TSTP Solution File: SEU268+2 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU268+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:43:46 EDT 2023
% Result : Theorem 212.99s 29.65s
% Output : Proof 214.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU268+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Wed Aug 23 16:20:16 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 8.02/1.86 Prover 1: Preprocessing ...
% 8.02/1.87 Prover 0: Preprocessing ...
% 8.02/1.87 Prover 6: Preprocessing ...
% 8.02/1.87 Prover 3: Preprocessing ...
% 8.02/1.87 Prover 2: Preprocessing ...
% 8.02/1.88 Prover 4: Preprocessing ...
% 8.02/1.90 Prover 5: Preprocessing ...
% 24.64/4.12 Prover 1: Warning: ignoring some quantifiers
% 26.68/4.40 Prover 1: Constructing countermodel ...
% 27.18/4.44 Prover 3: Warning: ignoring some quantifiers
% 27.34/4.47 Prover 3: Constructing countermodel ...
% 27.34/4.47 Prover 6: Proving ...
% 27.95/4.56 Prover 5: Proving ...
% 34.93/5.55 Prover 2: Proving ...
% 47.51/7.20 Prover 4: Warning: ignoring some quantifiers
% 49.01/7.40 Prover 4: Constructing countermodel ...
% 58.36/8.62 Prover 0: Proving ...
% 71.65/10.52 Prover 2: stopped
% 71.65/10.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.86/10.81 Prover 7: Preprocessing ...
% 79.82/11.47 Prover 7: Warning: ignoring some quantifiers
% 80.52/11.55 Prover 7: Constructing countermodel ...
% 98.23/13.96 Prover 5: stopped
% 98.23/13.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 100.15/14.20 Prover 8: Preprocessing ...
% 103.28/14.63 Prover 8: Warning: ignoring some quantifiers
% 104.04/14.67 Prover 8: Constructing countermodel ...
% 113.35/15.96 Prover 1: stopped
% 113.35/15.96 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 115.72/16.21 Prover 9: Preprocessing ...
% 127.99/17.86 Prover 6: stopped
% 128.15/17.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 130.48/18.20 Prover 9: Warning: ignoring some quantifiers
% 130.48/18.22 Prover 10: Preprocessing ...
% 130.48/18.23 Prover 9: Constructing countermodel ...
% 134.12/18.69 Prover 10: Warning: ignoring some quantifiers
% 134.87/18.76 Prover 10: Constructing countermodel ...
% 200.38/27.99 Prover 4: stopped
% 200.38/27.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 208.03/29.11 Prover 11: Preprocessing ...
% 212.38/29.62 Prover 8: Found proof (size 367)
% 212.38/29.62 Prover 8: proved (15542ms)
% 212.38/29.62 Prover 9: stopped
% 212.38/29.62 Prover 11: stopped
% 212.38/29.63 Prover 3: stopped
% 212.99/29.63 Prover 7: stopped
% 212.99/29.64 Prover 10: stopped
% 212.99/29.65 Prover 0: stopped
% 212.99/29.65
% 212.99/29.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 212.99/29.65
% 213.20/29.68 % SZS output start Proof for theBenchmark
% 213.20/29.69 Assumptions after simplification:
% 213.20/29.69 ---------------------------------
% 213.20/29.69
% 213.20/29.69 (cc2_funct_1)
% 213.20/29.72 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 213.20/29.72 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) =
% 213.20/29.72 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 213.20/29.72
% 213.20/29.72 (d10_xboole_0)
% 213.20/29.72 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ $i(v1) |
% 213.20/29.72 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0: $i]
% 213.20/29.72 : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0))
% 213.20/29.72
% 213.20/29.72 (d12_funct_1)
% 213.20/29.73 ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 213.20/29.73 : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ (v1 = 0) | ( ?
% 213.20/29.73 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~
% 213.20/29.73 (relation_image(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i]
% 213.20/29.73 : ? [v7: any] : (in(v6, v3) = v7 & $i(v6) & ( ~ (v7 = 0) | ! [v8:
% 213.20/29.73 $i] : ( ~ (in(v8, v2) = 0) | ~ $i(v8) | ? [v9: any] : ?
% 213.20/29.73 [v10: $i] : (apply(v0, v8) = v10 & in(v8, v4) = v9 & $i(v10) &
% 213.20/29.73 ( ~ (v10 = v6) | ~ (v9 = 0))))) & (v7 = 0 | ? [v8: $i] :
% 213.20/29.73 (apply(v0, v8) = v6 & in(v8, v4) = 0 & in(v8, v2) = 0 &
% 213.20/29.73 $i(v8))))) & ! [v3: $i] : ! [v4: $i] : ( ~
% 213.20/29.73 (relation_image(v0, v3) = v4) | ~ $i(v4) | ~ $i(v3) | ( ! [v5: $i]
% 213.20/29.73 : ! [v6: int] : (v6 = 0 | ~ (in(v5, v4) = v6) | ~ $i(v5) | !
% 213.20/29.73 [v7: $i] : ( ~ (in(v7, v2) = 0) | ~ $i(v7) | ? [v8: any] : ?
% 213.20/29.73 [v9: $i] : (apply(v0, v7) = v9 & in(v7, v3) = v8 & $i(v9) & (
% 213.20/29.73 ~ (v9 = v5) | ~ (v8 = 0))))) & ! [v5: $i] : ( ~ (in(v5,
% 213.20/29.73 v4) = 0) | ~ $i(v5) | ? [v6: $i] : (apply(v0, v6) = v5 &
% 213.20/29.73 in(v6, v3) = 0 & in(v6, v2) = 0 & $i(v6)))))))))
% 213.20/29.73
% 213.20/29.73 (d13_funct_1)
% 213.20/29.73 ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 213.20/29.74 : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ (v1 = 0) | ( ?
% 213.20/29.74 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~
% 213.20/29.74 (relation_inverse_image(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ?
% 213.20/29.74 [v6: $i] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: any]
% 213.20/29.74 : (apply(v0, v6) = v9 & in(v9, v4) = v10 & in(v6, v3) = v7 & in(v6,
% 213.20/29.74 v2) = v8 & $i(v9) & $i(v6) & ( ~ (v10 = 0) | ~ (v8 = 0) | ~
% 213.20/29.74 (v7 = 0)) & (v7 = 0 | (v10 = 0 & v8 = 0)))) & ! [v3: $i] : !
% 213.20/29.74 [v4: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ $i(v4) | ~
% 213.20/29.74 $i(v3) | ( ! [v5: $i] : ! [v6: $i] : ! [v7: any] : ( ~ (apply(v0,
% 213.20/29.74 v5) = v6) | ~ (in(v6, v3) = v7) | ~ $i(v5) | ? [v8: any]
% 213.20/29.74 : ? [v9: any] : (in(v5, v4) = v8 & in(v5, v2) = v9 & ( ~ (v8 =
% 213.20/29.74 0) | (v9 = 0 & v7 = 0)))) & ! [v5: $i] : ! [v6: $i] : (
% 213.20/29.74 ~ (apply(v0, v5) = v6) | ~ (in(v6, v3) = 0) | ~ $i(v5) | ?
% 213.20/29.74 [v7: any] : ? [v8: any] : (in(v5, v4) = v8 & in(v5, v2) = v7 &
% 213.20/29.74 ( ~ (v7 = 0) | v8 = 0)))))))))
% 213.20/29.74
% 213.20/29.74 (d1_wellord2)
% 213.20/29.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 213.20/29.74 (inclusion_relation(v0) = v2) | ~ (relation_field(v1) = v3) | ~ $i(v1) |
% 213.20/29.74 ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & relation(v1) = v4) | (( ~ (v3 = v0)
% 213.20/29.74 | v2 = v1 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] : ?
% 213.20/29.74 [v8: any] : (subset(v4, v5) = v8 & ordered_pair(v4, v5) = v6 & in(v6,
% 213.20/29.74 v1) = v7 & in(v5, v0) = 0 & in(v4, v0) = 0 & $i(v6) & $i(v5) &
% 213.20/29.74 $i(v4) & ( ~ (v8 = 0) | ~ (v7 = 0)) & (v8 = 0 | v7 = 0))) & ( ~ (v2 =
% 213.20/29.74 v1) | (v3 = v0 & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 213.20/29.74 any] : ( ~ (ordered_pair(v4, v5) = v6) | ~ (in(v6, v1) = v7) | ~
% 213.20/29.74 $i(v5) | ~ $i(v4) | ? [v8: any] : ? [v9: any] : ? [v10: any] :
% 213.20/29.74 (subset(v4, v5) = v10 & in(v5, v0) = v9 & in(v4, v0) = v8 & ( ~ (v9
% 213.20/29.74 = 0) | ~ (v8 = 0) | (( ~ (v10 = 0) | v7 = 0) & ( ~ (v7 = 0) |
% 213.20/29.74 v10 = 0)))))))))
% 213.20/29.74
% 213.20/29.74 (d4_funct_1)
% 213.20/29.74 $i(empty_set) & ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1:
% 213.20/29.74 any] : ? [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) &
% 213.20/29.74 ( ~ (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : (
% 213.20/29.74 ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = v6) | ~ $i(v4) |
% 213.20/29.74 ~ $i(v3) | ? [v7: any] : ? [v8: $i] : (apply(v0, v3) = v8 & in(v3,
% 213.20/29.74 v2) = v7 & $i(v8) & ( ~ (v7 = 0) | (( ~ (v8 = v4) | v6 = 0) & (
% 213.20/29.74 ~ (v6 = 0) | v8 = v4))))) & ? [v3: $i] : ! [v4: $i] : !
% 213.20/29.74 [v5: int] : (v5 = 0 | ~ (in(v4, v2) = v5) | ~ $i(v4) | ~ $i(v3) |
% 213.20/29.74 ? [v6: $i] : (apply(v0, v4) = v6 & $i(v6) & ( ~ (v6 = v3) | v3 =
% 213.20/29.74 empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set)))))))
% 213.20/29.74
% 213.20/29.74 (d4_relat_1)
% 213.20/29.75 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 213.20/29.75 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~
% 213.20/29.75 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~
% 213.20/29.75 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) =
% 213.20/29.75 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i]
% 213.20/29.75 : ? [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6)
% 213.20/29.75 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0
% 213.20/29.75 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 213.20/29.75 (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) &
% 213.20/29.75 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 213.20/29.75 $i] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) &
% 213.20/29.75 $i(v3)))))))
% 213.20/29.75
% 213.20/29.75 (d5_funct_1)
% 213.20/29.75 ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 213.20/29.75 : ? [v3: $i] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 &
% 213.20/29.75 relation(v0) = v1 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ( ! [v4: $i] : !
% 213.20/29.75 [v5: int] : (v5 = 0 | ~ (in(v4, v2) = v5) | ~ $i(v4) | ! [v6: $i] :
% 213.20/29.75 ( ~ (in(v6, v3) = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v4) &
% 213.20/29.75 apply(v0, v6) = v7 & $i(v7)))) & ! [v4: $i] : ( ~ (in(v4, v2) =
% 213.20/29.75 0) | ~ $i(v4) | ? [v5: $i] : (apply(v0, v5) = v4 & in(v5, v3) =
% 213.20/29.75 0 & $i(v5))) & ? [v4: $i] : (v4 = v2 | ~ $i(v4) | ? [v5: $i] :
% 213.20/29.75 ? [v6: any] : (in(v5, v4) = v6 & $i(v5) & ( ~ (v6 = 0) | ! [v7: $i]
% 213.20/29.75 : ( ~ (in(v7, v3) = 0) | ~ $i(v7) | ? [v8: $i] : ( ~ (v8 = v5)
% 213.20/29.75 & apply(v0, v7) = v8 & $i(v8)))) & (v6 = 0 | ? [v7: $i] :
% 213.20/29.75 (apply(v0, v7) = v5 & in(v7, v3) = 0 & $i(v7)))))))))
% 213.20/29.75
% 213.20/29.75 (d5_relat_1)
% 213.20/29.75 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 213.20/29.75 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~
% 213.20/29.75 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~
% 213.20/29.75 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) =
% 213.20/29.75 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i]
% 213.20/29.75 : ? [v6: $i] : (ordered_pair(v5, v3) = v6 & in(v6, v0) = 0 & $i(v6)
% 213.20/29.75 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0
% 213.20/29.75 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 213.20/29.75 (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) &
% 213.20/29.75 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 213.20/29.75 $i] : (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0 & $i(v4) &
% 213.20/29.75 $i(v3)))))))
% 213.20/29.75
% 213.20/29.75 (d7_wellord1)
% 213.20/29.76 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ?
% 213.20/29.76 [v2: int] : ( ~ (v2 = 0) & relation(v0) = v2) | ! [v2: $i] : ! [v3: $i] :
% 213.20/29.76 ( ~ (relation_field(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) &
% 213.20/29.76 relation(v2) = v4) | ! [v4: $i] : ! [v5: any] : ( ~
% 213.20/29.76 (relation_isomorphism(v0, v2, v4) = v5) | ~ $i(v4) | ? [v6: any] : ?
% 213.20/29.76 [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: any] :
% 213.20/29.76 (relation_rng(v4) = v9 & relation_dom(v4) = v8 & one_to_one(v4) = v10 &
% 213.20/29.76 relation(v4) = v6 & function(v4) = v7 & $i(v9) & $i(v8) & ( ~ (v7 = 0)
% 213.20/29.76 | ~ (v6 = 0) | (( ~ (v10 = 0) | ~ (v9 = v3) | ~ (v8 = v1) | v5 =
% 213.20/29.76 0 | ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: any] :
% 213.20/29.76 ? [v15: any] : ? [v16: any] : ? [v17: $i] : ? [v18: $i] : ?
% 213.20/29.76 [v19: $i] : ? [v20: any] : (apply(v4, v12) = v18 & apply(v4,
% 213.20/29.76 v11) = v17 & ordered_pair(v17, v18) = v19 &
% 213.20/29.76 ordered_pair(v11, v12) = v13 & in(v19, v2) = v20 & in(v13, v0)
% 213.20/29.76 = v14 & in(v12, v1) = v16 & in(v11, v1) = v15 & $i(v19) &
% 213.20/29.76 $i(v18) & $i(v17) & $i(v13) & $i(v12) & $i(v11) & ( ~ (v20 =
% 213.20/29.76 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0)) & (v14 =
% 213.20/29.76 0 | (v20 = 0 & v16 = 0 & v15 = 0)))) & ( ~ (v5 = 0) | (v10 =
% 213.20/29.76 0 & v9 = v3 & v8 = v1 & ! [v11: $i] : ! [v12: $i] : ! [v13:
% 213.20/29.76 $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: any] : ( ~
% 213.20/29.76 (apply(v4, v12) = v14) | ~ (apply(v4, v11) = v13) | ~
% 213.20/29.76 (ordered_pair(v13, v14) = v15) | ~ (in(v15, v2) = v16) | ~
% 213.20/29.76 $i(v12) | ~ $i(v11) | ? [v17: $i] : ? [v18: any] : ?
% 213.20/29.76 [v19: any] : ? [v20: any] : (ordered_pair(v11, v12) = v17 &
% 213.20/29.76 in(v17, v0) = v18 & in(v12, v1) = v20 & in(v11, v1) = v19
% 213.20/29.76 & $i(v17) & ( ~ (v18 = 0) | (v20 = 0 & v19 = 0 & v16 =
% 213.20/29.76 0)))) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] :
% 213.20/29.76 ! [v14: $i] : ! [v15: $i] : ( ~ (apply(v4, v12) = v14) | ~
% 213.20/29.76 (apply(v4, v11) = v13) | ~ (ordered_pair(v13, v14) = v15) |
% 213.20/29.76 ~ (in(v15, v2) = 0) | ~ $i(v12) | ~ $i(v11) | ? [v16:
% 213.20/29.76 any] : ? [v17: any] : ? [v18: $i] : ? [v19: any] :
% 213.20/29.76 (ordered_pair(v11, v12) = v18 & in(v18, v0) = v19 & in(v12,
% 213.20/29.76 v1) = v17 & in(v11, v1) = v16 & $i(v18) & ( ~ (v17 = 0)
% 213.20/29.76 | ~ (v16 = 0) | v19 = 0)))))))))))
% 213.20/29.76
% 213.20/29.76 (d8_funct_1)
% 213.20/29.76 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 213.20/29.76 any] : ? [v3: any] : ? [v4: $i] : (relation_dom(v0) = v4 & relation(v0)
% 213.20/29.76 = v2 & function(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v1
% 213.20/29.76 = 0) | ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~ (in(v6, v4) = 0)
% 213.20/29.76 | ~ (in(v5, v4) = 0) | ~ $i(v6) | ~ $i(v5) | ? [v7: $i] : ?
% 213.20/29.76 [v8: $i] : ( ~ (v8 = v7) & apply(v0, v6) = v8 & apply(v0, v5) = v7
% 213.20/29.76 & $i(v8) & $i(v7)))) & (v1 = 0 | ? [v5: $i] : ? [v6: $i] : ?
% 213.20/29.76 [v7: $i] : ( ~ (v6 = v5) & apply(v0, v6) = v7 & apply(v0, v5) = v7 &
% 213.20/29.76 in(v6, v4) = 0 & in(v5, v4) = 0 & $i(v7) & $i(v6) & $i(v5)))))))
% 213.20/29.76
% 213.20/29.76 (dt_k1_wellord2)
% 213.20/29.76 ! [v0: $i] : ! [v1: $i] : ( ~ (inclusion_relation(v0) = v1) | ~ $i(v0) |
% 213.20/29.76 relation(v1) = 0)
% 213.20/29.76
% 213.20/29.76 (fc5_relat_1)
% 213.20/29.76 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 213.20/29.76 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 &
% 213.20/29.76 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 =
% 213.20/29.76 0))))
% 213.20/29.76
% 213.20/29.76 (fc6_relat_1)
% 213.20/29.76 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 213.20/29.76 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_rng(v0) = v3 &
% 213.20/29.77 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 =
% 213.20/29.77 0))))
% 213.20/29.77
% 213.20/29.77 (l1_wellord1)
% 213.20/29.77 ! [v0: $i] : ! [v1: any] : ( ~ (reflexive(v0) = v1) | ~ $i(v0) | ? [v2:
% 213.20/29.77 any] : ? [v3: $i] : (relation_field(v0) = v3 & relation(v0) = v2 & $i(v3)
% 213.20/29.77 & ( ~ (v2 = 0) | (( ~ (v1 = 0) | ! [v4: $i] : ( ~ (in(v4, v3) = 0) | ~
% 213.20/29.77 $i(v4) | ? [v5: $i] : (ordered_pair(v4, v4) = v5 & in(v5, v0) = 0
% 213.20/29.77 & $i(v5)))) & (v1 = 0 | ? [v4: $i] : ? [v5: $i] : ? [v6: int]
% 213.20/29.77 : ( ~ (v6 = 0) & ordered_pair(v4, v4) = v5 & in(v5, v0) = v6 &
% 213.20/29.77 in(v4, v3) = 0 & $i(v5) & $i(v4)))))))
% 213.20/29.77
% 213.20/29.77 (rc1_funct_1)
% 213.20/29.77 ? [v0: $i] : (relation(v0) = 0 & function(v0) = 0 & $i(v0))
% 213.20/29.77
% 213.20/29.77 (rc1_subset_1)
% 213.20/29.77 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 213.20/29.77 [v2: $i] : (powerset(v0) = v2 & $i(v2) & ? [v3: $i] : ? [v4: int] : ( ~
% 213.20/29.77 (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3))))
% 213.20/29.77
% 213.20/29.77 (rc2_relat_1)
% 213.20/29.77 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & relation(v0) = 0 & empty(v0) = v1
% 213.20/29.77 & $i(v0))
% 213.20/29.77
% 213.20/29.77 (rc3_funct_1)
% 213.20/29.77 ? [v0: $i] : (one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0 &
% 213.20/29.77 $i(v0))
% 213.20/29.77
% 213.20/29.77 (rc3_ordinal1)
% 213.20/29.77 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & epsilon_connected(v0) = 0 &
% 213.20/29.77 ordinal(v0) = 0 & epsilon_transitive(v0) = 0 & empty(v0) = v1 & $i(v0))
% 213.20/29.77
% 213.20/29.77 (rc4_funct_1)
% 213.20/29.77 ? [v0: $i] : (relation_empty_yielding(v0) = 0 & relation(v0) = 0 &
% 213.20/29.77 function(v0) = 0 & $i(v0))
% 213.20/29.77
% 213.20/29.77 (t25_relat_1)
% 213.20/29.77 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 213.20/29.77 any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0) = v2 & $i(v3) &
% 213.20/29.77 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~
% 213.20/29.77 (relation_rng(v4) = v5) | ~ (subset(v1, v5) = v6) | ~ $i(v4) | ?
% 213.20/29.77 [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: any] :
% 213.20/29.77 (relation_dom(v4) = v9 & subset(v3, v9) = v10 & subset(v0, v4) = v8 &
% 213.20/29.77 relation(v4) = v7 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = 0 &
% 213.20/29.77 v6 = 0)))))))
% 213.20/29.77
% 213.20/29.77 (t2_wellord2)
% 213.20/29.77 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & reflexive(v1) = v2 &
% 213.20/29.77 inclusion_relation(v0) = v1 & $i(v1) & $i(v0))
% 213.20/29.77
% 213.20/29.77 (t46_relat_1)
% 213.20/29.77 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 213.20/29.77 any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0) = v2 & $i(v3) &
% 213.20/29.77 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ( ~ (relation_dom(v4) = v5) |
% 213.20/29.77 ~ (subset(v1, v5) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ?
% 213.20/29.77 [v8: $i] : (relation_composition(v0, v4) = v7 & relation_dom(v7) = v8
% 213.20/29.77 & relation(v4) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | v8 = v3))))))
% 213.20/29.77
% 213.20/29.77 (t47_relat_1)
% 213.20/29.78 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 213.20/29.78 any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0) = v2 & $i(v3) &
% 213.20/29.78 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ( ~ (relation_rng(v4) = v5) |
% 213.20/29.78 ~ (subset(v3, v5) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ?
% 213.20/29.78 [v8: $i] : (relation_composition(v4, v0) = v7 & relation_rng(v7) = v8
% 213.20/29.78 & relation(v4) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | v8 = v1))))))
% 213.20/29.78
% 213.20/29.78 (t65_relat_1)
% 213.20/29.78 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~
% 213.20/29.78 $i(v0) | ? [v2: any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0)
% 213.20/29.78 = v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 = empty_set) & (
% 213.20/29.78 ~ (v1 = empty_set) | v3 = empty_set)))))
% 213.20/29.78
% 213.20/29.78 (t8_funct_1)
% 213.20/29.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 213.20/29.78 (ordered_pair(v0, v1) = v3) | ~ (in(v3, v2) = v4) | ~ $i(v2) | ~ $i(v1) |
% 213.20/29.78 ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ?
% 213.20/29.78 [v9: $i] : (relation_dom(v2) = v7 & apply(v2, v0) = v9 & relation(v2) = v5 &
% 213.20/29.78 function(v2) = v6 & in(v0, v7) = v8 & $i(v9) & $i(v7) & ( ~ (v6 = 0) | ~
% 213.20/29.78 (v5 = 0) | (( ~ (v9 = v1) | ~ (v8 = 0) | v4 = 0) & ( ~ (v4 = 0) | (v9 =
% 213.20/29.78 v1 & v8 = 0))))))
% 213.20/29.78
% 213.20/29.78 (function-axioms)
% 213.20/29.81 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 213.20/29.81 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) =
% 213.20/29.81 v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0)) & ! [v0: $i] : !
% 213.20/29.81 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 213.20/29.81 (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) =
% 213.20/29.81 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 213.20/29.81 : (v1 = v0 | ~ (relation_rng_as_subset(v4, v3, v2) = v1) | ~
% 213.20/29.81 (relation_rng_as_subset(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 213.20/29.81 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 213.20/29.81 (relation_dom_as_subset(v4, v3, v2) = v1) | ~ (relation_dom_as_subset(v4,
% 213.20/29.81 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 213.20/29.81 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 213.20/29.81 (relation_isomorphism(v4, v3, v2) = v1) | ~ (relation_isomorphism(v4, v3,
% 213.20/29.81 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 213.20/29.81 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_of2(v4, v3,
% 213.20/29.81 v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 213.20/29.81 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 213.20/29.81 (unordered_triple(v4, v3, v2) = v1) | ~ (unordered_triple(v4, v3, v2) =
% 213.20/29.81 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 213.20/29.81 $i] : ! [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~
% 213.20/29.81 (are_equipotent(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 213.20/29.81 ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~
% 213.20/29.81 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 213.20/29.81 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~
% 213.20/29.81 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 213.20/29.81 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~
% 213.20/29.81 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.20/29.81 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~
% 213.20/29.81 (relation_composition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.20/29.81 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~
% 213.20/29.81 (relation_restriction(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 213.20/29.81 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 213.20/29.81 (well_orders(v3, v2) = v1) | ~ (well_orders(v3, v2) = v0)) & ! [v0: $i] :
% 213.20/29.81 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3,
% 213.20/29.81 v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 213.20/29.81 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) =
% 213.20/29.81 v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 213.20/29.81 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 213.20/29.81 (is_well_founded_in(v3, v2) = v1) | ~ (is_well_founded_in(v3, v2) = v0)) &
% 213.20/29.81 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 213.20/29.81 $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) &
% 213.20/29.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 213.20/29.81 (fiber(v3, v2) = v1) | ~ (fiber(v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 213.20/29.81 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 213.20/29.81 (is_reflexive_in(v3, v2) = v1) | ~ (is_reflexive_in(v3, v2) = v0)) & !
% 213.20/29.81 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 213.20/29.81 $i] : (v1 = v0 | ~ (is_transitive_in(v3, v2) = v1) | ~
% 213.20/29.81 (is_transitive_in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 213.20/29.81 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 213.20/29.81 (is_connected_in(v3, v2) = v1) | ~ (is_connected_in(v3, v2) = v0)) & !
% 213.20/29.81 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 213.20/29.81 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) =
% 213.20/29.81 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 213.20/29.81 $i] : ! [v3: $i] : (v1 = v0 | ~ (is_antisymmetric_in(v3, v2) = v1) | ~
% 213.20/29.81 (is_antisymmetric_in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.20/29.81 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) |
% 213.20/29.81 ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 213.20/29.81 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~
% 213.20/29.81 (relation_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 213.20/29.81 ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) &
% 213.20/29.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 213.20/29.81 (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3,
% 213.20/29.81 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 213.20/29.81 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~
% 213.20/29.81 (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 213.20/29.81 $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) =
% 213.20/29.81 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 213.20/29.81 $i] : ! [v3: $i] : (v1 = v0 | ~ (ordinal_subset(v3, v2) = v1) | ~
% 213.20/29.81 (ordinal_subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 213.20/29.81 ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~
% 213.20/29.81 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 213.20/29.81 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3,
% 213.20/29.81 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 213.20/29.81 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 213.20/29.81 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 213.20/29.81 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 213.20/29.81 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 213.20/29.81 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & !
% 213.20/29.81 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 213.20/29.81 $i] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2)
% 213.20/29.81 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 213.20/29.81 $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 213.20/29.81 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 213.20/29.81 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~
% 213.20/29.81 (relation_empty_yielding(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.20/29.81 $i] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) =
% 213.20/29.81 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 213.20/29.81 (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0:
% 213.20/29.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 213.20/29.81 ~ (being_limit_ordinal(v2) = v1) | ~ (being_limit_ordinal(v2) = v0)) & !
% 213.20/29.81 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) |
% 213.20/29.81 ~ (relation_rng(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 213.20/29.81 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (well_ordering(v2) = v1) |
% 213.20/29.81 ~ (well_ordering(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 213.20/29.81 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (reflexive(v2) = v1) | ~
% 213.20/29.81 (reflexive(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 213.20/29.81 ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 213.20/29.81 [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) =
% 213.20/29.81 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 213.20/29.81 $i] : (v1 = v0 | ~ (well_founded_relation(v2) = v1) | ~
% 213.20/29.81 (well_founded_relation(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 213.20/29.81 : (v1 = v0 | ~ (pair_second(v2) = v1) | ~ (pair_second(v2) = v0)) & ! [v0:
% 213.20/29.81 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inclusion_relation(v2) =
% 213.20/29.81 v1) | ~ (inclusion_relation(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 213.20/29.81 [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & !
% 213.20/29.81 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 213.20/29.81 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 213.20/29.81 ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 213.20/29.81 [v2: $i] : (v1 = v0 | ~ (pair_first(v2) = v1) | ~ (pair_first(v2) = v0)) &
% 213.20/29.81 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 213.20/29.81 v0 | ~ (transitive(v2) = v1) | ~ (transitive(v2) = v0)) & ! [v0:
% 213.20/29.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 213.20/29.81 ~ (connected(v2) = v1) | ~ (connected(v2) = v0)) & ! [v0: $i] : ! [v1:
% 213.20/29.81 $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~
% 213.20/29.81 (relation_field(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 213.20/29.81 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (antisymmetric(v2) = v1) |
% 213.20/29.81 ~ (antisymmetric(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 213.20/29.81 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0:
% 213.20/29.81 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (identity_relation(v2) = v1)
% 213.20/29.81 | ~ (identity_relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 213.20/29.81 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~
% 213.20/29.81 (one_to_one(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 213.20/29.81 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0:
% 213.20/29.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 213.20/29.81 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool]
% 213.20/29.81 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 213.20/29.81 (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0:
% 213.20/29.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 213.20/29.81 ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] :
% 213.20/29.81 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 213.20/29.81 (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0:
% 213.20/29.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 213.20/29.81 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool]
% 213.20/29.81 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) |
% 213.20/29.81 ~ (empty(v2) = v0)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 213.20/29.81 MultipleValueBool] : (relation_of2_as_subset(v2, v1, v0) = v3) & ? [v0: $i]
% 213.20/29.81 : ? [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] :
% 213.20/29.81 (relation_isomorphism(v2, v1, v0) = v3) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 213.20/29.81 $i] : ? [v3: MultipleValueBool] : (relation_of2(v2, v1, v0) = v3) & ? [v0:
% 213.20/29.81 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (subset_difference(v2, v1,
% 213.20/29.81 v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 213.20/29.81 : (relation_rng_as_subset(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1:
% 213.20/29.81 $i] : ? [v2: $i] : ? [v3: $i] : (relation_dom_as_subset(v2, v1, v0) = v3 &
% 213.20/29.81 $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 213.20/29.81 (unordered_triple(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : ?
% 213.20/29.81 [v2: MultipleValueBool] : (are_equipotent(v1, v0) = v2) & ? [v0: $i] : ?
% 213.20/29.81 [v1: $i] : ? [v2: MultipleValueBool] : (well_orders(v1, v0) = v2) & ? [v0:
% 213.20/29.81 $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (is_well_founded_in(v1, v0)
% 213.20/29.81 = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] :
% 213.20/29.81 (disjoint(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 213.20/29.81 MultipleValueBool] : (is_reflexive_in(v1, v0) = v2) & ? [v0: $i] : ? [v1:
% 213.20/29.81 $i] : ? [v2: MultipleValueBool] : (is_transitive_in(v1, v0) = v2) & ? [v0:
% 213.20/29.81 $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (is_connected_in(v1, v0) =
% 213.20/29.81 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] :
% 213.20/29.81 (is_antisymmetric_in(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 213.20/29.81 MultipleValueBool] : (subset(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ?
% 213.20/29.81 [v2: MultipleValueBool] : (ordinal_subset(v1, v0) = v2) & ? [v0: $i] : ?
% 213.20/29.81 [v1: $i] : ? [v2: MultipleValueBool] : (element(v1, v0) = v2) & ? [v0: $i] :
% 213.20/29.81 ? [v1: $i] : ? [v2: MultipleValueBool] : (proper_subset(v1, v0) = v2) & ?
% 213.20/29.81 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (in(v1, v0) = v2) & ?
% 213.20/29.81 [v0: $i] : ? [v1: $i] : ? [v2: $i] : (meet_of_subsets(v1, v0) = v2 & $i(v2))
% 213.20/29.81 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (union_of_subsets(v1, v0) = v2 &
% 213.20/29.81 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 213.20/29.81 (complements_of_subsets(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] :
% 213.20/29.81 ? [v2: $i] : (relation_composition(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ?
% 213.20/29.81 [v1: $i] : ? [v2: $i] : (relation_restriction(v1, v0) = v2 & $i(v2)) & ?
% 213.20/29.81 [v0: $i] : ? [v1: $i] : ? [v2: $i] : (subset_complement(v1, v0) = v2 &
% 213.20/29.81 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (set_difference(v1, v0)
% 213.20/29.81 = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (fiber(v1, v0) =
% 213.20/29.81 v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 213.20/29.81 (relation_inverse_image(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] :
% 213.20/29.81 ? [v2: $i] : (relation_rng_restriction(v1, v0) = v2 & $i(v2)) & ? [v0: $i] :
% 213.20/29.81 ? [v1: $i] : ? [v2: $i] : (relation_image(v1, v0) = v2 & $i(v2)) & ? [v0:
% 213.20/29.81 $i] : ? [v1: $i] : ? [v2: $i] : (apply(v1, v0) = v2 & $i(v2)) & ? [v0:
% 213.20/29.81 $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom_restriction(v1, v0) = v2 &
% 213.20/29.81 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) =
% 213.20/29.81 v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 213.20/29.81 (set_intersection2(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ?
% 213.20/29.81 [v2: $i] : (set_union2(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ?
% 213.20/29.81 [v2: $i] : (unordered_pair(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i]
% 213.20/29.81 : ? [v2: $i] : (cartesian_product2(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ?
% 213.20/29.81 [v1: MultipleValueBool] : (relation_empty_yielding(v0) = v1) & ? [v0: $i] :
% 213.20/29.81 ? [v1: MultipleValueBool] : (being_limit_ordinal(v0) = v1) & ? [v0: $i] : ?
% 213.20/29.81 [v1: MultipleValueBool] : (well_ordering(v0) = v1) & ? [v0: $i] : ? [v1:
% 213.20/29.81 MultipleValueBool] : (reflexive(v0) = v1) & ? [v0: $i] : ? [v1:
% 213.20/29.81 MultipleValueBool] : (well_founded_relation(v0) = v1) & ? [v0: $i] : ?
% 213.20/29.81 [v1: MultipleValueBool] : (transitive(v0) = v1) & ? [v0: $i] : ? [v1:
% 213.20/29.81 MultipleValueBool] : (connected(v0) = v1) & ? [v0: $i] : ? [v1:
% 213.20/29.81 MultipleValueBool] : (antisymmetric(v0) = v1) & ? [v0: $i] : ? [v1:
% 213.20/29.81 MultipleValueBool] : (one_to_one(v0) = v1) & ? [v0: $i] : ? [v1:
% 213.20/29.81 MultipleValueBool] : (relation(v0) = v1) & ? [v0: $i] : ? [v1:
% 213.20/29.81 MultipleValueBool] : (epsilon_connected(v0) = v1) & ? [v0: $i] : ? [v1:
% 213.20/29.81 MultipleValueBool] : (ordinal(v0) = v1) & ? [v0: $i] : ? [v1:
% 213.20/29.81 MultipleValueBool] : (epsilon_transitive(v0) = v1) & ? [v0: $i] : ? [v1:
% 213.20/29.81 MultipleValueBool] : (function(v0) = v1) & ? [v0: $i] : ? [v1:
% 213.20/29.81 MultipleValueBool] : (empty(v0) = v1) & ? [v0: $i] : ? [v1: $i] :
% 213.20/29.81 (function_inverse(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] :
% 213.20/29.81 (relation_inverse(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] :
% 213.20/29.81 (relation_rng(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (union(v0) = v1
% 213.20/29.81 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (cast_to_subset(v0) = v1 & $i(v1)) &
% 213.20/29.81 ? [v0: $i] : ? [v1: $i] : (pair_second(v0) = v1 & $i(v1)) & ? [v0: $i] : ?
% 213.20/29.81 [v1: $i] : (inclusion_relation(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i]
% 213.20/29.81 : (set_meet(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (singleton(v0) =
% 213.20/29.81 v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (succ(v0) = v1 & $i(v1)) & ?
% 213.20/29.81 [v0: $i] : ? [v1: $i] : (pair_first(v0) = v1 & $i(v1)) & ? [v0: $i] : ?
% 213.20/29.81 [v1: $i] : (relation_field(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] :
% 213.20/29.81 (relation_dom(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] :
% 213.20/29.81 (identity_relation(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] :
% 213.20/29.81 (powerset(v0) = v1 & $i(v1))
% 213.20/29.81
% 213.20/29.81 Further assumptions not needed in the proof:
% 213.20/29.81 --------------------------------------------
% 213.20/29.81 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_funct_1, cc1_ordinal1,
% 213.20/29.81 cc1_relat_1, cc1_relset_1, cc2_ordinal1, cc3_ordinal1, commutativity_k2_tarski,
% 213.20/29.81 commutativity_k2_xboole_0, commutativity_k3_xboole_0, connectedness_r1_ordinal1,
% 213.20/29.81 d10_relat_1, d11_relat_1, d12_relat_1, d12_relat_2, d13_relat_1, d14_relat_1,
% 213.20/29.81 d14_relat_2, d16_relat_2, d1_enumset1, d1_mcart_1, d1_ordinal1, d1_relat_1,
% 213.20/29.81 d1_relat_2, d1_relset_1, d1_setfam_1, d1_tarski, d1_wellord1, d1_xboole_0,
% 213.20/29.81 d1_zfmisc_1, d2_mcart_1, d2_ordinal1, d2_relat_1, d2_subset_1, d2_tarski,
% 213.20/29.81 d2_wellord1, d2_xboole_0, d2_zfmisc_1, d3_ordinal1, d3_relat_1, d3_tarski,
% 213.20/29.81 d3_wellord1, d3_xboole_0, d4_ordinal1, d4_relat_2, d4_subset_1, d4_tarski,
% 213.20/29.81 d4_wellord1, d4_xboole_0, d5_subset_1, d5_tarski, d5_wellord1, d6_ordinal1,
% 213.20/29.81 d6_relat_1, d6_relat_2, d6_wellord1, d7_relat_1, d7_xboole_0, d8_relat_1,
% 213.20/29.81 d8_relat_2, d8_setfam_1, d8_xboole_0, d9_funct_1, d9_relat_2, dt_k10_relat_1,
% 213.20/29.81 dt_k1_enumset1, dt_k1_funct_1, dt_k1_mcart_1, dt_k1_ordinal1, dt_k1_relat_1,
% 213.20/29.81 dt_k1_setfam_1, dt_k1_tarski, dt_k1_wellord1, dt_k1_xboole_0, dt_k1_zfmisc_1,
% 213.20/29.81 dt_k2_funct_1, dt_k2_mcart_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski,
% 213.20/29.81 dt_k2_wellord1, dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1,
% 213.20/29.81 dt_k3_tarski, dt_k3_xboole_0, dt_k4_relat_1, dt_k4_relset_1, dt_k4_tarski,
% 213.20/29.81 dt_k4_xboole_0, dt_k5_relat_1, dt_k5_relset_1, dt_k5_setfam_1, dt_k6_relat_1,
% 213.20/29.81 dt_k6_setfam_1, dt_k6_subset_1, dt_k7_relat_1, dt_k7_setfam_1, dt_k8_relat_1,
% 213.20/29.81 dt_k9_relat_1, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1,
% 213.20/29.81 existence_m1_relset_1, existence_m1_subset_1, existence_m2_relset_1,
% 213.20/29.81 fc10_relat_1, fc11_relat_1, fc12_relat_1, fc13_relat_1, fc1_funct_1,
% 213.20/29.81 fc1_ordinal1, fc1_relat_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1,
% 213.20/29.81 fc2_funct_1, fc2_ordinal1, fc2_relat_1, fc2_subset_1, fc2_xboole_0, fc3_funct_1,
% 213.20/29.81 fc3_ordinal1, fc3_relat_1, fc3_subset_1, fc3_xboole_0, fc4_funct_1,
% 213.20/29.81 fc4_ordinal1, fc4_relat_1, fc4_subset_1, fc5_funct_1, fc7_relat_1, fc8_relat_1,
% 213.20/29.81 fc9_relat_1, idempotence_k2_xboole_0, idempotence_k3_xboole_0,
% 213.20/29.81 involutiveness_k3_subset_1, involutiveness_k4_relat_1,
% 213.20/29.81 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_zfmisc_1,
% 213.20/29.81 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l29_wellord1, l2_wellord1,
% 213.20/29.81 l2_zfmisc_1, l32_xboole_1, l3_subset_1, l3_wellord1, l3_zfmisc_1, l4_wellord1,
% 213.20/29.81 l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, l82_funct_1,
% 213.20/29.81 rc1_ordinal1, rc1_relat_1, rc1_xboole_0, rc2_funct_1, rc2_ordinal1,
% 213.20/29.81 rc2_subset_1, rc2_xboole_0, rc3_relat_1, redefinition_k4_relset_1,
% 213.20/29.81 redefinition_k5_relset_1, redefinition_k5_setfam_1, redefinition_k6_setfam_1,
% 213.20/29.81 redefinition_k6_subset_1, redefinition_m2_relset_1, redefinition_r1_ordinal1,
% 213.20/29.81 reflexivity_r1_ordinal1, reflexivity_r1_tarski, symmetry_r1_xboole_0,
% 213.20/29.81 t106_zfmisc_1, t10_ordinal1, t10_zfmisc_1, t115_relat_1, t116_relat_1,
% 213.20/29.81 t117_relat_1, t118_relat_1, t118_zfmisc_1, t119_relat_1, t119_zfmisc_1,
% 213.20/29.81 t12_relset_1, t12_xboole_1, t136_zfmisc_1, t140_relat_1, t143_relat_1,
% 213.20/29.81 t144_relat_1, t145_funct_1, t145_relat_1, t146_funct_1, t146_relat_1,
% 213.20/29.81 t147_funct_1, t14_relset_1, t160_relat_1, t166_relat_1, t167_relat_1,
% 213.20/29.81 t16_relset_1, t16_wellord1, t174_relat_1, t178_relat_1, t17_wellord1,
% 213.20/29.81 t17_xboole_1, t18_wellord1, t19_wellord1, t19_xboole_1, t1_boole, t1_subset,
% 213.20/29.81 t1_xboole_1, t1_zfmisc_1, t20_relat_1, t20_wellord1, t21_funct_1, t21_ordinal1,
% 213.20/29.81 t21_relat_1, t21_wellord1, t22_funct_1, t22_relset_1, t22_wellord1, t23_funct_1,
% 213.20/29.81 t23_ordinal1, t23_relset_1, t23_wellord1, t24_ordinal1, t24_wellord1,
% 213.20/29.81 t25_wellord1, t26_xboole_1, t28_xboole_1, t2_boole, t2_subset, t2_tarski,
% 213.20/29.81 t2_xboole_1, t30_relat_1, t31_ordinal1, t31_wellord1, t32_ordinal1,
% 213.20/29.81 t32_wellord1, t33_ordinal1, t33_xboole_1, t33_zfmisc_1, t34_funct_1,
% 213.20/29.81 t35_funct_1, t36_xboole_1, t37_relat_1, t37_xboole_1, t37_zfmisc_1,
% 213.20/29.81 t38_zfmisc_1, t39_wellord1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_ordinal1,
% 213.20/29.81 t3_subset, t3_xboole_0, t3_xboole_1, t40_xboole_1, t41_ordinal1, t42_ordinal1,
% 213.20/29.81 t43_subset_1, t44_relat_1, t45_relat_1, t45_xboole_1, t46_setfam_1,
% 213.20/29.81 t46_zfmisc_1, t47_setfam_1, t48_setfam_1, t48_xboole_1, t49_wellord1, t4_boole,
% 213.20/29.81 t4_subset, t4_xboole_0, t50_subset_1, t53_wellord1, t54_funct_1, t54_subset_1,
% 213.20/29.81 t54_wellord1, t55_funct_1, t56_relat_1, t57_funct_1, t5_subset, t5_wellord1,
% 213.20/29.81 t60_relat_1, t60_xboole_1, t62_funct_1, t63_xboole_1, t64_relat_1, t65_zfmisc_1,
% 213.20/29.81 t68_funct_1, t69_enumset1, t6_boole, t6_zfmisc_1, t70_funct_1, t71_relat_1,
% 213.20/29.81 t72_funct_1, t74_relat_1, t7_boole, t7_mcart_1, t7_tarski, t7_xboole_1,
% 213.20/29.81 t83_xboole_1, t86_relat_1, t88_relat_1, t8_boole, t8_wellord1, t8_xboole_1,
% 213.20/29.81 t8_zfmisc_1, t90_relat_1, t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1,
% 213.20/29.81 t9_tarski, t9_zfmisc_1
% 213.20/29.81
% 213.20/29.81 Those formulas are unsatisfiable:
% 213.20/29.81 ---------------------------------
% 213.20/29.81
% 213.20/29.81 Begin of proof
% 213.20/29.81 |
% 213.20/29.81 | ALPHA: (d10_xboole_0) implies:
% 213.20/29.81 | (1) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~
% 213.20/29.81 | $i(v0))
% 213.20/29.81 |
% 213.20/29.81 | ALPHA: (d4_funct_1) implies:
% 213.20/29.82 | (2) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 213.20/29.82 | [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~
% 213.20/29.82 | (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 213.20/29.82 | any] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = v6)
% 213.20/29.82 | | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? [v8: $i] :
% 213.20/29.82 | (apply(v0, v3) = v8 & in(v3, v2) = v7 & $i(v8) & ( ~ (v7 = 0)
% 213.20/29.82 | | (( ~ (v8 = v4) | v6 = 0) & ( ~ (v6 = 0) | v8 = v4)))))
% 213.20/29.82 | & ? [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~
% 213.20/29.82 | (in(v4, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] :
% 213.20/29.82 | (apply(v0, v4) = v6 & $i(v6) & ( ~ (v6 = v3) | v3 =
% 213.20/29.82 | empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set)))))))
% 213.20/29.82 |
% 213.20/29.82 | ALPHA: (t65_relat_1) implies:
% 213.20/29.82 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 213.20/29.82 | ? [v2: any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0) =
% 213.20/29.82 | v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 =
% 213.20/29.82 | empty_set) & ( ~ (v1 = empty_set) | v3 = empty_set)))))
% 213.20/29.82 |
% 213.20/29.82 | ALPHA: (function-axioms) implies:
% 213.20/29.82 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 213.20/29.82 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 213.20/29.82 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 213.20/29.82 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 213.20/29.82 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 213.20/29.82 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 213.20/29.82 |
% 213.20/29.82 | DELTA: instantiating (rc1_funct_1) with fresh symbol all_437_0 gives:
% 213.20/29.82 | (7) relation(all_437_0) = 0 & function(all_437_0) = 0 & $i(all_437_0)
% 213.20/29.82 |
% 213.20/29.82 | ALPHA: (7) implies:
% 213.20/29.82 | (8) $i(all_437_0)
% 213.20/29.82 | (9) function(all_437_0) = 0
% 213.20/29.82 | (10) relation(all_437_0) = 0
% 213.20/29.82 |
% 213.20/29.82 | DELTA: instantiating (rc2_relat_1) with fresh symbols all_443_0, all_443_1
% 213.20/29.82 | gives:
% 213.20/29.82 | (11) ~ (all_443_0 = 0) & relation(all_443_1) = 0 & empty(all_443_1) =
% 213.20/29.82 | all_443_0 & $i(all_443_1)
% 213.20/29.82 |
% 213.20/29.82 | ALPHA: (11) implies:
% 213.20/29.82 | (12) ~ (all_443_0 = 0)
% 213.20/29.82 | (13) $i(all_443_1)
% 213.20/29.82 | (14) empty(all_443_1) = all_443_0
% 213.20/29.82 | (15) relation(all_443_1) = 0
% 213.20/29.82 |
% 213.20/29.82 | DELTA: instantiating (rc3_funct_1) with fresh symbol all_450_0 gives:
% 213.20/29.82 | (16) one_to_one(all_450_0) = 0 & relation(all_450_0) = 0 &
% 213.20/29.82 | function(all_450_0) = 0 & $i(all_450_0)
% 213.20/29.82 |
% 213.20/29.82 | ALPHA: (16) implies:
% 213.20/29.82 | (17) $i(all_450_0)
% 213.20/29.82 | (18) function(all_450_0) = 0
% 213.20/29.82 | (19) relation(all_450_0) = 0
% 213.20/29.82 | (20) one_to_one(all_450_0) = 0
% 213.20/29.82 |
% 213.20/29.82 | DELTA: instantiating (rc4_funct_1) with fresh symbol all_460_0 gives:
% 213.20/29.82 | (21) relation_empty_yielding(all_460_0) = 0 & relation(all_460_0) = 0 &
% 213.20/29.82 | function(all_460_0) = 0 & $i(all_460_0)
% 213.20/29.82 |
% 213.20/29.82 | ALPHA: (21) implies:
% 213.20/29.82 | (22) $i(all_460_0)
% 213.20/29.82 | (23) function(all_460_0) = 0
% 213.20/29.82 | (24) relation(all_460_0) = 0
% 213.20/29.82 |
% 213.20/29.82 | DELTA: instantiating (t2_wellord2) with fresh symbols all_462_0, all_462_1,
% 213.20/29.82 | all_462_2 gives:
% 213.20/29.82 | (25) ~ (all_462_0 = 0) & reflexive(all_462_1) = all_462_0 &
% 213.20/29.82 | inclusion_relation(all_462_2) = all_462_1 & $i(all_462_1) &
% 213.20/29.82 | $i(all_462_2)
% 213.20/29.82 |
% 213.20/29.82 | ALPHA: (25) implies:
% 213.20/29.82 | (26) ~ (all_462_0 = 0)
% 213.20/29.82 | (27) $i(all_462_2)
% 213.20/29.82 | (28) $i(all_462_1)
% 213.20/29.82 | (29) inclusion_relation(all_462_2) = all_462_1
% 213.20/29.82 | (30) reflexive(all_462_1) = all_462_0
% 213.20/29.82 |
% 213.20/29.82 | DELTA: instantiating (rc3_ordinal1) with fresh symbols all_464_0, all_464_1
% 213.20/29.82 | gives:
% 213.20/29.82 | (31) ~ (all_464_0 = 0) & epsilon_connected(all_464_1) = 0 &
% 213.20/29.82 | ordinal(all_464_1) = 0 & epsilon_transitive(all_464_1) = 0 &
% 213.20/29.82 | empty(all_464_1) = all_464_0 & $i(all_464_1)
% 213.20/29.82 |
% 213.20/29.82 | ALPHA: (31) implies:
% 213.20/29.82 | (32) ~ (all_464_0 = 0)
% 213.20/29.82 | (33) $i(all_464_1)
% 213.20/29.82 | (34) empty(all_464_1) = all_464_0
% 213.20/29.82 |
% 213.20/29.82 | GROUND_INST: instantiating (fc6_relat_1) with all_443_1, all_443_0,
% 213.20/29.82 | simplifying with (13), (14) gives:
% 213.20/29.83 | (35) all_443_0 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 213.20/29.83 | (relation_rng(all_443_1) = v1 & relation(all_443_1) = v0 & empty(v1) =
% 213.20/29.83 | v2 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 213.20/29.83 |
% 213.20/29.83 | GROUND_INST: instantiating (fc5_relat_1) with all_443_1, all_443_0,
% 213.20/29.83 | simplifying with (13), (14) gives:
% 213.20/29.83 | (36) all_443_0 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 213.20/29.83 | (relation_dom(all_443_1) = v1 & relation(all_443_1) = v0 & empty(v1) =
% 213.20/29.83 | v2 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 213.20/29.83 |
% 213.20/29.83 | GROUND_INST: instantiating (rc1_subset_1) with all_464_1, all_464_0,
% 213.20/29.83 | simplifying with (33), (34) gives:
% 213.20/29.83 | (37) all_464_0 = 0 | ? [v0: $i] : (powerset(all_464_1) = v0 & $i(v0) & ?
% 213.20/29.83 | [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 &
% 213.20/29.83 | empty(v1) = v2 & $i(v1)))
% 213.20/29.83 |
% 213.20/29.83 | GROUND_INST: instantiating (d5_funct_1) with all_437_0, simplifying with (8),
% 213.20/29.83 | (9) gives:
% 213.20/29.83 | (38) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (relation_rng(all_437_0) =
% 213.20/29.83 | v1 & relation_dom(all_437_0) = v2 & relation(all_437_0) = v0 &
% 213.20/29.83 | $i(v2) & $i(v1) & ( ~ (v0 = 0) | ( ! [v3: $i] : ! [v4: int] : (v4 =
% 213.20/29.83 | 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ! [v5: $i] : ( ~
% 213.20/29.83 | (in(v5, v2) = 0) | ~ $i(v5) | ? [v6: $i] : ( ~ (v6 = v3) &
% 213.20/29.83 | apply(all_437_0, v5) = v6 & $i(v6)))) & ! [v3: $i] : ( ~
% 213.20/29.83 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(all_437_0,
% 213.20/29.83 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 =
% 213.20/29.83 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: any] : (in(v4, v3) = v5
% 213.20/29.83 | & $i(v4) & ( ~ (v5 = 0) | ! [v6: $i] : ( ~ (in(v6, v2) = 0)
% 213.20/29.83 | | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v4) &
% 213.20/29.83 | apply(all_437_0, v6) = v7 & $i(v7)))) & (v5 = 0 | ?
