = 0) | ( ! [v5: $i] : ! [v6: $i] : ( ~ (domain(v0, v1,
% 141.09/20.93 v5) = v6) | ~ $i(v5) | ? [v7: any] : ? [v8: any] : ? [v9:
% 141.09/20.93 any] : ? [v10: $i] : (ilf_type(v5, v2) = v7 & range(v0, v1, v5) =
% 141.09/20.93 v10 & subset(v4, v5) = v8 & subset(v1, v6) = v9 & $i(v10) & ( ~
% 141.09/20.93 (v8 = 0) | ~ (v7 = 0) | (v10 = v1 & v9 = 0)))) & ! [v5: $i] :
% 141.09/20.93 ! [v6: $i] : ( ~ (range(v0, v1, v5) = v6) | ~ $i(v5) | ? [v7: any] :
% 141.09/20.93 ? [v8: any] : ? [v9: $i] : ? [v10: any] : (ilf_type(v5, v2) = v7
% 141.09/20.93 & domain(v0, v1, v5) = v9 & subset(v4, v5) = v8 & subset(v1, v9) =
% 141.09/20.93 v10 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = 0 & v6 = v1))))
% 141.09/20.93 & ! [v5: $i] : ( ~ (ilf_type(v5, v2) = 0) | ~ $i(v5) | ? [v6: any]
% 141.09/20.93 : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : (domain(v0, v1, v5) =
% 141.09/20.93 v7 & range(v0, v1, v5) = v9 & subset(v4, v5) = v6 & subset(v1, v7)
% 141.09/20.93 = v8 & $i(v9) & $i(v7) & ( ~ (v6 = 0) | (v9 = v1 & v8 = 0)))) & !
% 141.09/20.93 [v5: $i] : ( ~ (subset(v4, v5) = 0) | ~ $i(v5) | ? [v6: any] : ?
% 141.09/20.93 [v7: $i] : ? [v8: any] : ? [v9: $i] : (ilf_type(v5, v2) = v6 &
% 141.09/20.93 domain(v0, v1, v5) = v7 & range(v0, v1, v5) = v9 & subset(v1, v7)
% 141.09/20.93 = v8 & $i(v9) & $i(v7) & ( ~ (v6 = 0) | (v9 = v1 & v8 = 0))))))))
% 141.09/20.93 & ! [v0: $i] : ! [v1: $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~
% 141.09/20.93 (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3:
% 141.09/20.93 $i] : (identity_relation_of(v1) = v3 & relation_type(v0, v1) = v2 & $i(v3)
% 141.09/20.93 & $i(v2) & ! [v4: $i] : ! [v5: $i] : ( ~ (domain(v0, v1, v4) = v5) | ~
% 141.09/20.93 $i(v4) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] :
% 141.09/20.93 (ilf_type(v4, v2) = v6 & range(v0, v1, v4) = v9 & subset(v3, v4) = v7 &
% 141.09/20.93 subset(v1, v5) = v8 & $i(v9) & ( ~ (v7 = 0) | ~ (v6 = 0) | (v9 = v1 &
% 141.09/20.93 v8 = 0)))) & ! [v4: $i] : ! [v5: $i] : ( ~ (range(v0, v1, v4) =
% 141.09/20.93 v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9:
% 141.09/20.93 any] : (ilf_type(v4, v2) = v6 & domain(v0, v1, v4) = v8 & subset(v3,
% 141.09/20.93 v4) = v7 & subset(v1, v8) = v9 & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0)
% 141.09/20.93 | (v9 = 0 & v5 = v1)))) & ! [v4: $i] : ( ~ (ilf_type(v4, v2) = 0) |
% 141.09/20.93 ~ $i(v4) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] :
% 141.09/20.93 (domain(v0, v1, v4) = v6 & range(v0, v1, v4) = v8 & subset(v3, v4) = v5
% 141.09/20.93 & subset(v1, v6) = v7 & $i(v8) & $i(v6) & ( ~ (v5 = 0) | (v8 = v1 & v7
% 141.09/20.93 = 0)))) & ! [v4: $i] : ( ~ (subset(v3, v4) = 0) | ~ $i(v4) | ?
% 141.09/20.93 [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : (ilf_type(v4, v2)
% 141.09/20.93 = v5 & domain(v0, v1, v4) = v6 & range(v0, v1, v4) = v8 & subset(v1,
% 141.09/20.93 v6) = v7 & $i(v8) & $i(v6) & ( ~ (v5 = 0) | (v8 = v1 & v7 = 0))))))
% 141.09/20.93
% 141.09/20.93 (p3)
% 141.09/20.94 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : !
% 141.09/20.94 [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v2, v4) = v5) | ~ (member(v2, v0)
% 141.09/20.94 = v3) | ~ (identity_relation_of(v0) = v1) | ~ $i(v4) | ~ $i(v2) | ~
% 141.09/20.94 $i(v0) | ? [v6: int] : ? [v7: any] : (( ~ (v6 = 0) & ilf_type(v2,
% 141.09/20.94 set_type) = v6) | ( ~ (v6 = 0) & ilf_type(v0, set_type) = v6) |
% 141.09/20.94 (member(v5, v1) = v7 & ilf_type(v4, set_type) = v6 & ( ~ (v6 = 0) | (( ~
% 141.09/20.94 (v7 = 0) | (v4 = v2 & v3 = 0)) & ( ~ (v4 = v2) | ~ (v3 = 0) | v7
% 141.09/20.94 = 0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any]
% 141.09/20.94 : ! [v4: $i] : ( ~ (member(v2, v0) = v3) | ~ (identity_relation_of(v0) = v1)
% 141.09/20.94 | ~ (ilf_type(v4, set_type) = 0) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ?
% 141.09/20.94 [v5: any] : ? [v6: any] : (( ~ (v5 = 0) & ilf_type(v2, set_type) = v5) | (
% 141.09/20.94 ~ (v5 = 0) & ilf_type(v0, set_type) = v5) | (ordered_pair(v2, v4) = v5 &
% 141.09/20.94 member(v5, v1) = v6 & $i(v5) & ( ~ (v6 = 0) | (v4 = v2 & v3 = 0)) & ( ~
% 141.09/20.94 (v4 = v2) | ~ (v3 = 0) | v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 141.09/20.94 [v2: $i] : ( ~ (identity_relation_of(v0) = v1) | ~ (ilf_type(v2, set_type) =
% 141.09/20.94 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : (( ~ (v3 = 0) & ilf_type(v0,
% 141.09/20.94 set_type) = v3) | (member(v2, v0) = v3 & ! [v4: $i] : ! [v5: $i] : (
% 141.09/20.94 ~ (ordered_pair(v2, v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7:
% 141.09/20.94 any] : (member(v5, v1) = v7 & ilf_type(v4, set_type) = v6 & ( ~ (v6
% 141.09/20.94 = 0) | (( ~ (v7 = 0) | (v4 = v2 & v3 = 0)) & ( ~ (v4 = v2) | ~
% 141.09/20.94 (v3 = 0) | v7 = 0))))) & ! [v4: $i] : ( ~ (ilf_type(v4,
% 141.09/20.94 set_type) = 0) | ~ $i(v4) | ? [v5: $i] : ? [v6: any] :
% 141.09/20.94 (ordered_pair(v2, v4) = v5 & member(v5, v1) = v6 & $i(v5) & ( ~ (v6 =
% 141.09/20.94 0) | (v4 = v2 & v3 = 0)) & ( ~ (v4 = v2) | ~ (v3 = 0) | v6 =
% 141.09/20.94 0)))))) & ! [v0: $i] : ( ~ (ilf_type(v0, set_type) = 0) | ~
% 141.09/20.94 $i(v0) | ? [v1: $i] : (identity_relation_of(v0) = v1 & $i(v1) & ! [v2: $i]
% 141.09/20.94 : ! [v3: any] : ! [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v2, v4) =
% 141.09/20.94 v5) | ~ (member(v2, v0) = v3) | ~ $i(v4) | ~ $i(v2) | ? [v6: int]
% 141.09/20.94 : ? [v7: any] : (( ~ (v6 = 0) & ilf_type(v2, set_type) = v6) |
% 141.09/20.94 (member(v5, v1) = v7 & ilf_type(v4, set_type) = v6 & ( ~ (v6 = 0) | ((
% 141.09/20.94 ~ (v7 = 0) | (v4 = v2 & v3 = 0)) & ( ~ (v4 = v2) | ~ (v3 = 0)
% 141.09/20.94 | v7 = 0)))))) & ! [v2: $i] : ! [v3: any] : ! [v4: $i] : (
% 141.09/20.94 ~ (member(v2, v0) = v3) | ~ (ilf_type(v4, set_type) = 0) | ~ $i(v4) |
% 141.09/20.94 ~ $i(v2) | ? [v5: any] : ? [v6: any] : (( ~ (v5 = 0) & ilf_type(v2,
% 141.09/20.94 set_type) = v5) | (ordered_pair(v2, v4) = v5 & member(v5, v1) = v6
% 141.09/20.94 & $i(v5) & ( ~ (v6 = 0) | (v4 = v2 & v3 = 0)) & ( ~ (v4 = v2) | ~
% 141.09/20.94 (v3 = 0) | v6 = 0)))) & ! [v2: $i] : ( ~ (ilf_type(v2, set_type)
% 141.09/20.94 = 0) | ~ $i(v2) | ? [v3: any] : (member(v2, v0) = v3 & ! [v4: $i] :
% 141.09/20.94 ! [v5: $i] : ( ~ (ordered_pair(v2, v4) = v5) | ~ $i(v4) | ? [v6:
% 141.09/20.94 any] : ? [v7: any] : (member(v5, v1) = v7 & ilf_type(v4,
% 141.09/20.94 set_type) = v6 & ( ~ (v6 = 0) | (( ~ (v7 = 0) | (v4 = v2 & v3 =
% 141.09/20.94 0)) & ( ~ (v4 = v2) | ~ (v3 = 0) | v7 = 0))))) & ! [v4:
% 141.09/20.94 $i] : ( ~ (ilf_type(v4, set_type) = 0) | ~ $i(v4) | ? [v5: $i] :
% 141.09/20.94 ? [v6: any] : (ordered_pair(v2, v4) = v5 & member(v5, v1) = v6 &
% 141.09/20.94 $i(v5) & ( ~ (v6 = 0) | (v4 = v2 & v3 = 0)) & ( ~ (v4 = v2) | ~
% 141.09/20.94 (v3 = 0) | v6 = 0)))))))
% 141.09/20.94
% 141.09/20.94 (p30)
% 141.09/20.95 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 141.09/20.95 $i] : ( ~ (domain_of(v3) = v4) | ~ (relation_type(v0, v1) = v2) | ~
% 141.09/20.95 (ilf_type(v0, set_type) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 141.09/20.95 int] : ? [v6: $i] : (( ~ (v5 = 0) & ilf_type(v1, set_type) = v5) |
% 141.09/20.95 (ilf_type(v3, v2) = v5 & domain(v0, v1, v3) = v6 & $i(v6) & ( ~ (v5 = 0) |
% 141.09/20.95 v6 = v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 141.09/20.95 ! [v4: $i] : ( ~ (relation_type(v0, v1) = v2) | ~ (ilf_type(v0, set_type) =
% 141.09/20.95 0) | ~ (domain(v0, v1, v3) = v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ?
% 141.09/20.95 [v5: int] : ? [v6: $i] : (( ~ (v5 = 0) & ilf_type(v1, set_type) = v5) |
% 141.09/20.95 (domain_of(v3) = v6 & ilf_type(v3, v2) = v5 & $i(v6) & ( ~ (v5 = 0) | v6 =
% 141.09/20.95 v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 141.09/20.95 (relation_type(v0, v1) = v2) | ~ (ilf_type(v3, v2) = 0) | ~ (ilf_type(v0,
% 141.09/20.95 set_type) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ?
% 141.09/20.95 [v5: any] : ((v5 = v4 & domain_of(v3) = v4 & domain(v0, v1, v3) = v4 &
% 141.09/20.95 $i(v4)) | ( ~ (v4 = 0) & ilf_type(v1, set_type) = v4))) & ! [v0: $i] :
% 141.09/20.95 ! [v1: $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~ (ilf_type(v0, set_type) =
% 141.09/20.95 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (relation_type(v0, v1) = v2 &
% 141.09/20.95 $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ (domain_of(v3) = v4) | ~ $i(v3)
% 141.09/20.95 | ? [v5: any] : ? [v6: $i] : (ilf_type(v3, v2) = v5 & domain(v0, v1,
% 141.09/20.95 v3) = v6 & $i(v6) & ( ~ (v5 = 0) | v6 = v4))) & ! [v3: $i] : !
% 141.09/20.95 [v4: $i] : ( ~ (domain(v0, v1, v3) = v4) | ~ $i(v3) | ? [v5: any] : ?
% 141.09/20.95 [v6: $i] : (domain_of(v3) = v6 & ilf_type(v3, v2) = v5 & $i(v6) & ( ~
% 141.09/20.95 (v5 = 0) | v6 = v4))) & ! [v3: $i] : ( ~ (ilf_type(v3, v2) = 0) |
% 141.09/20.95 ~ $i(v3) | ? [v4: $i] : (domain_of(v3) = v4 & domain(v0, v1, v3) = v4 &
% 141.09/20.95 $i(v4)))))
% 141.09/20.95
% 141.09/20.95 (p31)
% 141.09/20.96 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 141.09/20.96 $i] : ! [v5: $i] : ( ~ (subset_type(v0) = v1) | ~ (relation_type(v0, v2) =
% 141.09/20.96 v3) | ~ (domain(v0, v2, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) |
% 141.09/20.96 ? [v6: int] : ? [v7: any] : (( ~ (v6 = 0) & ilf_type(v2, set_type) = v6) |
% 141.09/20.96 ( ~ (v6 = 0) & ilf_type(v0, set_type) = v6) | (ilf_type(v5, v1) = v7 &
% 141.09/20.96 ilf_type(v4, v3) = v6 & ( ~ (v6 = 0) | v7 = 0)))) & ! [v0: $i] : !
% 141.09/20.96 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (subset_type(v0) =
% 141.09/20.96 v1) | ~ (relation_type(v0, v2) = v3) | ~ (ilf_type(v4, v3) = 0) | ~
% 141.09/20.96 $i(v4) | ~ $i(v2) | ~ $i(v0) | ? [v5: any] : ? [v6: int] : ((v6 = 0 &
% 141.09/20.96 ilf_type(v5, v1) = 0 & domain(v0, v2, v4) = v5 & $i(v5)) | ( ~ (v5 = 0)
% 141.09/20.96 & ilf_type(v2, set_type) = v5) | ( ~ (v5 = 0) & ilf_type(v0, set_type) =
% 141.09/20.96 v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_type(v0) =
% 141.09/20.96 v1) | ~ (ilf_type(v2, set_type) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3:
% 141.09/20.96 any] : (( ~ (v3 = 0) & ilf_type(v0, set_type) = v3) | (relation_type(v0,
% 141.09/20.96 v2) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ (domain(v0, v2,
% 141.09/20.96 v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] :
% 141.09/20.96 (ilf_type(v5, v1) = v7 & ilf_type(v4, v3) = v6 & ( ~ (v6 = 0) | v7 =
% 141.09/20.96 0))) & ! [v4: $i] : ( ~ (ilf_type(v4, v3) = 0) | ~ $i(v4) | ?
% 141.09/20.96 [v5: $i] : (ilf_type(v5, v1) = 0 & domain(v0, v2, v4) = v5 &
% 141.09/20.96 $i(v5)))))) & ! [v0: $i] : ( ~ (ilf_type(v0, set_type) = 0) | ~
% 141.09/20.96 $i(v0) | ? [v1: $i] : (subset_type(v0) = v1 & $i(v1) & ! [v2: $i] : !
% 141.09/20.96 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (relation_type(v0, v2) = v3) |
% 141.09/20.96 ~ (domain(v0, v2, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ? [v6: int] : ?
% 141.09/20.96 [v7: any] : (( ~ (v6 = 0) & ilf_type(v2, set_type) = v6) | (ilf_type(v5,
% 141.09/20.96 v1) = v7 & ilf_type(v4, v3) = v6 & ( ~ (v6 = 0) | v7 = 0)))) & !
% 141.09/20.96 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (relation_type(v0, v2) = v3) |
% 141.09/20.96 ~ (ilf_type(v4, v3) = 0) | ~ $i(v4) | ~ $i(v2) | ? [v5: any] : ?
% 141.09/20.96 [v6: int] : ((v6 = 0 & ilf_type(v5, v1) = 0 & domain(v0, v2, v4) = v5 &
% 141.09/20.96 $i(v5)) | ( ~ (v5 = 0) & ilf_type(v2, set_type) = v5))) & ! [v2:
% 141.09/20.96 $i] : ( ~ (ilf_type(v2, set_type) = 0) | ~ $i(v2) | ? [v3: $i] :
% 141.09/20.96 (relation_type(v0, v2) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~
% 141.09/20.96 (domain(v0, v2, v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any]
% 141.09/20.96 : (ilf_type(v5, v1) = v7 & ilf_type(v4, v3) = v6 & ( ~ (v6 = 0) | v7
% 141.09/20.96 = 0))) & ! [v4: $i] : ( ~ (ilf_type(v4, v3) = 0) | ~ $i(v4) |
% 141.09/20.96 ? [v5: $i] : (ilf_type(v5, v1) = 0 & domain(v0, v2, v4) = v5 &
% 141.09/20.96 $i(v5)))))))
% 141.09/20.96
% 141.09/20.96 (p32)
% 141.44/20.97 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 141.44/20.97 $i] : ( ~ (range_of(v3) = v4) | ~ (relation_type(v0, v1) = v2) | ~
% 141.44/20.97 (ilf_type(v0, set_type) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 141.44/20.97 int] : ? [v6: $i] : (( ~ (v5 = 0) & ilf_type(v1, set_type) = v5) |
% 141.44/20.97 (ilf_type(v3, v2) = v5 & range(v0, v1, v3) = v6 & $i(v6) & ( ~ (v5 = 0) |
% 141.44/20.97 v6 = v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 141.44/20.97 ! [v4: $i] : ( ~ (relation_type(v0, v1) = v2) | ~ (ilf_type(v0, set_type) =
% 141.44/20.97 0) | ~ (range(v0, v1, v3) = v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ?
% 141.44/20.97 [v5: int] : ? [v6: $i] : (( ~ (v5 = 0) & ilf_type(v1, set_type) = v5) |
% 141.44/20.97 (range_of(v3) = v6 & ilf_type(v3, v2) = v5 & $i(v6) & ( ~ (v5 = 0) | v6 =
% 141.44/20.97 v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 141.45/20.97 (relation_type(v0, v1) = v2) | ~ (ilf_type(v3, v2) = 0) | ~ (ilf_type(v0,
% 141.45/20.97 set_type) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ?
% 141.45/20.97 [v5: any] : ((v5 = v4 & range_of(v3) = v4 & range(v0, v1, v3) = v4 & $i(v4))
% 141.45/20.97 | ( ~ (v4 = 0) & ilf_type(v1, set_type) = v4))) & ! [v0: $i] : ! [v1:
% 141.45/20.97 $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~ (ilf_type(v0, set_type) = 0) |
% 141.45/20.97 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (relation_type(v0, v1) = v2 & $i(v2) &
% 141.45/20.97 ! [v3: $i] : ! [v4: $i] : ( ~ (range_of(v3) = v4) | ~ $i(v3) | ? [v5:
% 141.45/20.97 any] : ? [v6: $i] : (ilf_type(v3, v2) = v5 & range(v0, v1, v3) = v6 &
% 141.45/20.97 $i(v6) & ( ~ (v5 = 0) | v6 = v4))) & ! [v3: $i] : ! [v4: $i] : ( ~
% 141.45/20.97 (range(v0, v1, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] :
% 141.45/20.97 (range_of(v3) = v6 & ilf_type(v3, v2) = v5 & $i(v6) & ( ~ (v5 = 0) | v6
% 141.45/20.97 = v4))) & ! [v3: $i] : ( ~ (ilf_type(v3, v2) = 0) | ~ $i(v3) | ?
% 141.45/20.97 [v4: $i] : (range_of(v3) = v4 & range(v0, v1, v3) = v4 & $i(v4)))))
% 141.45/20.97
% 141.45/20.97 (p33)
% 141.45/20.98 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_type(v1)
% 141.45/20.98 = v2) | ~ (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 141.45/20.98 any] : ? [v4: $i] : (relation_type(v0, v1) = v4 & ilf_type(v1, set_type)
% 141.45/20.98 = v3 & $i(v4) & ( ~ (v3 = 0) | ( ! [v5: $i] : ! [v6: $i] : ( ~ (range(v0,
% 141.45/20.98 v1, v5) = v6) | ~ $i(v5) | ? [v7: any] : ? [v8: any] :
% 141.45/20.98 (ilf_type(v6, v2) = v8 & ilf_type(v5, v4) = v7 & ( ~ (v7 = 0) | v8 =
% 141.45/20.98 0))) & ! [v5: $i] : ( ~ (ilf_type(v5, v4) = 0) | ~ $i(v5) | ?
% 141.45/20.98 [v6: $i] : (ilf_type(v6, v2) = 0 & range(v0, v1, v5) = v6 &
% 141.45/20.98 $i(v6))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 141.45/20.98 (relation_type(v0, v1) = v2) | ~ (ilf_type(v0, set_type) = 0) | ~ $i(v1) |
% 141.45/20.98 ~ $i(v0) | ? [v3: any] : ? [v4: $i] : (subset_type(v1) = v4 &
% 141.45/20.98 ilf_type(v1, set_type) = v3 & $i(v4) & ( ~ (v3 = 0) | ( ! [v5: $i] : !
% 141.45/20.98 [v6: $i] : ( ~ (range(v0, v1, v5) = v6) | ~ $i(v5) | ? [v7: any] :
% 141.45/20.98 ? [v8: any] : (ilf_type(v6, v4) = v8 & ilf_type(v5, v2) = v7 & ( ~
% 141.45/20.98 (v7 = 0) | v8 = 0))) & ! [v5: $i] : ( ~ (ilf_type(v5, v2) = 0)
% 141.45/20.98 | ~ $i(v5) | ? [v6: $i] : (ilf_type(v6, v4) = 0 & range(v0, v1,
% 141.45/20.98 v5) = v6 & $i(v6))))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 141.45/20.98 (ilf_type(v1, set_type) = 0) | ~ (ilf_type(v0, set_type) = 0) | ~ $i(v1) |
% 141.45/20.98 ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : (subset_type(v1) = v3 &
% 141.45/20.98 relation_type(v0, v1) = v2 & $i(v3) & $i(v2) & ! [v4: $i] : ! [v5: $i] :
% 141.45/20.98 ( ~ (range(v0, v1, v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] :
% 141.45/20.98 (ilf_type(v5, v3) = v7 & ilf_type(v4, v2) = v6 & ( ~ (v6 = 0) | v7 =
% 141.45/20.98 0))) & ! [v4: $i] : ( ~ (ilf_type(v4, v2) = 0) | ~ $i(v4) | ?
% 141.45/20.98 [v5: $i] : (ilf_type(v5, v3) = 0 & range(v0, v1, v4) = v5 & $i(v5)))))
% 141.45/20.98
% 141.45/20.98 (p34)
% 141.45/20.98 $i(set_type) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (ilf_type(v0,
% 141.45/20.98 set_type) = v1) | ~ $i(v0))
% 141.45/20.98
% 141.45/20.98 (p4)
% 141.45/20.98 $i(binary_relation_type) & $i(set_type) & ! [v0: $i] : ! [v1: $i] : ( ~
% 141.45/20.98 (identity_relation_of(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 141.45/20.98 (ilf_type(v1, binary_relation_type) = v3 & ilf_type(v0, set_type) = v2 & ( ~
% 141.45/20.98 (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (ilf_type(v0, set_type) = 0) |
% 141.45/20.98 ~ $i(v0) | ? [v1: $i] : (identity_relation_of(v0) = v1 & ilf_type(v1,
% 141.45/20.98 binary_relation_type) = 0 & $i(v1)))
% 141.45/20.98
% 141.45/20.98 (p5)
% 141.45/20.99 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation_of_type(v0)
% 141.45/20.99 = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (relation_type(v0, v0) =
% 141.45/20.99 v3 & ilf_type(v0, set_type) = v2 & $i(v3) & ( ~ (v2 = 0) | ( ! [v4: $i] :
% 141.45/20.99 ! [v5: any] : ( ~ (ilf_type(v4, v3) = v5) | ~ $i(v4) | ? [v6: any] :
% 141.45/20.99 ? [v7: any] : (ilf_type(v4, v1) = v7 & ilf_type(v4, set_type) = v6
% 141.45/20.99 & ( ~ (v6 = 0) | (( ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | v7 =
% 141.45/20.99 0))))) & ! [v4: $i] : ! [v5: any] : ( ~ (ilf_type(v4, v1)
% 141.45/20.99 = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : (ilf_type(v4,
% 141.45/20.99 v3) = v7 & ilf_type(v4, set_type) = v6 & ( ~ (v6 = 0) | (( ~ (v7
% 141.45/20.99 = 0) | v5 = 0) & ( ~ (v5 = 0) | v7 = 0))))) & ! [v4: $i]
% 141.45/20.99 : ( ~ (ilf_type(v4, set_type) = 0) | ~ $i(v4) | ? [v5: any] : ?
% 141.45/20.99 [v6: any] : (ilf_type(v4, v3) = v6 & ilf_type(v4, v1) = v5 & ( ~ (v6
% 141.45/20.99 = 0) | v5 = 0) & ( ~ (v5 = 0) | v6 = 0))))))) & ! [v0: $i] :
% 141.45/20.99 ! [v1: $i] : ( ~ (relation_type(v0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 141.45/20.99 [v3: $i] : (identity_relation_of_type(v0) = v3 & ilf_type(v0, set_type) = v2
% 141.45/20.99 & $i(v3) & ( ~ (v2 = 0) | ( ! [v4: $i] : ! [v5: any] : ( ~ (ilf_type(v4,
% 141.45/20.99 v3) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] :
% 141.45/20.99 (ilf_type(v4, v1) = v7 & ilf_type(v4, set_type) = v6 & ( ~ (v6 = 0)
% 141.45/20.99 | (( ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | v7 = 0))))) & ! [v4:
% 141.45/20.99 $i] : ! [v5: any] : ( ~ (ilf_type(v4, v1) = v5) | ~ $i(v4) | ?
