TSTP Solution File: SEU261+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU261+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 : n006.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 17:43:43 EDT 2023
% Result : Theorem 87.71s 12.48s
% Output : Proof 89.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU261+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 16:51:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 8.41/1.89 Prover 4: Preprocessing ...
% 8.41/1.89 Prover 1: Preprocessing ...
% 8.41/1.90 Prover 0: Preprocessing ...
% 8.41/1.90 Prover 5: Preprocessing ...
% 8.41/1.90 Prover 3: Preprocessing ...
% 8.41/1.90 Prover 2: Preprocessing ...
% 8.41/1.91 Prover 6: Preprocessing ...
% 24.76/4.12 Prover 1: Warning: ignoring some quantifiers
% 25.87/4.29 Prover 1: Constructing countermodel ...
% 25.87/4.30 Prover 3: Warning: ignoring some quantifiers
% 26.62/4.32 Prover 3: Constructing countermodel ...
% 26.62/4.39 Prover 5: Proving ...
% 27.18/4.41 Prover 6: Proving ...
% 32.32/5.11 Prover 2: Proving ...
% 43.24/6.52 Prover 4: Warning: ignoring some quantifiers
% 44.37/6.78 Prover 4: Constructing countermodel ...
% 49.80/7.51 Prover 0: Proving ...
% 85.44/12.10 Prover 2: stopped
% 85.44/12.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 85.65/12.25 Prover 1: Found proof (size 447)
% 85.65/12.25 Prover 1: proved (11626ms)
% 85.65/12.25 Prover 4: stopped
% 85.65/12.25 Prover 5: stopped
% 85.65/12.26 Prover 6: stopped
% 85.65/12.26 Prover 3: stopped
% 87.13/12.30 Prover 0: stopped
% 87.13/12.32 Prover 7: Preprocessing ...
% 87.71/12.48 Prover 7: stopped
% 87.71/12.48
% 87.71/12.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 87.71/12.48
% 88.01/12.56 % SZS output start Proof for theBenchmark
% 88.27/12.58 Assumptions after simplification:
% 88.27/12.58 ---------------------------------
% 88.27/12.58
% 88.27/12.58 (cc1_relat_1)
% 88.27/12.60 ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | relation(v0) = 0)
% 88.27/12.60
% 88.27/12.60 (d12_funct_1)
% 88.27/12.61 ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 88.27/12.61 : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ (v1 = 0) | ( ?
% 88.27/12.61 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~
% 88.27/12.61 (relation_image(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i]
% 88.27/12.61 : ? [v7: any] : (in(v6, v3) = v7 & $i(v6) & ( ~ (v7 = 0) | ! [v8:
% 88.27/12.61 $i] : ( ~ (in(v8, v2) = 0) | ~ $i(v8) | ? [v9: any] : ?
% 88.27/12.61 [v10: $i] : (apply(v0, v8) = v10 & in(v8, v4) = v9 & $i(v10) &
% 88.27/12.61 ( ~ (v10 = v6) | ~ (v9 = 0))))) & (v7 = 0 | ? [v8: $i] :
% 88.27/12.61 (apply(v0, v8) = v6 & in(v8, v4) = 0 & in(v8, v2) = 0 &
% 88.27/12.61 $i(v8))))) & ! [v3: $i] : ! [v4: $i] : ( ~
% 88.27/12.61 (relation_image(v0, v3) = v4) | ~ $i(v4) | ~ $i(v3) | ( ! [v5: $i]
% 88.27/12.61 : ! [v6: int] : (v6 = 0 | ~ (in(v5, v4) = v6) | ~ $i(v5) | !
% 88.27/12.61 [v7: $i] : ( ~ (in(v7, v2) = 0) | ~ $i(v7) | ? [v8: any] : ?
% 88.27/12.61 [v9: $i] : (apply(v0, v7) = v9 & in(v7, v3) = v8 & $i(v9) & (
% 88.27/12.61 ~ (v9 = v5) | ~ (v8 = 0))))) & ! [v5: $i] : ( ~ (in(v5,
% 88.27/12.61 v4) = 0) | ~ $i(v5) | ? [v6: $i] : (apply(v0, v6) = v5 &
% 88.27/12.61 in(v6, v3) = 0 & in(v6, v2) = 0 & $i(v6)))))))))
% 88.27/12.61
% 88.27/12.61 (d13_funct_1)
% 88.27/12.62 ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 88.27/12.62 : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ (v1 = 0) | ( ?
% 88.27/12.62 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~
% 88.27/12.62 (relation_inverse_image(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ?
% 88.27/12.62 [v6: $i] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: any]
% 88.27/12.62 : (apply(v0, v6) = v9 & in(v9, v4) = v10 & in(v6, v3) = v7 & in(v6,
% 88.27/12.62 v2) = v8 & $i(v9) & $i(v6) & ( ~ (v10 = 0) | ~ (v8 = 0) | ~
% 88.27/12.62 (v7 = 0)) & (v7 = 0 | (v10 = 0 & v8 = 0)))) & ! [v3: $i] : !
% 88.27/12.62 [v4: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ $i(v4) | ~
% 88.27/12.62 $i(v3) | ( ! [v5: $i] : ! [v6: $i] : ! [v7: any] : ( ~ (apply(v0,
% 88.27/12.62 v5) = v6) | ~ (in(v6, v3) = v7) | ~ $i(v5) | ? [v8: any]
% 88.27/12.62 : ? [v9: any] : (in(v5, v4) = v8 & in(v5, v2) = v9 & ( ~ (v8 =
% 88.27/12.62 0) | (v9 = 0 & v7 = 0)))) & ! [v5: $i] : ! [v6: $i] : (
% 88.27/12.62 ~ (apply(v0, v5) = v6) | ~ (in(v6, v3) = 0) | ~ $i(v5) | ?
% 88.27/12.62 [v7: any] : ? [v8: any] : (in(v5, v4) = v8 & in(v5, v2) = v7 &
% 88.27/12.62 ( ~ (v7 = 0) | v8 = 0)))))))))
% 88.27/12.62
% 88.27/12.62 (d2_wellord1)
% 88.27/12.62 $i(empty_set) & ! [v0: $i] : ! [v1: any] : ( ~ (well_founded_relation(v0) =
% 88.27/12.62 v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (relation_field(v0) = v3 &
% 88.27/12.62 relation(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v1 = 0) | ! [v4: $i] :
% 88.27/12.62 (v4 = empty_set | ~ (subset(v4, v3) = 0) | ~ $i(v4) | ? [v5: $i]
% 88.27/12.62 : ? [v6: $i] : (disjoint(v6, v4) = 0 & fiber(v0, v5) = v6 &
% 88.27/12.62 in(v5, v4) = 0 & $i(v6) & $i(v5)))) & (v1 = 0 | ? [v4: $i] : (
% 88.27/12.62 ~ (v4 = empty_set) & subset(v4, v3) = 0 & $i(v4) & ! [v5: $i] :
% 88.27/12.62 ! [v6: $i] : ( ~ (disjoint(v6, v4) = 0) | ~ (fiber(v0, v5) = v6)
% 88.27/12.62 | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & in(v5, v4) =
% 88.27/12.62 v7))))))))
% 88.27/12.62
% 88.27/12.62 (d4_funct_1)
% 88.27/12.63 $i(empty_set) & ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1:
% 88.27/12.63 any] : ? [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) &
% 88.27/12.63 ( ~ (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : (
% 88.27/12.63 ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = v6) | ~ $i(v4) |
% 88.27/12.63 ~ $i(v3) | ? [v7: any] : ? [v8: $i] : (apply(v0, v3) = v8 & in(v3,
% 88.27/12.63 v2) = v7 & $i(v8) & ( ~ (v7 = 0) | (( ~ (v8 = v4) | v6 = 0) & (
% 88.27/12.63 ~ (v6 = 0) | v8 = v4))))) & ? [v3: $i] : ! [v4: $i] : !
% 88.27/12.63 [v5: int] : (v5 = 0 | ~ (in(v4, v2) = v5) | ~ $i(v4) | ~ $i(v3) |
% 88.27/12.63 ? [v6: $i] : (apply(v0, v4) = v6 & $i(v6) & ( ~ (v6 = v3) | v3 =
% 88.27/12.63 empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set)))))))
% 88.27/12.63
% 88.27/12.63 (d4_wellord1)
% 88.27/12.63 ! [v0: $i] : ! [v1: any] : ( ~ (well_ordering(v0) = v1) | ~ $i(v0) | ?
% 88.27/12.63 [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] : ?
% 88.27/12.63 [v7: any] : (reflexive(v0) = v3 & well_founded_relation(v0) = v7 &
% 88.27/12.63 transitive(v0) = v4 & connected(v0) = v6 & antisymmetric(v0) = v5 &
% 88.27/12.63 relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 =
% 88.27/12.63 0) | ~ (v4 = 0) | ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | (v7 = 0
% 88.27/12.63 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0))))))
% 88.27/12.63
% 88.27/12.63 (d5_funct_1)
% 88.27/12.63 ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 88.27/12.63 : ? [v3: $i] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 &
% 88.27/12.63 relation(v0) = v1 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ( ! [v4: $i] : !
% 88.27/12.63 [v5: int] : (v5 = 0 | ~ (in(v4, v2) = v5) | ~ $i(v4) | ! [v6: $i] :
% 88.27/12.63 ( ~ (in(v6, v3) = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v4) &
% 88.27/12.63 apply(v0, v6) = v7 & $i(v7)))) & ! [v4: $i] : ( ~ (in(v4, v2) =
% 88.27/12.63 0) | ~ $i(v4) | ? [v5: $i] : (apply(v0, v5) = v4 & in(v5, v3) =
% 88.27/12.63 0 & $i(v5))) & ? [v4: $i] : (v4 = v2 | ~ $i(v4) | ? [v5: $i] :
% 88.27/12.63 ? [v6: any] : (in(v5, v4) = v6 & $i(v5) & ( ~ (v6 = 0) | ! [v7: $i]
% 88.27/12.63 : ( ~ (in(v7, v3) = 0) | ~ $i(v7) | ? [v8: $i] : ( ~ (v8 = v5)
% 88.27/12.63 & apply(v0, v7) = v8 & $i(v8)))) & (v6 = 0 | ? [v7: $i] :
% 88.27/12.63 (apply(v0, v7) = v5 & in(v7, v3) = 0 & $i(v7)))))))))
% 88.27/12.63
% 88.27/12.63 (d5_relat_1)
% 88.27/12.64 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 88.27/12.64 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~
% 88.27/12.64 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~
% 88.27/12.64 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) =
% 88.27/12.64 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i]
% 88.27/12.64 : ? [v6: $i] : (ordered_pair(v5, v3) = v6 & in(v6, v0) = 0 & $i(v6)
% 88.27/12.64 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0
% 88.27/12.64 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 88.27/12.64 (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) &
% 88.27/12.64 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 88.27/12.64 $i] : (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0 & $i(v4) &
% 88.27/12.64 $i(v3)))))))
% 88.27/12.64
% 88.27/12.64 (d8_funct_1)
% 88.27/12.64 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 88.27/12.64 any] : ? [v3: any] : ? [v4: $i] : (relation_dom(v0) = v4 & relation(v0)
% 88.27/12.64 = v2 & function(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v1
% 88.27/12.64 = 0) | ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~ (in(v6, v4) = 0)
% 88.27/12.64 | ~ (in(v5, v4) = 0) | ~ $i(v6) | ~ $i(v5) | ? [v7: $i] : ?