% 213.20/29.83 | [v6: $i] : (apply(all_437_0, v6) = v4 & in(v6, v2) = 0 &
% 213.20/29.83 | $i(v6))))))))
% 213.20/29.83 |
% 213.20/29.83 | GROUND_INST: instantiating (2) with all_437_0, simplifying with (8), (9)
% 213.20/29.83 | gives:
% 213.20/29.83 | (39) ? [v0: any] : ? [v1: $i] : (relation_dom(all_437_0) = v1 &
% 213.20/29.83 | relation(all_437_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : !
% 213.20/29.83 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (ordered_pair(v2,
% 213.20/29.83 | v3) = v4) | ~ (in(v4, all_437_0) = v5) | ~ $i(v3) | ~
% 213.20/29.83 | $i(v2) | ? [v6: any] : ? [v7: $i] : (apply(all_437_0, v2) =
% 213.20/29.83 | v7 & in(v2, v1) = v6 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 =
% 213.20/29.83 | v3) | v5 = 0) & ( ~ (v5 = 0) | v7 = v3))))) & ?
% 213.20/29.83 | [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v1)
% 213.20/29.83 | = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] :
% 213.20/29.83 | (apply(all_437_0, v3) = v5 & $i(v5) & ( ~ (v5 = v2) | v2 =
% 213.20/29.83 | empty_set) & ( ~ (v2 = empty_set) | v5 = empty_set))))))
% 213.20/29.83 |
% 213.20/29.83 | GROUND_INST: instantiating (d13_funct_1) with all_437_0, simplifying with (8),
% 213.20/29.83 | (9) gives:
% 213.20/29.83 | (40) ? [v0: any] : ? [v1: $i] : (relation_dom(all_437_0) = v1 &
% 213.20/29.83 | relation(all_437_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 213.20/29.83 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 213.20/29.83 | (relation_inverse_image(all_437_0, v3) = v4) | ~ $i(v3) | ~
% 213.20/29.83 | $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8:
% 213.20/29.83 | $i] : ? [v9: any] : (apply(all_437_0, v5) = v8 & in(v8, v3)
% 213.20/29.83 | = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & $i(v5) &
% 213.20/29.83 | ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 | (v9 =
% 213.20/29.83 | 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 213.20/29.83 | (relation_inverse_image(all_437_0, v2) = v3) | ~ $i(v3) | ~
% 213.20/29.83 | $i(v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~
% 213.20/29.83 | (apply(all_437_0, v4) = v5) | ~ (in(v5, v2) = v6) | ~
% 213.20/29.83 | $i(v4) | ? [v7: any] : ? [v8: any] : (in(v4, v3) = v7 &
% 213.20/29.83 | in(v4, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) &
% 213.20/29.83 | ! [v4: $i] : ! [v5: $i] : ( ~ (apply(all_437_0, v4) = v5) |
% 213.20/29.83 | ~ (in(v5, v2) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7:
% 213.20/29.83 | any] : (in(v4, v3) = v7 & in(v4, v1) = v6 & ( ~ (v6 = 0)
% 213.20/29.83 | | v7 = 0))))))))
% 213.20/29.83 |
% 213.20/29.83 | GROUND_INST: instantiating (d12_funct_1) with all_437_0, simplifying with (8),
% 213.20/29.83 | (9) gives:
% 213.20/29.84 | (41) ? [v0: any] : ? [v1: $i] : (relation_dom(all_437_0) = v1 &
% 213.20/29.84 | relation(all_437_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 213.20/29.84 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 213.20/29.84 | (relation_image(all_437_0, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 213.20/29.84 | ? [v5: $i] : ? [v6: any] : (in(v5, v2) = v6 & $i(v5) & ( ~
% 213.20/29.84 | (v6 = 0) | ! [v7: $i] : ( ~ (in(v7, v1) = 0) | ~ $i(v7)
% 213.20/29.84 | | ? [v8: any] : ? [v9: $i] : (apply(all_437_0, v7) =
% 213.20/29.84 | v9 & in(v7, v3) = v8 & $i(v9) & ( ~ (v9 = v5) | ~ (v8
% 213.20/29.84 | = 0))))) & (v6 = 0 | ? [v7: $i] :
% 213.20/29.84 | (apply(all_437_0, v7) = v5 & in(v7, v3) = 0 & in(v7, v1) =
% 213.20/29.84 | 0 & $i(v7))))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 213.20/29.84 | (relation_image(all_437_0, v2) = v3) | ~ $i(v3) | ~ $i(v2) |
% 213.20/29.84 | ( ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v3) = v5) |
% 213.20/29.84 | ~ $i(v4) | ! [v6: $i] : ( ~ (in(v6, v1) = 0) | ~ $i(v6)
% 213.20/29.84 | | ? [v7: any] : ? [v8: $i] : (apply(all_437_0, v6) =
% 213.20/29.84 | v8 & in(v6, v2) = v7 & $i(v8) & ( ~ (v8 = v4) | ~ (v7
% 213.20/29.84 | = 0))))) & ! [v4: $i] : ( ~ (in(v4, v3) = 0) | ~
% 213.20/29.84 | $i(v4) | ? [v5: $i] : (apply(all_437_0, v5) = v4 & in(v5,
% 213.20/29.84 | v2) = 0 & in(v5, v1) = 0 & $i(v5))))))))
% 213.20/29.84 |
% 213.20/29.84 | GROUND_INST: instantiating (d5_funct_1) with all_450_0, simplifying with (17),
% 213.20/29.84 | (18) gives:
% 213.20/29.84 | (42) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (relation_rng(all_450_0) =
% 213.20/29.84 | v1 & relation_dom(all_450_0) = v2 & relation(all_450_0) = v0 &
% 213.20/29.84 | $i(v2) & $i(v1) & ( ~ (v0 = 0) | ( ! [v3: $i] : ! [v4: int] : (v4 =
% 213.20/29.84 | 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ! [v5: $i] : ( ~
% 213.20/29.84 | (in(v5, v2) = 0) | ~ $i(v5) | ? [v6: $i] : ( ~ (v6 = v3) &
% 213.20/29.84 | apply(all_450_0, v5) = v6 & $i(v6)))) & ! [v3: $i] : ( ~
% 213.20/29.84 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(all_450_0,
% 213.20/29.84 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 =
% 213.20/29.84 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: any] : (in(v4, v3) = v5
% 213.20/29.84 | & $i(v4) & ( ~ (v5 = 0) | ! [v6: $i] : ( ~ (in(v6, v2) = 0)
% 213.20/29.84 | | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v4) &
% 213.20/29.84 | apply(all_450_0, v6) = v7 & $i(v7)))) & (v5 = 0 | ?
% 213.20/29.84 | [v6: $i] : (apply(all_450_0, v6) = v4 & in(v6, v2) = 0 &
% 213.20/29.84 | $i(v6))))))))
% 213.20/29.84 |
% 213.20/29.84 | GROUND_INST: instantiating (2) with all_450_0, simplifying with (17), (18)
% 213.20/29.84 | gives:
% 213.20/29.84 | (43) ? [v0: any] : ? [v1: $i] : (relation_dom(all_450_0) = v1 &
% 213.20/29.84 | relation(all_450_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : !
% 213.20/29.84 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (ordered_pair(v2,
% 213.20/29.84 | v3) = v4) | ~ (in(v4, all_450_0) = v5) | ~ $i(v3) | ~
% 213.20/29.84 | $i(v2) | ? [v6: any] : ? [v7: $i] : (apply(all_450_0, v2) =
% 213.20/29.84 | v7 & in(v2, v1) = v6 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 =
% 213.20/29.84 | v3) | v5 = 0) & ( ~ (v5 = 0) | v7 = v3))))) & ?
% 213.20/29.84 | [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v1)
% 213.20/29.84 | = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] :
% 213.20/29.84 | (apply(all_450_0, v3) = v5 & $i(v5) & ( ~ (v5 = v2) | v2 =
% 213.20/29.84 | empty_set) & ( ~ (v2 = empty_set) | v5 = empty_set))))))
% 213.20/29.84 |
% 213.20/29.84 | GROUND_INST: instantiating (d13_funct_1) with all_450_0, simplifying with
% 213.20/29.84 | (17), (18) gives:
% 213.20/29.84 | (44) ? [v0: any] : ? [v1: $i] : (relation_dom(all_450_0) = v1 &
% 213.20/29.84 | relation(all_450_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 213.20/29.84 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 213.20/29.84 | (relation_inverse_image(all_450_0, v3) = v4) | ~ $i(v3) | ~
% 213.20/29.84 | $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8:
% 213.20/29.84 | $i] : ? [v9: any] : (apply(all_450_0, v5) = v8 & in(v8, v3)
% 213.20/29.84 | = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & $i(v5) &
% 213.20/29.84 | ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 | (v9 =
% 213.20/29.84 | 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 213.20/29.84 | (relation_inverse_image(all_450_0, v2) = v3) | ~ $i(v3) | ~
% 213.20/29.84 | $i(v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~
% 213.20/29.84 | (apply(all_450_0, v4) = v5) | ~ (in(v5, v2) = v6) | ~
% 213.20/29.84 | $i(v4) | ? [v7: any] : ? [v8: any] : (in(v4, v3) = v7 &
% 213.20/29.84 | in(v4, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) &
% 213.20/29.84 | ! [v4: $i] : ! [v5: $i] : ( ~ (apply(all_450_0, v4) = v5) |
% 213.20/29.84 | ~ (in(v5, v2) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7:
% 213.20/29.84 | any] : (in(v4, v3) = v7 & in(v4, v1) = v6 & ( ~ (v6 = 0)
% 213.20/29.84 | | v7 = 0))))))))
% 213.20/29.84 |
% 213.20/29.84 | GROUND_INST: instantiating (d12_funct_1) with all_450_0, simplifying with
% 213.20/29.84 | (17), (18) gives:
% 213.20/29.85 | (45) ? [v0: any] : ? [v1: $i] : (relation_dom(all_450_0) = v1 &
% 213.20/29.85 | relation(all_450_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 213.20/29.85 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 213.20/29.85 | (relation_image(all_450_0, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 213.20/29.85 | ? [v5: $i] : ? [v6: any] : (in(v5, v2) = v6 & $i(v5) & ( ~
% 213.20/29.85 | (v6 = 0) | ! [v7: $i] : ( ~ (in(v7, v1) = 0) | ~ $i(v7)
% 213.20/29.85 | | ? [v8: any] : ? [v9: $i] : (apply(all_450_0, v7) =
% 213.20/29.85 | v9 & in(v7, v3) = v8 & $i(v9) & ( ~ (v9 = v5) | ~ (v8
% 213.20/29.85 | = 0))))) & (v6 = 0 | ? [v7: $i] :
% 213.20/29.85 | (apply(all_450_0, v7) = v5 & in(v7, v3) = 0 & in(v7, v1) =
% 213.20/29.85 | 0 & $i(v7))))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 213.20/29.85 | (relation_image(all_450_0, v2) = v3) | ~ $i(v3) | ~ $i(v2) |
% 213.20/29.85 | ( ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v3) = v5) |
% 213.20/29.85 | ~ $i(v4) | ! [v6: $i] : ( ~ (in(v6, v1) = 0) | ~ $i(v6)
% 213.20/29.85 | | ? [v7: any] : ? [v8: $i] : (apply(all_450_0, v6) =
% 213.20/29.85 | v8 & in(v6, v2) = v7 & $i(v8) & ( ~ (v8 = v4) | ~ (v7
% 213.20/29.85 | = 0))))) & ! [v4: $i] : ( ~ (in(v4, v3) = 0) | ~
% 213.20/29.85 | $i(v4) | ? [v5: $i] : (apply(all_450_0, v5) = v4 & in(v5,
% 213.20/29.85 | v2) = 0 & in(v5, v1) = 0 & $i(v5))))))))
% 213.20/29.85 |
% 213.20/29.85 | GROUND_INST: instantiating (d5_funct_1) with all_460_0, simplifying with (22),
% 213.20/29.85 | (23) gives:
% 213.20/29.85 | (46) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (relation_rng(all_460_0) =
% 213.20/29.85 | v1 & relation_dom(all_460_0) = v2 & relation(all_460_0) = v0 &
% 213.20/29.85 | $i(v2) & $i(v1) & ( ~ (v0 = 0) | ( ! [v3: $i] : ! [v4: int] : (v4 =
% 213.20/29.85 | 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ! [v5: $i] : ( ~
% 213.20/29.85 | (in(v5, v2) = 0) | ~ $i(v5) | ? [v6: $i] : ( ~ (v6 = v3) &
% 213.20/29.85 | apply(all_460_0, v5) = v6 & $i(v6)))) & ! [v3: $i] : ( ~
% 213.20/29.85 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(all_460_0,
% 213.20/29.85 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 =
% 213.20/29.85 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: any] : (in(v4, v3) = v5
% 213.20/29.85 | & $i(v4) & ( ~ (v5 = 0) | ! [v6: $i] : ( ~ (in(v6, v2) = 0)
% 213.20/29.85 | | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v4) &
% 213.20/29.85 | apply(all_460_0, v6) = v7 & $i(v7)))) & (v5 = 0 | ?
% 213.20/29.85 | [v6: $i] : (apply(all_460_0, v6) = v4 & in(v6, v2) = 0 &
% 213.20/29.85 | $i(v6))))))))
% 213.20/29.85 |
% 213.20/29.85 | GROUND_INST: instantiating (2) with all_460_0, simplifying with (22), (23)
% 213.20/29.85 | gives:
% 213.20/29.85 | (47) ? [v0: any] : ? [v1: $i] : (relation_dom(all_460_0) = v1 &
% 213.20/29.85 | relation(all_460_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : !
% 213.20/29.85 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (ordered_pair(v2,
% 213.20/29.85 | v3) = v4) | ~ (in(v4, all_460_0) = v5) | ~ $i(v3) | ~
% 213.20/29.85 | $i(v2) | ? [v6: any] : ? [v7: $i] : (apply(all_460_0, v2) =
% 213.20/29.85 | v7 & in(v2, v1) = v6 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 =
% 213.20/29.85 | v3) | v5 = 0) & ( ~ (v5 = 0) | v7 = v3))))) & ?
% 213.20/29.85 | [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v1)
% 213.20/29.85 | = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] :
% 213.20/29.85 | (apply(all_460_0, v3) = v5 & $i(v5) & ( ~ (v5 = v2) | v2 =
% 213.20/29.85 | empty_set) & ( ~ (v2 = empty_set) | v5 = empty_set))))))
% 213.20/29.85 |
% 213.20/29.85 | GROUND_INST: instantiating (d13_funct_1) with all_460_0, simplifying with
% 213.20/29.85 | (22), (23) gives:
% 213.20/29.85 | (48) ? [v0: any] : ? [v1: $i] : (relation_dom(all_460_0) = v1 &
% 213.20/29.85 | relation(all_460_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 213.20/29.85 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 213.20/29.85 | (relation_inverse_image(all_460_0, v3) = v4) | ~ $i(v3) | ~
% 213.20/29.85 | $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8:
% 213.20/29.85 | $i] : ? [v9: any] : (apply(all_460_0, v5) = v8 & in(v8, v3)
% 213.20/29.85 | = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & $i(v5) &
% 213.20/29.85 | ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 | (v9 =
% 213.20/29.85 | 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 213.20/29.85 | (relation_inverse_image(all_460_0, v2) = v3) | ~ $i(v3) | ~
% 213.20/29.85 | $i(v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~
% 213.20/29.85 | (apply(all_460_0, v4) = v5) | ~ (in(v5, v2) = v6) | ~
% 213.20/29.85 | $i(v4) | ? [v7: any] : ? [v8: any] : (in(v4, v3) = v7 &
% 213.20/29.85 | in(v4, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) &
% 213.20/29.85 | ! [v4: $i] : ! [v5: $i] : ( ~ (apply(all_460_0, v4) = v5) |
% 213.20/29.85 | ~ (in(v5, v2) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7:
% 213.20/29.85 | any] : (in(v4, v3) = v7 & in(v4, v1) = v6 & ( ~ (v6 = 0)
% 213.20/29.85 | | v7 = 0))))))))
% 213.20/29.85 |
% 213.20/29.85 | GROUND_INST: instantiating (d12_funct_1) with all_460_0, simplifying with
% 213.20/29.85 | (22), (23) gives:
% 213.20/29.85 | (49) ? [v0: any] : ? [v1: $i] : (relation_dom(all_460_0) = v1 &
% 213.99/29.85 | relation(all_460_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 213.99/29.85 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 213.99/29.85 | (relation_image(all_460_0, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 213.99/29.85 | ? [v5: $i] : ? [v6: any] : (in(v5, v2) = v6 & $i(v5) & ( ~
% 213.99/29.85 | (v6 = 0) | ! [v7: $i] : ( ~ (in(v7, v1) = 0) | ~ $i(v7)
% 213.99/29.85 | | ? [v8: any] : ? [v9: $i] : (apply(all_460_0, v7) =
% 213.99/29.85 | v9 & in(v7, v3) = v8 & $i(v9) & ( ~ (v9 = v5) | ~ (v8
% 213.99/29.85 | = 0))))) & (v6 = 0 | ? [v7: $i] :
% 213.99/29.85 | (apply(all_460_0, v7) = v5 & in(v7, v3) = 0 & in(v7, v1) =
% 213.99/29.85 | 0 & $i(v7))))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 213.99/29.85 | (relation_image(all_460_0, v2) = v3) | ~ $i(v3) | ~ $i(v2) |
% 213.99/29.85 | ( ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v3) = v5) |
% 213.99/29.85 | ~ $i(v4) | ! [v6: $i] : ( ~ (in(v6, v1) = 0) | ~ $i(v6)
% 213.99/29.85 | | ? [v7: any] : ? [v8: $i] : (apply(all_460_0, v6) =
% 213.99/29.85 | v8 & in(v6, v2) = v7 & $i(v8) & ( ~ (v8 = v4) | ~ (v7
% 213.99/29.85 | = 0))))) & ! [v4: $i] : ( ~ (in(v4, v3) = 0) | ~
% 213.99/29.85 | $i(v4) | ? [v5: $i] : (apply(all_460_0, v5) = v4 & in(v5,
% 213.99/29.85 | v2) = 0 & in(v5, v1) = 0 & $i(v5))))))))
% 213.99/29.85 |
% 213.99/29.85 | GROUND_INST: instantiating (d8_funct_1) with all_450_0, 0, simplifying with
% 213.99/29.85 | (17), (20) gives:
% 213.99/29.86 | (50) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (relation_dom(all_450_0) =
% 213.99/29.86 | v2 & relation(all_450_0) = v0 & function(all_450_0) = v1 & $i(v2) &
% 213.99/29.86 | ( ~ (v1 = 0) | ~ (v0 = 0) | ! [v3: $i] : ! [v4: $i] : (v4 = v3 |
% 213.99/29.86 | ~ (in(v4, v2) = 0) | ~ (in(v3, v2) = 0) | ~ $i(v4) | ~ $i(v3)
% 213.99/29.86 | | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(all_450_0,
% 213.99/29.86 | v4) = v6 & apply(all_450_0, v3) = v5 & $i(v6) & $i(v5)))))
% 213.99/29.86 |
% 213.99/29.86 | GROUND_INST: instantiating (cc2_funct_1) with all_450_0, 0, simplifying with
% 213.99/29.86 | (17), (20) gives:
% 213.99/29.86 | (51) ? [v0: MultipleValueBool] : ? [v1: MultipleValueBool] : ? [v2:
% 213.99/29.86 | MultipleValueBool] : (relation(all_450_0) = v0 & function(all_450_0)
% 213.99/29.86 | = v2 & empty(all_450_0) = v1)
% 213.99/29.86 |
% 213.99/29.86 | GROUND_INST: instantiating (dt_k1_wellord2) with all_462_2, all_462_1,
% 213.99/29.86 | simplifying with (27), (29) gives:
% 213.99/29.86 | (52) relation(all_462_1) = 0
% 213.99/29.86 |
% 213.99/29.86 | GROUND_INST: instantiating (l1_wellord1) with all_462_1, all_462_0,
% 213.99/29.86 | simplifying with (28), (30) gives:
% 213.99/29.86 | (53) ? [v0: any] : ? [v1: $i] : (relation_field(all_462_1) = v1 &
% 213.99/29.86 | relation(all_462_1) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~ (all_462_0 =
% 213.99/29.86 | 0) | ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ?
% 213.99/29.86 | [v3: $i] : (ordered_pair(v2, v2) = v3 & in(v3, all_462_1) =
% 213.99/29.86 | 0 & $i(v3)))) & (all_462_0 = 0 | ? [v2: $i] : ? [v3: $i]
% 213.99/29.86 | : ? [v4: int] : ( ~ (v4 = 0) & ordered_pair(v2, v2) = v3 &
% 213.99/29.86 | in(v3, all_462_1) = v4 & in(v2, v1) = 0 & $i(v3) &
% 213.99/29.86 | $i(v2))))))
% 213.99/29.86 |
% 213.99/29.86 | DELTA: instantiating (51) with fresh symbols all_759_0, all_759_1, all_759_2
% 213.99/29.86 | gives:
% 213.99/29.86 | (54) relation(all_450_0) = all_759_2 & function(all_450_0) = all_759_0 &
% 213.99/29.86 | empty(all_450_0) = all_759_1
% 213.99/29.86 |
% 213.99/29.86 | ALPHA: (54) implies:
% 213.99/29.86 | (55) relation(all_450_0) = all_759_2
% 213.99/29.86 |
% 213.99/29.86 | DELTA: instantiating (50) with fresh symbols all_805_0, all_805_1, all_805_2
% 213.99/29.86 | gives:
% 213.99/29.86 | (56) relation_dom(all_450_0) = all_805_0 & relation(all_450_0) = all_805_2
% 213.99/29.86 | & function(all_450_0) = all_805_1 & $i(all_805_0) & ( ~ (all_805_1 =
% 213.99/29.86 | 0) | ~ (all_805_2 = 0) | ! [v0: $i] : ! [v1: $i] : (v1 = v0 |
% 213.99/29.86 | ~ (in(v1, all_805_0) = 0) | ~ (in(v0, all_805_0) = 0) | ~ $i(v1)
% 213.99/29.86 | | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) &
% 213.99/29.86 | apply(all_450_0, v1) = v3 & apply(all_450_0, v0) = v2 & $i(v3) &
% 213.99/29.86 | $i(v2))))
% 213.99/29.86 |
% 213.99/29.86 | ALPHA: (56) implies:
% 213.99/29.86 | (57) relation(all_450_0) = all_805_2
% 213.99/29.86 |
% 213.99/29.86 | DELTA: instantiating (53) with fresh symbols all_811_0, all_811_1 gives:
% 213.99/29.86 | (58) relation_field(all_462_1) = all_811_0 & relation(all_462_1) =
% 213.99/29.86 | all_811_1 & $i(all_811_0) & ( ~ (all_811_1 = 0) | (( ~ (all_462_0 = 0)
% 213.99/29.86 | | ! [v0: $i] : ( ~ (in(v0, all_811_0) = 0) | ~ $i(v0) | ?
% 213.99/29.86 | [v1: $i] : (ordered_pair(v0, v0) = v1 & in(v1, all_462_1) = 0
% 213.99/29.86 | & $i(v1)))) & (all_462_0 = 0 | ? [v0: $i] : ? [v1: $i] :
% 213.99/29.86 | ? [v2: int] : ( ~ (v2 = 0) & ordered_pair(v0, v0) = v1 & in(v1,
% 213.99/29.86 | all_462_1) = v2 & in(v0, all_811_0) = 0 & $i(v1) &
% 213.99/29.86 | $i(v0)))))
% 213.99/29.86 |
% 213.99/29.86 | ALPHA: (58) implies:
% 213.99/29.86 | (59) relation(all_462_1) = all_811_1
% 213.99/29.86 | (60) relation_field(all_462_1) = all_811_0
% 213.99/29.86 | (61) ~ (all_811_1 = 0) | (( ~ (all_462_0 = 0) | ! [v0: $i] : ( ~ (in(v0,
% 213.99/29.86 | all_811_0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 213.99/29.86 | (ordered_pair(v0, v0) = v1 & in(v1, all_462_1) = 0 & $i(v1)))) &
% 213.99/29.86 | (all_462_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2
% 213.99/29.86 | = 0) & ordered_pair(v0, v0) = v1 & in(v1, all_462_1) = v2 &
% 213.99/29.86 | in(v0, all_811_0) = 0 & $i(v1) & $i(v0))))
% 213.99/29.86 |
% 213.99/29.86 | DELTA: instantiating (47) with fresh symbols all_849_0, all_849_1 gives:
% 213.99/29.86 | (62) relation_dom(all_460_0) = all_849_0 & relation(all_460_0) = all_849_1
% 213.99/29.86 | & $i(all_849_0) & ( ~ (all_849_1 = 0) | ( ! [v0: $i] : ! [v1: $i] :
% 213.99/29.86 | ! [v2: $i] : ! [v3: any] : ( ~ (ordered_pair(v0, v1) = v2) | ~
% 213.99/29.86 | (in(v2, all_460_0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any]
% 213.99/29.86 | : ? [v5: $i] : (apply(all_460_0, v0) = v5 & in(v0, all_849_0) =
% 213.99/29.86 | v4 & $i(v5) & ( ~ (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~
% 213.99/29.86 | (v3 = 0) | v5 = v1))))) & ? [v0: $i] : ! [v1: $i] : !
% 213.99/29.86 | [v2: int] : (v2 = 0 | ~ (in(v1, all_849_0) = v2) | ~ $i(v1) | ~
% 213.99/29.86 | $i(v0) | ? [v3: $i] : (apply(all_460_0, v1) = v3 & $i(v3) & ( ~
% 213.99/29.86 | (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 =
% 213.99/29.86 | empty_set)))))
% 213.99/29.86 |
% 213.99/29.86 | ALPHA: (62) implies:
% 213.99/29.86 | (63) relation(all_460_0) = all_849_1
% 213.99/29.86 | (64) relation_dom(all_460_0) = all_849_0
% 213.99/29.86 |
% 213.99/29.86 | DELTA: instantiating (39) with fresh symbols all_851_0, all_851_1 gives:
% 213.99/29.86 | (65) relation_dom(all_437_0) = all_851_0 & relation(all_437_0) = all_851_1
% 213.99/29.86 | & $i(all_851_0) & ( ~ (all_851_1 = 0) | ( ! [v0: $i] : ! [v1: $i] :
% 213.99/29.86 | ! [v2: $i] : ! [v3: any] : ( ~ (ordered_pair(v0, v1) = v2) | ~
% 213.99/29.86 | (in(v2, all_437_0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any]
% 213.99/29.86 | : ? [v5: $i] : (apply(all_437_0, v0) = v5 & in(v0, all_851_0) =
% 213.99/29.86 | v4 & $i(v5) & ( ~ (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~
% 213.99/29.86 | (v3 = 0) | v5 = v1))))) & ? [v0: $i] : ! [v1: $i] : !