% 141.45/20.99 [v6: any] : ? [v7: any] : (ilf_type(v4, v3) = v7 & ilf_type(v4,
% 141.45/20.99 set_type) = v6 & ( ~ (v6 = 0) | (( ~ (v7 = 0) | v5 = 0) & ( ~
% 141.45/20.99 (v5 = 0) | v7 = 0))))) & ! [v4: $i] : ( ~ (ilf_type(v4,
% 141.45/20.99 set_type) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: any] :
% 141.45/20.99 (ilf_type(v4, v3) = v5 & ilf_type(v4, v1) = v6 & ( ~ (v6 = 0) | v5 =
% 141.45/20.99 0) & ( ~ (v5 = 0) | v6 = 0))))))) & ! [v0: $i] : ( ~
% 141.45/20.99 (ilf_type(v0, set_type) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 141.45/20.99 (identity_relation_of_type(v0) = v1 & relation_type(v0, v0) = v2 & $i(v2) &
% 141.45/20.99 $i(v1) & ! [v3: $i] : ! [v4: any] : ( ~ (ilf_type(v3, v2) = v4) | ~
% 141.45/20.99 $i(v3) | ? [v5: any] : ? [v6: any] : (ilf_type(v3, v1) = v6 &
% 141.45/20.99 ilf_type(v3, set_type) = v5 & ( ~ (v5 = 0) | (( ~ (v6 = 0) | v4 = 0) &
% 141.45/20.99 ( ~ (v4 = 0) | v6 = 0))))) & ! [v3: $i] : ! [v4: any] : ( ~
% 141.45/20.99 (ilf_type(v3, v1) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] :
% 141.45/20.99 (ilf_type(v3, v2) = v6 & ilf_type(v3, set_type) = v5 & ( ~ (v5 = 0) | ((
% 141.45/20.99 ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0))))) & ! [v3: $i]
% 141.45/20.99 : ( ~ (ilf_type(v3, set_type) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5:
% 141.45/20.99 any] : (ilf_type(v3, v2) = v5 & ilf_type(v3, v1) = v4 & ( ~ (v5 = 0) |
% 141.45/20.99 v4 = 0) & ( ~ (v4 = 0) | v5 = 0)))))
% 141.45/20.99
% 141.45/20.99 (p8)
% 141.45/20.99 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (ilf_type(v0,
% 141.45/20.99 set_type) = 0) | ~ (subset(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 141.45/20.99 [v3: any] : ? [v4: any] : (ilf_type(v1, set_type) = v3 & subset(v0, v1) =
% 141.45/20.99 v4 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | ~ (v2 = 0) | v1 = v0) & ( ~ (v1 = v0)
% 141.45/20.99 | (v4 = 0 & v2 = 0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any]
% 141.45/20.99 : ( ~ (ilf_type(v0, set_type) = 0) | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 141.45/20.99 $i(v0) | ? [v3: any] : ? [v4: any] : (ilf_type(v1, set_type) = v3 &
% 141.45/20.99 subset(v1, v0) = v4 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | ~ (v2 = 0) | v1 =
% 141.45/20.99 v0) & ( ~ (v1 = v0) | (v4 = 0 & v2 = 0)))))) & ! [v0: $i] : ! [v1:
% 141.45/20.99 $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~ (ilf_type(v0, set_type) = 0) |
% 141.45/20.99 ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (subset(v1, v0) = v3 &
% 141.45/20.99 subset(v0, v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v1 = v0) & ( ~ (v1 =
% 141.45/20.99 v0) | (v3 = 0 & v2 = 0))))
% 141.45/20.99
% 141.45/20.99 (prove_relset_1_44)
% 141.45/20.99 $i(set_type) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 141.45/20.99 $i] : ? [v5: $i] : (identity_relation_of_type(v0) = v1 &
% 141.45/20.99 identity_relation_of(v0) = v2 & ilf_type(v3, v1) = 0 & ilf_type(v0,
% 141.45/20.99 set_type) = 0 & domain(v0, v0, v3) = v4 & range(v0, v0, v3) = v5 &
% 141.45/20.99 subset(v2, v3) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (
% 141.45/20.99 ~ (v5 = v0) | ~ (v4 = v0)))
% 141.45/20.99
% 141.45/20.99 (function-axioms)
% 141.45/21.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 141.45/21.00 | ~ (domain(v4, v3, v2) = v1) | ~ (domain(v4, v3, v2) = v0)) & ! [v0: $i]
% 141.45/21.00 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 141.45/21.00 (range(v4, v3, v2) = v1) | ~ (range(v4, v3, v2) = v0)) & ! [v0: $i] : !
% 141.45/21.00 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cross_product(v3, v2) =
% 141.45/21.00 v1) | ~ (cross_product(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 141.45/21.00 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~
% 141.45/21.00 (ordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 141.45/21.00 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (member(v3,
% 141.45/21.00 v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 141.45/21.00 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_type(v3, v2) = v1) | ~
% 141.45/21.00 (relation_type(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 141.45/21.00 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ilf_type(v3,
% 141.45/21.00 v2) = v1) | ~ (ilf_type(v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 141.45/21.00 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.45/21.00 (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 141.45/21.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 141.45/21.00 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 141.45/21.00 [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & !
% 141.45/21.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (member_type(v2) = v1) |
% 141.45/21.00 ~ (member_type(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 141.45/21.00 v0 | ~ (subset_type(v2) = v1) | ~ (subset_type(v2) = v0)) & ! [v0:
% 141.45/21.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 141.45/21.00 ~ (relation_like(v2) = v1) | ~ (relation_like(v2) = v0)) & ! [v0: $i] : !
% 141.45/21.00 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2)
% 141.45/21.00 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 141.45/21.00 (domain_of(v2) = v1) | ~ (domain_of(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 141.45/21.00 : ! [v2: $i] : (v1 = v0 | ~ (identity_relation_of_type(v2) = v1) | ~
% 141.45/21.00 (identity_relation_of_type(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 141.45/21.00 $i] : (v1 = v0 | ~ (identity_relation_of(v2) = v1) | ~
% 141.45/21.00 (identity_relation_of(v2) = v0))
% 141.45/21.00
% 141.45/21.00 Further assumptions not needed in the proof:
% 141.45/21.00 --------------------------------------------
% 141.58/21.00 p10, p11, p12, p13, p16, p17, p19, p20, p21, p22, p23, p24, p25, p26, p27, p28,
% 141.58/21.00 p29, p6, p7, p9
% 141.58/21.00
% 141.58/21.00 Those formulas are unsatisfiable:
% 141.58/21.00 ---------------------------------
% 141.58/21.00
% 141.58/21.00 Begin of proof
% 141.58/21.00 |
% 141.58/21.00 | ALPHA: (p1) implies:
% 141.58/21.00 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~
% 141.58/21.00 | (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 141.58/21.00 | ? [v3: $i] : (identity_relation_of(v1) = v3 & relation_type(v1, v0) =
% 141.58/21.00 | v2 & $i(v3) & $i(v2) & ! [v4: $i] : ! [v5: $i] : ( ~ (domain(v1,
% 141.58/21.00 | v0, v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : ?
% 141.58/21.00 | [v8: $i] : ? [v9: any] : (ilf_type(v4, v2) = v6 & range(v1, v0,
% 141.58/21.00 | v4) = v8 & subset(v3, v4) = v7 & subset(v1, v8) = v9 & $i(v8)
% 141.58/21.00 | & ( ~ (v7 = 0) | ~ (v6 = 0) | (v9 = 0 & v5 = v1)))) & ! [v4:
% 141.58/21.00 | $i] : ! [v5: $i] : ( ~ (range(v1, v0, v4) = v5) | ~ $i(v4) | ?
% 141.58/21.00 | [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] :
% 141.58/21.00 | (ilf_type(v4, v2) = v6 & domain(v1, v0, v4) = v8 & subset(v3, v4)
% 141.58/21.00 | = v7 & subset(v1, v5) = v9 & $i(v8) & ( ~ (v7 = 0) | ~ (v6 =
% 141.58/21.00 | 0) | (v9 = 0 & v8 = v1)))) & ! [v4: $i] : ( ~
% 141.58/21.00 | (ilf_type(v4, v2) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: $i] :
% 141.58/21.00 | ? [v7: $i] : ? [v8: any] : (domain(v1, v0, v4) = v6 & range(v1,
% 141.58/21.00 | v0, v4) = v7 & subset(v3, v4) = v5 & subset(v1, v7) = v8 &
% 141.58/21.00 | $i(v7) & $i(v6) & ( ~ (v5 = 0) | (v8 = 0 & v6 = v1)))) & !
% 141.58/21.00 | [v4: $i] : ( ~ (subset(v3, v4) = 0) | ~ $i(v4) | ? [v5: any] : ?
% 141.58/21.00 | [v6: $i] : ? [v7: $i] : ? [v8: any] : (ilf_type(v4, v2) = v5 &
% 141.58/21.00 | domain(v1, v0, v4) = v6 & range(v1, v0, v4) = v7 & subset(v1,
% 141.58/21.00 | v7) = v8 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | (v8 = 0 & v6 =
% 141.58/21.00 | v1))))))
% 141.58/21.01 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (identity_relation_of(v1)
% 141.58/21.01 | = v2) | ~ (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) |
% 141.58/21.01 | ? [v3: any] : ? [v4: $i] : (relation_type(v1, v0) = v4 &
% 141.58/21.01 | ilf_type(v1, set_type) = v3 & $i(v4) & ( ~ (v3 = 0) | ( ! [v5: $i]
% 141.58/21.01 | : ! [v6: $i] : ( ~ (domain(v1, v0, v5) = v6) | ~ $i(v5) | ?
% 141.58/21.01 | [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: any] :
% 141.58/21.01 | (ilf_type(v5, v4) = v7 & range(v1, v0, v5) = v9 & subset(v2,
% 141.58/21.01 | v5) = v8 & subset(v1, v9) = v10 & $i(v9) & ( ~ (v8 = 0) |
% 141.58/21.01 | ~ (v7 = 0) | (v10 = 0 & v6 = v1)))) & ! [v5: $i] : !
% 141.58/21.01 | [v6: $i] : ( ~ (range(v1, v0, v5) = v6) | ~ $i(v5) | ? [v7:
% 141.58/21.01 | any] : ? [v8: any] : ? [v9: $i] : ? [v10: any] :
% 141.58/21.01 | (ilf_type(v5, v4) = v7 & domain(v1, v0, v5) = v9 & subset(v2,
% 141.58/21.01 | v5) = v8 & subset(v1, v6) = v10 & $i(v9) & ( ~ (v8 = 0) |
% 141.58/21.01 | ~ (v7 = 0) | (v10 = 0 & v9 = v1)))) & ! [v5: $i] : ( ~
% 141.58/21.01 | (ilf_type(v5, v4) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7:
% 141.58/21.01 | $i] : ? [v8: $i] : ? [v9: any] : (domain(v1, v0, v5) = v7
% 141.58/21.01 | & range(v1, v0, v5) = v8 & subset(v2, v5) = v6 & subset(v1,
% 141.58/21.01 | v8) = v9 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | (v9 = 0 & v7
% 141.58/21.01 | = v1)))) & ! [v5: $i] : ( ~ (subset(v2, v5) = 0) | ~
% 141.58/21.01 | $i(v5) | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 141.58/21.01 | any] : (ilf_type(v5, v4) = v6 & domain(v1, v0, v5) = v7 &
% 141.58/21.01 | range(v1, v0, v5) = v8 & subset(v1, v8) = v9 & $i(v8) &
% 141.58/21.01 | $i(v7) & ( ~ (v6 = 0) | (v9 = 0 & v7 = v1))))))))
% 141.58/21.01 |
% 141.58/21.01 | ALPHA: (p2) implies:
% 141.58/21.01 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~
% 141.58/21.01 | (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 141.58/21.01 | ? [v3: $i] : (identity_relation_of(v1) = v3 & relation_type(v0, v1) =
% 141.58/21.01 | v2 & $i(v3) & $i(v2) & ! [v4: $i] : ! [v5: $i] : ( ~ (domain(v0,
% 141.58/21.01 | v1, v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : ?
% 141.58/21.01 | [v8: any] : ? [v9: $i] : (ilf_type(v4, v2) = v6 & range(v0, v1,
% 141.58/21.01 | v4) = v9 & subset(v3, v4) = v7 & subset(v1, v5) = v8 & $i(v9)
% 141.58/21.01 | & ( ~ (v7 = 0) | ~ (v6 = 0) | (v9 = v1 & v8 = 0)))) & ! [v4:
% 141.58/21.01 | $i] : ! [v5: $i] : ( ~ (range(v0, v1, v4) = v5) | ~ $i(v4) | ?
% 141.58/21.01 | [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] :
% 141.58/21.01 | (ilf_type(v4, v2) = v6 & domain(v0, v1, v4) = v8 & subset(v3, v4)
% 141.58/21.01 | = v7 & subset(v1, v8) = v9 & $i(v8) & ( ~ (v7 = 0) | ~ (v6 =
% 141.58/21.01 | 0) | (v9 = 0 & v5 = v1)))) & ! [v4: $i] : ( ~
% 141.58/21.01 | (ilf_type(v4, v2) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: $i] :
% 141.58/21.01 | ? [v7: any] : ? [v8: $i] : (domain(v0, v1, v4) = v6 & range(v0,
% 141.58/21.01 | v1, v4) = v8 & subset(v3, v4) = v5 & subset(v1, v6) = v7 &
% 141.58/21.01 | $i(v8) & $i(v6) & ( ~ (v5 = 0) | (v8 = v1 & v7 = 0)))) & !
% 141.58/21.01 | [v4: $i] : ( ~ (subset(v3, v4) = 0) | ~ $i(v4) | ? [v5: any] : ?
% 141.58/21.01 | [v6: $i] : ? [v7: any] : ? [v8: $i] : (ilf_type(v4, v2) = v5 &
% 141.58/21.01 | domain(v0, v1, v4) = v6 & range(v0, v1, v4) = v8 & subset(v1,
% 141.58/21.01 | v6) = v7 & $i(v8) & $i(v6) & ( ~ (v5 = 0) | (v8 = v1 & v7 =
% 141.58/21.01 | 0))))))
% 141.58/21.01 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (identity_relation_of(v1)
% 141.58/21.01 | = v2) | ~ (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) |
% 141.58/21.01 | ? [v3: any] : ? [v4: $i] : (relation_type(v0, v1) = v4 &
% 141.58/21.01 | ilf_type(v1, set_type) = v3 & $i(v4) & ( ~ (v3 = 0) | ( ! [v5: $i]
% 141.58/21.01 | : ! [v6: $i] : ( ~ (domain(v0, v1, v5) = v6) | ~ $i(v5) | ?
% 141.58/21.01 | [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: $i] :
% 141.58/21.01 | (ilf_type(v5, v4) = v7 & range(v0, v1, v5) = v10 & subset(v2,
% 141.58/21.01 | v5) = v8 & subset(v1, v6) = v9 & $i(v10) & ( ~ (v8 = 0) |
% 141.58/21.01 | ~ (v7 = 0) | (v10 = v1 & v9 = 0)))) & ! [v5: $i] : !
% 141.58/21.01 | [v6: $i] : ( ~ (range(v0, v1, v5) = v6) | ~ $i(v5) | ? [v7:
% 141.58/21.01 | any] : ? [v8: any] : ? [v9: $i] : ? [v10: any] :
% 141.58/21.01 | (ilf_type(v5, v4) = v7 & domain(v0, v1, v5) = v9 & subset(v2,
% 141.58/21.01 | v5) = v8 & subset(v1, v9) = v10 & $i(v9) & ( ~ (v8 = 0) |
% 141.58/21.01 | ~ (v7 = 0) | (v10 = 0 & v6 = v1)))) & ! [v5: $i] : ( ~
% 141.58/21.01 | (ilf_type(v5, v4) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7:
% 141.58/21.01 | $i] : ? [v8: any] : ? [v9: $i] : (domain(v0, v1, v5) = v7
% 141.58/21.01 | & range(v0, v1, v5) = v9 & subset(v2, v5) = v6 & subset(v1,
% 141.58/21.01 | v7) = v8 & $i(v9) & $i(v7) & ( ~ (v6 = 0) | (v9 = v1 & v8
% 141.58/21.01 | = 0)))) & ! [v5: $i] : ( ~ (subset(v2, v5) = 0) | ~
% 141.58/21.01 | $i(v5) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9:
% 141.58/21.01 | $i] : (ilf_type(v5, v4) = v6 & domain(v0, v1, v5) = v7 &
% 141.58/21.01 | range(v0, v1, v5) = v9 & subset(v1, v7) = v8 & $i(v9) &
% 141.58/21.01 | $i(v7) & ( ~ (v6 = 0) | (v9 = v1 & v8 = 0))))))))
% 141.58/21.02 |
% 141.58/21.02 | ALPHA: (p3) implies:
% 141.58/21.02 | (5) ! [v0: $i] : ( ~ (ilf_type(v0, set_type) = 0) | ~ $i(v0) | ? [v1:
% 141.58/21.02 | $i] : (identity_relation_of(v0) = v1 & $i(v1) & ! [v2: $i] : !
% 141.58/21.02 | [v3: any] : ! [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v2, v4) =
% 141.58/21.02 | v5) | ~ (member(v2, v0) = v3) | ~ $i(v4) | ~ $i(v2) | ?
% 141.58/21.02 | [v6: int] : ? [v7: any] : (( ~ (v6 = 0) & ilf_type(v2, set_type)
% 141.58/21.02 | = v6) | (member(v5, v1) = v7 & ilf_type(v4, set_type) = v6 &
% 141.58/21.02 | ( ~ (v6 = 0) | (( ~ (v7 = 0) | (v4 = v2 & v3 = 0)) & ( ~ (v4
% 141.58/21.02 | = v2) | ~ (v3 = 0) | v7 = 0)))))) & ! [v2: $i] : !
% 141.58/21.02 | [v3: any] : ! [v4: $i] : ( ~ (member(v2, v0) = v3) | ~
% 141.58/21.02 | (ilf_type(v4, set_type) = 0) | ~ $i(v4) | ~ $i(v2) | ? [v5:
% 141.58/21.02 | any] : ? [v6: any] : (( ~ (v5 = 0) & ilf_type(v2, set_type) =
% 141.58/21.02 | v5) | (ordered_pair(v2, v4) = v5 & member(v5, v1) = v6 &
% 141.58/21.02 | $i(v5) & ( ~ (v6 = 0) | (v4 = v2 & v3 = 0)) & ( ~ (v4 = v2) |
% 141.58/21.02 | ~ (v3 = 0) | v6 = 0)))) & ! [v2: $i] : ( ~ (ilf_type(v2,
% 141.58/21.02 | set_type) = 0) | ~ $i(v2) | ? [v3: any] : (member(v2, v0) =
% 141.58/21.02 | v3 & ! [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v2, v4) =
% 141.58/21.02 | v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : (member(v5,
% 141.58/21.02 | v1) = v7 & ilf_type(v4, set_type) = v6 & ( ~ (v6 = 0) |
% 141.58/21.02 | (( ~ (v7 = 0) | (v4 = v2 & v3 = 0)) & ( ~ (v4 = v2) | ~
% 141.58/21.02 | (v3 = 0) | v7 = 0))))) & ! [v4: $i] : ( ~
% 141.58/21.02 | (ilf_type(v4, set_type) = 0) | ~ $i(v4) | ? [v5: $i] : ?
% 141.58/21.02 | [v6: any] : (ordered_pair(v2, v4) = v5 & member(v5, v1) = v6
% 141.58/21.02 | & $i(v5) & ( ~ (v6 = 0) | (v4 = v2 & v3 = 0)) & ( ~ (v4 =
% 141.58/21.02 | v2) | ~ (v3 = 0) | v6 = 0)))))))
% 141.58/21.02 |
% 141.58/21.02 | ALPHA: (p4) implies:
% 141.58/21.02 | (6) ! [v0: $i] : ( ~ (ilf_type(v0, set_type) = 0) | ~ $i(v0) | ? [v1:
% 141.58/21.02 | $i] : (identity_relation_of(v0) = v1 & ilf_type(v1,
% 141.58/21.02 | binary_relation_type) = 0 & $i(v1)))
% 141.58/21.02 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation_of(v0) = v1) | ~
% 141.58/21.02 | $i(v0) | ? [v2: any] : ? [v3: any] : (ilf_type(v1,
% 141.58/21.02 | binary_relation_type) = v3 & ilf_type(v0, set_type) = v2 & ( ~
% 141.58/21.02 | (v2 = 0) | v3 = 0)))
% 141.58/21.02 |
% 141.58/21.02 | ALPHA: (p5) implies:
% 141.69/21.02 | (8) ! [v0: $i] : ( ~ (ilf_type(v0, set_type) = 0) | ~ $i(v0) | ? [v1:
% 141.69/21.02 | $i] : ? [v2: $i] : (identity_relation_of_type(v0) = v1 &
% 141.69/21.02 | relation_type(v0, v0) = v2 & $i(v2) & $i(v1) & ! [v3: $i] : !
% 141.69/21.02 | [v4: any] : ( ~ (ilf_type(v3, v2) = v4) | ~ $i(v3) | ? [v5: any]
% 141.69/21.02 | : ? [v6: any] : (ilf_type(v3, v1) = v6 & ilf_type(v3, set_type)
% 141.69/21.02 | = v5 & ( ~ (v5 = 0) | (( ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) |
% 141.69/21.02 | v6 = 0))))) & ! [v3: $i] : ! [v4: any] : ( ~
% 141.69/21.02 | (ilf_type(v3, v1) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any]
% 141.69/21.02 | : (ilf_type(v3, v2) = v6 & ilf_type(v3, set_type) = v5 & ( ~ (v5
% 141.69/21.02 | = 0) | (( ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0)))))
% 141.69/21.02 | & ! [v3: $i] : ( ~ (ilf_type(v3, set_type) = 0) | ~ $i(v3) | ?
% 141.69/21.02 | [v4: any] : ? [v5: any] : (ilf_type(v3, v2) = v5 & ilf_type(v3,
% 141.69/21.02 | v1) = v4 & ( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 =
% 141.69/21.02 | 0)))))
% 141.69/21.03 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation_of_type(v0) = v1) |
% 141.69/21.03 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (relation_type(v0, v0) = v3 &
% 141.69/21.03 | ilf_type(v0, set_type) = v2 & $i(v3) & ( ~ (v2 = 0) | ( ! [v4: $i]
% 141.69/21.03 | : ! [v5: any] : ( ~ (ilf_type(v4, v3) = v5) | ~ $i(v4) | ?
% 141.69/21.03 | [v6: any] : ? [v7: any] : (ilf_type(v4, v1) = v7 &
% 141.69/21.03 | ilf_type(v4, set_type) = v6 & ( ~ (v6 = 0) | (( ~ (v7 = 0)
% 141.69/21.03 | | v5 = 0) & ( ~ (v5 = 0) | v7 = 0))))) & ! [v4: $i]
% 141.69/21.03 | : ! [v5: any] : ( ~ (ilf_type(v4, v1) = v5) | ~ $i(v4) | ?
% 141.69/21.03 | [v6: any] : ? [v7: any] : (ilf_type(v4, v3) = v7 &
% 141.69/21.03 | ilf_type(v4, set_type) = v6 & ( ~ (v6 = 0) | (( ~ (v7 = 0)
% 141.69/21.03 | | v5 = 0) & ( ~ (v5 = 0) | v7 = 0))))) & ! [v4: $i]
% 141.69/21.03 | : ( ~ (ilf_type(v4, set_type) = 0) | ~ $i(v4) | ? [v5: any] :
% 141.69/21.03 | ? [v6: any] : (ilf_type(v4, v3) = v6 & ilf_type(v4, v1) = v5
% 141.69/21.03 | & ( ~ (v6 = 0) | v5 = 0) & ( ~ (v5 = 0) | v6 = 0)))))))
% 141.69/21.03 |
% 141.69/21.03 | ALPHA: (p8) implies:
% 141.69/21.03 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~
% 141.69/21.03 | (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any]
% 141.69/21.03 | : ? [v3: any] : (subset(v1, v0) = v3 & subset(v0, v1) = v2 & ( ~
% 141.69/21.03 | (v3 = 0) | ~ (v2 = 0) | v1 = v0) & ( ~ (v1 = v0) | (v3 = 0 & v2
% 141.69/21.03 | = 0))))
% 141.69/21.03 |
% 141.69/21.03 | ALPHA: (p14) implies:
% 141.69/21.03 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~
% 141.69/21.03 | (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 141.69/21.03 | ? [v3: $i] : ? [v4: $i] : (cross_product(v0, v1) = v2 &
% 141.69/21.03 | subset_type(v2) = v3 & relation_type(v0, v1) = v4 & $i(v4) &
% 141.69/21.03 | $i(v3) & $i(v2) & ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~
% 141.69/21.03 | (ilf_type(v5, v4) = v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 =
% 141.69/21.03 | 0) & ilf_type(v5, v3) = v7)) & ! [v5: $i] : ! [v6: int] :
% 141.69/21.03 | (v6 = 0 | ~ (ilf_type(v5, v3) = v6) | ~ $i(v5) | ? [v7: int] :
% 141.69/21.03 | ( ~ (v7 = 0) & ilf_type(v5, v4) = v7)) & ! [v5: $i] : ( ~
% 141.69/21.03 | (ilf_type(v5, v4) = 0) | ~ $i(v5) | ilf_type(v5, v3) = 0) & !