% 88.27/12.64 [v8: $i] : ( ~ (v8 = v7) & apply(v0, v6) = v8 & apply(v0, v5) = v7
% 88.27/12.64 & $i(v8) & $i(v7)))) & (v1 = 0 | ? [v5: $i] : ? [v6: $i] : ?
% 88.27/12.64 [v7: $i] : ( ~ (v6 = v5) & apply(v0, v6) = v7 & apply(v0, v5) = v7 &
% 88.27/12.64 in(v6, v4) = 0 & in(v5, v4) = 0 & $i(v7) & $i(v6) & $i(v5)))))))
% 88.27/12.64
% 88.27/12.64 (fc2_ordinal1)
% 88.27/12.64 relation_empty_yielding(empty_set) = 0 & one_to_one(empty_set) = 0 &
% 88.27/12.64 relation(empty_set) = 0 & epsilon_connected(empty_set) = 0 &
% 88.27/12.64 ordinal(empty_set) = 0 & epsilon_transitive(empty_set) = 0 &
% 88.27/12.64 function(empty_set) = 0 & empty(empty_set) = 0 & $i(empty_set)
% 88.27/12.64
% 88.27/12.64 (fc5_relat_1)
% 88.27/12.64 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 88.27/12.64 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 &
% 88.27/12.64 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 =
% 88.27/12.64 0))))
% 88.27/12.64
% 88.27/12.64 (fc6_relat_1)
% 88.27/12.64 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 88.27/12.64 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 &
% 88.27/12.64 empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 88.27/12.64
% 88.27/12.64 (l1_wellord1)
% 88.27/12.64 ! [v0: $i] : ! [v1: any] : ( ~ (reflexive(v0) = v1) | ~ $i(v0) | ? [v2:
% 88.27/12.64 any] : ? [v3: $i] : (relation_field(v0) = v3 & relation(v0) = v2 & $i(v3)
% 88.27/12.64 & ( ~ (v2 = 0) | (( ~ (v1 = 0) | ! [v4: $i] : ( ~ (in(v4, v3) = 0) | ~
% 88.27/12.64 $i(v4) | ? [v5: $i] : (ordered_pair(v4, v4) = v5 & in(v5, v0) = 0
% 88.27/12.64 & $i(v5)))) & (v1 = 0 | ? [v4: $i] : ? [v5: $i] : ? [v6: int]
% 88.27/12.64 : ( ~ (v6 = 0) & ordered_pair(v4, v4) = v5 & in(v5, v0) = v6 &
% 88.27/12.64 in(v4, v3) = 0 & $i(v5) & $i(v4)))))))
% 88.27/12.64
% 88.27/12.64 (l4_wellord1)
% 88.27/12.65 ! [v0: $i] : ! [v1: any] : ( ~ (connected(v0) = v1) | ~ $i(v0) | ? [v2:
% 88.27/12.65 any] : ? [v3: $i] : (relation_field(v0) = v3 & relation(v0) = v2 & $i(v3)
% 88.27/12.65 & ( ~ (v2 = 0) | (( ~ (v1 = 0) | ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 88.27/12.65 (in(v5, v3) = 0) | ~ (in(v4, v3) = 0) | ~ $i(v5) | ~ $i(v4) |
% 88.27/12.65 ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: any] :
% 88.27/12.65 (ordered_pair(v5, v4) = v8 & ordered_pair(v4, v5) = v6 & in(v8,
% 88.27/12.65 v0) = v9 & in(v6, v0) = v7 & $i(v8) & $i(v6) & (v9 = 0 | v7 =
% 88.27/12.65 0)))) & (v1 = 0 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ?
% 88.27/12.65 [v7: int] : ? [v8: $i] : ? [v9: int] : ( ~ (v9 = 0) & ~ (v7 = 0)
% 88.27/12.65 & ~ (v5 = v4) & ordered_pair(v5, v4) = v8 & ordered_pair(v4, v5)
% 88.27/12.65 = v6 & in(v8, v0) = v9 & in(v6, v0) = v7 & in(v5, v3) = 0 & in(v4,
% 88.27/12.65 v3) = 0 & $i(v8) & $i(v6) & $i(v5) & $i(v4)))))))
% 88.27/12.65
% 88.27/12.65 (rc1_relat_1)
% 88.27/12.65 ? [v0: $i] : (relation(v0) = 0 & empty(v0) = 0 & $i(v0))
% 88.27/12.65
% 88.27/12.65 (rc1_subset_1)
% 88.27/12.65 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 88.27/12.65 [v2: $i] : (powerset(v0) = v2 & $i(v2) & ? [v3: $i] : ? [v4: int] : ( ~
% 88.27/12.65 (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3))))
% 88.27/12.65
% 88.27/12.65 (rc1_xboole_0)
% 88.27/12.65 ? [v0: $i] : (empty(v0) = 0 & $i(v0))
% 88.27/12.65
% 88.27/12.65 (rc2_funct_1)
% 88.27/12.65 ? [v0: $i] : (relation(v0) = 0 & function(v0) = 0 & empty(v0) = 0 & $i(v0))
% 88.27/12.65
% 88.27/12.65 (rc2_ordinal1)
% 88.27/12.65 ? [v0: $i] : (one_to_one(v0) = 0 & relation(v0) = 0 & epsilon_connected(v0) =
% 88.27/12.65 0 & ordinal(v0) = 0 & epsilon_transitive(v0) = 0 & function(v0) = 0 &
% 88.27/12.65 empty(v0) = 0 & $i(v0))
% 88.27/12.65
% 88.27/12.65 (rc2_relat_1)
% 88.27/12.65 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & relation(v0) = 0 & empty(v0) = v1
% 88.27/12.65 & $i(v0))
% 88.27/12.65
% 88.27/12.65 (rc4_funct_1)
% 88.27/12.65 ? [v0: $i] : (relation_empty_yielding(v0) = 0 & relation(v0) = 0 &
% 88.27/12.65 function(v0) = 0 & $i(v0))
% 88.27/12.65
% 88.27/12.65 (t25_relat_1)
% 88.27/12.65 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 88.27/12.65 any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0) = v2 & $i(v3) &
% 88.27/12.65 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~
% 88.27/12.65 (relation_rng(v4) = v5) | ~ (subset(v1, v5) = v6) | ~ $i(v4) | ?
% 88.27/12.65 [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: any] :
% 88.27/12.65 (relation_dom(v4) = v9 & subset(v3, v9) = v10 & subset(v0, v4) = v8 &
% 88.27/12.65 relation(v4) = v7 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = 0 &
% 88.27/12.65 v6 = 0)))))))
% 88.27/12.65
% 88.27/12.65 (t46_relat_1)
% 88.27/12.65 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 88.27/12.65 any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0) = v2 & $i(v3) &
% 88.27/12.65 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ( ~ (relation_dom(v4) = v5) |
% 88.27/12.65 ~ (subset(v1, v5) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ?
% 88.27/12.65 [v8: $i] : (relation_composition(v0, v4) = v7 & relation_dom(v7) = v8
% 88.27/12.65 & relation(v4) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | v8 = v3))))))
% 88.27/12.65
% 88.27/12.65 (t47_relat_1)
% 88.27/12.66 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 88.27/12.66 any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0) = v2 & $i(v3) &
% 88.27/12.66 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ( ~ (relation_rng(v4) = v5) |
% 88.27/12.66 ~ (subset(v3, v5) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ?
% 88.27/12.66 [v8: $i] : (relation_composition(v4, v0) = v7 & relation_rng(v7) = v8
% 88.27/12.66 & relation(v4) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | v8 = v1))))))
% 88.27/12.66
% 88.27/12.66 (t53_wellord1)
% 88.27/12.66 ! [v0: $i] : ! [v1: any] : ( ~ (well_founded_relation(v0) = v1) | ~ $i(v0)
% 88.27/12.66 | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 88.27/12.66 (reflexive(v0) = v3 & transitive(v0) = v4 & connected(v0) = v5 &
% 88.27/12.66 antisymmetric(v0) = v6 & relation(v0) = v2 & ( ~ (v2 = 0) | ! [v7: $i] :
% 88.27/12.66 ! [v8: any] : ( ~ (well_founded_relation(v7) = v8) | ~ $i(v7) | ? [v9:
% 88.27/12.66 any] : ? [v10: any] : ? [v11: any] : ? [v12: any] : ? [v13: any]
% 88.27/12.66 : (reflexive(v7) = v10 & transitive(v7) = v11 & connected(v7) = v12 &
% 88.27/12.66 antisymmetric(v7) = v13 & relation(v7) = v9 & ( ~ (v9 = 0) | !
% 88.27/12.66 [v14: $i] : ( ~ (relation_isomorphism(v0, v7, v14) = 0) | ~
% 88.27/12.66 $i(v14) | ? [v15: any] : ? [v16: any] : (relation(v14) = v15 &
% 88.27/12.66 function(v14) = v16 & ( ~ (v16 = 0) | ~ (v15 = 0))) | (( ~
% 88.27/12.66 (v6 = 0) | v13 = 0) & ( ~ (v5 = 0) | v12 = 0) & ( ~ (v4 = 0)
% 88.27/12.66 | v11 = 0) & ( ~ (v3 = 0) | v10 = 0) & ( ~ (v1 = 0) | v8 =
% 88.27/12.66 0)))))))))
% 88.27/12.66
% 88.27/12.66 (t54_wellord1)
% 88.27/12.66 ? [v0: $i] : ? [v1: any] : (well_ordering(v0) = v1 & relation(v0) = 0 &
% 88.27/12.66 $i(v0) & ? [v2: $i] : ? [v3: any] : (well_ordering(v2) = v3 & relation(v2)
% 88.27/12.66 = 0 & $i(v2) & ? [v4: $i] : (v1 = 0 & ~ (v3 = 0) &
% 88.27/12.66 relation_isomorphism(v0, v2, v4) = 0 & relation(v4) = 0 & function(v4) =
% 88.27/12.66 0 & $i(v4))))
% 88.27/12.66
% 88.27/12.66 (t60_relat_1)
% 88.27/12.66 relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set &
% 88.27/12.66 $i(empty_set)
% 88.27/12.66
% 88.27/12.66 (t65_relat_1)
% 88.27/12.66 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~
% 88.27/12.66 $i(v0) | ? [v2: any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0)
% 88.27/12.66 = v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 = empty_set) & (
% 88.27/12.66 ~ (v1 = empty_set) | v3 = empty_set)))))
% 88.27/12.66
% 88.27/12.66 (t6_boole)
% 88.27/12.66 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~
% 88.27/12.66 $i(v0))
% 88.27/12.66
% 88.27/12.66 (t8_boole)
% 88.27/12.66 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)
% 88.27/12.66 | ~ $i(v1) | ~ $i(v0))
% 88.27/12.66
% 88.27/12.66 (function-axioms)
% 88.75/12.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 88.75/12.68 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3,
% 88.75/12.68 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 88.75/12.68 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 88.75/12.68 (relation_isomorphism(v4, v3, v2) = v1) | ~ (relation_isomorphism(v4, v3,
% 88.75/12.68 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 88.75/12.68 [v4: $i] : (v1 = v0 | ~ (unordered_triple(v4, v3, v2) = v1) | ~
% 88.75/12.68 (unordered_triple(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 88.75/12.68 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 88.75/12.68 (are_equipotent(v3, v2) = v1) | ~ (are_equipotent(v3, v2) = v0)) & ! [v0:
% 88.75/12.68 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 88.75/12.68 (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) & !