% 213.99/29.86 | [v2: int] : (v2 = 0 | ~ (in(v1, all_851_0) = v2) | ~ $i(v1) | ~
% 213.99/29.86 | $i(v0) | ? [v3: $i] : (apply(all_437_0, v1) = v3 & $i(v3) & ( ~
% 213.99/29.86 | (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 =
% 213.99/29.86 | empty_set)))))
% 213.99/29.86 |
% 213.99/29.86 | ALPHA: (65) implies:
% 213.99/29.86 | (66) relation(all_437_0) = all_851_1
% 213.99/29.86 |
% 213.99/29.86 | DELTA: instantiating (43) with fresh symbols all_855_0, all_855_1 gives:
% 213.99/29.87 | (67) relation_dom(all_450_0) = all_855_0 & relation(all_450_0) = all_855_1
% 213.99/29.87 | & $i(all_855_0) & ( ~ (all_855_1 = 0) | ( ! [v0: $i] : ! [v1: $i] :
% 213.99/29.87 | ! [v2: $i] : ! [v3: any] : ( ~ (ordered_pair(v0, v1) = v2) | ~
% 213.99/29.87 | (in(v2, all_450_0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any]
% 213.99/29.87 | : ? [v5: $i] : (apply(all_450_0, v0) = v5 & in(v0, all_855_0) =
% 213.99/29.87 | v4 & $i(v5) & ( ~ (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~
% 213.99/29.87 | (v3 = 0) | v5 = v1))))) & ? [v0: $i] : ! [v1: $i] : !
% 213.99/29.87 | [v2: int] : (v2 = 0 | ~ (in(v1, all_855_0) = v2) | ~ $i(v1) | ~
% 213.99/29.87 | $i(v0) | ? [v3: $i] : (apply(all_450_0, v1) = v3 & $i(v3) & ( ~
% 213.99/29.87 | (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 =
% 213.99/29.87 | empty_set)))))
% 213.99/29.87 |
% 213.99/29.87 | ALPHA: (67) implies:
% 213.99/29.87 | (68) relation(all_450_0) = all_855_1
% 213.99/29.87 |
% 213.99/29.87 | DELTA: instantiating (38) with fresh symbols all_861_0, all_861_1, all_861_2
% 213.99/29.87 | gives:
% 213.99/29.87 | (69) relation_rng(all_437_0) = all_861_1 & relation_dom(all_437_0) =
% 213.99/29.87 | all_861_0 & relation(all_437_0) = all_861_2 & $i(all_861_0) &
% 213.99/29.87 | $i(all_861_1) & ( ~ (all_861_2 = 0) | ( ! [v0: $i] : ! [v1: int] :
% 213.99/29.87 | (v1 = 0 | ~ (in(v0, all_861_1) = v1) | ~ $i(v0) | ! [v2: $i] :
% 213.99/29.87 | ( ~ (in(v2, all_861_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ (v3
% 213.99/29.87 | = v0) & apply(all_437_0, v2) = v3 & $i(v3)))) & ! [v0:
% 213.99/29.87 | $i] : ( ~ (in(v0, all_861_1) = 0) | ~ $i(v0) | ? [v1: $i] :
% 213.99/29.87 | (apply(all_437_0, v1) = v0 & in(v1, all_861_0) = 0 & $i(v1))) &
% 213.99/29.87 | ? [v0: any] : (v0 = all_861_1 | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 213.99/29.87 | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i]
% 213.99/29.87 | : ( ~ (in(v3, all_861_0) = 0) | ~ $i(v3) | ? [v4: $i] : (
% 213.99/29.87 | ~ (v4 = v1) & apply(all_437_0, v3) = v4 & $i(v4)))) &
% 213.99/29.87 | (v2 = 0 | ? [v3: $i] : (apply(all_437_0, v3) = v1 & in(v3,
% 213.99/29.87 | all_861_0) = 0 & $i(v3)))))))
% 213.99/29.87 |
% 213.99/29.87 | ALPHA: (69) implies:
% 213.99/29.87 | (70) $i(all_861_1)
% 213.99/29.87 | (71) relation(all_437_0) = all_861_2
% 213.99/29.87 | (72) relation_rng(all_437_0) = all_861_1
% 213.99/29.87 |
% 213.99/29.87 | DELTA: instantiating (46) with fresh symbols all_865_0, all_865_1, all_865_2
% 213.99/29.87 | gives:
% 213.99/29.87 | (73) relation_rng(all_460_0) = all_865_1 & relation_dom(all_460_0) =
% 213.99/29.87 | all_865_0 & relation(all_460_0) = all_865_2 & $i(all_865_0) &
% 213.99/29.87 | $i(all_865_1) & ( ~ (all_865_2 = 0) | ( ! [v0: $i] : ! [v1: int] :
% 213.99/29.87 | (v1 = 0 | ~ (in(v0, all_865_1) = v1) | ~ $i(v0) | ! [v2: $i] :
% 213.99/29.87 | ( ~ (in(v2, all_865_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ (v3
% 213.99/29.87 | = v0) & apply(all_460_0, v2) = v3 & $i(v3)))) & ! [v0:
% 213.99/29.87 | $i] : ( ~ (in(v0, all_865_1) = 0) | ~ $i(v0) | ? [v1: $i] :
% 213.99/29.87 | (apply(all_460_0, v1) = v0 & in(v1, all_865_0) = 0 & $i(v1))) &
% 213.99/29.87 | ? [v0: any] : (v0 = all_865_1 | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 213.99/29.87 | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i]
% 213.99/29.87 | : ( ~ (in(v3, all_865_0) = 0) | ~ $i(v3) | ? [v4: $i] : (
% 213.99/29.87 | ~ (v4 = v1) & apply(all_460_0, v3) = v4 & $i(v4)))) &
% 213.99/29.87 | (v2 = 0 | ? [v3: $i] : (apply(all_460_0, v3) = v1 & in(v3,
% 213.99/29.87 | all_865_0) = 0 & $i(v3)))))))
% 213.99/29.87 |
% 213.99/29.87 | ALPHA: (73) implies:
% 213.99/29.87 | (74) relation(all_460_0) = all_865_2
% 213.99/29.87 | (75) relation_dom(all_460_0) = all_865_0
% 213.99/29.87 | (76) relation_rng(all_460_0) = all_865_1
% 213.99/29.87 |
% 213.99/29.87 | DELTA: instantiating (42) with fresh symbols all_869_0, all_869_1, all_869_2
% 213.99/29.87 | gives:
% 213.99/29.87 | (77) relation_rng(all_450_0) = all_869_1 & relation_dom(all_450_0) =
% 213.99/29.87 | all_869_0 & relation(all_450_0) = all_869_2 & $i(all_869_0) &
% 213.99/29.87 | $i(all_869_1) & ( ~ (all_869_2 = 0) | ( ! [v0: $i] : ! [v1: int] :
% 213.99/29.87 | (v1 = 0 | ~ (in(v0, all_869_1) = v1) | ~ $i(v0) | ! [v2: $i] :
% 213.99/29.87 | ( ~ (in(v2, all_869_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ (v3
% 213.99/29.87 | = v0) & apply(all_450_0, v2) = v3 & $i(v3)))) & ! [v0:
% 213.99/29.87 | $i] : ( ~ (in(v0, all_869_1) = 0) | ~ $i(v0) | ? [v1: $i] :
% 213.99/29.87 | (apply(all_450_0, v1) = v0 & in(v1, all_869_0) = 0 & $i(v1))) &
% 213.99/29.87 | ? [v0: any] : (v0 = all_869_1 | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 213.99/29.87 | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i]
% 213.99/29.87 | : ( ~ (in(v3, all_869_0) = 0) | ~ $i(v3) | ? [v4: $i] : (
% 213.99/29.87 | ~ (v4 = v1) & apply(all_450_0, v3) = v4 & $i(v4)))) &
% 213.99/29.87 | (v2 = 0 | ? [v3: $i] : (apply(all_450_0, v3) = v1 & in(v3,
% 213.99/29.87 | all_869_0) = 0 & $i(v3)))))))
% 213.99/29.87 |
% 213.99/29.87 | ALPHA: (77) implies:
% 213.99/29.87 | (78) relation(all_450_0) = all_869_2
% 213.99/29.87 | (79) relation_rng(all_450_0) = all_869_1
% 213.99/29.87 |
% 213.99/29.87 | DELTA: instantiating (48) with fresh symbols all_873_0, all_873_1 gives:
% 213.99/29.88 | (80) relation_dom(all_460_0) = all_873_0 & relation(all_460_0) = all_873_1
% 213.99/29.88 | & $i(all_873_0) & ( ~ (all_873_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 213.99/29.88 | ! [v2: $i] : (v2 = v0 | ~ (relation_inverse_image(all_460_0, v1)
% 213.99/29.88 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] :
% 213.99/29.88 | ? [v5: any] : ? [v6: $i] : ? [v7: any] : (apply(all_460_0, v3)
% 213.99/29.88 | = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_873_0) =
% 213.99/29.88 | v5 & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 =
% 213.99/29.88 | 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))) & ! [v0: $i] : !
% 213.99/29.88 | [v1: $i] : ( ~ (relation_inverse_image(all_460_0, v0) = v1) | ~
% 213.99/29.88 | $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 213.99/29.88 | ( ~ (apply(all_460_0, v2) = v3) | ~ (in(v3, v0) = v4) | ~
% 213.99/29.88 | $i(v2) | ? [v5: any] : ? [v6: any] : (in(v2, v1) = v5 &
% 213.99/29.88 | in(v2, all_873_0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 =
% 213.99/29.88 | 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 213.99/29.88 | (apply(all_460_0, v2) = v3) | ~ (in(v3, v0) = 0) | ~
% 213.99/29.88 | $i(v2) | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 &
% 213.99/29.88 | in(v2, all_873_0) = v4 & ( ~ (v4 = 0) | v5 = 0)))))))
% 213.99/29.88 |
% 213.99/29.88 | ALPHA: (80) implies:
% 213.99/29.88 | (81) relation(all_460_0) = all_873_1
% 213.99/29.88 | (82) relation_dom(all_460_0) = all_873_0
% 213.99/29.88 |
% 213.99/29.88 | DELTA: instantiating (40) with fresh symbols all_877_0, all_877_1 gives:
% 214.13/29.88 | (83) relation_dom(all_437_0) = all_877_0 & relation(all_437_0) = all_877_1
% 214.13/29.88 | & $i(all_877_0) & ( ~ (all_877_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 214.13/29.88 | ! [v2: $i] : (v2 = v0 | ~ (relation_inverse_image(all_437_0, v1)
% 214.13/29.88 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] :
% 214.13/29.88 | ? [v5: any] : ? [v6: $i] : ? [v7: any] : (apply(all_437_0, v3)
% 214.13/29.88 | = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_877_0) =
% 214.13/29.88 | v5 & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 =
% 214.13/29.88 | 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))) & ! [v0: $i] : !
% 214.13/29.88 | [v1: $i] : ( ~ (relation_inverse_image(all_437_0, v0) = v1) | ~
% 214.13/29.88 | $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 214.13/29.88 | ( ~ (apply(all_437_0, v2) = v3) | ~ (in(v3, v0) = v4) | ~
% 214.13/29.88 | $i(v2) | ? [v5: any] : ? [v6: any] : (in(v2, v1) = v5 &
% 214.13/29.88 | in(v2, all_877_0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 =
% 214.13/29.88 | 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 214.13/29.88 | (apply(all_437_0, v2) = v3) | ~ (in(v3, v0) = 0) | ~
% 214.13/29.88 | $i(v2) | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 &
% 214.13/29.88 | in(v2, all_877_0) = v4 & ( ~ (v4 = 0) | v5 = 0)))))))
% 214.13/29.88 |
% 214.13/29.88 | ALPHA: (83) implies:
% 214.13/29.88 | (84) relation(all_437_0) = all_877_1
% 214.13/29.88 |
% 214.13/29.88 | DELTA: instantiating (44) with fresh symbols all_881_0, all_881_1 gives:
% 214.13/29.88 | (85) relation_dom(all_450_0) = all_881_0 & relation(all_450_0) = all_881_1
% 214.13/29.88 | & $i(all_881_0) & ( ~ (all_881_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 214.13/29.88 | ! [v2: $i] : (v2 = v0 | ~ (relation_inverse_image(all_450_0, v1)
% 214.13/29.88 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] :
% 214.13/29.88 | ? [v5: any] : ? [v6: $i] : ? [v7: any] : (apply(all_450_0, v3)
% 214.13/29.88 | = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_881_0) =
% 214.13/29.88 | v5 & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 =
% 214.13/29.88 | 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))) & ! [v0: $i] : !
% 214.13/29.88 | [v1: $i] : ( ~ (relation_inverse_image(all_450_0, v0) = v1) | ~
% 214.13/29.88 | $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 214.13/29.88 | ( ~ (apply(all_450_0, v2) = v3) | ~ (in(v3, v0) = v4) | ~
% 214.13/29.88 | $i(v2) | ? [v5: any] : ? [v6: any] : (in(v2, v1) = v5 &
% 214.13/29.88 | in(v2, all_881_0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 =
% 214.13/29.88 | 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 214.13/29.88 | (apply(all_450_0, v2) = v3) | ~ (in(v3, v0) = 0) | ~
% 214.13/29.88 | $i(v2) | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 &
% 214.13/29.88 | in(v2, all_881_0) = v4 & ( ~ (v4 = 0) | v5 = 0)))))))
% 214.13/29.88 |
% 214.13/29.88 | ALPHA: (85) implies:
% 214.13/29.88 | (86) relation(all_450_0) = all_881_1
% 214.13/29.88 |
% 214.13/29.88 | DELTA: instantiating (41) with fresh symbols all_889_0, all_889_1 gives:
% 214.13/29.88 | (87) relation_dom(all_437_0) = all_889_0 & relation(all_437_0) = all_889_1
% 214.13/29.88 | & $i(all_889_0) & ( ~ (all_889_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 214.13/29.88 | ! [v2: $i] : (v2 = v0 | ~ (relation_image(all_437_0, v1) = v2) |
% 214.13/29.88 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0)
% 214.13/29.88 | = v4 & $i(v3) & ( ~ (v4 = 0) | ! [v5: $i] : ( ~ (in(v5,
% 214.13/29.88 | all_889_0) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7:
% 214.13/29.88 | $i] : (apply(all_437_0, v5) = v7 & in(v5, v1) = v6 &
% 214.13/29.88 | $i(v7) & ( ~ (v7 = v3) | ~ (v6 = 0))))) & (v4 = 0 | ?
% 214.13/29.88 | [v5: $i] : (apply(all_437_0, v5) = v3 & in(v5, v1) = 0 &
% 214.13/29.88 | in(v5, all_889_0) = 0 & $i(v5))))) & ! [v0: $i] : ! [v1:
% 214.13/29.88 | $i] : ( ~ (relation_image(all_437_0, v0) = v1) | ~ $i(v1) | ~
% 214.13/29.88 | $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1)
% 214.13/29.88 | = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4, all_889_0) =
% 214.13/29.88 | 0) | ~ $i(v4) | ? [v5: any] : ? [v6: $i] :
% 214.13/29.88 | (apply(all_437_0, v4) = v6 & in(v4, v0) = v5 & $i(v6) & (
% 214.13/29.88 | ~ (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i] : ( ~
% 214.13/29.88 | (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] :
% 214.13/29.88 | (apply(all_437_0, v3) = v2 & in(v3, v0) = 0 & in(v3,
% 214.13/29.88 | all_889_0) = 0 & $i(v3)))))))
% 214.13/29.88 |
% 214.13/29.88 | ALPHA: (87) implies:
% 214.13/29.88 | (88) relation(all_437_0) = all_889_1
% 214.13/29.88 |
% 214.13/29.88 | DELTA: instantiating (49) with fresh symbols all_891_0, all_891_1 gives:
% 214.13/29.89 | (89) relation_dom(all_460_0) = all_891_0 & relation(all_460_0) = all_891_1
% 214.13/29.89 | & $i(all_891_0) & ( ~ (all_891_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 214.13/29.89 | ! [v2: $i] : (v2 = v0 | ~ (relation_image(all_460_0, v1) = v2) |
% 214.13/29.89 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0)
% 214.13/29.89 | = v4 & $i(v3) & ( ~ (v4 = 0) | ! [v5: $i] : ( ~ (in(v5,
% 214.13/29.89 | all_891_0) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7:
% 214.13/29.89 | $i] : (apply(all_460_0, v5) = v7 & in(v5, v1) = v6 &
% 214.13/29.89 | $i(v7) & ( ~ (v7 = v3) | ~ (v6 = 0))))) & (v4 = 0 | ?
% 214.13/29.89 | [v5: $i] : (apply(all_460_0, v5) = v3 & in(v5, v1) = 0 &
% 214.13/29.89 | in(v5, all_891_0) = 0 & $i(v5))))) & ! [v0: $i] : ! [v1:
% 214.13/29.89 | $i] : ( ~ (relation_image(all_460_0, v0) = v1) | ~ $i(v1) | ~
% 214.13/29.89 | $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1)
% 214.13/29.89 | = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4, all_891_0) =
% 214.13/29.89 | 0) | ~ $i(v4) | ? [v5: any] : ? [v6: $i] :
% 214.13/29.89 | (apply(all_460_0, v4) = v6 & in(v4, v0) = v5 & $i(v6) & (
% 214.13/29.89 | ~ (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i] : ( ~
% 214.13/29.89 | (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] :
% 214.13/29.89 | (apply(all_460_0, v3) = v2 & in(v3, v0) = 0 & in(v3,
% 214.13/29.89 | all_891_0) = 0 & $i(v3)))))))
% 214.13/29.89 |
% 214.13/29.89 | ALPHA: (89) implies:
% 214.13/29.89 | (90) relation(all_460_0) = all_891_1
% 214.13/29.89 | (91) relation_dom(all_460_0) = all_891_0
% 214.13/29.89 |
% 214.13/29.89 | DELTA: instantiating (45) with fresh symbols all_895_0, all_895_1 gives:
% 214.13/29.89 | (92) relation_dom(all_450_0) = all_895_0 & relation(all_450_0) = all_895_1
% 214.13/29.89 | & $i(all_895_0) & ( ~ (all_895_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 214.13/29.89 | ! [v2: $i] : (v2 = v0 | ~ (relation_image(all_450_0, v1) = v2) |
% 214.13/29.89 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0)
% 214.13/29.89 | = v4 & $i(v3) & ( ~ (v4 = 0) | ! [v5: $i] : ( ~ (in(v5,
% 214.13/29.89 | all_895_0) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7:
% 214.13/29.89 | $i] : (apply(all_450_0, v5) = v7 & in(v5, v1) = v6 &
% 214.13/29.89 | $i(v7) & ( ~ (v7 = v3) | ~ (v6 = 0))))) & (v4 = 0 | ?
% 214.13/29.89 | [v5: $i] : (apply(all_450_0, v5) = v3 & in(v5, v1) = 0 &
% 214.13/29.89 | in(v5, all_895_0) = 0 & $i(v5))))) & ! [v0: $i] : ! [v1:
% 214.13/29.89 | $i] : ( ~ (relation_image(all_450_0, v0) = v1) | ~ $i(v1) | ~
% 214.13/29.89 | $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1)
% 214.13/29.89 | = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4, all_895_0) =
% 214.13/29.89 | 0) | ~ $i(v4) | ? [v5: any] : ? [v6: $i] :
% 214.13/29.89 | (apply(all_450_0, v4) = v6 & in(v4, v0) = v5 & $i(v6) & (
% 214.13/29.89 | ~ (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i] : ( ~
% 214.13/29.89 | (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] :
% 214.13/29.89 | (apply(all_450_0, v3) = v2 & in(v3, v0) = 0 & in(v3,
% 214.13/29.89 | all_895_0) = 0 & $i(v3)))))))
% 214.13/29.89 |
% 214.13/29.89 | ALPHA: (92) implies:
% 214.13/29.89 | (93) relation(all_450_0) = all_895_1
% 214.13/29.89 |
% 214.13/29.89 | BETA: splitting (35) gives:
% 214.13/29.89 |
% 214.13/29.89 | Case 1:
% 214.13/29.89 | |
% 214.13/29.89 | | (94) all_443_0 = 0
% 214.13/29.89 | |
% 214.13/29.89 | | REDUCE: (12), (94) imply:
% 214.13/29.89 | | (95) $false
% 214.13/29.89 | |
% 214.13/29.89 | | CLOSE: (95) is inconsistent.
% 214.13/29.89 | |
% 214.13/29.89 | Case 2:
% 214.13/29.89 | |
% 214.13/29.89 | | (96) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_rng(all_443_1)
% 214.13/29.89 | | = v1 & relation(all_443_1) = v0 & empty(v1) = v2 & $i(v1) & ( ~
% 214.13/29.89 | | (v2 = 0) | ~ (v0 = 0)))
% 214.13/29.89 | |
% 214.13/29.89 | | DELTA: instantiating (96) with fresh symbols all_901_0, all_901_1, all_901_2
% 214.13/29.89 | | gives:
% 214.13/29.89 | | (97) relation_rng(all_443_1) = all_901_1 & relation(all_443_1) =
% 214.13/29.89 | | all_901_2 & empty(all_901_1) = all_901_0 & $i(all_901_1) & ( ~
% 214.13/29.89 | | (all_901_0 = 0) | ~ (all_901_2 = 0))
% 214.13/29.89 | |
% 214.13/29.89 | | ALPHA: (97) implies:
% 214.13/29.89 | | (98) relation(all_443_1) = all_901_2
% 214.13/29.89 | | (99) relation_rng(all_443_1) = all_901_1
% 214.13/29.89 | |
% 214.13/29.89 | | BETA: splitting (36) gives:
% 214.13/29.89 | |
% 214.13/29.89 | | Case 1:
% 214.13/29.89 | | |
% 214.13/29.89 | | | (100) all_443_0 = 0
% 214.13/29.89 | | |
% 214.13/29.89 | | | REDUCE: (12), (100) imply:
% 214.13/29.89 | | | (101) $false
% 214.13/29.89 | | |
% 214.13/29.89 | | | CLOSE: (101) is inconsistent.
% 214.13/29.89 | | |
% 214.13/29.89 | | Case 2:
% 214.13/29.89 | | |
% 214.13/29.89 | | | (102) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 214.13/29.89 | | | (relation_dom(all_443_1) = v1 & relation(all_443_1) = v0 &
% 214.13/29.89 | | | empty(v1) = v2 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 214.13/29.89 | | |
% 214.13/29.89 | | | DELTA: instantiating (102) with fresh symbols all_906_0, all_906_1,
% 214.13/29.89 | | | all_906_2 gives:
% 214.13/29.89 | | | (103) relation_dom(all_443_1) = all_906_1 & relation(all_443_1) =
% 214.13/29.89 | | | all_906_2 & empty(all_906_1) = all_906_0 & $i(all_906_1) & ( ~
% 214.13/29.89 | | | (all_906_0 = 0) | ~ (all_906_2 = 0))
% 214.13/29.89 | | |
% 214.13/29.89 | | | ALPHA: (103) implies:
% 214.13/29.89 | | | (104) relation(all_443_1) = all_906_2
% 214.13/29.89 | | |
% 214.13/29.89 | | | BETA: splitting (37) gives:
% 214.13/29.89 | | |
% 214.13/29.89 | | | Case 1:
% 214.13/29.89 | | | |
% 214.13/29.89 | | | | (105) all_464_0 = 0
% 214.13/29.89 | | | |
% 214.13/29.89 | | | | REDUCE: (32), (105) imply:
% 214.13/29.89 | | | | (106) $false
% 214.13/29.89 | | | |
% 214.13/29.89 | | | | CLOSE: (106) is inconsistent.