% 141.69/21.03 | [v5: $i] : ( ~ (ilf_type(v5, v3) = 0) | ~ $i(v5) | ilf_type(v5,
% 141.69/21.03 | v4) = 0)))
% 141.69/21.03 |
% 141.69/21.03 | ALPHA: (p15) implies:
% 141.69/21.03 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~
% 141.69/21.03 | (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 141.69/21.03 | ? [v3: $i] : (relation_type(v1, v0) = v2 & ilf_type(v3, v2) = 0 &
% 141.69/21.03 | $i(v3) & $i(v2)))
% 141.69/21.03 |
% 141.69/21.03 | ALPHA: (p18) implies:
% 141.69/21.03 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~
% 141.69/21.03 | (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any]
% 141.69/21.03 | : ? [v3: $i] : ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 141.69/21.03 | (subset(v0, v1) = v2 & $i(v3) & ( ~ (v2 = 0) | ( ! [v7: $i] : !
% 141.69/21.03 | [v8: int] : (v8 = 0 | ~ (member(v7, v1) = v8) | ~ $i(v7) |
% 141.69/21.03 | ? [v9: any] : ? [v10: any] : (member(v7, v0) = v10 &
% 141.69/21.03 | ilf_type(v7, set_type) = v9 & ( ~ (v10 = 0) | ~ (v9 =
% 141.69/21.03 | 0)))) & ! [v7: $i] : ( ~ (member(v7, v0) = 0) | ~
% 141.69/21.03 | $i(v7) | ? [v8: any] : ? [v9: any] : (member(v7, v1) = v9
% 141.69/21.03 | & ilf_type(v7, set_type) = v8 & ( ~ (v8 = 0) | v9 = 0))) &
% 141.69/21.03 | ! [v7: $i] : ( ~ (ilf_type(v7, set_type) = 0) | ~ $i(v7) |
% 141.69/21.03 | ? [v8: any] : ? [v9: any] : (member(v7, v1) = v9 &
% 141.69/21.03 | member(v7, v0) = v8 & ( ~ (v8 = 0) | v9 = 0))))) & (v2 = 0
% 141.69/21.03 | | (v5 = 0 & v4 = 0 & ~ (v6 = 0) & member(v3, v1) = v6 &
% 141.69/21.03 | member(v3, v0) = 0 & ilf_type(v3, set_type) = 0))))
% 141.69/21.03 |
% 141.69/21.03 | ALPHA: (p30) implies:
% 141.69/21.03 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~
% 141.69/21.03 | (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 141.69/21.03 | (relation_type(v0, v1) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : (
% 141.69/21.03 | ~ (domain_of(v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i]
% 141.69/21.03 | : (ilf_type(v3, v2) = v5 & domain(v0, v1, v3) = v6 & $i(v6) & (
% 141.69/21.03 | ~ (v5 = 0) | v6 = v4))) & ! [v3: $i] : ! [v4: $i] : ( ~
% 141.69/21.03 | (domain(v0, v1, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6:
% 141.69/21.03 | $i] : (domain_of(v3) = v6 & ilf_type(v3, v2) = v5 & $i(v6) & (
% 141.69/21.03 | ~ (v5 = 0) | v6 = v4))) & ! [v3: $i] : ( ~ (ilf_type(v3,
% 141.69/21.03 | v2) = 0) | ~ $i(v3) | ? [v4: $i] : (domain_of(v3) = v4 &
% 141.69/21.03 | domain(v0, v1, v3) = v4 & $i(v4)))))
% 141.69/21.03 |
% 141.69/21.03 | ALPHA: (p31) implies:
% 141.69/21.04 | (15) ! [v0: $i] : ( ~ (ilf_type(v0, set_type) = 0) | ~ $i(v0) | ? [v1:
% 141.69/21.04 | $i] : (subset_type(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] :
% 141.69/21.04 | ! [v4: $i] : ! [v5: $i] : ( ~ (relation_type(v0, v2) = v3) | ~
% 141.69/21.04 | (domain(v0, v2, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ? [v6: int]
% 141.69/21.04 | : ? [v7: any] : (( ~ (v6 = 0) & ilf_type(v2, set_type) = v6) |
% 141.69/21.04 | (ilf_type(v5, v1) = v7 & ilf_type(v4, v3) = v6 & ( ~ (v6 = 0)
% 141.69/21.04 | | v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 141.69/21.04 | ~ (relation_type(v0, v2) = v3) | ~ (ilf_type(v4, v3) = 0) | ~
% 141.69/21.04 | $i(v4) | ~ $i(v2) | ? [v5: any] : ? [v6: int] : ((v6 = 0 &
% 141.69/21.04 | ilf_type(v5, v1) = 0 & domain(v0, v2, v4) = v5 & $i(v5)) | (
% 141.69/21.04 | ~ (v5 = 0) & ilf_type(v2, set_type) = v5))) & ! [v2: $i] :
% 141.69/21.04 | ( ~ (ilf_type(v2, set_type) = 0) | ~ $i(v2) | ? [v3: $i] :
% 141.69/21.04 | (relation_type(v0, v2) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i]
% 141.69/21.04 | : ( ~ (domain(v0, v2, v4) = v5) | ~ $i(v4) | ? [v6: any] :
% 141.69/21.04 | ? [v7: any] : (ilf_type(v5, v1) = v7 & ilf_type(v4, v3) = v6
% 141.69/21.04 | & ( ~ (v6 = 0) | v7 = 0))) & ! [v4: $i] : ( ~
% 141.69/21.04 | (ilf_type(v4, v3) = 0) | ~ $i(v4) | ? [v5: $i] :
% 141.69/21.04 | (ilf_type(v5, v1) = 0 & domain(v0, v2, v4) = v5 &
% 141.69/21.04 | $i(v5)))))))
% 141.69/21.04 |
% 141.69/21.04 | ALPHA: (p32) implies:
% 141.69/21.04 | (16) ! [v0: $i] : ! [v1: $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~
% 141.69/21.04 | (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 141.69/21.04 | (relation_type(v0, v1) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : (
% 141.69/21.04 | ~ (range_of(v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] :
% 141.69/21.04 | (ilf_type(v3, v2) = v5 & range(v0, v1, v3) = v6 & $i(v6) & ( ~
% 141.69/21.04 | (v5 = 0) | v6 = v4))) & ! [v3: $i] : ! [v4: $i] : ( ~
% 141.69/21.04 | (range(v0, v1, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6:
% 141.69/21.04 | $i] : (range_of(v3) = v6 & ilf_type(v3, v2) = v5 & $i(v6) & (
% 141.69/21.04 | ~ (v5 = 0) | v6 = v4))) & ! [v3: $i] : ( ~ (ilf_type(v3,
% 141.69/21.04 | v2) = 0) | ~ $i(v3) | ? [v4: $i] : (range_of(v3) = v4 &
% 141.69/21.04 | range(v0, v1, v3) = v4 & $i(v4)))))
% 141.69/21.04 |
% 141.69/21.04 | ALPHA: (p33) implies:
% 141.69/21.04 | (17) ! [v0: $i] : ! [v1: $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~
% 141.69/21.04 | (ilf_type(v0, set_type) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 141.69/21.04 | ? [v3: $i] : (subset_type(v1) = v3 & relation_type(v0, v1) = v2 &
% 141.69/21.04 | $i(v3) & $i(v2) & ! [v4: $i] : ! [v5: $i] : ( ~ (range(v0, v1,
% 141.69/21.04 | v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] :
% 141.69/21.04 | (ilf_type(v5, v3) = v7 & ilf_type(v4, v2) = v6 & ( ~ (v6 = 0) |
% 141.69/21.04 | v7 = 0))) & ! [v4: $i] : ( ~ (ilf_type(v4, v2) = 0) | ~
% 141.69/21.04 | $i(v4) | ? [v5: $i] : (ilf_type(v5, v3) = 0 & range(v0, v1, v4)
% 141.69/21.04 | = v5 & $i(v5)))))
% 141.69/21.04 |
% 141.69/21.04 | ALPHA: (p34) implies:
% 141.69/21.04 | (18) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (ilf_type(v0, set_type) =
% 141.69/21.04 | v1) | ~ $i(v0))
% 141.69/21.04 |
% 141.69/21.04 | ALPHA: (prove_relset_1_44) implies:
% 141.69/21.04 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 141.69/21.04 | ? [v5: $i] : (identity_relation_of_type(v0) = v1 &
% 141.69/21.04 | identity_relation_of(v0) = v2 & ilf_type(v3, v1) = 0 & ilf_type(v0,
% 141.69/21.04 | set_type) = 0 & domain(v0, v0, v3) = v4 & range(v0, v0, v3) = v5 &
% 141.69/21.04 | subset(v2, v3) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 141.69/21.04 | $i(v0) & ( ~ (v5 = v0) | ~ (v4 = v0)))
% 141.69/21.04 |
% 141.69/21.04 | ALPHA: (function-axioms) implies:
% 141.69/21.04 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 141.69/21.04 | (identity_relation_of(v2) = v1) | ~ (identity_relation_of(v2) =
% 141.69/21.04 | v0))
% 141.69/21.04 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 141.69/21.04 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3,
% 141.69/21.04 | v2) = v0))
% 141.69/21.04 | (22) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 141.69/21.04 | : ! [v3: $i] : (v1 = v0 | ~ (ilf_type(v3, v2) = v1) | ~
% 141.69/21.04 | (ilf_type(v3, v2) = v0))
% 141.69/21.04 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.69/21.04 | (relation_type(v3, v2) = v1) | ~ (relation_type(v3, v2) = v0))
% 141.69/21.04 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 141.69/21.04 | (v1 = v0 | ~ (range(v4, v3, v2) = v1) | ~ (range(v4, v3, v2) = v0))
% 141.69/21.04 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 141.69/21.04 | (v1 = v0 | ~ (domain(v4, v3, v2) = v1) | ~ (domain(v4, v3, v2) =
% 141.69/21.04 | v0))
% 141.69/21.04 |
% 141.69/21.04 | DELTA: instantiating (19) with fresh symbols all_39_0, all_39_1, all_39_2,
% 141.69/21.04 | all_39_3, all_39_4, all_39_5 gives:
% 141.69/21.04 | (26) identity_relation_of_type(all_39_5) = all_39_4 &
% 141.69/21.04 | identity_relation_of(all_39_5) = all_39_3 & ilf_type(all_39_2,
% 141.69/21.04 | all_39_4) = 0 & ilf_type(all_39_5, set_type) = 0 & domain(all_39_5,
% 141.69/21.04 | all_39_5, all_39_2) = all_39_1 & range(all_39_5, all_39_5, all_39_2)
% 141.69/21.04 | = all_39_0 & subset(all_39_3, all_39_2) = 0 & $i(all_39_0) &
% 141.69/21.04 | $i(all_39_1) & $i(all_39_2) & $i(all_39_3) & $i(all_39_4) &
% 141.69/21.04 | $i(all_39_5) & ( ~ (all_39_0 = all_39_5) | ~ (all_39_1 = all_39_5))
% 141.69/21.04 |
% 141.69/21.04 | ALPHA: (26) implies:
% 141.69/21.04 | (27) $i(all_39_5)
% 141.69/21.04 | (28) $i(all_39_2)
% 141.69/21.04 | (29) subset(all_39_3, all_39_2) = 0
% 141.69/21.04 | (30) range(all_39_5, all_39_5, all_39_2) = all_39_0
% 141.69/21.04 | (31) domain(all_39_5, all_39_5, all_39_2) = all_39_1
% 141.69/21.04 | (32) ilf_type(all_39_5, set_type) = 0
% 141.69/21.04 | (33) ilf_type(all_39_2, all_39_4) = 0
% 141.69/21.04 | (34) identity_relation_of(all_39_5) = all_39_3
% 141.69/21.05 | (35) identity_relation_of_type(all_39_5) = all_39_4
% 141.69/21.05 | (36) ~ (all_39_0 = all_39_5) | ~ (all_39_1 = all_39_5)
% 141.69/21.05 |
% 141.69/21.05 | GROUND_INST: instantiating (13) with all_39_5, all_39_5, simplifying with
% 141.69/21.05 | (27), (32) gives:
% 141.69/21.05 | (37) ? [v0: any] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ? [v4:
% 141.69/21.05 | int] : (subset(all_39_5, all_39_5) = v0 & $i(v1) & ( ~ (v0 = 0) | (
% 141.69/21.05 | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (member(v5, all_39_5) =
% 141.69/21.05 | v6) | ~ $i(v5) | ? [v7: any] : ? [v8: any] : (member(v5,
% 141.69/21.05 | all_39_5) = v8 & ilf_type(v5, set_type) = v7 & ( ~ (v8 =
% 141.69/21.05 | 0) | ~ (v7 = 0)))) & ! [v5: $i] : ( ~ (member(v5,
% 141.69/21.05 | all_39_5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: any] :
% 141.69/21.05 | (member(v5, all_39_5) = v7 & ilf_type(v5, set_type) = v6 & ( ~
% 141.69/21.05 | (v6 = 0) | v7 = 0))) & ! [v5: $i] : ( ~ (ilf_type(v5,
% 141.69/21.05 | set_type) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: any] :
% 141.69/21.05 | (member(v5, all_39_5) = v7 & member(v5, all_39_5) = v6 & ( ~
% 141.69/21.05 | (v6 = 0) | v7 = 0))))) & (v0 = 0 | (v3 = 0 & v2 = 0 & ~
% 141.69/21.05 | (v4 = 0) & member(v1, all_39_5) = v4 & member(v1, all_39_5) = 0
% 141.69/21.05 | & ilf_type(v1, set_type) = 0)))
% 141.69/21.05 |
% 141.69/21.05 | GROUND_INST: instantiating (11) with all_39_5, all_39_5, simplifying with
% 141.69/21.05 | (27), (32) gives:
% 141.69/21.05 | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (cross_product(all_39_5,
% 141.69/21.05 | all_39_5) = v0 & subset_type(v0) = v1 & relation_type(all_39_5,
% 141.69/21.05 | all_39_5) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4:
% 141.69/21.05 | int] : (v4 = 0 | ~ (ilf_type(v3, v2) = v4) | ~ $i(v3) | ? [v5:
% 141.69/21.05 | int] : ( ~ (v5 = 0) & ilf_type(v3, v1) = v5)) & ! [v3: $i] : !
% 141.69/21.05 | [v4: int] : (v4 = 0 | ~ (ilf_type(v3, v1) = v4) | ~ $i(v3) | ?
% 141.69/21.05 | [v5: int] : ( ~ (v5 = 0) & ilf_type(v3, v2) = v5)) & ! [v3: $i] :
% 141.69/21.05 | ( ~ (ilf_type(v3, v2) = 0) | ~ $i(v3) | ilf_type(v3, v1) = 0) & !
% 141.69/21.05 | [v3: $i] : ( ~ (ilf_type(v3, v1) = 0) | ~ $i(v3) | ilf_type(v3, v2)
% 141.69/21.05 | = 0))
% 141.69/21.05 |
% 141.69/21.05 | GROUND_INST: instantiating (17) with all_39_5, all_39_5, simplifying with
% 141.69/21.05 | (27), (32) gives:
% 141.69/21.05 | (39) ? [v0: $i] : ? [v1: $i] : (subset_type(all_39_5) = v1 &
% 141.69/21.05 | relation_type(all_39_5, all_39_5) = v0 & $i(v1) & $i(v0) & ! [v2:
% 141.69/21.05 | $i] : ! [v3: $i] : ( ~ (range(all_39_5, all_39_5, v2) = v3) | ~
% 141.69/21.05 | $i(v2) | ? [v4: any] : ? [v5: any] : (ilf_type(v3, v1) = v5 &
% 141.69/21.05 | ilf_type(v2, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2: $i] :
% 141.69/21.05 | ( ~ (ilf_type(v2, v0) = 0) | ~ $i(v2) | ? [v3: $i] : (ilf_type(v3,
% 141.69/21.05 | v1) = 0 & range(all_39_5, all_39_5, v2) = v3 & $i(v3))))
% 141.69/21.05 |
% 141.69/21.05 | GROUND_INST: instantiating (1) with all_39_5, all_39_5, simplifying with (27),
% 141.69/21.05 | (32) gives:
% 141.69/21.05 | (40) ? [v0: $i] : ? [v1: $i] : (identity_relation_of(all_39_5) = v1 &
% 141.69/21.05 | relation_type(all_39_5, all_39_5) = v0 & $i(v1) & $i(v0) & ! [v2:
% 141.69/21.05 | $i] : ! [v3: $i] : ( ~ (domain(all_39_5, all_39_5, v2) = v3) | ~
% 141.69/21.05 | $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any]
% 141.69/21.05 | : (ilf_type(v2, v0) = v4 & range(all_39_5, all_39_5, v2) = v6 &
% 141.69/21.05 | subset(v1, v2) = v5 & subset(all_39_5, v6) = v7 & $i(v6) & ( ~
% 141.69/21.05 | (v5 = 0) | ~ (v4 = 0) | (v7 = 0 & v3 = all_39_5)))) & ! [v2:
% 141.69/21.05 | $i] : ! [v3: $i] : ( ~ (range(all_39_5, all_39_5, v2) = v3) | ~
% 141.69/21.05 | $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any]
% 141.69/21.05 | : (ilf_type(v2, v0) = v4 & domain(all_39_5, all_39_5, v2) = v6 &
% 141.69/21.05 | subset(v1, v2) = v5 & subset(all_39_5, v3) = v7 & $i(v6) & ( ~
% 141.69/21.05 | (v5 = 0) | ~ (v4 = 0) | (v7 = 0 & v6 = all_39_5)))) & ! [v2:
% 141.69/21.05 | $i] : ( ~ (ilf_type(v2, v0) = 0) | ~ $i(v2) | ? [v3: any] : ?
% 141.69/21.05 | [v4: $i] : ? [v5: $i] : ? [v6: any] : (domain(all_39_5,
% 141.69/21.05 | all_39_5, v2) = v4 & range(all_39_5, all_39_5, v2) = v5 &
% 141.69/21.05 | subset(v1, v2) = v3 & subset(all_39_5, v5) = v6 & $i(v5) &
% 141.69/21.05 | $i(v4) & ( ~ (v3 = 0) | (v6 = 0 & v4 = all_39_5)))) & ! [v2:
% 141.69/21.05 | $i] : ( ~ (subset(v1, v2) = 0) | ~ $i(v2) | ? [v3: any] : ?
% 141.69/21.05 | [v4: $i] : ? [v5: $i] : ? [v6: any] : (ilf_type(v2, v0) = v3 &
% 141.69/21.05 | domain(all_39_5, all_39_5, v2) = v4 & range(all_39_5, all_39_5,
% 141.69/21.05 | v2) = v5 & subset(all_39_5, v5) = v6 & $i(v5) & $i(v4) & ( ~
% 141.69/21.05 | (v3 = 0) | (v6 = 0 & v4 = all_39_5)))))
% 141.69/21.05 |
% 141.69/21.05 | GROUND_INST: instantiating (3) with all_39_5, all_39_5, simplifying with (27),
% 141.69/21.05 | (32) gives:
% 141.69/21.06 | (41) ? [v0: $i] : ? [v1: $i] : (identity_relation_of(all_39_5) = v1 &
% 141.69/21.06 | relation_type(all_39_5, all_39_5) = v0 & $i(v1) & $i(v0) & ! [v2:
% 141.69/21.06 | $i] : ! [v3: $i] : ( ~ (domain(all_39_5, all_39_5, v2) = v3) | ~
% 141.69/21.06 | $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: $i]
% 141.69/21.06 | : (ilf_type(v2, v0) = v4 & range(all_39_5, all_39_5, v2) = v7 &
% 141.69/21.06 | subset(v1, v2) = v5 & subset(all_39_5, v3) = v6 & $i(v7) & ( ~
% 141.69/21.06 | (v5 = 0) | ~ (v4 = 0) | (v7 = all_39_5 & v6 = 0)))) & ! [v2:
% 141.69/21.06 | $i] : ! [v3: $i] : ( ~ (range(all_39_5, all_39_5, v2) = v3) | ~
% 141.69/21.06 | $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any]
% 141.69/21.06 | : (ilf_type(v2, v0) = v4 & domain(all_39_5, all_39_5, v2) = v6 &
% 141.69/21.06 | subset(v1, v2) = v5 & subset(all_39_5, v6) = v7 & $i(v6) & ( ~
% 141.69/21.06 | (v5 = 0) | ~ (v4 = 0) | (v7 = 0 & v3 = all_39_5)))) & ! [v2:
% 141.69/21.06 | $i] : ( ~ (ilf_type(v2, v0) = 0) | ~ $i(v2) | ? [v3: any] : ?
% 141.69/21.06 | [v4: $i] : ? [v5: any] : ? [v6: $i] : (domain(all_39_5,
% 141.69/21.06 | all_39_5, v2) = v4 & range(all_39_5, all_39_5, v2) = v6 &
% 141.69/21.06 | subset(v1, v2) = v3 & subset(all_39_5, v4) = v5 & $i(v6) &
% 141.69/21.06 | $i(v4) & ( ~ (v3 = 0) | (v6 = all_39_5 & v5 = 0)))) & ! [v2:
% 141.69/21.06 | $i] : ( ~ (subset(v1, v2) = 0) | ~ $i(v2) | ? [v3: any] : ?
% 141.69/21.06 | [v4: $i] : ? [v5: any] : ? [v6: $i] : (ilf_type(v2, v0) = v3 &
% 141.69/21.06 | domain(all_39_5, all_39_5, v2) = v4 & range(all_39_5, all_39_5,
% 141.69/21.06 | v2) = v6 & subset(all_39_5, v4) = v5 & $i(v6) & $i(v4) & ( ~
% 141.69/21.06 | (v3 = 0) | (v6 = all_39_5 & v5 = 0)))))
% 141.69/21.06 |
% 141.69/21.06 | GROUND_INST: instantiating (12) with all_39_5, all_39_5, simplifying with
% 141.69/21.06 | (27), (32) gives:
% 141.69/21.06 | (42) ? [v0: $i] : ? [v1: $i] : (relation_type(all_39_5, all_39_5) = v0 &
% 141.69/21.06 | ilf_type(v1, v0) = 0 & $i(v1) & $i(v0))
% 141.69/21.06 |
% 141.69/21.06 | GROUND_INST: instantiating (10) with all_39_5, all_39_5, simplifying with
% 141.69/21.06 | (27), (32) gives:
% 141.69/21.06 | (43) subset(all_39_5, all_39_5) = 0
% 141.69/21.06 |
% 141.69/21.06 | GROUND_INST: instantiating (16) with all_39_5, all_39_5, simplifying with
% 141.69/21.06 | (27), (32) gives:
% 141.69/21.06 | (44) ? [v0: $i] : (relation_type(all_39_5, all_39_5) = v0 & $i(v0) & !
% 141.69/21.06 | [v1: $i] : ! [v2: $i] : ( ~ (range_of(v1) = v2) | ~ $i(v1) | ?
% 141.69/21.06 | [v3: any] : ? [v4: $i] : (ilf_type(v1, v0) = v3 & range(all_39_5,
% 141.69/21.06 | all_39_5, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | v4 = v2))) & !
% 141.69/21.06 | [v1: $i] : ! [v2: $i] : ( ~ (range(all_39_5, all_39_5, v1) = v2) |
% 141.69/21.06 | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (range_of(v1) = v4 &
% 141.69/21.06 | ilf_type(v1, v0) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v2))) & !
% 141.69/21.06 | [v1: $i] : ( ~ (ilf_type(v1, v0) = 0) | ~ $i(v1) | ? [v2: $i] :
% 141.69/21.06 | (range_of(v1) = v2 & range(all_39_5, all_39_5, v1) = v2 &
% 141.69/21.06 | $i(v2))))
% 141.69/21.06 |
% 141.69/21.06 | GROUND_INST: instantiating (14) with all_39_5, all_39_5, simplifying with
% 141.69/21.06 | (27), (32) gives:
% 141.69/21.06 | (45) ? [v0: $i] : (relation_type(all_39_5, all_39_5) = v0 & $i(v0) & !
% 141.69/21.06 | [v1: $i] : ! [v2: $i] : ( ~ (domain_of(v1) = v2) | ~ $i(v1) | ?
% 141.69/21.06 | [v3: any] : ? [v4: $i] : (ilf_type(v1, v0) = v3 &
% 141.69/21.06 | domain(all_39_5, all_39_5, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | v4
% 141.69/21.06 | = v2))) & ! [v1: $i] : ! [v2: $i] : ( ~ (domain(all_39_5,
% 141.69/21.06 | all_39_5, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] :
% 141.69/21.06 | (domain_of(v1) = v4 & ilf_type(v1, v0) = v3 & $i(v4) & ( ~ (v3 =
% 141.69/21.06 | 0) | v4 = v2))) & ! [v1: $i] : ( ~ (ilf_type(v1, v0) = 0) |
% 141.69/21.06 | ~ $i(v1) | ? [v2: $i] : (domain_of(v1) = v2 & domain(all_39_5,
% 141.69/21.06 | all_39_5, v1) = v2 & $i(v2))))
% 141.69/21.06 |
% 141.69/21.06 | GROUND_INST: instantiating (8) with all_39_5, simplifying with (27), (32)
% 141.69/21.06 | gives:
% 141.69/21.06 | (46) ? [v0: $i] : ? [v1: $i] : (identity_relation_of_type(all_39_5) = v0
% 141.69/21.06 | & relation_type(all_39_5, all_39_5) = v1 & $i(v1) & $i(v0) & ! [v2:
% 141.69/21.06 | $i] : ! [v3: any] : ( ~ (ilf_type(v2, v1) = v3) | ~ $i(v2) | ?