% 88.75/12.68 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 88.75/12.68 (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & !
% 88.75/12.68 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 88.75/12.68 (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) =
% 88.75/12.68 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 88.75/12.68 ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) =
% 88.75/12.68 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 88.75/12.68 ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) =
% 88.75/12.68 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 88.75/12.68 $i] : ! [v3: $i] : (v1 = v0 | ~ (well_orders(v3, v2) = v1) | ~
% 88.75/12.68 (well_orders(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 88.75/12.68 [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~
% 88.75/12.68 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 88.75/12.68 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~
% 88.75/12.68 (set_difference(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 88.75/12.68 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 88.75/12.68 (is_well_founded_in(v3, v2) = v1) | ~ (is_well_founded_in(v3, v2) = v0)) &
% 88.75/12.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 88.75/12.68 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 88.75/12.68 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 88.75/12.68 $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) &
% 88.75/12.68 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 88.75/12.68 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & !
% 88.75/12.68 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (fiber(v3,
% 88.75/12.68 v2) = v1) | ~ (fiber(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 88.75/12.68 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 88.75/12.68 (is_reflexive_in(v3, v2) = v1) | ~ (is_reflexive_in(v3, v2) = v0)) & !
% 88.75/12.68 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 88.75/12.68 $i] : (v1 = v0 | ~ (is_transitive_in(v3, v2) = v1) | ~
% 88.75/12.68 (is_transitive_in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 88.75/12.68 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 88.75/12.68 (is_connected_in(v3, v2) = v1) | ~ (is_connected_in(v3, v2) = v0)) & !
% 88.75/12.68 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 88.75/12.68 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) =
% 88.75/12.68 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 88.75/12.68 $i] : ! [v3: $i] : (v1 = v0 | ~ (is_antisymmetric_in(v3, v2) = v1) | ~
% 88.75/12.68 (is_antisymmetric_in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 88.75/12.69 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) |
% 88.75/12.69 ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 88.75/12.69 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~
% 88.75/12.69 (relation_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 88.75/12.69 ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) &
% 88.75/12.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 88.75/12.69 (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3,
% 88.75/12.69 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 88.75/12.69 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~
% 88.75/12.69 (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 88.75/12.69 $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) =
% 88.75/12.69 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 88.75/12.69 $i] : ! [v3: $i] : (v1 = v0 | ~ (ordinal_subset(v3, v2) = v1) | ~
% 88.75/12.69 (ordinal_subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 88.75/12.69 ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~
% 88.75/12.69 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 88.75/12.69 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3,
% 88.75/12.69 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 88.75/12.69 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 88.75/12.69 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 88.75/12.69 [v3: $i] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3,
% 88.75/12.69 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 88.75/12.69 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 88.75/12.69 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 88.75/12.69 $i] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~
% 88.75/12.69 (relation_empty_yielding(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 88.75/12.69 $i] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) =
% 88.75/12.69 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 88.75/12.69 (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0:
% 88.75/12.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 88.75/12.69 ~ (being_limit_ordinal(v2) = v1) | ~ (being_limit_ordinal(v2) = v0)) & !
% 88.75/12.69 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) |
% 88.75/12.69 ~ (relation_rng(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 88.75/12.69 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (well_ordering(v2) = v1) |
% 88.75/12.69 ~ (well_ordering(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 88.75/12.69 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (reflexive(v2) = v1) | ~
% 88.75/12.69 (reflexive(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 88.75/12.69 ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 88.75/12.69 [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) =
% 88.75/12.69 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 88.75/12.69 $i] : (v1 = v0 | ~ (well_founded_relation(v2) = v1) | ~
% 88.75/12.69 (well_founded_relation(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 88.75/12.69 : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] :
% 88.75/12.69 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~
% 88.75/12.69 (set_meet(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 88.75/12.69 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1:
% 88.75/12.69 $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & !
% 88.75/12.69 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 88.75/12.69 | ~ (transitive(v2) = v1) | ~ (transitive(v2) = v0)) & ! [v0:
% 88.75/12.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 88.75/12.69 ~ (connected(v2) = v1) | ~ (connected(v2) = v0)) & ! [v0: $i] : ! [v1:
% 88.75/12.69 $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~
% 88.75/12.69 (relation_field(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 88.75/12.69 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (antisymmetric(v2) = v1) |
% 88.75/12.69 ~ (antisymmetric(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 88.75/12.69 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0:
% 88.75/12.69 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (identity_relation(v2) = v1)
% 88.75/12.69 | ~ (identity_relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 88.75/12.69 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~
% 88.75/12.69 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 88.75/12.69 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 88.75/12.69 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 88.75/12.69 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_connected(v2) =
% 88.75/12.69 v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 88.75/12.69 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~
% 88.75/12.69 (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 88.75/12.69 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_transitive(v2) =
% 88.75/12.69 v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 88.75/12.69 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~
% 88.75/12.69 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 88.75/12.69 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 88.75/12.69 (empty(v2) = v0))
% 88.75/12.69
% 88.75/12.69 Further assumptions not needed in the proof:
% 88.75/12.69 --------------------------------------------
% 88.75/12.69 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_funct_1, cc1_ordinal1,
% 88.75/12.69 cc2_funct_1, cc2_ordinal1, cc3_ordinal1, commutativity_k2_tarski,
% 88.75/12.69 commutativity_k2_xboole_0, commutativity_k3_xboole_0, connectedness_r1_ordinal1,
% 88.75/12.69 d10_relat_1, d10_xboole_0, d11_relat_1, d12_relat_1, d12_relat_2, d13_relat_1,
% 88.75/12.69 d14_relat_1, d14_relat_2, d16_relat_2, d1_enumset1, d1_ordinal1, d1_relat_1,
% 88.75/12.69 d1_relat_2, d1_setfam_1, d1_tarski, d1_wellord1, d1_xboole_0, d1_zfmisc_1,
% 88.75/12.69 d2_ordinal1, d2_relat_1, d2_subset_1, d2_tarski, d2_xboole_0, d2_zfmisc_1,
% 88.75/12.69 d3_ordinal1, d3_relat_1, d3_tarski, d3_wellord1, d3_xboole_0, d4_ordinal1,
% 88.75/12.69 d4_relat_1, d4_relat_2, d4_subset_1, d4_tarski, d4_xboole_0, d5_subset_1,
% 88.75/12.69 d5_tarski, d5_wellord1, d6_ordinal1, d6_relat_1, d6_relat_2, d6_wellord1,
% 88.75/12.69 d7_relat_1, d7_wellord1, d7_xboole_0, d8_relat_1, d8_relat_2, d8_setfam_1,
% 88.75/12.69 d8_xboole_0, d9_funct_1, d9_relat_2, dt_k10_relat_1, dt_k1_enumset1,
% 88.75/12.69 dt_k1_funct_1, dt_k1_ordinal1, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski,
% 88.75/12.69 dt_k1_wellord1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_funct_1, dt_k2_relat_1,
% 88.75/12.69 dt_k2_subset_1, dt_k2_tarski, dt_k2_wellord1, dt_k2_xboole_0, dt_k2_zfmisc_1,
% 88.75/12.69 dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_relat_1,
% 88.75/12.69 dt_k4_tarski, dt_k4_xboole_0, dt_k5_relat_1, dt_k5_setfam_1, dt_k6_relat_1,
% 88.75/12.69 dt_k6_setfam_1, dt_k6_subset_1, dt_k7_relat_1, dt_k7_setfam_1, dt_k8_relat_1,
% 88.75/12.69 dt_k9_relat_1, dt_m1_subset_1, existence_m1_subset_1, fc10_relat_1,
% 88.75/12.69 fc11_relat_1, fc12_relat_1, fc13_relat_1, fc1_funct_1, fc1_ordinal1,
% 88.75/12.69 fc1_relat_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_funct_1, fc2_relat_1,