% 214.13/29.89 | | | |
% 214.13/29.89 | | | Case 2:
% 214.13/29.89 | | | |
% 214.13/29.89 | | | | (107) ? [v0: $i] : (powerset(all_464_1) = v0 & $i(v0) & ? [v1: $i]
% 214.13/29.89 | | | | : ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 &
% 214.13/29.89 | | | | empty(v1) = v2 & $i(v1)))
% 214.13/29.89 | | | |
% 214.13/29.89 | | | | DELTA: instantiating (107) with fresh symbol all_938_0 gives:
% 214.13/29.89 | | | | (108) powerset(all_464_1) = all_938_0 & $i(all_938_0) & ? [v0: $i] :
% 214.13/29.89 | | | | ? [v1: int] : ( ~ (v1 = 0) & element(v0, all_938_0) = 0 &
% 214.13/29.89 | | | | empty(v0) = v1 & $i(v0))
% 214.13/29.89 | | | |
% 214.13/29.89 | | | | ALPHA: (108) implies:
% 214.13/29.89 | | | | (109) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0,
% 214.13/29.89 | | | | all_938_0) = 0 & empty(v0) = v1 & $i(v0))
% 214.13/29.89 | | | |
% 214.13/29.89 | | | | DELTA: instantiating (109) with fresh symbols all_940_0, all_940_1
% 214.13/29.89 | | | | gives:
% 214.13/29.89 | | | | (110) ~ (all_940_0 = 0) & element(all_940_1, all_938_0) = 0 &
% 214.13/29.89 | | | | empty(all_940_1) = all_940_0 & $i(all_940_1)
% 214.13/29.89 | | | |
% 214.13/29.89 | | | | ALPHA: (110) implies:
% 214.13/29.89 | | | | (111) ~ (all_940_0 = 0)
% 214.13/29.89 | | | | (112) $i(all_940_1)
% 214.13/29.89 | | | | (113) empty(all_940_1) = all_940_0
% 214.13/29.89 | | | |
% 214.13/29.89 | | | | GROUND_INST: instantiating (4) with 0, all_861_2, all_437_0, simplifying
% 214.13/29.89 | | | | with (10), (71) gives:
% 214.13/29.90 | | | | (114) all_861_2 = 0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with all_861_2, all_877_1, all_437_0,
% 214.13/29.90 | | | | simplifying with (71), (84) gives:
% 214.13/29.90 | | | | (115) all_877_1 = all_861_2
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with all_877_1, all_889_1, all_437_0,
% 214.13/29.90 | | | | simplifying with (84), (88) gives:
% 214.13/29.90 | | | | (116) all_889_1 = all_877_1
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with all_851_1, all_889_1, all_437_0,
% 214.13/29.90 | | | | simplifying with (66), (88) gives:
% 214.13/29.90 | | | | (117) all_889_1 = all_851_1
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with 0, all_906_2, all_443_1, simplifying
% 214.13/29.90 | | | | with (15), (104) gives:
% 214.13/29.90 | | | | (118) all_906_2 = 0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with all_901_2, all_906_2, all_443_1,
% 214.13/29.90 | | | | simplifying with (98), (104) gives:
% 214.13/29.90 | | | | (119) all_906_2 = all_901_2
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with 0, all_805_2, all_450_0, simplifying
% 214.13/29.90 | | | | with (19), (57) gives:
% 214.13/29.90 | | | | (120) all_805_2 = 0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with all_805_2, all_855_1, all_450_0,
% 214.13/29.90 | | | | simplifying with (57), (68) gives:
% 214.13/29.90 | | | | (121) all_855_1 = all_805_2
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with all_881_1, all_895_1, all_450_0,
% 214.13/29.90 | | | | simplifying with (86), (93) gives:
% 214.13/29.90 | | | | (122) all_895_1 = all_881_1
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with all_869_2, all_895_1, all_450_0,
% 214.13/29.90 | | | | simplifying with (78), (93) gives:
% 214.13/29.90 | | | | (123) all_895_1 = all_869_2
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with all_855_1, all_895_1, all_450_0,
% 214.13/29.90 | | | | simplifying with (68), (93) gives:
% 214.13/29.90 | | | | (124) all_895_1 = all_855_1
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with all_759_2, all_895_1, all_450_0,
% 214.13/29.90 | | | | simplifying with (55), (93) gives:
% 214.13/29.90 | | | | (125) all_895_1 = all_759_2
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with all_849_1, all_865_2, all_460_0,
% 214.13/29.90 | | | | simplifying with (63), (74) gives:
% 214.13/29.90 | | | | (126) all_865_2 = all_849_1
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with 0, all_891_1, all_460_0, simplifying
% 214.13/29.90 | | | | with (24), (90) gives:
% 214.13/29.90 | | | | (127) all_891_1 = 0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with all_873_1, all_891_1, all_460_0,
% 214.13/29.90 | | | | simplifying with (81), (90) gives:
% 214.13/29.90 | | | | (128) all_891_1 = all_873_1
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with all_865_2, all_891_1, all_460_0,
% 214.13/29.90 | | | | simplifying with (74), (90) gives:
% 214.13/29.90 | | | | (129) all_891_1 = all_865_2
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (4) with 0, all_811_1, all_462_1, simplifying
% 214.13/29.90 | | | | with (52), (59) gives:
% 214.13/29.90 | | | | (130) all_811_1 = 0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (5) with all_865_0, all_873_0, all_460_0,
% 214.13/29.90 | | | | simplifying with (75), (82) gives:
% 214.13/29.90 | | | | (131) all_873_0 = all_865_0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (5) with all_873_0, all_891_0, all_460_0,
% 214.13/29.90 | | | | simplifying with (82), (91) gives:
% 214.13/29.90 | | | | (132) all_891_0 = all_873_0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | GROUND_INST: instantiating (5) with all_849_0, all_891_0, all_460_0,
% 214.13/29.90 | | | | simplifying with (64), (91) gives:
% 214.13/29.90 | | | | (133) all_891_0 = all_849_0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (118), (119) imply:
% 214.13/29.90 | | | | (134) all_901_2 = 0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | SIMP: (134) implies:
% 214.13/29.90 | | | | (135) all_901_2 = 0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (122), (125) imply:
% 214.13/29.90 | | | | (136) all_881_1 = all_759_2
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (122), (124) imply:
% 214.13/29.90 | | | | (137) all_881_1 = all_855_1
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (122), (123) imply:
% 214.13/29.90 | | | | (138) all_881_1 = all_869_2
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (132), (133) imply:
% 214.13/29.90 | | | | (139) all_873_0 = all_849_0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | SIMP: (139) implies:
% 214.13/29.90 | | | | (140) all_873_0 = all_849_0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (127), (128) imply:
% 214.13/29.90 | | | | (141) all_873_1 = 0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (128), (129) imply:
% 214.13/29.90 | | | | (142) all_873_1 = all_865_2
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (116), (117) imply:
% 214.13/29.90 | | | | (143) all_877_1 = all_851_1
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | SIMP: (143) implies:
% 214.13/29.90 | | | | (144) all_877_1 = all_851_1
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (136), (138) imply:
% 214.13/29.90 | | | | (145) all_869_2 = all_759_2
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (137), (138) imply:
% 214.13/29.90 | | | | (146) all_869_2 = all_855_1
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (115), (144) imply:
% 214.13/29.90 | | | | (147) all_861_2 = all_851_1
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | SIMP: (147) implies:
% 214.13/29.90 | | | | (148) all_861_2 = all_851_1
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (131), (140) imply:
% 214.13/29.90 | | | | (149) all_865_0 = all_849_0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | SIMP: (149) implies:
% 214.13/29.90 | | | | (150) all_865_0 = all_849_0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (141), (142) imply:
% 214.13/29.90 | | | | (151) all_865_2 = 0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | SIMP: (151) implies:
% 214.13/29.90 | | | | (152) all_865_2 = 0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (145), (146) imply:
% 214.13/29.90 | | | | (153) all_855_1 = all_759_2
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | SIMP: (153) implies:
% 214.13/29.90 | | | | (154) all_855_1 = all_759_2
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (126), (152) imply:
% 214.13/29.90 | | | | (155) all_849_1 = 0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | SIMP: (155) implies:
% 214.13/29.90 | | | | (156) all_849_1 = 0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (114), (148) imply:
% 214.13/29.90 | | | | (157) all_851_1 = 0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (121), (154) imply:
% 214.13/29.90 | | | | (158) all_805_2 = all_759_2
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | SIMP: (158) implies:
% 214.13/29.90 | | | | (159) all_805_2 = all_759_2
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | COMBINE_EQS: (120), (159) imply:
% 214.13/29.90 | | | | (160) all_759_2 = 0
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | BETA: splitting (61) gives:
% 214.13/29.90 | | | |
% 214.13/29.90 | | | | Case 1:
% 214.13/29.90 | | | | |
% 214.13/29.90 | | | | | (161) ~ (all_811_1 = 0)
% 214.13/29.90 | | | | |
% 214.13/29.90 | | | | | REDUCE: (130), (161) imply:
% 214.13/29.90 | | | | | (162) $false
% 214.13/29.90 | | | | |
% 214.13/29.90 | | | | | CLOSE: (162) is inconsistent.
% 214.13/29.90 | | | | |
% 214.13/29.90 | | | | Case 2:
% 214.13/29.90 | | | | |
% 214.13/29.90 | | | | | (163) ( ~ (all_462_0 = 0) | ! [v0: $i] : ( ~ (in(v0, all_811_0) =
% 214.13/29.90 | | | | | 0) | ~ $i(v0) | ? [v1: $i] : (ordered_pair(v0, v0) =
% 214.13/29.90 | | | | | v1 & in(v1, all_462_1) = 0 & $i(v1)))) & (all_462_0 = 0
% 214.13/29.90 | | | | | | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 214.13/29.90 | | | | | ordered_pair(v0, v0) = v1 & in(v1, all_462_1) = v2 &
% 214.13/29.90 | | | | | in(v0, all_811_0) = 0 & $i(v1) & $i(v0)))
% 214.13/29.90 | | | | |
% 214.13/29.90 | | | | | ALPHA: (163) implies:
% 214.13/29.90 | | | | | (164) all_462_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : (
% 214.13/29.90 | | | | | ~ (v2 = 0) & ordered_pair(v0, v0) = v1 & in(v1, all_462_1)
% 214.13/29.90 | | | | | = v2 & in(v0, all_811_0) = 0 & $i(v1) & $i(v0))
% 214.13/29.90 | | | | |
% 214.13/29.90 | | | | | BETA: splitting (164) gives:
% 214.13/29.90 | | | | |
% 214.13/29.90 | | | | | Case 1:
% 214.13/29.90 | | | | | |
% 214.13/29.90 | | | | | | (165) all_462_0 = 0
% 214.13/29.90 | | | | | |
% 214.13/29.90 | | | | | | REDUCE: (26), (165) imply:
% 214.13/29.90 | | | | | | (166) $false
% 214.13/29.90 | | | | | |
% 214.13/29.90 | | | | | | CLOSE: (166) is inconsistent.
% 214.13/29.90 | | | | | |
% 214.13/29.90 | | | | | Case 2:
% 214.13/29.90 | | | | | |
% 214.13/29.91 | | | | | | (167) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 214.13/29.91 | | | | | | ordered_pair(v0, v0) = v1 & in(v1, all_462_1) = v2 &
% 214.13/29.91 | | | | | | in(v0, all_811_0) = 0 & $i(v1) & $i(v0))
% 214.13/29.91 | | | | | |
% 214.13/29.91 | | | | | | DELTA: instantiating (167) with fresh symbols all_1149_0,
% 214.13/29.91 | | | | | | all_1149_1, all_1149_2 gives:
% 214.13/29.91 | | | | | | (168) ~ (all_1149_0 = 0) & ordered_pair(all_1149_2, all_1149_2)
% 214.13/29.91 | | | | | | = all_1149_1 & in(all_1149_1, all_462_1) = all_1149_0 &
% 214.13/29.91 | | | | | | in(all_1149_2, all_811_0) = 0 & $i(all_1149_1) &
% 214.13/29.91 | | | | | | $i(all_1149_2)
% 214.13/29.91 | | | | | |
% 214.13/29.91 | | | | | | ALPHA: (168) implies:
% 214.13/29.91 | | | | | | (169) ~ (all_1149_0 = 0)
% 214.13/29.91 | | | | | | (170) $i(all_1149_2)
% 214.13/29.91 | | | | | | (171) in(all_1149_2, all_811_0) = 0
% 214.13/29.91 | | | | | | (172) in(all_1149_1, all_462_1) = all_1149_0
% 214.13/29.91 | | | | | | (173) ordered_pair(all_1149_2, all_1149_2) = all_1149_1
% 214.13/29.91 | | | | | |
% 214.13/29.91 | | | | | | GROUND_INST: instantiating (fc5_relat_1) with all_940_1, all_940_0,
% 214.13/29.91 | | | | | | simplifying with (112), (113) gives:
% 214.13/29.91 | | | | | | (174) all_940_0 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 214.13/29.91 | | | | | | (relation_dom(all_940_1) = v1 & relation(all_940_1) = v0 &
% 214.13/29.91 | | | | | | empty(v1) = v2 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 214.13/29.91 | | | | | |
% 214.13/29.91 | | | | | | GROUND_INST: instantiating (t8_funct_1) with all_1149_2, all_1149_2,
% 214.13/29.91 | | | | | | all_462_1, all_1149_1, all_1149_0, simplifying with
% 214.13/29.91 | | | | | | (28), (170), (172), (173) gives:
% 214.13/29.91 | | | | | | (175) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 214.13/29.91 | | | | | | ? [v4: $i] : (relation_dom(all_462_1) = v2 &
% 214.13/29.91 | | | | | | apply(all_462_1, all_1149_2) = v4 & relation(all_462_1) =
% 214.13/29.91 | | | | | | v0 & function(all_462_1) = v1 & in(all_1149_2, v2) = v3 &
% 214.13/29.91 | | | | | | $i(v4) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v4 =
% 214.13/29.91 | | | | | | all_1149_2) | ~ (v3 = 0) | all_1149_0 = 0) & ( ~
% 214.13/29.91 | | | | | | (all_1149_0 = 0) | (v4 = all_1149_2 & v3 = 0)))))
% 214.13/29.91 | | | | | |
% 214.13/29.91 | | | | | | GROUND_INST: instantiating (d4_relat_1) with all_460_0, all_849_0,
% 214.13/29.91 | | | | | | simplifying with (22), (64) gives:
% 214.13/29.92 | | | | | | (176) ? [v0: int] : ( ~ (v0 = 0) & relation(all_460_0) = v0) | (
% 214.13/29.92 | | | | | | ? [v0: any] : (v0 = all_849_0 | ~ $i(v0) | ? [v1: $i] :
% 214.13/29.92 | | | | | | ? [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0)
% 214.13/29.92 | | | | | | | ! [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v1,
% 214.13/29.92 | | | | | | v3) = v4) | ~ (in(v4, all_460_0) = 0) | ~
% 214.13/29.92 | | | | | | $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] :
% 214.13/29.92 | | | | | | (ordered_pair(v1, v3) = v4 & in(v4, all_460_0) = 0
% 214.13/29.92 | | | | | | & $i(v4) & $i(v3))))) & ( ~ $i(all_849_0) | ( !
% 214.13/29.92 | | | | | | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 214.13/29.92 | | | | | | all_849_0) = v1) | ~ $i(v0) | ! [v2: $i] : !
% 214.13/29.92 | | | | | | [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~
% 214.13/29.92 | | | | | | (in(v3, all_460_0) = 0) | ~ $i(v2))) & ! [v0:
% 214.13/29.92 | | | | | | $i] : ( ~ (in(v0, all_849_0) = 0) | ~ $i(v0) | ?
% 214.13/29.92 | | | | | | [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2
% 214.13/29.92 | | | | | | & in(v2, all_460_0) = 0 & $i(v2) & $i(v1))))))
% 214.13/29.92 | | | | | |
% 214.13/29.92 | | | | | | GROUND_INST: instantiating (d1_wellord2) with all_462_2, all_462_1,
% 214.13/29.92 | | | | | | all_462_1, all_811_0, simplifying with (27), (28),
% 214.13/29.92 | | | | | | (29), (60) gives:
% 214.13/29.92 | | | | | | (177) ? [v0: int] : ( ~ (v0 = 0) & relation(all_462_1) = v0) |
% 214.13/29.92 | | | | | | (all_811_0 = all_462_2 & ! [v0: $i] : ! [v1: $i] : !
% 214.13/29.92 | | | | | | [v2: $i] : ! [v3: any] : ( ~ (ordered_pair(v0, v1) = v2)
% 214.13/29.92 | | | | | | | ~ (in(v2, all_462_1) = v3) | ~ $i(v1) | ~ $i(v0) |
% 214.13/29.92 | | | | | | ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 214.13/29.92 | | | | | | (subset(v0, v1) = v6 & in(v1, all_462_2) = v5 & in(v0,
% 214.13/29.92 | | | | | | all_462_2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (( ~
% 214.13/29.92 | | | | | | (v6 = 0) | v3 = 0) & ( ~ (v3 = 0) | v6 =
% 214.13/29.92 | | | | | | 0))))))
% 214.13/29.92 | | | | | |
% 214.13/29.92 | | | | | | GROUND_INST: instantiating (d7_wellord1) with all_462_1, all_811_0,
% 214.13/29.92 | | | | | | simplifying with (28), (60) gives:
% 214.13/29.92 | | | | | | (178) ? [v0: int] : ( ~ (v0 = 0) & relation(all_462_1) = v0) |
% 214.13/29.92 | | | | | | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) |
% 214.13/29.92 | | | | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & relation(v0) =
% 214.13/29.92 | | | | | | v2) | ! [v2: $i] : ! [v3: any] : ( ~
% 214.13/29.92 | | | | | | (relation_isomorphism(all_462_1, v0, v2) = v3) | ~
% 214.13/29.92 | | | | | | $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: $i] : ?
% 214.13/29.92 | | | | | | [v7: $i] : ? [v8: any] : (relation_rng(v2) = v7 &
% 214.13/29.92 | | | | | | relation_dom(v2) = v6 & one_to_one(v2) = v8 &
% 214.13/29.92 | | | | | | relation(v2) = v4 & function(v2) = v5 & $i(v7) &
% 214.13/29.92 | | | | | | $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | (( ~ (v8 = 0) |
% 214.13/29.92 | | | | | | ~ (v7 = v1) | ~ (v6 = all_811_0) | v3 = 0 |
% 214.13/29.92 | | | | | | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ?
% 214.13/29.92 | | | | | | [v12: any] : ? [v13: any] : ? [v14: any] : ?
% 214.13/29.92 | | | | | | [v15: $i] : ? [v16: $i] : ? [v17: $i] : ?
% 214.13/29.92 | | | | | | [v18: any] : (apply(v2, v10) = v16 & apply(v2,
% 214.13/29.92 | | | | | | v9) = v15 & ordered_pair(v15, v16) = v17 &
% 214.13/29.92 | | | | | | ordered_pair(v9, v10) = v11 & in(v17, v0) =
% 214.13/29.92 | | | | | | v18 & in(v11, all_462_1) = v12 & in(v10,
% 214.13/29.92 | | | | | | all_811_0) = v14 & in(v9, all_811_0) = v13
% 214.13/29.92 | | | | | | & $i(v17) & $i(v16) & $i(v15) & $i(v11) &
% 214.13/29.92 | | | | | | $i(v10) & $i(v9) & ( ~ (v18 = 0) | ~ (v14 =
% 214.13/29.92 | | | | | | 0) | ~ (v13 = 0) | ~ (v12 = 0)) & (v12
% 214.13/29.92 | | | | | | = 0 | (v18 = 0 & v14 = 0 & v13 = 0)))) & (
% 214.13/29.92 | | | | | | ~ (v3 = 0) | (v8 = 0 & v7 = v1 & v6 = all_811_0
% 214.13/29.92 | | | | | | & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] :
% 214.13/29.92 | | | | | | ! [v12: $i] : ! [v13: $i] : ! [v14: any] :
% 214.13/29.92 | | | | | | ( ~ (apply(v2, v10) = v12) | ~ (apply(v2,
% 214.13/29.92 | | | | | | v9) = v11) | ~ (ordered_pair(v11, v12)
% 214.13/29.92 | | | | | | = v13) | ~ (in(v13, v0) = v14) | ~
% 214.13/29.92 | | | | | | $i(v10) | ~ $i(v9) | ? [v15: $i] : ?
% 214.13/29.92 | | | | | | [v16: any] : ? [v17: any] : ? [v18: any]
% 214.13/29.92 | | | | | | : (ordered_pair(v9, v10) = v15 & in(v15,
% 214.13/29.92 | | | | | | all_462_1) = v16 & in(v10, all_811_0) =
% 214.13/29.92 | | | | | | v18 & in(v9, all_811_0) = v17 & $i(v15) &
% 214.13/29.92 | | | | | | ( ~ (v16 = 0) | (v18 = 0 & v17 = 0 & v14
% 214.13/29.92 | | | | | | = 0)))) & ! [v9: $i] : ! [v10: $i]
% 214.13/29.92 | | | | | | : ! [v11: $i] : ! [v12: $i] : ! [v13: $i]
% 214.13/29.92 | | | | | | : ( ~ (apply(v2, v10) = v12) | ~ (apply(v2,
% 214.13/29.92 | | | | | | v9) = v11) | ~ (ordered_pair(v11, v12)
% 214.13/29.92 | | | | | | = v13) | ~ (in(v13, v0) = 0) | ~
% 214.13/29.92 | | | | | | $i(v10) | ~ $i(v9) | ? [v14: any] : ?
% 214.13/29.92 | | | | | | [v15: any] : ? [v16: $i] : ? [v17: any] :
% 214.13/29.92 | | | | | | (ordered_pair(v9, v10) = v16 & in(v16,
% 214.13/29.92 | | | | | | all_462_1) = v17 & in(v10, all_811_0) =
% 214.13/29.92 | | | | | | v15 & in(v9, all_811_0) = v14 & $i(v16) &
% 214.13/29.92 | | | | | | ( ~ (v15 = 0) | ~ (v14 = 0) | v17 =
% 214.13/29.92 | | | | | | 0))))))))))
% 214.13/29.92 | | | | | |
% 214.13/29.92 | | | | | | GROUND_INST: instantiating (t25_relat_1) with all_437_0, all_861_1,
% 214.13/29.92 | | | | | | simplifying with (8), (72) gives:
% 214.13/29.92 | | | | | | (179) ? [v0: any] : ? [v1: $i] : (relation_dom(all_437_0) = v1
% 214.13/29.92 | | | | | | & relation(all_437_0) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 214.13/29.92 | | | | | | [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 214.13/29.92 | | | | | | (relation_rng(v2) = v3) | ~ (subset(all_861_1, v3) =
% 214.13/29.92 | | | | | | v4) | ~ $i(v2) | ? [v5: any] : ? [v6: any] : ?
% 214.13/29.92 | | | | | | [v7: $i] : ? [v8: any] : (relation_dom(v2) = v7 &
% 214.13/29.92 | | | | | | subset(v1, v7) = v8 & subset(all_437_0, v2) = v6 &
% 214.13/29.92 | | | | | | relation(v2) = v5 & $i(v7) & ( ~ (v6 = 0) | ~ (v5
% 214.13/29.92 | | | | | | = 0) | (v8 = 0 & v4 = 0))))))
% 214.13/29.92 | | | | | |
% 214.13/29.92 | | | | | | GROUND_INST: instantiating (t47_relat_1) with all_437_0, all_861_1,
% 214.13/29.92 | | | | | | simplifying with (8), (72) gives:
% 214.13/29.92 | | | | | | (180) ? [v0: any] : ? [v1: $i] : (relation_dom(all_437_0) = v1
% 214.13/29.92 | | | | | | & relation(all_437_0) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 214.13/29.92 | | | | | | [v2: $i] : ! [v3: $i] : ( ~ (relation_rng(v2) = v3) |
% 214.13/29.92 | | | | | | ~ (subset(v1, v3) = 0) | ~ $i(v2) | ? [v4: any] :
% 214.13/29.92 | | | | | | ? [v5: $i] : ? [v6: $i] : (relation_composition(v2,
% 214.13/29.92 | | | | | | all_437_0) = v5 & relation_rng(v5) = v6 &
% 214.13/29.92 | | | | | | relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0)
% 214.13/29.92 | | | | | | | v6 = all_861_1)))))
% 214.13/29.92 | | | | | |
% 214.13/29.92 | | | | | | GROUND_INST: instantiating (t46_relat_1) with all_437_0, all_861_1,
% 214.13/29.92 | | | | | | simplifying with (8), (72) gives:
% 214.13/29.92 | | | | | | (181) ? [v0: any] : ? [v1: $i] : (relation_dom(all_437_0) = v1
% 214.13/29.92 | | | | | | & relation(all_437_0) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 214.13/29.92 | | | | | | [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v2) = v3) |
% 214.13/29.92 | | | | | | ~ (subset(all_861_1, v3) = 0) | ~ $i(v2) | ? [v4:
% 214.13/29.92 | | | | | | any] : ? [v5: $i] : ? [v6: $i] :
% 214.13/29.92 | | | | | | (relation_composition(all_437_0, v2) = v5 &
% 214.13/29.92 | | | | | | relation_dom(v5) = v6 & relation(v2) = v4 & $i(v6)
% 214.13/29.93 | | | | | | & $i(v5) & ( ~ (v4 = 0) | v6 = v1)))))
% 214.13/29.93 | | | | | |
% 214.13/29.93 | | | | | | GROUND_INST: instantiating (3) with all_437_0, all_861_1,
% 214.13/29.93 | | | | | | simplifying with (8), (72) gives:
% 214.13/29.93 | | | | | | (182) ? [v0: any] : ? [v1: $i] : (relation_dom(all_437_0) = v1
% 214.13/29.93 | | | | | | & relation(all_437_0) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~
% 214.13/29.93 | | | | | | (v1 = empty_set) | all_861_1 = empty_set) & ( ~
% 214.13/29.93 | | | | | | (all_861_1 = empty_set) | v1 = empty_set))))
% 214.13/29.93 | | | | | |
% 214.13/29.93 | | | | | | GROUND_INST: instantiating (d5_relat_1) with all_437_0, all_861_1,
% 214.13/29.93 | | | | | | simplifying with (8), (72) gives:
% 214.13/29.93 | | | | | | (183) ? [v0: int] : ( ~ (v0 = 0) & relation(all_437_0) = v0) | (
% 214.13/29.93 | | | | | | ? [v0: any] : (v0 = all_861_1 | ~ $i(v0) | ? [v1: $i] :
% 214.13/29.93 | | | | | | ? [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0)
% 214.13/29.93 | | | | | | | ! [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v3,
% 214.13/29.93 | | | | | | v1) = v4) | ~ (in(v4, all_437_0) = 0) | ~
% 214.13/29.93 | | | | | | $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] :
% 214.13/29.93 | | | | | | (ordered_pair(v3, v1) = v4 & in(v4, all_437_0) = 0
% 214.13/29.93 | | | | | | & $i(v4) & $i(v3))))) & ( ~ $i(all_861_1) | ( !
% 214.13/29.93 | | | | | | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 214.13/29.93 | | | | | | all_861_1) = v1) | ~ $i(v0) | ! [v2: $i] : !
% 214.13/29.93 | | | | | | [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~
% 214.13/29.93 | | | | | | (in(v3, all_437_0) = 0) | ~ $i(v2))) & ! [v0:
% 214.13/29.93 | | | | | | $i] : ( ~ (in(v0, all_861_1) = 0) | ~ $i(v0) | ?
% 214.13/29.93 | | | | | | [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) = v2
% 214.13/29.93 | | | | | | & in(v2, all_437_0) = 0 & $i(v2) & $i(v1))))))
% 214.13/29.93 | | | | | |
% 214.13/29.93 | | | | | | GROUND_INST: instantiating (t25_relat_1) with all_443_1, all_901_1,
% 214.13/29.93 | | | | | | simplifying with (13), (99) gives:
% 214.13/29.93 | | | | | | (184) ? [v0: any] : ? [v1: $i] : (relation_dom(all_443_1) = v1
% 214.13/29.93 | | | | | | & relation(all_443_1) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 214.13/29.93 | | | | | | [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 214.13/29.93 | | | | | | (relation_rng(v2) = v3) | ~ (subset(all_901_1, v3) =
% 214.13/29.93 | | | | | | v4) | ~ $i(v2) | ? [v5: any] : ? [v6: any] : ?
