TSTP Solution File: NUM409+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM409+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:47:36 EDT 2023
% Result : Theorem 16.98s 3.02s
% Output : Proof 49.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM409+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n016.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 : Fri Aug 25 18:06:55 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.95/1.09 Prover 1: Preprocessing ...
% 2.95/1.09 Prover 4: Preprocessing ...
% 2.95/1.13 Prover 0: Preprocessing ...
% 2.95/1.13 Prover 6: Preprocessing ...
% 2.95/1.13 Prover 3: Preprocessing ...
% 2.95/1.13 Prover 2: Preprocessing ...
% 2.95/1.14 Prover 5: Preprocessing ...
% 7.00/1.68 Prover 1: Warning: ignoring some quantifiers
% 7.44/1.74 Prover 2: Proving ...
% 7.44/1.74 Prover 5: Proving ...
% 7.44/1.74 Prover 6: Proving ...
% 7.44/1.75 Prover 3: Warning: ignoring some quantifiers
% 7.44/1.75 Prover 1: Constructing countermodel ...
% 7.80/1.76 Prover 3: Constructing countermodel ...
% 7.80/1.80 Prover 4: Warning: ignoring some quantifiers
% 8.44/1.86 Prover 4: Constructing countermodel ...
% 9.14/1.95 Prover 0: Proving ...
% 12.79/2.45 Prover 3: gave up
% 12.79/2.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.00/2.50 Prover 7: Preprocessing ...
% 13.63/2.60 Prover 7: Warning: ignoring some quantifiers
% 13.63/2.61 Prover 7: Constructing countermodel ...
% 15.32/2.79 Prover 7: gave up
% 15.32/2.79 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.32/2.87 Prover 1: gave up
% 15.32/2.87 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 15.32/2.88 Prover 8: Preprocessing ...
% 15.32/2.93 Prover 9: Preprocessing ...
% 16.98/3.02 Prover 0: proved (2394ms)
% 16.98/3.02
% 16.98/3.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.98/3.02
% 16.98/3.02 Prover 2: stopped
% 16.98/3.02 Prover 6: stopped
% 16.98/3.03 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 16.98/3.03 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 16.98/3.03 Prover 5: stopped
% 16.98/3.04 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.98/3.04 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 16.98/3.04 Prover 8: Warning: ignoring some quantifiers
% 16.98/3.05 Prover 8: Constructing countermodel ...
% 16.98/3.06 Prover 11: Preprocessing ...
% 17.55/3.09 Prover 16: Preprocessing ...
% 17.55/3.09 Prover 10: Preprocessing ...
% 17.55/3.11 Prover 13: Preprocessing ...
% 18.32/3.20 Prover 9: Warning: ignoring some quantifiers
% 18.32/3.20 Prover 16: Warning: ignoring some quantifiers
% 18.32/3.20 Prover 10: Warning: ignoring some quantifiers
% 18.32/3.20 Prover 13: Warning: ignoring some quantifiers
% 18.32/3.21 Prover 10: Constructing countermodel ...
% 18.52/3.21 Prover 16: Constructing countermodel ...
% 18.52/3.22 Prover 9: Constructing countermodel ...
% 18.52/3.22 Prover 13: Constructing countermodel ...
% 18.62/3.22 Prover 9: stopped
% 18.62/3.23 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 18.62/3.27 Prover 19: Preprocessing ...
% 18.62/3.28 Prover 11: Warning: ignoring some quantifiers
% 18.62/3.29 Prover 11: Constructing countermodel ...
% 19.22/3.35 Prover 10: gave up
% 19.22/3.36 Prover 19: Warning: ignoring some quantifiers
% 19.22/3.37 Prover 19: Constructing countermodel ...
% 21.99/3.70 Prover 8: gave up
% 24.16/3.99 Prover 19: gave up
% 43.13/6.71 Prover 13: gave up
% 47.88/7.51 Prover 4: Found proof (size 704)
% 47.88/7.51 Prover 4: proved (6882ms)
% 47.88/7.52 Prover 16: stopped
% 47.88/7.52 Prover 11: stopped
% 47.88/7.52
% 47.88/7.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 47.88/7.52
% 48.37/7.67 % SZS output start Proof for theBenchmark
% 48.37/7.67 Assumptions after simplification:
% 48.37/7.67 ---------------------------------
% 48.37/7.67
% 48.37/7.67 (cc1_funct_1)
% 48.37/7.70 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (function(v0) = v1) | ~ $i(v0) | ?
% 48.37/7.70 [v2: int] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0: $i] : ( ~ (empty(v0) =
% 48.37/7.70 0) | ~ $i(v0) | function(v0) = 0)
% 48.37/7.70
% 48.37/7.70 (cc1_relat_1)
% 48.37/7.70 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (relation(v0) = v1) | ~ $i(v0) | ?
% 48.37/7.70 [v2: int] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0: $i] : ( ~ (empty(v0) =
% 48.37/7.70 0) | ~ $i(v0) | relation(v0) = 0)
% 48.37/7.70
% 48.37/7.70 (cc2_funct_1)
% 48.37/7.71 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 48.37/7.71 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) =
% 48.37/7.71 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 48.37/7.71 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 48.37/7.71 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0)
% 48.37/7.71 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 48.37/7.71 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any]
% 48.37/7.71 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) |
% 48.37/7.71 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0)
% 48.37/7.71 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 &
% 48.37/7.71 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 =
% 48.37/7.71 0)))
% 48.37/7.71
% 48.37/7.71 (cc3_ordinal1)
% 48.37/7.71 ! [v0: $i] : ! [v1: any] : ( ~ (epsilon_transitive(v0) = v1) | ~ $i(v0) |
% 48.37/7.71 ? [v2: any] : ? [v3: any] : ? [v4: any] : (ordinal(v0) = v4 &
% 48.37/7.71 epsilon_connected(v0) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3
% 48.37/7.71 = 0 & v1 = 0)))) & ! [v0: $i] : ! [v1: any] : ( ~ (ordinal(v0) = v1)
% 48.37/7.71 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 48.37/7.71 (epsilon_transitive(v0) = v3 & epsilon_connected(v0) = v4 & empty(v0) = v2 &
% 48.37/7.71 ( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0)))) & ! [v0: $i] : ! [v1: any]
% 48.37/7.71 : ( ~ (epsilon_connected(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 48.37/7.71 ? [v4: any] : (epsilon_transitive(v0) = v3 & ordinal(v0) = v4 & empty(v0) =
% 48.37/7.71 v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0)))) & ! [v0: $i] : ( ~
% 48.37/7.71 (empty(v0) = 0) | ~ $i(v0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0
% 48.37/7.71 & epsilon_connected(v0) = 0))
% 48.37/7.71
% 48.37/7.71 (d4_relat_1)
% 48.37/7.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : ! [v5:
% 48.37/7.72 $i] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5)
% 48.37/7.72 | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 48.37/7.72 [v6: int] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) =
% 48.37/7.72 v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0)
% 48.37/7.72 = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 48.37/7.72 int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ($i(v4) & ((v6 = 0 &
% 48.37/7.72 ordered_pair(v2, v4) = v5 & in(v5, v0) = 0 & $i(v5)) | ( ~ (v3 = 0) &
% 48.37/7.72 relation(v0) = v3)))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2
% 48.37/7.72 = v0 | ~ (relation_dom(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] :
% 48.37/7.72 ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] :
% 48.37/7.72 ($i(v6) & $i(v4) & (( ~ (v3 = 0) & relation(v1) = v3) | (in(v4, v0) = v5 & (
% 48.37/7.72 ~ (v5 = 0) | ! [v9: $i] : ! [v10: $i] : ( ~ (ordered_pair(v4, v9)
% 48.37/7.72 = v10) | ~ $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & in(v10, v1)
% 48.37/7.72 = v11))) & (v5 = 0 | (v8 = 0 & ordered_pair(v4, v6) = v7 &
% 48.37/7.72 in(v7, v1) = 0 & $i(v7))))))) & ! [v0: $i] : ( ~ (relation(v0) =
% 48.37/7.72 0) | ~ $i(v0) | ? [v1: $i] : (relation_dom(v0) = v1 & $i(v1) & ! [v2:
% 48.37/7.72 $i] : ! [v3: int] : ! [v4: $i] : ! [v5: $i] : (v3 = 0 | ~
% 48.37/7.72 (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~
% 48.37/7.72 $i(v2) | ? [v6: int] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2: $i] :
% 48.37/7.72 ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] :
% 48.37/7.72 (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) & $i(v3))) & ?
% 48.37/7.72 [v2: $i] : (v2 = v1 | ~ $i(v2) | ? [v3: $i] : ? [v4: any] : ? [v5: $i]
% 48.37/7.72 : ? [v6: $i] : ? [v7: int] : (in(v3, v2) = v4 & $i(v5) & $i(v3) & ( ~
% 48.37/7.72 (v4 = 0) | ! [v8: $i] : ! [v9: $i] : ( ~ (ordered_pair(v3, v8) =
% 48.37/7.72 v9) | ~ $i(v8) | ? [v10: int] : ( ~ (v10 = 0) & in(v9, v0) =
% 48.37/7.72 v10))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6,
% 48.37/7.72 v0) = 0 & $i(v6)))))))
% 48.37/7.72
% 48.37/7.72 (d7_ordinal1)
% 48.37/7.73 ! [v0: $i] : ! [v1: any] : ( ~ (transfinite_sequence(v0) = v1) | ~ $i(v0) |
% 48.37/7.73 ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] : (relation_dom(v0)
% 48.37/7.73 = v4 & relation(v0) = v2 & ordinal(v4) = v5 & function(v0) = v3 & $i(v4) &
% 48.37/7.73 ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v5 = 0) | v1 = 0) & ( ~ (v1 = 0) | v5 =
% 48.37/7.73 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) |
% 48.37/7.73 ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 48.37/7.73 (transfinite_sequence(v0) = v4 & relation(v0) = v2 & ordinal(v1) = v5 &
% 48.37/7.73 function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v5 = 0) | v4 = 0) &
% 48.37/7.73 ( ~ (v4 = 0) | v5 = 0))))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~
% 48.37/7.73 $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 48.37/7.73 (transfinite_sequence(v0) = v2 & relation_dom(v0) = v3 & ordinal(v3) = v4 &
% 48.37/7.73 function(v0) = v1 & $i(v3) & ( ~ (v1 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~
% 48.37/7.73 (v2 = 0) | v4 = 0))))) & ! [v0: $i] : ( ~ (function(v0) = 0) | ~
% 48.37/7.73 $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 48.37/7.73 (transfinite_sequence(v0) = v2 & relation_dom(v0) = v3 & relation(v0) = v1 &
% 48.37/7.73 ordinal(v3) = v4 & $i(v3) & ( ~ (v1 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~
% 48.37/7.73 (v2 = 0) | v4 = 0)))))
% 48.37/7.73
% 48.37/7.73 (d8_ordinal1)
% 48.37/7.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (relation_rng(v1)
% 48.37/7.73 = v2) | ~ (subset(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] :
% 48.37/7.73 ? [v5: any] : ? [v6: any] : ? [v7: any] : (transfinite_sequence_of(v1, v0)
% 48.37/7.73 = v7 & transfinite_sequence(v1) = v6 & relation(v1) = v4 & function(v1) =
% 48.37/7.73 v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | (( ~ (v7 = 0) | v3 = 0) &
% 48.37/7.73 ( ~ (v3 = 0) | v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any]
% 48.37/7.73 : ( ~ (transfinite_sequence_of(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 48.37/7.73 any] : ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] :
% 48.37/7.73 (relation_rng(v1) = v6 & subset(v6, v0) = v7 & transfinite_sequence(v1) = v5
% 48.37/7.73 & relation(v1) = v3 & function(v1) = v4 & $i(v6) & ( ~ (v5 = 0) | ~ (v4 =
% 48.37/7.73 0) | ~ (v3 = 0) | (( ~ (v7 = 0) | v2 = 0) & ( ~ (v2 = 0) | v7 =
% 48.37/7.73 0)))))
% 48.37/7.73
% 48.37/7.73 (fc2_ordinal1)
% 48.37/7.73 relation_empty_yielding(empty_set) = 0 & one_to_one(empty_set) = 0 &
% 48.37/7.73 relation(empty_set) = 0 & epsilon_transitive(empty_set) = 0 &
% 48.37/7.73 ordinal(empty_set) = 0 & epsilon_connected(empty_set) = 0 &
% 48.37/7.73 function(empty_set) = 0 & empty(empty_set) = 0 & $i(empty_set)
% 48.37/7.73
% 48.37/7.73 (fc4_relat_1)
% 48.37/7.73 relation(empty_set) = 0 & empty(empty_set) = 0 & $i(empty_set)
% 48.37/7.73
% 48.37/7.73 (fc5_relat_1)
% 48.76/7.74 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 48.76/7.74 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 &
% 48.76/7.74 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 =
% 48.76/7.74 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~
% 48.76/7.74 $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 &
% 48.76/7.74 empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) &
% 48.76/7.74 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 48.76/7.74 : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 &
% 48.76/7.74 $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 48.76/7.74
% 48.76/7.74 (fc6_funct_1)
% 48.76/7.74 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 48.76/7.74 any] : ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 48.76/7.74 (relation_non_empty(v0) = v3 & with_non_empty_elements(v1) = v5 &
% 48.76/7.74 relation(v0) = v2 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~
% 48.76/7.74 (v2 = 0) | v5 = 0))) & ! [v0: $i] : ( ~ (relation_non_empty(v0) = 0) |
% 48.76/7.74 ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 48.76/7.74 (with_non_empty_elements(v3) = v4 & relation_rng(v0) = v3 & relation(v0) =
% 48.76/7.74 v1 & function(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = 0))) &
% 48.76/7.74 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any]
% 48.76/7.74 : ? [v3: $i] : ? [v4: any] : (relation_non_empty(v0) = v1 &
% 48.76/7.74 with_non_empty_elements(v3) = v4 & relation_rng(v0) = v3 & function(v0) =
% 48.76/7.74 v2 & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = 0))) & ! [v0: $i] : ( ~
% 48.76/7.74 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: $i] :
% 48.76/7.74 ? [v4: any] : (relation_non_empty(v0) = v2 & with_non_empty_elements(v3) =
% 48.76/7.74 v4 & relation_rng(v0) = v3 & relation(v0) = v1 & $i(v3) & ( ~ (v2 = 0) |
% 48.76/7.74 ~ (v1 = 0) | v4 = 0)))
% 48.76/7.74
% 48.76/7.74 (fc6_relat_1)
% 48.76/7.74 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 48.76/7.74 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_rng(v0) = v3 &
% 48.76/7.74 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 =
% 48.76/7.74 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~
% 48.76/7.74 $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 &
% 48.76/7.74 empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) &
% 48.76/7.74 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 48.76/7.74 : ? [v3: any] : (relation_rng(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 &
% 48.76/7.74 $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 48.76/7.74
% 48.76/7.74 (fc7_relat_1)
% 48.76/7.74 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 48.76/7.74 any] : ? [v3: any] : ? [v4: any] : (relation(v1) = v4 & empty(v1) = v3 &
% 48.76/7.74 empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ( ~
% 48.76/7.74 (empty(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (relation_dom(v0) = v1 &
% 48.76/7.74 relation(v1) = 0 & empty(v1) = 0 & $i(v1)))
% 48.76/7.74
% 48.76/7.75 (fc8_relat_1)
% 48.76/7.75 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 48.76/7.75 any] : ? [v3: any] : ? [v4: any] : (relation(v1) = v4 & empty(v1) = v3 &
% 48.76/7.75 empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ( ~
% 48.76/7.75 (empty(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (relation_rng(v0) = v1 &
% 48.76/7.75 relation(v1) = 0 & empty(v1) = 0 & $i(v1)))
% 48.76/7.75
% 48.76/7.75 (rc1_relat_1)
% 48.76/7.75 ? [v0: $i] : (relation(v0) = 0 & empty(v0) = 0 & $i(v0))
% 48.76/7.75
% 48.76/7.75 (rc1_xboole_0)
% 48.76/7.75 ? [v0: $i] : (empty(v0) = 0 & $i(v0))
% 48.76/7.75
% 48.76/7.75 (rc2_funct_1)
% 48.76/7.75 ? [v0: $i] : (relation(v0) = 0 & function(v0) = 0 & empty(v0) = 0 & $i(v0))
% 48.76/7.75
% 48.76/7.75 (rc2_ordinal1)
% 48.76/7.75 ? [v0: $i] : (one_to_one(v0) = 0 & relation(v0) = 0 & epsilon_transitive(v0)
% 48.76/7.75 = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0 & function(v0) = 0 &
% 48.76/7.75 empty(v0) = 0 & $i(v0))
% 48.76/7.75
% 48.76/7.75 (rc2_xboole_0)
% 48.76/7.75 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0))
% 48.76/7.75
% 48.76/7.75 (rc4_ordinal1)
% 48.76/7.75 ? [v0: $i] : (transfinite_sequence(v0) = 0 & relation(v0) = 0 & function(v0)
% 48.76/7.75 = 0 & $i(v0))
% 48.76/7.75
% 48.76/7.75 (t2_xboole_1)
% 48.76/7.75 $i(empty_set) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(empty_set,
% 48.76/7.75 v0) = v1) | ~ $i(v0))
% 48.76/7.75
% 48.76/7.75 (t45_ordinal1)
% 48.76/7.75 $i(empty_set) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 48.76/7.75 transfinite_sequence_of(empty_set, v0) = v1 & $i(v0))
% 48.76/7.75
% 48.76/7.75 (t65_relat_1)
% 48.76/7.75 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~
% 48.76/7.75 $i(v0) | ? [v2: any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0)
% 48.76/7.75 = v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 = empty_set) & (
% 48.76/7.75 ~ (v1 = empty_set) | v3 = empty_set))))) & ! [v0: $i] : ! [v1: $i]
% 48.76/7.75 : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] :
% 48.76/7.75 (relation_rng(v0) = v3 & relation(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (( ~
% 48.76/7.75 (v3 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v3 =
% 48.76/7.75 empty_set))))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) |
% 48.76/7.75 ? [v1: $i] : ? [v2: $i] : (relation_rng(v0) = v2 & relation_dom(v0) = v1 &
% 48.76/7.75 $i(v2) & $i(v1) & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 =
% 48.76/7.75 empty_set) | v2 = empty_set)))
% 48.76/7.75
% 48.76/7.75 (t6_boole)
% 48.76/7.75 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~
% 48.76/7.75 $i(v0))
% 48.76/7.75
% 48.76/7.75 (t8_boole)
% 48.76/7.75 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)
% 48.76/7.75 | ~ $i(v1) | ~ $i(v0))
% 48.76/7.75
% 48.76/7.75 (function-axioms)
% 48.76/7.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 48.76/7.76 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 48.76/7.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 48.76/7.76 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 48.76/7.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 48.76/7.76 $i] : (v1 = v0 | ~ (transfinite_sequence_of(v3, v2) = v1) | ~
% 48.76/7.76 (transfinite_sequence_of(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 48.76/7.76 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~
% 48.76/7.76 (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 48.76/7.76 [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~
% 48.76/7.76 (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 48.76/7.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) =
% 48.76/7.76 v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 48.76/7.76 (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0:
% 48.76/7.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 48.76/7.76 ~ (relation_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0)) & !
% 48.76/7.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 48.76/7.76 | ~ (with_non_empty_elements(v2) = v1) | ~ (with_non_empty_elements(v2) =
% 48.76/7.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 48.76/7.76 $i] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~
% 48.76/7.76 (relation_empty_yielding(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 48.76/7.76 $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) &
% 48.76/7.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 48.76/7.76 v0 | ~ (transfinite_sequence(v2) = v1) | ~ (transfinite_sequence(v2) =
% 48.76/7.76 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 48.76/7.76 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 48.76/7.76 : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) =
% 48.76/7.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 48.76/7.76 $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & !
% 48.76/7.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 48.76/7.76 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0:
% 48.76/7.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 48.76/7.76 ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & !
% 48.76/7.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 48.76/7.76 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0:
% 48.76/7.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 48.76/7.76 ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0:
% 48.76/7.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 48.76/7.76 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool]
% 48.76/7.76 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) |
% 48.76/7.76 ~ (empty(v2) = v0))
% 48.76/7.76
% 48.76/7.76 Further assumptions not needed in the proof:
% 48.76/7.76 --------------------------------------------
% 48.76/7.76 antisymmetry_r2_hidden, cc1_ordinal1, cc2_ordinal1, commutativity_k2_tarski,
% 48.76/7.76 d5_tarski, dt_m1_ordinal1, existence_m1_ordinal1, existence_m1_subset_1,
% 48.76/7.76 fc12_relat_1, fc1_xboole_0, fc1_zfmisc_1, rc1_funct_1, rc1_ordinal1,
% 48.76/7.76 rc2_relat_1, rc3_funct_1, rc3_ordinal1, rc3_relat_1, rc4_funct_1, rc5_funct_1,
% 48.76/7.76 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 48.76/7.76 t7_boole
% 48.76/7.76
% 48.76/7.76 Those formulas are unsatisfiable:
% 48.76/7.76 ---------------------------------
% 48.76/7.76
% 48.76/7.76 Begin of proof
% 48.76/7.76 |
% 48.76/7.76 | ALPHA: (cc1_funct_1) implies:
% 48.76/7.76 | (1) ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | function(v0) = 0)
% 48.76/7.76 |
% 48.76/7.76 | ALPHA: (cc1_relat_1) implies:
% 48.76/7.76 | (2) ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | relation(v0) = 0)
% 48.76/7.76 |
% 48.76/7.76 | ALPHA: (cc2_funct_1) implies:
% 48.76/7.77 | (3) ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 48.76/7.77 | any] : ? [v3: any] : (one_to_one(v0) = v3 & relation(v0) = v1 &
% 48.76/7.77 | function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 48.76/7.77 | (4) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 48.76/7.77 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & relation(v0) = v1 &
% 48.76/7.77 | empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 48.76/7.77 | (5) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 48.76/7.77 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 &
% 48.76/7.77 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 48.76/7.77 |
% 48.76/7.77 | ALPHA: (cc3_ordinal1) implies:
% 48.76/7.77 | (6) ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | (epsilon_transitive(v0)
% 48.76/7.77 | = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0))
% 48.76/7.77 |
% 48.76/7.77 | ALPHA: (d4_relat_1) implies:
% 48.76/7.77 | (7) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 48.76/7.77 | (relation_dom(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: int] : !