% 141.69/21.06 | [v4: any] : ? [v5: any] : (ilf_type(v2, v0) = v5 & ilf_type(v2,
% 141.69/21.06 | set_type) = v4 & ( ~ (v4 = 0) | (( ~ (v5 = 0) | v3 = 0) & ( ~
% 141.69/21.06 | (v3 = 0) | v5 = 0))))) & ! [v2: $i] : ! [v3: any] : ( ~
% 141.69/21.06 | (ilf_type(v2, v0) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any]
% 141.69/21.06 | : (ilf_type(v2, v1) = v5 & ilf_type(v2, set_type) = v4 & ( ~ (v4 =
% 141.69/21.06 | 0) | (( ~ (v5 = 0) | v3 = 0) & ( ~ (v3 = 0) | v5 = 0))))) &
% 141.69/21.06 | ! [v2: $i] : ( ~ (ilf_type(v2, set_type) = 0) | ~ $i(v2) | ? [v3:
% 141.69/21.06 | any] : ? [v4: any] : (ilf_type(v2, v1) = v4 & ilf_type(v2, v0)
% 141.69/21.06 | = v3 & ( ~ (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) | v4 = 0))))
% 141.69/21.06 |
% 141.69/21.06 | GROUND_INST: instantiating (15) with all_39_5, simplifying with (27), (32)
% 141.69/21.06 | gives:
% 141.69/21.07 | (47) ? [v0: $i] : (subset_type(all_39_5) = v0 & $i(v0) & ! [v1: $i] : !
% 141.69/21.07 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (relation_type(all_39_5,
% 141.69/21.07 | v1) = v2) | ~ (domain(all_39_5, v1, v3) = v4) | ~ $i(v3) |
% 141.69/21.07 | ~ $i(v1) | ? [v5: int] : ? [v6: any] : (( ~ (v5 = 0) &
% 141.69/21.07 | ilf_type(v1, set_type) = v5) | (ilf_type(v4, v0) = v6 &
% 141.69/21.07 | ilf_type(v3, v2) = v5 & ( ~ (v5 = 0) | v6 = 0)))) & ! [v1:
% 141.69/21.07 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (relation_type(all_39_5, v1)
% 141.69/21.07 | = v2) | ~ (ilf_type(v3, v2) = 0) | ~ $i(v3) | ~ $i(v1) | ?
% 141.69/21.07 | [v4: any] : ? [v5: int] : ((v5 = 0 & ilf_type(v4, v0) = 0 &
% 141.69/21.07 | domain(all_39_5, v1, v3) = v4 & $i(v4)) | ( ~ (v4 = 0) &
% 141.69/21.07 | ilf_type(v1, set_type) = v4))) & ! [v1: $i] : ( ~
% 141.69/21.07 | (ilf_type(v1, set_type) = 0) | ~ $i(v1) | ? [v2: $i] :
% 141.69/21.07 | (relation_type(all_39_5, v1) = v2 & $i(v2) & ! [v3: $i] : ! [v4:
% 141.69/21.07 | $i] : ( ~ (domain(all_39_5, v1, v3) = v4) | ~ $i(v3) | ?
% 141.69/21.07 | [v5: any] : ? [v6: any] : (ilf_type(v4, v0) = v6 &
% 141.69/21.07 | ilf_type(v3, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v3:
% 141.69/21.07 | $i] : ( ~ (ilf_type(v3, v2) = 0) | ~ $i(v3) | ? [v4: $i] :
% 141.69/21.07 | (ilf_type(v4, v0) = 0 & domain(all_39_5, v1, v3) = v4 &
% 141.69/21.07 | $i(v4))))))
% 141.69/21.07 |
% 141.69/21.07 | GROUND_INST: instantiating (6) with all_39_5, simplifying with (27), (32)
% 141.69/21.07 | gives:
% 141.69/21.07 | (48) ? [v0: $i] : (identity_relation_of(all_39_5) = v0 & ilf_type(v0,
% 141.69/21.07 | binary_relation_type) = 0 & $i(v0))
% 141.69/21.07 |
% 141.69/21.07 | GROUND_INST: instantiating (5) with all_39_5, simplifying with (27), (32)
% 141.69/21.07 | gives:
% 141.69/21.07 | (49) ? [v0: $i] : (identity_relation_of(all_39_5) = v0 & $i(v0) & ! [v1:
% 141.69/21.07 | $i] : ! [v2: any] : ! [v3: $i] : ! [v4: $i] : ( ~
% 141.69/21.07 | (ordered_pair(v1, v3) = v4) | ~ (member(v1, all_39_5) = v2) | ~
% 141.69/21.07 | $i(v3) | ~ $i(v1) | ? [v5: int] : ? [v6: any] : (( ~ (v5 = 0) &
% 141.69/21.07 | ilf_type(v1, set_type) = v5) | (member(v4, v0) = v6 &
% 141.69/21.07 | ilf_type(v3, set_type) = v5 & ( ~ (v5 = 0) | (( ~ (v6 = 0) |
% 141.69/21.07 | (v3 = v1 & v2 = 0)) & ( ~ (v3 = v1) | ~ (v2 = 0) | v6 =
% 141.69/21.07 | 0)))))) & ! [v1: $i] : ! [v2: any] : ! [v3: $i] : ( ~
% 141.69/21.07 | (member(v1, all_39_5) = v2) | ~ (ilf_type(v3, set_type) = 0) | ~
% 141.69/21.07 | $i(v3) | ~ $i(v1) | ? [v4: any] : ? [v5: any] : (( ~ (v4 = 0) &
% 141.69/21.07 | ilf_type(v1, set_type) = v4) | (ordered_pair(v1, v3) = v4 &
% 141.69/21.07 | member(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | (v3 = v1 & v2 =
% 141.69/21.07 | 0)) & ( ~ (v3 = v1) | ~ (v2 = 0) | v5 = 0)))) & ! [v1:
% 141.69/21.07 | $i] : ( ~ (ilf_type(v1, set_type) = 0) | ~ $i(v1) | ? [v2: any]
% 141.69/21.07 | : (member(v1, all_39_5) = v2 & ! [v3: $i] : ! [v4: $i] : ( ~
% 141.69/21.07 | (ordered_pair(v1, v3) = v4) | ~ $i(v3) | ? [v5: any] : ?
% 141.69/21.07 | [v6: any] : (member(v4, v0) = v6 & ilf_type(v3, set_type) = v5
% 141.69/21.07 | & ( ~ (v5 = 0) | (( ~ (v6 = 0) | (v3 = v1 & v2 = 0)) & ( ~
% 141.69/21.07 | (v3 = v1) | ~ (v2 = 0) | v6 = 0))))) & ! [v3: $i] :
% 141.69/21.07 | ( ~ (ilf_type(v3, set_type) = 0) | ~ $i(v3) | ? [v4: $i] : ?
% 141.69/21.07 | [v5: any] : (ordered_pair(v1, v3) = v4 & member(v4, v0) = v5 &
% 141.69/21.07 | $i(v4) & ( ~ (v5 = 0) | (v3 = v1 & v2 = 0)) & ( ~ (v3 = v1)
% 141.69/21.07 | | ~ (v2 = 0) | v5 = 0))))))
% 141.69/21.07 |
% 141.69/21.07 | GROUND_INST: instantiating (2) with all_39_5, all_39_5, all_39_3, simplifying
% 141.69/21.07 | with (27), (32), (34) gives:
% 141.69/21.07 | (50) ? [v0: any] : ? [v1: $i] : (relation_type(all_39_5, all_39_5) = v1 &
% 141.69/21.07 | ilf_type(all_39_5, set_type) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2:
% 141.69/21.07 | $i] : ! [v3: $i] : ( ~ (domain(all_39_5, all_39_5, v2) = v3)
% 141.69/21.07 | | ~ $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: $i] : ?
% 141.69/21.07 | [v7: any] : (ilf_type(v2, v1) = v4 & range(all_39_5, all_39_5,
% 141.69/21.07 | v2) = v6 & subset(all_39_3, v2) = v5 & subset(all_39_5,
% 141.69/21.07 | v6) = v7 & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | (v7 = 0 &
% 141.69/21.07 | v3 = all_39_5)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 141.69/21.07 | (range(all_39_5, all_39_5, v2) = v3) | ~ $i(v2) | ? [v4:
% 141.69/21.07 | any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] :
% 141.69/21.07 | (ilf_type(v2, v1) = v4 & domain(all_39_5, all_39_5, v2) = v6 &
% 141.69/21.07 | subset(all_39_3, v2) = v5 & subset(all_39_5, v3) = v7 &
% 141.69/21.07 | $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | (v7 = 0 & v6 =
% 141.69/21.07 | all_39_5)))) & ! [v2: $i] : ( ~ (ilf_type(v2, v1) = 0)
% 141.69/21.07 | | ~ $i(v2) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ?
% 141.69/21.07 | [v6: any] : (domain(all_39_5, all_39_5, v2) = v4 &
% 141.69/21.07 | range(all_39_5, all_39_5, v2) = v5 & subset(all_39_3, v2) =
% 141.69/21.07 | v3 & subset(all_39_5, v5) = v6 & $i(v5) & $i(v4) & ( ~ (v3 =
% 141.69/21.07 | 0) | (v6 = 0 & v4 = all_39_5)))) & ! [v2: $i] : ( ~
% 141.69/21.07 | (subset(all_39_3, v2) = 0) | ~ $i(v2) | ? [v3: any] : ?
% 141.69/21.07 | [v4: $i] : ? [v5: $i] : ? [v6: any] : (ilf_type(v2, v1) = v3
% 141.69/21.07 | & domain(all_39_5, all_39_5, v2) = v4 & range(all_39_5,
% 141.69/21.07 | all_39_5, v2) = v5 & subset(all_39_5, v5) = v6 & $i(v5) &
% 141.69/21.07 | $i(v4) & ( ~ (v3 = 0) | (v6 = 0 & v4 = all_39_5)))))))
% 141.69/21.07 |
% 141.69/21.07 | GROUND_INST: instantiating (4) with all_39_5, all_39_5, all_39_3, simplifying
% 141.69/21.07 | with (27), (32), (34) gives:
% 141.69/21.08 | (51) ? [v0: any] : ? [v1: $i] : (relation_type(all_39_5, all_39_5) = v1 &
% 141.69/21.08 | ilf_type(all_39_5, set_type) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2:
% 141.69/21.08 | $i] : ! [v3: $i] : ( ~ (domain(all_39_5, all_39_5, v2) = v3)
% 141.69/21.08 | | ~ $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ?
% 141.69/21.08 | [v7: $i] : (ilf_type(v2, v1) = v4 & range(all_39_5, all_39_5,
% 141.69/21.08 | v2) = v7 & subset(all_39_3, v2) = v5 & subset(all_39_5,
% 141.69/21.08 | v3) = v6 & $i(v7) & ( ~ (v5 = 0) | ~ (v4 = 0) | (v7 =
% 141.69/21.08 | all_39_5 & v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 141.69/21.08 | (range(all_39_5, all_39_5, v2) = v3) | ~ $i(v2) | ? [v4:
% 141.69/21.08 | any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] :
% 141.69/21.08 | (ilf_type(v2, v1) = v4 & domain(all_39_5, all_39_5, v2) = v6 &
% 141.69/21.08 | subset(all_39_3, v2) = v5 & subset(all_39_5, v6) = v7 &
% 141.69/21.08 | $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | (v7 = 0 & v3 =
% 141.69/21.08 | all_39_5)))) & ! [v2: $i] : ( ~ (ilf_type(v2, v1) = 0)
% 141.69/21.08 | | ~ $i(v2) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : ?
% 141.69/21.08 | [v6: $i] : (domain(all_39_5, all_39_5, v2) = v4 &
% 141.69/21.08 | range(all_39_5, all_39_5, v2) = v6 & subset(all_39_3, v2) =
% 141.69/21.08 | v3 & subset(all_39_5, v4) = v5 & $i(v6) & $i(v4) & ( ~ (v3 =
% 141.69/21.08 | 0) | (v6 = all_39_5 & v5 = 0)))) & ! [v2: $i] : ( ~
% 141.69/21.08 | (subset(all_39_3, v2) = 0) | ~ $i(v2) | ? [v3: any] : ?
% 141.69/21.08 | [v4: $i] : ? [v5: any] : ? [v6: $i] : (ilf_type(v2, v1) = v3
% 141.69/21.08 | & domain(all_39_5, all_39_5, v2) = v4 & range(all_39_5,
% 141.69/21.08 | all_39_5, v2) = v6 & subset(all_39_5, v4) = v5 & $i(v6) &
% 141.69/21.08 | $i(v4) & ( ~ (v3 = 0) | (v6 = all_39_5 & v5 = 0)))))))
% 141.69/21.08 |
% 141.69/21.08 | GROUND_INST: instantiating (7) with all_39_5, all_39_3, simplifying with (27),
% 141.69/21.08 | (34) gives:
% 141.69/21.08 | (52) ? [v0: any] : ? [v1: any] : (ilf_type(all_39_3,
% 141.69/21.08 | binary_relation_type) = v1 & ilf_type(all_39_5, set_type) = v0 & (
% 141.69/21.08 | ~ (v0 = 0) | v1 = 0))
% 141.69/21.08 |
% 141.69/21.08 | GROUND_INST: instantiating (9) with all_39_5, all_39_4, simplifying with (27),
% 141.69/21.08 | (35) gives:
% 141.69/21.08 | (53) ? [v0: any] : ? [v1: $i] : (relation_type(all_39_5, all_39_5) = v1 &
% 141.69/21.08 | ilf_type(all_39_5, set_type) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2:
% 141.69/21.08 | $i] : ! [v3: any] : ( ~ (ilf_type(v2, v1) = v3) | ~ $i(v2) |
% 141.69/21.08 | ? [v4: any] : ? [v5: any] : (ilf_type(v2, all_39_4) = v5 &
% 141.69/21.08 | ilf_type(v2, set_type) = v4 & ( ~ (v4 = 0) | (( ~ (v5 = 0) |
% 141.69/21.08 | v3 = 0) & ( ~ (v3 = 0) | v5 = 0))))) & ! [v2: $i] :
% 141.69/21.08 | ! [v3: any] : ( ~ (ilf_type(v2, all_39_4) = v3) | ~ $i(v2) | ?
% 141.69/21.08 | [v4: any] : ? [v5: any] : (ilf_type(v2, v1) = v5 &
% 141.69/21.08 | ilf_type(v2, set_type) = v4 & ( ~ (v4 = 0) | (( ~ (v5 = 0) |
% 141.69/21.08 | v3 = 0) & ( ~ (v3 = 0) | v5 = 0))))) & ! [v2: $i] : (
% 141.69/21.08 | ~ (ilf_type(v2, set_type) = 0) | ~ $i(v2) | ? [v3: any] : ?
% 141.69/21.08 | [v4: any] : (ilf_type(v2, v1) = v4 & ilf_type(v2, all_39_4) =
% 141.69/21.08 | v3 & ( ~ (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) | v4 = 0))))))
% 141.69/21.08 |
% 141.69/21.08 | DELTA: instantiating (48) with fresh symbol all_47_0 gives:
% 141.69/21.08 | (54) identity_relation_of(all_39_5) = all_47_0 & ilf_type(all_47_0,
% 141.69/21.08 | binary_relation_type) = 0 & $i(all_47_0)
% 141.69/21.08 |
% 141.69/21.08 | ALPHA: (54) implies:
% 141.69/21.08 | (55) identity_relation_of(all_39_5) = all_47_0
% 141.69/21.08 |
% 141.69/21.08 | DELTA: instantiating (52) with fresh symbols all_65_0, all_65_1 gives:
% 141.69/21.08 | (56) ilf_type(all_39_3, binary_relation_type) = all_65_0 &
% 141.69/21.08 | ilf_type(all_39_5, set_type) = all_65_1 & ( ~ (all_65_1 = 0) |
% 141.69/21.08 | all_65_0 = 0)
% 141.69/21.08 |
% 141.69/21.08 | ALPHA: (56) implies:
% 141.69/21.08 | (57) ilf_type(all_39_5, set_type) = all_65_1
% 141.69/21.08 |
% 141.69/21.08 | DELTA: instantiating (42) with fresh symbols all_67_0, all_67_1 gives:
% 141.69/21.08 | (58) relation_type(all_39_5, all_39_5) = all_67_1 & ilf_type(all_67_0,
% 141.69/21.08 | all_67_1) = 0 & $i(all_67_0) & $i(all_67_1)
% 141.69/21.08 |
% 141.69/21.08 | ALPHA: (58) implies:
% 141.69/21.08 | (59) relation_type(all_39_5, all_39_5) = all_67_1
% 141.69/21.08 |
% 141.69/21.08 | DELTA: instantiating (39) with fresh symbols all_82_0, all_82_1 gives:
% 141.69/21.08 | (60) subset_type(all_39_5) = all_82_0 & relation_type(all_39_5, all_39_5) =
% 141.69/21.08 | all_82_1 & $i(all_82_0) & $i(all_82_1) & ! [v0: $i] : ! [v1: $i] : (
% 141.69/21.08 | ~ (range(all_39_5, all_39_5, v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 141.69/21.08 | ? [v3: any] : (ilf_type(v1, all_82_0) = v3 & ilf_type(v0, all_82_1)
% 141.69/21.08 | = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (ilf_type(v0,
% 141.69/21.08 | all_82_1) = 0) | ~ $i(v0) | ? [v1: $i] : (ilf_type(v1,
% 141.69/21.08 | all_82_0) = 0 & range(all_39_5, all_39_5, v0) = v1 & $i(v1)))
% 141.69/21.08 |
% 141.69/21.08 | ALPHA: (60) implies:
% 141.69/21.08 | (61) relation_type(all_39_5, all_39_5) = all_82_1
% 141.69/21.08 | (62) ! [v0: $i] : ! [v1: $i] : ( ~ (range(all_39_5, all_39_5, v0) = v1) |
% 141.69/21.08 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (ilf_type(v1, all_82_0) =
% 141.69/21.08 | v3 & ilf_type(v0, all_82_1) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 141.69/21.08 |
% 141.69/21.08 | GROUND_INST: instantiating (62) with all_39_2, all_39_0, simplifying with
% 141.69/21.08 | (28), (30) gives:
% 141.69/21.08 | (63) ? [v0: any] : ? [v1: any] : (ilf_type(all_39_0, all_82_0) = v1 &
% 141.69/21.08 | ilf_type(all_39_2, all_82_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 141.69/21.08 |
% 141.69/21.08 | DELTA: instantiating (45) with fresh symbol all_87_0 gives:
% 141.69/21.08 | (64) relation_type(all_39_5, all_39_5) = all_87_0 & $i(all_87_0) & ! [v0:
% 141.69/21.08 | $i] : ! [v1: $i] : ( ~ (domain_of(v0) = v1) | ~ $i(v0) | ? [v2:
% 141.69/21.08 | any] : ? [v3: $i] : (ilf_type(v0, all_87_0) = v2 &
% 141.69/21.08 | domain(all_39_5, all_39_5, v0) = v3 & $i(v3) & ( ~ (v2 = 0) | v3 =
% 141.69/21.08 | v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (domain(all_39_5,
% 141.69/21.08 | all_39_5, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] :
% 141.69/21.08 | (domain_of(v0) = v3 & ilf_type(v0, all_87_0) = v2 & $i(v3) & ( ~ (v2
% 141.69/21.08 | = 0) | v3 = v1))) & ! [v0: $i] : ( ~ (ilf_type(v0, all_87_0)
% 141.69/21.08 | = 0) | ~ $i(v0) | ? [v1: $i] : (domain_of(v0) = v1 &
% 141.69/21.08 | domain(all_39_5, all_39_5, v0) = v1 & $i(v1)))
% 141.69/21.08 |
% 141.69/21.08 | ALPHA: (64) implies:
% 141.69/21.08 | (65) relation_type(all_39_5, all_39_5) = all_87_0
% 141.69/21.09 | (66) ! [v0: $i] : ! [v1: $i] : ( ~ (domain(all_39_5, all_39_5, v0) = v1)
% 141.69/21.09 | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (domain_of(v0) = v3 &
% 141.69/21.09 | ilf_type(v0, all_87_0) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = v1)))
% 141.69/21.09 |
% 141.69/21.09 | GROUND_INST: instantiating (66) with all_39_2, all_39_1, simplifying with
% 141.69/21.09 | (28), (31) gives:
% 141.69/21.09 | (67) ? [v0: any] : ? [v1: $i] : (domain_of(all_39_2) = v1 &
% 141.69/21.09 | ilf_type(all_39_2, all_87_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 141.69/21.09 | all_39_1))
% 141.69/21.09 |
% 141.69/21.09 | DELTA: instantiating (44) with fresh symbol all_90_0 gives:
% 141.69/21.09 | (68) relation_type(all_39_5, all_39_5) = all_90_0 & $i(all_90_0) & ! [v0:
% 141.69/21.09 | $i] : ! [v1: $i] : ( ~ (range_of(v0) = v1) | ~ $i(v0) | ? [v2:
% 141.69/21.09 | any] : ? [v3: $i] : (ilf_type(v0, all_90_0) = v2 &
% 141.69/21.09 | range(all_39_5, all_39_5, v0) = v3 & $i(v3) & ( ~ (v2 = 0) | v3 =
% 141.69/21.09 | v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (range(all_39_5,
% 141.69/21.09 | all_39_5, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] :
% 141.69/21.09 | (range_of(v0) = v3 & ilf_type(v0, all_90_0) = v2 & $i(v3) & ( ~ (v2
% 141.69/21.09 | = 0) | v3 = v1))) & ! [v0: $i] : ( ~ (ilf_type(v0, all_90_0)
% 141.69/21.09 | = 0) | ~ $i(v0) | ? [v1: $i] : (range_of(v0) = v1 &
% 141.69/21.09 | range(all_39_5, all_39_5, v0) = v1 & $i(v1)))
% 141.69/21.09 |
% 141.69/21.09 | ALPHA: (68) implies:
% 141.69/21.09 | (69) relation_type(all_39_5, all_39_5) = all_90_0
% 141.69/21.09 | (70) ! [v0: $i] : ! [v1: $i] : ( ~ (range(all_39_5, all_39_5, v0) = v1) |
% 141.69/21.09 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (range_of(v0) = v3 &
% 141.69/21.09 | ilf_type(v0, all_90_0) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = v1)))
% 141.69/21.09 |
% 141.69/21.09 | GROUND_INST: instantiating (70) with all_39_2, all_39_0, simplifying with
% 141.69/21.09 | (28), (30) gives:
% 141.69/21.09 | (71) ? [v0: any] : ? [v1: $i] : (range_of(all_39_2) = v1 &
% 141.69/21.09 | ilf_type(all_39_2, all_90_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 141.69/21.09 | all_39_0))
% 141.69/21.09 |
% 141.69/21.09 | DELTA: instantiating (38) with fresh symbols all_93_0, all_93_1, all_93_2
% 141.69/21.09 | gives:
% 141.69/21.09 | (72) cross_product(all_39_5, all_39_5) = all_93_2 & subset_type(all_93_2) =
% 141.69/21.09 | all_93_1 & relation_type(all_39_5, all_39_5) = all_93_0 & $i(all_93_0)
% 141.69/21.09 | & $i(all_93_1) & $i(all_93_2) & ! [v0: $i] : ! [v1: int] : (v1 = 0 |
% 141.69/21.09 | ~ (ilf_type(v0, all_93_0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~
% 141.69/21.09 | (v2 = 0) & ilf_type(v0, all_93_1) = v2)) & ! [v0: $i] : ! [v1:
% 141.69/21.09 | int] : (v1 = 0 | ~ (ilf_type(v0, all_93_1) = v1) | ~ $i(v0) | ?