% 214.13/29.93 | | | | | | [v7: $i] : ? [v8: any] : (relation_dom(v2) = v7 &
% 214.13/29.93 | | | | | | subset(v1, v7) = v8 & subset(all_443_1, v2) = v6 &
% 214.13/29.93 | | | | | | relation(v2) = v5 & $i(v7) & ( ~ (v6 = 0) | ~ (v5
% 214.13/29.93 | | | | | | = 0) | (v8 = 0 & v4 = 0))))))
% 214.13/29.93 | | | | | |
% 214.13/29.93 | | | | | | GROUND_INST: instantiating (t47_relat_1) with all_443_1, all_901_1,
% 214.13/29.93 | | | | | | simplifying with (13), (99) gives:
% 214.13/29.93 | | | | | | (185) ? [v0: any] : ? [v1: $i] : (relation_dom(all_443_1) = v1
% 214.13/29.93 | | | | | | & relation(all_443_1) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 214.13/29.93 | | | | | | [v2: $i] : ! [v3: $i] : ( ~ (relation_rng(v2) = v3) |
% 214.13/29.93 | | | | | | ~ (subset(v1, v3) = 0) | ~ $i(v2) | ? [v4: any] :
% 214.13/29.93 | | | | | | ? [v5: $i] : ? [v6: $i] : (relation_composition(v2,
% 214.13/29.93 | | | | | | all_443_1) = v5 & relation_rng(v5) = v6 &
% 214.13/29.93 | | | | | | relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0)
% 214.13/29.93 | | | | | | | v6 = all_901_1)))))
% 214.13/29.93 | | | | | |
% 214.13/29.93 | | | | | | GROUND_INST: instantiating (t46_relat_1) with all_443_1, all_901_1,
% 214.13/29.93 | | | | | | simplifying with (13), (99) gives:
% 214.38/29.93 | | | | | | (186) ? [v0: any] : ? [v1: $i] : (relation_dom(all_443_1) = v1
% 214.38/29.93 | | | | | | & relation(all_443_1) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 214.38/29.93 | | | | | | [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v2) = v3) |
% 214.38/29.93 | | | | | | ~ (subset(all_901_1, v3) = 0) | ~ $i(v2) | ? [v4:
% 214.38/29.93 | | | | | | any] : ? [v5: $i] : ? [v6: $i] :
% 214.38/29.93 | | | | | | (relation_composition(all_443_1, v2) = v5 &
% 214.38/29.93 | | | | | | relation_dom(v5) = v6 & relation(v2) = v4 & $i(v6)
% 214.38/29.93 | | | | | | & $i(v5) & ( ~ (v4 = 0) | v6 = v1)))))
% 214.38/29.93 | | | | | |
% 214.38/29.93 | | | | | | GROUND_INST: instantiating (3) with all_443_1, all_901_1,
% 214.38/29.93 | | | | | | simplifying with (13), (99) gives:
% 214.38/29.93 | | | | | | (187) ? [v0: any] : ? [v1: $i] : (relation_dom(all_443_1) = v1
% 214.38/29.93 | | | | | | & relation(all_443_1) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~
% 214.38/29.93 | | | | | | (v1 = empty_set) | all_901_1 = empty_set) & ( ~
% 214.38/29.93 | | | | | | (all_901_1 = empty_set) | v1 = empty_set))))
% 214.38/29.93 | | | | | |
% 214.38/29.93 | | | | | | GROUND_INST: instantiating (d5_relat_1) with all_443_1, all_901_1,
% 214.38/29.93 | | | | | | simplifying with (13), (99) gives:
% 214.38/29.93 | | | | | | (188) ? [v0: int] : ( ~ (v0 = 0) & relation(all_443_1) = v0) | (
% 214.38/29.93 | | | | | | ? [v0: any] : (v0 = all_901_1 | ~ $i(v0) | ? [v1: $i] :
% 214.38/29.93 | | | | | | ? [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0)
% 214.38/29.93 | | | | | | | ! [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v3,
% 214.38/29.93 | | | | | | v1) = v4) | ~ (in(v4, all_443_1) = 0) | ~
% 214.38/29.93 | | | | | | $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] :
% 214.38/29.93 | | | | | | (ordered_pair(v3, v1) = v4 & in(v4, all_443_1) = 0
% 214.38/29.93 | | | | | | & $i(v4) & $i(v3))))) & ( ~ $i(all_901_1) | ( !
% 214.38/29.93 | | | | | | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 214.38/29.93 | | | | | | all_901_1) = v1) | ~ $i(v0) | ! [v2: $i] : !
% 214.38/29.93 | | | | | | [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~
% 214.38/29.93 | | | | | | (in(v3, all_443_1) = 0) | ~ $i(v2))) & ! [v0:
% 214.38/29.93 | | | | | | $i] : ( ~ (in(v0, all_901_1) = 0) | ~ $i(v0) | ?
% 214.38/29.93 | | | | | | [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) = v2
% 214.38/29.93 | | | | | | & in(v2, all_443_1) = 0 & $i(v2) & $i(v1))))))
% 214.38/29.93 | | | | | |
% 214.38/29.93 | | | | | | GROUND_INST: instantiating (t25_relat_1) with all_450_0, all_869_1,
% 214.38/29.93 | | | | | | simplifying with (17), (79) gives:
% 214.38/29.93 | | | | | | (189) ? [v0: any] : ? [v1: $i] : (relation_dom(all_450_0) = v1
% 214.38/29.93 | | | | | | & relation(all_450_0) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 214.38/29.93 | | | | | | [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 214.38/29.93 | | | | | | (relation_rng(v2) = v3) | ~ (subset(all_869_1, v3) =
% 214.38/29.93 | | | | | | v4) | ~ $i(v2) | ? [v5: any] : ? [v6: any] : ?
% 214.38/29.93 | | | | | | [v7: $i] : ? [v8: any] : (relation_dom(v2) = v7 &
% 214.38/29.93 | | | | | | subset(v1, v7) = v8 & subset(all_450_0, v2) = v6 &
% 214.38/29.93 | | | | | | relation(v2) = v5 & $i(v7) & ( ~ (v6 = 0) | ~ (v5
% 214.38/29.93 | | | | | | = 0) | (v8 = 0 & v4 = 0))))))
% 214.38/29.93 | | | | | |
% 214.38/29.93 | | | | | | GROUND_INST: instantiating (t47_relat_1) with all_450_0, all_869_1,
% 214.38/29.93 | | | | | | simplifying with (17), (79) gives:
% 214.38/29.93 | | | | | | (190) ? [v0: any] : ? [v1: $i] : (relation_dom(all_450_0) = v1
% 214.38/29.93 | | | | | | & relation(all_450_0) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 214.38/29.93 | | | | | | [v2: $i] : ! [v3: $i] : ( ~ (relation_rng(v2) = v3) |
% 214.38/29.93 | | | | | | ~ (subset(v1, v3) = 0) | ~ $i(v2) | ? [v4: any] :
% 214.38/29.93 | | | | | | ? [v5: $i] : ? [v6: $i] : (relation_composition(v2,
% 214.38/29.93 | | | | | | all_450_0) = v5 & relation_rng(v5) = v6 &
% 214.38/29.93 | | | | | | relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0)
% 214.38/29.93 | | | | | | | v6 = all_869_1)))))
% 214.38/29.93 | | | | | |
% 214.38/29.93 | | | | | | GROUND_INST: instantiating (t46_relat_1) with all_450_0, all_869_1,
% 214.38/29.93 | | | | | | simplifying with (17), (79) gives:
% 214.38/29.94 | | | | | | (191) ? [v0: any] : ? [v1: $i] : (relation_dom(all_450_0) = v1
% 214.38/29.94 | | | | | | & relation(all_450_0) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 214.38/29.94 | | | | | | [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v2) = v3) |
% 214.38/29.94 | | | | | | ~ (subset(all_869_1, v3) = 0) | ~ $i(v2) | ? [v4:
% 214.38/29.94 | | | | | | any] : ? [v5: $i] : ? [v6: $i] :
% 214.38/29.94 | | | | | | (relation_composition(all_450_0, v2) = v5 &
% 214.38/29.94 | | | | | | relation_dom(v5) = v6 & relation(v2) = v4 & $i(v6)
% 214.38/29.94 | | | | | | & $i(v5) & ( ~ (v4 = 0) | v6 = v1)))))
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | GROUND_INST: instantiating (3) with all_450_0, all_869_1,
% 214.38/29.94 | | | | | | simplifying with (17), (79) gives:
% 214.38/29.94 | | | | | | (192) ? [v0: any] : ? [v1: $i] : (relation_dom(all_450_0) = v1
% 214.38/29.94 | | | | | | & relation(all_450_0) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~
% 214.38/29.94 | | | | | | (v1 = empty_set) | all_869_1 = empty_set) & ( ~
% 214.38/29.94 | | | | | | (all_869_1 = empty_set) | v1 = empty_set))))
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | GROUND_INST: instantiating (t25_relat_1) with all_460_0, all_865_1,
% 214.38/29.94 | | | | | | simplifying with (22), (76) gives:
% 214.38/29.94 | | | | | | (193) ? [v0: any] : ? [v1: $i] : (relation_dom(all_460_0) = v1
% 214.38/29.94 | | | | | | & relation(all_460_0) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 214.38/29.94 | | | | | | [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 214.38/29.94 | | | | | | (relation_rng(v2) = v3) | ~ (subset(all_865_1, v3) =
% 214.38/29.94 | | | | | | v4) | ~ $i(v2) | ? [v5: any] : ? [v6: any] : ?
% 214.38/29.94 | | | | | | [v7: $i] : ? [v8: any] : (relation_dom(v2) = v7 &
% 214.38/29.94 | | | | | | subset(v1, v7) = v8 & subset(all_460_0, v2) = v6 &
% 214.38/29.94 | | | | | | relation(v2) = v5 & $i(v7) & ( ~ (v6 = 0) | ~ (v5
% 214.38/29.94 | | | | | | = 0) | (v8 = 0 & v4 = 0))))))
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | GROUND_INST: instantiating (t47_relat_1) with all_460_0, all_865_1,
% 214.38/29.94 | | | | | | simplifying with (22), (76) gives:
% 214.38/29.94 | | | | | | (194) ? [v0: any] : ? [v1: $i] : (relation_dom(all_460_0) = v1
% 214.38/29.94 | | | | | | & relation(all_460_0) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 214.38/29.94 | | | | | | [v2: $i] : ! [v3: $i] : ( ~ (relation_rng(v2) = v3) |
% 214.38/29.94 | | | | | | ~ (subset(v1, v3) = 0) | ~ $i(v2) | ? [v4: any] :
% 214.38/29.94 | | | | | | ? [v5: $i] : ? [v6: $i] : (relation_composition(v2,
% 214.38/29.94 | | | | | | all_460_0) = v5 & relation_rng(v5) = v6 &
% 214.38/29.94 | | | | | | relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0)
% 214.38/29.94 | | | | | | | v6 = all_865_1)))))
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | GROUND_INST: instantiating (t46_relat_1) with all_460_0, all_865_1,
% 214.38/29.94 | | | | | | simplifying with (22), (76) gives:
% 214.38/29.94 | | | | | | (195) ? [v0: any] : ? [v1: $i] : (relation_dom(all_460_0) = v1
% 214.38/29.94 | | | | | | & relation(all_460_0) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 214.38/29.94 | | | | | | [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v2) = v3) |
% 214.38/29.94 | | | | | | ~ (subset(all_865_1, v3) = 0) | ~ $i(v2) | ? [v4:
% 214.38/29.94 | | | | | | any] : ? [v5: $i] : ? [v6: $i] :
% 214.38/29.94 | | | | | | (relation_composition(all_460_0, v2) = v5 &
% 214.38/29.94 | | | | | | relation_dom(v5) = v6 & relation(v2) = v4 & $i(v6)
% 214.38/29.94 | | | | | | & $i(v5) & ( ~ (v4 = 0) | v6 = v1)))))
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | GROUND_INST: instantiating (3) with all_460_0, all_865_1,
% 214.38/29.94 | | | | | | simplifying with (22), (76) gives:
% 214.38/29.94 | | | | | | (196) ? [v0: any] : ? [v1: $i] : (relation_dom(all_460_0) = v1
% 214.38/29.94 | | | | | | & relation(all_460_0) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~
% 214.38/29.94 | | | | | | (v1 = empty_set) | all_865_1 = empty_set) & ( ~
% 214.38/29.94 | | | | | | (all_865_1 = empty_set) | v1 = empty_set))))
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | DELTA: instantiating (192) with fresh symbols all_1261_0, all_1261_1
% 214.38/29.94 | | | | | | gives:
% 214.38/29.94 | | | | | | (197) relation_dom(all_450_0) = all_1261_0 & relation(all_450_0)
% 214.38/29.94 | | | | | | = all_1261_1 & $i(all_1261_0) & ( ~ (all_1261_1 = 0) | (( ~
% 214.38/29.94 | | | | | | (all_1261_0 = empty_set) | all_869_1 = empty_set) & (
% 214.38/29.94 | | | | | | ~ (all_869_1 = empty_set) | all_1261_0 = empty_set)))
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | ALPHA: (197) implies:
% 214.38/29.94 | | | | | | (198) relation(all_450_0) = all_1261_1
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | DELTA: instantiating (187) with fresh symbols all_1263_0, all_1263_1
% 214.38/29.94 | | | | | | gives:
% 214.38/29.94 | | | | | | (199) relation_dom(all_443_1) = all_1263_0 & relation(all_443_1)
% 214.38/29.94 | | | | | | = all_1263_1 & $i(all_1263_0) & ( ~ (all_1263_1 = 0) | (( ~
% 214.38/29.94 | | | | | | (all_1263_0 = empty_set) | all_901_1 = empty_set) & (
% 214.38/29.94 | | | | | | ~ (all_901_1 = empty_set) | all_1263_0 = empty_set)))
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | ALPHA: (199) implies:
% 214.38/29.94 | | | | | | (200) relation(all_443_1) = all_1263_1
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | DELTA: instantiating (196) with fresh symbols all_1265_0, all_1265_1
% 214.38/29.94 | | | | | | gives:
% 214.38/29.94 | | | | | | (201) relation_dom(all_460_0) = all_1265_0 & relation(all_460_0)
% 214.38/29.94 | | | | | | = all_1265_1 & $i(all_1265_0) & ( ~ (all_1265_1 = 0) | (( ~
% 214.38/29.94 | | | | | | (all_1265_0 = empty_set) | all_865_1 = empty_set) & (
% 214.38/29.94 | | | | | | ~ (all_865_1 = empty_set) | all_1265_0 = empty_set)))
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | ALPHA: (201) implies:
% 214.38/29.94 | | | | | | (202) $i(all_1265_0)
% 214.38/29.94 | | | | | | (203) relation(all_460_0) = all_1265_1
% 214.38/29.94 | | | | | | (204) relation_dom(all_460_0) = all_1265_0
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | DELTA: instantiating (182) with fresh symbols all_1269_0, all_1269_1
% 214.38/29.94 | | | | | | gives:
% 214.38/29.94 | | | | | | (205) relation_dom(all_437_0) = all_1269_0 & relation(all_437_0)
% 214.38/29.94 | | | | | | = all_1269_1 & $i(all_1269_0) & ( ~ (all_1269_1 = 0) | (( ~
% 214.38/29.94 | | | | | | (all_1269_0 = empty_set) | all_861_1 = empty_set) & (
% 214.38/29.94 | | | | | | ~ (all_861_1 = empty_set) | all_1269_0 = empty_set)))
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | ALPHA: (205) implies:
% 214.38/29.94 | | | | | | (206) relation(all_437_0) = all_1269_1
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | DELTA: instantiating (190) with fresh symbols all_1279_0, all_1279_1
% 214.38/29.94 | | | | | | gives:
% 214.38/29.94 | | | | | | (207) relation_dom(all_450_0) = all_1279_0 & relation(all_450_0)
% 214.38/29.94 | | | | | | = all_1279_1 & $i(all_1279_0) & ( ~ (all_1279_1 = 0) | !
% 214.38/29.94 | | | | | | [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~
% 214.38/29.94 | | | | | | (subset(all_1279_0, v1) = 0) | ~ $i(v0) | ? [v2: any]
% 214.38/29.94 | | | | | | : ? [v3: $i] : ? [v4: $i] : (relation_composition(v0,
% 214.38/29.94 | | | | | | all_450_0) = v3 & relation_rng(v3) = v4 &
% 214.38/29.94 | | | | | | relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) |
% 214.38/29.94 | | | | | | v4 = all_869_1))))
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | ALPHA: (207) implies:
% 214.38/29.94 | | | | | | (208) relation(all_450_0) = all_1279_1
% 214.38/29.94 | | | | | | (209) ~ (all_1279_1 = 0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 214.38/29.94 | | | | | | (relation_rng(v0) = v1) | ~ (subset(all_1279_0, v1) = 0)
% 214.38/29.94 | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] :
% 214.38/29.94 | | | | | | (relation_composition(v0, all_450_0) = v3 &
% 214.38/29.94 | | | | | | relation_rng(v3) = v4 & relation(v0) = v2 & $i(v4) &
% 214.38/29.94 | | | | | | $i(v3) & ( ~ (v2 = 0) | v4 = all_869_1)))
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | DELTA: instantiating (186) with fresh symbols all_1281_0, all_1281_1
% 214.38/29.94 | | | | | | gives:
% 214.38/29.94 | | | | | | (210) relation_dom(all_443_1) = all_1281_0 & relation(all_443_1)
% 214.38/29.94 | | | | | | = all_1281_1 & $i(all_1281_0) & ( ~ (all_1281_1 = 0) | !
% 214.38/29.94 | | | | | | [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~
% 214.38/29.94 | | | | | | (subset(all_901_1, v1) = 0) | ~ $i(v0) | ? [v2: any]
% 214.38/29.94 | | | | | | : ? [v3: $i] : ? [v4: $i] :
% 214.38/29.94 | | | | | | (relation_composition(all_443_1, v0) = v3 &
% 214.38/29.94 | | | | | | relation_dom(v3) = v4 & relation(v0) = v2 & $i(v4) &
% 214.38/29.94 | | | | | | $i(v3) & ( ~ (v2 = 0) | v4 = all_1281_0))))
% 214.38/29.94 | | | | | |
% 214.38/29.94 | | | | | | ALPHA: (210) implies:
% 214.38/29.95 | | | | | | (211) relation(all_443_1) = all_1281_1
% 214.38/29.95 | | | | | | (212) ~ (all_1281_1 = 0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 214.38/29.95 | | | | | | (relation_dom(v0) = v1) | ~ (subset(all_901_1, v1) = 0)
% 214.38/29.95 | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] :
% 214.38/29.95 | | | | | | (relation_composition(all_443_1, v0) = v3 &
% 214.38/29.95 | | | | | | relation_dom(v3) = v4 & relation(v0) = v2 & $i(v4) &
% 214.38/29.95 | | | | | | $i(v3) & ( ~ (v2 = 0) | v4 = all_1281_0)))
% 214.38/29.95 | | | | | |
% 214.38/29.95 | | | | | | DELTA: instantiating (185) with fresh symbols all_1283_0, all_1283_1
% 214.38/29.95 | | | | | | gives:
% 214.38/29.95 | | | | | | (213) relation_dom(all_443_1) = all_1283_0 & relation(all_443_1)
% 214.38/29.95 | | | | | | = all_1283_1 & $i(all_1283_0) & ( ~ (all_1283_1 = 0) | !
% 214.38/29.95 | | | | | | [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~
% 214.38/29.95 | | | | | | (subset(all_1283_0, v1) = 0) | ~ $i(v0) | ? [v2: any]
% 214.38/29.95 | | | | | | : ? [v3: $i] : ? [v4: $i] : (relation_composition(v0,
% 214.38/29.95 | | | | | | all_443_1) = v3 & relation_rng(v3) = v4 &
% 214.38/29.95 | | | | | | relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) |
% 214.38/29.95 | | | | | | v4 = all_901_1))))
% 214.38/29.95 | | | | | |
% 214.38/29.95 | | | | | | ALPHA: (213) implies:
% 214.38/29.95 | | | | | | (214) relation(all_443_1) = all_1283_1
% 214.38/29.95 | | | | | |
% 214.38/29.95 | | | | | | DELTA: instantiating (191) with fresh symbols all_1285_0, all_1285_1
% 214.38/29.95 | | | | | | gives:
% 214.38/29.95 | | | | | | (215) relation_dom(all_450_0) = all_1285_0 & relation(all_450_0)
% 214.38/29.95 | | | | | | = all_1285_1 & $i(all_1285_0) & ( ~ (all_1285_1 = 0) | !
% 214.38/29.95 | | | | | | [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~
% 214.38/29.95 | | | | | | (subset(all_869_1, v1) = 0) | ~ $i(v0) | ? [v2: any]
% 214.38/29.95 | | | | | | : ? [v3: $i] : ? [v4: $i] :
% 214.38/29.95 | | | | | | (relation_composition(all_450_0, v0) = v3 &
% 214.38/29.95 | | | | | | relation_dom(v3) = v4 & relation(v0) = v2 & $i(v4) &
% 214.38/29.95 | | | | | | $i(v3) & ( ~ (v2 = 0) | v4 = all_1285_0))))
% 214.38/29.95 | | | | | |
% 214.38/29.95 | | | | | | ALPHA: (215) implies:
% 214.38/29.95 | | | | | | (216) relation(all_450_0) = all_1285_1
% 214.38/29.95 | | | | | |
% 214.38/29.95 | | | | | | DELTA: instantiating (195) with fresh symbols all_1291_0, all_1291_1
% 214.38/29.95 | | | | | | gives:
% 214.38/29.95 | | | | | | (217) relation_dom(all_460_0) = all_1291_0 & relation(all_460_0)
% 214.38/29.95 | | | | | | = all_1291_1 & $i(all_1291_0) & ( ~ (all_1291_1 = 0) | !
% 214.38/29.95 | | | | | | [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~
% 214.38/29.95 | | | | | | (subset(all_865_1, v1) = 0) | ~ $i(v0) | ? [v2: any]
% 214.38/29.95 | | | | | | : ? [v3: $i] : ? [v4: $i] :
% 214.38/29.95 | | | | | | (relation_composition(all_460_0, v0) = v3 &
% 214.38/29.95 | | | | | | relation_dom(v3) = v4 & relation(v0) = v2 & $i(v4) &
% 214.38/29.95 | | | | | | $i(v3) & ( ~ (v2 = 0) | v4 = all_1291_0))))
% 214.38/29.95 | | | | | |
% 214.38/29.95 | | | | | | ALPHA: (217) implies:
% 214.38/29.95 | | | | | | (218) relation(all_460_0) = all_1291_1
% 214.38/29.95 | | | | | | (219) relation_dom(all_460_0) = all_1291_0
% 214.38/29.95 | | | | | | (220) ~ (all_1291_1 = 0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 214.38/29.95 | | | | | | (relation_dom(v0) = v1) | ~ (subset(all_865_1, v1) = 0)
% 214.38/29.95 | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] :
% 214.38/29.95 | | | | | | (relation_composition(all_460_0, v0) = v3 &
% 214.38/29.95 | | | | | | relation_dom(v3) = v4 & relation(v0) = v2 & $i(v4) &
% 214.38/29.95 | | | | | | $i(v3) & ( ~ (v2 = 0) | v4 = all_1291_0)))
% 214.38/29.95 | | | | | |
% 214.38/29.95 | | | | | | DELTA: instantiating (194) with fresh symbols all_1293_0, all_1293_1
% 214.38/29.95 | | | | | | gives:
% 214.47/29.95 | | | | | | (221) relation_dom(all_460_0) = all_1293_0 & relation(all_460_0)
% 214.47/29.95 | | | | | | = all_1293_1 & $i(all_1293_0) & ( ~ (all_1293_1 = 0) | !
% 214.47/29.95 | | | | | | [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~
% 214.47/29.95 | | | | | | (subset(all_1293_0, v1) = 0) | ~ $i(v0) | ? [v2: any]
% 214.47/29.95 | | | | | | : ? [v3: $i] : ? [v4: $i] : (relation_composition(v0,
% 214.47/29.95 | | | | | | all_460_0) = v3 & relation_rng(v3) = v4 &
% 214.47/29.95 | | | | | | relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) |
% 214.47/29.95 | | | | | | v4 = all_865_1))))
% 214.47/29.95 | | | | | |
% 214.47/29.95 | | | | | | ALPHA: (221) implies:
% 214.47/29.95 | | | | | | (222) relation(all_460_0) = all_1293_1
% 214.47/29.95 | | | | | | (223) relation_dom(all_460_0) = all_1293_0
% 214.47/29.95 | | | | | |
% 214.47/29.95 | | | | | | DELTA: instantiating (181) with fresh symbols all_1295_0, all_1295_1
% 214.47/29.95 | | | | | | gives:
% 214.47/29.95 | | | | | | (224) relation_dom(all_437_0) = all_1295_0 & relation(all_437_0)
% 214.47/29.95 | | | | | | = all_1295_1 & $i(all_1295_0) & ( ~ (all_1295_1 = 0) | !
% 214.47/29.95 | | | | | | [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~
% 214.47/29.95 | | | | | | (subset(all_861_1, v1) = 0) | ~ $i(v0) | ? [v2: any]
% 214.47/29.95 | | | | | | : ? [v3: $i] : ? [v4: $i] :
% 214.47/29.95 | | | | | | (relation_composition(all_437_0, v0) = v3 &
% 214.47/29.95 | | | | | | relation_dom(v3) = v4 & relation(v0) = v2 & $i(v4) &
% 214.47/29.95 | | | | | | $i(v3) & ( ~ (v2 = 0) | v4 = all_1295_0))))
% 214.47/29.95 | | | | | |
% 214.47/29.95 | | | | | | ALPHA: (224) implies:
% 214.47/29.95 | | | | | | (225) relation(all_437_0) = all_1295_1
% 214.47/29.95 | | | | | |
% 214.47/29.95 | | | | | | DELTA: instantiating (180) with fresh symbols all_1297_0, all_1297_1
% 214.47/29.95 | | | | | | gives:
% 214.47/29.95 | | | | | | (226) relation_dom(all_437_0) = all_1297_0 & relation(all_437_0)
% 214.47/29.95 | | | | | | = all_1297_1 & $i(all_1297_0) & ( ~ (all_1297_1 = 0) | !