% 48.76/7.77 | [v4: $i] : ! [v5: $i] : (v3 = 0 | ~ (ordered_pair(v2, v4) = v5) |
% 48.76/7.77 | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ? [v6: int] : ( ~
% 48.76/7.77 | (v6 = 0) & in(v5, v0) = v6)) & ! [v2: $i] : ( ~ (in(v2, v1) =
% 48.76/7.77 | 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2,
% 48.76/7.77 | v3) = v4 & in(v4, v0) = 0 & $i(v4) & $i(v3))) & ? [v2: $i] :
% 48.76/7.77 | (v2 = v1 | ~ $i(v2) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] :
% 48.76/7.77 | ? [v6: $i] : ? [v7: int] : (in(v3, v2) = v4 & $i(v5) & $i(v3) &
% 48.76/7.77 | ( ~ (v4 = 0) | ! [v8: $i] : ! [v9: $i] : ( ~
% 48.76/7.77 | (ordered_pair(v3, v8) = v9) | ~ $i(v8) | ? [v10: int] : (
% 48.76/7.77 | ~ (v10 = 0) & in(v9, v0) = v10))) & (v4 = 0 | (v7 = 0 &
% 48.76/7.77 | ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6)))))))
% 48.76/7.77 |
% 48.76/7.77 | ALPHA: (d7_ordinal1) implies:
% 48.76/7.77 | (8) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 48.76/7.77 | [v2: any] : ? [v3: $i] : ? [v4: any] : (transfinite_sequence(v0) =
% 48.76/7.77 | v2 & relation_dom(v0) = v3 & relation(v0) = v1 & ordinal(v3) = v4 &
% 48.76/7.77 | $i(v3) & ( ~ (v1 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4
% 48.76/7.77 | = 0)))))
% 48.76/7.77 | (9) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 48.76/7.77 | [v2: any] : ? [v3: $i] : ? [v4: any] : (transfinite_sequence(v0) =
% 48.76/7.77 | v2 & relation_dom(v0) = v3 & ordinal(v3) = v4 & function(v0) = v1 &
% 48.76/7.77 | $i(v3) & ( ~ (v1 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4
% 48.76/7.77 | = 0)))))
% 48.76/7.77 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 48.76/7.77 | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 48.76/7.77 | (transfinite_sequence(v0) = v4 & relation(v0) = v2 & ordinal(v1) =
% 48.76/7.77 | v5 & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v5 =
% 48.76/7.77 | 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = 0)))))
% 48.76/7.77 | (11) ! [v0: $i] : ! [v1: any] : ( ~ (transfinite_sequence(v0) = v1) | ~
% 48.76/7.77 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] :
% 48.76/7.77 | (relation_dom(v0) = v4 & relation(v0) = v2 & ordinal(v4) = v5 &
% 48.76/7.77 | function(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v5
% 48.76/7.77 | = 0) | v1 = 0) & ( ~ (v1 = 0) | v5 = 0)))))
% 48.76/7.77 |
% 48.76/7.77 | ALPHA: (d8_ordinal1) implies:
% 48.76/7.78 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 48.76/7.78 | (transfinite_sequence_of(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 48.76/7.78 | [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: any]
% 48.76/7.78 | : (relation_rng(v1) = v6 & subset(v6, v0) = v7 &
% 48.76/7.78 | transfinite_sequence(v1) = v5 & relation(v1) = v3 & function(v1) =
% 48.76/7.78 | v4 & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v7
% 48.76/7.78 | = 0) | v2 = 0) & ( ~ (v2 = 0) | v7 = 0)))))
% 48.76/7.78 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 48.76/7.78 | (relation_rng(v1) = v2) | ~ (subset(v2, v0) = v3) | ~ $i(v1) | ~
% 48.76/7.78 | $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 48.76/7.78 | (transfinite_sequence_of(v1, v0) = v7 & transfinite_sequence(v1) =
% 48.76/7.78 | v6 & relation(v1) = v4 & function(v1) = v5 & ( ~ (v6 = 0) | ~ (v5
% 48.76/7.78 | = 0) | ~ (v4 = 0) | (( ~ (v7 = 0) | v3 = 0) & ( ~ (v3 = 0) |
% 48.76/7.78 | v7 = 0)))))
% 48.76/7.78 |
% 48.76/7.78 | ALPHA: (fc2_ordinal1) implies:
% 48.76/7.78 | (14) function(empty_set) = 0
% 48.76/7.78 |
% 48.76/7.78 | ALPHA: (fc4_relat_1) implies:
% 48.76/7.78 | (15) empty(empty_set) = 0
% 48.76/7.78 | (16) relation(empty_set) = 0
% 48.76/7.78 |
% 48.76/7.78 | ALPHA: (fc5_relat_1) implies:
% 48.76/7.78 | (17) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 48.76/7.78 | [v2: $i] : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 &
% 48.76/7.78 | empty(v0) = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 48.76/7.78 |
% 48.76/7.78 | ALPHA: (fc6_funct_1) implies:
% 48.76/7.78 | (18) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 48.76/7.78 | [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_non_empty(v0) =
% 48.76/7.78 | v2 & with_non_empty_elements(v3) = v4 & relation_rng(v0) = v3 &
% 48.76/7.78 | relation(v0) = v1 & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 =
% 48.76/7.78 | 0)))
% 48.76/7.78 | (19) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 48.76/7.78 | [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_non_empty(v0) =
% 48.76/7.78 | v1 & with_non_empty_elements(v3) = v4 & relation_rng(v0) = v3 &
% 48.76/7.78 | function(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 =
% 48.76/7.78 | 0)))
% 48.76/7.78 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 48.76/7.78 | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 48.76/7.78 | (relation_non_empty(v0) = v3 & with_non_empty_elements(v1) = v5 &
% 48.76/7.78 | relation(v0) = v2 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0)
% 48.76/7.78 | | ~ (v2 = 0) | v5 = 0)))
% 48.76/7.78 |
% 48.76/7.78 | ALPHA: (fc6_relat_1) implies:
% 48.76/7.78 | (21) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 48.76/7.78 | [v2: $i] : ? [v3: any] : (relation_rng(v0) = v2 & empty(v2) = v3 &
% 48.76/7.78 | empty(v0) = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 48.76/7.78 | (22) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0)
% 48.76/7.78 | | ? [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_rng(v0) = v3
% 48.76/7.78 | & relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~
% 48.76/7.78 | (v2 = 0))))
% 48.76/7.78 |
% 48.76/7.78 | ALPHA: (fc7_relat_1) implies:
% 48.76/7.78 | (23) ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 48.76/7.78 | (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0 & $i(v1)))
% 48.76/7.78 |
% 48.76/7.78 | ALPHA: (fc8_relat_1) implies:
% 48.76/7.78 | (24) ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 48.76/7.78 | (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0 & $i(v1)))
% 48.76/7.78 |
% 48.76/7.78 | ALPHA: (t2_xboole_1) implies:
% 48.76/7.78 | (25) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)
% 48.76/7.79 | | ~ $i(v0))
% 48.76/7.79 |
% 48.76/7.79 | ALPHA: (t65_relat_1) implies:
% 48.76/7.79 | (26) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 48.76/7.79 | [v2: $i] : (relation_rng(v0) = v2 & relation_dom(v0) = v1 & $i(v2) &
% 48.76/7.79 | $i(v1) & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 =
% 48.76/7.79 | empty_set) | v2 = empty_set)))
% 48.76/7.79 | (27) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 48.76/7.79 | ? [v2: any] : ? [v3: $i] : (relation_rng(v0) = v3 & relation(v0) =
% 48.76/7.79 | v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 =
% 48.76/7.79 | empty_set) & ( ~ (v1 = empty_set) | v3 = empty_set)))))
% 48.76/7.79 | (28) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 48.76/7.79 | ? [v2: any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0) =
% 48.76/7.79 | v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 =
% 48.76/7.79 | empty_set) & ( ~ (v1 = empty_set) | v3 = empty_set)))))
% 48.76/7.79 |
% 48.76/7.79 | ALPHA: (t6_boole) implies:
% 48.76/7.79 | (29) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 48.76/7.79 |
% 48.76/7.79 | ALPHA: (t45_ordinal1) implies:
% 48.76/7.79 | (30) $i(empty_set)
% 48.76/7.79 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 48.76/7.79 | transfinite_sequence_of(empty_set, v0) = v1 & $i(v0))
% 48.76/7.79 |
% 48.76/7.79 | ALPHA: (function-axioms) implies:
% 48.76/7.79 | (32) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 48.76/7.79 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 48.76/7.79 | (33) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 48.76/7.79 | : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 48.76/7.79 | (34) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 48.76/7.79 | : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 48.76/7.79 | (35) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 48.76/7.79 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 48.76/7.79 | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 48.76/7.79 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 48.76/7.79 | (37) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 48.76/7.79 | : (v1 = v0 | ~ (transfinite_sequence(v2) = v1) | ~
% 48.76/7.79 | (transfinite_sequence(v2) = v0))
% 48.76/7.79 | (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 48.76/7.79 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 48.76/7.79 | (39) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 48.76/7.79 | : ! [v3: $i] : (v1 = v0 | ~ (transfinite_sequence_of(v3, v2) = v1) |
% 48.76/7.79 | ~ (transfinite_sequence_of(v3, v2) = v0))
% 48.76/7.79 |
% 48.76/7.79 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_34_0 gives:
% 48.76/7.79 | (40) empty(all_34_0) = 0 & $i(all_34_0)
% 48.76/7.79 |
% 48.76/7.79 | ALPHA: (40) implies:
% 48.76/7.79 | (41) $i(all_34_0)
% 48.76/7.79 | (42) empty(all_34_0) = 0
% 48.76/7.79 |
% 48.76/7.79 | DELTA: instantiating (31) with fresh symbols all_42_0, all_42_1 gives:
% 48.76/7.79 | (43) ~ (all_42_0 = 0) & transfinite_sequence_of(empty_set, all_42_1) =
% 48.76/7.79 | all_42_0 & $i(all_42_1)
% 48.76/7.79 |
% 48.76/7.79 | ALPHA: (43) implies:
% 48.76/7.79 | (44) ~ (all_42_0 = 0)
% 48.76/7.79 | (45) $i(all_42_1)
% 48.76/7.79 | (46) transfinite_sequence_of(empty_set, all_42_1) = all_42_0
% 48.76/7.79 |
% 48.76/7.79 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_44_0 gives:
% 48.76/7.79 | (47) relation(all_44_0) = 0 & empty(all_44_0) = 0 & $i(all_44_0)
% 48.76/7.79 |
% 48.76/7.79 | ALPHA: (47) implies:
% 48.76/7.79 | (48) $i(all_44_0)
% 48.76/7.79 | (49) empty(all_44_0) = 0
% 48.76/7.79 | (50) relation(all_44_0) = 0
% 48.76/7.79 |
% 48.76/7.79 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_46_0, all_46_1
% 48.76/7.79 | gives:
% 48.76/7.80 | (51) ~ (all_46_0 = 0) & empty(all_46_1) = all_46_0 & $i(all_46_1)
% 48.76/7.80 |
% 48.76/7.80 | ALPHA: (51) implies:
% 48.76/7.80 | (52) ~ (all_46_0 = 0)
% 48.76/7.80 | (53) $i(all_46_1)
% 48.76/7.80 | (54) empty(all_46_1) = all_46_0
% 48.76/7.80 |
% 48.76/7.80 | DELTA: instantiating (rc2_funct_1) with fresh symbol all_48_0 gives:
% 48.76/7.80 | (55) relation(all_48_0) = 0 & function(all_48_0) = 0 & empty(all_48_0) = 0
% 48.76/7.80 | & $i(all_48_0)
% 48.76/7.80 |
% 48.76/7.80 | ALPHA: (55) implies:
% 48.76/7.80 | (56) $i(all_48_0)
% 48.76/7.80 | (57) empty(all_48_0) = 0
% 48.76/7.80 | (58) function(all_48_0) = 0
% 48.76/7.80 | (59) relation(all_48_0) = 0
% 48.76/7.80 |
% 48.76/7.80 | DELTA: instantiating (rc4_ordinal1) with fresh symbol all_56_0 gives:
% 48.76/7.80 | (60) transfinite_sequence(all_56_0) = 0 & relation(all_56_0) = 0 &
% 48.76/7.80 | function(all_56_0) = 0 & $i(all_56_0)
% 48.76/7.80 |
% 48.76/7.80 | ALPHA: (60) implies:
% 48.76/7.80 | (61) $i(all_56_0)
% 48.76/7.80 | (62) function(all_56_0) = 0
% 48.76/7.80 | (63) relation(all_56_0) = 0
% 48.76/7.80 | (64) transfinite_sequence(all_56_0) = 0
% 48.76/7.80 |
% 48.76/7.80 | DELTA: instantiating (rc2_ordinal1) with fresh symbol all_64_0 gives:
% 48.76/7.80 | (65) one_to_one(all_64_0) = 0 & relation(all_64_0) = 0 &
% 48.76/7.80 | epsilon_transitive(all_64_0) = 0 & ordinal(all_64_0) = 0 &
% 48.76/7.80 | epsilon_connected(all_64_0) = 0 & function(all_64_0) = 0 &
% 48.76/7.80 | empty(all_64_0) = 0 & $i(all_64_0)
% 48.76/7.80 |
% 48.76/7.80 | ALPHA: (65) implies:
% 48.76/7.80 | (66) $i(all_64_0)
% 48.76/7.80 | (67) empty(all_64_0) = 0
% 48.76/7.80 | (68) function(all_64_0) = 0
% 48.76/7.80 | (69) relation(all_64_0) = 0
% 48.76/7.80 |
% 48.76/7.80 | GROUND_INST: instantiating (24) with empty_set, simplifying with (15), (30)
% 48.76/7.80 | gives:
% 48.76/7.80 | (70) ? [v0: $i] : (relation_rng(empty_set) = v0 & relation(v0) = 0 &
% 48.76/7.80 | empty(v0) = 0 & $i(v0))
% 48.76/7.80 |
% 48.76/7.80 | GROUND_INST: instantiating (23) with empty_set, simplifying with (15), (30)
% 48.76/7.80 | gives:
% 48.76/7.80 | (71) ? [v0: $i] : (relation_dom(empty_set) = v0 & relation(v0) = 0 &
% 48.76/7.80 | empty(v0) = 0 & $i(v0))
% 48.76/7.80 |
% 48.76/7.80 | GROUND_INST: instantiating (2) with all_34_0, simplifying with (41), (42)
% 48.76/7.80 | gives:
% 48.76/7.80 | (72) relation(all_34_0) = 0
% 48.76/7.80 |
% 48.76/7.80 | GROUND_INST: instantiating (3) with all_34_0, simplifying with (41), (42)
% 48.76/7.80 | gives:
% 48.76/7.80 | (73) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_34_0) =
% 48.76/7.80 | v2 & relation(all_34_0) = v0 & function(all_34_0) = v1 & ( ~ (v1 =
% 48.76/7.80 | 0) | ~ (v0 = 0) | v2 = 0))
% 48.76/7.80 |
% 48.76/7.80 | GROUND_INST: instantiating (24) with all_34_0, simplifying with (41), (42)
% 48.76/7.80 | gives:
% 48.76/7.80 | (74) ? [v0: $i] : (relation_rng(all_34_0) = v0 & relation(v0) = 0 &
% 48.76/7.80 | empty(v0) = 0 & $i(v0))
% 48.76/7.80 |
% 48.76/7.80 | GROUND_INST: instantiating (23) with all_34_0, simplifying with (41), (42)
% 48.76/7.80 | gives:
% 48.76/7.80 | (75) ? [v0: $i] : (relation_dom(all_34_0) = v0 & relation(v0) = 0 &
% 48.76/7.80 | empty(v0) = 0 & $i(v0))
% 48.76/7.80 |
% 48.76/7.80 | GROUND_INST: instantiating (3) with all_44_0, simplifying with (48), (49)
% 48.76/7.80 | gives:
% 48.76/7.80 | (76) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_44_0) =
% 48.76/7.81 | v2 & relation(all_44_0) = v0 & function(all_44_0) = v1 & ( ~ (v1 =
% 48.76/7.81 | 0) | ~ (v0 = 0) | v2 = 0))
% 48.76/7.81 |
% 48.76/7.81 | GROUND_INST: instantiating (24) with all_44_0, simplifying with (48), (49)
% 48.76/7.81 | gives:
% 48.76/7.81 | (77) ? [v0: $i] : (relation_rng(all_44_0) = v0 & relation(v0) = 0 &
% 48.76/7.81 | empty(v0) = 0 & $i(v0))
% 48.76/7.81 |
% 48.76/7.81 | GROUND_INST: instantiating (23) with all_44_0, simplifying with (48), (49)
% 48.76/7.81 | gives:
% 48.76/7.81 | (78) ? [v0: $i] : (relation_dom(all_44_0) = v0 & relation(v0) = 0 &
% 48.76/7.81 | empty(v0) = 0 & $i(v0))
% 48.76/7.81 |
% 48.76/7.81 | GROUND_INST: instantiating (22) with all_46_1, all_46_0, simplifying with
% 48.76/7.81 | (53), (54) gives:
% 48.76/7.81 | (79) all_46_0 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 48.76/7.81 | (relation_rng(all_46_1) = v1 & relation(all_46_1) = v0 & empty(v1) =
% 48.76/7.81 | v2 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 48.76/7.81 |
% 48.76/7.81 | GROUND_INST: instantiating (t8_boole) with all_44_0, all_48_0, simplifying
% 48.76/7.81 | with (48), (49), (56), (57) gives:
% 48.76/7.81 | (80) all_48_0 = all_44_0
% 48.76/7.81 |
% 48.76/7.81 | GROUND_INST: instantiating (t8_boole) with all_34_0, all_48_0, simplifying
% 48.76/7.81 | with (41), (42), (56), (57) gives:
% 48.76/7.81 | (81) all_48_0 = all_34_0
% 48.76/7.81 |
% 48.76/7.81 | GROUND_INST: instantiating (3) with all_48_0, simplifying with (56), (57)
% 48.76/7.81 | gives:
% 48.76/7.81 | (82) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_48_0) =
% 48.76/7.81 | v2 & relation(all_48_0) = v0 & function(all_48_0) = v1 & ( ~ (v1 =
% 48.76/7.81 | 0) | ~ (v0 = 0) | v2 = 0))
% 48.76/7.81 |
% 48.76/7.81 | GROUND_INST: instantiating (24) with all_48_0, simplifying with (56), (57)
% 48.76/7.81 | gives:
% 48.76/7.81 | (83) ? [v0: $i] : (relation_rng(all_48_0) = v0 & relation(v0) = 0 &
% 48.76/7.81 | empty(v0) = 0 & $i(v0))
% 48.76/7.81 |
% 48.76/7.81 | GROUND_INST: instantiating (23) with all_48_0, simplifying with (56), (57)
% 48.76/7.81 | gives:
% 48.76/7.81 | (84) ? [v0: $i] : (relation_dom(all_48_0) = v0 & relation(v0) = 0 &
% 48.76/7.81 | empty(v0) = 0 & $i(v0))
% 48.76/7.81 |
% 48.76/7.81 | GROUND_INST: instantiating (t8_boole) with all_48_0, all_64_0, simplifying
% 48.76/7.81 | with (56), (57), (66), (67) gives:
% 48.76/7.81 | (85) all_64_0 = all_48_0
% 48.76/7.81 |
% 48.76/7.81 | GROUND_INST: instantiating (29) with all_64_0, simplifying with (66), (67)
% 48.76/7.81 | gives:
% 48.76/7.81 | (86) all_64_0 = empty_set
% 48.76/7.81 |
% 48.76/7.81 | GROUND_INST: instantiating (24) with all_64_0, simplifying with (66), (67)
% 48.76/7.81 | gives:
% 48.76/7.81 | (87) ? [v0: $i] : (relation_rng(all_64_0) = v0 & relation(v0) = 0 &
% 48.76/7.81 | empty(v0) = 0 & $i(v0))
% 48.76/7.81 |
% 48.76/7.81 | GROUND_INST: instantiating (23) with all_64_0, simplifying with (66), (67)
% 48.76/7.81 | gives:
% 48.76/7.81 | (88) ? [v0: $i] : (relation_dom(all_64_0) = v0 & relation(v0) = 0 &
% 48.76/7.81 | empty(v0) = 0 & $i(v0))
% 48.76/7.81 |
% 48.76/7.81 | GROUND_INST: instantiating (18) with empty_set, simplifying with (14), (30)
% 48.76/7.81 | gives:
% 48.76/7.81 | (89) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 48.76/7.81 | (relation_non_empty(empty_set) = v1 & with_non_empty_elements(v2) = v3
% 48.76/7.81 | & relation_rng(empty_set) = v2 & relation(empty_set) = v0 & $i(v2) &
% 48.76/7.81 | ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 48.76/7.81 |
% 48.76/7.81 | GROUND_INST: instantiating (8) with empty_set, simplifying with (14), (30)
% 48.76/7.81 | gives:
% 48.76/7.82 | (90) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 48.76/7.82 | (transfinite_sequence(empty_set) = v1 & relation_dom(empty_set) = v2 &
% 48.76/7.82 | relation(empty_set) = v0 & ordinal(v2) = v3 & $i(v2) & ( ~ (v0 = 0)
% 48.76/7.82 | | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))))
% 48.76/7.82 |
% 48.76/7.82 | GROUND_INST: instantiating (18) with all_48_0, simplifying with (56), (58)
% 48.76/7.82 | gives:
% 48.76/7.82 | (91) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 48.76/7.82 | (relation_non_empty(all_48_0) = v1 & with_non_empty_elements(v2) = v3
% 48.76/7.82 | & relation_rng(all_48_0) = v2 & relation(all_48_0) = v0 & $i(v2) & (
% 48.76/7.82 | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 48.76/7.82 |
% 48.76/7.82 | GROUND_INST: instantiating (8) with all_48_0, simplifying with (56), (58)
% 48.76/7.82 | gives:
% 48.76/7.82 | (92) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 48.76/7.82 | (transfinite_sequence(all_48_0) = v1 & relation_dom(all_48_0) = v2 &
% 48.76/7.82 | relation(all_48_0) = v0 & ordinal(v2) = v3 & $i(v2) & ( ~ (v0 = 0) |
% 48.76/7.82 | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))))
% 48.76/7.82 |
% 48.76/7.82 | GROUND_INST: instantiating (4) with all_48_0, simplifying with (56), (58)
% 48.76/7.82 | gives:
% 48.76/7.82 | (93) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_48_0) =
% 48.76/7.82 | v2 & relation(all_48_0) = v0 & empty(all_48_0) = v1 & ( ~ (v1 = 0) |
% 48.76/7.82 | ~ (v0 = 0) | v2 = 0))
% 48.76/7.82 |
% 48.76/7.82 | GROUND_INST: instantiating (18) with all_56_0, simplifying with (61), (62)
% 48.76/7.82 | gives:
% 48.76/7.82 | (94) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 48.76/7.82 | (relation_non_empty(all_56_0) = v1 & with_non_empty_elements(v2) = v3
% 48.76/7.82 | & relation_rng(all_56_0) = v2 & relation(all_56_0) = v0 & $i(v2) & (
% 48.76/7.82 | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 48.76/7.82 |
% 48.76/7.82 | GROUND_INST: instantiating (8) with all_56_0, simplifying with (61), (62)
% 48.76/7.82 | gives:
% 48.76/7.82 | (95) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 48.76/7.82 | (transfinite_sequence(all_56_0) = v1 & relation_dom(all_56_0) = v2 &
% 48.76/7.82 | relation(all_56_0) = v0 & ordinal(v2) = v3 & $i(v2) & ( ~ (v0 = 0) |
% 48.76/7.82 | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))))
% 48.76/7.82 |
% 48.76/7.82 | GROUND_INST: instantiating (4) with all_56_0, simplifying with (61), (62)
% 48.76/7.82 | gives:
% 48.76/7.82 | (96) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_56_0) =
% 48.76/7.82 | v2 & relation(all_56_0) = v0 & empty(all_56_0) = v1 & ( ~ (v1 = 0) |
% 48.76/7.82 | ~ (v0 = 0) | v2 = 0))
% 48.76/7.82 |
% 48.76/7.82 | GROUND_INST: instantiating (18) with all_64_0, simplifying with (66), (68)
% 48.76/7.82 | gives:
% 48.76/7.82 | (97) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 48.76/7.82 | (relation_non_empty(all_64_0) = v1 & with_non_empty_elements(v2) = v3
% 48.76/7.82 | & relation_rng(all_64_0) = v2 & relation(all_64_0) = v0 & $i(v2) & (
% 48.76/7.82 | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 48.76/7.82 |
% 48.76/7.82 | GROUND_INST: instantiating (8) with all_64_0, simplifying with (66), (68)
% 48.76/7.82 | gives:
% 48.76/7.82 | (98) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 48.76/7.82 | (transfinite_sequence(all_64_0) = v1 & relation_dom(all_64_0) = v2 &
% 48.76/7.82 | relation(all_64_0) = v0 & ordinal(v2) = v3 & $i(v2) & ( ~ (v0 = 0) |
% 48.76/7.82 | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))))
% 48.76/7.82 |
% 48.76/7.82 | GROUND_INST: instantiating (19) with empty_set, simplifying with (16), (30)
% 48.76/7.82 | gives:
% 48.76/7.82 | (99) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 48.76/7.82 | (relation_non_empty(empty_set) = v0 & with_non_empty_elements(v2) = v3
% 48.76/7.82 | & relation_rng(empty_set) = v2 & function(empty_set) = v1 & $i(v2) &
% 48.76/7.82 | ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 48.76/7.82 |
% 48.76/7.82 | GROUND_INST: instantiating (9) with empty_set, simplifying with (16), (30)
% 48.76/7.82 | gives:
% 48.76/7.82 | (100) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 48.76/7.82 | (transfinite_sequence(empty_set) = v1 & relation_dom(empty_set) = v2
% 48.76/7.82 | & ordinal(v2) = v3 & function(empty_set) = v0 & $i(v2) & ( ~ (v0 =
% 48.76/7.82 | 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))))
% 48.76/7.82 |
% 48.76/7.82 | GROUND_INST: instantiating (21) with empty_set, simplifying with (16), (30)
% 48.76/7.82 | gives:
% 48.76/7.82 | (101) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_rng(empty_set)
% 48.76/7.82 | = v1 & empty(v1) = v2 & empty(empty_set) = v0 & $i(v1) & ( ~ (v2 =
% 48.76/7.82 | 0) | v0 = 0))
% 48.76/7.82 |
% 48.76/7.82 | GROUND_INST: instantiating (17) with empty_set, simplifying with (16), (30)
% 48.76/7.82 | gives:
% 48.76/7.82 | (102) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(empty_set)
% 48.76/7.82 | = v1 & empty(v1) = v2 & empty(empty_set) = v0 & $i(v1) & ( ~ (v2 =
% 48.76/7.82 | 0) | v0 = 0))
% 48.76/7.82 |
% 48.76/7.83 | GROUND_INST: instantiating (26) with empty_set, simplifying with (16), (30)
% 48.76/7.83 | gives:
% 48.76/7.83 | (103) ? [v0: $i] : ? [v1: $i] : (relation_rng(empty_set) = v1 &
% 48.76/7.83 | relation_dom(empty_set) = v0 & $i(v1) & $i(v0) & ( ~ (v1 =
% 48.76/7.83 | empty_set) | v0 = empty_set) & ( ~ (v0 = empty_set) | v1 =
% 48.76/7.83 | empty_set))
% 48.76/7.83 |
% 48.76/7.83 | GROUND_INST: instantiating (7) with empty_set, simplifying with (16), (30)
% 48.76/7.83 | gives:
% 48.76/7.83 | (104) ? [v0: $i] : (relation_dom(empty_set) = v0 & $i(v0) & ! [v1: $i] :
% 48.76/7.83 | ! [v2: int] : ! [v3: $i] : ! [v4: $i] : (v2 = 0 | ~
% 48.76/7.83 | (ordered_pair(v1, v3) = v4) | ~ (in(v1, v0) = v2) | ~ $i(v3) |
% 48.76/7.83 | ~ $i(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v4, empty_set) = v5))
% 48.76/7.83 | & ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ? [v2: $i] : ?