% 141.69/21.09 | [v2: int] : ( ~ (v2 = 0) & ilf_type(v0, all_93_0) = v2)) & ! [v0:
% 141.69/21.09 | $i] : ( ~ (ilf_type(v0, all_93_0) = 0) | ~ $i(v0) | ilf_type(v0,
% 141.69/21.09 | all_93_1) = 0) & ! [v0: $i] : ( ~ (ilf_type(v0, all_93_1) = 0) |
% 141.69/21.09 | ~ $i(v0) | ilf_type(v0, all_93_0) = 0)
% 141.69/21.09 |
% 141.69/21.09 | ALPHA: (72) implies:
% 141.69/21.09 | (73) relation_type(all_39_5, all_39_5) = all_93_0
% 141.69/21.09 |
% 141.69/21.09 | DELTA: instantiating (37) with fresh symbols all_97_0, all_97_1, all_97_2,
% 141.69/21.09 | all_97_3, all_97_4 gives:
% 141.69/21.09 | (74) subset(all_39_5, all_39_5) = all_97_4 & $i(all_97_3) & ( ~ (all_97_4 =
% 141.69/21.09 | 0) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (member(v0,
% 141.69/21.09 | all_39_5) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 141.69/21.09 | (member(v0, all_39_5) = v3 & ilf_type(v0, set_type) = v2 & ( ~
% 141.69/21.09 | (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ( ~ (member(v0,
% 141.69/21.09 | all_39_5) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] :
% 141.69/21.09 | (member(v0, all_39_5) = v2 & ilf_type(v0, set_type) = v1 & ( ~
% 141.69/21.09 | (v1 = 0) | v2 = 0))) & ! [v0: $i] : ( ~ (ilf_type(v0,
% 141.69/21.09 | set_type) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] :
% 141.69/21.09 | (member(v0, all_39_5) = v2 & member(v0, all_39_5) = v1 & ( ~ (v1
% 141.69/21.09 | = 0) | v2 = 0))))) & (all_97_4 = 0 | (all_97_1 = 0 &
% 141.69/21.09 | all_97_2 = 0 & ~ (all_97_0 = 0) & member(all_97_3, all_39_5) =
% 141.69/21.09 | all_97_0 & member(all_97_3, all_39_5) = 0 & ilf_type(all_97_3,
% 141.69/21.09 | set_type) = 0))
% 141.69/21.09 |
% 141.69/21.09 | ALPHA: (74) implies:
% 141.69/21.09 | (75) subset(all_39_5, all_39_5) = all_97_4
% 141.69/21.09 | (76) ~ (all_97_4 = 0) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 141.69/21.09 | (member(v0, all_39_5) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 141.69/21.09 | any] : (member(v0, all_39_5) = v3 & ilf_type(v0, set_type) = v2
% 141.69/21.09 | & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ( ~ (member(v0,
% 141.69/21.09 | all_39_5) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] :
% 141.69/21.09 | (member(v0, all_39_5) = v2 & ilf_type(v0, set_type) = v1 & ( ~ (v1
% 141.69/21.09 | = 0) | v2 = 0))) & ! [v0: $i] : ( ~ (ilf_type(v0, set_type)
% 141.69/21.09 | = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (member(v0,
% 141.69/21.09 | all_39_5) = v2 & member(v0, all_39_5) = v1 & ( ~ (v1 = 0) | v2
% 141.69/21.09 | = 0))))
% 141.69/21.09 |
% 141.69/21.09 | DELTA: instantiating (53) with fresh symbols all_99_0, all_99_1 gives:
% 141.69/21.10 | (77) relation_type(all_39_5, all_39_5) = all_99_0 & ilf_type(all_39_5,
% 141.69/21.10 | set_type) = all_99_1 & $i(all_99_0) & ( ~ (all_99_1 = 0) | ( ! [v0:
% 141.69/21.10 | $i] : ! [v1: any] : ( ~ (ilf_type(v0, all_99_0) = v1) | ~
% 141.69/21.10 | $i(v0) | ? [v2: any] : ? [v3: any] : (ilf_type(v0, all_39_4) =
% 141.69/21.10 | v3 & ilf_type(v0, set_type) = v2 & ( ~ (v2 = 0) | (( ~ (v3 =
% 141.69/21.10 | 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))))) & ! [v0:
% 141.69/21.10 | $i] : ! [v1: any] : ( ~ (ilf_type(v0, all_39_4) = v1) | ~
% 141.69/21.10 | $i(v0) | ? [v2: any] : ? [v3: any] : (ilf_type(v0, all_99_0) =
% 141.69/21.10 | v3 & ilf_type(v0, set_type) = v2 & ( ~ (v2 = 0) | (( ~ (v3 =
% 141.69/21.10 | 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))))) & ! [v0:
% 141.69/21.10 | $i] : ( ~ (ilf_type(v0, set_type) = 0) | ~ $i(v0) | ? [v1:
% 141.69/21.10 | any] : ? [v2: any] : (ilf_type(v0, all_99_0) = v2 &
% 141.69/21.10 | ilf_type(v0, all_39_4) = v1 & ( ~ (v2 = 0) | v1 = 0) & ( ~ (v1
% 141.69/21.10 | = 0) | v2 = 0)))))
% 141.69/21.10 |
% 141.69/21.10 | ALPHA: (77) implies:
% 141.69/21.10 | (78) ilf_type(all_39_5, set_type) = all_99_1
% 141.69/21.10 | (79) relation_type(all_39_5, all_39_5) = all_99_0
% 141.69/21.10 | (80) ~ (all_99_1 = 0) | ( ! [v0: $i] : ! [v1: any] : ( ~ (ilf_type(v0,
% 141.69/21.10 | all_99_0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 141.69/21.10 | (ilf_type(v0, all_39_4) = v3 & ilf_type(v0, set_type) = v2 & ( ~
% 141.69/21.10 | (v2 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 =
% 141.69/21.10 | 0))))) & ! [v0: $i] : ! [v1: any] : ( ~ (ilf_type(v0,
% 141.69/21.10 | all_39_4) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 141.69/21.10 | (ilf_type(v0, all_99_0) = v3 & ilf_type(v0, set_type) = v2 & ( ~
% 141.69/21.10 | (v2 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 =
% 141.69/21.10 | 0))))) & ! [v0: $i] : ( ~ (ilf_type(v0, set_type) = 0) |
% 141.69/21.10 | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (ilf_type(v0, all_99_0) =
% 141.69/21.10 | v2 & ilf_type(v0, all_39_4) = v1 & ( ~ (v2 = 0) | v1 = 0) & ( ~
% 141.69/21.10 | (v1 = 0) | v2 = 0))))
% 141.69/21.10 |
% 141.69/21.10 | DELTA: instantiating (46) with fresh symbols all_101_0, all_101_1 gives:
% 141.69/21.10 | (81) identity_relation_of_type(all_39_5) = all_101_1 &
% 141.69/21.10 | relation_type(all_39_5, all_39_5) = all_101_0 & $i(all_101_0) &
% 141.69/21.10 | $i(all_101_1) & ! [v0: $i] : ! [v1: any] : ( ~ (ilf_type(v0,
% 141.69/21.10 | all_101_0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 141.69/21.10 | (ilf_type(v0, all_101_1) = v3 & ilf_type(v0, set_type) = v2 & ( ~
% 141.69/21.10 | (v2 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))))
% 141.69/21.10 | & ! [v0: $i] : ! [v1: any] : ( ~ (ilf_type(v0, all_101_1) = v1) | ~
% 141.69/21.10 | $i(v0) | ? [v2: any] : ? [v3: any] : (ilf_type(v0, all_101_0) = v3
% 141.69/21.10 | & ilf_type(v0, set_type) = v2 & ( ~ (v2 = 0) | (( ~ (v3 = 0) | v1
% 141.69/21.10 | = 0) & ( ~ (v1 = 0) | v3 = 0))))) & ! [v0: $i] : ( ~
% 141.69/21.10 | (ilf_type(v0, set_type) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 141.69/21.10 | any] : (ilf_type(v0, all_101_0) = v2 & ilf_type(v0, all_101_1) =
% 141.69/21.10 | v1 & ( ~ (v2 = 0) | v1 = 0) & ( ~ (v1 = 0) | v2 = 0)))
% 141.69/21.10 |
% 141.69/21.10 | ALPHA: (81) implies:
% 141.69/21.10 | (82) relation_type(all_39_5, all_39_5) = all_101_0
% 141.69/21.10 |
% 141.69/21.10 | DELTA: instantiating (47) with fresh symbol all_111_0 gives:
% 141.69/21.10 | (83) subset_type(all_39_5) = all_111_0 & $i(all_111_0) & ! [v0: $i] : !
% 141.69/21.10 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (relation_type(all_39_5,
% 141.69/21.10 | v0) = v1) | ~ (domain(all_39_5, v0, v2) = v3) | ~ $i(v2) | ~
% 141.69/21.10 | $i(v0) | ? [v4: int] : ? [v5: any] : (( ~ (v4 = 0) & ilf_type(v0,
% 141.69/21.10 | set_type) = v4) | (ilf_type(v3, all_111_0) = v5 & ilf_type(v2,
% 141.69/21.10 | v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))) & ! [v0: $i] : ! [v1:
% 141.69/21.10 | $i] : ! [v2: $i] : ( ~ (relation_type(all_39_5, v0) = v1) | ~
% 141.69/21.10 | (ilf_type(v2, v1) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: any] : ?
% 141.69/21.10 | [v4: int] : ((v4 = 0 & ilf_type(v3, all_111_0) = 0 &
% 141.69/21.10 | domain(all_39_5, v0, v2) = v3 & $i(v3)) | ( ~ (v3 = 0) &
% 141.69/21.10 | ilf_type(v0, set_type) = v3))) & ! [v0: $i] : ( ~ (ilf_type(v0,
% 141.69/21.10 | set_type) = 0) | ~ $i(v0) | ? [v1: $i] :
% 141.69/21.10 | (relation_type(all_39_5, v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3:
% 141.69/21.10 | $i] : ( ~ (domain(all_39_5, v0, v2) = v3) | ~ $i(v2) | ? [v4:
% 141.69/21.10 | any] : ? [v5: any] : (ilf_type(v3, all_111_0) = v5 &
% 141.69/21.10 | ilf_type(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2: $i]
% 141.69/21.10 | : ( ~ (ilf_type(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] :
% 141.69/21.10 | (ilf_type(v3, all_111_0) = 0 & domain(all_39_5, v0, v2) = v3 &
% 141.69/21.10 | $i(v3)))))
% 141.69/21.10 |
% 141.69/21.10 | ALPHA: (83) implies:
% 141.69/21.10 | (84) ! [v0: $i] : ( ~ (ilf_type(v0, set_type) = 0) | ~ $i(v0) | ? [v1:
% 141.69/21.10 | $i] : (relation_type(all_39_5, v0) = v1 & $i(v1) & ! [v2: $i] :
% 141.69/21.10 | ! [v3: $i] : ( ~ (domain(all_39_5, v0, v2) = v3) | ~ $i(v2) | ?
% 141.69/21.10 | [v4: any] : ? [v5: any] : (ilf_type(v3, all_111_0) = v5 &
% 141.69/21.10 | ilf_type(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2: $i]
% 141.69/21.10 | : ( ~ (ilf_type(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] :
% 141.69/21.10 | (ilf_type(v3, all_111_0) = 0 & domain(all_39_5, v0, v2) = v3 &
% 141.69/21.10 | $i(v3)))))
% 141.69/21.10 |
% 141.69/21.10 | GROUND_INST: instantiating (84) with all_39_5, simplifying with (27), (32)
% 141.69/21.10 | gives:
% 141.69/21.10 | (85) ? [v0: $i] : (relation_type(all_39_5, all_39_5) = v0 & $i(v0) & !
% 141.69/21.10 | [v1: $i] : ! [v2: $i] : ( ~ (domain(all_39_5, all_39_5, v1) = v2) |
% 141.69/21.10 | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (ilf_type(v2, all_111_0)
% 141.69/21.10 | = v4 & ilf_type(v1, v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) & !
% 141.69/21.10 | [v1: $i] : ( ~ (ilf_type(v1, v0) = 0) | ~ $i(v1) | ? [v2: $i] :
% 141.69/21.10 | (ilf_type(v2, all_111_0) = 0 & domain(all_39_5, all_39_5, v1) = v2
% 141.69/21.10 | & $i(v2))))
% 141.69/21.10 |
% 141.69/21.10 | DELTA: instantiating (63) with fresh symbols all_114_0, all_114_1 gives:
% 141.69/21.10 | (86) ilf_type(all_39_0, all_82_0) = all_114_0 & ilf_type(all_39_2,
% 141.69/21.10 | all_82_1) = all_114_1 & ( ~ (all_114_1 = 0) | all_114_0 = 0)
% 141.69/21.10 |
% 141.69/21.10 | ALPHA: (86) implies:
% 141.69/21.10 | (87) ilf_type(all_39_2, all_82_1) = all_114_1
% 141.69/21.10 |
% 141.69/21.10 | DELTA: instantiating (50) with fresh symbols all_118_0, all_118_1 gives:
% 141.69/21.11 | (88) relation_type(all_39_5, all_39_5) = all_118_0 & ilf_type(all_39_5,
% 141.69/21.11 | set_type) = all_118_1 & $i(all_118_0) & ( ~ (all_118_1 = 0) | ( !
% 141.69/21.11 | [v0: $i] : ! [v1: $i] : ( ~ (domain(all_39_5, all_39_5, v0) = v1)
% 141.69/21.11 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ?
% 141.69/21.11 | [v5: any] : (ilf_type(v0, all_118_0) = v2 & range(all_39_5,
% 141.69/21.11 | all_39_5, v0) = v4 & subset(all_39_3, v0) = v3 &
% 141.69/21.11 | subset(all_39_5, v4) = v5 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 =
% 141.69/21.11 | 0) | (v5 = 0 & v1 = all_39_5)))) & ! [v0: $i] : ! [v1:
% 141.69/21.11 | $i] : ( ~ (range(all_39_5, all_39_5, v0) = v1) | ~ $i(v0) | ?
% 141.69/21.11 | [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] :
% 141.69/21.11 | (ilf_type(v0, all_118_0) = v2 & domain(all_39_5, all_39_5, v0) =
% 141.69/21.11 | v4 & subset(all_39_3, v0) = v3 & subset(all_39_5, v1) = v5 &
% 141.69/21.11 | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = 0 & v4 =
% 141.69/21.11 | all_39_5)))) & ! [v0: $i] : ( ~ (ilf_type(v0, all_118_0)
% 141.69/21.11 | = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 141.69/21.11 | ? [v4: any] : (domain(all_39_5, all_39_5, v0) = v2 &
% 141.69/21.11 | range(all_39_5, all_39_5, v0) = v3 & subset(all_39_3, v0) = v1
% 141.69/21.11 | & subset(all_39_5, v3) = v4 & $i(v3) & $i(v2) & ( ~ (v1 = 0) |
% 141.69/21.11 | (v4 = 0 & v2 = all_39_5)))) & ! [v0: $i] : ( ~
% 141.69/21.11 | (subset(all_39_3, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 141.69/21.11 | $i] : ? [v3: $i] : ? [v4: any] : (ilf_type(v0, all_118_0) =
% 141.69/21.11 | v1 & domain(all_39_5, all_39_5, v0) = v2 & range(all_39_5,
% 141.69/21.11 | all_39_5, v0) = v3 & subset(all_39_5, v3) = v4 & $i(v3) &
% 141.69/21.11 | $i(v2) & ( ~ (v1 = 0) | (v4 = 0 & v2 = all_39_5))))))
% 141.69/21.11 |
% 141.69/21.11 | ALPHA: (88) implies:
% 141.69/21.11 | (89) ilf_type(all_39_5, set_type) = all_118_1
% 141.69/21.11 | (90) relation_type(all_39_5, all_39_5) = all_118_0
% 141.69/21.11 | (91) ~ (all_118_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ( ~
% 141.69/21.11 | (domain(all_39_5, all_39_5, v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 141.69/21.11 | ? [v3: any] : ? [v4: $i] : ? [v5: any] : (ilf_type(v0,
% 141.69/21.11 | all_118_0) = v2 & range(all_39_5, all_39_5, v0) = v4 &
% 141.69/21.11 | subset(all_39_3, v0) = v3 & subset(all_39_5, v4) = v5 & $i(v4) &
% 141.69/21.11 | ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = 0 & v1 = all_39_5)))) & !
% 141.69/21.11 | [v0: $i] : ! [v1: $i] : ( ~ (range(all_39_5, all_39_5, v0) = v1) |
% 141.69/21.11 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5:
% 141.69/21.11 | any] : (ilf_type(v0, all_118_0) = v2 & domain(all_39_5,
% 141.69/21.11 | all_39_5, v0) = v4 & subset(all_39_3, v0) = v3 &
% 141.69/21.11 | subset(all_39_5, v1) = v5 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0)
% 141.69/21.11 | | (v5 = 0 & v4 = all_39_5)))) & ! [v0: $i] : ( ~
% 141.69/21.11 | (ilf_type(v0, all_118_0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 141.69/21.11 | $i] : ? [v3: $i] : ? [v4: any] : (domain(all_39_5, all_39_5,
% 141.69/21.11 | v0) = v2 & range(all_39_5, all_39_5, v0) = v3 &
% 141.69/21.11 | subset(all_39_3, v0) = v1 & subset(all_39_5, v3) = v4 & $i(v3) &
% 141.69/21.11 | $i(v2) & ( ~ (v1 = 0) | (v4 = 0 & v2 = all_39_5)))) & ! [v0:
% 141.69/21.11 | $i] : ( ~ (subset(all_39_3, v0) = 0) | ~ $i(v0) | ? [v1: any] :
% 141.69/21.11 | ? [v2: $i] : ? [v3: $i] : ? [v4: any] : (ilf_type(v0, all_118_0)
% 141.69/21.11 | = v1 & domain(all_39_5, all_39_5, v0) = v2 & range(all_39_5,
% 141.69/21.11 | all_39_5, v0) = v3 & subset(all_39_5, v3) = v4 & $i(v3) &
% 141.69/21.11 | $i(v2) & ( ~ (v1 = 0) | (v4 = 0 & v2 = all_39_5)))))
% 141.69/21.11 |
% 141.69/21.11 | DELTA: instantiating (41) with fresh symbols all_120_0, all_120_1 gives:
% 141.69/21.11 | (92) identity_relation_of(all_39_5) = all_120_0 & relation_type(all_39_5,
% 141.69/21.11 | all_39_5) = all_120_1 & $i(all_120_0) & $i(all_120_1) & ! [v0: $i]
% 141.69/21.11 | : ! [v1: $i] : ( ~ (domain(all_39_5, all_39_5, v0) = v1) | ~ $i(v0)
% 141.69/21.11 | | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 141.69/21.11 | (ilf_type(v0, all_120_1) = v2 & range(all_39_5, all_39_5, v0) = v5 &
% 141.69/21.11 | subset(all_120_0, v0) = v3 & subset(all_39_5, v1) = v4 & $i(v5) &
% 141.69/21.11 | ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = all_39_5 & v4 = 0)))) & ! [v0:
% 141.69/21.11 | $i] : ! [v1: $i] : ( ~ (range(all_39_5, all_39_5, v0) = v1) | ~
% 141.69/21.11 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] :
% 141.69/21.11 | (ilf_type(v0, all_120_1) = v2 & domain(all_39_5, all_39_5, v0) = v4
% 141.69/21.11 | & subset(all_120_0, v0) = v3 & subset(all_39_5, v4) = v5 & $i(v4)
% 141.69/21.11 | & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = 0 & v1 = all_39_5)))) & !
% 141.69/21.11 | [v0: $i] : ( ~ (ilf_type(v0, all_120_1) = 0) | ~ $i(v0) | ? [v1:
% 141.69/21.11 | any] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] :
% 141.69/21.11 | (domain(all_39_5, all_39_5, v0) = v2 & range(all_39_5, all_39_5, v0)
% 141.69/21.11 | = v4 & subset(all_120_0, v0) = v1 & subset(all_39_5, v2) = v3 &
% 141.69/21.11 | $i(v4) & $i(v2) & ( ~ (v1 = 0) | (v4 = all_39_5 & v3 = 0)))) & !
% 141.69/21.11 | [v0: $i] : ( ~ (subset(all_120_0, v0) = 0) | ~ $i(v0) | ? [v1: any]
% 141.69/21.11 | : ? [v2: $i] : ? [v3: any] : ? [v4: $i] : (ilf_type(v0,
% 141.69/21.11 | all_120_1) = v1 & domain(all_39_5, all_39_5, v0) = v2 &
% 141.69/21.11 | range(all_39_5, all_39_5, v0) = v4 & subset(all_39_5, v2) = v3 &
% 141.69/21.11 | $i(v4) & $i(v2) & ( ~ (v1 = 0) | (v4 = all_39_5 & v3 = 0))))
% 141.69/21.11 |
% 141.69/21.11 | ALPHA: (92) implies:
% 141.69/21.11 | (93) relation_type(all_39_5, all_39_5) = all_120_1
% 141.69/21.11 | (94) identity_relation_of(all_39_5) = all_120_0
% 141.69/21.11 | (95) ! [v0: $i] : ! [v1: $i] : ( ~ (range(all_39_5, all_39_5, v0) = v1) |
% 141.69/21.11 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any]
% 141.69/21.11 | : (ilf_type(v0, all_120_1) = v2 & domain(all_39_5, all_39_5, v0) =
% 141.69/21.11 | v4 & subset(all_120_0, v0) = v3 & subset(all_39_5, v4) = v5 &
% 141.69/21.11 | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = 0 & v1 = all_39_5))))
% 141.69/21.12 | (96) ! [v0: $i] : ! [v1: $i] : ( ~ (domain(all_39_5, all_39_5, v0) = v1)
% 141.69/21.12 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5:
% 141.69/21.12 | $i] : (ilf_type(v0, all_120_1) = v2 & range(all_39_5, all_39_5,
% 141.69/21.12 | v0) = v5 & subset(all_120_0, v0) = v3 & subset(all_39_5, v1) =
% 141.69/21.12 | v4 & $i(v5) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = all_39_5 & v4 =
% 141.69/21.12 | 0))))
% 141.69/21.12 |
% 141.69/21.12 | GROUND_INST: instantiating (95) with all_39_2, all_39_0, simplifying with
% 141.69/21.12 | (28), (30) gives:
% 141.69/21.12 | (97) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 141.69/21.12 | (ilf_type(all_39_2, all_120_1) = v0 & domain(all_39_5, all_39_5,
% 141.69/21.12 | all_39_2) = v2 & subset(all_120_0, all_39_2) = v1 &
% 141.69/21.12 | subset(all_39_5, v2) = v3 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 141.69/21.12 | (v3 = 0 & all_39_0 = all_39_5)))
% 141.69/21.12 |
% 141.69/21.12 | GROUND_INST: instantiating (96) with all_39_2, all_39_1, simplifying with
% 141.69/21.12 | (28), (31) gives:
% 141.69/21.12 | (98) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] :
% 141.69/21.12 | (ilf_type(all_39_2, all_120_1) = v0 & range(all_39_5, all_39_5,
% 141.69/21.12 | all_39_2) = v3 & subset(all_120_0, all_39_2) = v1 &
% 141.69/21.12 | subset(all_39_5, all_39_1) = v2 & $i(v3) & ( ~ (v1 = 0) | ~ (v0 =
% 141.69/21.12 | 0) | (v3 = all_39_5 & v2 = 0)))
% 141.69/21.12 |
% 141.69/21.12 | DELTA: instantiating (51) with fresh symbols all_123_0, all_123_1 gives:
% 141.69/21.12 | (99) relation_type(all_39_5, all_39_5) = all_123_0 & ilf_type(all_39_5,
% 142.09/21.12 | set_type) = all_123_1 & $i(all_123_0) & ( ~ (all_123_1 = 0) | ( !
% 142.09/21.12 | [v0: $i] : ! [v1: $i] : ( ~ (domain(all_39_5, all_39_5, v0) = v1)
% 142.09/21.12 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : ?
% 142.09/21.12 | [v5: $i] : (ilf_type(v0, all_123_0) = v2 & range(all_39_5,
% 142.09/21.12 | all_39_5, v0) = v5 & subset(all_39_3, v0) = v3 &
% 142.09/21.12 | subset(all_39_5, v1) = v4 & $i(v5) & ( ~ (v3 = 0) | ~ (v2 =
% 142.09/21.12 | 0) | (v5 = all_39_5 & v4 = 0)))) & ! [v0: $i] : ! [v1:
% 142.09/21.12 | $i] : ( ~ (range(all_39_5, all_39_5, v0) = v1) | ~ $i(v0) | ?
% 142.09/21.12 | [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] :
% 142.09/21.12 | (ilf_type(v0, all_123_0) = v2 & domain(all_39_5, all_39_5, v0) =
% 142.09/21.12 | v4 & subset(all_39_3, v0) = v3 & subset(all_39_5, v4) = v5 &
% 142.09/21.12 | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = 0 & v1 =
% 142.09/21.12 | all_39_5)))) & ! [v0: $i] : ( ~ (ilf_type(v0, all_123_0)
% 142.09/21.12 | = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 142.09/21.12 | ? [v4: $i] : (domain(all_39_5, all_39_5, v0) = v2 &
% 142.09/21.12 | range(all_39_5, all_39_5, v0) = v4 & subset(all_39_3, v0) = v1
% 142.09/21.12 | & subset(all_39_5, v2) = v3 & $i(v4) & $i(v2) & ( ~ (v1 = 0) |
% 142.09/21.12 | (v4 = all_39_5 & v3 = 0)))) & ! [v0: $i] : ( ~
% 142.09/21.12 | (subset(all_39_3, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 142.09/21.12 | $i] : ? [v3: any] : ? [v4: $i] : (ilf_type(v0, all_123_0) =
% 142.09/21.12 | v1 & domain(all_39_5, all_39_5, v0) = v2 & range(all_39_5,
% 142.09/21.12 | all_39_5, v0) = v4 & subset(all_39_5, v2) = v3 & $i(v4) &
% 142.09/21.12 | $i(v2) & ( ~ (v1 = 0) | (v4 = all_39_5 & v3 = 0))))))
% 142.09/21.12 |
% 142.09/21.12 | ALPHA: (99) implies:
% 142.09/21.12 | (100) ilf_type(all_39_5, set_type) = all_123_1
% 142.09/21.12 | (101) relation_type(all_39_5, all_39_5) = all_123_0
% 142.09/21.12 | (102) ~ (all_123_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ( ~
% 142.09/21.12 | (domain(all_39_5, all_39_5, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 142.09/21.12 | : ? [v3: any] : ? [v4: any] : ? [v5: $i] : (ilf_type(v0,
% 142.09/21.12 | all_123_0) = v2 & range(all_39_5, all_39_5, v0) = v5 &
% 142.09/21.12 | subset(all_39_3, v0) = v3 & subset(all_39_5, v1) = v4 & $i(v5)
% 142.09/21.12 | & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = all_39_5 & v4 = 0)))) & !
% 142.09/21.12 | [v0: $i] : ! [v1: $i] : ( ~ (range(all_39_5, all_39_5, v0) = v1) |
% 142.09/21.12 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5:
% 142.09/21.12 | any] : (ilf_type(v0, all_123_0) = v2 & domain(all_39_5,
% 142.09/21.12 | all_39_5, v0) = v4 & subset(all_39_3, v0) = v3 &
% 142.09/21.12 | subset(all_39_5, v4) = v5 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0)
% 142.09/21.12 | | (v5 = 0 & v1 = all_39_5)))) & ! [v0: $i] : ( ~
% 142.09/21.12 | (ilf_type(v0, all_123_0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 142.09/21.12 | [v2: $i] : ? [v3: any] : ? [v4: $i] : (domain(all_39_5,
% 142.09/21.12 | all_39_5, v0) = v2 & range(all_39_5, all_39_5, v0) = v4 &
% 142.09/21.12 | subset(all_39_3, v0) = v1 & subset(all_39_5, v2) = v3 & $i(v4)
% 142.09/21.12 | & $i(v2) & ( ~ (v1 = 0) | (v4 = all_39_5 & v3 = 0)))) & ! [v0:
% 142.09/21.12 | $i] : ( ~ (subset(all_39_3, v0) = 0) | ~ $i(v0) | ? [v1: any] :
% 142.09/21.12 | ? [v2: $i] : ? [v3: any] : ? [v4: $i] : (ilf_type(v0,
% 142.09/21.12 | all_123_0) = v1 & domain(all_39_5, all_39_5, v0) = v2 &
% 142.09/21.12 | range(all_39_5, all_39_5, v0) = v4 & subset(all_39_5, v2) = v3
% 142.09/21.12 | & $i(v4) & $i(v2) & ( ~ (v1 = 0) | (v4 = all_39_5 & v3 = 0)))))
% 142.09/21.12 |
% 142.09/21.12 | DELTA: instantiating (40) with fresh symbols all_125_0, all_125_1 gives:
% 142.09/21.13 | (103) identity_relation_of(all_39_5) = all_125_0 & relation_type(all_39_5,
% 142.09/21.13 | all_39_5) = all_125_1 & $i(all_125_0) & $i(all_125_1) & ! [v0: $i]
% 142.09/21.13 | : ! [v1: $i] : ( ~ (domain(all_39_5, all_39_5, v0) = v1) | ~ $i(v0)
% 142.09/21.13 | | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] :
% 142.09/21.13 | (ilf_type(v0, all_125_1) = v2 & range(all_39_5, all_39_5, v0) = v4
% 142.09/21.13 | & subset(all_125_0, v0) = v3 & subset(all_39_5, v4) = v5 & $i(v4)
% 142.09/21.13 | & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = 0 & v1 = all_39_5)))) & !