% 214.47/29.95 | | | | | | [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~
% 214.47/29.95 | | | | | | (subset(all_1297_0, v1) = 0) | ~ $i(v0) | ? [v2: any]
% 214.47/29.95 | | | | | | : ? [v3: $i] : ? [v4: $i] : (relation_composition(v0,
% 214.47/29.95 | | | | | | all_437_0) = v3 & relation_rng(v3) = v4 &
% 214.47/29.95 | | | | | | relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) |
% 214.47/29.95 | | | | | | v4 = all_861_1))))
% 214.47/29.95 | | | | | |
% 214.47/29.95 | | | | | | ALPHA: (226) implies:
% 214.47/29.95 | | | | | | (227) relation(all_437_0) = all_1297_1
% 214.47/29.95 | | | | | |
% 214.47/29.95 | | | | | | DELTA: instantiating (175) with fresh symbols all_1301_0,
% 214.47/29.95 | | | | | | all_1301_1, all_1301_2, all_1301_3, all_1301_4 gives:
% 214.47/29.95 | | | | | | (228) relation_dom(all_462_1) = all_1301_2 & apply(all_462_1,
% 214.47/29.95 | | | | | | all_1149_2) = all_1301_0 & relation(all_462_1) =
% 214.47/29.95 | | | | | | all_1301_4 & function(all_462_1) = all_1301_3 &
% 214.47/29.95 | | | | | | in(all_1149_2, all_1301_2) = all_1301_1 & $i(all_1301_0) &
% 214.47/29.95 | | | | | | $i(all_1301_2) & ( ~ (all_1301_3 = 0) | ~ (all_1301_4 = 0)
% 214.47/29.95 | | | | | | | (( ~ (all_1301_0 = all_1149_2) | ~ (all_1301_1 = 0) |
% 214.47/29.95 | | | | | | all_1149_0 = 0) & ( ~ (all_1149_0 = 0) | (all_1301_0
% 214.47/29.95 | | | | | | = all_1149_2 & all_1301_1 = 0))))
% 214.47/29.95 | | | | | |
% 214.47/29.95 | | | | | | ALPHA: (228) implies:
% 214.47/29.95 | | | | | | (229) relation(all_462_1) = all_1301_4
% 214.47/29.95 | | | | | |
% 214.47/29.95 | | | | | | DELTA: instantiating (179) with fresh symbols all_1303_0, all_1303_1
% 214.47/29.95 | | | | | | gives:
% 214.47/29.95 | | | | | | (230) relation_dom(all_437_0) = all_1303_0 & relation(all_437_0)
% 214.47/29.95 | | | | | | = all_1303_1 & $i(all_1303_0) & ( ~ (all_1303_1 = 0) | !
% 214.47/29.95 | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 214.47/29.95 | | | | | | (relation_rng(v0) = v1) | ~ (subset(all_861_1, v1) =
% 214.47/29.95 | | | | | | v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 214.47/29.95 | | | | | | [v5: $i] : ? [v6: any] : (relation_dom(v0) = v5 &
% 214.47/29.95 | | | | | | subset(all_1303_0, v5) = v6 & subset(all_437_0, v0) =
% 214.47/29.95 | | | | | | v4 & relation(v0) = v3 & $i(v5) & ( ~ (v4 = 0) | ~
% 214.47/29.95 | | | | | | (v3 = 0) | (v6 = 0 & v2 = 0)))))
% 214.47/29.95 | | | | | |
% 214.47/29.95 | | | | | | ALPHA: (230) implies:
% 214.47/29.95 | | | | | | (231) relation(all_437_0) = all_1303_1
% 214.47/29.95 | | | | | |
% 214.47/29.95 | | | | | | DELTA: instantiating (184) with fresh symbols all_1305_0, all_1305_1
% 214.47/29.95 | | | | | | gives:
% 214.47/29.96 | | | | | | (232) relation_dom(all_443_1) = all_1305_0 & relation(all_443_1)
% 214.47/29.96 | | | | | | = all_1305_1 & $i(all_1305_0) & ( ~ (all_1305_1 = 0) | !
% 214.47/29.96 | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 214.47/29.96 | | | | | | (relation_rng(v0) = v1) | ~ (subset(all_901_1, v1) =
% 214.47/29.96 | | | | | | v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 214.47/29.96 | | | | | | [v5: $i] : ? [v6: any] : (relation_dom(v0) = v5 &
% 214.47/29.96 | | | | | | subset(all_1305_0, v5) = v6 & subset(all_443_1, v0) =
% 214.47/29.96 | | | | | | v4 & relation(v0) = v3 & $i(v5) & ( ~ (v4 = 0) | ~
% 214.47/29.96 | | | | | | (v3 = 0) | (v6 = 0 & v2 = 0)))))
% 214.47/29.96 | | | | | |
% 214.47/29.96 | | | | | | ALPHA: (232) implies:
% 214.47/29.96 | | | | | | (233) relation(all_443_1) = all_1305_1
% 214.47/29.96 | | | | | |
% 214.47/29.96 | | | | | | DELTA: instantiating (189) with fresh symbols all_1309_0, all_1309_1
% 214.47/29.96 | | | | | | gives:
% 214.47/29.96 | | | | | | (234) relation_dom(all_450_0) = all_1309_0 & relation(all_450_0)
% 214.47/29.96 | | | | | | = all_1309_1 & $i(all_1309_0) & ( ~ (all_1309_1 = 0) | !
% 214.47/29.96 | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 214.47/29.96 | | | | | | (relation_rng(v0) = v1) | ~ (subset(all_869_1, v1) =
% 214.47/29.96 | | | | | | v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 214.47/29.96 | | | | | | [v5: $i] : ? [v6: any] : (relation_dom(v0) = v5 &
% 214.47/29.96 | | | | | | subset(all_1309_0, v5) = v6 & subset(all_450_0, v0) =
% 214.47/29.96 | | | | | | v4 & relation(v0) = v3 & $i(v5) & ( ~ (v4 = 0) | ~
% 214.47/29.96 | | | | | | (v3 = 0) | (v6 = 0 & v2 = 0)))))
% 214.47/29.96 | | | | | |
% 214.47/29.96 | | | | | | ALPHA: (234) implies:
% 214.47/29.96 | | | | | | (235) relation(all_450_0) = all_1309_1
% 214.47/29.96 | | | | | |
% 214.47/29.96 | | | | | | DELTA: instantiating (193) with fresh symbols all_1313_0, all_1313_1
% 214.47/29.96 | | | | | | gives:
% 214.47/29.96 | | | | | | (236) relation_dom(all_460_0) = all_1313_0 & relation(all_460_0)
% 214.47/29.96 | | | | | | = all_1313_1 & $i(all_1313_0) & ( ~ (all_1313_1 = 0) | !
% 214.47/29.96 | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 214.47/29.96 | | | | | | (relation_rng(v0) = v1) | ~ (subset(all_865_1, v1) =
% 214.47/29.96 | | | | | | v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 214.47/29.96 | | | | | | [v5: $i] : ? [v6: any] : (relation_dom(v0) = v5 &
% 214.47/29.96 | | | | | | subset(all_1313_0, v5) = v6 & subset(all_460_0, v0) =
% 214.47/29.96 | | | | | | v4 & relation(v0) = v3 & $i(v5) & ( ~ (v4 = 0) | ~
% 214.47/29.96 | | | | | | (v3 = 0) | (v6 = 0 & v2 = 0)))))
% 214.47/29.96 | | | | | |
% 214.47/29.96 | | | | | | ALPHA: (236) implies:
% 214.47/29.96 | | | | | | (237) relation(all_460_0) = all_1313_1
% 214.47/29.96 | | | | | | (238) relation_dom(all_460_0) = all_1313_0
% 214.47/29.96 | | | | | |
% 214.47/29.96 | | | | | | BETA: splitting (174) gives:
% 214.47/29.96 | | | | | |
% 214.47/29.96 | | | | | | Case 1:
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | (239) all_940_0 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | REDUCE: (111), (239) imply:
% 214.47/29.96 | | | | | | | (240) $false
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | CLOSE: (240) is inconsistent.
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | Case 2:
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with all_1269_1, all_1295_1,
% 214.47/29.96 | | | | | | | all_437_0, simplifying with (206), (225) gives:
% 214.47/29.96 | | | | | | | (241) all_1295_1 = all_1269_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with all_1295_1, all_1297_1,
% 214.47/29.96 | | | | | | | all_437_0, simplifying with (225), (227) gives:
% 214.47/29.96 | | | | | | | (242) all_1297_1 = all_1295_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with 0, all_1303_1, all_437_0,
% 214.47/29.96 | | | | | | | simplifying with (10), (231) gives:
% 214.47/29.96 | | | | | | | (243) all_1303_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with all_1297_1, all_1303_1,
% 214.47/29.96 | | | | | | | all_437_0, simplifying with (227), (231) gives:
% 214.47/29.96 | | | | | | | (244) all_1303_1 = all_1297_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with all_1281_1, all_1283_1,
% 214.47/29.96 | | | | | | | all_443_1, simplifying with (211), (214) gives:
% 214.47/29.96 | | | | | | | (245) all_1283_1 = all_1281_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with all_1263_1, all_1283_1,
% 214.47/29.96 | | | | | | | all_443_1, simplifying with (200), (214) gives:
% 214.47/29.96 | | | | | | | (246) all_1283_1 = all_1263_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with 0, all_1305_1, all_443_1,
% 214.47/29.96 | | | | | | | simplifying with (15), (233) gives:
% 214.47/29.96 | | | | | | | (247) all_1305_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with all_1283_1, all_1305_1,
% 214.47/29.96 | | | | | | | all_443_1, simplifying with (214), (233) gives:
% 214.47/29.96 | | | | | | | (248) all_1305_1 = all_1283_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with all_1261_1, all_1285_1,
% 214.47/29.96 | | | | | | | all_450_0, simplifying with (198), (216) gives:
% 214.47/29.96 | | | | | | | (249) all_1285_1 = all_1261_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with 0, all_1309_1, all_450_0,
% 214.47/29.96 | | | | | | | simplifying with (19), (235) gives:
% 214.47/29.96 | | | | | | | (250) all_1309_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with all_1285_1, all_1309_1,
% 214.47/29.96 | | | | | | | all_450_0, simplifying with (216), (235) gives:
% 214.47/29.96 | | | | | | | (251) all_1309_1 = all_1285_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with all_1279_1, all_1309_1,
% 214.47/29.96 | | | | | | | all_450_0, simplifying with (208), (235) gives:
% 214.47/29.96 | | | | | | | (252) all_1309_1 = all_1279_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with 0, all_1291_1, all_460_0,
% 214.47/29.96 | | | | | | | simplifying with (24), (218) gives:
% 214.47/29.96 | | | | | | | (253) all_1291_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with all_1291_1, all_1293_1,
% 214.47/29.96 | | | | | | | all_460_0, simplifying with (218), (222) gives:
% 214.47/29.96 | | | | | | | (254) all_1293_1 = all_1291_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with all_1293_1, all_1313_1,
% 214.47/29.96 | | | | | | | all_460_0, simplifying with (222), (237) gives:
% 214.47/29.96 | | | | | | | (255) all_1313_1 = all_1293_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with all_1265_1, all_1313_1,
% 214.47/29.96 | | | | | | | all_460_0, simplifying with (203), (237) gives:
% 214.47/29.96 | | | | | | | (256) all_1313_1 = all_1265_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (4) with 0, all_1301_4, all_462_1,
% 214.47/29.96 | | | | | | | simplifying with (52), (229) gives:
% 214.47/29.96 | | | | | | | (257) all_1301_4 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (5) with all_849_0, all_1293_0,
% 214.47/29.96 | | | | | | | all_460_0, simplifying with (64), (223) gives:
% 214.47/29.96 | | | | | | | (258) all_1293_0 = all_849_0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (5) with all_1291_0, all_1293_0,
% 214.47/29.96 | | | | | | | all_460_0, simplifying with (219), (223) gives:
% 214.47/29.96 | | | | | | | (259) all_1293_0 = all_1291_0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (5) with all_1291_0, all_1313_0,
% 214.47/29.96 | | | | | | | all_460_0, simplifying with (219), (238) gives:
% 214.47/29.96 | | | | | | | (260) all_1313_0 = all_1291_0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | GROUND_INST: instantiating (5) with all_1265_0, all_1313_0,
% 214.47/29.96 | | | | | | | all_460_0, simplifying with (204), (238) gives:
% 214.47/29.96 | | | | | | | (261) all_1313_0 = all_1265_0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (260), (261) imply:
% 214.47/29.96 | | | | | | | (262) all_1291_0 = all_1265_0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | SIMP: (262) implies:
% 214.47/29.96 | | | | | | | (263) all_1291_0 = all_1265_0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (255), (256) imply:
% 214.47/29.96 | | | | | | | (264) all_1293_1 = all_1265_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | SIMP: (264) implies:
% 214.47/29.96 | | | | | | | (265) all_1293_1 = all_1265_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (251), (252) imply:
% 214.47/29.96 | | | | | | | (266) all_1285_1 = all_1279_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | SIMP: (266) implies:
% 214.47/29.96 | | | | | | | (267) all_1285_1 = all_1279_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (250), (252) imply:
% 214.47/29.96 | | | | | | | (268) all_1279_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (247), (248) imply:
% 214.47/29.96 | | | | | | | (269) all_1283_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | SIMP: (269) implies:
% 214.47/29.96 | | | | | | | (270) all_1283_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (243), (244) imply:
% 214.47/29.96 | | | | | | | (271) all_1297_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | SIMP: (271) implies:
% 214.47/29.96 | | | | | | | (272) all_1297_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (242), (272) imply:
% 214.47/29.96 | | | | | | | (273) all_1295_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | SIMP: (273) implies:
% 214.47/29.96 | | | | | | | (274) all_1295_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (241), (274) imply:
% 214.47/29.96 | | | | | | | (275) all_1269_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (258), (259) imply:
% 214.47/29.96 | | | | | | | (276) all_1291_0 = all_849_0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | SIMP: (276) implies:
% 214.47/29.96 | | | | | | | (277) all_1291_0 = all_849_0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (254), (265) imply:
% 214.47/29.96 | | | | | | | (278) all_1291_1 = all_1265_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | SIMP: (278) implies:
% 214.47/29.96 | | | | | | | (279) all_1291_1 = all_1265_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (263), (277) imply:
% 214.47/29.96 | | | | | | | (280) all_1265_0 = all_849_0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (253), (279) imply:
% 214.47/29.96 | | | | | | | (281) all_1265_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | SIMP: (281) implies:
% 214.47/29.96 | | | | | | | (282) all_1265_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (249), (267) imply:
% 214.47/29.96 | | | | | | | (283) all_1279_1 = all_1261_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | SIMP: (283) implies:
% 214.47/29.96 | | | | | | | (284) all_1279_1 = all_1261_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (245), (246) imply:
% 214.47/29.96 | | | | | | | (285) all_1281_1 = all_1263_1
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (245), (270) imply:
% 214.47/29.96 | | | | | | | (286) all_1281_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (285), (286) imply:
% 214.47/29.96 | | | | | | | (287) all_1263_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | COMBINE_EQS: (268), (284) imply:
% 214.47/29.96 | | | | | | | (288) all_1261_1 = 0
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | REDUCE: (202), (280) imply:
% 214.47/29.96 | | | | | | | (289) $i(all_849_0)
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | BETA: splitting (178) gives:
% 214.47/29.96 | | | | | | |
% 214.47/29.96 | | | | | | | Case 1:
% 214.47/29.96 | | | | | | | |
% 214.47/29.97 | | | | | | | | (290) ? [v0: int] : ( ~ (v0 = 0) & relation(all_462_1) = v0)
% 214.47/29.97 | | | | | | | |
% 214.47/29.97 | | | | | | | | DELTA: instantiating (290) with fresh symbol all_1455_0 gives:
% 214.47/29.97 | | | | | | | | (291) ~ (all_1455_0 = 0) & relation(all_462_1) = all_1455_0
% 214.47/29.97 | | | | | | | |
% 214.47/29.97 | | | | | | | | ALPHA: (291) implies:
% 214.47/29.97 | | | | | | | | (292) ~ (all_1455_0 = 0)
% 214.47/29.97 | | | | | | | | (293) relation(all_462_1) = all_1455_0
% 214.47/29.97 | | | | | | | |
% 214.47/29.97 | | | | | | | | GROUND_INST: instantiating (4) with 0, all_1455_0, all_462_1,
% 214.47/29.97 | | | | | | | | simplifying with (52), (293) gives:
% 214.47/29.97 | | | | | | | | (294) all_1455_0 = 0
% 214.47/29.97 | | | | | | | |
% 214.47/29.97 | | | | | | | | REDUCE: (292), (294) imply:
% 214.47/29.97 | | | | | | | | (295) $false
% 214.47/29.97 | | | | | | | |
% 214.47/29.97 | | | | | | | | CLOSE: (295) is inconsistent.
% 214.47/29.97 | | | | | | | |
% 214.47/29.97 | | | | | | | Case 2:
% 214.47/29.97 | | | | | | | |
% 214.47/29.97 | | | | | | | | (296) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) =
% 214.47/29.97 | | | | | | | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 214.47/29.97 | | | | | | | | relation(v0) = v2) | ! [v2: $i] : ! [v3: any] : (
% 214.47/29.97 | | | | | | | | ~ (relation_isomorphism(all_462_1, v0, v2) = v3) |
% 214.47/29.97 | | | | | | | | ~ $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6:
% 214.47/29.97 | | | | | | | | $i] : ? [v7: $i] : ? [v8: any] :
% 214.47/29.97 | | | | | | | | (relation_rng(v2) = v7 & relation_dom(v2) = v6 &
% 214.47/29.97 | | | | | | | | one_to_one(v2) = v8 & relation(v2) = v4 &
% 214.47/29.97 | | | | | | | | function(v2) = v5 & $i(v7) & $i(v6) & ( ~ (v5 =
% 214.47/29.97 | | | | | | | | 0) | ~ (v4 = 0) | (( ~ (v8 = 0) | ~ (v7 =
% 214.47/29.97 | | | | | | | | v1) | ~ (v6 = all_811_0) | v3 = 0 | ?
% 214.47/29.97 | | | | | | | | [v9: $i] : ? [v10: $i] : ? [v11: $i] : ?
% 214.47/29.97 | | | | | | | | [v12: any] : ? [v13: any] : ? [v14: any]
% 214.47/29.97 | | | | | | | | : ? [v15: $i] : ? [v16: $i] : ? [v17:
% 214.47/29.97 | | | | | | | | $i] : ? [v18: any] : (apply(v2, v10) =
% 214.47/29.97 | | | | | | | | v16 & apply(v2, v9) = v15 &
% 214.47/29.97 | | | | | | | | ordered_pair(v15, v16) = v17 &
% 214.47/29.97 | | | | | | | | ordered_pair(v9, v10) = v11 & in(v17, v0)
% 214.47/29.97 | | | | | | | | = v18 & in(v11, all_462_1) = v12 &
% 214.47/29.97 | | | | | | | | in(v10, all_811_0) = v14 & in(v9,
% 214.47/29.97 | | | | | | | | all_811_0) = v13 & $i(v17) & $i(v16) &
% 214.47/29.97 | | | | | | | | $i(v15) & $i(v11) & $i(v10) & $i(v9) & (
% 214.47/29.97 | | | | | | | | ~ (v18 = 0) | ~ (v14 = 0) | ~ (v13 =
% 214.47/29.97 | | | | | | | | 0) | ~ (v12 = 0)) & (v12 = 0 | (v18
% 214.47/29.97 | | | | | | | | = 0 & v14 = 0 & v13 = 0)))) & ( ~ (v3
% 214.47/29.97 | | | | | | | | = 0) | (v8 = 0 & v7 = v1 & v6 = all_811_0
% 214.47/29.97 | | | | | | | | & ! [v9: $i] : ! [v10: $i] : ! [v11:
% 214.47/29.97 | | | | | | | | $i] : ! [v12: $i] : ! [v13: $i] : !
% 214.47/29.97 | | | | | | | | [v14: any] : ( ~ (apply(v2, v10) = v12) |
% 214.47/29.97 | | | | | | | | ~ (apply(v2, v9) = v11) | ~
% 214.47/29.97 | | | | | | | | (ordered_pair(v11, v12) = v13) | ~
% 214.47/29.97 | | | | | | | | (in(v13, v0) = v14) | ~ $i(v10) | ~
% 214.47/29.97 | | | | | | | | $i(v9) | ? [v15: $i] : ? [v16: any] :
% 214.47/29.97 | | | | | | | | ? [v17: any] : ? [v18: any] :
% 214.47/29.97 | | | | | | | | (ordered_pair(v9, v10) = v15 & in(v15,
% 214.47/29.97 | | | | | | | | all_462_1) = v16 & in(v10,
% 214.47/29.97 | | | | | | | | all_811_0) = v18 & in(v9,
% 214.47/29.97 | | | | | | | | all_811_0) = v17 & $i(v15) & ( ~
% 214.47/29.97 | | | | | | | | (v16 = 0) | (v18 = 0 & v17 = 0 &
% 214.47/29.97 | | | | | | | | v14 = 0)))) & ! [v9: $i] : !
% 214.47/29.97 | | | | | | | | [v10: $i] : ! [v11: $i] : ! [v12: $i] :
% 214.47/29.97 | | | | | | | | ! [v13: $i] : ( ~ (apply(v2, v10) = v12)
% 214.47/29.97 | | | | | | | | | ~ (apply(v2, v9) = v11) | ~
% 214.47/29.97 | | | | | | | | (ordered_pair(v11, v12) = v13) | ~
% 214.47/29.97 | | | | | | | | (in(v13, v0) = 0) | ~ $i(v10) | ~
% 214.47/29.97 | | | | | | | | $i(v9) | ? [v14: any] : ? [v15: any]
% 214.47/29.97 | | | | | | | | : ? [v16: $i] : ? [v17: any] :
% 214.47/29.97 | | | | | | | | (ordered_pair(v9, v10) = v16 & in(v16,
% 214.47/29.97 | | | | | | | | all_462_1) = v17 & in(v10,
% 214.47/29.97 | | | | | | | | all_811_0) = v15 & in(v9,
% 214.47/29.97 | | | | | | | | all_811_0) = v14 & $i(v16) & ( ~
% 214.47/29.97 | | | | | | | | (v15 = 0) | ~ (v14 = 0) | v17 =
% 214.47/29.97 | | | | | | | | 0))))))))))
% 214.47/29.97 | | | | | | | |
% 214.47/29.97 | | | | | | | | GROUND_INST: instantiating (296) with all_462_1, all_811_0,
% 214.47/29.97 | | | | | | | | simplifying with (28), (60) gives:
% 214.47/29.97 | | | | | | | | (297) ? [v0: int] : ( ~ (v0 = 0) & relation(all_462_1) = v0)
% 214.47/29.97 | | | | | | | | | ! [v0: $i] : ! [v1: any] : ( ~
% 214.47/29.97 | | | | | | | | (relation_isomorphism(all_462_1, all_462_1, v0) = v1)
% 214.47/29.97 | | | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4:
% 214.47/29.97 | | | | | | | | $i] : ? [v5: $i] : ? [v6: any] :
% 214.47/29.97 | | | | | | | | (relation_rng(v0) = v5 & relation_dom(v0) = v4 &
% 214.47/29.97 | | | | | | | | one_to_one(v0) = v6 & relation(v0) = v2 &
% 214.47/29.97 | | | | | | | | function(v0) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0)
% 214.47/29.97 | | | | | | | | | ~ (v2 = 0) | (( ~ (v6 = 0) | ~ (v5 =
% 214.47/29.97 | | | | | | | | all_811_0) | ~ (v4 = all_811_0) | v1 = 0 |
% 214.47/29.97 | | | | | | | | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 214.47/29.97 | | | | | | | | [v10: any] : ? [v11: any] : ? [v12: any] :
% 214.47/29.97 | | | | | | | | ? [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 214.47/29.97 | | | | | | | | ? [v16: any] : (apply(v0, v8) = v14 &
% 214.47/29.97 | | | | | | | | apply(v0, v7) = v13 & ordered_pair(v13,
% 214.47/29.97 | | | | | | | | v14) = v15 & ordered_pair(v7, v8) = v9 &
% 214.47/29.97 | | | | | | | | in(v15, all_462_1) = v16 & in(v9,
% 214.47/29.97 | | | | | | | | all_462_1) = v10 & in(v8, all_811_0) =
% 214.47/29.97 | | | | | | | | v12 & in(v7, all_811_0) = v11 & $i(v15) &
% 214.47/29.97 | | | | | | | | $i(v14) & $i(v13) & $i(v9) & $i(v8) &
% 214.47/29.97 | | | | | | | | $i(v7) & ( ~ (v16 = 0) | ~ (v12 = 0) | ~
% 214.47/29.97 | | | | | | | | (v11 = 0) | ~ (v10 = 0)) & (v10 = 0 |
% 214.47/29.97 | | | | | | | | (v16 = 0 & v12 = 0 & v11 = 0)))) & ( ~
% 214.47/29.97 | | | | | | | | (v1 = 0) | (v6 = 0 & v5 = all_811_0 & v4 =
% 214.47/29.97 | | | | | | | | all_811_0 & ! [v7: $i] : ! [v8: $i] : !
% 214.47/29.97 | | | | | | | | [v9: $i] : ! [v10: $i] : ! [v11: $i] : !