% 48.76/7.83 | [v3: $i] : (ordered_pair(v1, v2) = v3 & in(v3, empty_set) = 0 &
% 48.76/7.83 | $i(v3) & $i(v2))) & ? [v1: $i] : (v1 = v0 | ~ $i(v1) | ?
% 48.76/7.83 | [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6:
% 48.76/7.83 | int] : (in(v2, v1) = v3 & $i(v4) & $i(v2) & ( ~ (v3 = 0) | !
% 48.76/7.83 | [v7: $i] : ! [v8: $i] : ( ~ (ordered_pair(v2, v7) = v8) | ~
% 48.76/7.83 | $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & in(v8, empty_set) =
% 48.76/7.83 | v9))) & (v3 = 0 | (v6 = 0 & ordered_pair(v2, v4) = v5 &
% 48.76/7.83 | in(v5, empty_set) = 0 & $i(v5))))))
% 48.76/7.83 |
% 48.76/7.83 | GROUND_INST: instantiating (19) with all_44_0, simplifying with (48), (50)
% 48.76/7.83 | gives:
% 48.76/7.83 | (105) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 48.76/7.83 | (relation_non_empty(all_44_0) = v0 & with_non_empty_elements(v2) = v3
% 48.76/7.83 | & relation_rng(all_44_0) = v2 & function(all_44_0) = v1 & $i(v2) &
% 48.76/7.83 | ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 48.76/7.83 |
% 48.76/7.83 | GROUND_INST: instantiating (9) with all_44_0, simplifying with (48), (50)
% 48.76/7.83 | gives:
% 48.76/7.83 | (106) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 48.76/7.83 | (transfinite_sequence(all_44_0) = v1 & relation_dom(all_44_0) = v2 &
% 48.76/7.83 | ordinal(v2) = v3 & function(all_44_0) = v0 & $i(v2) & ( ~ (v0 = 0)
% 48.76/7.83 | | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))))
% 48.76/7.83 |
% 48.76/7.83 | GROUND_INST: instantiating (21) with all_44_0, simplifying with (48), (50)
% 48.76/7.83 | gives:
% 48.76/7.83 | (107) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_rng(all_44_0) =
% 48.76/7.83 | v1 & empty(v1) = v2 & empty(all_44_0) = v0 & $i(v1) & ( ~ (v2 = 0)
% 48.76/7.83 | | v0 = 0))
% 48.76/7.83 |
% 48.76/7.83 | GROUND_INST: instantiating (17) with all_44_0, simplifying with (48), (50)
% 48.76/7.83 | gives:
% 48.76/7.83 | (108) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(all_44_0) =
% 48.76/7.83 | v1 & empty(v1) = v2 & empty(all_44_0) = v0 & $i(v1) & ( ~ (v2 = 0)
% 48.76/7.83 | | v0 = 0))
% 48.76/7.83 |
% 48.76/7.83 | GROUND_INST: instantiating (26) with all_44_0, simplifying with (48), (50)
% 48.76/7.83 | gives:
% 48.76/7.83 | (109) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_44_0) = v1 &
% 48.76/7.83 | relation_dom(all_44_0) = v0 & $i(v1) & $i(v0) & ( ~ (v1 =
% 48.76/7.83 | empty_set) | v0 = empty_set) & ( ~ (v0 = empty_set) | v1 =
% 48.76/7.83 | empty_set))
% 48.76/7.83 |
% 48.76/7.83 | GROUND_INST: instantiating (7) with all_44_0, simplifying with (48), (50)
% 48.76/7.83 | gives:
% 49.39/7.83 | (110) ? [v0: $i] : (relation_dom(all_44_0) = v0 & $i(v0) & ! [v1: $i] :
% 49.39/7.83 | ! [v2: int] : ! [v3: $i] : ! [v4: $i] : (v2 = 0 | ~
% 49.39/7.83 | (ordered_pair(v1, v3) = v4) | ~ (in(v1, v0) = v2) | ~ $i(v3) |
% 49.39/7.83 | ~ $i(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v4, all_44_0) = v5))
% 49.39/7.83 | & ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ? [v2: $i] : ?
% 49.39/7.83 | [v3: $i] : (ordered_pair(v1, v2) = v3 & in(v3, all_44_0) = 0 &
% 49.39/7.83 | $i(v3) & $i(v2))) & ? [v1: $i] : (v1 = v0 | ~ $i(v1) | ?
% 49.39/7.83 | [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6:
% 49.39/7.83 | int] : (in(v2, v1) = v3 & $i(v4) & $i(v2) & ( ~ (v3 = 0) | !
% 49.39/7.83 | [v7: $i] : ! [v8: $i] : ( ~ (ordered_pair(v2, v7) = v8) | ~
% 49.39/7.83 | $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & in(v8, all_44_0) =
% 49.39/7.83 | v9))) & (v3 = 0 | (v6 = 0 & ordered_pair(v2, v4) = v5 &
% 49.39/7.83 | in(v5, all_44_0) = 0 & $i(v5))))))
% 49.39/7.83 |
% 49.39/7.83 | GROUND_INST: instantiating (19) with all_48_0, simplifying with (56), (59)
% 49.39/7.83 | gives:
% 49.39/7.83 | (111) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 49.39/7.83 | (relation_non_empty(all_48_0) = v0 & with_non_empty_elements(v2) = v3
% 49.39/7.83 | & relation_rng(all_48_0) = v2 & function(all_48_0) = v1 & $i(v2) &
% 49.39/7.83 | ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 49.39/7.83 |
% 49.39/7.83 | GROUND_INST: instantiating (9) with all_48_0, simplifying with (56), (59)
% 49.39/7.83 | gives:
% 49.39/7.83 | (112) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 49.39/7.83 | (transfinite_sequence(all_48_0) = v1 & relation_dom(all_48_0) = v2 &
% 49.39/7.83 | ordinal(v2) = v3 & function(all_48_0) = v0 & $i(v2) & ( ~ (v0 = 0)
% 49.39/7.83 | | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))))
% 49.39/7.83 |
% 49.39/7.83 | GROUND_INST: instantiating (21) with all_48_0, simplifying with (56), (59)
% 49.39/7.83 | gives:
% 49.39/7.83 | (113) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_rng(all_48_0) =
% 49.39/7.83 | v1 & empty(v1) = v2 & empty(all_48_0) = v0 & $i(v1) & ( ~ (v2 = 0)
% 49.39/7.83 | | v0 = 0))
% 49.39/7.83 |
% 49.39/7.83 | GROUND_INST: instantiating (17) with all_48_0, simplifying with (56), (59)
% 49.39/7.83 | gives:
% 49.39/7.83 | (114) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(all_48_0) =
% 49.39/7.84 | v1 & empty(v1) = v2 & empty(all_48_0) = v0 & $i(v1) & ( ~ (v2 = 0)
% 49.39/7.84 | | v0 = 0))
% 49.39/7.84 |
% 49.39/7.84 | GROUND_INST: instantiating (26) with all_48_0, simplifying with (56), (59)
% 49.39/7.84 | gives:
% 49.39/7.84 | (115) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_48_0) = v1 &
% 49.39/7.84 | relation_dom(all_48_0) = v0 & $i(v1) & $i(v0) & ( ~ (v1 =
% 49.39/7.84 | empty_set) | v0 = empty_set) & ( ~ (v0 = empty_set) | v1 =
% 49.39/7.84 | empty_set))
% 49.39/7.84 |
% 49.39/7.84 | GROUND_INST: instantiating (7) with all_48_0, simplifying with (56), (59)
% 49.39/7.84 | gives:
% 49.39/7.84 | (116) ? [v0: $i] : (relation_dom(all_48_0) = v0 & $i(v0) & ! [v1: $i] :
% 49.39/7.84 | ! [v2: int] : ! [v3: $i] : ! [v4: $i] : (v2 = 0 | ~
% 49.39/7.84 | (ordered_pair(v1, v3) = v4) | ~ (in(v1, v0) = v2) | ~ $i(v3) |
% 49.39/7.84 | ~ $i(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v4, all_48_0) = v5))
% 49.39/7.84 | & ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ? [v2: $i] : ?
% 49.39/7.84 | [v3: $i] : (ordered_pair(v1, v2) = v3 & in(v3, all_48_0) = 0 &
% 49.39/7.84 | $i(v3) & $i(v2))) & ? [v1: $i] : (v1 = v0 | ~ $i(v1) | ?
% 49.39/7.84 | [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6:
% 49.39/7.84 | int] : (in(v2, v1) = v3 & $i(v4) & $i(v2) & ( ~ (v3 = 0) | !
% 49.39/7.84 | [v7: $i] : ! [v8: $i] : ( ~ (ordered_pair(v2, v7) = v8) | ~
% 49.39/7.84 | $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & in(v8, all_48_0) =
% 49.39/7.84 | v9))) & (v3 = 0 | (v6 = 0 & ordered_pair(v2, v4) = v5 &
% 49.39/7.84 | in(v5, all_48_0) = 0 & $i(v5))))))
% 49.39/7.84 |
% 49.39/7.84 | GROUND_INST: instantiating (19) with all_64_0, simplifying with (66), (69)
% 49.39/7.84 | gives:
% 49.39/7.84 | (117) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 49.39/7.84 | (relation_non_empty(all_64_0) = v0 & with_non_empty_elements(v2) = v3
% 49.39/7.84 | & relation_rng(all_64_0) = v2 & function(all_64_0) = v1 & $i(v2) &
% 49.39/7.84 | ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 49.39/7.84 |
% 49.39/7.84 | GROUND_INST: instantiating (9) with all_64_0, simplifying with (66), (69)
% 49.39/7.84 | gives:
% 49.39/7.84 | (118) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 49.39/7.84 | (transfinite_sequence(all_64_0) = v1 & relation_dom(all_64_0) = v2 &
% 49.39/7.84 | ordinal(v2) = v3 & function(all_64_0) = v0 & $i(v2) & ( ~ (v0 = 0)
% 49.39/7.84 | | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))))
% 49.39/7.84 |
% 49.39/7.84 | GROUND_INST: instantiating (21) with all_64_0, simplifying with (66), (69)
% 49.39/7.84 | gives:
% 49.39/7.84 | (119) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_rng(all_64_0) =
% 49.39/7.84 | v1 & empty(v1) = v2 & empty(all_64_0) = v0 & $i(v1) & ( ~ (v2 = 0)
% 49.39/7.84 | | v0 = 0))
% 49.39/7.84 |
% 49.39/7.84 | GROUND_INST: instantiating (17) with all_64_0, simplifying with (66), (69)
% 49.39/7.84 | gives:
% 49.39/7.84 | (120) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(all_64_0) =
% 49.39/7.84 | v1 & empty(v1) = v2 & empty(all_64_0) = v0 & $i(v1) & ( ~ (v2 = 0)
% 49.39/7.84 | | v0 = 0))
% 49.39/7.84 |
% 49.39/7.84 | GROUND_INST: instantiating (26) with all_64_0, simplifying with (66), (69)
% 49.39/7.84 | gives:
% 49.39/7.84 | (121) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_64_0) = v1 &
% 49.39/7.84 | relation_dom(all_64_0) = v0 & $i(v1) & $i(v0) & ( ~ (v1 =
% 49.39/7.84 | empty_set) | v0 = empty_set) & ( ~ (v0 = empty_set) | v1 =
% 49.39/7.84 | empty_set))
% 49.39/7.84 |
% 49.39/7.84 | GROUND_INST: instantiating (7) with all_64_0, simplifying with (66), (69)
% 49.39/7.84 | gives:
% 49.39/7.84 | (122) ? [v0: $i] : (relation_dom(all_64_0) = v0 & $i(v0) & ! [v1: $i] :
% 49.39/7.84 | ! [v2: int] : ! [v3: $i] : ! [v4: $i] : (v2 = 0 | ~
% 49.39/7.84 | (ordered_pair(v1, v3) = v4) | ~ (in(v1, v0) = v2) | ~ $i(v3) |
% 49.39/7.84 | ~ $i(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v4, all_64_0) = v5))
% 49.39/7.84 | & ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ? [v2: $i] : ?
% 49.39/7.84 | [v3: $i] : (ordered_pair(v1, v2) = v3 & in(v3, all_64_0) = 0 &
% 49.39/7.84 | $i(v3) & $i(v2))) & ? [v1: $i] : (v1 = v0 | ~ $i(v1) | ?
% 49.39/7.84 | [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6:
% 49.39/7.84 | int] : (in(v2, v1) = v3 & $i(v4) & $i(v2) & ( ~ (v3 = 0) | !