% 88.75/12.69 fc2_subset_1, fc2_xboole_0, fc3_funct_1, fc3_ordinal1, fc3_relat_1,
% 88.75/12.69 fc3_subset_1, fc3_xboole_0, fc4_funct_1, fc4_ordinal1, fc4_relat_1,
% 88.75/12.69 fc4_subset_1, fc5_funct_1, fc7_relat_1, fc8_relat_1, fc9_relat_1,
% 88.75/12.69 idempotence_k2_xboole_0, idempotence_k3_xboole_0, involutiveness_k3_subset_1,
% 88.75/12.69 involutiveness_k4_relat_1, involutiveness_k7_setfam_1,
% 88.75/12.69 irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1,
% 88.75/12.69 l28_zfmisc_1, l29_wellord1, l2_wellord1, l2_zfmisc_1, l32_xboole_1, l3_subset_1,
% 88.75/12.69 l3_wellord1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1,
% 88.75/12.69 l82_funct_1, rc1_funct_1, rc1_ordinal1, rc2_subset_1, rc2_xboole_0, rc3_funct_1,
% 88.75/12.69 rc3_ordinal1, rc3_relat_1, redefinition_k5_setfam_1, redefinition_k6_setfam_1,
% 88.75/12.69 redefinition_k6_subset_1, redefinition_r1_ordinal1, reflexivity_r1_ordinal1,
% 88.75/12.69 reflexivity_r1_tarski, symmetry_r1_xboole_0, t106_zfmisc_1, t10_ordinal1,
% 88.75/12.69 t10_zfmisc_1, t115_relat_1, t116_relat_1, t117_relat_1, t118_relat_1,
% 88.75/12.69 t118_zfmisc_1, t119_relat_1, t119_zfmisc_1, t12_xboole_1, t136_zfmisc_1,
% 88.75/12.69 t140_relat_1, t143_relat_1, t144_relat_1, t145_funct_1, t145_relat_1,
% 88.75/12.69 t146_funct_1, t146_relat_1, t147_funct_1, t160_relat_1, t166_relat_1,
% 88.75/12.69 t167_relat_1, t16_wellord1, t174_relat_1, t178_relat_1, t17_wellord1,
% 88.75/12.69 t17_xboole_1, t18_wellord1, t19_wellord1, t19_xboole_1, t1_boole, t1_subset,
% 88.75/12.69 t1_xboole_1, t1_zfmisc_1, t20_relat_1, t20_wellord1, t21_funct_1, t21_ordinal1,
% 88.75/12.69 t21_relat_1, t21_wellord1, t22_funct_1, t22_wellord1, t23_funct_1, t23_ordinal1,
% 88.75/12.69 t23_wellord1, t24_ordinal1, t24_wellord1, t25_wellord1, t26_xboole_1,
% 88.75/12.69 t28_xboole_1, t2_boole, t2_subset, t2_tarski, t2_xboole_1, t30_relat_1,
% 88.75/12.69 t31_ordinal1, t31_wellord1, t32_ordinal1, t32_wellord1, t33_ordinal1,
% 88.75/12.69 t33_xboole_1, t33_zfmisc_1, t34_funct_1, t35_funct_1, t36_xboole_1, t37_relat_1,
% 88.75/12.69 t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, t39_wellord1, t39_xboole_1,
% 88.75/12.69 t39_zfmisc_1, t3_boole, t3_ordinal1, t3_subset, t3_xboole_0, t3_xboole_1,
% 88.75/12.69 t40_xboole_1, t41_ordinal1, t42_ordinal1, t43_subset_1, t44_relat_1,
% 88.75/12.69 t45_relat_1, t45_xboole_1, t46_setfam_1, t46_zfmisc_1, t47_setfam_1,
% 88.75/12.69 t48_setfam_1, t48_xboole_1, t49_wellord1, t4_boole, t4_subset, t4_xboole_0,
% 88.75/12.69 t50_subset_1, t54_funct_1, t54_subset_1, t55_funct_1, t56_relat_1, t57_funct_1,
% 88.75/12.69 t5_subset, t5_wellord1, t60_xboole_1, t62_funct_1, t63_xboole_1, t64_relat_1,
% 88.75/12.69 t65_zfmisc_1, t68_funct_1, t69_enumset1, t6_zfmisc_1, t70_funct_1, t71_relat_1,
% 88.75/12.69 t72_funct_1, t74_relat_1, t7_boole, t7_tarski, t7_xboole_1, t83_xboole_1,
% 88.75/12.69 t86_relat_1, t88_relat_1, t8_funct_1, t8_wellord1, t8_xboole_1, t8_zfmisc_1,
% 88.75/12.69 t90_relat_1, t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1, t9_tarski,
% 88.75/12.69 t9_zfmisc_1
% 88.75/12.69
% 88.75/12.69 Those formulas are unsatisfiable:
% 88.75/12.69 ---------------------------------
% 88.75/12.69
% 88.75/12.69 Begin of proof
% 88.75/12.69 |
% 88.75/12.69 | ALPHA: (d2_wellord1) implies:
% 88.75/12.69 | (1) ! [v0: $i] : ! [v1: any] : ( ~ (well_founded_relation(v0) = v1) | ~
% 88.75/12.69 | $i(v0) | ? [v2: any] : ? [v3: $i] : (relation_field(v0) = v3 &
% 88.75/12.69 | relation(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v1 = 0) | ! [v4:
% 88.75/12.69 | $i] : (v4 = empty_set | ~ (subset(v4, v3) = 0) | ~ $i(v4)
% 88.75/12.69 | | ? [v5: $i] : ? [v6: $i] : (disjoint(v6, v4) = 0 &
% 88.75/12.69 | fiber(v0, v5) = v6 & in(v5, v4) = 0 & $i(v6) & $i(v5))))
% 88.75/12.69 | & (v1 = 0 | ? [v4: $i] : ( ~ (v4 = empty_set) & subset(v4, v3)
% 88.75/12.69 | = 0 & $i(v4) & ! [v5: $i] : ! [v6: $i] : ( ~
% 88.75/12.69 | (disjoint(v6, v4) = 0) | ~ (fiber(v0, v5) = v6) | ~
% 88.75/12.69 | $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & in(v5, v4) =
% 88.75/12.69 | v7))))))))
% 88.75/12.69 |
% 88.75/12.69 | ALPHA: (d4_funct_1) implies:
% 88.89/12.70 | (2) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 88.89/12.70 | [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~
% 88.89/12.70 | (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 88.89/12.70 | any] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = v6)
% 88.89/12.70 | | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? [v8: $i] :
% 88.89/12.70 | (apply(v0, v3) = v8 & in(v3, v2) = v7 & $i(v8) & ( ~ (v7 = 0)
% 88.89/12.70 | | (( ~ (v8 = v4) | v6 = 0) & ( ~ (v6 = 0) | v8 = v4)))))
% 88.89/12.70 | & ? [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~
% 88.89/12.70 | (in(v4, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] :
% 88.89/12.70 | (apply(v0, v4) = v6 & $i(v6) & ( ~ (v6 = v3) | v3 =
% 88.89/12.70 | empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set)))))))
% 88.89/12.70 |
% 88.89/12.70 | ALPHA: (fc2_ordinal1) implies:
% 88.89/12.70 | (3) function(empty_set) = 0
% 88.89/12.70 | (4) one_to_one(empty_set) = 0
% 88.89/12.70 |
% 88.89/12.70 | ALPHA: (t60_relat_1) implies:
% 88.89/12.70 | (5) relation_rng(empty_set) = empty_set
% 88.89/12.70 |
% 88.89/12.70 | ALPHA: (t65_relat_1) implies:
% 88.89/12.70 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 88.89/12.70 | ? [v2: any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0) =
% 88.89/12.70 | v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 =
% 88.89/12.70 | empty_set) & ( ~ (v1 = empty_set) | v3 = empty_set)))))
% 88.89/12.70 |
% 88.89/12.70 | ALPHA: (t6_boole) implies:
% 88.89/12.70 | (7) $i(empty_set)
% 88.89/12.70 | (8) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 88.89/12.70 |
% 88.89/12.70 | ALPHA: (function-axioms) implies:
% 88.89/12.70 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 88.89/12.70 | (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 88.89/12.70 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 88.89/12.70 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 88.89/12.70 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 88.89/12.70 | : (v1 = v0 | ~ (antisymmetric(v2) = v1) | ~ (antisymmetric(v2) =
% 88.89/12.70 | v0))
% 88.89/12.70 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 88.89/12.70 | : (v1 = v0 | ~ (connected(v2) = v1) | ~ (connected(v2) = v0))
% 88.89/12.70 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 88.89/12.70 | : (v1 = v0 | ~ (transitive(v2) = v1) | ~ (transitive(v2) = v0))
% 88.89/12.70 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 88.89/12.70 | : (v1 = v0 | ~ (reflexive(v2) = v1) | ~ (reflexive(v2) = v0))
% 88.89/12.70 |
% 88.89/12.70 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_273_0 gives:
% 88.89/12.70 | (15) empty(all_273_0) = 0 & $i(all_273_0)
% 88.89/12.70 |
% 88.89/12.70 | ALPHA: (15) implies:
% 88.89/12.70 | (16) $i(all_273_0)
% 88.89/12.70 | (17) empty(all_273_0) = 0
% 88.89/12.71 |
% 88.89/12.71 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_286_0 gives:
% 88.89/12.71 | (18) relation(all_286_0) = 0 & empty(all_286_0) = 0 & $i(all_286_0)
% 88.89/12.71 |
% 88.89/12.71 | ALPHA: (18) implies:
% 88.89/12.71 | (19) $i(all_286_0)
% 88.89/12.71 | (20) empty(all_286_0) = 0
% 88.89/12.71 |
% 88.89/12.71 | DELTA: instantiating (rc4_funct_1) with fresh symbol all_288_0 gives:
% 88.89/12.71 | (21) relation_empty_yielding(all_288_0) = 0 & relation(all_288_0) = 0 &
% 88.89/12.71 | function(all_288_0) = 0 & $i(all_288_0)
% 88.89/12.71 |
% 88.89/12.71 | ALPHA: (21) implies:
% 88.89/12.71 | (22) $i(all_288_0)
% 88.89/12.71 | (23) function(all_288_0) = 0
% 88.89/12.71 | (24) relation(all_288_0) = 0
% 88.89/12.71 |
% 88.89/12.71 | DELTA: instantiating (rc2_relat_1) with fresh symbols all_292_0, all_292_1
% 88.89/12.71 | gives:
% 88.89/12.71 | (25) ~ (all_292_0 = 0) & relation(all_292_1) = 0 & empty(all_292_1) =
% 88.89/12.71 | all_292_0 & $i(all_292_1)
% 88.89/12.71 |
% 88.89/12.71 | ALPHA: (25) implies:
% 88.89/12.71 | (26) ~ (all_292_0 = 0)
% 88.89/12.71 | (27) $i(all_292_1)
% 88.89/12.71 | (28) empty(all_292_1) = all_292_0
% 88.89/12.71 | (29) relation(all_292_1) = 0
% 88.89/12.71 |
% 88.89/12.71 | DELTA: instantiating (rc2_funct_1) with fresh symbol all_294_0 gives:
% 88.89/12.71 | (30) relation(all_294_0) = 0 & function(all_294_0) = 0 & empty(all_294_0) =
% 88.89/12.71 | 0 & $i(all_294_0)
% 88.89/12.71 |
% 88.89/12.71 | ALPHA: (30) implies:
% 88.89/12.71 | (31) $i(all_294_0)
% 88.89/12.71 | (32) empty(all_294_0) = 0
% 88.89/12.71 | (33) function(all_294_0) = 0
% 88.89/12.71 |
% 88.89/12.71 | DELTA: instantiating (rc2_ordinal1) with fresh symbol all_309_0 gives:
% 88.89/12.71 | (34) one_to_one(all_309_0) = 0 & relation(all_309_0) = 0 &
% 88.89/12.71 | epsilon_connected(all_309_0) = 0 & ordinal(all_309_0) = 0 &
% 88.89/12.71 | epsilon_transitive(all_309_0) = 0 & function(all_309_0) = 0 &
% 88.89/12.71 | empty(all_309_0) = 0 & $i(all_309_0)
% 88.89/12.71 |
% 88.89/12.71 | ALPHA: (34) implies:
% 88.89/12.71 | (35) $i(all_309_0)
% 88.89/12.71 | (36) empty(all_309_0) = 0
% 88.89/12.71 | (37) function(all_309_0) = 0
% 88.89/12.71 | (38) one_to_one(all_309_0) = 0
% 88.89/12.71 |
% 88.89/12.71 | DELTA: instantiating (t54_wellord1) with fresh symbols all_316_0, all_316_1
% 88.89/12.71 | gives:
% 88.89/12.71 | (39) well_ordering(all_316_1) = all_316_0 & relation(all_316_1) = 0 &
% 88.89/12.71 | $i(all_316_1) & ? [v0: $i] : ? [v1: any] : (well_ordering(v0) = v1 &
% 88.89/12.71 | relation(v0) = 0 & $i(v0) & ? [v2: $i] : (all_316_0 = 0 & ~ (v1 =
% 88.89/12.71 | 0) & relation_isomorphism(all_316_1, v0, v2) = 0 & relation(v2)
% 88.89/12.71 | = 0 & function(v2) = 0 & $i(v2)))
% 88.89/12.71 |
% 88.89/12.71 | ALPHA: (39) implies:
% 88.89/12.71 | (40) $i(all_316_1)