% 142.09/21.13 | [v0: $i] : ! [v1: $i] : ( ~ (range(all_39_5, all_39_5, v0) = v1) |
% 142.09/21.13 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any]
% 142.09/21.13 | : (ilf_type(v0, all_125_1) = v2 & domain(all_39_5, all_39_5, v0) =
% 142.09/21.13 | v4 & subset(all_125_0, v0) = v3 & subset(all_39_5, v1) = v5 &
% 142.09/21.13 | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = 0 & v4 = all_39_5))))
% 142.09/21.13 | & ! [v0: $i] : ( ~ (ilf_type(v0, all_125_1) = 0) | ~ $i(v0) | ?
% 142.09/21.13 | [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] :
% 142.09/21.13 | (domain(all_39_5, all_39_5, v0) = v2 & range(all_39_5, all_39_5,
% 142.09/21.13 | v0) = v3 & subset(all_125_0, v0) = v1 & subset(all_39_5, v3) =
% 142.09/21.13 | v4 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | (v4 = 0 & v2 = all_39_5))))
% 142.09/21.13 | & ! [v0: $i] : ( ~ (subset(all_125_0, v0) = 0) | ~ $i(v0) | ? [v1:
% 142.09/21.13 | any] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : (ilf_type(v0,
% 142.09/21.13 | all_125_1) = v1 & domain(all_39_5, all_39_5, v0) = v2 &
% 142.09/21.13 | range(all_39_5, all_39_5, v0) = v3 & subset(all_39_5, v3) = v4 &
% 142.09/21.13 | $i(v3) & $i(v2) & ( ~ (v1 = 0) | (v4 = 0 & v2 = all_39_5))))
% 142.09/21.13 |
% 142.09/21.13 | ALPHA: (103) implies:
% 142.09/21.13 | (104) relation_type(all_39_5, all_39_5) = all_125_1
% 142.09/21.13 | (105) identity_relation_of(all_39_5) = all_125_0
% 142.09/21.13 | (106) ! [v0: $i] : ! [v1: $i] : ( ~ (range(all_39_5, all_39_5, v0) = v1)
% 142.09/21.13 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5:
% 142.09/21.13 | any] : (ilf_type(v0, all_125_1) = v2 & domain(all_39_5, all_39_5,
% 142.09/21.13 | v0) = v4 & subset(all_125_0, v0) = v3 & subset(all_39_5, v1) =
% 142.09/21.13 | v5 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = 0 & v4 =
% 142.09/21.13 | all_39_5))))
% 142.09/21.13 | (107) ! [v0: $i] : ! [v1: $i] : ( ~ (domain(all_39_5, all_39_5, v0) = v1)
% 142.09/21.13 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5:
% 142.09/21.13 | any] : (ilf_type(v0, all_125_1) = v2 & range(all_39_5, all_39_5,
% 142.09/21.13 | v0) = v4 & subset(all_125_0, v0) = v3 & subset(all_39_5, v4) =
% 142.09/21.13 | v5 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = 0 & v1 =
% 142.09/21.13 | all_39_5))))
% 142.09/21.13 |
% 142.09/21.13 | GROUND_INST: instantiating (106) with all_39_2, all_39_0, simplifying with
% 142.09/21.13 | (28), (30) gives:
% 142.09/21.13 | (108) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 142.09/21.13 | (ilf_type(all_39_2, all_125_1) = v0 & domain(all_39_5, all_39_5,
% 142.09/21.13 | all_39_2) = v2 & subset(all_125_0, all_39_2) = v1 &
% 142.09/21.13 | subset(all_39_5, all_39_0) = v3 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 =
% 142.09/21.13 | 0) | (v3 = 0 & v2 = all_39_5)))
% 142.09/21.13 |
% 142.09/21.13 | GROUND_INST: instantiating (107) with all_39_2, all_39_1, simplifying with
% 142.09/21.13 | (28), (31) gives:
% 142.09/21.13 | (109) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 142.09/21.13 | (ilf_type(all_39_2, all_125_1) = v0 & range(all_39_5, all_39_5,
% 142.09/21.13 | all_39_2) = v2 & subset(all_125_0, all_39_2) = v1 &
% 142.09/21.13 | subset(all_39_5, v2) = v3 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 142.09/21.13 | (v3 = 0 & all_39_1 = all_39_5)))
% 142.09/21.13 |
% 142.09/21.13 | DELTA: instantiating (67) with fresh symbols all_128_0, all_128_1 gives:
% 142.09/21.13 | (110) domain_of(all_39_2) = all_128_0 & ilf_type(all_39_2, all_87_0) =
% 142.09/21.13 | all_128_1 & $i(all_128_0) & ( ~ (all_128_1 = 0) | all_128_0 =
% 142.09/21.13 | all_39_1)
% 142.09/21.13 |
% 142.09/21.13 | ALPHA: (110) implies:
% 142.09/21.13 | (111) ilf_type(all_39_2, all_87_0) = all_128_1
% 142.09/21.13 |
% 142.09/21.13 | DELTA: instantiating (71) with fresh symbols all_130_0, all_130_1 gives:
% 142.09/21.13 | (112) range_of(all_39_2) = all_130_0 & ilf_type(all_39_2, all_90_0) =
% 142.09/21.13 | all_130_1 & $i(all_130_0) & ( ~ (all_130_1 = 0) | all_130_0 =
% 142.09/21.13 | all_39_0)
% 142.09/21.13 |
% 142.09/21.13 | ALPHA: (112) implies:
% 142.09/21.13 | (113) ilf_type(all_39_2, all_90_0) = all_130_1
% 142.09/21.13 |
% 142.09/21.13 | DELTA: instantiating (49) with fresh symbol all_132_0 gives:
% 142.09/21.13 | (114) identity_relation_of(all_39_5) = all_132_0 & $i(all_132_0) & ! [v0:
% 142.09/21.13 | $i] : ! [v1: any] : ! [v2: $i] : ! [v3: $i] : ( ~
% 142.09/21.13 | (ordered_pair(v0, v2) = v3) | ~ (member(v0, all_39_5) = v1) | ~
% 142.09/21.13 | $i(v2) | ~ $i(v0) | ? [v4: int] : ? [v5: any] : (( ~ (v4 = 0) &
% 142.09/21.13 | ilf_type(v0, set_type) = v4) | (member(v3, all_132_0) = v5 &
% 142.09/21.13 | ilf_type(v2, set_type) = v4 & ( ~ (v4 = 0) | (( ~ (v5 = 0) |
% 142.09/21.13 | (v2 = v0 & v1 = 0)) & ( ~ (v2 = v0) | ~ (v1 = 0) | v5 =
% 142.09/21.13 | 0)))))) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : ( ~
% 142.09/21.13 | (member(v0, all_39_5) = v1) | ~ (ilf_type(v2, set_type) = 0) | ~
% 142.09/21.13 | $i(v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (( ~ (v3 = 0) &
% 142.09/21.13 | ilf_type(v0, set_type) = v3) | (ordered_pair(v0, v2) = v3 &
% 142.09/21.13 | member(v3, all_132_0) = v4 & $i(v3) & ( ~ (v4 = 0) | (v2 = v0 &
% 142.09/21.13 | v1 = 0)) & ( ~ (v2 = v0) | ~ (v1 = 0) | v4 = 0)))) & !
% 142.09/21.13 | [v0: $i] : ( ~ (ilf_type(v0, set_type) = 0) | ~ $i(v0) | ? [v1:
% 142.09/21.13 | any] : (member(v0, all_39_5) = v1 & ! [v2: $i] : ! [v3: $i] : (
% 142.09/21.13 | ~ (ordered_pair(v0, v2) = v3) | ~ $i(v2) | ? [v4: any] : ?
% 142.09/21.13 | [v5: any] : (member(v3, all_132_0) = v5 & ilf_type(v2,
% 142.09/21.13 | set_type) = v4 & ( ~ (v4 = 0) | (( ~ (v5 = 0) | (v2 = v0 &
% 142.09/21.13 | v1 = 0)) & ( ~ (v2 = v0) | ~ (v1 = 0) | v5 = 0)))))
% 142.09/21.13 | & ! [v2: $i] : ( ~ (ilf_type(v2, set_type) = 0) | ~ $i(v2) | ?
% 142.09/21.13 | [v3: $i] : ? [v4: any] : (ordered_pair(v0, v2) = v3 &
% 142.09/21.13 | member(v3, all_132_0) = v4 & $i(v3) & ( ~ (v4 = 0) | (v2 = v0
% 142.09/21.13 | & v1 = 0)) & ( ~ (v2 = v0) | ~ (v1 = 0) | v4 = 0)))))
% 142.09/21.13 |
% 142.09/21.13 | ALPHA: (114) implies:
% 142.09/21.13 | (115) identity_relation_of(all_39_5) = all_132_0
% 142.09/21.13 |
% 142.09/21.13 | DELTA: instantiating (85) with fresh symbol all_139_0 gives:
% 142.09/21.14 | (116) relation_type(all_39_5, all_39_5) = all_139_0 & $i(all_139_0) & !
% 142.09/21.14 | [v0: $i] : ! [v1: $i] : ( ~ (domain(all_39_5, all_39_5, v0) = v1) |
% 142.09/21.14 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (ilf_type(v1, all_111_0) =
% 142.09/21.14 | v3 & ilf_type(v0, all_139_0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & !
% 142.09/21.14 | [v0: $i] : ( ~ (ilf_type(v0, all_139_0) = 0) | ~ $i(v0) | ? [v1:
% 142.09/21.14 | $i] : (ilf_type(v1, all_111_0) = 0 & domain(all_39_5, all_39_5,
% 142.09/21.14 | v0) = v1 & $i(v1)))
% 142.09/21.14 |
% 142.09/21.14 | ALPHA: (116) implies:
% 142.09/21.14 | (117) relation_type(all_39_5, all_39_5) = all_139_0
% 142.09/21.14 | (118) ! [v0: $i] : ! [v1: $i] : ( ~ (domain(all_39_5, all_39_5, v0) = v1)
% 142.09/21.14 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (ilf_type(v1,
% 142.09/21.14 | all_111_0) = v3 & ilf_type(v0, all_139_0) = v2 & ( ~ (v2 = 0) |
% 142.09/21.14 | v3 = 0)))
% 142.09/21.14 |
% 142.09/21.14 | GROUND_INST: instantiating (118) with all_39_2, all_39_1, simplifying with
% 142.09/21.14 | (28), (31) gives:
% 142.09/21.14 | (119) ? [v0: any] : ? [v1: any] : (ilf_type(all_39_1, all_111_0) = v1 &
% 142.09/21.14 | ilf_type(all_39_2, all_139_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 142.09/21.14 |
% 142.09/21.14 | DELTA: instantiating (98) with fresh symbols all_142_0, all_142_1, all_142_2,
% 142.09/21.14 | all_142_3 gives:
% 142.09/21.14 | (120) ilf_type(all_39_2, all_120_1) = all_142_3 & range(all_39_5, all_39_5,
% 142.09/21.14 | all_39_2) = all_142_0 & subset(all_120_0, all_39_2) = all_142_2 &
% 142.09/21.14 | subset(all_39_5, all_39_1) = all_142_1 & $i(all_142_0) & ( ~
% 142.09/21.14 | (all_142_2 = 0) | ~ (all_142_3 = 0) | (all_142_0 = all_39_5 &
% 142.09/21.14 | all_142_1 = 0))
% 142.09/21.14 |
% 142.09/21.14 | ALPHA: (120) implies:
% 142.09/21.14 | (121) subset(all_120_0, all_39_2) = all_142_2
% 142.09/21.14 | (122) range(all_39_5, all_39_5, all_39_2) = all_142_0
% 142.09/21.14 | (123) ilf_type(all_39_2, all_120_1) = all_142_3
% 142.09/21.14 |
% 142.09/21.14 | DELTA: instantiating (97) with fresh symbols all_144_0, all_144_1, all_144_2,
% 142.09/21.14 | all_144_3 gives:
% 142.09/21.14 | (124) ilf_type(all_39_2, all_120_1) = all_144_3 & domain(all_39_5,
% 142.09/21.14 | all_39_5, all_39_2) = all_144_1 & subset(all_120_0, all_39_2) =
% 142.09/21.14 | all_144_2 & subset(all_39_5, all_144_1) = all_144_0 & $i(all_144_1) &
% 142.09/21.14 | ( ~ (all_144_2 = 0) | ~ (all_144_3 = 0) | (all_144_0 = 0 & all_39_0
% 142.09/21.14 | = all_39_5))
% 142.09/21.14 |
% 142.09/21.14 | ALPHA: (124) implies:
% 142.09/21.14 | (125) domain(all_39_5, all_39_5, all_39_2) = all_144_1
% 142.09/21.14 |
% 142.09/21.14 | DELTA: instantiating (109) with fresh symbols all_146_0, all_146_1, all_146_2,
% 142.09/21.14 | all_146_3 gives:
% 142.09/21.14 | (126) ilf_type(all_39_2, all_125_1) = all_146_3 & range(all_39_5, all_39_5,
% 142.09/21.14 | all_39_2) = all_146_1 & subset(all_125_0, all_39_2) = all_146_2 &
% 142.09/21.14 | subset(all_39_5, all_146_1) = all_146_0 & $i(all_146_1) & ( ~
% 142.09/21.14 | (all_146_2 = 0) | ~ (all_146_3 = 0) | (all_146_0 = 0 & all_39_1 =
% 142.09/21.14 | all_39_5))
% 142.09/21.14 |
% 142.09/21.14 | ALPHA: (126) implies:
% 142.09/21.14 | (127) subset(all_125_0, all_39_2) = all_146_2
% 142.09/21.14 | (128) range(all_39_5, all_39_5, all_39_2) = all_146_1
% 142.09/21.14 | (129) ilf_type(all_39_2, all_125_1) = all_146_3
% 142.09/21.14 |
% 142.09/21.14 | DELTA: instantiating (108) with fresh symbols all_148_0, all_148_1, all_148_2,
% 142.09/21.14 | all_148_3 gives:
% 142.09/21.14 | (130) ilf_type(all_39_2, all_125_1) = all_148_3 & domain(all_39_5,
% 142.09/21.14 | all_39_5, all_39_2) = all_148_1 & subset(all_125_0, all_39_2) =
% 142.09/21.14 | all_148_2 & subset(all_39_5, all_39_0) = all_148_0 & $i(all_148_1) &
% 142.09/21.14 | ( ~ (all_148_2 = 0) | ~ (all_148_3 = 0) | (all_148_0 = 0 & all_148_1
% 142.09/21.14 | = all_39_5))
% 142.09/21.14 |
% 142.09/21.14 | ALPHA: (130) implies:
% 142.09/21.14 | (131) domain(all_39_5, all_39_5, all_39_2) = all_148_1
% 142.09/21.14 |
% 142.09/21.14 | DELTA: instantiating (119) with fresh symbols all_150_0, all_150_1 gives:
% 142.09/21.14 | (132) ilf_type(all_39_1, all_111_0) = all_150_0 & ilf_type(all_39_2,
% 142.09/21.14 | all_139_0) = all_150_1 & ( ~ (all_150_1 = 0) | all_150_0 = 0)
% 142.09/21.14 |
% 142.09/21.14 | ALPHA: (132) implies:
% 142.09/21.14 | (133) ilf_type(all_39_2, all_139_0) = all_150_1
% 142.09/21.14 |
% 142.09/21.14 | BETA: splitting (76) gives:
% 142.09/21.14 |
% 142.09/21.14 | Case 1:
% 142.09/21.14 | |
% 142.09/21.14 | | (134) ~ (all_97_4 = 0)
% 142.09/21.14 | |
% 142.09/21.14 | | GROUND_INST: instantiating (21) with 0, all_97_4, all_39_5, all_39_5,
% 142.09/21.14 | | simplifying with (43), (75) gives:
% 142.09/21.14 | | (135) all_97_4 = 0
% 142.09/21.14 | |
% 142.09/21.14 | | REDUCE: (134), (135) imply:
% 142.09/21.14 | | (136) $false
% 142.09/21.14 | |
% 142.09/21.14 | | CLOSE: (136) is inconsistent.
% 142.09/21.14 | |
% 142.09/21.14 | Case 2:
% 142.09/21.14 | |
% 142.09/21.14 | |
% 142.09/21.14 | | GROUND_INST: instantiating (24) with all_39_0, all_146_1, all_39_2,
% 142.09/21.14 | | all_39_5, all_39_5, simplifying with (30), (128) gives:
% 142.09/21.14 | | (137) all_146_1 = all_39_0
% 142.09/21.14 | |
% 142.09/21.14 | | GROUND_INST: instantiating (24) with all_142_0, all_146_1, all_39_2,
% 142.09/21.14 | | all_39_5, all_39_5, simplifying with (122), (128) gives:
% 142.09/21.14 | | (138) all_146_1 = all_142_0
% 142.09/21.14 | |
% 142.09/21.14 | | GROUND_INST: instantiating (25) with all_39_1, all_148_1, all_39_2,
% 142.09/21.14 | | all_39_5, all_39_5, simplifying with (31), (131) gives:
% 142.09/21.14 | | (139) all_148_1 = all_39_1
% 142.09/21.14 | |
% 142.09/21.14 | | GROUND_INST: instantiating (25) with all_144_1, all_148_1, all_39_2,
% 142.09/21.14 | | all_39_5, all_39_5, simplifying with (125), (131) gives:
% 142.09/21.14 | | (140) all_148_1 = all_144_1
% 142.09/21.14 | |
% 142.09/21.14 | | GROUND_INST: instantiating (22) with 0, all_118_1, set_type, all_39_5,
% 142.09/21.14 | | simplifying with (32), (89) gives:
% 142.09/21.14 | | (141) all_118_1 = 0
% 142.09/21.14 | |
% 142.09/21.15 | | GROUND_INST: instantiating (22) with all_99_1, all_118_1, set_type,
% 142.09/21.15 | | all_39_5, simplifying with (78), (89) gives:
% 142.09/21.15 | | (142) all_118_1 = all_99_1
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (22) with all_118_1, all_123_1, set_type,
% 142.09/21.15 | | all_39_5, simplifying with (89), (100) gives:
% 142.09/21.15 | | (143) all_123_1 = all_118_1
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (22) with all_65_1, all_123_1, set_type,
% 142.09/21.15 | | all_39_5, simplifying with (57), (100) gives:
% 142.09/21.15 | | (144) all_123_1 = all_65_1
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (23) with all_90_0, all_93_0, all_39_5, all_39_5,
% 142.09/21.15 | | simplifying with (69), (73) gives:
% 142.09/21.15 | | (145) all_93_0 = all_90_0
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (23) with all_90_0, all_118_0, all_39_5,
% 142.09/21.15 | | all_39_5, simplifying with (69), (90) gives:
% 142.09/21.15 | | (146) all_118_0 = all_90_0
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (23) with all_87_0, all_118_0, all_39_5,
% 142.09/21.15 | | all_39_5, simplifying with (65), (90) gives:
% 142.09/21.15 | | (147) all_118_0 = all_87_0
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (23) with all_67_1, all_118_0, all_39_5,
% 142.09/21.15 | | all_39_5, simplifying with (59), (90) gives:
% 142.09/21.15 | | (148) all_118_0 = all_67_1
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (23) with all_120_1, all_123_0, all_39_5,
% 142.09/21.15 | | all_39_5, simplifying with (93), (101) gives:
% 142.09/21.15 | | (149) all_123_0 = all_120_1
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (23) with all_123_0, all_125_1, all_39_5,
% 142.09/21.15 | | all_39_5, simplifying with (101), (104) gives:
% 142.09/21.15 | | (150) all_125_1 = all_123_0
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (23) with all_99_0, all_125_1, all_39_5,
% 142.09/21.15 | | all_39_5, simplifying with (79), (104) gives:
% 142.09/21.15 | | (151) all_125_1 = all_99_0
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (23) with all_120_1, all_139_0, all_39_5,
% 142.09/21.15 | | all_39_5, simplifying with (93), (117) gives:
% 142.09/21.15 | | (152) all_139_0 = all_120_1
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (23) with all_101_0, all_139_0, all_39_5,
% 142.09/21.15 | | all_39_5, simplifying with (82), (117) gives:
% 142.09/21.15 | | (153) all_139_0 = all_101_0
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (23) with all_93_0, all_139_0, all_39_5,
% 142.09/21.15 | | all_39_5, simplifying with (73), (117) gives:
% 142.09/21.15 | | (154) all_139_0 = all_93_0
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (23) with all_82_1, all_139_0, all_39_5,
% 142.09/21.15 | | all_39_5, simplifying with (61), (117) gives:
% 142.09/21.15 | | (155) all_139_0 = all_82_1
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (20) with all_47_0, all_125_0, all_39_5,
% 142.09/21.15 | | simplifying with (55), (105) gives:
% 142.09/21.15 | | (156) all_125_0 = all_47_0
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (20) with all_39_3, all_132_0, all_39_5,
% 142.09/21.15 | | simplifying with (34), (115) gives:
% 142.09/21.15 | | (157) all_132_0 = all_39_3
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (20) with all_125_0, all_132_0, all_39_5,
% 142.09/21.15 | | simplifying with (105), (115) gives:
% 142.09/21.15 | | (158) all_132_0 = all_125_0
% 142.09/21.15 | |
% 142.09/21.15 | | GROUND_INST: instantiating (20) with all_120_0, all_132_0, all_39_5,
% 142.09/21.15 | | simplifying with (94), (115) gives:
% 142.09/21.15 | | (159) all_132_0 = all_120_0
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (139), (140) imply:
% 142.09/21.15 | | (160) all_144_1 = all_39_1
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (137), (138) imply:
% 142.09/21.15 | | (161) all_142_0 = all_39_0
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (152), (153) imply:
% 142.09/21.15 | | (162) all_120_1 = all_101_0
% 142.09/21.15 | |
% 142.09/21.15 | | SIMP: (162) implies:
% 142.09/21.15 | | (163) all_120_1 = all_101_0
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (153), (154) imply:
% 142.09/21.15 | | (164) all_101_0 = all_93_0
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (153), (155) imply:
% 142.09/21.15 | | (165) all_101_0 = all_82_1
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (157), (159) imply:
% 142.09/21.15 | | (166) all_120_0 = all_39_3
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (158), (159) imply:
% 142.09/21.15 | | (167) all_125_0 = all_120_0
% 142.09/21.15 | |
% 142.09/21.15 | | SIMP: (167) implies:
% 142.09/21.15 | | (168) all_125_0 = all_120_0
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (156), (168) imply:
% 142.09/21.15 | | (169) all_120_0 = all_47_0
% 142.09/21.15 | |
% 142.09/21.15 | | SIMP: (169) implies:
% 142.09/21.15 | | (170) all_120_0 = all_47_0
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (150), (151) imply:
% 142.09/21.15 | | (171) all_123_0 = all_99_0
% 142.09/21.15 | |
% 142.09/21.15 | | SIMP: (171) implies:
% 142.09/21.15 | | (172) all_123_0 = all_99_0
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (149), (172) imply:
% 142.09/21.15 | | (173) all_120_1 = all_99_0
% 142.09/21.15 | |
% 142.09/21.15 | | SIMP: (173) implies:
% 142.09/21.15 | | (174) all_120_1 = all_99_0
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (143), (144) imply:
% 142.09/21.15 | | (175) all_118_1 = all_65_1
% 142.09/21.15 | |
% 142.09/21.15 | | SIMP: (175) implies:
% 142.09/21.15 | | (176) all_118_1 = all_65_1
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (166), (170) imply:
% 142.09/21.15 | | (177) all_47_0 = all_39_3
% 142.09/21.15 | |
% 142.09/21.15 | | SIMP: (177) implies:
% 142.09/21.15 | | (178) all_47_0 = all_39_3
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (163), (174) imply:
% 142.09/21.15 | | (179) all_101_0 = all_99_0
% 142.09/21.15 | |
% 142.09/21.15 | | SIMP: (179) implies:
% 142.09/21.15 | | (180) all_101_0 = all_99_0
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (146), (147) imply:
% 142.09/21.15 | | (181) all_90_0 = all_87_0
% 142.09/21.15 | |
% 142.09/21.15 | | SIMP: (181) implies:
% 142.09/21.15 | | (182) all_90_0 = all_87_0
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (147), (148) imply:
% 142.09/21.15 | | (183) all_87_0 = all_67_1
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (142), (176) imply:
% 142.09/21.15 | | (184) all_99_1 = all_65_1
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (141), (142) imply:
% 142.09/21.15 | | (185) all_99_1 = 0
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (164), (180) imply:
% 142.09/21.15 | | (186) all_99_0 = all_93_0
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (165), (180) imply:
% 142.09/21.15 | | (187) all_99_0 = all_82_1
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (186), (187) imply:
% 142.09/21.15 | | (188) all_93_0 = all_82_1
% 142.09/21.15 | |
% 142.09/21.15 | | SIMP: (188) implies:
% 142.09/21.15 | | (189) all_93_0 = all_82_1
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (184), (185) imply:
% 142.09/21.15 | | (190) all_65_1 = 0
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (145), (189) imply:
% 142.09/21.15 | | (191) all_90_0 = all_82_1
% 142.09/21.15 | |
% 142.09/21.15 | | SIMP: (191) implies:
% 142.09/21.15 | | (192) all_90_0 = all_82_1
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (182), (192) imply:
% 142.09/21.15 | | (193) all_87_0 = all_82_1
% 142.09/21.15 | |
% 142.09/21.15 | | SIMP: (193) implies:
% 142.09/21.15 | | (194) all_87_0 = all_82_1
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (183), (194) imply:
% 142.09/21.15 | | (195) all_82_1 = all_67_1
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (192), (195) imply:
% 142.09/21.15 | | (196) all_90_0 = all_67_1
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (187), (195) imply:
% 142.09/21.15 | | (197) all_99_0 = all_67_1
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (180), (197) imply:
% 142.09/21.15 | | (198) all_101_0 = all_67_1
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (174), (197) imply:
% 142.09/21.15 | | (199) all_120_1 = all_67_1
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (144), (190) imply:
% 142.09/21.15 | | (200) all_123_1 = 0
% 142.09/21.15 | |
% 142.09/21.15 | | COMBINE_EQS: (172), (197) imply:
% 142.09/21.16 | | (201) all_123_0 = all_67_1
% 142.09/21.16 | |
% 142.09/21.16 | | COMBINE_EQS: (151), (197) imply:
% 142.09/21.16 | | (202) all_125_1 = all_67_1
% 142.09/21.16 | |
% 142.09/21.16 | | COMBINE_EQS: (156), (178) imply:
% 142.09/21.16 | | (203) all_125_0 = all_39_3
% 142.09/21.16 | |
% 142.09/21.16 | | COMBINE_EQS: (153), (198) imply:
% 142.09/21.16 | | (204) all_139_0 = all_67_1
% 142.09/21.16 | |
% 142.09/21.16 | | REDUCE: (133), (204) imply:
% 142.09/21.16 | | (205) ilf_type(all_39_2, all_67_1) = all_150_1
% 142.09/21.16 | |
% 142.09/21.16 | | REDUCE: (129), (202) imply:
% 142.09/21.16 | | (206) ilf_type(all_39_2, all_67_1) = all_146_3
% 142.09/21.16 | |
% 142.09/21.16 | | REDUCE: (123), (199) imply:
% 142.09/21.16 | | (207) ilf_type(all_39_2, all_67_1) = all_142_3
% 142.09/21.16 | |
% 142.09/21.16 | | REDUCE: (113), (196) imply:
% 142.09/21.16 | | (208) ilf_type(all_39_2, all_67_1) = all_130_1
% 142.09/21.16 | |
% 142.09/21.16 | | REDUCE: (111), (183) imply:
% 142.09/21.16 | | (209) ilf_type(all_39_2, all_67_1) = all_128_1
% 142.09/21.16 | |
% 142.09/21.16 | | REDUCE: (87), (195) imply:
% 142.09/21.16 | | (210) ilf_type(all_39_2, all_67_1) = all_114_1
% 142.09/21.16 | |
% 142.09/21.16 | | REDUCE: (127), (203) imply:
% 142.09/21.16 | | (211) subset(all_39_3, all_39_2) = all_146_2
% 142.09/21.16 | |
% 142.09/21.16 | | REDUCE: (121), (166) imply:
% 142.09/21.16 | | (212) subset(all_39_3, all_39_2) = all_142_2
% 142.09/21.16 | |
% 142.09/21.16 | | BETA: splitting (91) gives:
% 142.09/21.16 | |
% 142.09/21.16 | | Case 1:
% 142.09/21.16 | | |
% 142.09/21.16 | | | (213) ~ (all_118_1 = 0)
% 142.09/21.16 | | |
% 142.09/21.16 | | | REDUCE: (141), (213) imply:
% 142.09/21.16 | | | (214) $false
% 142.09/21.16 | | |
% 142.09/21.16 | | | CLOSE: (214) is inconsistent.