% 49.39/7.84 | [v7: $i] : ! [v8: $i] : ( ~ (ordered_pair(v2, v7) = v8) | ~
% 49.39/7.84 | $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & in(v8, all_64_0) =
% 49.39/7.84 | v9))) & (v3 = 0 | (v6 = 0 & ordered_pair(v2, v4) = v5 &
% 49.39/7.84 | in(v5, all_64_0) = 0 & $i(v5))))))
% 49.39/7.84 |
% 49.39/7.84 | GROUND_INST: instantiating (11) with all_56_0, 0, simplifying with (61), (64)
% 49.39/7.84 | gives:
% 49.39/7.84 | (123) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 49.39/7.84 | (relation_dom(all_56_0) = v2 & relation(all_56_0) = v0 & ordinal(v2)
% 49.39/7.84 | = v3 & function(all_56_0) = v1 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 =
% 49.39/7.84 | 0) | v3 = 0))
% 49.39/7.84 |
% 49.39/7.84 | GROUND_INST: instantiating (12) with all_42_1, empty_set, all_42_0,
% 49.39/7.84 | simplifying with (30), (45), (46) gives:
% 49.39/7.84 | (124) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 49.39/7.84 | any] : (relation_rng(empty_set) = v3 & subset(v3, all_42_1) = v4 &
% 49.39/7.84 | transfinite_sequence(empty_set) = v2 & relation(empty_set) = v0 &
% 49.39/7.84 | function(empty_set) = v1 & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 49.39/7.84 | (v0 = 0) | (( ~ (v4 = 0) | all_42_0 = 0) & ( ~ (all_42_0 = 0) |
% 49.39/7.84 | v4 = 0))))
% 49.39/7.84 |
% 49.39/7.84 | COMBINE_EQS: (85), (86) imply:
% 49.39/7.84 | (125) all_48_0 = empty_set
% 49.39/7.84 |
% 49.39/7.84 | SIMP: (125) implies:
% 49.39/7.84 | (126) all_48_0 = empty_set
% 49.39/7.84 |
% 49.39/7.84 | COMBINE_EQS: (80), (81) imply:
% 49.39/7.84 | (127) all_44_0 = all_34_0
% 49.39/7.84 |
% 49.39/7.84 | COMBINE_EQS: (80), (126) imply:
% 49.39/7.84 | (128) all_44_0 = empty_set
% 49.39/7.84 |
% 49.39/7.84 | COMBINE_EQS: (127), (128) imply:
% 49.39/7.84 | (129) all_34_0 = empty_set
% 49.39/7.84 |
% 49.39/7.84 | SIMP: (129) implies:
% 49.39/7.84 | (130) all_34_0 = empty_set
% 49.39/7.84 |
% 49.39/7.84 | DELTA: instantiating (88) with fresh symbol all_76_0 gives:
% 49.39/7.84 | (131) relation_dom(all_64_0) = all_76_0 & relation(all_76_0) = 0 &
% 49.39/7.84 | empty(all_76_0) = 0 & $i(all_76_0)
% 49.39/7.84 |
% 49.39/7.84 | ALPHA: (131) implies:
% 49.39/7.84 | (132) relation_dom(all_64_0) = all_76_0
% 49.39/7.84 |
% 49.39/7.84 | DELTA: instantiating (87) with fresh symbol all_78_0 gives:
% 49.39/7.84 | (133) relation_rng(all_64_0) = all_78_0 & relation(all_78_0) = 0 &
% 49.39/7.84 | empty(all_78_0) = 0 & $i(all_78_0)
% 49.39/7.84 |
% 49.39/7.84 | ALPHA: (133) implies:
% 49.39/7.84 | (134) relation_rng(all_64_0) = all_78_0
% 49.39/7.84 |
% 49.39/7.84 | DELTA: instantiating (71) with fresh symbol all_80_0 gives:
% 49.39/7.84 | (135) relation_dom(empty_set) = all_80_0 & relation(all_80_0) = 0 &
% 49.39/7.84 | empty(all_80_0) = 0 & $i(all_80_0)
% 49.39/7.84 |
% 49.39/7.84 | ALPHA: (135) implies:
% 49.39/7.85 | (136) $i(all_80_0)
% 49.39/7.85 | (137) empty(all_80_0) = 0
% 49.39/7.85 | (138) relation(all_80_0) = 0
% 49.39/7.85 | (139) relation_dom(empty_set) = all_80_0
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (70) with fresh symbol all_82_0 gives:
% 49.39/7.85 | (140) relation_rng(empty_set) = all_82_0 & relation(all_82_0) = 0 &
% 49.39/7.85 | empty(all_82_0) = 0 & $i(all_82_0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (140) implies:
% 49.39/7.85 | (141) $i(all_82_0)
% 49.39/7.85 | (142) empty(all_82_0) = 0
% 49.39/7.85 | (143) relation(all_82_0) = 0
% 49.39/7.85 | (144) relation_rng(empty_set) = all_82_0
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (77) with fresh symbol all_84_0 gives:
% 49.39/7.85 | (145) relation_rng(all_44_0) = all_84_0 & relation(all_84_0) = 0 &
% 49.39/7.85 | empty(all_84_0) = 0 & $i(all_84_0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (145) implies:
% 49.39/7.85 | (146) relation_rng(all_44_0) = all_84_0
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (84) with fresh symbol all_86_0 gives:
% 49.39/7.85 | (147) relation_dom(all_48_0) = all_86_0 & relation(all_86_0) = 0 &
% 49.39/7.85 | empty(all_86_0) = 0 & $i(all_86_0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (147) implies:
% 49.39/7.85 | (148) relation_dom(all_48_0) = all_86_0
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (83) with fresh symbol all_88_0 gives:
% 49.39/7.85 | (149) relation_rng(all_48_0) = all_88_0 & relation(all_88_0) = 0 &
% 49.39/7.85 | empty(all_88_0) = 0 & $i(all_88_0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (149) implies:
% 49.39/7.85 | (150) relation_rng(all_48_0) = all_88_0
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (75) with fresh symbol all_90_0 gives:
% 49.39/7.85 | (151) relation_dom(all_34_0) = all_90_0 & relation(all_90_0) = 0 &
% 49.39/7.85 | empty(all_90_0) = 0 & $i(all_90_0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (151) implies:
% 49.39/7.85 | (152) relation_dom(all_34_0) = all_90_0
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (74) with fresh symbol all_92_0 gives:
% 49.39/7.85 | (153) relation_rng(all_34_0) = all_92_0 & relation(all_92_0) = 0 &
% 49.39/7.85 | empty(all_92_0) = 0 & $i(all_92_0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (153) implies:
% 49.39/7.85 | (154) relation_rng(all_34_0) = all_92_0
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (78) with fresh symbol all_94_0 gives:
% 49.39/7.85 | (155) relation_dom(all_44_0) = all_94_0 & relation(all_94_0) = 0 &
% 49.39/7.85 | empty(all_94_0) = 0 & $i(all_94_0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (155) implies:
% 49.39/7.85 | (156) relation_dom(all_44_0) = all_94_0
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (96) with fresh symbols all_108_0, all_108_1, all_108_2
% 49.39/7.85 | gives:
% 49.39/7.85 | (157) one_to_one(all_56_0) = all_108_0 & relation(all_56_0) = all_108_2 &
% 49.39/7.85 | empty(all_56_0) = all_108_1 & ( ~ (all_108_1 = 0) | ~ (all_108_2 =
% 49.39/7.85 | 0) | all_108_0 = 0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (157) implies:
% 49.39/7.85 | (158) relation(all_56_0) = all_108_2
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (73) with fresh symbols all_132_0, all_132_1, all_132_2
% 49.39/7.85 | gives:
% 49.39/7.85 | (159) one_to_one(all_34_0) = all_132_0 & relation(all_34_0) = all_132_2 &
% 49.39/7.85 | function(all_34_0) = all_132_1 & ( ~ (all_132_1 = 0) | ~ (all_132_2
% 49.39/7.85 | = 0) | all_132_0 = 0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (159) implies:
% 49.39/7.85 | (160) relation(all_34_0) = all_132_2
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (82) with fresh symbols all_134_0, all_134_1, all_134_2
% 49.39/7.85 | gives:
% 49.39/7.85 | (161) one_to_one(all_48_0) = all_134_0 & relation(all_48_0) = all_134_2 &
% 49.39/7.85 | function(all_48_0) = all_134_1 & ( ~ (all_134_1 = 0) | ~ (all_134_2
% 49.39/7.85 | = 0) | all_134_0 = 0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (161) implies:
% 49.39/7.85 | (162) relation(all_48_0) = all_134_2
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (114) with fresh symbols all_140_0, all_140_1, all_140_2
% 49.39/7.85 | gives:
% 49.39/7.85 | (163) relation_dom(all_48_0) = all_140_1 & empty(all_140_1) = all_140_0 &
% 49.39/7.85 | empty(all_48_0) = all_140_2 & $i(all_140_1) & ( ~ (all_140_0 = 0) |
% 49.39/7.85 | all_140_2 = 0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (163) implies:
% 49.39/7.85 | (164) empty(all_140_1) = all_140_0
% 49.39/7.85 | (165) relation_dom(all_48_0) = all_140_1
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (113) with fresh symbols all_142_0, all_142_1, all_142_2
% 49.39/7.85 | gives:
% 49.39/7.85 | (166) relation_rng(all_48_0) = all_142_1 & empty(all_142_1) = all_142_0 &
% 49.39/7.85 | empty(all_48_0) = all_142_2 & $i(all_142_1) & ( ~ (all_142_0 = 0) |
% 49.39/7.85 | all_142_2 = 0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (166) implies:
% 49.39/7.85 | (167) empty(all_142_1) = all_142_0
% 49.39/7.85 | (168) relation_rng(all_48_0) = all_142_1
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (108) with fresh symbols all_158_0, all_158_1, all_158_2
% 49.39/7.85 | gives:
% 49.39/7.85 | (169) relation_dom(all_44_0) = all_158_1 & empty(all_158_1) = all_158_0 &
% 49.39/7.85 | empty(all_44_0) = all_158_2 & $i(all_158_1) & ( ~ (all_158_0 = 0) |
% 49.39/7.85 | all_158_2 = 0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (169) implies:
% 49.39/7.85 | (170) empty(all_158_1) = all_158_0
% 49.39/7.85 | (171) relation_dom(all_44_0) = all_158_1
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (107) with fresh symbols all_160_0, all_160_1, all_160_2
% 49.39/7.85 | gives:
% 49.39/7.85 | (172) relation_rng(all_44_0) = all_160_1 & empty(all_160_1) = all_160_0 &
% 49.39/7.85 | empty(all_44_0) = all_160_2 & $i(all_160_1) & ( ~ (all_160_0 = 0) |
% 49.39/7.85 | all_160_2 = 0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (172) implies:
% 49.39/7.85 | (173) empty(all_160_1) = all_160_0
% 49.39/7.85 | (174) relation_rng(all_44_0) = all_160_1
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (76) with fresh symbols all_164_0, all_164_1, all_164_2
% 49.39/7.85 | gives:
% 49.39/7.85 | (175) one_to_one(all_44_0) = all_164_0 & relation(all_44_0) = all_164_2 &
% 49.39/7.85 | function(all_44_0) = all_164_1 & ( ~ (all_164_1 = 0) | ~ (all_164_2
% 49.39/7.85 | = 0) | all_164_0 = 0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (175) implies:
% 49.39/7.85 | (176) relation(all_44_0) = all_164_2
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (93) with fresh symbols all_168_0, all_168_1, all_168_2
% 49.39/7.85 | gives:
% 49.39/7.85 | (177) one_to_one(all_48_0) = all_168_0 & relation(all_48_0) = all_168_2 &
% 49.39/7.85 | empty(all_48_0) = all_168_1 & ( ~ (all_168_1 = 0) | ~ (all_168_2 =
% 49.39/7.85 | 0) | all_168_0 = 0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (177) implies:
% 49.39/7.85 | (178) relation(all_48_0) = all_168_2
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (102) with fresh symbols all_170_0, all_170_1, all_170_2
% 49.39/7.85 | gives:
% 49.39/7.85 | (179) relation_dom(empty_set) = all_170_1 & empty(all_170_1) = all_170_0 &
% 49.39/7.85 | empty(empty_set) = all_170_2 & $i(all_170_1) & ( ~ (all_170_0 = 0) |
% 49.39/7.85 | all_170_2 = 0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (179) implies:
% 49.39/7.85 | (180) empty(all_170_1) = all_170_0
% 49.39/7.85 | (181) relation_dom(empty_set) = all_170_1
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (101) with fresh symbols all_172_0, all_172_1, all_172_2
% 49.39/7.85 | gives:
% 49.39/7.85 | (182) relation_rng(empty_set) = all_172_1 & empty(all_172_1) = all_172_0 &
% 49.39/7.85 | empty(empty_set) = all_172_2 & $i(all_172_1) & ( ~ (all_172_0 = 0) |
% 49.39/7.85 | all_172_2 = 0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (182) implies:
% 49.39/7.85 | (183) empty(all_172_1) = all_172_0
% 49.39/7.85 | (184) relation_rng(empty_set) = all_172_1
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (120) with fresh symbols all_176_0, all_176_1, all_176_2
% 49.39/7.85 | gives:
% 49.39/7.85 | (185) relation_dom(all_64_0) = all_176_1 & empty(all_176_1) = all_176_0 &
% 49.39/7.85 | empty(all_64_0) = all_176_2 & $i(all_176_1) & ( ~ (all_176_0 = 0) |
% 49.39/7.85 | all_176_2 = 0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (185) implies:
% 49.39/7.85 | (186) empty(all_176_1) = all_176_0
% 49.39/7.85 | (187) relation_dom(all_64_0) = all_176_1
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (119) with fresh symbols all_180_0, all_180_1, all_180_2
% 49.39/7.85 | gives:
% 49.39/7.85 | (188) relation_rng(all_64_0) = all_180_1 & empty(all_180_1) = all_180_0 &
% 49.39/7.85 | empty(all_64_0) = all_180_2 & $i(all_180_1) & ( ~ (all_180_0 = 0) |
% 49.39/7.85 | all_180_2 = 0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (188) implies:
% 49.39/7.85 | (189) empty(all_180_1) = all_180_0
% 49.39/7.85 | (190) relation_rng(all_64_0) = all_180_1
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (89) with fresh symbols all_182_0, all_182_1, all_182_2,
% 49.39/7.85 | all_182_3 gives:
% 49.39/7.85 | (191) relation_non_empty(empty_set) = all_182_2 &
% 49.39/7.85 | with_non_empty_elements(all_182_1) = all_182_0 &
% 49.39/7.85 | relation_rng(empty_set) = all_182_1 & relation(empty_set) = all_182_3
% 49.39/7.85 | & $i(all_182_1) & ( ~ (all_182_2 = 0) | ~ (all_182_3 = 0) |
% 49.39/7.85 | all_182_0 = 0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (191) implies:
% 49.39/7.85 | (192) relation(empty_set) = all_182_3
% 49.39/7.85 | (193) relation_rng(empty_set) = all_182_1
% 49.39/7.85 |
% 49.39/7.85 | DELTA: instantiating (123) with fresh symbols all_184_0, all_184_1, all_184_2,
% 49.39/7.85 | all_184_3 gives:
% 49.39/7.85 | (194) relation_dom(all_56_0) = all_184_1 & relation(all_56_0) = all_184_3 &
% 49.39/7.85 | ordinal(all_184_1) = all_184_0 & function(all_56_0) = all_184_2 &
% 49.39/7.85 | $i(all_184_1) & ( ~ (all_184_2 = 0) | ~ (all_184_3 = 0) | all_184_0
% 49.39/7.85 | = 0)
% 49.39/7.85 |
% 49.39/7.85 | ALPHA: (194) implies:
% 49.39/7.85 | (195) relation(all_56_0) = all_184_3
% 49.39/7.85 |
% 49.39/7.86 | DELTA: instantiating (117) with fresh symbols all_186_0, all_186_1, all_186_2,
% 49.39/7.86 | all_186_3 gives:
% 49.39/7.86 | (196) relation_non_empty(all_64_0) = all_186_3 &
% 49.39/7.86 | with_non_empty_elements(all_186_1) = all_186_0 &
% 49.39/7.86 | relation_rng(all_64_0) = all_186_1 & function(all_64_0) = all_186_2 &
% 49.39/7.86 | $i(all_186_1) & ( ~ (all_186_2 = 0) | ~ (all_186_3 = 0) | all_186_0
% 49.39/7.86 | = 0)
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (196) implies:
% 49.39/7.86 | (197) relation_rng(all_64_0) = all_186_1
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (91) with fresh symbols all_190_0, all_190_1, all_190_2,
% 49.39/7.86 | all_190_3 gives:
% 49.39/7.86 | (198) relation_non_empty(all_48_0) = all_190_2 &
% 49.39/7.86 | with_non_empty_elements(all_190_1) = all_190_0 &
% 49.39/7.86 | relation_rng(all_48_0) = all_190_1 & relation(all_48_0) = all_190_3 &
% 49.39/7.86 | $i(all_190_1) & ( ~ (all_190_2 = 0) | ~ (all_190_3 = 0) | all_190_0
% 49.39/7.86 | = 0)
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (198) implies:
% 49.39/7.86 | (199) relation(all_48_0) = all_190_3
% 49.39/7.86 | (200) relation_rng(all_48_0) = all_190_1
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (121) with fresh symbols all_192_0, all_192_1 gives:
% 49.39/7.86 | (201) relation_rng(all_64_0) = all_192_0 & relation_dom(all_64_0) =
% 49.39/7.86 | all_192_1 & $i(all_192_0) & $i(all_192_1) & ( ~ (all_192_0 =
% 49.39/7.86 | empty_set) | all_192_1 = empty_set) & ( ~ (all_192_1 = empty_set)
% 49.39/7.86 | | all_192_0 = empty_set)
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (201) implies:
% 49.39/7.86 | (202) relation_dom(all_64_0) = all_192_1
% 49.39/7.86 | (203) relation_rng(all_64_0) = all_192_0
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (111) with fresh symbols all_200_0, all_200_1, all_200_2,
% 49.39/7.86 | all_200_3 gives:
% 49.39/7.86 | (204) relation_non_empty(all_48_0) = all_200_3 &
% 49.39/7.86 | with_non_empty_elements(all_200_1) = all_200_0 &
% 49.39/7.86 | relation_rng(all_48_0) = all_200_1 & function(all_48_0) = all_200_2 &
% 49.39/7.86 | $i(all_200_1) & ( ~ (all_200_2 = 0) | ~ (all_200_3 = 0) | all_200_0
% 49.39/7.86 | = 0)
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (204) implies:
% 49.39/7.86 | (205) relation_rng(all_48_0) = all_200_1
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (103) with fresh symbols all_206_0, all_206_1 gives:
% 49.39/7.86 | (206) relation_rng(empty_set) = all_206_0 & relation_dom(empty_set) =
% 49.39/7.86 | all_206_1 & $i(all_206_0) & $i(all_206_1) & ( ~ (all_206_0 =
% 49.39/7.86 | empty_set) | all_206_1 = empty_set) & ( ~ (all_206_1 = empty_set)
% 49.39/7.86 | | all_206_0 = empty_set)
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (206) implies:
% 49.39/7.86 | (207) relation_dom(empty_set) = all_206_1
% 49.39/7.86 | (208) relation_rng(empty_set) = all_206_0
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (115) with fresh symbols all_210_0, all_210_1 gives:
% 49.39/7.86 | (209) relation_rng(all_48_0) = all_210_0 & relation_dom(all_48_0) =
% 49.39/7.86 | all_210_1 & $i(all_210_0) & $i(all_210_1) & ( ~ (all_210_0 =
% 49.39/7.86 | empty_set) | all_210_1 = empty_set) & ( ~ (all_210_1 = empty_set)
% 49.39/7.86 | | all_210_0 = empty_set)
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (209) implies:
% 49.39/7.86 | (210) relation_dom(all_48_0) = all_210_1
% 49.39/7.86 | (211) relation_rng(all_48_0) = all_210_0
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (97) with fresh symbols all_214_0, all_214_1, all_214_2,
% 49.39/7.86 | all_214_3 gives:
% 49.39/7.86 | (212) relation_non_empty(all_64_0) = all_214_2 &
% 49.39/7.86 | with_non_empty_elements(all_214_1) = all_214_0 &
% 49.39/7.86 | relation_rng(all_64_0) = all_214_1 & relation(all_64_0) = all_214_3 &
% 49.39/7.86 | $i(all_214_1) & ( ~ (all_214_2 = 0) | ~ (all_214_3 = 0) | all_214_0
% 49.39/7.86 | = 0)
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (212) implies:
% 49.39/7.86 | (213) relation(all_64_0) = all_214_3
% 49.39/7.86 | (214) relation_rng(all_64_0) = all_214_1
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (109) with fresh symbols all_222_0, all_222_1 gives:
% 49.39/7.86 | (215) relation_rng(all_44_0) = all_222_0 & relation_dom(all_44_0) =
% 49.39/7.86 | all_222_1 & $i(all_222_0) & $i(all_222_1) & ( ~ (all_222_0 =
% 49.39/7.86 | empty_set) | all_222_1 = empty_set) & ( ~ (all_222_1 = empty_set)
% 49.39/7.86 | | all_222_0 = empty_set)
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (215) implies:
% 49.39/7.86 | (216) relation_dom(all_44_0) = all_222_1
% 49.39/7.86 | (217) relation_rng(all_44_0) = all_222_0
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (105) with fresh symbols all_224_0, all_224_1, all_224_2,
% 49.39/7.86 | all_224_3 gives:
% 49.39/7.86 | (218) relation_non_empty(all_44_0) = all_224_3 &
% 49.39/7.86 | with_non_empty_elements(all_224_1) = all_224_0 &
% 49.39/7.86 | relation_rng(all_44_0) = all_224_1 & function(all_44_0) = all_224_2 &
% 49.39/7.86 | $i(all_224_1) & ( ~ (all_224_2 = 0) | ~ (all_224_3 = 0) | all_224_0
% 49.39/7.86 | = 0)
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (218) implies:
% 49.39/7.86 | (219) relation_rng(all_44_0) = all_224_1
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (94) with fresh symbols all_232_0, all_232_1, all_232_2,
% 49.39/7.86 | all_232_3 gives:
% 49.39/7.86 | (220) relation_non_empty(all_56_0) = all_232_2 &
% 49.39/7.86 | with_non_empty_elements(all_232_1) = all_232_0 &
% 49.39/7.86 | relation_rng(all_56_0) = all_232_1 & relation(all_56_0) = all_232_3 &
% 49.39/7.86 | $i(all_232_1) & ( ~ (all_232_2 = 0) | ~ (all_232_3 = 0) | all_232_0
% 49.39/7.86 | = 0)
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (220) implies:
% 49.39/7.86 | (221) relation(all_56_0) = all_232_3
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (99) with fresh symbols all_242_0, all_242_1, all_242_2,
% 49.39/7.86 | all_242_3 gives:
% 49.39/7.86 | (222) relation_non_empty(empty_set) = all_242_3 &
% 49.39/7.86 | with_non_empty_elements(all_242_1) = all_242_0 &
% 49.39/7.86 | relation_rng(empty_set) = all_242_1 & function(empty_set) = all_242_2
% 49.39/7.86 | & $i(all_242_1) & ( ~ (all_242_2 = 0) | ~ (all_242_3 = 0) |
% 49.39/7.86 | all_242_0 = 0)
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (222) implies:
% 49.39/7.86 | (223) relation_rng(empty_set) = all_242_1
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (112) with fresh symbols all_246_0, all_246_1, all_246_2,
% 49.39/7.86 | all_246_3 gives:
% 49.39/7.86 | (224) transfinite_sequence(all_48_0) = all_246_2 & relation_dom(all_48_0) =
% 49.39/7.86 | all_246_1 & ordinal(all_246_1) = all_246_0 & function(all_48_0) =
% 49.39/7.86 | all_246_3 & $i(all_246_1) & ( ~ (all_246_3 = 0) | (( ~ (all_246_0 =
% 49.39/7.86 | 0) | all_246_2 = 0) & ( ~ (all_246_2 = 0) | all_246_0 = 0)))
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (224) implies:
% 49.39/7.86 | (225) ordinal(all_246_1) = all_246_0
% 49.39/7.86 | (226) relation_dom(all_48_0) = all_246_1
% 49.39/7.86 | (227) transfinite_sequence(all_48_0) = all_246_2
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (98) with fresh symbols all_250_0, all_250_1, all_250_2,
% 49.39/7.86 | all_250_3 gives:
% 49.39/7.86 | (228) transfinite_sequence(all_64_0) = all_250_2 & relation_dom(all_64_0) =
% 49.39/7.86 | all_250_1 & relation(all_64_0) = all_250_3 & ordinal(all_250_1) =
% 49.39/7.86 | all_250_0 & $i(all_250_1) & ( ~ (all_250_3 = 0) | (( ~ (all_250_0 =
% 49.39/7.86 | 0) | all_250_2 = 0) & ( ~ (all_250_2 = 0) | all_250_0 = 0)))
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (228) implies:
% 49.39/7.86 | (229) ordinal(all_250_1) = all_250_0
% 49.39/7.86 | (230) relation(all_64_0) = all_250_3
% 49.39/7.86 | (231) relation_dom(all_64_0) = all_250_1
% 49.39/7.86 | (232) transfinite_sequence(all_64_0) = all_250_2
% 49.39/7.86 | (233) ~ (all_250_3 = 0) | (( ~ (all_250_0 = 0) | all_250_2 = 0) & ( ~
% 49.39/7.86 | (all_250_2 = 0) | all_250_0 = 0))
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (106) with fresh symbols all_256_0, all_256_1, all_256_2,
% 49.39/7.86 | all_256_3 gives:
% 49.39/7.86 | (234) transfinite_sequence(all_44_0) = all_256_2 & relation_dom(all_44_0) =
% 49.39/7.86 | all_256_1 & ordinal(all_256_1) = all_256_0 & function(all_44_0) =
% 49.39/7.86 | all_256_3 & $i(all_256_1) & ( ~ (all_256_3 = 0) | (( ~ (all_256_0 =
% 49.39/7.86 | 0) | all_256_2 = 0) & ( ~ (all_256_2 = 0) | all_256_0 = 0)))
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (234) implies:
% 49.39/7.86 | (235) ordinal(all_256_1) = all_256_0
% 49.39/7.86 | (236) relation_dom(all_44_0) = all_256_1
% 49.39/7.86 | (237) transfinite_sequence(all_44_0) = all_256_2
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (92) with fresh symbols all_266_0, all_266_1, all_266_2,
% 49.39/7.86 | all_266_3 gives:
% 49.39/7.86 | (238) transfinite_sequence(all_48_0) = all_266_2 & relation_dom(all_48_0) =
% 49.39/7.86 | all_266_1 & relation(all_48_0) = all_266_3 & ordinal(all_266_1) =
% 49.39/7.86 | all_266_0 & $i(all_266_1) & ( ~ (all_266_3 = 0) | (( ~ (all_266_0 =
% 49.39/7.86 | 0) | all_266_2 = 0) & ( ~ (all_266_2 = 0) | all_266_0 = 0)))
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (238) implies:
% 49.39/7.86 | (239) ordinal(all_266_1) = all_266_0
% 49.39/7.86 | (240) relation(all_48_0) = all_266_3
% 49.39/7.86 | (241) relation_dom(all_48_0) = all_266_1
% 49.39/7.86 | (242) transfinite_sequence(all_48_0) = all_266_2
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (118) with fresh symbols all_268_0, all_268_1, all_268_2,
% 49.39/7.86 | all_268_3 gives:
% 49.39/7.86 | (243) transfinite_sequence(all_64_0) = all_268_2 & relation_dom(all_64_0) =
% 49.39/7.86 | all_268_1 & ordinal(all_268_1) = all_268_0 & function(all_64_0) =
% 49.39/7.86 | all_268_3 & $i(all_268_1) & ( ~ (all_268_3 = 0) | (( ~ (all_268_0 =
% 49.39/7.86 | 0) | all_268_2 = 0) & ( ~ (all_268_2 = 0) | all_268_0 = 0)))
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (243) implies:
% 49.39/7.86 | (244) ordinal(all_268_1) = all_268_0
% 49.39/7.86 | (245) relation_dom(all_64_0) = all_268_1
% 49.39/7.86 | (246) transfinite_sequence(all_64_0) = all_268_2
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (90) with fresh symbols all_274_0, all_274_1, all_274_2,
% 49.39/7.86 | all_274_3 gives:
% 49.39/7.86 | (247) transfinite_sequence(empty_set) = all_274_2 & relation_dom(empty_set)
% 49.39/7.86 | = all_274_1 & relation(empty_set) = all_274_3 & ordinal(all_274_1) =
% 49.39/7.86 | all_274_0 & $i(all_274_1) & ( ~ (all_274_3 = 0) | (( ~ (all_274_0 =
% 49.39/7.86 | 0) | all_274_2 = 0) & ( ~ (all_274_2 = 0) | all_274_0 = 0)))
% 49.39/7.86 |
% 49.39/7.86 | ALPHA: (247) implies:
% 49.39/7.86 | (248) ordinal(all_274_1) = all_274_0
% 49.39/7.86 | (249) relation(empty_set) = all_274_3
% 49.39/7.86 | (250) relation_dom(empty_set) = all_274_1
% 49.39/7.86 | (251) transfinite_sequence(empty_set) = all_274_2
% 49.39/7.86 |
% 49.39/7.86 | DELTA: instantiating (95) with fresh symbols all_278_0, all_278_1, all_278_2,
% 49.39/7.86 | all_278_3 gives:
% 49.39/7.86 | (252) transfinite_sequence(all_56_0) = all_278_2 & relation_dom(all_56_0) =
% 49.39/7.86 | all_278_1 & relation(all_56_0) = all_278_3 & ordinal(all_278_1) =
% 49.39/7.86 | all_278_0 & $i(all_278_1) & ( ~ (all_278_3 = 0) | (( ~ (all_278_0 =
% 49.39/7.86 | 0) | all_278_2 = 0) & ( ~ (all_278_2 = 0) | all_278_0 = 0)))
% 49.39/7.86 |
% 49.39/7.87 | ALPHA: (252) implies:
% 49.39/7.87 | (253) relation(all_56_0) = all_278_3
% 49.39/7.87 | (254) transfinite_sequence(all_56_0) = all_278_2
% 49.39/7.87 | (255) ~ (all_278_3 = 0) | (( ~ (all_278_0 = 0) | all_278_2 = 0) & ( ~
% 49.39/7.87 | (all_278_2 = 0) | all_278_0 = 0))
% 49.39/7.87 |
% 49.39/7.87 | DELTA: instantiating (100) with fresh symbols all_280_0, all_280_1, all_280_2,
% 49.39/7.87 | all_280_3 gives:
% 49.39/7.87 | (256) transfinite_sequence(empty_set) = all_280_2 & relation_dom(empty_set)
% 49.39/7.87 | = all_280_1 & ordinal(all_280_1) = all_280_0 & function(empty_set) =
% 49.39/7.87 | all_280_3 & $i(all_280_1) & ( ~ (all_280_3 = 0) | (( ~ (all_280_0 =
% 49.39/7.87 | 0) | all_280_2 = 0) & ( ~ (all_280_2 = 0) | all_280_0 = 0)))
% 49.39/7.87 |
% 49.39/7.87 | ALPHA: (256) implies:
% 49.39/7.87 | (257) ordinal(all_280_1) = all_280_0
% 49.39/7.87 | (258) relation_dom(empty_set) = all_280_1
% 49.39/7.87 | (259) transfinite_sequence(empty_set) = all_280_2
% 49.39/7.87 |
% 49.39/7.87 | DELTA: instantiating (124) with fresh symbols all_284_0, all_284_1, all_284_2,
% 49.39/7.87 | all_284_3, all_284_4 gives:
% 49.39/7.87 | (260) relation_rng(empty_set) = all_284_1 & subset(all_284_1, all_42_1) =
% 49.39/7.87 | all_284_0 & transfinite_sequence(empty_set) = all_284_2 &
% 49.39/7.87 | relation(empty_set) = all_284_4 & function(empty_set) = all_284_3 &
% 49.39/7.87 | $i(all_284_1) & ( ~ (all_284_2 = 0) | ~ (all_284_3 = 0) | ~
% 49.39/7.87 | (all_284_4 = 0) | (( ~ (all_284_0 = 0) | all_42_0 = 0) & ( ~
% 49.39/7.87 | (all_42_0 = 0) | all_284_0 = 0)))
% 49.39/7.87 |
% 49.39/7.87 | ALPHA: (260) implies:
% 49.39/7.87 | (261) relation(empty_set) = all_284_4
% 49.39/7.87 | (262) transfinite_sequence(empty_set) = all_284_2
% 49.39/7.87 | (263) subset(all_284_1, all_42_1) = all_284_0
% 49.39/7.87 | (264) relation_rng(empty_set) = all_284_1
% 49.39/7.87 |
% 49.39/7.87 | DELTA: instantiating (116) with fresh symbol all_292_0 gives:
% 49.39/7.87 | (265) relation_dom(all_48_0) = all_292_0 & $i(all_292_0) & ! [v0: $i] : !