% 88.89/12.71 | (41) relation(all_316_1) = 0
% 88.89/12.71 | (42) well_ordering(all_316_1) = all_316_0
% 88.89/12.71 | (43) ? [v0: $i] : ? [v1: any] : (well_ordering(v0) = v1 & relation(v0) =
% 88.89/12.71 | 0 & $i(v0) & ? [v2: $i] : (all_316_0 = 0 & ~ (v1 = 0) &
% 88.89/12.71 | relation_isomorphism(all_316_1, v0, v2) = 0 & relation(v2) = 0 &
% 88.89/12.71 | function(v2) = 0 & $i(v2)))
% 88.89/12.71 |
% 88.89/12.71 | DELTA: instantiating (43) with fresh symbols all_342_0, all_342_1 gives:
% 88.89/12.71 | (44) well_ordering(all_342_1) = all_342_0 & relation(all_342_1) = 0 &
% 88.89/12.71 | $i(all_342_1) & ? [v0: $i] : (all_316_0 = 0 & ~ (all_342_0 = 0) &
% 88.89/12.71 | relation_isomorphism(all_316_1, all_342_1, v0) = 0 & relation(v0) =
% 88.89/12.71 | 0 & function(v0) = 0 & $i(v0))
% 88.89/12.71 |
% 88.89/12.71 | ALPHA: (44) implies:
% 88.89/12.71 | (45) $i(all_342_1)
% 88.89/12.71 | (46) relation(all_342_1) = 0
% 88.89/12.71 | (47) well_ordering(all_342_1) = all_342_0
% 88.89/12.71 | (48) ? [v0: $i] : (all_316_0 = 0 & ~ (all_342_0 = 0) &
% 88.89/12.71 | relation_isomorphism(all_316_1, all_342_1, v0) = 0 & relation(v0) =
% 88.89/12.71 | 0 & function(v0) = 0 & $i(v0))
% 88.89/12.71 |
% 88.89/12.71 | DELTA: instantiating (48) with fresh symbol all_344_0 gives:
% 88.89/12.71 | (49) all_316_0 = 0 & ~ (all_342_0 = 0) & relation_isomorphism(all_316_1,
% 88.89/12.71 | all_342_1, all_344_0) = 0 & relation(all_344_0) = 0 &
% 88.89/12.71 | function(all_344_0) = 0 & $i(all_344_0)
% 88.89/12.71 |
% 88.89/12.71 | ALPHA: (49) implies:
% 88.89/12.71 | (50) all_316_0 = 0
% 88.89/12.71 | (51) ~ (all_342_0 = 0)
% 88.89/12.71 | (52) $i(all_344_0)
% 88.89/12.72 | (53) function(all_344_0) = 0
% 88.89/12.72 | (54) relation(all_344_0) = 0
% 88.89/12.72 | (55) relation_isomorphism(all_316_1, all_342_1, all_344_0) = 0
% 88.89/12.72 |
% 88.89/12.72 | REDUCE: (42), (50) imply:
% 88.89/12.72 | (56) well_ordering(all_316_1) = 0
% 88.89/12.72 |
% 88.89/12.72 | GROUND_INST: instantiating (cc1_relat_1) with all_273_0, simplifying with
% 88.89/12.72 | (16), (17) gives:
% 88.89/12.72 | (57) relation(all_273_0) = 0
% 88.89/12.72 |
% 88.89/12.72 | GROUND_INST: instantiating (fc5_relat_1) with all_292_1, all_292_0,
% 88.89/12.72 | simplifying with (27), (28) gives:
% 88.89/12.72 | (58) all_292_0 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 88.89/12.72 | (relation_dom(all_292_1) = v1 & relation(all_292_1) = v0 & empty(v1) =
% 88.89/12.72 | v2 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 88.89/12.72 |
% 88.89/12.72 | GROUND_INST: instantiating (t8_boole) with all_286_0, all_294_0, simplifying
% 88.89/12.72 | with (19), (20), (31), (32) gives:
% 88.89/12.72 | (59) all_294_0 = all_286_0
% 88.89/12.72 |
% 88.89/12.72 | GROUND_INST: instantiating (t8_boole) with all_273_0, all_294_0, simplifying
% 88.89/12.72 | with (16), (17), (31), (32) gives:
% 88.89/12.72 | (60) all_294_0 = all_273_0
% 88.89/12.72 |
% 88.89/12.72 | GROUND_INST: instantiating (t8_boole) with all_286_0, all_309_0, simplifying
% 88.89/12.72 | with (19), (20), (35), (36) gives:
% 88.89/12.72 | (61) all_309_0 = all_286_0
% 88.89/12.72 |
% 88.89/12.72 | GROUND_INST: instantiating (8) with all_309_0, simplifying with (35), (36)
% 88.89/12.72 | gives:
% 88.89/12.72 | (62) all_309_0 = empty_set
% 88.89/12.72 |
% 88.89/12.72 | GROUND_INST: instantiating (d5_funct_1) with empty_set, simplifying with (3),
% 88.89/12.72 | (7) gives:
% 88.89/12.72 | (63) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (relation_rng(empty_set) =
% 88.89/12.72 | v1 & relation_dom(empty_set) = v2 & relation(empty_set) = v0 &
% 88.89/12.72 | $i(v2) & $i(v1) & ( ~ (v0 = 0) | ( ! [v3: $i] : ! [v4: int] : (v4 =
% 88.89/12.72 | 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ! [v5: $i] : ( ~
% 88.89/12.72 | (in(v5, v2) = 0) | ~ $i(v5) | ? [v6: $i] : ( ~ (v6 = v3) &
% 88.89/12.72 | apply(empty_set, v5) = v6 & $i(v6)))) & ! [v3: $i] : ( ~
% 88.89/12.72 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(empty_set,
% 88.89/12.72 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 =
% 88.89/12.72 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: any] : (in(v4, v3) = v5
% 88.89/12.72 | & $i(v4) & ( ~ (v5 = 0) | ! [v6: $i] : ( ~ (in(v6, v2) = 0)
% 88.89/12.72 | | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v4) &
% 88.89/12.72 | apply(empty_set, v6) = v7 & $i(v7)))) & (v5 = 0 | ?
% 88.89/12.72 | [v6: $i] : (apply(empty_set, v6) = v4 & in(v6, v2) = 0 &
% 88.89/12.72 | $i(v6))))))))
% 88.89/12.72 |
% 88.89/12.72 | GROUND_INST: instantiating (2) with empty_set, simplifying with (3), (7)
% 88.89/12.72 | gives:
% 88.89/12.72 | (64) ? [v0: any] : ? [v1: $i] : (relation_dom(empty_set) = v1 &
% 88.89/12.72 | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : !
% 88.89/12.72 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (ordered_pair(v2,
% 88.89/12.72 | v3) = v4) | ~ (in(v4, empty_set) = v5) | ~ $i(v3) | ~
% 88.89/12.72 | $i(v2) | ? [v6: any] : ? [v7: $i] : (apply(empty_set, v2) =
% 88.89/12.72 | v7 & in(v2, v1) = v6 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 =
% 88.89/12.72 | v3) | v5 = 0) & ( ~ (v5 = 0) | v7 = v3))))) & ?
% 88.89/12.72 | [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v1)
% 88.89/12.72 | = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] :
% 88.89/12.72 | (apply(empty_set, v3) = v5 & $i(v5) & ( ~ (v5 = v2) | v2 =
% 88.89/12.72 | empty_set) & ( ~ (v2 = empty_set) | v5 = empty_set))))))
% 88.89/12.72 |
% 88.89/12.72 | GROUND_INST: instantiating (d13_funct_1) with empty_set, simplifying with (3),
% 88.89/12.72 | (7) gives:
% 89.03/12.73 | (65) ? [v0: any] : ? [v1: $i] : (relation_dom(empty_set) = v1 &
% 89.03/12.73 | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 89.03/12.73 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 89.03/12.73 | (relation_inverse_image(empty_set, v3) = v4) | ~ $i(v3) | ~
% 89.03/12.73 | $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8:
% 89.03/12.73 | $i] : ? [v9: any] : (apply(empty_set, v5) = v8 & in(v8, v3)
% 89.03/12.73 | = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & $i(v5) &
% 89.03/12.73 | ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 | (v9 =
% 89.03/12.73 | 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 89.03/12.73 | (relation_inverse_image(empty_set, v2) = v3) | ~ $i(v3) | ~
% 89.03/12.73 | $i(v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~
% 89.03/12.73 | (apply(empty_set, v4) = v5) | ~ (in(v5, v2) = v6) | ~
% 89.03/12.73 | $i(v4) | ? [v7: any] : ? [v8: any] : (in(v4, v3) = v7 &
% 89.03/12.73 | in(v4, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) &
% 89.03/12.73 | ! [v4: $i] : ! [v5: $i] : ( ~ (apply(empty_set, v4) = v5) |
% 89.03/12.73 | ~ (in(v5, v2) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7:
% 89.03/12.73 | any] : (in(v4, v3) = v7 & in(v4, v1) = v6 & ( ~ (v6 = 0)
% 89.03/12.73 | | v7 = 0))))))))
% 89.03/12.73 |
% 89.03/12.73 | GROUND_INST: instantiating (d12_funct_1) with empty_set, simplifying with (3),
% 89.03/12.73 | (7) gives:
% 89.03/12.73 | (66) ? [v0: any] : ? [v1: $i] : (relation_dom(empty_set) = v1 &
% 89.03/12.73 | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 89.03/12.73 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 89.03/12.73 | (relation_image(empty_set, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 89.03/12.73 | ? [v5: $i] : ? [v6: any] : (in(v5, v2) = v6 & $i(v5) & ( ~
% 89.03/12.73 | (v6 = 0) | ! [v7: $i] : ( ~ (in(v7, v1) = 0) | ~ $i(v7)
% 89.03/12.73 | | ? [v8: any] : ? [v9: $i] : (apply(empty_set, v7) =
% 89.03/12.73 | v9 & in(v7, v3) = v8 & $i(v9) & ( ~ (v9 = v5) | ~ (v8
% 89.03/12.73 | = 0))))) & (v6 = 0 | ? [v7: $i] :
% 89.03/12.73 | (apply(empty_set, v7) = v5 & in(v7, v3) = 0 & in(v7, v1) =
% 89.03/12.73 | 0 & $i(v7))))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 89.03/12.73 | (relation_image(empty_set, v2) = v3) | ~ $i(v3) | ~ $i(v2) |
% 89.03/12.73 | ( ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v3) = v5) |
% 89.03/12.73 | ~ $i(v4) | ! [v6: $i] : ( ~ (in(v6, v1) = 0) | ~ $i(v6)
% 89.03/12.73 | | ? [v7: any] : ? [v8: $i] : (apply(empty_set, v6) =
% 89.03/12.73 | v8 & in(v6, v2) = v7 & $i(v8) & ( ~ (v8 = v4) | ~ (v7
% 89.03/12.73 | = 0))))) & ! [v4: $i] : ( ~ (in(v4, v3) = 0) | ~
% 89.03/12.73 | $i(v4) | ? [v5: $i] : (apply(empty_set, v5) = v4 & in(v5,
% 89.03/12.73 | v2) = 0 & in(v5, v1) = 0 & $i(v5))))))))
% 89.03/12.73 |
% 89.03/12.73 | GROUND_INST: instantiating (d5_funct_1) with all_288_0, simplifying with (22),
% 89.03/12.73 | (23) gives:
% 89.03/12.73 | (67) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (relation_rng(all_288_0) =
% 89.03/12.73 | v1 & relation_dom(all_288_0) = v2 & relation(all_288_0) = v0 &
% 89.03/12.73 | $i(v2) & $i(v1) & ( ~ (v0 = 0) | ( ! [v3: $i] : ! [v4: int] : (v4 =
% 89.03/12.73 | 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ! [v5: $i] : ( ~
% 89.03/12.73 | (in(v5, v2) = 0) | ~ $i(v5) | ? [v6: $i] : ( ~ (v6 = v3) &
% 89.03/12.73 | apply(all_288_0, v5) = v6 & $i(v6)))) & ! [v3: $i] : ( ~
% 89.03/12.73 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(all_288_0,
% 89.03/12.73 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 =
% 89.03/12.73 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: any] : (in(v4, v3) = v5
% 89.03/12.73 | & $i(v4) & ( ~ (v5 = 0) | ! [v6: $i] : ( ~ (in(v6, v2) = 0)
% 89.03/12.73 | | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v4) &
% 89.03/12.73 | apply(all_288_0, v6) = v7 & $i(v7)))) & (v5 = 0 | ?
% 89.03/12.73 | [v6: $i] : (apply(all_288_0, v6) = v4 & in(v6, v2) = 0 &
% 89.03/12.73 | $i(v6))))))))
% 89.03/12.73 |
% 89.03/12.73 | GROUND_INST: instantiating (2) with all_288_0, simplifying with (22), (23)
% 89.03/12.73 | gives:
% 89.03/12.73 | (68) ? [v0: any] : ? [v1: $i] : (relation_dom(all_288_0) = v1 &
% 89.03/12.73 | relation(all_288_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : !
% 89.03/12.73 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (ordered_pair(v2,
% 89.03/12.73 | v3) = v4) | ~ (in(v4, all_288_0) = v5) | ~ $i(v3) | ~
% 89.03/12.73 | $i(v2) | ? [v6: any] : ? [v7: $i] : (apply(all_288_0, v2) =
% 89.03/12.73 | v7 & in(v2, v1) = v6 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 =
% 89.03/12.73 | v3) | v5 = 0) & ( ~ (v5 = 0) | v7 = v3))))) & ?
% 89.03/12.73 | [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v1)
% 89.03/12.73 | = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] :
% 89.03/12.73 | (apply(all_288_0, v3) = v5 & $i(v5) & ( ~ (v5 = v2) | v2 =
% 89.03/12.73 | empty_set) & ( ~ (v2 = empty_set) | v5 = empty_set))))))
% 89.03/12.73 |
% 89.03/12.73 | GROUND_INST: instantiating (d13_funct_1) with all_288_0, simplifying with
% 89.03/12.73 | (22), (23) gives:
% 89.03/12.74 | (69) ? [v0: any] : ? [v1: $i] : (relation_dom(all_288_0) = v1 &
% 89.03/12.74 | relation(all_288_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 89.03/12.74 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 89.03/12.74 | (relation_inverse_image(all_288_0, v3) = v4) | ~ $i(v3) | ~
% 89.03/12.74 | $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8:
% 89.03/12.74 | $i] : ? [v9: any] : (apply(all_288_0, v5) = v8 & in(v8, v3)
% 89.03/12.74 | = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & $i(v5) &
% 89.03/12.74 | ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 | (v9 =
% 89.03/12.74 | 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 89.03/12.74 | (relation_inverse_image(all_288_0, v2) = v3) | ~ $i(v3) | ~
% 89.03/12.74 | $i(v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~
% 89.03/12.74 | (apply(all_288_0, v4) = v5) | ~ (in(v5, v2) = v6) | ~
% 89.03/12.74 | $i(v4) | ? [v7: any] : ? [v8: any] : (in(v4, v3) = v7 &
% 89.03/12.74 | in(v4, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) &
% 89.03/12.74 | ! [v4: $i] : ! [v5: $i] : ( ~ (apply(all_288_0, v4) = v5) |
% 89.03/12.74 | ~ (in(v5, v2) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7:
% 89.03/12.74 | any] : (in(v4, v3) = v7 & in(v4, v1) = v6 & ( ~ (v6 = 0)
% 89.03/12.74 | | v7 = 0))))))))
% 89.03/12.74 |
% 89.03/12.74 | GROUND_INST: instantiating (d12_funct_1) with all_288_0, simplifying with
% 89.03/12.74 | (22), (23) gives:
% 89.03/12.74 | (70) ? [v0: any] : ? [v1: $i] : (relation_dom(all_288_0) = v1 &
% 89.03/12.74 | relation(all_288_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 89.03/12.74 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 89.03/12.74 | (relation_image(all_288_0, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 89.03/12.74 | ? [v5: $i] : ? [v6: any] : (in(v5, v2) = v6 & $i(v5) & ( ~
% 89.03/12.74 | (v6 = 0) | ! [v7: $i] : ( ~ (in(v7, v1) = 0) | ~ $i(v7)
% 89.03/12.74 | | ? [v8: any] : ? [v9: $i] : (apply(all_288_0, v7) =
% 89.03/12.74 | v9 & in(v7, v3) = v8 & $i(v9) & ( ~ (v9 = v5) | ~ (v8
% 89.03/12.74 | = 0))))) & (v6 = 0 | ? [v7: $i] :
% 89.03/12.74 | (apply(all_288_0, v7) = v5 & in(v7, v3) = 0 & in(v7, v1) =
% 89.03/12.74 | 0 & $i(v7))))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 89.03/12.74 | (relation_image(all_288_0, v2) = v3) | ~ $i(v3) | ~ $i(v2) |
% 89.03/12.74 | ( ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v3) = v5) |
% 89.03/12.74 | ~ $i(v4) | ! [v6: $i] : ( ~ (in(v6, v1) = 0) | ~ $i(v6)
% 89.03/12.74 | | ? [v7: any] : ? [v8: $i] : (apply(all_288_0, v6) =
% 89.03/12.74 | v8 & in(v6, v2) = v7 & $i(v8) & ( ~ (v8 = v4) | ~ (v7
% 89.03/12.74 | = 0))))) & ! [v4: $i] : ( ~ (in(v4, v3) = 0) | ~
% 89.03/12.74 | $i(v4) | ? [v5: $i] : (apply(all_288_0, v5) = v4 & in(v5,
% 89.03/12.74 | v2) = 0 & in(v5, v1) = 0 & $i(v5))))))))
% 89.03/12.74 |
% 89.03/12.74 | GROUND_INST: instantiating (d5_funct_1) with all_294_0, simplifying with (31),
% 89.03/12.74 | (33) gives:
% 89.03/12.74 | (71) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (relation_rng(all_294_0) =
% 89.03/12.74 | v1 & relation_dom(all_294_0) = v2 & relation(all_294_0) = v0 &
% 89.03/12.74 | $i(v2) & $i(v1) & ( ~ (v0 = 0) | ( ! [v3: $i] : ! [v4: int] : (v4 =
% 89.03/12.74 | 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ! [v5: $i] : ( ~
% 89.03/12.74 | (in(v5, v2) = 0) | ~ $i(v5) | ? [v6: $i] : ( ~ (v6 = v3) &
% 89.03/12.74 | apply(all_294_0, v5) = v6 & $i(v6)))) & ! [v3: $i] : ( ~
% 89.03/12.74 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(all_294_0,
% 89.03/12.74 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 =
% 89.03/12.74 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: any] : (in(v4, v3) = v5
% 89.03/12.74 | & $i(v4) & ( ~ (v5 = 0) | ! [v6: $i] : ( ~ (in(v6, v2) = 0)
% 89.03/12.74 | | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v4) &
% 89.03/12.74 | apply(all_294_0, v6) = v7 & $i(v7)))) & (v5 = 0 | ?
% 89.03/12.74 | [v6: $i] : (apply(all_294_0, v6) = v4 & in(v6, v2) = 0 &
% 89.03/12.74 | $i(v6))))))))
% 89.03/12.74 |
% 89.03/12.74 | GROUND_INST: instantiating (2) with all_294_0, simplifying with (31), (33)
% 89.03/12.74 | gives:
% 89.03/12.74 | (72) ? [v0: any] : ? [v1: $i] : (relation_dom(all_294_0) = v1 &
% 89.03/12.74 | relation(all_294_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : !
% 89.03/12.74 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (ordered_pair(v2,
% 89.03/12.74 | v3) = v4) | ~ (in(v4, all_294_0) = v5) | ~ $i(v3) | ~
% 89.03/12.74 | $i(v2) | ? [v6: any] : ? [v7: $i] : (apply(all_294_0, v2) =
% 89.03/12.74 | v7 & in(v2, v1) = v6 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 =
% 89.03/12.74 | v3) | v5 = 0) & ( ~ (v5 = 0) | v7 = v3))))) & ?
% 89.03/12.74 | [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v1)
% 89.03/12.74 | = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] :
% 89.03/12.74 | (apply(all_294_0, v3) = v5 & $i(v5) & ( ~ (v5 = v2) | v2 =
% 89.03/12.74 | empty_set) & ( ~ (v2 = empty_set) | v5 = empty_set))))))
% 89.03/12.74 |
% 89.03/12.74 | GROUND_INST: instantiating (d13_funct_1) with all_294_0, simplifying with
% 89.03/12.74 | (31), (33) gives:
% 89.03/12.75 | (73) ? [v0: any] : ? [v1: $i] : (relation_dom(all_294_0) = v1 &
% 89.03/12.75 | relation(all_294_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 89.03/12.75 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 89.03/12.75 | (relation_inverse_image(all_294_0, v3) = v4) | ~ $i(v3) | ~
% 89.03/12.75 | $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8:
% 89.03/12.75 | $i] : ? [v9: any] : (apply(all_294_0, v5) = v8 & in(v8, v3)
% 89.03/12.75 | = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & $i(v5) &
% 89.03/12.75 | ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 | (v9 =
% 89.03/12.75 | 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 89.03/12.75 | (relation_inverse_image(all_294_0, v2) = v3) | ~ $i(v3) | ~
% 89.03/12.75 | $i(v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~
% 89.03/12.75 | (apply(all_294_0, v4) = v5) | ~ (in(v5, v2) = v6) | ~
% 89.03/12.75 | $i(v4) | ? [v7: any] : ? [v8: any] : (in(v4, v3) = v7 &
% 89.03/12.75 | in(v4, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) &
% 89.03/12.75 | ! [v4: $i] : ! [v5: $i] : ( ~ (apply(all_294_0, v4) = v5) |
% 89.03/12.75 | ~ (in(v5, v2) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7:
% 89.03/12.75 | any] : (in(v4, v3) = v7 & in(v4, v1) = v6 & ( ~ (v6 = 0)
% 89.03/12.75 | | v7 = 0))))))))
% 89.03/12.75 |
% 89.03/12.75 | GROUND_INST: instantiating (d12_funct_1) with all_294_0, simplifying with
% 89.03/12.75 | (31), (33) gives:
% 89.03/12.75 | (74) ? [v0: any] : ? [v1: $i] : (relation_dom(all_294_0) = v1 &
% 89.03/12.75 | relation(all_294_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 89.03/12.75 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 89.03/12.75 | (relation_image(all_294_0, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 89.03/12.75 | ? [v5: $i] : ? [v6: any] : (in(v5, v2) = v6 & $i(v5) & ( ~
% 89.03/12.75 | (v6 = 0) | ! [v7: $i] : ( ~ (in(v7, v1) = 0) | ~ $i(v7)
% 89.03/12.75 | | ? [v8: any] : ? [v9: $i] : (apply(all_294_0, v7) =
% 89.03/12.75 | v9 & in(v7, v3) = v8 & $i(v9) & ( ~ (v9 = v5) | ~ (v8
% 89.03/12.75 | = 0))))) & (v6 = 0 | ? [v7: $i] :
% 89.03/12.75 | (apply(all_294_0, v7) = v5 & in(v7, v3) = 0 & in(v7, v1) =
% 89.03/12.75 | 0 & $i(v7))))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 89.03/12.75 | (relation_image(all_294_0, v2) = v3) | ~ $i(v3) | ~ $i(v2) |
% 89.03/12.75 | ( ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v3) = v5) |
% 89.03/12.75 | ~ $i(v4) | ! [v6: $i] : ( ~ (in(v6, v1) = 0) | ~ $i(v6)
% 89.03/12.75 | | ? [v7: any] : ? [v8: $i] : (apply(all_294_0, v6) =
% 89.03/12.75 | v8 & in(v6, v2) = v7 & $i(v8) & ( ~ (v8 = v4) | ~ (v7
% 89.03/12.75 | = 0))))) & ! [v4: $i] : ( ~ (in(v4, v3) = 0) | ~
% 89.03/12.75 | $i(v4) | ? [v5: $i] : (apply(all_294_0, v5) = v4 & in(v5,
% 89.03/12.75 | v2) = 0 & in(v5, v1) = 0 & $i(v5))))))))
% 89.03/12.75 |
% 89.03/12.75 | GROUND_INST: instantiating (d5_funct_1) with all_309_0, simplifying with (35),
% 89.03/12.75 | (37) gives:
% 89.03/12.75 | (75) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (relation_rng(all_309_0) =
% 89.03/12.75 | v1 & relation_dom(all_309_0) = v2 & relation(all_309_0) = v0 &
% 89.03/12.75 | $i(v2) & $i(v1) & ( ~ (v0 = 0) | ( ! [v3: $i] : ! [v4: int] : (v4 =
% 89.03/12.75 | 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ! [v5: $i] : ( ~
% 89.03/12.75 | (in(v5, v2) = 0) | ~ $i(v5) | ? [v6: $i] : ( ~ (v6 = v3) &
% 89.03/12.75 | apply(all_309_0, v5) = v6 & $i(v6)))) & ! [v3: $i] : ( ~
% 89.03/12.75 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(all_309_0,
% 89.03/12.75 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 =
% 89.03/12.75 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: any] : (in(v4, v3) = v5
% 89.03/12.75 | & $i(v4) & ( ~ (v5 = 0) | ! [v6: $i] : ( ~ (in(v6, v2) = 0)
% 89.03/12.75 | | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v4) &
% 89.03/12.75 | apply(all_309_0, v6) = v7 & $i(v7)))) & (v5 = 0 | ?