% 142.09/21.16 | | |
% 142.09/21.16 | | Case 2:
% 142.09/21.16 | | |
% 142.09/21.16 | | | (215) ! [v0: $i] : ! [v1: $i] : ( ~ (domain(all_39_5, all_39_5, v0) =
% 142.09/21.16 | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] :
% 142.09/21.16 | | | ? [v5: any] : (ilf_type(v0, all_118_0) = v2 & range(all_39_5,
% 142.09/21.16 | | | all_39_5, v0) = v4 & subset(all_39_3, v0) = v3 &
% 142.09/21.16 | | | subset(all_39_5, v4) = v5 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 =
% 142.09/21.16 | | | 0) | (v5 = 0 & v1 = all_39_5)))) & ! [v0: $i] : ! [v1:
% 142.09/21.16 | | | $i] : ( ~ (range(all_39_5, all_39_5, v0) = v1) | ~ $i(v0) | ?
% 142.09/21.16 | | | [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] :
% 142.09/21.16 | | | (ilf_type(v0, all_118_0) = v2 & domain(all_39_5, all_39_5, v0)
% 142.09/21.16 | | | = v4 & subset(all_39_3, v0) = v3 & subset(all_39_5, v1) = v5
% 142.09/21.16 | | | & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = 0 & v4 =
% 142.09/21.16 | | | all_39_5)))) & ! [v0: $i] : ( ~ (ilf_type(v0, all_118_0)
% 142.09/21.16 | | | = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 142.09/21.16 | | | ? [v4: any] : (domain(all_39_5, all_39_5, v0) = v2 &
% 142.09/21.16 | | | range(all_39_5, all_39_5, v0) = v3 & subset(all_39_3, v0) =
% 142.09/21.16 | | | v1 & subset(all_39_5, v3) = v4 & $i(v3) & $i(v2) & ( ~ (v1 =
% 142.09/21.16 | | | 0) | (v4 = 0 & v2 = all_39_5)))) & ! [v0: $i] : ( ~
% 142.09/21.16 | | | (subset(all_39_3, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 142.09/21.16 | | | $i] : ? [v3: $i] : ? [v4: any] : (ilf_type(v0, all_118_0) =
% 142.09/21.16 | | | v1 & domain(all_39_5, all_39_5, v0) = v2 & range(all_39_5,
% 142.09/21.16 | | | all_39_5, v0) = v3 & subset(all_39_5, v3) = v4 & $i(v3) &
% 142.09/21.16 | | | $i(v2) & ( ~ (v1 = 0) | (v4 = 0 & v2 = all_39_5))))
% 142.09/21.16 | | |
% 142.09/21.16 | | | ALPHA: (215) implies:
% 142.09/21.16 | | | (216) ! [v0: $i] : ( ~ (subset(all_39_3, v0) = 0) | ~ $i(v0) | ?
% 142.09/21.16 | | | [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] :
% 142.09/21.16 | | | (ilf_type(v0, all_118_0) = v1 & domain(all_39_5, all_39_5, v0)
% 142.09/21.16 | | | = v2 & range(all_39_5, all_39_5, v0) = v3 & subset(all_39_5,
% 142.09/21.16 | | | v3) = v4 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | (v4 = 0 & v2 =
% 142.09/21.16 | | | all_39_5))))
% 142.09/21.16 | | | (217) ! [v0: $i] : ! [v1: $i] : ( ~ (range(all_39_5, all_39_5, v0) =
% 142.09/21.16 | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] :
% 142.09/21.16 | | | ? [v5: any] : (ilf_type(v0, all_118_0) = v2 & domain(all_39_5,
% 142.09/21.16 | | | all_39_5, v0) = v4 & subset(all_39_3, v0) = v3 &
% 142.09/21.16 | | | subset(all_39_5, v1) = v5 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 =
% 142.09/21.16 | | | 0) | (v5 = 0 & v4 = all_39_5))))
% 142.09/21.16 | | | (218) ! [v0: $i] : ! [v1: $i] : ( ~ (domain(all_39_5, all_39_5, v0) =
% 142.09/21.16 | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] :
% 142.09/21.16 | | | ? [v5: any] : (ilf_type(v0, all_118_0) = v2 & range(all_39_5,
% 142.09/21.16 | | | all_39_5, v0) = v4 & subset(all_39_3, v0) = v3 &
% 142.09/21.16 | | | subset(all_39_5, v4) = v5 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 =
% 142.09/21.16 | | | 0) | (v5 = 0 & v1 = all_39_5))))
% 142.09/21.16 | | |
% 142.09/21.16 | | | GROUND_INST: instantiating (216) with all_39_2, simplifying with (28),
% 142.09/21.16 | | | (29) gives:
% 142.09/21.16 | | | (219) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] :
% 142.09/21.16 | | | (ilf_type(all_39_2, all_118_0) = v0 & domain(all_39_5, all_39_5,
% 142.09/21.16 | | | all_39_2) = v1 & range(all_39_5, all_39_5, all_39_2) = v2 &
% 142.09/21.16 | | | subset(all_39_5, v2) = v3 & $i(v2) & $i(v1) & ( ~ (v0 = 0) |
% 142.09/21.16 | | | (v3 = 0 & v1 = all_39_5)))
% 142.09/21.16 | | |
% 142.09/21.16 | | | GROUND_INST: instantiating (217) with all_39_2, all_39_0, simplifying with
% 142.09/21.16 | | | (28), (30) gives:
% 142.09/21.16 | | | (220) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 142.09/21.16 | | | (ilf_type(all_39_2, all_118_0) = v0 & domain(all_39_5, all_39_5,
% 142.09/21.16 | | | all_39_2) = v2 & subset(all_39_3, all_39_2) = v1 &
% 142.09/21.16 | | | subset(all_39_5, all_39_0) = v3 & $i(v2) & ( ~ (v1 = 0) | ~
% 142.09/21.16 | | | (v0 = 0) | (v3 = 0 & v2 = all_39_5)))
% 142.09/21.16 | | |
% 142.09/21.16 | | | GROUND_INST: instantiating (218) with all_39_2, all_39_1, simplifying with
% 142.09/21.16 | | | (28), (31) gives:
% 142.09/21.16 | | | (221) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 142.09/21.16 | | | (ilf_type(all_39_2, all_118_0) = v0 & range(all_39_5, all_39_5,
% 142.09/21.16 | | | all_39_2) = v2 & subset(all_39_3, all_39_2) = v1 &
% 142.09/21.16 | | | subset(all_39_5, v2) = v3 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0)
% 142.09/21.16 | | | | (v3 = 0 & all_39_1 = all_39_5)))
% 142.09/21.16 | | |
% 142.09/21.16 | | | BETA: splitting (102) gives:
% 142.09/21.16 | | |
% 142.09/21.16 | | | Case 1:
% 142.09/21.16 | | | |
% 142.09/21.16 | | | | (222) ~ (all_123_1 = 0)
% 142.09/21.16 | | | |
% 142.09/21.16 | | | | REDUCE: (200), (222) imply:
% 142.09/21.17 | | | | (223) $false
% 142.09/21.17 | | | |
% 142.09/21.17 | | | | CLOSE: (223) is inconsistent.
% 142.09/21.17 | | | |
% 142.09/21.17 | | | Case 2:
% 142.09/21.17 | | | |
% 142.09/21.17 | | | | (224) ! [v0: $i] : ! [v1: $i] : ( ~ (domain(all_39_5, all_39_5, v0)
% 142.09/21.17 | | | | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4:
% 142.09/21.17 | | | | any] : ? [v5: $i] : (ilf_type(v0, all_123_0) = v2 &
% 142.09/21.17 | | | | range(all_39_5, all_39_5, v0) = v5 & subset(all_39_3, v0) =
% 142.09/21.17 | | | | v3 & subset(all_39_5, v1) = v4 & $i(v5) & ( ~ (v3 = 0) | ~
% 142.09/21.17 | | | | (v2 = 0) | (v5 = all_39_5 & v4 = 0)))) & ! [v0: $i] : !
% 142.09/21.17 | | | | [v1: $i] : ( ~ (range(all_39_5, all_39_5, v0) = v1) | ~ $i(v0)
% 142.09/21.17 | | | | | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] :
% 142.09/21.17 | | | | (ilf_type(v0, all_123_0) = v2 & domain(all_39_5, all_39_5,
% 142.09/21.17 | | | | v0) = v4 & subset(all_39_3, v0) = v3 & subset(all_39_5,
% 142.09/21.17 | | | | v4) = v5 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = 0
% 142.09/21.17 | | | | & v1 = all_39_5)))) & ! [v0: $i] : ( ~ (ilf_type(v0,
% 142.09/21.17 | | | | all_123_0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 142.09/21.17 | | | | : ? [v3: any] : ? [v4: $i] : (domain(all_39_5, all_39_5,
% 142.09/21.17 | | | | v0) = v2 & range(all_39_5, all_39_5, v0) = v4 &
% 142.09/21.17 | | | | subset(all_39_3, v0) = v1 & subset(all_39_5, v2) = v3 &
% 142.09/21.17 | | | | $i(v4) & $i(v2) & ( ~ (v1 = 0) | (v4 = all_39_5 & v3 =
% 142.09/21.17 | | | | 0)))) & ! [v0: $i] : ( ~ (subset(all_39_3, v0) = 0) |
% 142.09/21.17 | | | | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: any] : ?
% 142.09/21.17 | | | | [v4: $i] : (ilf_type(v0, all_123_0) = v1 & domain(all_39_5,
% 142.09/21.17 | | | | all_39_5, v0) = v2 & range(all_39_5, all_39_5, v0) = v4 &
% 142.09/21.17 | | | | subset(all_39_5, v2) = v3 & $i(v4) & $i(v2) & ( ~ (v1 = 0)
% 142.09/21.17 | | | | | (v4 = all_39_5 & v3 = 0))))
% 142.09/21.17 | | | |
% 142.09/21.17 | | | | ALPHA: (224) implies:
% 142.09/21.17 | | | | (225) ! [v0: $i] : ( ~ (subset(all_39_3, v0) = 0) | ~ $i(v0) | ?
% 142.09/21.17 | | | | [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] :
% 142.09/21.17 | | | | (ilf_type(v0, all_123_0) = v1 & domain(all_39_5, all_39_5,
% 142.09/21.17 | | | | v0) = v2 & range(all_39_5, all_39_5, v0) = v4 &
% 142.09/21.17 | | | | subset(all_39_5, v2) = v3 & $i(v4) & $i(v2) & ( ~ (v1 = 0)
% 142.09/21.17 | | | | | (v4 = all_39_5 & v3 = 0))))
% 142.09/21.17 | | | | (226) ! [v0: $i] : ! [v1: $i] : ( ~ (range(all_39_5, all_39_5, v0)
% 142.09/21.17 | | | | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4:
% 142.09/21.17 | | | | $i] : ? [v5: any] : (ilf_type(v0, all_123_0) = v2 &
% 142.09/21.17 | | | | domain(all_39_5, all_39_5, v0) = v4 & subset(all_39_3, v0)
% 142.09/21.17 | | | | = v3 & subset(all_39_5, v4) = v5 & $i(v4) & ( ~ (v3 = 0) |
% 142.09/21.17 | | | | ~ (v2 = 0) | (v5 = 0 & v1 = all_39_5))))
% 142.09/21.17 | | | | (227) ! [v0: $i] : ! [v1: $i] : ( ~ (domain(all_39_5, all_39_5, v0)
% 142.09/21.17 | | | | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4:
% 142.09/21.17 | | | | any] : ? [v5: $i] : (ilf_type(v0, all_123_0) = v2 &
% 142.09/21.17 | | | | range(all_39_5, all_39_5, v0) = v5 & subset(all_39_3, v0) =
% 142.09/21.17 | | | | v3 & subset(all_39_5, v1) = v4 & $i(v5) & ( ~ (v3 = 0) | ~
% 142.09/21.17 | | | | (v2 = 0) | (v5 = all_39_5 & v4 = 0))))
% 142.09/21.17 | | | |
% 142.09/21.17 | | | | GROUND_INST: instantiating (225) with all_39_2, simplifying with (28),
% 142.09/21.17 | | | | (29) gives:
% 142.09/21.17 | | | | (228) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] :
% 142.09/21.17 | | | | (ilf_type(all_39_2, all_123_0) = v0 & domain(all_39_5,
% 142.09/21.17 | | | | all_39_5, all_39_2) = v1 & range(all_39_5, all_39_5,
% 142.09/21.17 | | | | all_39_2) = v3 & subset(all_39_5, v1) = v2 & $i(v3) &
% 142.09/21.17 | | | | $i(v1) & ( ~ (v0 = 0) | (v3 = all_39_5 & v2 = 0)))
% 142.09/21.17 | | | |
% 142.09/21.17 | | | | GROUND_INST: instantiating (226) with all_39_2, all_39_0, simplifying
% 142.09/21.17 | | | | with (28), (30) gives:
% 142.09/21.17 | | | | (229) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 142.09/21.17 | | | | (ilf_type(all_39_2, all_123_0) = v0 & domain(all_39_5,
% 142.09/21.17 | | | | all_39_5, all_39_2) = v2 & subset(all_39_3, all_39_2) = v1
% 142.09/21.17 | | | | & subset(all_39_5, v2) = v3 & $i(v2) & ( ~ (v1 = 0) | ~ (v0
% 142.09/21.17 | | | | = 0) | (v3 = 0 & all_39_0 = all_39_5)))
% 142.09/21.17 | | | |
% 142.09/21.17 | | | | GROUND_INST: instantiating (227) with all_39_2, all_39_1, simplifying
% 142.09/21.17 | | | | with (28), (31) gives:
% 142.09/21.17 | | | | (230) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] :
% 142.09/21.17 | | | | (ilf_type(all_39_2, all_123_0) = v0 & range(all_39_5, all_39_5,
% 142.09/21.17 | | | | all_39_2) = v3 & subset(all_39_3, all_39_2) = v1 &
% 142.09/21.17 | | | | subset(all_39_5, all_39_1) = v2 & $i(v3) & ( ~ (v1 = 0) | ~
% 142.09/21.17 | | | | (v0 = 0) | (v3 = all_39_5 & v2 = 0)))
% 142.09/21.17 | | | |
% 142.09/21.17 | | | | DELTA: instantiating (221) with fresh symbols all_207_0, all_207_1,
% 142.09/21.17 | | | | all_207_2, all_207_3 gives:
% 142.09/21.17 | | | | (231) ilf_type(all_39_2, all_118_0) = all_207_3 & range(all_39_5,
% 142.09/21.17 | | | | all_39_5, all_39_2) = all_207_1 & subset(all_39_3, all_39_2)
% 142.09/21.17 | | | | = all_207_2 & subset(all_39_5, all_207_1) = all_207_0 &
% 142.09/21.17 | | | | $i(all_207_1) & ( ~ (all_207_2 = 0) | ~ (all_207_3 = 0) |
% 142.09/21.17 | | | | (all_207_0 = 0 & all_39_1 = all_39_5))
% 142.09/21.17 | | | |
% 142.09/21.17 | | | | ALPHA: (231) implies:
% 142.09/21.17 | | | | (232) subset(all_39_3, all_39_2) = all_207_2
% 142.09/21.17 | | | | (233) range(all_39_5, all_39_5, all_39_2) = all_207_1
% 142.09/21.17 | | | | (234) ilf_type(all_39_2, all_118_0) = all_207_3
% 142.09/21.17 | | | |
% 142.09/21.17 | | | | DELTA: instantiating (220) with fresh symbols all_209_0, all_209_1,
% 142.09/21.17 | | | | all_209_2, all_209_3 gives:
% 142.09/21.17 | | | | (235) ilf_type(all_39_2, all_118_0) = all_209_3 & domain(all_39_5,
% 142.09/21.17 | | | | all_39_5, all_39_2) = all_209_1 & subset(all_39_3, all_39_2)
% 142.09/21.17 | | | | = all_209_2 & subset(all_39_5, all_39_0) = all_209_0 &
% 142.09/21.17 | | | | $i(all_209_1) & ( ~ (all_209_2 = 0) | ~ (all_209_3 = 0) |
% 142.09/21.17 | | | | (all_209_0 = 0 & all_209_1 = all_39_5))
% 142.09/21.17 | | | |
% 142.09/21.17 | | | | ALPHA: (235) implies:
% 142.09/21.17 | | | | (236) subset(all_39_3, all_39_2) = all_209_2
% 142.09/21.17 | | | | (237) domain(all_39_5, all_39_5, all_39_2) = all_209_1
% 142.09/21.17 | | | | (238) ilf_type(all_39_2, all_118_0) = all_209_3
% 142.09/21.17 | | | | (239) ~ (all_209_2 = 0) | ~ (all_209_3 = 0) | (all_209_0 = 0 &
% 142.09/21.17 | | | | all_209_1 = all_39_5)
% 142.09/21.17 | | | |
% 142.09/21.17 | | | | DELTA: instantiating (219) with fresh symbols all_211_0, all_211_1,
% 142.09/21.17 | | | | all_211_2, all_211_3 gives:
% 142.09/21.18 | | | | (240) ilf_type(all_39_2, all_118_0) = all_211_3 & domain(all_39_5,
% 142.09/21.18 | | | | all_39_5, all_39_2) = all_211_2 & range(all_39_5, all_39_5,
% 142.09/21.18 | | | | all_39_2) = all_211_1 & subset(all_39_5, all_211_1) =
% 142.09/21.18 | | | | all_211_0 & $i(all_211_1) & $i(all_211_2) & ( ~ (all_211_3 = 0)
% 142.09/21.18 | | | | | (all_211_0 = 0 & all_211_2 = all_39_5))
% 142.09/21.18 | | | |
% 142.09/21.18 | | | | ALPHA: (240) implies:
% 142.09/21.18 | | | | (241) range(all_39_5, all_39_5, all_39_2) = all_211_1
% 142.09/21.18 | | | | (242) domain(all_39_5, all_39_5, all_39_2) = all_211_2
% 142.09/21.18 | | | | (243) ilf_type(all_39_2, all_118_0) = all_211_3
% 142.09/21.18 | | | |
% 142.09/21.18 | | | | DELTA: instantiating (230) with fresh symbols all_213_0, all_213_1,
% 142.09/21.18 | | | | all_213_2, all_213_3 gives:
% 142.09/21.18 | | | | (244) ilf_type(all_39_2, all_123_0) = all_213_3 & range(all_39_5,
% 142.09/21.18 | | | | all_39_5, all_39_2) = all_213_0 & subset(all_39_3, all_39_2)
% 142.09/21.18 | | | | = all_213_2 & subset(all_39_5, all_39_1) = all_213_1 &
% 142.09/21.18 | | | | $i(all_213_0) & ( ~ (all_213_2 = 0) | ~ (all_213_3 = 0) |
% 142.09/21.18 | | | | (all_213_0 = all_39_5 & all_213_1 = 0))
% 142.09/21.18 | | | |
% 142.09/21.18 | | | | ALPHA: (244) implies:
% 142.09/21.18 | | | | (245) subset(all_39_3, all_39_2) = all_213_2
% 142.09/21.18 | | | | (246) range(all_39_5, all_39_5, all_39_2) = all_213_0
% 142.09/21.18 | | | | (247) ilf_type(all_39_2, all_123_0) = all_213_3
% 142.09/21.18 | | | |
% 142.09/21.18 | | | | DELTA: instantiating (229) with fresh symbols all_215_0, all_215_1,
% 142.09/21.18 | | | | all_215_2, all_215_3 gives:
% 142.09/21.18 | | | | (248) ilf_type(all_39_2, all_123_0) = all_215_3 & domain(all_39_5,
% 142.09/21.18 | | | | all_39_5, all_39_2) = all_215_1 & subset(all_39_3, all_39_2)
% 142.09/21.18 | | | | = all_215_2 & subset(all_39_5, all_215_1) = all_215_0 &
% 142.09/21.18 | | | | $i(all_215_1) & ( ~ (all_215_2 = 0) | ~ (all_215_3 = 0) |
% 142.09/21.18 | | | | (all_215_0 = 0 & all_39_0 = all_39_5))
% 142.09/21.18 | | | |
% 142.09/21.18 | | | | ALPHA: (248) implies:
% 142.09/21.18 | | | | (249) subset(all_39_3, all_39_2) = all_215_2
% 142.09/21.18 | | | | (250) domain(all_39_5, all_39_5, all_39_2) = all_215_1
% 142.09/21.18 | | | | (251) ilf_type(all_39_2, all_123_0) = all_215_3
% 142.09/21.18 | | | |
% 142.09/21.18 | | | | DELTA: instantiating (228) with fresh symbols all_217_0, all_217_1,
% 142.09/21.18 | | | | all_217_2, all_217_3 gives:
% 142.09/21.18 | | | | (252) ilf_type(all_39_2, all_123_0) = all_217_3 & domain(all_39_5,
% 142.09/21.18 | | | | all_39_5, all_39_2) = all_217_2 & range(all_39_5, all_39_5,
% 142.09/21.18 | | | | all_39_2) = all_217_0 & subset(all_39_5, all_217_2) =
% 142.09/21.18 | | | | all_217_1 & $i(all_217_0) & $i(all_217_2) & ( ~ (all_217_3 = 0)
% 142.09/21.18 | | | | | (all_217_0 = all_39_5 & all_217_1 = 0))
% 142.09/21.18 | | | |
% 142.09/21.18 | | | | ALPHA: (252) implies:
% 142.09/21.18 | | | | (253) range(all_39_5, all_39_5, all_39_2) = all_217_0
% 142.09/21.18 | | | | (254) domain(all_39_5, all_39_5, all_39_2) = all_217_2
% 142.09/21.18 | | | | (255) ilf_type(all_39_2, all_123_0) = all_217_3
% 142.09/21.18 | | | | (256) ~ (all_217_3 = 0) | (all_217_0 = all_39_5 & all_217_1 = 0)
% 142.09/21.18 | | | |
% 142.09/21.18 | | | | REDUCE: (201), (255) imply:
% 142.09/21.18 | | | | (257) ilf_type(all_39_2, all_67_1) = all_217_3
% 142.09/21.18 | | | |
% 142.09/21.18 | | | | REDUCE: (201), (251) imply:
% 142.09/21.18 | | | | (258) ilf_type(all_39_2, all_67_1) = all_215_3
% 142.09/21.18 | | | |
% 142.09/21.18 | | | | REDUCE: (201), (247) imply:
% 142.09/21.18 | | | | (259) ilf_type(all_39_2, all_67_1) = all_213_3
% 142.09/21.18 | | | |
% 142.09/21.18 | | | | REDUCE: (148), (243) imply:
% 142.09/21.18 | | | | (260) ilf_type(all_39_2, all_67_1) = all_211_3
% 142.09/21.18 | | | |
% 142.09/21.18 | | | | REDUCE: (148), (238) imply:
% 142.09/21.18 | | | | (261) ilf_type(all_39_2, all_67_1) = all_209_3
% 142.09/21.18 | | | |
% 142.09/21.18 | | | | REDUCE: (148), (234) imply:
% 142.09/21.18 | | | | (262) ilf_type(all_39_2, all_67_1) = all_207_3
% 142.09/21.18 | | | |
% 142.09/21.18 | | | | BETA: splitting (80) gives:
% 142.09/21.18 | | | |
% 142.09/21.18 | | | | Case 1:
% 142.09/21.18 | | | | |
% 142.09/21.18 | | | | | (263) ~ (all_99_1 = 0)
% 142.09/21.18 | | | | |
% 142.09/21.18 | | | | | REDUCE: (185), (263) imply:
% 142.09/21.18 | | | | | (264) $false
% 142.09/21.18 | | | | |
% 142.09/21.18 | | | | | CLOSE: (264) is inconsistent.