% 49.39/7.87 | [v1: int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~
% 49.39/7.87 | (ordered_pair(v0, v2) = v3) | ~ (in(v0, all_292_0) = v1) | ~
% 49.39/7.87 | $i(v2) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v3, all_48_0)
% 49.39/7.87 | = v4)) & ! [v0: $i] : ( ~ (in(v0, all_292_0) = 0) | ~ $i(v0) |
% 49.39/7.87 | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2,
% 49.39/7.87 | all_48_0) = 0 & $i(v2) & $i(v1))) & ? [v0: any] : (v0 =
% 49.39/7.87 | all_292_0 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : ? [v3: $i] :
% 49.39/7.87 | ? [v4: $i] : ? [v5: int] : (in(v1, v0) = v2 & $i(v3) & $i(v1) & (
% 49.39/7.87 | ~ (v2 = 0) | ! [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v1,
% 49.39/7.87 | v6) = v7) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) &
% 49.39/7.87 | in(v7, all_48_0) = v8))) & (v2 = 0 | (v5 = 0 &
% 49.39/7.87 | ordered_pair(v1, v3) = v4 & in(v4, all_48_0) = 0 & $i(v4)))))
% 49.39/7.87 |
% 49.39/7.87 | ALPHA: (265) implies:
% 49.39/7.87 | (266) relation_dom(all_48_0) = all_292_0
% 49.39/7.87 |
% 49.39/7.87 | DELTA: instantiating (104) with fresh symbol all_304_0 gives:
% 49.39/7.87 | (267) relation_dom(empty_set) = all_304_0 & $i(all_304_0) & ! [v0: $i] :
% 49.39/7.87 | ! [v1: int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~
% 49.39/7.87 | (ordered_pair(v0, v2) = v3) | ~ (in(v0, all_304_0) = v1) | ~
% 49.39/7.87 | $i(v2) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 49.39/7.87 | empty_set) = v4)) & ! [v0: $i] : ( ~ (in(v0, all_304_0) = 0) |
% 49.39/7.87 | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2
% 49.39/7.87 | & in(v2, empty_set) = 0 & $i(v2) & $i(v1))) & ? [v0: any] : (v0
% 49.39/7.87 | = all_304_0 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : ? [v3: $i]
% 49.39/7.87 | : ? [v4: $i] : ? [v5: int] : (in(v1, v0) = v2 & $i(v3) & $i(v1) &
% 49.39/7.87 | ( ~ (v2 = 0) | ! [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v1,
% 49.39/7.87 | v6) = v7) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) &
% 49.39/7.87 | in(v7, empty_set) = v8))) & (v2 = 0 | (v5 = 0 &
% 49.39/7.87 | ordered_pair(v1, v3) = v4 & in(v4, empty_set) = 0 &
% 49.39/7.87 | $i(v4)))))
% 49.39/7.87 |
% 49.39/7.87 | ALPHA: (267) implies:
% 49.39/7.87 | (268) relation_dom(empty_set) = all_304_0
% 49.39/7.87 |
% 49.39/7.87 | DELTA: instantiating (110) with fresh symbol all_307_0 gives:
% 49.39/7.87 | (269) relation_dom(all_44_0) = all_307_0 & $i(all_307_0) & ! [v0: $i] : !
% 49.39/7.87 | [v1: int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~
% 49.39/7.87 | (ordered_pair(v0, v2) = v3) | ~ (in(v0, all_307_0) = v1) | ~
% 49.39/7.87 | $i(v2) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v3, all_44_0)
% 49.39/7.87 | = v4)) & ! [v0: $i] : ( ~ (in(v0, all_307_0) = 0) | ~ $i(v0) |
% 49.39/7.87 | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2,
% 49.39/7.87 | all_44_0) = 0 & $i(v2) & $i(v1))) & ? [v0: any] : (v0 =
% 49.39/7.87 | all_307_0 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : ? [v3: $i] :
% 49.39/7.87 | ? [v4: $i] : ? [v5: int] : (in(v1, v0) = v2 & $i(v3) & $i(v1) & (
% 49.39/7.87 | ~ (v2 = 0) | ! [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v1,
% 49.39/7.87 | v6) = v7) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) &
% 49.39/7.87 | in(v7, all_44_0) = v8))) & (v2 = 0 | (v5 = 0 &
% 49.39/7.87 | ordered_pair(v1, v3) = v4 & in(v4, all_44_0) = 0 & $i(v4)))))
% 49.39/7.87 |
% 49.39/7.87 | ALPHA: (269) implies:
% 49.39/7.87 | (270) relation_dom(all_44_0) = all_307_0
% 49.39/7.87 |
% 49.39/7.87 | DELTA: instantiating (122) with fresh symbol all_310_0 gives:
% 49.39/7.87 | (271) relation_dom(all_64_0) = all_310_0 & $i(all_310_0) & ! [v0: $i] : !
% 49.39/7.87 | [v1: int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~
% 49.39/7.87 | (ordered_pair(v0, v2) = v3) | ~ (in(v0, all_310_0) = v1) | ~
% 49.39/7.87 | $i(v2) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v3, all_64_0)
% 49.39/7.87 | = v4)) & ! [v0: $i] : ( ~ (in(v0, all_310_0) = 0) | ~ $i(v0) |
% 49.39/7.87 | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2,
% 49.39/7.87 | all_64_0) = 0 & $i(v2) & $i(v1))) & ? [v0: any] : (v0 =
% 49.39/7.87 | all_310_0 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : ? [v3: $i] :
% 49.39/7.87 | ? [v4: $i] : ? [v5: int] : (in(v1, v0) = v2 & $i(v3) & $i(v1) & (
% 49.39/7.87 | ~ (v2 = 0) | ! [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v1,
% 49.39/7.87 | v6) = v7) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) &
% 49.39/7.87 | in(v7, all_64_0) = v8))) & (v2 = 0 | (v5 = 0 &
% 49.39/7.87 | ordered_pair(v1, v3) = v4 & in(v4, all_64_0) = 0 & $i(v4)))))
% 49.39/7.87 |
% 49.39/7.87 | ALPHA: (271) implies:
% 49.39/7.87 | (272) relation_dom(all_64_0) = all_310_0
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (86), (214) imply:
% 49.39/7.87 | (273) relation_rng(empty_set) = all_214_1
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (86), (203) imply:
% 49.39/7.87 | (274) relation_rng(empty_set) = all_192_0
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (86), (197) imply:
% 49.39/7.87 | (275) relation_rng(empty_set) = all_186_1
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (86), (190) imply:
% 49.39/7.87 | (276) relation_rng(empty_set) = all_180_1
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (86), (134) imply:
% 49.39/7.87 | (277) relation_rng(empty_set) = all_78_0
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (126), (211) imply:
% 49.39/7.87 | (278) relation_rng(empty_set) = all_210_0
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (126), (205) imply:
% 49.39/7.87 | (279) relation_rng(empty_set) = all_200_1
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (126), (200) imply:
% 49.39/7.87 | (280) relation_rng(empty_set) = all_190_1
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (126), (168) imply:
% 49.39/7.87 | (281) relation_rng(empty_set) = all_142_1
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (126), (150) imply:
% 49.39/7.87 | (282) relation_rng(empty_set) = all_88_0
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (128), (219) imply:
% 49.39/7.87 | (283) relation_rng(empty_set) = all_224_1
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (128), (217) imply:
% 49.39/7.87 | (284) relation_rng(empty_set) = all_222_0
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (128), (174) imply:
% 49.39/7.87 | (285) relation_rng(empty_set) = all_160_1
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (128), (146) imply:
% 49.39/7.87 | (286) relation_rng(empty_set) = all_84_0
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (130), (154) imply:
% 49.39/7.87 | (287) relation_rng(empty_set) = all_92_0
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (86), (246) imply:
% 49.39/7.87 | (288) transfinite_sequence(empty_set) = all_268_2
% 49.39/7.87 |
% 49.39/7.87 | REDUCE: (86), (232) imply:
% 49.39/7.88 | (289) transfinite_sequence(empty_set) = all_250_2
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (126), (242) imply:
% 49.39/7.88 | (290) transfinite_sequence(empty_set) = all_266_2
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (126), (227) imply:
% 49.39/7.88 | (291) transfinite_sequence(empty_set) = all_246_2
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (128), (237) imply:
% 49.39/7.88 | (292) transfinite_sequence(empty_set) = all_256_2
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (86), (272) imply:
% 49.39/7.88 | (293) relation_dom(empty_set) = all_310_0
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (86), (245) imply:
% 49.39/7.88 | (294) relation_dom(empty_set) = all_268_1
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (86), (231) imply:
% 49.39/7.88 | (295) relation_dom(empty_set) = all_250_1
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (86), (202) imply:
% 49.39/7.88 | (296) relation_dom(empty_set) = all_192_1
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (86), (187) imply:
% 49.39/7.88 | (297) relation_dom(empty_set) = all_176_1
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (86), (132) imply:
% 49.39/7.88 | (298) relation_dom(empty_set) = all_76_0
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (126), (266) imply:
% 49.39/7.88 | (299) relation_dom(empty_set) = all_292_0
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (126), (241) imply:
% 49.39/7.88 | (300) relation_dom(empty_set) = all_266_1
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (126), (226) imply:
% 49.39/7.88 | (301) relation_dom(empty_set) = all_246_1
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (126), (210) imply:
% 49.39/7.88 | (302) relation_dom(empty_set) = all_210_1
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (126), (165) imply:
% 49.39/7.88 | (303) relation_dom(empty_set) = all_140_1
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (126), (148) imply:
% 49.39/7.88 | (304) relation_dom(empty_set) = all_86_0
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (128), (270) imply:
% 49.39/7.88 | (305) relation_dom(empty_set) = all_307_0
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (128), (236) imply:
% 49.39/7.88 | (306) relation_dom(empty_set) = all_256_1
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (128), (216) imply:
% 49.39/7.88 | (307) relation_dom(empty_set) = all_222_1
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (128), (171) imply:
% 49.39/7.88 | (308) relation_dom(empty_set) = all_158_1
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (128), (156) imply:
% 49.39/7.88 | (309) relation_dom(empty_set) = all_94_0
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (130), (152) imply:
% 49.39/7.88 | (310) relation_dom(empty_set) = all_90_0
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (86), (230) imply:
% 49.39/7.88 | (311) relation(empty_set) = all_250_3
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (86), (213) imply:
% 49.39/7.88 | (312) relation(empty_set) = all_214_3
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (126), (240) imply:
% 49.39/7.88 | (313) relation(empty_set) = all_266_3
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (126), (199) imply:
% 49.39/7.88 | (314) relation(empty_set) = all_190_3
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (126), (178) imply:
% 49.39/7.88 | (315) relation(empty_set) = all_168_2
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (126), (162) imply:
% 49.39/7.88 | (316) relation(empty_set) = all_134_2
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (128), (176) imply:
% 49.39/7.88 | (317) relation(empty_set) = all_164_2
% 49.39/7.88 |
% 49.39/7.88 | REDUCE: (130), (160) imply:
% 49.39/7.88 | (318) relation(empty_set) = all_132_2
% 49.39/7.88 |
% 49.39/7.88 | BETA: splitting (79) gives:
% 49.39/7.88 |
% 49.39/7.88 | Case 1:
% 49.39/7.88 | |
% 49.39/7.88 | | (319) all_46_0 = 0
% 49.39/7.88 | |
% 49.39/7.88 | | REDUCE: (52), (319) imply:
% 49.39/7.88 | | (320) $false
% 49.39/7.88 | |
% 49.39/7.88 | | CLOSE: (320) is inconsistent.
% 49.39/7.88 | |
% 49.39/7.88 | Case 2:
% 49.39/7.88 | |
% 49.39/7.88 | |
% 49.39/7.88 | | GROUND_INST: instantiating (35) with 0, all_168_2, empty_set, simplifying
% 49.39/7.88 | | with (16), (315) gives:
% 49.39/7.88 | | (321) all_168_2 = 0
% 49.39/7.88 | |
% 49.39/7.88 | | GROUND_INST: instantiating (35) with all_134_2, all_168_2, empty_set,
% 49.39/7.88 | | simplifying with (315), (316) gives:
% 49.39/7.88 | | (322) all_168_2 = all_134_2
% 49.39/7.88 | |
% 49.39/7.88 | | GROUND_INST: instantiating (35) with all_132_2, all_168_2, empty_set,
% 49.39/7.88 | | simplifying with (315), (318) gives:
% 49.39/7.88 | | (323) all_168_2 = all_132_2
% 49.39/7.88 | |
% 49.39/7.88 | | GROUND_INST: instantiating (35) with all_168_2, all_190_3, empty_set,
% 49.39/7.88 | | simplifying with (314), (315) gives:
% 49.39/7.88 | | (324) all_190_3 = all_168_2
% 49.39/7.88 | |
% 49.39/7.88 | | GROUND_INST: instantiating (35) with all_164_2, all_190_3, empty_set,
% 49.39/7.88 | | simplifying with (314), (317) gives:
% 49.39/7.88 | | (325) all_190_3 = all_164_2
% 49.39/7.88 | |
% 49.39/7.88 | | GROUND_INST: instantiating (35) with all_190_3, all_214_3, empty_set,
% 49.39/7.88 | | simplifying with (312), (314) gives:
% 49.39/7.88 | | (326) all_214_3 = all_190_3
% 49.39/7.88 | |
% 49.39/7.88 | | GROUND_INST: instantiating (35) with all_214_3, all_250_3, empty_set,
% 49.39/7.88 | | simplifying with (311), (312) gives:
% 49.39/7.88 | | (327) all_250_3 = all_214_3
% 49.39/7.88 | |
% 49.39/7.88 | | GROUND_INST: instantiating (35) with all_250_3, all_266_3, empty_set,
% 49.39/7.88 | | simplifying with (311), (313) gives:
% 49.39/7.88 | | (328) all_266_3 = all_250_3
% 49.39/7.88 | |
% 49.39/7.88 | | GROUND_INST: instantiating (35) with all_266_3, all_274_3, empty_set,
% 49.39/7.88 | | simplifying with (249), (313) gives:
% 49.39/7.88 | | (329) all_274_3 = all_266_3
% 49.39/7.88 | |
% 49.39/7.88 | | GROUND_INST: instantiating (35) with all_274_3, all_284_4, empty_set,
% 49.39/7.88 | | simplifying with (249), (261) gives:
% 49.39/7.88 | | (330) all_284_4 = all_274_3
% 49.39/7.88 | |
% 49.39/7.88 | | GROUND_INST: instantiating (35) with all_182_3, all_284_4, empty_set,
% 49.39/7.88 | | simplifying with (192), (261) gives:
% 49.39/7.88 | | (331) all_284_4 = all_182_3
% 49.39/7.88 | |
% 49.39/7.88 | | GROUND_INST: instantiating (35) with 0, all_232_3, all_56_0, simplifying
% 49.39/7.88 | | with (63), (221) gives:
% 49.39/7.88 | | (332) all_232_3 = 0
% 49.39/7.88 | |
% 49.39/7.88 | | GROUND_INST: instantiating (35) with all_184_3, all_232_3, all_56_0,
% 49.39/7.88 | | simplifying with (195), (221) gives:
% 49.39/7.88 | | (333) all_232_3 = all_184_3
% 49.39/7.88 | |
% 49.39/7.89 | | GROUND_INST: instantiating (35) with all_232_3, all_278_3, all_56_0,
% 49.39/7.89 | | simplifying with (221), (253) gives:
% 49.39/7.89 | | (334) all_278_3 = all_232_3
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (35) with all_108_2, all_278_3, all_56_0,
% 49.39/7.89 | | simplifying with (158), (253) gives:
% 49.39/7.89 | | (335) all_278_3 = all_108_2
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_80_0, all_140_1, empty_set,
% 49.39/7.89 | | simplifying with (139), (303) gives:
% 49.39/7.89 | | (336) all_140_1 = all_80_0
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_158_1, all_176_1, empty_set,
% 49.39/7.89 | | simplifying with (297), (308) gives:
% 49.39/7.89 | | (337) all_176_1 = all_158_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_140_1, all_176_1, empty_set,
% 49.39/7.89 | | simplifying with (297), (303) gives:
% 49.39/7.89 | | (338) all_176_1 = all_140_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_94_0, all_176_1, empty_set,
% 49.39/7.89 | | simplifying with (297), (309) gives:
% 49.39/7.89 | | (339) all_176_1 = all_94_0
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_86_0, all_192_1, empty_set,
% 49.39/7.89 | | simplifying with (296), (304) gives:
% 49.39/7.89 | | (340) all_192_1 = all_86_0
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_222_1, all_246_1, empty_set,
% 49.39/7.89 | | simplifying with (301), (307) gives:
% 49.39/7.89 | | (341) all_246_1 = all_222_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_210_1, all_246_1, empty_set,
% 49.39/7.89 | | simplifying with (301), (302) gives:
% 49.39/7.89 | | (342) all_246_1 = all_210_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_222_1, all_256_1, empty_set,
% 49.39/7.89 | | simplifying with (306), (307) gives:
% 49.39/7.89 | | (343) all_256_1 = all_222_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_256_1, all_266_1, empty_set,
% 49.39/7.89 | | simplifying with (300), (306) gives:
% 49.39/7.89 | | (344) all_266_1 = all_256_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_266_1, all_268_1, empty_set,
% 49.39/7.89 | | simplifying with (294), (300) gives:
% 49.39/7.89 | | (345) all_268_1 = all_266_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_268_1, all_274_1, empty_set,
% 49.39/7.89 | | simplifying with (250), (294) gives:
% 49.39/7.89 | | (346) all_274_1 = all_268_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_250_1, all_280_1, empty_set,
% 49.39/7.89 | | simplifying with (258), (295) gives:
% 49.39/7.89 | | (347) all_280_1 = all_250_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_192_1, all_280_1, empty_set,
% 49.39/7.89 | | simplifying with (258), (296) gives:
% 49.39/7.89 | | (348) all_280_1 = all_192_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_158_1, all_280_1, empty_set,
% 49.39/7.89 | | simplifying with (258), (308) gives:
% 49.39/7.89 | | (349) all_280_1 = all_158_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_274_1, all_292_0, empty_set,
% 49.39/7.89 | | simplifying with (250), (299) gives:
% 49.39/7.89 | | (350) all_292_0 = all_274_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_90_0, all_292_0, empty_set,
% 49.39/7.89 | | simplifying with (299), (310) gives:
% 49.39/7.89 | | (351) all_292_0 = all_90_0
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_246_1, all_304_0, empty_set,
% 49.39/7.89 | | simplifying with (268), (301) gives:
% 49.39/7.89 | | (352) all_304_0 = all_246_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_206_1, all_304_0, empty_set,
% 49.39/7.89 | | simplifying with (207), (268) gives:
% 49.39/7.89 | | (353) all_304_0 = all_206_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_158_1, all_304_0, empty_set,
% 49.39/7.89 | | simplifying with (268), (308) gives:
% 49.39/7.89 | | (354) all_304_0 = all_158_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_250_1, all_307_0, empty_set,
% 49.39/7.89 | | simplifying with (295), (305) gives:
% 49.39/7.89 | | (355) all_307_0 = all_250_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_76_0, all_307_0, empty_set,
% 49.39/7.89 | | simplifying with (298), (305) gives:
% 49.39/7.89 | | (356) all_307_0 = all_76_0
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_280_1, all_310_0, empty_set,
% 49.39/7.89 | | simplifying with (258), (293) gives:
% 49.39/7.89 | | (357) all_310_0 = all_280_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (36) with all_170_1, all_310_0, empty_set,
% 49.39/7.89 | | simplifying with (181), (293) gives:
% 49.39/7.89 | | (358) all_310_0 = all_170_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (37) with all_250_2, all_256_2, empty_set,
% 49.39/7.89 | | simplifying with (289), (292) gives:
% 49.39/7.89 | | (359) all_256_2 = all_250_2
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (37) with all_256_2, all_266_2, empty_set,
% 49.39/7.89 | | simplifying with (290), (292) gives:
% 49.39/7.89 | | (360) all_266_2 = all_256_2
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (37) with all_266_2, all_268_2, empty_set,
% 49.39/7.89 | | simplifying with (288), (290) gives:
% 49.39/7.89 | | (361) all_268_2 = all_266_2
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (37) with all_268_2, all_280_2, empty_set,
% 49.39/7.89 | | simplifying with (259), (288) gives:
% 49.39/7.89 | | (362) all_280_2 = all_268_2
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (37) with all_246_2, all_280_2, empty_set,
% 49.39/7.89 | | simplifying with (259), (291) gives:
% 49.39/7.89 | | (363) all_280_2 = all_246_2
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (37) with all_280_2, all_284_2, empty_set,
% 49.39/7.89 | | simplifying with (259), (262) gives:
% 49.39/7.89 | | (364) all_284_2 = all_280_2
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (37) with all_274_2, all_284_2, empty_set,
% 49.39/7.89 | | simplifying with (251), (262) gives:
% 49.39/7.89 | | (365) all_284_2 = all_274_2
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (37) with 0, all_278_2, all_56_0, simplifying
% 49.39/7.89 | | with (64), (254) gives:
% 49.39/7.89 | | (366) all_278_2 = 0
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_82_0, all_84_0, empty_set,
% 49.39/7.89 | | simplifying with (144), (286) gives:
% 49.39/7.89 | | (367) all_84_0 = all_82_0
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_84_0, all_88_0, empty_set,
% 49.39/7.89 | | simplifying with (282), (286) gives:
% 49.39/7.89 | | (368) all_88_0 = all_84_0
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_182_1, all_186_1, empty_set,
% 49.39/7.89 | | simplifying with (193), (275) gives:
% 49.39/7.89 | | (369) all_186_1 = all_182_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_88_0, all_192_0, empty_set,
% 49.39/7.89 | | simplifying with (274), (282) gives:
% 49.39/7.89 | | (370) all_192_0 = all_88_0
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_192_0, all_200_1, empty_set,
% 49.39/7.89 | | simplifying with (274), (279) gives:
% 49.39/7.89 | | (371) all_200_1 = all_192_0
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_200_1, all_206_0, empty_set,
% 49.39/7.89 | | simplifying with (208), (279) gives:
% 49.39/7.89 | | (372) all_206_0 = all_200_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_92_0, all_206_0, empty_set,
% 49.39/7.89 | | simplifying with (208), (287) gives:
% 49.39/7.89 | | (373) all_206_0 = all_92_0
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_182_1, all_210_0, empty_set,
% 49.39/7.89 | | simplifying with (193), (278) gives:
% 49.39/7.89 | | (374) all_210_0 = all_182_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_180_1, all_210_0, empty_set,
% 49.39/7.89 | | simplifying with (276), (278) gives:
% 49.39/7.89 | | (375) all_210_0 = all_180_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_192_0, all_214_1, empty_set,
% 49.39/7.89 | | simplifying with (273), (274) gives:
% 49.39/7.89 | | (376) all_214_1 = all_192_0
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_182_1, all_214_1, empty_set,
% 49.39/7.89 | | simplifying with (193), (273) gives:
% 49.39/7.89 | | (377) all_214_1 = all_182_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_142_1, all_214_1, empty_set,
% 49.39/7.89 | | simplifying with (273), (281) gives:
% 49.39/7.89 | | (378) all_214_1 = all_142_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_186_1, all_222_0, empty_set,
% 49.39/7.89 | | simplifying with (275), (284) gives:
% 49.39/7.89 | | (379) all_222_0 = all_186_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_190_1, all_224_1, empty_set,
% 49.39/7.89 | | simplifying with (280), (283) gives:
% 49.39/7.89 | | (380) all_224_1 = all_190_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_182_1, all_224_1, empty_set,
% 49.39/7.89 | | simplifying with (193), (283) gives:
% 49.39/7.89 | | (381) all_224_1 = all_182_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_160_1, all_224_1, empty_set,
% 49.39/7.89 | | simplifying with (283), (285) gives:
% 49.39/7.89 | | (382) all_224_1 = all_160_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_192_0, all_242_1, empty_set,
% 49.39/7.89 | | simplifying with (223), (274) gives:
% 49.39/7.89 | | (383) all_242_1 = all_192_0
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_172_1, all_242_1, empty_set,
% 49.39/7.89 | | simplifying with (184), (223) gives:
% 49.39/7.89 | | (384) all_242_1 = all_172_1
% 49.39/7.89 | |
% 49.39/7.89 | | GROUND_INST: instantiating (38) with all_222_0, all_284_1, empty_set,
% 49.39/7.89 | | simplifying with (264), (284) gives:
% 49.39/7.89 | | (385) all_284_1 = all_222_0
% 49.39/7.89 | |
% 49.39/7.90 | | GROUND_INST: instantiating (38) with all_78_0, all_284_1, empty_set,
% 49.39/7.90 | | simplifying with (264), (277) gives:
% 49.39/7.90 | | (386) all_284_1 = all_78_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (357), (358) imply:
% 49.39/7.90 | | (387) all_280_1 = all_170_1
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (387) implies:
% 49.39/7.90 | | (388) all_280_1 = all_170_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (355), (356) imply:
% 49.39/7.90 | | (389) all_250_1 = all_76_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (389) implies:
% 49.39/7.90 | | (390) all_250_1 = all_76_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (352), (353) imply:
% 49.39/7.90 | | (391) all_246_1 = all_206_1
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (391) implies:
% 49.39/7.90 | | (392) all_246_1 = all_206_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (353), (354) imply:
% 49.39/7.90 | | (393) all_206_1 = all_158_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (350), (351) imply:
% 49.39/7.90 | | (394) all_274_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (394) implies:
% 49.39/7.90 | | (395) all_274_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (385), (386) imply:
% 49.39/7.90 | | (396) all_222_0 = all_78_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (396) implies:
% 49.39/7.90 | | (397) all_222_0 = all_78_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (364), (365) imply:
% 49.39/7.90 | | (398) all_280_2 = all_274_2
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (398) implies:
% 49.39/7.90 | | (399) all_280_2 = all_274_2
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (330), (331) imply:
% 49.39/7.90 | | (400) all_274_3 = all_182_3
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (400) implies:
% 49.39/7.90 | | (401) all_274_3 = all_182_3
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (349), (388) imply:
% 49.39/7.90 | | (402) all_170_1 = all_158_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (348), (388) imply:
% 49.39/7.90 | | (403) all_192_1 = all_170_1
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (403) implies:
% 49.39/7.90 | | (404) all_192_1 = all_170_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (347), (388) imply:
% 49.39/7.90 | | (405) all_250_1 = all_170_1
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (405) implies:
% 49.39/7.90 | | (406) all_250_1 = all_170_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (362), (399) imply:
% 49.39/7.90 | | (407) all_274_2 = all_268_2
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (363), (399) imply:
% 49.39/7.90 | | (408) all_274_2 = all_246_2
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (334), (335) imply:
% 49.39/7.90 | | (409) all_232_3 = all_108_2
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (409) implies:
% 49.39/7.90 | | (410) all_232_3 = all_108_2
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (346), (395) imply:
% 49.39/7.90 | | (411) all_268_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (411) implies:
% 49.39/7.90 | | (412) all_268_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (407), (408) imply:
% 49.39/7.90 | | (413) all_268_2 = all_246_2
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (413) implies:
% 49.39/7.90 | | (414) all_268_2 = all_246_2
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (329), (401) imply:
% 49.39/7.90 | | (415) all_266_3 = all_182_3
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (415) implies:
% 49.39/7.90 | | (416) all_266_3 = all_182_3
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (345), (412) imply:
% 49.39/7.90 | | (417) all_266_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (417) implies:
% 49.39/7.90 | | (418) all_266_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (361), (414) imply:
% 49.39/7.90 | | (419) all_266_2 = all_246_2
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (419) implies:
% 49.39/7.90 | | (420) all_266_2 = all_246_2
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (344), (418) imply:
% 49.39/7.90 | | (421) all_256_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (421) implies:
% 49.39/7.90 | | (422) all_256_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (360), (420) imply:
% 49.39/7.90 | | (423) all_256_2 = all_246_2
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (423) implies:
% 49.39/7.90 | | (424) all_256_2 = all_246_2
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (328), (416) imply:
% 49.39/7.90 | | (425) all_250_3 = all_182_3
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (425) implies:
% 49.39/7.90 | | (426) all_250_3 = all_182_3
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (343), (422) imply:
% 49.39/7.90 | | (427) all_222_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (427) implies:
% 49.39/7.90 | | (428) all_222_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (359), (424) imply:
% 49.39/7.90 | | (429) all_250_2 = all_246_2
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (429) implies:
% 49.39/7.90 | | (430) all_250_2 = all_246_2
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (390), (406) imply:
% 49.39/7.90 | | (431) all_170_1 = all_76_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (431) implies:
% 49.39/7.90 | | (432) all_170_1 = all_76_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (327), (426) imply:
% 49.39/7.90 | | (433) all_214_3 = all_182_3
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (433) implies:
% 49.39/7.90 | | (434) all_214_3 = all_182_3
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (341), (342) imply:
% 49.39/7.90 | | (435) all_222_1 = all_210_1
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (435) implies:
% 49.39/7.90 | | (436) all_222_1 = all_210_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (342), (392) imply:
% 49.39/7.90 | | (437) all_210_1 = all_206_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (383), (384) imply:
% 49.39/7.90 | | (438) all_192_0 = all_172_1
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (438) implies:
% 49.39/7.90 | | (439) all_192_0 = all_172_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (333), (410) imply:
% 49.39/7.90 | | (440) all_184_3 = all_108_2
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (332), (333) imply:
% 49.39/7.90 | | (441) all_184_3 = 0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (380), (381) imply:
% 49.39/7.90 | | (442) all_190_1 = all_182_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (380), (382) imply:
% 49.39/7.90 | | (443) all_190_1 = all_160_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (379), (397) imply:
% 49.39/7.90 | | (444) all_186_1 = all_78_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (444) implies:
% 49.39/7.90 | | (445) all_186_1 = all_78_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (428), (436) imply:
% 49.39/7.90 | | (446) all_210_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (446) implies:
% 49.39/7.90 | | (447) all_210_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (377), (378) imply:
% 49.39/7.90 | | (448) all_182_1 = all_142_1
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (448) implies:
% 49.39/7.90 | | (449) all_182_1 = all_142_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (376), (378) imply:
% 49.39/7.90 | | (450) all_192_0 = all_142_1
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (450) implies:
% 49.39/7.90 | | (451) all_192_0 = all_142_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (326), (434) imply:
% 49.39/7.90 | | (452) all_190_3 = all_182_3
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (452) implies:
% 49.39/7.90 | | (453) all_190_3 = all_182_3
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (374), (375) imply:
% 49.39/7.90 | | (454) all_182_1 = all_180_1
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (454) implies:
% 49.39/7.90 | | (455) all_182_1 = all_180_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (437), (447) imply:
% 49.39/7.90 | | (456) all_206_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (456) implies:
% 49.39/7.90 | | (457) all_206_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (372), (373) imply:
% 49.39/7.90 | | (458) all_200_1 = all_92_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (458) implies:
% 49.39/7.90 | | (459) all_200_1 = all_92_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (393), (457) imply:
% 49.39/7.90 | | (460) all_158_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (460) implies:
% 49.39/7.90 | | (461) all_158_1 = all_90_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (371), (459) imply:
% 49.39/7.90 | | (462) all_192_0 = all_92_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (462) implies:
% 49.39/7.90 | | (463) all_192_0 = all_92_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (370), (439) imply:
% 49.39/7.90 | | (464) all_172_1 = all_88_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (439), (463) imply:
% 49.39/7.90 | | (465) all_172_1 = all_92_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (439), (451) imply:
% 49.39/7.90 | | (466) all_172_1 = all_142_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (340), (404) imply:
% 49.39/7.90 | | (467) all_170_1 = all_86_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (467) implies:
% 49.39/7.90 | | (468) all_170_1 = all_86_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (442), (443) imply:
% 49.39/7.90 | | (469) all_182_1 = all_160_1
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (469) implies:
% 49.39/7.90 | | (470) all_182_1 = all_160_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (324), (453) imply:
% 49.39/7.90 | | (471) all_182_3 = all_168_2
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (325), (453) imply:
% 49.39/7.90 | | (472) all_182_3 = all_164_2
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (369), (445) imply:
% 49.39/7.90 | | (473) all_182_1 = all_78_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (473) implies:
% 49.39/7.90 | | (474) all_182_1 = all_78_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (440), (441) imply:
% 49.39/7.90 | | (475) all_108_2 = 0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (475) implies:
% 49.39/7.90 | | (476) all_108_2 = 0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (455), (474) imply:
% 49.39/7.90 | | (477) all_180_1 = all_78_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (449), (455) imply:
% 49.39/7.90 | | (478) all_180_1 = all_142_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (455), (470) imply:
% 49.39/7.90 | | (479) all_180_1 = all_160_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (471), (472) imply:
% 49.39/7.90 | | (480) all_168_2 = all_164_2
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (480) implies:
% 49.39/7.90 | | (481) all_168_2 = all_164_2
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (478), (479) imply:
% 49.39/7.90 | | (482) all_160_1 = all_142_1
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (477), (479) imply:
% 49.39/7.90 | | (483) all_160_1 = all_78_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (338), (339) imply:
% 49.39/7.90 | | (484) all_140_1 = all_94_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (484) implies:
% 49.39/7.90 | | (485) all_140_1 = all_94_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (337), (339) imply:
% 49.39/7.90 | | (486) all_158_1 = all_94_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (486) implies:
% 49.39/7.90 | | (487) all_158_1 = all_94_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (465), (466) imply:
% 49.39/7.90 | | (488) all_142_1 = all_92_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (488) implies:
% 49.39/7.90 | | (489) all_142_1 = all_92_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (464), (465) imply:
% 49.39/7.90 | | (490) all_92_0 = all_88_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (402), (468) imply:
% 49.39/7.90 | | (491) all_158_1 = all_86_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (491) implies:
% 49.39/7.90 | | (492) all_158_1 = all_86_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (432), (468) imply:
% 49.39/7.90 | | (493) all_86_0 = all_76_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (323), (481) imply:
% 49.39/7.90 | | (494) all_164_2 = all_132_2
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (321), (481) imply:
% 49.39/7.90 | | (495) all_164_2 = 0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (322), (481) imply:
% 49.39/7.90 | | (496) all_164_2 = all_134_2
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (495), (496) imply:
% 49.39/7.90 | | (497) all_134_2 = 0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (494), (496) imply:
% 49.39/7.90 | | (498) all_134_2 = all_132_2
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (482), (483) imply:
% 49.39/7.90 | | (499) all_142_1 = all_78_0
% 49.39/7.90 | |
% 49.39/7.90 | | SIMP: (499) implies:
% 49.39/7.90 | | (500) all_142_1 = all_78_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (461), (492) imply:
% 49.39/7.90 | | (501) all_90_0 = all_86_0
% 49.39/7.90 | |
% 49.39/7.90 | | COMBINE_EQS: (461), (487) imply:
% 49.39/7.91 | | (502) all_94_0 = all_90_0
% 49.39/7.91 | |
% 49.39/7.91 | | SIMP: (502) implies:
% 49.39/7.91 | | (503) all_94_0 = all_90_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (489), (500) imply:
% 49.39/7.91 | | (504) all_92_0 = all_78_0
% 49.39/7.91 | |
% 49.39/7.91 | | SIMP: (504) implies:
% 49.39/7.91 | | (505) all_92_0 = all_78_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (336), (485) imply:
% 49.39/7.91 | | (506) all_94_0 = all_80_0
% 49.39/7.91 | |
% 49.39/7.91 | | SIMP: (506) implies:
% 49.39/7.91 | | (507) all_94_0 = all_80_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (497), (498) imply:
% 49.39/7.91 | | (508) all_132_2 = 0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (503), (507) imply:
% 49.39/7.91 | | (509) all_90_0 = all_80_0
% 49.39/7.91 | |
% 49.39/7.91 | | SIMP: (509) implies:
% 49.39/7.91 | | (510) all_90_0 = all_80_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (490), (505) imply:
% 49.39/7.91 | | (511) all_88_0 = all_78_0
% 49.39/7.91 | |
% 49.39/7.91 | | SIMP: (511) implies:
% 49.39/7.91 | | (512) all_88_0 = all_78_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (501), (510) imply:
% 49.39/7.91 | | (513) all_86_0 = all_80_0
% 49.39/7.91 | |
% 49.39/7.91 | | SIMP: (513) implies:
% 49.39/7.91 | | (514) all_86_0 = all_80_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (368), (512) imply:
% 49.39/7.91 | | (515) all_84_0 = all_78_0
% 49.39/7.91 | |
% 49.39/7.91 | | SIMP: (515) implies:
% 49.39/7.91 | | (516) all_84_0 = all_78_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (493), (514) imply:
% 49.39/7.91 | | (517) all_80_0 = all_76_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (367), (516) imply:
% 49.39/7.91 | | (518) all_82_0 = all_78_0
% 49.39/7.91 | |
% 49.39/7.91 | | SIMP: (518) implies:
% 49.39/7.91 | | (519) all_82_0 = all_78_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (510), (517) imply:
% 49.39/7.91 | | (520) all_90_0 = all_76_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (507), (517) imply:
% 49.39/7.91 | | (521) all_94_0 = all_76_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (336), (517) imply:
% 49.39/7.91 | | (522) all_140_1 = all_76_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (461), (520) imply:
% 49.39/7.91 | | (523) all_158_1 = all_76_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (465), (505) imply:
% 49.39/7.91 | | (524) all_172_1 = all_78_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (339), (521) imply:
% 49.39/7.91 | | (525) all_176_1 = all_76_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (472), (495) imply:
% 49.39/7.91 | | (526) all_182_3 = 0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (447), (520) imply:
% 49.39/7.91 | | (527) all_210_1 = all_76_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (342), (527) imply:
% 49.39/7.91 | | (528) all_246_1 = all_76_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (426), (526) imply:
% 49.39/7.91 | | (529) all_250_3 = 0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (422), (520) imply:
% 49.39/7.91 | | (530) all_256_1 = all_76_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (418), (520) imply:
% 49.39/7.91 | | (531) all_266_1 = all_76_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (412), (520) imply:
% 49.39/7.91 | | (532) all_268_1 = all_76_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (395), (520) imply:
% 49.39/7.91 | | (533) all_274_1 = all_76_0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (335), (476) imply:
% 49.39/7.91 | | (534) all_278_3 = 0
% 49.39/7.91 | |
% 49.39/7.91 | | COMBINE_EQS: (388), (432) imply:
% 49.39/7.91 | | (535) all_280_1 = all_76_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (263), (386) imply:
% 49.39/7.91 | | (536) subset(all_78_0, all_42_1) = all_284_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (143), (519) imply:
% 49.39/7.91 | | (537) relation(all_78_0) = 0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (138), (517) imply:
% 49.39/7.91 | | (538) relation(all_76_0) = 0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (257), (535) imply:
% 49.39/7.91 | | (539) ordinal(all_76_0) = all_280_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (248), (533) imply:
% 49.39/7.91 | | (540) ordinal(all_76_0) = all_274_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (244), (532) imply:
% 49.39/7.91 | | (541) ordinal(all_76_0) = all_268_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (239), (531) imply:
% 49.39/7.91 | | (542) ordinal(all_76_0) = all_266_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (235), (530) imply:
% 49.39/7.91 | | (543) ordinal(all_76_0) = all_256_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (229), (390) imply:
% 49.39/7.91 | | (544) ordinal(all_76_0) = all_250_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (225), (528) imply:
% 49.39/7.91 | | (545) ordinal(all_76_0) = all_246_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (189), (477) imply:
% 49.39/7.91 | | (546) empty(all_78_0) = all_180_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (186), (525) imply:
% 49.39/7.91 | | (547) empty(all_76_0) = all_176_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (183), (524) imply:
% 49.39/7.91 | | (548) empty(all_78_0) = all_172_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (180), (432) imply:
% 49.39/7.91 | | (549) empty(all_76_0) = all_170_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (173), (483) imply:
% 49.39/7.91 | | (550) empty(all_78_0) = all_160_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (170), (523) imply:
% 49.39/7.91 | | (551) empty(all_76_0) = all_158_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (167), (500) imply:
% 49.39/7.91 | | (552) empty(all_78_0) = all_142_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (164), (522) imply:
% 49.39/7.91 | | (553) empty(all_76_0) = all_140_0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (142), (519) imply:
% 49.39/7.91 | | (554) empty(all_78_0) = 0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (137), (517) imply:
% 49.39/7.91 | | (555) empty(all_76_0) = 0
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (141), (519) imply:
% 49.39/7.91 | | (556) $i(all_78_0)
% 49.39/7.91 | |
% 49.39/7.91 | | REDUCE: (136), (517) imply:
% 49.39/7.91 | | (557) $i(all_76_0)
% 49.39/7.91 | |
% 49.39/7.91 | | BETA: splitting (255) gives:
% 49.39/7.91 | |
% 49.39/7.91 | | Case 1:
% 49.39/7.91 | | |
% 49.39/7.91 | | | (558) ~ (all_278_3 = 0)
% 49.39/7.91 | | |
% 49.39/7.91 | | | REDUCE: (534), (558) imply:
% 49.39/7.91 | | | (559) $false
% 49.39/7.91 | | |
% 49.39/7.91 | | | CLOSE: (559) is inconsistent.
% 49.39/7.91 | | |
% 49.39/7.91 | | Case 2:
% 49.39/7.91 | | |
% 49.39/7.91 | | | (560) ( ~ (all_278_0 = 0) | all_278_2 = 0) & ( ~ (all_278_2 = 0) |
% 49.39/7.91 | | | all_278_0 = 0)
% 49.39/7.91 | | |
% 49.39/7.91 | | | ALPHA: (560) implies:
% 49.39/7.91 | | | (561) ~ (all_278_2 = 0) | all_278_0 = 0
% 49.39/7.91 | | |
% 49.39/7.91 | | | BETA: splitting (561) gives:
% 49.39/7.91 | | |
% 49.39/7.91 | | | Case 1:
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | (562) ~ (all_278_2 = 0)
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | REDUCE: (366), (562) imply:
% 49.39/7.91 | | | | (563) $false
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | CLOSE: (563) is inconsistent.