% 214.47/29.97 | | | | | | | | [v12: any] : ( ~ (apply(v0, v8) = v10) | ~
% 214.47/29.97 | | | | | | | | (apply(v0, v7) = v9) | ~
% 214.47/29.97 | | | | | | | | (ordered_pair(v9, v10) = v11) | ~
% 214.47/29.97 | | | | | | | | (in(v11, all_462_1) = v12) | ~ $i(v8) |
% 214.47/29.97 | | | | | | | | ~ $i(v7) | ? [v13: $i] : ? [v14: any] :
% 214.47/29.97 | | | | | | | | ? [v15: any] : ? [v16: any] :
% 214.47/29.97 | | | | | | | | (ordered_pair(v7, v8) = v13 & in(v13,
% 214.47/29.97 | | | | | | | | all_462_1) = v14 & in(v8, all_811_0)
% 214.47/29.97 | | | | | | | | = v16 & in(v7, all_811_0) = v15 &
% 214.47/29.97 | | | | | | | | $i(v13) & ( ~ (v14 = 0) | (v16 = 0 &
% 214.47/29.97 | | | | | | | | v15 = 0 & v12 = 0)))) & ! [v7: $i]
% 214.47/29.97 | | | | | | | | : ! [v8: $i] : ! [v9: $i] : ! [v10: $i]
% 214.47/29.97 | | | | | | | | : ! [v11: $i] : ( ~ (apply(v0, v8) = v10)
% 214.47/29.97 | | | | | | | | | ~ (apply(v0, v7) = v9) | ~
% 214.47/29.97 | | | | | | | | (ordered_pair(v9, v10) = v11) | ~
% 214.47/29.97 | | | | | | | | (in(v11, all_462_1) = 0) | ~ $i(v8) | ~
% 214.47/29.97 | | | | | | | | $i(v7) | ? [v12: any] : ? [v13: any] :
% 214.47/29.97 | | | | | | | | ? [v14: $i] : ? [v15: any] :
% 214.47/29.97 | | | | | | | | (ordered_pair(v7, v8) = v14 & in(v14,
% 214.47/29.97 | | | | | | | | all_462_1) = v15 & in(v8, all_811_0)
% 214.47/29.97 | | | | | | | | = v13 & in(v7, all_811_0) = v12 &
% 214.47/29.97 | | | | | | | | $i(v14) & ( ~ (v13 = 0) | ~ (v12 = 0)
% 214.47/29.97 | | | | | | | | | v15 = 0)))))))))
% 214.47/29.97 | | | | | | | |
% 214.47/29.97 | | | | | | | | BETA: splitting (177) gives:
% 214.47/29.97 | | | | | | | |
% 214.47/29.97 | | | | | | | | Case 1:
% 214.47/29.97 | | | | | | | | |
% 214.47/29.97 | | | | | | | | | (298) ? [v0: int] : ( ~ (v0 = 0) & relation(all_462_1) =
% 214.47/29.97 | | | | | | | | | v0)
% 214.47/29.97 | | | | | | | | |
% 214.47/29.97 | | | | | | | | | BETA: splitting (176) gives:
% 214.47/29.97 | | | | | | | | |
% 214.47/29.97 | | | | | | | | | Case 1:
% 214.47/29.97 | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | (299) ? [v0: int] : ( ~ (v0 = 0) & relation(all_460_0) =
% 214.47/29.97 | | | | | | | | | | v0)
% 214.47/29.97 | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | BETA: splitting (212) gives:
% 214.47/29.97 | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | Case 1:
% 214.47/29.97 | | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | | (300) ~ (all_1281_1 = 0)
% 214.47/29.97 | | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | | REDUCE: (286), (300) imply:
% 214.47/29.97 | | | | | | | | | | | (301) $false
% 214.47/29.97 | | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | | CLOSE: (301) is inconsistent.
% 214.47/29.97 | | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | Case 2:
% 214.47/29.97 | | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | | DELTA: instantiating (299) with fresh symbol all_1445_0
% 214.47/29.97 | | | | | | | | | | | gives:
% 214.47/29.97 | | | | | | | | | | | (302) ~ (all_1445_0 = 0) & relation(all_460_0) =
% 214.47/29.97 | | | | | | | | | | | all_1445_0
% 214.47/29.97 | | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | | ALPHA: (302) implies:
% 214.47/29.97 | | | | | | | | | | | (303) ~ (all_1445_0 = 0)
% 214.47/29.97 | | | | | | | | | | | (304) relation(all_460_0) = all_1445_0
% 214.47/29.97 | | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | | BETA: splitting (220) gives:
% 214.47/29.97 | | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | | Case 1:
% 214.47/29.97 | | | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | | | (305) ~ (all_1291_1 = 0)
% 214.47/29.97 | | | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | | | REDUCE: (253), (305) imply:
% 214.47/29.97 | | | | | | | | | | | | (306) $false
% 214.47/29.97 | | | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | | | CLOSE: (306) is inconsistent.
% 214.47/29.97 | | | | | | | | | | | |
% 214.47/29.97 | | | | | | | | | | | Case 2:
% 214.47/29.97 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | DELTA: instantiating (299) with fresh symbol all_1473_0
% 214.47/29.98 | | | | | | | | | | | | gives:
% 214.47/29.98 | | | | | | | | | | | | (307) ~ (all_1473_0 = 0) & relation(all_460_0) =
% 214.47/29.98 | | | | | | | | | | | | all_1473_0
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | ALPHA: (307) implies:
% 214.47/29.98 | | | | | | | | | | | | (308) relation(all_460_0) = all_1473_0
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_1473_0, all_460_0,
% 214.47/29.98 | | | | | | | | | | | | simplifying with (24), (308) gives:
% 214.47/29.98 | | | | | | | | | | | | (309) all_1473_0 = 0
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_1445_0, all_1473_0,
% 214.47/29.98 | | | | | | | | | | | | all_460_0, simplifying with (304), (308) gives:
% 214.47/29.98 | | | | | | | | | | | | (310) all_1473_0 = all_1445_0
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | COMBINE_EQS: (309), (310) imply:
% 214.47/29.98 | | | | | | | | | | | | (311) all_1445_0 = 0
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | REDUCE: (303), (311) imply:
% 214.47/29.98 | | | | | | | | | | | | (312) $false
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | CLOSE: (312) is inconsistent.
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | End of split
% 214.47/29.98 | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | End of split
% 214.47/29.98 | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | Case 2:
% 214.47/29.98 | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | (313) ? [v0: any] : (v0 = all_849_0 | ~ $i(v0) | ?
% 214.47/29.98 | | | | | | | | | | [v1: $i] : ? [v2: any] : (in(v1, v0) = v2 &
% 214.47/29.98 | | | | | | | | | | $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4:
% 214.47/29.98 | | | | | | | | | | $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~
% 214.47/29.98 | | | | | | | | | | (in(v4, all_460_0) = 0) | ~ $i(v3))) & (v2
% 214.47/29.98 | | | | | | | | | | = 0 | ? [v3: $i] : ? [v4: $i] :
% 214.47/29.98 | | | | | | | | | | (ordered_pair(v1, v3) = v4 & in(v4,
% 214.47/29.98 | | | | | | | | | | all_460_0) = 0 & $i(v4) & $i(v3))))) & (
% 214.47/29.98 | | | | | | | | | | ~ $i(all_849_0) | ( ! [v0: $i] : ! [v1: int] :
% 214.47/29.98 | | | | | | | | | | (v1 = 0 | ~ (in(v0, all_849_0) = v1) | ~
% 214.47/29.98 | | | | | | | | | | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 214.47/29.98 | | | | | | | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3,
% 214.47/29.98 | | | | | | | | | | all_460_0) = 0) | ~ $i(v2))) & ! [v0:
% 214.47/29.98 | | | | | | | | | | $i] : ( ~ (in(v0, all_849_0) = 0) | ~ $i(v0)
% 214.47/29.98 | | | | | | | | | | | ? [v1: $i] : ? [v2: $i] :
% 214.47/29.98 | | | | | | | | | | (ordered_pair(v0, v1) = v2 & in(v2,
% 214.47/29.98 | | | | | | | | | | all_460_0) = 0 & $i(v2) & $i(v1)))))
% 214.47/29.98 | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | ALPHA: (313) implies:
% 214.47/29.98 | | | | | | | | | | (314) ~ $i(all_849_0) | ( ! [v0: $i] : ! [v1: int] :
% 214.47/29.98 | | | | | | | | | | (v1 = 0 | ~ (in(v0, all_849_0) = v1) | ~ $i(v0)
% 214.47/29.98 | | | | | | | | | | | ! [v2: $i] : ! [v3: $i] : ( ~
% 214.47/29.98 | | | | | | | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3,
% 214.47/29.98 | | | | | | | | | | all_460_0) = 0) | ~ $i(v2))) & ! [v0:
% 214.47/29.98 | | | | | | | | | | $i] : ( ~ (in(v0, all_849_0) = 0) | ~ $i(v0) |
% 214.47/29.98 | | | | | | | | | | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0,
% 214.47/29.98 | | | | | | | | | | v1) = v2 & in(v2, all_460_0) = 0 & $i(v2) &
% 214.47/29.98 | | | | | | | | | | $i(v1))))
% 214.47/29.98 | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | BETA: splitting (183) gives:
% 214.47/29.98 | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | Case 1:
% 214.47/29.98 | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | (315) ? [v0: int] : ( ~ (v0 = 0) & relation(all_437_0)
% 214.47/29.98 | | | | | | | | | | | = v0)
% 214.47/29.98 | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | BETA: splitting (209) gives:
% 214.47/29.98 | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | Case 1:
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | (316) ~ (all_1279_1 = 0)
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | REDUCE: (268), (316) imply:
% 214.47/29.98 | | | | | | | | | | | | (317) $false
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | CLOSE: (317) is inconsistent.
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | Case 2:
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | DELTA: instantiating (315) with fresh symbol all_1505_0
% 214.47/29.98 | | | | | | | | | | | | gives:
% 214.47/29.98 | | | | | | | | | | | | (318) ~ (all_1505_0 = 0) & relation(all_437_0) =
% 214.47/29.98 | | | | | | | | | | | | all_1505_0
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | ALPHA: (318) implies:
% 214.47/29.98 | | | | | | | | | | | | (319) ~ (all_1505_0 = 0)
% 214.47/29.98 | | | | | | | | | | | | (320) relation(all_437_0) = all_1505_0
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | BETA: splitting (314) gives:
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | Case 1:
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | (321) ~ $i(all_849_0)
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | PRED_UNIFY: (289), (321) imply:
% 214.47/29.98 | | | | | | | | | | | | | (322) $false
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | CLOSE: (322) is inconsistent.
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | Case 2:
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | DELTA: instantiating (315) with fresh symbol all_1553_0
% 214.47/29.98 | | | | | | | | | | | | | gives:
% 214.47/29.98 | | | | | | | | | | | | | (323) ~ (all_1553_0 = 0) & relation(all_437_0) =
% 214.47/29.98 | | | | | | | | | | | | | all_1553_0
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | ALPHA: (323) implies:
% 214.47/29.98 | | | | | | | | | | | | | (324) relation(all_437_0) = all_1553_0
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_1553_0, all_437_0,
% 214.47/29.98 | | | | | | | | | | | | | simplifying with (10), (324) gives:
% 214.47/29.98 | | | | | | | | | | | | | (325) all_1553_0 = 0
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_1505_0, all_1553_0,
% 214.47/29.98 | | | | | | | | | | | | | all_437_0, simplifying with (320), (324) gives:
% 214.47/29.98 | | | | | | | | | | | | | (326) all_1553_0 = all_1505_0
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | COMBINE_EQS: (325), (326) imply:
% 214.47/29.98 | | | | | | | | | | | | | (327) all_1505_0 = 0
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | REDUCE: (319), (327) imply:
% 214.47/29.98 | | | | | | | | | | | | | (328) $false
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | CLOSE: (328) is inconsistent.
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | End of split
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | End of split
% 214.47/29.98 | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | Case 2:
% 214.47/29.98 | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | (329) ? [v0: any] : (v0 = all_861_1 | ~ $i(v0) | ?
% 214.47/29.98 | | | | | | | | | | | [v1: $i] : ? [v2: any] : (in(v1, v0) = v2 &
% 214.47/29.98 | | | | | | | | | | | $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4:
% 214.47/29.98 | | | | | | | | | | | $i] : ( ~ (ordered_pair(v3, v1) = v4) | ~
% 214.47/29.98 | | | | | | | | | | | (in(v4, all_437_0) = 0) | ~ $i(v3))) &
% 214.47/29.98 | | | | | | | | | | | (v2 = 0 | ? [v3: $i] : ? [v4: $i] :
% 214.47/29.98 | | | | | | | | | | | (ordered_pair(v3, v1) = v4 & in(v4,
% 214.47/29.98 | | | | | | | | | | | all_437_0) = 0 & $i(v4) & $i(v3))))) & (
% 214.47/29.98 | | | | | | | | | | | ~ $i(all_861_1) | ( ! [v0: $i] : ! [v1: int] :
% 214.47/29.98 | | | | | | | | | | | (v1 = 0 | ~ (in(v0, all_861_1) = v1) | ~
% 214.47/29.98 | | | | | | | | | | | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 214.47/29.98 | | | | | | | | | | | (ordered_pair(v2, v0) = v3) | ~ (in(v3,
% 214.47/29.98 | | | | | | | | | | | all_437_0) = 0) | ~ $i(v2))) & !
% 214.47/29.98 | | | | | | | | | | | [v0: $i] : ( ~ (in(v0, all_861_1) = 0) | ~
% 214.47/29.98 | | | | | | | | | | | $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 214.47/29.98 | | | | | | | | | | | (ordered_pair(v1, v0) = v2 & in(v2,
% 214.47/29.98 | | | | | | | | | | | all_437_0) = 0 & $i(v2) & $i(v1)))))
% 214.47/29.98 | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | ALPHA: (329) implies:
% 214.47/29.98 | | | | | | | | | | | (330) ~ $i(all_861_1) | ( ! [v0: $i] : ! [v1: int] :
% 214.47/29.98 | | | | | | | | | | | (v1 = 0 | ~ (in(v0, all_861_1) = v1) | ~
% 214.47/29.98 | | | | | | | | | | | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 214.47/29.98 | | | | | | | | | | | (ordered_pair(v2, v0) = v3) | ~ (in(v3,
% 214.47/29.98 | | | | | | | | | | | all_437_0) = 0) | ~ $i(v2))) & ! [v0:
% 214.47/29.98 | | | | | | | | | | | $i] : ( ~ (in(v0, all_861_1) = 0) | ~ $i(v0)
% 214.47/29.98 | | | | | | | | | | | | ? [v1: $i] : ? [v2: $i] :
% 214.47/29.98 | | | | | | | | | | | (ordered_pair(v1, v0) = v2 & in(v2, all_437_0)
% 214.47/29.98 | | | | | | | | | | | = 0 & $i(v2) & $i(v1))))
% 214.47/29.98 | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | BETA: splitting (188) gives:
% 214.47/29.98 | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | Case 1:
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | (331) ? [v0: int] : ( ~ (v0 = 0) & relation(all_443_1)
% 214.47/29.98 | | | | | | | | | | | | = v0)
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | BETA: splitting (330) gives:
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | Case 1:
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | (332) ~ $i(all_861_1)
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | PRED_UNIFY: (70), (332) imply:
% 214.47/29.98 | | | | | | | | | | | | | (333) $false
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | CLOSE: (333) is inconsistent.
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | Case 2:
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | DELTA: instantiating (331) with fresh symbol all_1549_0
% 214.47/29.98 | | | | | | | | | | | | | gives:
% 214.47/29.98 | | | | | | | | | | | | | (334) ~ (all_1549_0 = 0) & relation(all_443_1) =
% 214.47/29.98 | | | | | | | | | | | | | all_1549_0
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | ALPHA: (334) implies:
% 214.47/29.98 | | | | | | | | | | | | | (335) ~ (all_1549_0 = 0)
% 214.47/29.98 | | | | | | | | | | | | | (336) relation(all_443_1) = all_1549_0
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_1549_0, all_443_1,
% 214.47/29.98 | | | | | | | | | | | | | simplifying with (15), (336) gives:
% 214.47/29.98 | | | | | | | | | | | | | (337) all_1549_0 = 0
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | REDUCE: (335), (337) imply:
% 214.47/29.98 | | | | | | | | | | | | | (338) $false
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | | CLOSE: (338) is inconsistent.
% 214.47/29.98 | | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | End of split
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | Case 2:
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | DELTA: instantiating (298) with fresh symbol all_1504_0
% 214.47/29.98 | | | | | | | | | | | | gives:
% 214.47/29.98 | | | | | | | | | | | | (339) ~ (all_1504_0 = 0) & relation(all_462_1) =
% 214.47/29.98 | | | | | | | | | | | | all_1504_0
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | ALPHA: (339) implies:
% 214.47/29.98 | | | | | | | | | | | | (340) ~ (all_1504_0 = 0)
% 214.47/29.98 | | | | | | | | | | | | (341) relation(all_462_1) = all_1504_0
% 214.47/29.98 | | | | | | | | | | | |
% 214.47/29.98 | | | | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_1504_0, all_462_1,
% 214.47/29.98 | | | | | | | | | | | | simplifying with (52), (341) gives:
% 214.47/29.99 | | | | | | | | | | | | (342) all_1504_0 = 0
% 214.47/29.99 | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | REDUCE: (340), (342) imply:
% 214.47/29.99 | | | | | | | | | | | | (343) $false
% 214.47/29.99 | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | CLOSE: (343) is inconsistent.
% 214.47/29.99 | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | End of split
% 214.47/29.99 | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | End of split
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | End of split
% 214.47/29.99 | | | | | | | | |
% 214.47/29.99 | | | | | | | | Case 2:
% 214.47/29.99 | | | | | | | | |
% 214.47/29.99 | | | | | | | | | (344) all_811_0 = all_462_2 & ! [v0: $i] : ! [v1: $i] :
% 214.47/29.99 | | | | | | | | | ! [v2: $i] : ! [v3: any] : ( ~ (ordered_pair(v0, v1)
% 214.47/29.99 | | | | | | | | | = v2) | ~ (in(v2, all_462_1) = v3) | ~ $i(v1) |
% 214.47/29.99 | | | | | | | | | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 214.47/29.99 | | | | | | | | | any] : (subset(v0, v1) = v6 & in(v1, all_462_2) =
% 214.47/29.99 | | | | | | | | | v5 & in(v0, all_462_2) = v4 & ( ~ (v5 = 0) | ~
% 214.47/29.99 | | | | | | | | | (v4 = 0) | (( ~ (v6 = 0) | v3 = 0) & ( ~ (v3 =
% 214.47/29.99 | | | | | | | | | 0) | v6 = 0)))))
% 214.47/29.99 | | | | | | | | |
% 214.47/29.99 | | | | | | | | | ALPHA: (344) implies:
% 214.47/29.99 | | | | | | | | | (345) all_811_0 = all_462_2
% 214.47/29.99 | | | | | | | | | (346) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 214.47/29.99 | | | | | | | | | any] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (in(v2,
% 214.47/29.99 | | | | | | | | | all_462_1) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 214.47/29.99 | | | | | | | | | [v4: any] : ? [v5: any] : ? [v6: any] :
% 214.47/29.99 | | | | | | | | | (subset(v0, v1) = v6 & in(v1, all_462_2) = v5 &
% 214.47/29.99 | | | | | | | | | in(v0, all_462_2) = v4 & ( ~ (v5 = 0) | ~ (v4 =
% 214.47/29.99 | | | | | | | | | 0) | (( ~ (v6 = 0) | v3 = 0) & ( ~ (v3 = 0) |
% 214.47/29.99 | | | | | | | | | v6 = 0)))))
% 214.47/29.99 | | | | | | | | |
% 214.47/29.99 | | | | | | | | | GROUND_INST: instantiating (346) with all_1149_2, all_1149_2,
% 214.47/29.99 | | | | | | | | | all_1149_1, all_1149_0, simplifying with (170),
% 214.47/29.99 | | | | | | | | | (172), (173) gives:
% 214.47/29.99 | | | | | | | | | (347) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 214.47/29.99 | | | | | | | | | (subset(all_1149_2, all_1149_2) = v2 & in(all_1149_2,
% 214.47/29.99 | | | | | | | | | all_462_2) = v1 & in(all_1149_2, all_462_2) = v0
% 214.47/29.99 | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v2 = 0) |
% 214.47/29.99 | | | | | | | | | all_1149_0 = 0) & ( ~ (all_1149_0 = 0) | v2 =
% 214.47/29.99 | | | | | | | | | 0))))
% 214.47/29.99 | | | | | | | | |
% 214.47/29.99 | | | | | | | | | REDUCE: (171), (345) imply:
% 214.47/29.99 | | | | | | | | | (348) in(all_1149_2, all_462_2) = 0
% 214.47/29.99 | | | | | | | | |
% 214.47/29.99 | | | | | | | | | BETA: splitting (297) gives:
% 214.47/29.99 | | | | | | | | |
% 214.47/29.99 | | | | | | | | | Case 1:
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | (349) ? [v0: int] : ( ~ (v0 = 0) & relation(all_462_1) =
% 214.47/29.99 | | | | | | | | | | v0)
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | DELTA: instantiating (349) with fresh symbol all_1509_0
% 214.47/29.99 | | | | | | | | | | gives:
% 214.47/29.99 | | | | | | | | | | (350) ~ (all_1509_0 = 0) & relation(all_462_1) =
% 214.47/29.99 | | | | | | | | | | all_1509_0
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | ALPHA: (350) implies:
% 214.47/29.99 | | | | | | | | | | (351) ~ (all_1509_0 = 0)
% 214.47/29.99 | | | | | | | | | | (352) relation(all_462_1) = all_1509_0
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_1509_0, all_462_1,
% 214.47/29.99 | | | | | | | | | | simplifying with (52), (352) gives:
% 214.47/29.99 | | | | | | | | | | (353) all_1509_0 = 0
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | REDUCE: (351), (353) imply:
% 214.47/29.99 | | | | | | | | | | (354) $false
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | CLOSE: (354) is inconsistent.
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | Case 2:
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | DELTA: instantiating (347) with fresh symbols all_1507_0,
% 214.47/29.99 | | | | | | | | | | all_1507_1, all_1507_2 gives:
% 214.47/29.99 | | | | | | | | | | (355) subset(all_1149_2, all_1149_2) = all_1507_0 &
% 214.47/29.99 | | | | | | | | | | in(all_1149_2, all_462_2) = all_1507_1 &
% 214.47/29.99 | | | | | | | | | | in(all_1149_2, all_462_2) = all_1507_2 & ( ~
% 214.47/29.99 | | | | | | | | | | (all_1507_1 = 0) | ~ (all_1507_2 = 0) | (( ~
% 214.47/29.99 | | | | | | | | | | (all_1507_0 = 0) | all_1149_0 = 0) & ( ~
% 214.47/29.99 | | | | | | | | | | (all_1149_0 = 0) | all_1507_0 = 0)))
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | ALPHA: (355) implies:
% 214.47/29.99 | | | | | | | | | | (356) in(all_1149_2, all_462_2) = all_1507_2
% 214.47/29.99 | | | | | | | | | | (357) in(all_1149_2, all_462_2) = all_1507_1
% 214.47/29.99 | | | | | | | | | | (358) subset(all_1149_2, all_1149_2) = all_1507_0
% 214.47/29.99 | | | | | | | | | | (359) ~ (all_1507_1 = 0) | ~ (all_1507_2 = 0) | (( ~
% 214.47/29.99 | | | | | | | | | | (all_1507_0 = 0) | all_1149_0 = 0) & ( ~
% 214.47/29.99 | | | | | | | | | | (all_1149_0 = 0) | all_1507_0 = 0))
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | GROUND_INST: instantiating (6) with all_1507_2, all_1507_1,
% 214.47/29.99 | | | | | | | | | | all_462_2, all_1149_2, simplifying with (356),
% 214.47/29.99 | | | | | | | | | | (357) gives:
% 214.47/29.99 | | | | | | | | | | (360) all_1507_1 = all_1507_2
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_1507_1, all_462_2,
% 214.47/29.99 | | | | | | | | | | all_1149_2, simplifying with (348), (357) gives:
% 214.47/29.99 | | | | | | | | | | (361) all_1507_1 = 0
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | COMBINE_EQS: (360), (361) imply:
% 214.47/29.99 | | | | | | | | | | (362) all_1507_2 = 0
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | SIMP: (362) implies:
% 214.47/29.99 | | | | | | | | | | (363) all_1507_2 = 0
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | BETA: splitting (359) gives:
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | Case 1:
% 214.47/29.99 | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | (364) ~ (all_1507_1 = 0)
% 214.47/29.99 | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | REDUCE: (361), (364) imply:
% 214.47/29.99 | | | | | | | | | | | (365) $false
% 214.47/29.99 | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | CLOSE: (365) is inconsistent.
% 214.47/29.99 | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | Case 2:
% 214.47/29.99 | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | (366) ~ (all_1507_2 = 0) | (( ~ (all_1507_0 = 0) |
% 214.47/29.99 | | | | | | | | | | | all_1149_0 = 0) & ( ~ (all_1149_0 = 0) |
% 214.47/29.99 | | | | | | | | | | | all_1507_0 = 0))
% 214.47/29.99 | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | BETA: splitting (366) gives:
% 214.47/29.99 | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | Case 1:
% 214.47/29.99 | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | (367) ~ (all_1507_2 = 0)
% 214.47/29.99 | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | REDUCE: (363), (367) imply:
% 214.47/29.99 | | | | | | | | | | | | (368) $false
% 214.47/29.99 | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | CLOSE: (368) is inconsistent.
% 214.47/29.99 | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | Case 2:
% 214.47/29.99 | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | (369) ( ~ (all_1507_0 = 0) | all_1149_0 = 0) & ( ~
% 214.47/29.99 | | | | | | | | | | | | (all_1149_0 = 0) | all_1507_0 = 0)
% 214.47/29.99 | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | ALPHA: (369) implies:
% 214.47/29.99 | | | | | | | | | | | | (370) ~ (all_1507_0 = 0) | all_1149_0 = 0
% 214.47/29.99 | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | BETA: splitting (370) gives:
% 214.47/29.99 | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | Case 1:
% 214.47/29.99 | | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | | (371) ~ (all_1507_0 = 0)
% 214.47/29.99 | | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_1149_2, all_1507_0,
% 214.47/29.99 | | | | | | | | | | | | | simplifying with (170), (358) gives:
% 214.47/29.99 | | | | | | | | | | | | | (372) all_1507_0 = 0
% 214.47/29.99 | | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | | REDUCE: (371), (372) imply:
% 214.47/29.99 | | | | | | | | | | | | | (373) $false
% 214.47/29.99 | | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | | CLOSE: (373) is inconsistent.
% 214.47/29.99 | | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | Case 2:
% 214.47/29.99 | | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | | (374) all_1149_0 = 0
% 214.47/29.99 | | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | | REDUCE: (169), (374) imply:
% 214.47/29.99 | | | | | | | | | | | | | (375) $false
% 214.47/29.99 | | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | | CLOSE: (375) is inconsistent.
% 214.47/29.99 | | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | | End of split
% 214.47/29.99 | | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | | End of split
% 214.47/29.99 | | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | | End of split
% 214.47/29.99 | | | | | | | | | |
% 214.47/29.99 | | | | | | | | | End of split
% 214.47/29.99 | | | | | | | | |
% 214.47/29.99 | | | | | | | | End of split
% 214.47/29.99 | | | | | | | |
% 214.47/29.99 | | | | | | | End of split
% 214.47/29.99 | | | | | | |
% 214.47/29.99 | | | | | | End of split
% 214.47/29.99 | | | | | |
% 214.47/29.99 | | | | | End of split
% 214.47/29.99 | | | | |
% 214.47/29.99 | | | | End of split
% 214.47/29.99 | | | |
% 214.47/29.99 | | | End of split
% 214.47/29.99 | | |
% 214.47/29.99 | | End of split
% 214.47/29.99 | |
% 214.47/29.99 | End of split
% 214.47/29.99 |
% 214.47/29.99 End of proof
% 214.47/29.99 % SZS output end Proof for theBenchmark
% 214.47/29.99
% 214.47/29.99 29403ms
%------------------------------------------------------------------------------