% 142.09/21.18 | | | | |
% 142.09/21.18 | | | | Case 2:
% 142.09/21.18 | | | | |
% 142.09/21.18 | | | | | (265) ! [v0: $i] : ! [v1: any] : ( ~ (ilf_type(v0, all_99_0) =
% 142.09/21.18 | | | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 142.09/21.18 | | | | | (ilf_type(v0, all_39_4) = v3 & ilf_type(v0, set_type) = v2
% 142.09/21.18 | | | | | & ( ~ (v2 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) |
% 142.09/21.18 | | | | | v3 = 0))))) & ! [v0: $i] : ! [v1: any] : ( ~
% 142.09/21.18 | | | | | (ilf_type(v0, all_39_4) = v1) | ~ $i(v0) | ? [v2: any] :
% 142.09/21.18 | | | | | ? [v3: any] : (ilf_type(v0, all_99_0) = v3 & ilf_type(v0,
% 142.09/21.18 | | | | | set_type) = v2 & ( ~ (v2 = 0) | (( ~ (v3 = 0) | v1 = 0)
% 142.09/21.18 | | | | | & ( ~ (v1 = 0) | v3 = 0))))) & ! [v0: $i] : ( ~
% 142.09/21.18 | | | | | (ilf_type(v0, set_type) = 0) | ~ $i(v0) | ? [v1: any] :
% 142.09/21.18 | | | | | ? [v2: any] : (ilf_type(v0, all_99_0) = v2 & ilf_type(v0,
% 142.09/21.18 | | | | | all_39_4) = v1 & ( ~ (v2 = 0) | v1 = 0) & ( ~ (v1 = 0)
% 142.09/21.18 | | | | | | v2 = 0)))
% 142.09/21.18 | | | | |
% 142.09/21.18 | | | | | ALPHA: (265) implies:
% 142.09/21.18 | | | | | (266) ! [v0: $i] : ! [v1: any] : ( ~ (ilf_type(v0, all_39_4) =
% 142.09/21.18 | | | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 142.09/21.18 | | | | | (ilf_type(v0, all_99_0) = v3 & ilf_type(v0, set_type) = v2
% 142.09/21.18 | | | | | & ( ~ (v2 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) |
% 142.09/21.18 | | | | | v3 = 0)))))
% 142.09/21.18 | | | | |
% 142.09/21.18 | | | | | GROUND_INST: instantiating (266) with all_39_2, 0, simplifying with
% 142.09/21.18 | | | | | (28), (33) gives:
% 142.09/21.18 | | | | | (267) ? [v0: any] : ? [v1: any] : (ilf_type(all_39_2, all_99_0) =
% 142.09/21.18 | | | | | v1 & ilf_type(all_39_2, set_type) = v0 & ( ~ (v0 = 0) | v1
% 142.09/21.18 | | | | | = 0))
% 142.09/21.18 | | | | |
% 142.09/21.18 | | | | | DELTA: instantiating (267) with fresh symbols all_227_0, all_227_1
% 142.09/21.18 | | | | | gives:
% 142.09/21.18 | | | | | (268) ilf_type(all_39_2, all_99_0) = all_227_0 & ilf_type(all_39_2,
% 142.09/21.18 | | | | | set_type) = all_227_1 & ( ~ (all_227_1 = 0) | all_227_0 =
% 142.09/21.18 | | | | | 0)
% 142.09/21.18 | | | | |
% 142.09/21.18 | | | | | ALPHA: (268) implies:
% 142.09/21.18 | | | | | (269) ilf_type(all_39_2, set_type) = all_227_1
% 142.09/21.18 | | | | | (270) ilf_type(all_39_2, all_99_0) = all_227_0
% 142.09/21.18 | | | | | (271) ~ (all_227_1 = 0) | all_227_0 = 0
% 142.09/21.18 | | | | |
% 142.09/21.18 | | | | | REDUCE: (197), (270) imply:
% 142.09/21.18 | | | | | (272) ilf_type(all_39_2, all_67_1) = all_227_0
% 142.09/21.18 | | | | |
% 142.09/21.18 | | | | | GROUND_INST: instantiating (21) with 0, all_207_2, all_39_2, all_39_3,
% 142.09/21.18 | | | | | simplifying with (29), (232) gives:
% 142.09/21.18 | | | | | (273) all_207_2 = 0
% 142.09/21.18 | | | | |
% 142.09/21.18 | | | | | GROUND_INST: instantiating (21) with all_142_2, all_207_2, all_39_2,
% 142.09/21.18 | | | | | all_39_3, simplifying with (212), (232) gives:
% 142.09/21.18 | | | | | (274) all_207_2 = all_142_2
% 142.09/21.18 | | | | |
% 142.09/21.18 | | | | | GROUND_INST: instantiating (21) with all_207_2, all_209_2, all_39_2,
% 142.09/21.18 | | | | | all_39_3, simplifying with (232), (236) gives:
% 142.09/21.18 | | | | | (275) all_209_2 = all_207_2
% 142.09/21.18 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (21) with all_213_2, all_215_2, all_39_2,
% 142.09/21.19 | | | | | all_39_3, simplifying with (245), (249) gives:
% 142.09/21.19 | | | | | (276) all_215_2 = all_213_2
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (21) with all_209_2, all_215_2, all_39_2,
% 142.09/21.19 | | | | | all_39_3, simplifying with (236), (249) gives:
% 142.09/21.19 | | | | | (277) all_215_2 = all_209_2
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (21) with all_146_2, all_215_2, all_39_2,
% 142.09/21.19 | | | | | all_39_3, simplifying with (211), (249) gives:
% 142.09/21.19 | | | | | (278) all_215_2 = all_146_2
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (24) with all_207_1, all_213_0, all_39_2,
% 142.09/21.19 | | | | | all_39_5, all_39_5, simplifying with (233), (246) gives:
% 142.09/21.19 | | | | | (279) all_213_0 = all_207_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (24) with all_39_0, all_217_0, all_39_2,
% 142.09/21.19 | | | | | all_39_5, all_39_5, simplifying with (30), (253) gives:
% 142.09/21.19 | | | | | (280) all_217_0 = all_39_0
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (24) with all_213_0, all_217_0, all_39_2,
% 142.09/21.19 | | | | | all_39_5, all_39_5, simplifying with (246), (253) gives:
% 142.09/21.19 | | | | | (281) all_217_0 = all_213_0
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (24) with all_211_1, all_217_0, all_39_2,
% 142.09/21.19 | | | | | all_39_5, all_39_5, simplifying with (241), (253) gives:
% 142.09/21.19 | | | | | (282) all_217_0 = all_211_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (25) with all_39_1, all_211_2, all_39_2,
% 142.09/21.19 | | | | | all_39_5, all_39_5, simplifying with (31), (242) gives:
% 142.09/21.19 | | | | | (283) all_211_2 = all_39_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (25) with all_211_2, all_215_1, all_39_2,
% 142.09/21.19 | | | | | all_39_5, all_39_5, simplifying with (242), (250) gives:
% 142.09/21.19 | | | | | (284) all_215_1 = all_211_2
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (25) with all_215_1, all_217_2, all_39_2,
% 142.09/21.19 | | | | | all_39_5, all_39_5, simplifying with (250), (254) gives:
% 142.09/21.19 | | | | | (285) all_217_2 = all_215_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (25) with all_209_1, all_217_2, all_39_2,
% 142.09/21.19 | | | | | all_39_5, all_39_5, simplifying with (237), (254) gives:
% 142.09/21.19 | | | | | (286) all_217_2 = all_209_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (22) with all_128_1, all_209_3, all_67_1,
% 142.09/21.19 | | | | | all_39_2, simplifying with (209), (261) gives:
% 142.09/21.19 | | | | | (287) all_209_3 = all_128_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (22) with all_209_3, all_211_3, all_67_1,
% 142.09/21.19 | | | | | all_39_2, simplifying with (260), (261) gives:
% 142.09/21.19 | | | | | (288) all_211_3 = all_209_3
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (22) with all_207_3, all_211_3, all_67_1,
% 142.09/21.19 | | | | | all_39_2, simplifying with (260), (262) gives:
% 142.09/21.19 | | | | | (289) all_211_3 = all_207_3
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (22) with all_146_3, all_211_3, all_67_1,
% 142.09/21.19 | | | | | all_39_2, simplifying with (206), (260) gives:
% 142.09/21.19 | | | | | (290) all_211_3 = all_146_3
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (22) with all_130_1, all_211_3, all_67_1,
% 142.09/21.19 | | | | | all_39_2, simplifying with (208), (260) gives:
% 142.09/21.19 | | | | | (291) all_211_3 = all_130_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (22) with all_150_1, all_213_3, all_67_1,
% 142.09/21.19 | | | | | all_39_2, simplifying with (205), (259) gives:
% 142.09/21.19 | | | | | (292) all_213_3 = all_150_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (22) with all_213_3, all_215_3, all_67_1,
% 142.09/21.19 | | | | | all_39_2, simplifying with (258), (259) gives:
% 142.09/21.19 | | | | | (293) all_215_3 = all_213_3
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (22) with all_150_1, all_217_3, all_67_1,
% 142.09/21.19 | | | | | all_39_2, simplifying with (205), (257) gives:
% 142.09/21.19 | | | | | (294) all_217_3 = all_150_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (22) with all_142_3, all_217_3, all_67_1,
% 142.09/21.19 | | | | | all_39_2, simplifying with (207), (257) gives:
% 142.09/21.19 | | | | | (295) all_217_3 = all_142_3
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (22) with all_130_1, all_217_3, all_67_1,
% 142.09/21.19 | | | | | all_39_2, simplifying with (208), (257) gives:
% 142.09/21.19 | | | | | (296) all_217_3 = all_130_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (22) with all_215_3, all_227_0, all_67_1,
% 142.09/21.19 | | | | | all_39_2, simplifying with (258), (272) gives:
% 142.09/21.19 | | | | | (297) all_227_0 = all_215_3
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | GROUND_INST: instantiating (22) with all_114_1, all_227_0, all_67_1,
% 142.09/21.19 | | | | | all_39_2, simplifying with (210), (272) gives:
% 142.09/21.19 | | | | | (298) all_227_0 = all_114_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (297), (298) imply:
% 142.09/21.19 | | | | | (299) all_215_3 = all_114_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | SIMP: (299) implies:
% 142.09/21.19 | | | | | (300) all_215_3 = all_114_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (280), (282) imply:
% 142.09/21.19 | | | | | (301) all_211_1 = all_39_0
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (281), (282) imply:
% 142.09/21.19 | | | | | (302) all_213_0 = all_211_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | SIMP: (302) implies:
% 142.09/21.19 | | | | | (303) all_213_0 = all_211_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (285), (286) imply:
% 142.09/21.19 | | | | | (304) all_215_1 = all_209_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | SIMP: (304) implies:
% 142.09/21.19 | | | | | (305) all_215_1 = all_209_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (294), (295) imply:
% 142.09/21.19 | | | | | (306) all_150_1 = all_142_3
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | SIMP: (306) implies:
% 142.09/21.19 | | | | | (307) all_150_1 = all_142_3
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (295), (296) imply:
% 142.09/21.19 | | | | | (308) all_142_3 = all_130_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (284), (305) imply:
% 142.09/21.19 | | | | | (309) all_211_2 = all_209_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | SIMP: (309) implies:
% 142.09/21.19 | | | | | (310) all_211_2 = all_209_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (276), (278) imply:
% 142.09/21.19 | | | | | (311) all_213_2 = all_146_2
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (276), (277) imply:
% 142.09/21.19 | | | | | (312) all_213_2 = all_209_2
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (293), (300) imply:
% 142.09/21.19 | | | | | (313) all_213_3 = all_114_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | SIMP: (313) implies:
% 142.09/21.19 | | | | | (314) all_213_3 = all_114_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (279), (303) imply:
% 142.09/21.19 | | | | | (315) all_211_1 = all_207_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | SIMP: (315) implies:
% 142.09/21.19 | | | | | (316) all_211_1 = all_207_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (311), (312) imply:
% 142.09/21.19 | | | | | (317) all_209_2 = all_146_2
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | SIMP: (317) implies:
% 142.09/21.19 | | | | | (318) all_209_2 = all_146_2
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (292), (314) imply:
% 142.09/21.19 | | | | | (319) all_150_1 = all_114_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | SIMP: (319) implies:
% 142.09/21.19 | | | | | (320) all_150_1 = all_114_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (301), (316) imply:
% 142.09/21.19 | | | | | (321) all_207_1 = all_39_0
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (283), (310) imply:
% 142.09/21.19 | | | | | (322) all_209_1 = all_39_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | SIMP: (322) implies:
% 142.09/21.19 | | | | | (323) all_209_1 = all_39_1
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (288), (289) imply:
% 142.09/21.19 | | | | | (324) all_209_3 = all_207_3
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | SIMP: (324) implies:
% 142.09/21.19 | | | | | (325) all_209_3 = all_207_3
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (289), (290) imply:
% 142.09/21.19 | | | | | (326) all_207_3 = all_146_3
% 142.09/21.19 | | | | |
% 142.09/21.19 | | | | | COMBINE_EQS: (289), (291) imply:
% 142.09/21.19 | | | | | (327) all_207_3 = all_130_1
% 142.43/21.19 | | | | |
% 142.43/21.19 | | | | | COMBINE_EQS: (275), (318) imply:
% 142.43/21.19 | | | | | (328) all_207_2 = all_146_2
% 142.43/21.19 | | | | |
% 142.43/21.19 | | | | | SIMP: (328) implies:
% 142.43/21.19 | | | | | (329) all_207_2 = all_146_2
% 142.43/21.19 | | | | |
% 142.43/21.19 | | | | | COMBINE_EQS: (287), (325) imply:
% 142.43/21.19 | | | | | (330) all_207_3 = all_128_1
% 142.43/21.19 | | | | |
% 142.43/21.19 | | | | | SIMP: (330) implies:
% 142.43/21.19 | | | | | (331) all_207_3 = all_128_1
% 142.43/21.19 | | | | |
% 142.43/21.19 | | | | | COMBINE_EQS: (274), (329) imply:
% 142.43/21.19 | | | | | (332) all_146_2 = all_142_2
% 142.43/21.19 | | | | |
% 142.43/21.19 | | | | | COMBINE_EQS: (273), (329) imply:
% 142.43/21.19 | | | | | (333) all_146_2 = 0
% 142.43/21.19 | | | | |
% 142.43/21.19 | | | | | COMBINE_EQS: (326), (327) imply:
% 142.43/21.19 | | | | | (334) all_146_3 = all_130_1
% 142.43/21.19 | | | | |
% 142.43/21.19 | | | | | COMBINE_EQS: (326), (331) imply:
% 142.43/21.19 | | | | | (335) all_146_3 = all_128_1
% 142.43/21.19 | | | | |
% 142.43/21.19 | | | | | COMBINE_EQS: (307), (320) imply:
% 142.43/21.19 | | | | | (336) all_142_3 = all_114_1
% 142.43/21.19 | | | | |
% 142.43/21.19 | | | | | SIMP: (336) implies:
% 142.43/21.19 | | | | | (337) all_142_3 = all_114_1
% 142.43/21.20 | | | | |
% 142.43/21.20 | | | | | COMBINE_EQS: (332), (333) imply:
% 142.43/21.20 | | | | | (338) all_142_2 = 0
% 142.43/21.20 | | | | |
% 142.43/21.20 | | | | | COMBINE_EQS: (334), (335) imply:
% 142.43/21.20 | | | | | (339) all_130_1 = all_128_1
% 142.43/21.20 | | | | |
% 142.43/21.20 | | | | | SIMP: (339) implies:
% 142.43/21.20 | | | | | (340) all_130_1 = all_128_1
% 142.43/21.20 | | | | |
% 142.43/21.20 | | | | | COMBINE_EQS: (308), (337) imply:
% 142.43/21.20 | | | | | (341) all_130_1 = all_114_1
% 142.43/21.20 | | | | |
% 142.43/21.20 | | | | | SIMP: (341) implies:
% 142.43/21.20 | | | | | (342) all_130_1 = all_114_1
% 142.43/21.20 | | | | |
% 142.43/21.20 | | | | | COMBINE_EQS: (340), (342) imply:
% 142.43/21.20 | | | | | (343) all_128_1 = all_114_1
% 142.43/21.20 | | | | |
% 142.43/21.20 | | | | | SIMP: (343) implies:
% 142.43/21.20 | | | | | (344) all_128_1 = all_114_1
% 142.43/21.20 | | | | |
% 142.43/21.20 | | | | | COMBINE_EQS: (287), (344) imply:
% 142.43/21.20 | | | | | (345) all_209_3 = all_114_1
% 142.43/21.20 | | | | |
% 142.43/21.20 | | | | | COMBINE_EQS: (318), (333) imply:
% 142.43/21.20 | | | | | (346) all_209_2 = 0
% 142.43/21.20 | | | | |
% 142.43/21.20 | | | | | COMBINE_EQS: (295), (337) imply:
% 142.43/21.20 | | | | | (347) all_217_3 = all_114_1
% 142.43/21.20 | | | | |
% 142.43/21.20 | | | | | GROUND_INST: instantiating (18) with all_39_2, all_227_1, simplifying
% 142.43/21.20 | | | | | with (28), (269) gives:
% 142.43/21.20 | | | | | (348) all_227_1 = 0
% 142.43/21.20 | | | | |
% 142.43/21.20 | | | | | BETA: splitting (271) gives:
% 142.43/21.20 | | | | |
% 142.43/21.20 | | | | | Case 1:
% 142.43/21.20 | | | | | |
% 142.43/21.20 | | | | | | (349) ~ (all_227_1 = 0)
% 142.43/21.20 | | | | | |
% 142.43/21.20 | | | | | | REDUCE: (348), (349) imply:
% 142.43/21.20 | | | | | | (350) $false
% 142.43/21.20 | | | | | |
% 142.43/21.20 | | | | | | CLOSE: (350) is inconsistent.
% 142.43/21.20 | | | | | |
% 142.43/21.20 | | | | | Case 2:
% 142.43/21.20 | | | | | |
% 142.43/21.20 | | | | | | (351) all_227_0 = 0
% 142.43/21.20 | | | | | |
% 142.43/21.20 | | | | | | COMBINE_EQS: (298), (351) imply:
% 142.43/21.20 | | | | | | (352) all_114_1 = 0
% 142.43/21.20 | | | | | |
% 142.43/21.20 | | | | | | COMBINE_EQS: (345), (352) imply:
% 142.43/21.20 | | | | | | (353) all_209_3 = 0
% 142.43/21.20 | | | | | |
% 142.43/21.20 | | | | | | COMBINE_EQS: (347), (352) imply:
% 142.43/21.20 | | | | | | (354) all_217_3 = 0
% 142.43/21.20 | | | | | |
% 142.43/21.20 | | | | | | BETA: splitting (239) gives:
% 142.43/21.20 | | | | | |
% 142.43/21.20 | | | | | | Case 1:
% 142.43/21.20 | | | | | | |
% 142.43/21.20 | | | | | | | (355) ~ (all_209_2 = 0)
% 142.43/21.20 | | | | | | |
% 142.43/21.20 | | | | | | | REDUCE: (346), (355) imply:
% 142.43/21.20 | | | | | | | (356) $false
% 142.43/21.20 | | | | | | |
% 142.43/21.20 | | | | | | | CLOSE: (356) is inconsistent.
% 142.43/21.20 | | | | | | |
% 142.43/21.20 | | | | | | Case 2:
% 142.43/21.20 | | | | | | |
% 142.43/21.20 | | | | | | | (357) ~ (all_209_3 = 0) | (all_209_0 = 0 & all_209_1 =
% 142.43/21.20 | | | | | | | all_39_5)
% 142.43/21.20 | | | | | | |
% 142.43/21.20 | | | | | | | BETA: splitting (357) gives:
% 142.43/21.20 | | | | | | |
% 142.43/21.20 | | | | | | | Case 1:
% 142.43/21.20 | | | | | | | |
% 142.43/21.20 | | | | | | | | (358) ~ (all_209_3 = 0)
% 142.43/21.20 | | | | | | | |
% 142.43/21.20 | | | | | | | | REDUCE: (353), (358) imply:
% 142.43/21.20 | | | | | | | | (359) $false
% 142.43/21.20 | | | | | | | |
% 142.43/21.20 | | | | | | | | CLOSE: (359) is inconsistent.
% 142.43/21.20 | | | | | | | |
% 142.43/21.20 | | | | | | | Case 2:
% 142.43/21.20 | | | | | | | |
% 142.43/21.20 | | | | | | | | (360) all_209_0 = 0 & all_209_1 = all_39_5
% 142.43/21.20 | | | | | | | |
% 142.43/21.20 | | | | | | | | ALPHA: (360) implies:
% 142.43/21.20 | | | | | | | | (361) all_209_1 = all_39_5
% 142.43/21.20 | | | | | | | |
% 142.43/21.20 | | | | | | | | COMBINE_EQS: (323), (361) imply:
% 142.43/21.20 | | | | | | | | (362) all_39_1 = all_39_5
% 142.43/21.20 | | | | | | | |
% 142.43/21.20 | | | | | | | | BETA: splitting (36) gives:
% 142.43/21.20 | | | | | | | |
% 142.43/21.20 | | | | | | | | Case 1:
% 142.43/21.20 | | | | | | | | |
% 142.43/21.20 | | | | | | | | | (363) ~ (all_39_0 = all_39_5)
% 142.43/21.20 | | | | | | | | |
% 142.43/21.20 | | | | | | | | | BETA: splitting (256) gives:
% 142.43/21.20 | | | | | | | | |
% 142.43/21.20 | | | | | | | | | Case 1:
% 142.43/21.20 | | | | | | | | | |
% 142.43/21.20 | | | | | | | | | | (364) ~ (all_217_3 = 0)
% 142.43/21.20 | | | | | | | | | |
% 142.43/21.20 | | | | | | | | | | REDUCE: (354), (364) imply:
% 142.43/21.20 | | | | | | | | | | (365) $false
% 142.43/21.20 | | | | | | | | | |
% 142.43/21.20 | | | | | | | | | | CLOSE: (365) is inconsistent.
% 142.43/21.20 | | | | | | | | | |
% 142.43/21.20 | | | | | | | | | Case 2:
% 142.43/21.20 | | | | | | | | | |
% 142.43/21.20 | | | | | | | | | | (366) all_217_0 = all_39_5 & all_217_1 = 0
% 142.43/21.20 | | | | | | | | | |
% 142.43/21.20 | | | | | | | | | | ALPHA: (366) implies:
% 142.43/21.20 | | | | | | | | | | (367) all_217_0 = all_39_5
% 142.43/21.20 | | | | | | | | | |
% 142.43/21.20 | | | | | | | | | | COMBINE_EQS: (280), (367) imply:
% 142.43/21.20 | | | | | | | | | | (368) all_39_0 = all_39_5
% 142.43/21.20 | | | | | | | | | |
% 142.43/21.20 | | | | | | | | | | REDUCE: (363), (368) imply:
% 142.43/21.20 | | | | | | | | | | (369) $false
% 142.43/21.20 | | | | | | | | | |
% 142.43/21.20 | | | | | | | | | | CLOSE: (369) is inconsistent.
% 142.43/21.20 | | | | | | | | | |
% 142.43/21.20 | | | | | | | | | End of split
% 142.43/21.20 | | | | | | | | |
% 142.43/21.20 | | | | | | | | Case 2:
% 142.43/21.20 | | | | | | | | |
% 142.43/21.20 | | | | | | | | | (370) ~ (all_39_1 = all_39_5)
% 142.43/21.20 | | | | | | | | |
% 142.43/21.20 | | | | | | | | | REDUCE: (362), (370) imply:
% 142.43/21.20 | | | | | | | | | (371) $false
% 142.43/21.20 | | | | | | | | |
% 142.43/21.20 | | | | | | | | | CLOSE: (371) is inconsistent.
% 142.43/21.20 | | | | | | | | |
% 142.43/21.20 | | | | | | | | End of split
% 142.43/21.20 | | | | | | | |
% 142.43/21.20 | | | | | | | End of split
% 142.43/21.20 | | | | | | |
% 142.43/21.20 | | | | | | End of split
% 142.43/21.20 | | | | | |
% 142.43/21.20 | | | | | End of split
% 142.43/21.20 | | | | |
% 142.43/21.20 | | | | End of split
% 142.43/21.20 | | | |
% 142.43/21.20 | | | End of split
% 142.43/21.20 | | |
% 142.43/21.20 | | End of split
% 142.43/21.20 | |
% 142.43/21.20 | End of split
% 142.43/21.20 |
% 142.43/21.20 End of proof
% 142.43/21.20 % SZS output end Proof for theBenchmark
% 142.43/21.20
% 142.43/21.20 20590ms
%------------------------------------------------------------------------------