% 49.39/7.91 | | | |
% 49.39/7.91 | | | Case 2:
% 49.39/7.91 | | | |
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | GROUND_INST: instantiating (32) with 0, all_176_0, all_76_0, simplifying
% 49.39/7.91 | | | | with (547), (555) gives:
% 49.39/7.91 | | | | (564) all_176_0 = 0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | GROUND_INST: instantiating (32) with all_170_0, all_176_0, all_76_0,
% 49.39/7.91 | | | | simplifying with (547), (549) gives:
% 49.39/7.91 | | | | (565) all_176_0 = all_170_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | GROUND_INST: instantiating (32) with all_158_0, all_176_0, all_76_0,
% 49.39/7.91 | | | | simplifying with (547), (551) gives:
% 49.39/7.91 | | | | (566) all_176_0 = all_158_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | GROUND_INST: instantiating (32) with all_140_0, all_176_0, all_76_0,
% 49.39/7.91 | | | | simplifying with (547), (553) gives:
% 49.39/7.91 | | | | (567) all_176_0 = all_140_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | GROUND_INST: instantiating (32) with 0, all_160_0, all_78_0, simplifying
% 49.39/7.91 | | | | with (550), (554) gives:
% 49.39/7.91 | | | | (568) all_160_0 = 0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | GROUND_INST: instantiating (32) with all_172_0, all_180_0, all_78_0,
% 49.39/7.91 | | | | simplifying with (546), (548) gives:
% 49.39/7.91 | | | | (569) all_180_0 = all_172_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | GROUND_INST: instantiating (32) with all_160_0, all_180_0, all_78_0,
% 49.39/7.91 | | | | simplifying with (546), (550) gives:
% 49.39/7.91 | | | | (570) all_180_0 = all_160_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | GROUND_INST: instantiating (32) with all_142_0, all_180_0, all_78_0,
% 49.39/7.91 | | | | simplifying with (546), (552) gives:
% 49.39/7.91 | | | | (571) all_180_0 = all_142_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | GROUND_INST: instantiating (34) with all_246_0, all_256_0, all_76_0,
% 49.39/7.91 | | | | simplifying with (543), (545) gives:
% 49.39/7.91 | | | | (572) all_256_0 = all_246_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | GROUND_INST: instantiating (34) with all_268_0, all_274_0, all_76_0,
% 49.39/7.91 | | | | simplifying with (540), (541) gives:
% 49.39/7.91 | | | | (573) all_274_0 = all_268_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | GROUND_INST: instantiating (34) with all_250_0, all_274_0, all_76_0,
% 49.39/7.91 | | | | simplifying with (540), (544) gives:
% 49.39/7.91 | | | | (574) all_274_0 = all_250_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | GROUND_INST: instantiating (34) with all_268_0, all_280_0, all_76_0,
% 49.39/7.91 | | | | simplifying with (539), (541) gives:
% 49.39/7.91 | | | | (575) all_280_0 = all_268_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | GROUND_INST: instantiating (34) with all_266_0, all_280_0, all_76_0,
% 49.39/7.91 | | | | simplifying with (539), (542) gives:
% 49.39/7.91 | | | | (576) all_280_0 = all_266_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | GROUND_INST: instantiating (34) with all_256_0, all_280_0, all_76_0,
% 49.39/7.91 | | | | simplifying with (539), (543) gives:
% 49.39/7.91 | | | | (577) all_280_0 = all_256_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | COMBINE_EQS: (575), (576) imply:
% 49.39/7.91 | | | | (578) all_268_0 = all_266_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | SIMP: (578) implies:
% 49.39/7.91 | | | | (579) all_268_0 = all_266_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | COMBINE_EQS: (576), (577) imply:
% 49.39/7.91 | | | | (580) all_266_0 = all_256_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | COMBINE_EQS: (573), (574) imply:
% 49.39/7.91 | | | | (581) all_268_0 = all_250_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | SIMP: (581) implies:
% 49.39/7.91 | | | | (582) all_268_0 = all_250_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | COMBINE_EQS: (579), (582) imply:
% 49.39/7.91 | | | | (583) all_266_0 = all_250_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | SIMP: (583) implies:
% 49.39/7.91 | | | | (584) all_266_0 = all_250_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | COMBINE_EQS: (580), (584) imply:
% 49.39/7.91 | | | | (585) all_256_0 = all_250_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | SIMP: (585) implies:
% 49.39/7.91 | | | | (586) all_256_0 = all_250_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | COMBINE_EQS: (572), (586) imply:
% 49.39/7.91 | | | | (587) all_250_0 = all_246_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | COMBINE_EQS: (569), (571) imply:
% 49.39/7.91 | | | | (588) all_172_0 = all_142_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | COMBINE_EQS: (569), (570) imply:
% 49.39/7.91 | | | | (589) all_172_0 = all_160_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | COMBINE_EQS: (565), (566) imply:
% 49.39/7.91 | | | | (590) all_170_0 = all_158_0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | COMBINE_EQS: (564), (565) imply:
% 49.39/7.91 | | | | (591) all_170_0 = 0
% 49.39/7.91 | | | |
% 49.39/7.91 | | | | COMBINE_EQS: (565), (567) imply:
% 49.39/7.92 | | | | (592) all_170_0 = all_140_0
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | COMBINE_EQS: (588), (589) imply:
% 49.39/7.92 | | | | (593) all_160_0 = all_142_0
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | SIMP: (593) implies:
% 49.39/7.92 | | | | (594) all_160_0 = all_142_0
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | COMBINE_EQS: (590), (592) imply:
% 49.39/7.92 | | | | (595) all_158_0 = all_140_0
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | COMBINE_EQS: (590), (591) imply:
% 49.39/7.92 | | | | (596) all_158_0 = 0
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | COMBINE_EQS: (568), (594) imply:
% 49.39/7.92 | | | | (597) all_142_0 = 0
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | COMBINE_EQS: (595), (596) imply:
% 49.39/7.92 | | | | (598) all_140_0 = 0
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | SIMP: (598) implies:
% 49.39/7.92 | | | | (599) all_140_0 = 0
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | GROUND_INST: instantiating (1) with all_76_0, simplifying with (555),
% 49.39/7.92 | | | | (557) gives:
% 49.39/7.92 | | | | (600) function(all_76_0) = 0
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | GROUND_INST: instantiating (3) with all_76_0, simplifying with (555),
% 49.39/7.92 | | | | (557) gives:
% 49.39/7.92 | | | | (601) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 49.39/7.92 | | | | (one_to_one(all_76_0) = v2 & relation(all_76_0) = v0 &
% 49.39/7.92 | | | | function(all_76_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 =
% 49.39/7.92 | | | | 0))
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | GROUND_INST: instantiating (6) with all_76_0, simplifying with (555),
% 49.39/7.92 | | | | (557) gives:
% 49.39/7.92 | | | | (602) epsilon_transitive(all_76_0) = 0 & ordinal(all_76_0) = 0 &
% 49.39/7.92 | | | | epsilon_connected(all_76_0) = 0
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | ALPHA: (602) implies:
% 49.39/7.92 | | | | (603) ordinal(all_76_0) = 0
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | GROUND_INST: instantiating (t8_boole) with all_76_0, all_78_0,
% 49.39/7.92 | | | | simplifying with (554), (555), (556), (557) gives:
% 49.39/7.92 | | | | (604) all_78_0 = all_76_0
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | GROUND_INST: instantiating (29) with all_78_0, simplifying with (554),
% 49.39/7.92 | | | | (556) gives:
% 49.39/7.92 | | | | (605) all_78_0 = empty_set
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | GROUND_INST: instantiating (3) with all_78_0, simplifying with (554),
% 49.39/7.92 | | | | (556) gives:
% 49.39/7.92 | | | | (606) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 49.39/7.92 | | | | (one_to_one(all_78_0) = v2 & relation(all_78_0) = v0 &
% 49.39/7.92 | | | | function(all_78_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 =
% 49.39/7.92 | | | | 0))
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | GROUND_INST: instantiating (19) with all_76_0, simplifying with (538),
% 49.39/7.92 | | | | (557) gives:
% 49.39/7.92 | | | | (607) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 49.39/7.92 | | | | (relation_non_empty(all_76_0) = v0 &
% 49.39/7.92 | | | | with_non_empty_elements(v2) = v3 & relation_rng(all_76_0) =
% 49.39/7.92 | | | | v2 & function(all_76_0) = v1 & $i(v2) & ( ~ (v1 = 0) | ~ (v0
% 49.39/7.92 | | | | = 0) | v3 = 0))
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | GROUND_INST: instantiating (9) with all_76_0, simplifying with (538),
% 49.39/7.92 | | | | (557) gives:
% 49.39/7.92 | | | | (608) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 49.39/7.92 | | | | (transfinite_sequence(all_76_0) = v1 & relation_dom(all_76_0) =
% 49.39/7.92 | | | | v2 & ordinal(v2) = v3 & function(all_76_0) = v0 & $i(v2) & (
% 49.39/7.92 | | | | ~ (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 =
% 49.39/7.92 | | | | 0))))
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | GROUND_INST: instantiating (5) with all_76_0, simplifying with (538),
% 49.39/7.92 | | | | (557) gives:
% 49.39/7.92 | | | | (609) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 49.39/7.92 | | | | (one_to_one(all_76_0) = v2 & function(all_76_0) = v1 &
% 49.39/7.92 | | | | empty(all_76_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | GROUND_INST: instantiating (19) with all_78_0, simplifying with (537),
% 49.39/7.92 | | | | (556) gives:
% 49.39/7.92 | | | | (610) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 49.39/7.92 | | | | (relation_non_empty(all_78_0) = v0 &
% 49.39/7.92 | | | | with_non_empty_elements(v2) = v3 & relation_rng(all_78_0) =
% 49.39/7.92 | | | | v2 & function(all_78_0) = v1 & $i(v2) & ( ~ (v1 = 0) | ~ (v0
% 49.39/7.92 | | | | = 0) | v3 = 0))
% 49.39/7.92 | | | |
% 49.39/7.92 | | | | GROUND_INST: instantiating (9) with all_78_0, simplifying with (537),
% 49.39/7.92 | | | | (556) gives:
% 49.80/7.92 | | | | (611) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 49.80/7.92 | | | | (transfinite_sequence(all_78_0) = v1 & relation_dom(all_78_0) =
% 49.80/7.92 | | | | v2 & ordinal(v2) = v3 & function(all_78_0) = v0 & $i(v2) & (
% 49.80/7.92 | | | | ~ (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 =
% 49.80/7.92 | | | | 0))))
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | GROUND_INST: instantiating (5) with all_78_0, simplifying with (537),
% 49.80/7.92 | | | | (556) gives:
% 49.80/7.92 | | | | (612) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 49.80/7.92 | | | | (one_to_one(all_78_0) = v2 & function(all_78_0) = v1 &
% 49.80/7.92 | | | | empty(all_78_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | GROUND_INST: instantiating (10) with empty_set, all_76_0, simplifying
% 49.80/7.92 | | | | with (30), (298) gives:
% 49.80/7.92 | | | | (613) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 49.80/7.92 | | | | (transfinite_sequence(empty_set) = v2 & relation(empty_set) =
% 49.80/7.92 | | | | v0 & ordinal(all_76_0) = v3 & function(empty_set) = v1 & ( ~
% 49.80/7.92 | | | | (v1 = 0) | ~ (v0 = 0) | (( ~ (v3 = 0) | v2 = 0) & ( ~ (v2
% 49.80/7.92 | | | | = 0) | v3 = 0))))
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | GROUND_INST: instantiating (27) with empty_set, all_76_0, simplifying
% 49.80/7.92 | | | | with (30), (298) gives:
% 49.80/7.92 | | | | (614) ? [v0: any] : ? [v1: $i] : (relation_rng(empty_set) = v1 &
% 49.80/7.92 | | | | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~ (v1 =
% 49.80/7.92 | | | | empty_set) | all_76_0 = empty_set) & ( ~ (all_76_0 =
% 49.80/7.92 | | | | empty_set) | v1 = empty_set))))
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | GROUND_INST: instantiating (11) with empty_set, all_246_2, simplifying
% 49.80/7.92 | | | | with (30), (291) gives:
% 49.80/7.92 | | | | (615) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 49.80/7.92 | | | | (relation_dom(empty_set) = v2 & relation(empty_set) = v0 &
% 49.80/7.92 | | | | ordinal(v2) = v3 & function(empty_set) = v1 & $i(v2) & ( ~
% 49.80/7.92 | | | | (v1 = 0) | ~ (v0 = 0) | (( ~ (v3 = 0) | all_246_2 = 0) & (
% 49.80/7.92 | | | | ~ (all_246_2 = 0) | v3 = 0))))
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | GROUND_INST: instantiating (13) with all_42_1, empty_set, all_78_0,
% 49.80/7.92 | | | | all_284_0, simplifying with (30), (45), (277), (536) gives:
% 49.80/7.92 | | | | (616) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 49.80/7.92 | | | | (transfinite_sequence_of(empty_set, all_42_1) = v3 &
% 49.80/7.92 | | | | transfinite_sequence(empty_set) = v2 & relation(empty_set) =
% 49.80/7.92 | | | | v0 & function(empty_set) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) |
% 49.80/7.92 | | | | ~ (v0 = 0) | (( ~ (v3 = 0) | all_284_0 = 0) & ( ~
% 49.80/7.92 | | | | (all_284_0 = 0) | v3 = 0))))
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | GROUND_INST: instantiating (20) with empty_set, all_78_0, simplifying
% 49.80/7.92 | | | | with (30), (277) gives:
% 49.80/7.92 | | | | (617) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 49.80/7.92 | | | | (relation_non_empty(empty_set) = v1 &
% 49.80/7.92 | | | | with_non_empty_elements(all_78_0) = v3 & relation(empty_set)
% 49.80/7.92 | | | | = v0 & function(empty_set) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0)
% 49.80/7.92 | | | | | ~ (v0 = 0) | v3 = 0))
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | GROUND_INST: instantiating (28) with empty_set, all_78_0, simplifying
% 49.80/7.92 | | | | with (30), (277) gives:
% 49.80/7.92 | | | | (618) ? [v0: any] : ? [v1: $i] : (relation_dom(empty_set) = v1 &
% 49.80/7.92 | | | | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~ (v1 =
% 49.80/7.92 | | | | empty_set) | all_78_0 = empty_set) & ( ~ (all_78_0 =
% 49.80/7.92 | | | | empty_set) | v1 = empty_set))))
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | COMBINE_EQS: (604), (605) imply:
% 49.80/7.92 | | | | (619) all_76_0 = empty_set
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | DELTA: instantiating (606) with fresh symbols all_447_0, all_447_1,
% 49.80/7.92 | | | | all_447_2 gives:
% 49.80/7.92 | | | | (620) one_to_one(all_78_0) = all_447_0 & relation(all_78_0) =
% 49.80/7.92 | | | | all_447_2 & function(all_78_0) = all_447_1 & ( ~ (all_447_1 =
% 49.80/7.92 | | | | 0) | ~ (all_447_2 = 0) | all_447_0 = 0)
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | ALPHA: (620) implies:
% 49.80/7.92 | | | | (621) relation(all_78_0) = all_447_2
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | DELTA: instantiating (612) with fresh symbols all_513_0, all_513_1,
% 49.80/7.92 | | | | all_513_2 gives:
% 49.80/7.92 | | | | (622) one_to_one(all_78_0) = all_513_0 & function(all_78_0) =
% 49.80/7.92 | | | | all_513_1 & empty(all_78_0) = all_513_2 & ( ~ (all_513_1 = 0) |
% 49.80/7.92 | | | | ~ (all_513_2 = 0) | all_513_0 = 0)
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | ALPHA: (622) implies:
% 49.80/7.92 | | | | (623) function(all_78_0) = all_513_1
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | DELTA: instantiating (601) with fresh symbols all_519_0, all_519_1,
% 49.80/7.92 | | | | all_519_2 gives:
% 49.80/7.92 | | | | (624) one_to_one(all_76_0) = all_519_0 & relation(all_76_0) =
% 49.80/7.92 | | | | all_519_2 & function(all_76_0) = all_519_1 & ( ~ (all_519_1 =
% 49.80/7.92 | | | | 0) | ~ (all_519_2 = 0) | all_519_0 = 0)
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | ALPHA: (624) implies:
% 49.80/7.92 | | | | (625) function(all_76_0) = all_519_1
% 49.80/7.92 | | | | (626) relation(all_76_0) = all_519_2
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | DELTA: instantiating (609) with fresh symbols all_523_0, all_523_1,
% 49.80/7.92 | | | | all_523_2 gives:
% 49.80/7.92 | | | | (627) one_to_one(all_76_0) = all_523_0 & function(all_76_0) =
% 49.80/7.92 | | | | all_523_1 & empty(all_76_0) = all_523_2 & ( ~ (all_523_1 = 0) |
% 49.80/7.92 | | | | ~ (all_523_2 = 0) | all_523_0 = 0)
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | ALPHA: (627) implies:
% 49.80/7.92 | | | | (628) function(all_76_0) = all_523_1
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | DELTA: instantiating (618) with fresh symbols all_575_0, all_575_1
% 49.80/7.92 | | | | gives:
% 49.80/7.92 | | | | (629) relation_dom(empty_set) = all_575_0 & relation(empty_set) =
% 49.80/7.92 | | | | all_575_1 & $i(all_575_0) & ( ~ (all_575_1 = 0) | (( ~
% 49.80/7.92 | | | | (all_575_0 = empty_set) | all_78_0 = empty_set) & ( ~
% 49.80/7.92 | | | | (all_78_0 = empty_set) | all_575_0 = empty_set)))
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | ALPHA: (629) implies:
% 49.80/7.92 | | | | (630) relation(empty_set) = all_575_1
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | DELTA: instantiating (617) with fresh symbols all_577_0, all_577_1,
% 49.80/7.92 | | | | all_577_2, all_577_3 gives:
% 49.80/7.92 | | | | (631) relation_non_empty(empty_set) = all_577_2 &
% 49.80/7.92 | | | | with_non_empty_elements(all_78_0) = all_577_0 &
% 49.80/7.92 | | | | relation(empty_set) = all_577_3 & function(empty_set) =
% 49.80/7.92 | | | | all_577_1 & ( ~ (all_577_1 = 0) | ~ (all_577_2 = 0) | ~
% 49.80/7.92 | | | | (all_577_3 = 0) | all_577_0 = 0)
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | ALPHA: (631) implies:
% 49.80/7.92 | | | | (632) function(empty_set) = all_577_1
% 49.80/7.92 | | | | (633) relation(empty_set) = all_577_3
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | DELTA: instantiating (610) with fresh symbols all_595_0, all_595_1,
% 49.80/7.92 | | | | all_595_2, all_595_3 gives:
% 49.80/7.92 | | | | (634) relation_non_empty(all_78_0) = all_595_3 &
% 49.80/7.92 | | | | with_non_empty_elements(all_595_1) = all_595_0 &
% 49.80/7.92 | | | | relation_rng(all_78_0) = all_595_1 & function(all_78_0) =
% 49.80/7.92 | | | | all_595_2 & $i(all_595_1) & ( ~ (all_595_2 = 0) | ~ (all_595_3
% 49.80/7.92 | | | | = 0) | all_595_0 = 0)
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | ALPHA: (634) implies:
% 49.80/7.92 | | | | (635) function(all_78_0) = all_595_2
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | DELTA: instantiating (607) with fresh symbols all_597_0, all_597_1,
% 49.80/7.92 | | | | all_597_2, all_597_3 gives:
% 49.80/7.92 | | | | (636) relation_non_empty(all_76_0) = all_597_3 &
% 49.80/7.92 | | | | with_non_empty_elements(all_597_1) = all_597_0 &
% 49.80/7.92 | | | | relation_rng(all_76_0) = all_597_1 & function(all_76_0) =
% 49.80/7.92 | | | | all_597_2 & $i(all_597_1) & ( ~ (all_597_2 = 0) | ~ (all_597_3
% 49.80/7.92 | | | | = 0) | all_597_0 = 0)
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | ALPHA: (636) implies:
% 49.80/7.92 | | | | (637) function(all_76_0) = all_597_2
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | DELTA: instantiating (614) with fresh symbols all_601_0, all_601_1
% 49.80/7.92 | | | | gives:
% 49.80/7.92 | | | | (638) relation_rng(empty_set) = all_601_0 & relation(empty_set) =
% 49.80/7.92 | | | | all_601_1 & $i(all_601_0) & ( ~ (all_601_1 = 0) | (( ~
% 49.80/7.92 | | | | (all_601_0 = empty_set) | all_76_0 = empty_set) & ( ~
% 49.80/7.92 | | | | (all_76_0 = empty_set) | all_601_0 = empty_set)))
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | ALPHA: (638) implies:
% 49.80/7.92 | | | | (639) relation(empty_set) = all_601_1
% 49.80/7.92 | | | |
% 49.80/7.92 | | | | DELTA: instantiating (611) with fresh symbols all_625_0, all_625_1,
% 49.80/7.92 | | | | all_625_2, all_625_3 gives:
% 49.80/7.93 | | | | (640) transfinite_sequence(all_78_0) = all_625_2 &
% 49.80/7.93 | | | | relation_dom(all_78_0) = all_625_1 & ordinal(all_625_1) =
% 49.80/7.93 | | | | all_625_0 & function(all_78_0) = all_625_3 & $i(all_625_1) & (
% 49.80/7.93 | | | | ~ (all_625_3 = 0) | (( ~ (all_625_0 = 0) | all_625_2 = 0) & (
% 49.80/7.93 | | | | ~ (all_625_2 = 0) | all_625_0 = 0)))
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | ALPHA: (640) implies:
% 49.80/7.93 | | | | (641) function(all_78_0) = all_625_3
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | DELTA: instantiating (613) with fresh symbols all_631_0, all_631_1,
% 49.80/7.93 | | | | all_631_2, all_631_3 gives:
% 49.80/7.93 | | | | (642) transfinite_sequence(empty_set) = all_631_1 &
% 49.80/7.93 | | | | relation(empty_set) = all_631_3 & ordinal(all_76_0) = all_631_0
% 49.80/7.93 | | | | & function(empty_set) = all_631_2 & ( ~ (all_631_2 = 0) | ~
% 49.80/7.93 | | | | (all_631_3 = 0) | (( ~ (all_631_0 = 0) | all_631_1 = 0) & ( ~
% 49.80/7.93 | | | | (all_631_1 = 0) | all_631_0 = 0)))
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | ALPHA: (642) implies:
% 49.80/7.93 | | | | (643) function(empty_set) = all_631_2
% 49.80/7.93 | | | | (644) ordinal(all_76_0) = all_631_0
% 49.80/7.93 | | | | (645) relation(empty_set) = all_631_3
% 49.80/7.93 | | | | (646) transfinite_sequence(empty_set) = all_631_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | DELTA: instantiating (608) with fresh symbols all_641_0, all_641_1,
% 49.80/7.93 | | | | all_641_2, all_641_3 gives:
% 49.80/7.93 | | | | (647) transfinite_sequence(all_76_0) = all_641_2 &
% 49.80/7.93 | | | | relation_dom(all_76_0) = all_641_1 & ordinal(all_641_1) =
% 49.80/7.93 | | | | all_641_0 & function(all_76_0) = all_641_3 & $i(all_641_1) & (
% 49.80/7.93 | | | | ~ (all_641_3 = 0) | (( ~ (all_641_0 = 0) | all_641_2 = 0) & (
% 49.80/7.93 | | | | ~ (all_641_2 = 0) | all_641_0 = 0)))
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | ALPHA: (647) implies:
% 49.80/7.93 | | | | (648) function(all_76_0) = all_641_3
% 49.80/7.93 | | | | (649) transfinite_sequence(all_76_0) = all_641_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | DELTA: instantiating (615) with fresh symbols all_645_0, all_645_1,
% 49.80/7.93 | | | | all_645_2, all_645_3 gives:
% 49.80/7.93 | | | | (650) relation_dom(empty_set) = all_645_1 & relation(empty_set) =
% 49.80/7.93 | | | | all_645_3 & ordinal(all_645_1) = all_645_0 &
% 49.80/7.93 | | | | function(empty_set) = all_645_2 & $i(all_645_1) & ( ~
% 49.80/7.93 | | | | (all_645_2 = 0) | ~ (all_645_3 = 0) | (( ~ (all_645_0 = 0) |
% 49.80/7.93 | | | | all_246_2 = 0) & ( ~ (all_246_2 = 0) | all_645_0 = 0)))
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | ALPHA: (650) implies:
% 49.80/7.93 | | | | (651) function(empty_set) = all_645_2
% 49.80/7.93 | | | | (652) relation(empty_set) = all_645_3
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | DELTA: instantiating (616) with fresh symbols all_647_0, all_647_1,
% 49.80/7.93 | | | | all_647_2, all_647_3 gives:
% 49.80/7.93 | | | | (653) transfinite_sequence_of(empty_set, all_42_1) = all_647_0 &
% 49.80/7.93 | | | | transfinite_sequence(empty_set) = all_647_1 &
% 49.80/7.93 | | | | relation(empty_set) = all_647_3 & function(empty_set) =
% 49.80/7.93 | | | | all_647_2 & ( ~ (all_647_1 = 0) | ~ (all_647_2 = 0) | ~
% 49.80/7.93 | | | | (all_647_3 = 0) | (( ~ (all_647_0 = 0) | all_284_0 = 0) & ( ~
% 49.80/7.93 | | | | (all_284_0 = 0) | all_647_0 = 0)))
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | ALPHA: (653) implies:
% 49.80/7.93 | | | | (654) function(empty_set) = all_647_2
% 49.80/7.93 | | | | (655) relation(empty_set) = all_647_3
% 49.80/7.93 | | | | (656) transfinite_sequence(empty_set) = all_647_1
% 49.80/7.93 | | | | (657) transfinite_sequence_of(empty_set, all_42_1) = all_647_0
% 49.80/7.93 | | | | (658) ~ (all_647_1 = 0) | ~ (all_647_2 = 0) | ~ (all_647_3 = 0) |
% 49.80/7.93 | | | | (( ~ (all_647_0 = 0) | all_284_0 = 0) & ( ~ (all_284_0 = 0) |
% 49.80/7.93 | | | | all_647_0 = 0))
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | REDUCE: (536), (605) imply:
% 49.80/7.93 | | | | (659) subset(empty_set, all_42_1) = all_284_0
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | REDUCE: (619), (649) imply:
% 49.80/7.93 | | | | (660) transfinite_sequence(empty_set) = all_641_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | REDUCE: (605), (621) imply:
% 49.80/7.93 | | | | (661) relation(empty_set) = all_447_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | REDUCE: (619), (626) imply:
% 49.80/7.93 | | | | (662) relation(empty_set) = all_519_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | REDUCE: (619), (644) imply:
% 49.80/7.93 | | | | (663) ordinal(empty_set) = all_631_0
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | REDUCE: (545), (619) imply:
% 49.80/7.93 | | | | (664) ordinal(empty_set) = all_246_0
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | REDUCE: (603), (619) imply:
% 49.80/7.93 | | | | (665) ordinal(empty_set) = 0
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | REDUCE: (605), (641) imply:
% 49.80/7.93 | | | | (666) function(empty_set) = all_625_3
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | REDUCE: (605), (635) imply:
% 49.80/7.93 | | | | (667) function(empty_set) = all_595_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | REDUCE: (605), (623) imply:
% 49.80/7.93 | | | | (668) function(empty_set) = all_513_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | REDUCE: (619), (648) imply:
% 49.80/7.93 | | | | (669) function(empty_set) = all_641_3
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | REDUCE: (619), (637) imply:
% 49.80/7.93 | | | | (670) function(empty_set) = all_597_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | REDUCE: (619), (628) imply:
% 49.80/7.93 | | | | (671) function(empty_set) = all_523_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | REDUCE: (619), (625) imply:
% 49.80/7.93 | | | | (672) function(empty_set) = all_519_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (33) with all_595_2, all_597_2, empty_set,
% 49.80/7.93 | | | | simplifying with (667), (670) gives:
% 49.80/7.93 | | | | (673) all_597_2 = all_595_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (33) with all_523_1, all_597_2, empty_set,
% 49.80/7.93 | | | | simplifying with (670), (671) gives:
% 49.80/7.93 | | | | (674) all_597_2 = all_523_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (33) with all_595_2, all_625_3, empty_set,
% 49.80/7.93 | | | | simplifying with (666), (667) gives:
% 49.80/7.93 | | | | (675) all_625_3 = all_595_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (33) with all_577_1, all_625_3, empty_set,
% 49.80/7.93 | | | | simplifying with (632), (666) gives:
% 49.80/7.93 | | | | (676) all_625_3 = all_577_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (33) with all_595_2, all_641_3, empty_set,
% 49.80/7.93 | | | | simplifying with (667), (669) gives:
% 49.80/7.93 | | | | (677) all_641_3 = all_595_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (33) with all_513_1, all_641_3, empty_set,
% 49.80/7.93 | | | | simplifying with (668), (669) gives:
% 49.80/7.93 | | | | (678) all_641_3 = all_513_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (33) with 0, all_645_2, empty_set,
% 49.80/7.93 | | | | simplifying with (14), (651) gives:
% 49.80/7.93 | | | | (679) all_645_2 = 0
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (33) with all_597_2, all_645_2, empty_set,
% 49.80/7.93 | | | | simplifying with (651), (670) gives:
% 49.80/7.93 | | | | (680) all_645_2 = all_597_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (33) with all_519_1, all_645_2, empty_set,
% 49.80/7.93 | | | | simplifying with (651), (672) gives:
% 49.80/7.93 | | | | (681) all_645_2 = all_519_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (33) with all_641_3, all_647_2, empty_set,
% 49.80/7.93 | | | | simplifying with (654), (669) gives:
% 49.80/7.93 | | | | (682) all_647_2 = all_641_3
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (33) with all_631_2, all_647_2, empty_set,
% 49.80/7.93 | | | | simplifying with (643), (654) gives:
% 49.80/7.93 | | | | (683) all_647_2 = all_631_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (34) with 0, all_631_0, empty_set,
% 49.80/7.93 | | | | simplifying with (663), (665) gives:
% 49.80/7.93 | | | | (684) all_631_0 = 0
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (34) with all_246_0, all_631_0, empty_set,
% 49.80/7.93 | | | | simplifying with (663), (664) gives:
% 49.80/7.93 | | | | (685) all_631_0 = all_246_0
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (35) with 0, all_519_2, empty_set,
% 49.80/7.93 | | | | simplifying with (16), (662) gives:
% 49.80/7.93 | | | | (686) all_519_2 = 0
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (35) with all_447_2, all_601_1, empty_set,
% 49.80/7.93 | | | | simplifying with (639), (661) gives:
% 49.80/7.93 | | | | (687) all_601_1 = all_447_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (35) with all_601_1, all_645_3, empty_set,
% 49.80/7.93 | | | | simplifying with (639), (652) gives:
% 49.80/7.93 | | | | (688) all_645_3 = all_601_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (35) with all_575_1, all_645_3, empty_set,
% 49.80/7.93 | | | | simplifying with (630), (652) gives:
% 49.80/7.93 | | | | (689) all_645_3 = all_575_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (35) with all_519_2, all_645_3, empty_set,
% 49.80/7.93 | | | | simplifying with (652), (662) gives:
% 49.80/7.93 | | | | (690) all_645_3 = all_519_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (35) with all_631_3, all_647_3, empty_set,
% 49.80/7.93 | | | | simplifying with (645), (655) gives:
% 49.80/7.93 | | | | (691) all_647_3 = all_631_3
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (35) with all_601_1, all_647_3, empty_set,
% 49.80/7.93 | | | | simplifying with (639), (655) gives:
% 49.80/7.93 | | | | (692) all_647_3 = all_601_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (35) with all_577_3, all_647_3, empty_set,
% 49.80/7.93 | | | | simplifying with (633), (655) gives:
% 49.80/7.93 | | | | (693) all_647_3 = all_577_3
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (37) with all_246_2, all_641_2, empty_set,
% 49.80/7.93 | | | | simplifying with (291), (660) gives:
% 49.80/7.93 | | | | (694) all_641_2 = all_246_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (37) with all_641_2, all_647_1, empty_set,
% 49.80/7.93 | | | | simplifying with (656), (660) gives:
% 49.80/7.93 | | | | (695) all_647_1 = all_641_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (37) with all_631_1, all_647_1, empty_set,
% 49.80/7.93 | | | | simplifying with (646), (656) gives:
% 49.80/7.93 | | | | (696) all_647_1 = all_631_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | GROUND_INST: instantiating (39) with all_42_0, all_647_0, all_42_1,
% 49.80/7.93 | | | | empty_set, simplifying with (46), (657) gives:
% 49.80/7.93 | | | | (697) all_647_0 = all_42_0
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (695), (696) imply:
% 49.80/7.93 | | | | (698) all_641_2 = all_631_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | SIMP: (698) implies:
% 49.80/7.93 | | | | (699) all_641_2 = all_631_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (682), (683) imply:
% 49.80/7.93 | | | | (700) all_641_3 = all_631_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | SIMP: (700) implies:
% 49.80/7.93 | | | | (701) all_641_3 = all_631_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (691), (692) imply:
% 49.80/7.93 | | | | (702) all_631_3 = all_601_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (691), (693) imply:
% 49.80/7.93 | | | | (703) all_631_3 = all_577_3
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (679), (681) imply:
% 49.80/7.93 | | | | (704) all_519_1 = 0
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (680), (681) imply:
% 49.80/7.93 | | | | (705) all_597_2 = all_519_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | SIMP: (705) implies:
% 49.80/7.93 | | | | (706) all_597_2 = all_519_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (688), (689) imply:
% 49.80/7.93 | | | | (707) all_601_1 = all_575_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | SIMP: (707) implies:
% 49.80/7.93 | | | | (708) all_601_1 = all_575_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (689), (690) imply:
% 49.80/7.93 | | | | (709) all_575_1 = all_519_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (694), (699) imply:
% 49.80/7.93 | | | | (710) all_631_1 = all_246_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (678), (701) imply:
% 49.80/7.93 | | | | (711) all_631_2 = all_513_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (677), (701) imply:
% 49.80/7.93 | | | | (712) all_631_2 = all_595_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (684), (685) imply:
% 49.80/7.93 | | | | (713) all_246_0 = 0
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (711), (712) imply:
% 49.80/7.93 | | | | (714) all_595_2 = all_513_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | SIMP: (714) implies:
% 49.80/7.93 | | | | (715) all_595_2 = all_513_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (702), (703) imply:
% 49.80/7.93 | | | | (716) all_601_1 = all_577_3
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | SIMP: (716) implies:
% 49.80/7.93 | | | | (717) all_601_1 = all_577_3
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (675), (676) imply:
% 49.80/7.93 | | | | (718) all_595_2 = all_577_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | SIMP: (718) implies:
% 49.80/7.93 | | | | (719) all_595_2 = all_577_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (708), (717) imply:
% 49.80/7.93 | | | | (720) all_577_3 = all_575_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (687), (717) imply:
% 49.80/7.93 | | | | (721) all_577_3 = all_447_2
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (673), (674) imply:
% 49.80/7.93 | | | | (722) all_595_2 = all_523_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | SIMP: (722) implies:
% 49.80/7.93 | | | | (723) all_595_2 = all_523_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (674), (706) imply:
% 49.80/7.93 | | | | (724) all_523_1 = all_519_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (719), (723) imply:
% 49.80/7.93 | | | | (725) all_577_1 = all_523_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (715), (719) imply:
% 49.80/7.93 | | | | (726) all_577_1 = all_513_1
% 49.80/7.93 | | | |
% 49.80/7.93 | | | | COMBINE_EQS: (725), (726) imply:
% 49.80/7.94 | | | | (727) all_523_1 = all_513_1
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | SIMP: (727) implies:
% 49.80/7.94 | | | | (728) all_523_1 = all_513_1
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | COMBINE_EQS: (720), (721) imply:
% 49.80/7.94 | | | | (729) all_575_1 = all_447_2
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | SIMP: (729) implies:
% 49.80/7.94 | | | | (730) all_575_1 = all_447_2
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | COMBINE_EQS: (709), (730) imply:
% 49.80/7.94 | | | | (731) all_519_2 = all_447_2
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | SIMP: (731) implies:
% 49.80/7.94 | | | | (732) all_519_2 = all_447_2
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | COMBINE_EQS: (724), (728) imply:
% 49.80/7.94 | | | | (733) all_519_1 = all_513_1
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | SIMP: (733) implies:
% 49.80/7.94 | | | | (734) all_519_1 = all_513_1
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | COMBINE_EQS: (704), (734) imply:
% 49.80/7.94 | | | | (735) all_513_1 = 0
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | COMBINE_EQS: (686), (732) imply:
% 49.80/7.94 | | | | (736) all_447_2 = 0
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | COMBINE_EQS: (587), (713) imply:
% 49.80/7.94 | | | | (737) all_250_0 = 0
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | COMBINE_EQS: (721), (736) imply:
% 49.80/7.94 | | | | (738) all_577_3 = 0
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | COMBINE_EQS: (703), (738) imply:
% 49.80/7.94 | | | | (739) all_631_3 = 0
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | COMBINE_EQS: (711), (735) imply:
% 49.80/7.94 | | | | (740) all_631_2 = 0
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | COMBINE_EQS: (691), (739) imply:
% 49.80/7.94 | | | | (741) all_647_3 = 0
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | COMBINE_EQS: (683), (740) imply:
% 49.80/7.94 | | | | (742) all_647_2 = 0
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | COMBINE_EQS: (696), (710) imply:
% 49.80/7.94 | | | | (743) all_647_1 = all_246_2
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | BETA: splitting (233) gives:
% 49.80/7.94 | | | |
% 49.80/7.94 | | | | Case 1:
% 49.80/7.94 | | | | |
% 49.80/7.94 | | | | | (744) ~ (all_250_3 = 0)
% 49.80/7.94 | | | | |
% 49.80/7.94 | | | | | REDUCE: (529), (744) imply:
% 49.80/7.94 | | | | | (745) $false
% 49.80/7.94 | | | | |
% 49.80/7.94 | | | | | CLOSE: (745) is inconsistent.
% 49.80/7.94 | | | | |
% 49.80/7.94 | | | | Case 2:
% 49.80/7.94 | | | | |
% 49.80/7.94 | | | | | (746) ( ~ (all_250_0 = 0) | all_250_2 = 0) & ( ~ (all_250_2 = 0) |
% 49.80/7.94 | | | | | all_250_0 = 0)
% 49.80/7.94 | | | | |
% 49.80/7.94 | | | | | ALPHA: (746) implies:
% 49.80/7.94 | | | | | (747) ~ (all_250_0 = 0) | all_250_2 = 0
% 49.80/7.94 | | | | |
% 49.80/7.94 | | | | | BETA: splitting (747) gives:
% 49.80/7.94 | | | | |
% 49.80/7.94 | | | | | Case 1:
% 49.80/7.94 | | | | | |
% 49.80/7.94 | | | | | | (748) ~ (all_250_0 = 0)
% 49.80/7.94 | | | | | |
% 49.80/7.94 | | | | | | REDUCE: (737), (748) imply:
% 49.80/7.94 | | | | | | (749) $false
% 49.80/7.94 | | | | | |
% 49.80/7.94 | | | | | | CLOSE: (749) is inconsistent.
% 49.80/7.94 | | | | | |
% 49.80/7.94 | | | | | Case 2:
% 49.80/7.94 | | | | | |
% 49.80/7.94 | | | | | | (750) all_250_2 = 0
% 49.80/7.94 | | | | | |
% 49.80/7.94 | | | | | | COMBINE_EQS: (430), (750) imply:
% 49.80/7.94 | | | | | | (751) all_246_2 = 0
% 49.80/7.94 | | | | | |
% 49.80/7.94 | | | | | | SIMP: (751) implies:
% 49.80/7.94 | | | | | | (752) all_246_2 = 0
% 49.80/7.94 | | | | | |
% 49.80/7.94 | | | | | | COMBINE_EQS: (743), (752) imply:
% 49.80/7.94 | | | | | | (753) all_647_1 = 0
% 49.80/7.94 | | | | | |
% 49.80/7.94 | | | | | | BETA: splitting (658) gives:
% 49.80/7.94 | | | | | |
% 49.80/7.94 | | | | | | Case 1:
% 49.80/7.94 | | | | | | |
% 49.80/7.94 | | | | | | | (754) ~ (all_647_1 = 0)
% 49.80/7.94 | | | | | | |
% 49.80/7.94 | | | | | | | REDUCE: (753), (754) imply:
% 49.80/7.94 | | | | | | | (755) $false
% 49.80/7.94 | | | | | | |
% 49.80/7.94 | | | | | | | CLOSE: (755) is inconsistent.
% 49.80/7.94 | | | | | | |
% 49.80/7.94 | | | | | | Case 2:
% 49.80/7.94 | | | | | | |
% 49.80/7.94 | | | | | | | (756) ~ (all_647_2 = 0) | ~ (all_647_3 = 0) | (( ~ (all_647_0
% 49.80/7.94 | | | | | | | = 0) | all_284_0 = 0) & ( ~ (all_284_0 = 0) |
% 49.80/7.94 | | | | | | | all_647_0 = 0))
% 49.80/7.94 | | | | | | |
% 49.80/7.94 | | | | | | | BETA: splitting (756) gives:
% 49.80/7.94 | | | | | | |
% 49.80/7.94 | | | | | | | Case 1:
% 49.80/7.94 | | | | | | | |
% 49.80/7.94 | | | | | | | | (757) ~ (all_647_2 = 0)
% 49.80/7.94 | | | | | | | |
% 49.80/7.94 | | | | | | | | REDUCE: (742), (757) imply:
% 49.80/7.94 | | | | | | | | (758) $false
% 49.80/7.94 | | | | | | | |
% 49.80/7.94 | | | | | | | | CLOSE: (758) is inconsistent.
% 49.80/7.94 | | | | | | | |
% 49.80/7.94 | | | | | | | Case 2:
% 49.80/7.94 | | | | | | | |
% 49.80/7.94 | | | | | | | | (759) ~ (all_647_3 = 0) | (( ~ (all_647_0 = 0) | all_284_0 =
% 49.80/7.94 | | | | | | | | 0) & ( ~ (all_284_0 = 0) | all_647_0 = 0))
% 49.80/7.94 | | | | | | | |
% 49.80/7.94 | | | | | | | | BETA: splitting (759) gives:
% 49.80/7.94 | | | | | | | |
% 49.80/7.94 | | | | | | | | Case 1:
% 49.80/7.94 | | | | | | | | |
% 49.80/7.94 | | | | | | | | | (760) ~ (all_647_3 = 0)
% 49.80/7.94 | | | | | | | | |
% 49.80/7.94 | | | | | | | | | REDUCE: (741), (760) imply:
% 49.80/7.94 | | | | | | | | | (761) $false
% 49.80/7.94 | | | | | | | | |
% 49.80/7.94 | | | | | | | | | CLOSE: (761) is inconsistent.
% 49.80/7.94 | | | | | | | | |
% 49.80/7.94 | | | | | | | | Case 2:
% 49.80/7.94 | | | | | | | | |
% 49.80/7.94 | | | | | | | | | (762) ( ~ (all_647_0 = 0) | all_284_0 = 0) & ( ~ (all_284_0
% 49.80/7.94 | | | | | | | | | = 0) | all_647_0 = 0)
% 49.80/7.94 | | | | | | | | |
% 49.80/7.94 | | | | | | | | | ALPHA: (762) implies:
% 49.80/7.94 | | | | | | | | | (763) ~ (all_284_0 = 0) | all_647_0 = 0
% 49.80/7.94 | | | | | | | | |
% 49.80/7.94 | | | | | | | | | BETA: splitting (763) gives:
% 49.80/7.94 | | | | | | | | |
% 49.80/7.94 | | | | | | | | | Case 1:
% 49.80/7.94 | | | | | | | | | |
% 49.80/7.94 | | | | | | | | | | (764) ~ (all_284_0 = 0)
% 49.80/7.94 | | | | | | | | | |
% 49.80/7.94 | | | | | | | | | | GROUND_INST: instantiating (25) with all_42_1, all_284_0,
% 49.80/7.94 | | | | | | | | | | simplifying with (45), (659) gives:
% 49.80/7.94 | | | | | | | | | | (765) all_284_0 = 0
% 49.80/7.94 | | | | | | | | | |
% 49.80/7.94 | | | | | | | | | | REDUCE: (764), (765) imply:
% 49.80/7.94 | | | | | | | | | | (766) $false
% 49.80/7.94 | | | | | | | | | |
% 49.80/7.94 | | | | | | | | | | CLOSE: (766) is inconsistent.
% 49.80/7.94 | | | | | | | | | |
% 49.80/7.94 | | | | | | | | | Case 2:
% 49.80/7.94 | | | | | | | | | |
% 49.80/7.94 | | | | | | | | | | (767) all_647_0 = 0
% 49.80/7.94 | | | | | | | | | |
% 49.80/7.94 | | | | | | | | | | COMBINE_EQS: (697), (767) imply:
% 49.80/7.94 | | | | | | | | | | (768) all_42_0 = 0
% 49.80/7.94 | | | | | | | | | |
% 49.80/7.94 | | | | | | | | | | REDUCE: (44), (768) imply:
% 49.80/7.94 | | | | | | | | | | (769) $false
% 49.80/7.94 | | | | | | | | | |
% 49.80/7.94 | | | | | | | | | | CLOSE: (769) is inconsistent.
% 49.80/7.94 | | | | | | | | | |
% 49.80/7.94 | | | | | | | | | End of split
% 49.80/7.94 | | | | | | | | |
% 49.80/7.94 | | | | | | | | End of split
% 49.80/7.94 | | | | | | | |
% 49.80/7.94 | | | | | | | End of split
% 49.80/7.94 | | | | | | |
% 49.80/7.94 | | | | | | End of split
% 49.80/7.94 | | | | | |
% 49.80/7.94 | | | | | End of split
% 49.80/7.94 | | | | |
% 49.80/7.94 | | | | End of split
% 49.80/7.94 | | | |
% 49.80/7.95 | | | End of split
% 49.80/7.95 | | |
% 49.80/7.95 | | End of split
% 49.80/7.95 | |
% 49.80/7.95 | End of split
% 49.80/7.95 |
% 49.80/7.95 End of proof
% 49.80/7.95 % SZS output end Proof for theBenchmark
% 49.80/7.95
% 49.80/7.95 7345ms
%------------------------------------------------------------------------------