% 89.03/12.75 | [v6: $i] : (apply(all_309_0, v6) = v4 & in(v6, v2) = 0 &
% 89.03/12.75 | $i(v6))))))))
% 89.03/12.75 |
% 89.03/12.75 | GROUND_INST: instantiating (2) with all_309_0, simplifying with (35), (37)
% 89.03/12.75 | gives:
% 89.03/12.75 | (76) ? [v0: any] : ? [v1: $i] : (relation_dom(all_309_0) = v1 &
% 89.03/12.75 | relation(all_309_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : !
% 89.03/12.75 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (ordered_pair(v2,
% 89.03/12.75 | v3) = v4) | ~ (in(v4, all_309_0) = v5) | ~ $i(v3) | ~
% 89.03/12.75 | $i(v2) | ? [v6: any] : ? [v7: $i] : (apply(all_309_0, v2) =
% 89.03/12.75 | v7 & in(v2, v1) = v6 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 =
% 89.03/12.75 | v3) | v5 = 0) & ( ~ (v5 = 0) | v7 = v3))))) & ?
% 89.03/12.75 | [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v1)
% 89.03/12.75 | = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] :
% 89.03/12.75 | (apply(all_309_0, v3) = v5 & $i(v5) & ( ~ (v5 = v2) | v2 =
% 89.03/12.75 | empty_set) & ( ~ (v2 = empty_set) | v5 = empty_set))))))
% 89.03/12.75 |
% 89.03/12.75 | GROUND_INST: instantiating (d13_funct_1) with all_309_0, simplifying with
% 89.03/12.75 | (35), (37) gives:
% 89.03/12.76 | (77) ? [v0: any] : ? [v1: $i] : (relation_dom(all_309_0) = v1 &
% 89.03/12.76 | relation(all_309_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 89.03/12.76 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 89.03/12.76 | (relation_inverse_image(all_309_0, v3) = v4) | ~ $i(v3) | ~
% 89.03/12.76 | $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8:
% 89.03/12.76 | $i] : ? [v9: any] : (apply(all_309_0, v5) = v8 & in(v8, v3)
% 89.03/12.76 | = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & $i(v5) &
% 89.03/12.76 | ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 | (v9 =
% 89.03/12.76 | 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 89.03/12.76 | (relation_inverse_image(all_309_0, v2) = v3) | ~ $i(v3) | ~
% 89.03/12.76 | $i(v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~
% 89.03/12.76 | (apply(all_309_0, v4) = v5) | ~ (in(v5, v2) = v6) | ~
% 89.03/12.76 | $i(v4) | ? [v7: any] : ? [v8: any] : (in(v4, v3) = v7 &
% 89.03/12.76 | in(v4, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) &
% 89.03/12.76 | ! [v4: $i] : ! [v5: $i] : ( ~ (apply(all_309_0, v4) = v5) |
% 89.03/12.76 | ~ (in(v5, v2) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7:
% 89.03/12.76 | any] : (in(v4, v3) = v7 & in(v4, v1) = v6 & ( ~ (v6 = 0)
% 89.03/12.76 | | v7 = 0))))))))
% 89.03/12.76 |
% 89.03/12.76 | GROUND_INST: instantiating (d12_funct_1) with all_309_0, simplifying with
% 89.03/12.76 | (35), (37) gives:
% 89.03/12.76 | (78) ? [v0: any] : ? [v1: $i] : (relation_dom(all_309_0) = v1 &
% 89.03/12.76 | relation(all_309_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 89.03/12.76 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 89.03/12.76 | (relation_image(all_309_0, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 89.03/12.76 | ? [v5: $i] : ? [v6: any] : (in(v5, v2) = v6 & $i(v5) & ( ~
% 89.03/12.76 | (v6 = 0) | ! [v7: $i] : ( ~ (in(v7, v1) = 0) | ~ $i(v7)
% 89.03/12.76 | | ? [v8: any] : ? [v9: $i] : (apply(all_309_0, v7) =
% 89.03/12.76 | v9 & in(v7, v3) = v8 & $i(v9) & ( ~ (v9 = v5) | ~ (v8
% 89.03/12.76 | = 0))))) & (v6 = 0 | ? [v7: $i] :
% 89.03/12.76 | (apply(all_309_0, v7) = v5 & in(v7, v3) = 0 & in(v7, v1) =
% 89.03/12.76 | 0 & $i(v7))))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 89.03/12.76 | (relation_image(all_309_0, v2) = v3) | ~ $i(v3) | ~ $i(v2) |
% 89.03/12.76 | ( ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v3) = v5) |
% 89.03/12.76 | ~ $i(v4) | ! [v6: $i] : ( ~ (in(v6, v1) = 0) | ~ $i(v6)
% 89.03/12.76 | | ? [v7: any] : ? [v8: $i] : (apply(all_309_0, v6) =
% 89.03/12.76 | v8 & in(v6, v2) = v7 & $i(v8) & ( ~ (v8 = v4) | ~ (v7
% 89.03/12.76 | = 0))))) & ! [v4: $i] : ( ~ (in(v4, v3) = 0) | ~
% 89.03/12.76 | $i(v4) | ? [v5: $i] : (apply(all_309_0, v5) = v4 & in(v5,
% 89.03/12.76 | v2) = 0 & in(v5, v1) = 0 & $i(v5))))))))
% 89.03/12.76 |
% 89.03/12.76 | GROUND_INST: instantiating (d5_funct_1) with all_344_0, simplifying with (52),
% 89.03/12.76 | (53) gives:
% 89.03/12.76 | (79) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (relation_rng(all_344_0) =
% 89.03/12.76 | v1 & relation_dom(all_344_0) = v2 & relation(all_344_0) = v0 &
% 89.03/12.76 | $i(v2) & $i(v1) & ( ~ (v0 = 0) | ( ! [v3: $i] : ! [v4: int] : (v4 =
% 89.03/12.76 | 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ! [v5: $i] : ( ~
% 89.03/12.76 | (in(v5, v2) = 0) | ~ $i(v5) | ? [v6: $i] : ( ~ (v6 = v3) &
% 89.03/12.76 | apply(all_344_0, v5) = v6 & $i(v6)))) & ! [v3: $i] : ( ~
% 89.03/12.76 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(all_344_0,
% 89.03/12.76 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 =
% 89.03/12.76 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: any] : (in(v4, v3) = v5
% 89.03/12.76 | & $i(v4) & ( ~ (v5 = 0) | ! [v6: $i] : ( ~ (in(v6, v2) = 0)
% 89.03/12.76 | | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v4) &
% 89.03/12.76 | apply(all_344_0, v6) = v7 & $i(v7)))) & (v5 = 0 | ?
% 89.03/12.76 | [v6: $i] : (apply(all_344_0, v6) = v4 & in(v6, v2) = 0 &
% 89.03/12.76 | $i(v6))))))))
% 89.03/12.76 |
% 89.03/12.76 | GROUND_INST: instantiating (2) with all_344_0, simplifying with (52), (53)
% 89.03/12.76 | gives:
% 89.03/12.76 | (80) ? [v0: any] : ? [v1: $i] : (relation_dom(all_344_0) = v1 &
% 89.03/12.76 | relation(all_344_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : !
% 89.03/12.76 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (ordered_pair(v2,
% 89.03/12.76 | v3) = v4) | ~ (in(v4, all_344_0) = v5) | ~ $i(v3) | ~
% 89.03/12.76 | $i(v2) | ? [v6: any] : ? [v7: $i] : (apply(all_344_0, v2) =
% 89.03/12.76 | v7 & in(v2, v1) = v6 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 =
% 89.03/12.76 | v3) | v5 = 0) & ( ~ (v5 = 0) | v7 = v3))))) & ?
% 89.03/12.76 | [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v1)
% 89.03/12.76 | = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] :
% 89.03/12.76 | (apply(all_344_0, v3) = v5 & $i(v5) & ( ~ (v5 = v2) | v2 =
% 89.03/12.76 | empty_set) & ( ~ (v2 = empty_set) | v5 = empty_set))))))
% 89.03/12.76 |
% 89.03/12.76 | GROUND_INST: instantiating (d13_funct_1) with all_344_0, simplifying with
% 89.03/12.76 | (52), (53) gives:
% 89.03/12.76 | (81) ? [v0: any] : ? [v1: $i] : (relation_dom(all_344_0) = v1 &
% 89.03/12.76 | relation(all_344_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 89.03/12.76 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 89.03/12.76 | (relation_inverse_image(all_344_0, v3) = v4) | ~ $i(v3) | ~
% 89.03/12.76 | $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8:
% 89.03/12.76 | $i] : ? [v9: any] : (apply(all_344_0, v5) = v8 & in(v8, v3)
% 89.03/12.76 | = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & $i(v5) &
% 89.03/12.76 | ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 | (v9 =
% 89.03/12.76 | 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 89.03/12.76 | (relation_inverse_image(all_344_0, v2) = v3) | ~ $i(v3) | ~
% 89.03/12.76 | $i(v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~
% 89.03/12.76 | (apply(all_344_0, v4) = v5) | ~ (in(v5, v2) = v6) | ~
% 89.03/12.76 | $i(v4) | ? [v7: any] : ? [v8: any] : (in(v4, v3) = v7 &
% 89.03/12.76 | in(v4, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) &
% 89.03/12.76 | ! [v4: $i] : ! [v5: $i] : ( ~ (apply(all_344_0, v4) = v5) |
% 89.03/12.76 | ~ (in(v5, v2) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7:
% 89.03/12.76 | any] : (in(v4, v3) = v7 & in(v4, v1) = v6 & ( ~ (v6 = 0)
% 89.03/12.76 | | v7 = 0))))))))
% 89.03/12.76 |
% 89.03/12.76 | GROUND_INST: instantiating (d12_funct_1) with all_344_0, simplifying with
% 89.03/12.76 | (52), (53) gives:
% 89.03/12.77 | (82) ? [v0: any] : ? [v1: $i] : (relation_dom(all_344_0) = v1 &
% 89.03/12.77 | relation(all_344_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : !
% 89.03/12.77 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 89.03/12.77 | (relation_image(all_344_0, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 89.03/12.77 | ? [v5: $i] : ? [v6: any] : (in(v5, v2) = v6 & $i(v5) & ( ~
% 89.03/12.77 | (v6 = 0) | ! [v7: $i] : ( ~ (in(v7, v1) = 0) | ~ $i(v7)
% 89.03/12.77 | | ? [v8: any] : ? [v9: $i] : (apply(all_344_0, v7) =
% 89.03/12.77 | v9 & in(v7, v3) = v8 & $i(v9) & ( ~ (v9 = v5) | ~ (v8
% 89.03/12.77 | = 0))))) & (v6 = 0 | ? [v7: $i] :
% 89.03/12.77 | (apply(all_344_0, v7) = v5 & in(v7, v3) = 0 & in(v7, v1) =
% 89.03/12.77 | 0 & $i(v7))))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 89.03/12.77 | (relation_image(all_344_0, v2) = v3) | ~ $i(v3) | ~ $i(v2) |
% 89.03/12.77 | ( ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v3) = v5) |
% 89.03/12.77 | ~ $i(v4) | ! [v6: $i] : ( ~ (in(v6, v1) = 0) | ~ $i(v6)
% 89.03/12.77 | | ? [v7: any] : ? [v8: $i] : (apply(all_344_0, v6) =
% 89.03/12.77 | v8 & in(v6, v2) = v7 & $i(v8) & ( ~ (v8 = v4) | ~ (v7
% 89.03/12.77 | = 0))))) & ! [v4: $i] : ( ~ (in(v4, v3) = 0) | ~
% 89.03/12.77 | $i(v4) | ? [v5: $i] : (apply(all_344_0, v5) = v4 & in(v5,
% 89.03/12.77 | v2) = 0 & in(v5, v1) = 0 & $i(v5))))))))
% 89.03/12.77 |
% 89.03/12.77 | GROUND_INST: instantiating (d8_funct_1) with empty_set, 0, simplifying with
% 89.03/12.77 | (4), (7) gives:
% 89.03/12.77 | (83) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (relation_dom(empty_set) =
% 89.03/12.77 | v2 & relation(empty_set) = v0 & function(empty_set) = v1 & $i(v2) &
% 89.03/12.77 | ( ~ (v1 = 0) | ~ (v0 = 0) | ! [v3: $i] : ! [v4: $i] : (v4 = v3 |
% 89.03/12.77 | ~ (in(v4, v2) = 0) | ~ (in(v3, v2) = 0) | ~ $i(v4) | ~ $i(v3)
% 89.03/12.77 | | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(empty_set,
% 89.03/12.77 | v4) = v6 & apply(empty_set, v3) = v5 & $i(v6) & $i(v5)))))
% 89.03/12.77 |
% 89.03/12.77 | GROUND_INST: instantiating (d8_funct_1) with all_309_0, 0, simplifying with
% 89.03/12.77 | (35), (38) gives:
% 89.03/12.77 | (84) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (relation_dom(all_309_0) =
% 89.03/12.77 | v2 & relation(all_309_0) = v0 & function(all_309_0) = v1 & $i(v2) &
% 89.03/12.77 | ( ~ (v1 = 0) | ~ (v0 = 0) | ! [v3: $i] : ! [v4: $i] : (v4 = v3 |
% 89.03/12.77 | ~ (in(v4, v2) = 0) | ~ (in(v3, v2) = 0) | ~ $i(v4) | ~ $i(v3)
% 89.03/12.77 | | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(all_309_0,
% 89.03/12.77 | v4) = v6 & apply(all_309_0, v3) = v5 & $i(v6) & $i(v5)))))
% 89.03/12.77 |
% 89.03/12.77 | GROUND_INST: instantiating (d4_wellord1) with all_316_1, 0, simplifying with
% 89.03/12.77 | (40), (56) gives:
% 89.03/12.77 | (85) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 89.03/12.77 | any] : ? [v5: any] : (reflexive(all_316_1) = v1 &
% 89.03/12.77 | well_founded_relation(all_316_1) = v5 & transitive(all_316_1) = v2 &
% 89.03/12.77 | connected(all_316_1) = v4 & antisymmetric(all_316_1) = v3 &
% 89.03/12.77 | relation(all_316_1) = v0 & ( ~ (v0 = 0) | (v5 = 0 & v4 = 0 & v3 = 0
% 89.03/12.77 | & v2 = 0 & v1 = 0)))
% 89.03/12.77 |
% 89.03/12.77 | GROUND_INST: instantiating (d4_wellord1) with all_342_1, all_342_0,
% 89.03/12.77 | simplifying with (45), (47) gives:
% 89.03/12.77 | (86) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 89.03/12.77 | any] : ? [v5: any] : (reflexive(all_342_1) = v1 &
% 89.03/12.77 | well_founded_relation(all_342_1) = v5 & transitive(all_342_1) = v2 &
% 89.03/12.77 | connected(all_342_1) = v4 & antisymmetric(all_342_1) = v3 &
% 89.03/12.77 | relation(all_342_1) = v0 & ( ~ (v0 = 0) | (( ~ (v5 = 0) | ~ (v4 =
% 89.03/12.77 | 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | all_342_0 =
% 89.03/12.77 | 0) & ( ~ (all_342_0 = 0) | (v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0
% 89.03/12.77 | & v1 = 0)))))
% 89.03/12.77 |
% 89.03/12.77 | GROUND_INST: instantiating (t25_relat_1) with empty_set, empty_set,
% 89.03/12.77 | simplifying with (5), (7) gives:
% 89.03/12.77 | (87) ? [v0: any] : ? [v1: $i] : (relation_dom(empty_set) = v1 &
% 89.03/12.77 | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : !
% 89.03/12.77 | [v3: $i] : ! [v4: any] : ( ~ (relation_rng(v2) = v3) | ~
% 89.03/12.77 | (subset(empty_set, v3) = v4) | ~ $i(v2) | ? [v5: any] : ?
% 89.03/12.77 | [v6: any] : ? [v7: $i] : ? [v8: any] : (relation_dom(v2) = v7
% 89.03/12.77 | & subset(v1, v7) = v8 & subset(empty_set, v2) = v6 &
% 89.03/12.77 | relation(v2) = v5 & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8
% 89.03/12.77 | = 0 & v4 = 0))))))
% 89.03/12.77 |
% 89.03/12.77 | GROUND_INST: instantiating (t47_relat_1) with empty_set, empty_set,
% 89.03/12.77 | simplifying with (5), (7) gives:
% 89.03/12.77 | (88) ? [v0: any] : ? [v1: $i] : (relation_dom(empty_set) = v1 &
% 89.03/12.77 | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : !
% 89.03/12.77 | [v3: $i] : ( ~ (relation_rng(v2) = v3) | ~ (subset(v1, v3) = 0) |
% 89.03/12.77 | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] :
% 89.03/12.77 | (relation_composition(v2, empty_set) = v5 & relation_rng(v5) =
% 89.03/12.77 | v6 & relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 =
% 89.03/12.77 | empty_set)))))
% 89.03/12.77 |
% 89.03/12.77 | GROUND_INST: instantiating (t46_relat_1) with empty_set, empty_set,
% 89.03/12.77 | simplifying with (5), (7) gives:
% 89.03/12.77 | (89) ? [v0: any] : ? [v1: $i] : (relation_dom(empty_set) = v1 &
% 89.03/12.77 | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : !
% 89.03/12.77 | [v3: $i] : ( ~ (relation_dom(v2) = v3) | ~ (subset(empty_set, v3)
% 89.03/12.77 | = 0) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] :
% 89.03/12.77 | (relation_composition(empty_set, v2) = v5 & relation_dom(v5) =
% 89.03/12.77 | v6 & relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 =
% 89.03/12.77 | v1)))))
% 89.03/12.77 |
% 89.03/12.77 | COMBINE_EQS: (61), (62) imply:
% 89.03/12.78 | (90) all_286_0 = empty_set
% 89.03/12.78 |
% 89.03/12.78 | SIMP: (90) implies:
% 89.03/12.78 | (91) all_286_0 = empty_set
% 89.03/12.78 |
% 89.03/12.78 | COMBINE_EQS: (59), (60) imply:
% 89.03/12.78 | (92) all_286_0 = all_273_0
% 89.03/12.78 |
% 89.03/12.78 | SIMP: (92) implies:
% 89.03/12.78 | (93) all_286_0 = all_273_0
% 89.03/12.78 |
% 89.03/12.78 | COMBINE_EQS: (91), (93) imply:
% 89.03/12.78 | (94) all_273_0 = empty_set
% 89.03/12.78 |
% 89.03/12.78 | COMBINE_EQS: (60), (94) imply:
% 89.03/12.78 | (95) all_294_0 = empty_set
% 89.03/12.78 |
% 89.03/12.78 | DELTA: instantiating (85) with fresh symbols all_734_0, all_734_1, all_734_2,
% 89.03/12.78 | all_734_3, all_734_4, all_734_5 gives:
% 89.03/12.78 | (96) reflexive(all_316_1) = all_734_4 & well_founded_relation(all_316_1) =
% 89.03/12.78 | all_734_0 & transitive(all_316_1) = all_734_3 & connected(all_316_1) =
% 89.03/12.78 | all_734_1 & antisymmetric(all_316_1) = all_734_2 & relation(all_316_1)
% 89.03/12.78 | = all_734_5 & ( ~ (all_734_5 = 0) | (all_734_0 = 0 & all_734_1 = 0 &
% 89.03/12.78 | all_734_2 = 0 & all_734_3 = 0 & all_734_4 = 0))
% 89.03/12.78 |
% 89.03/12.78 | ALPHA: (96) implies:
% 89.03/12.78 | (97) relation(all_316_1) = all_734_5
% 89.03/12.78 | (98) antisymmetric(all_316_1) = all_734_2
% 89.03/12.78 | (99) connected(all_316_1) = all_734_1
% 89.03/12.78 | (100) transitive(all_316_1) = all_734_3
% 89.03/12.78 | (101) well_founded_relation(all_316_1) = all_734_0
% 89.03/12.78 | (102) reflexive(all_316_1) = all_734_4
% 89.03/12.78 | (103) ~ (all_734_5 = 0) | (all_734_0 = 0 & all_734_1 = 0 & all_734_2 = 0 &
% 89.03/12.78 | all_734_3 = 0 & all_734_4 = 0)
% 89.03/12.78 |
% 89.03/12.78 | DELTA: instantiating (89) with fresh symbols all_736_0, all_736_1 gives:
% 89.03/12.78 | (104) relation_dom(empty_set) = all_736_0 & relation(empty_set) = all_736_1
% 89.03/12.78 | & $i(all_736_0) & ( ~ (all_736_1 = 0) | ! [v0: $i] : ! [v1: $i] : (
% 89.03/12.78 | ~ (relation_dom(v0) = v1) | ~ (subset(empty_set, v1) = 0) | ~
% 89.03/12.78 | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] :
% 89.03/12.78 | (relation_composition(empty_set, v0) = v3 & relation_dom(v3) = v4
% 89.03/12.78 | & relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v4 =
% 89.03/12.78 | all_736_0))))
% 89.03/12.78 |
% 89.03/12.78 | ALPHA: (104) implies:
% 89.03/12.78 | (105) relation(empty_set) = all_736_1
% 89.03/12.78 |
% 89.03/12.78 | DELTA: instantiating (88) with fresh symbols all_738_0, all_738_1 gives:
% 89.03/12.78 | (106) relation_dom(empty_set) = all_738_0 & relation(empty_set) = all_738_1
% 89.03/12.78 | & $i(all_738_0) & ( ~ (all_738_1 = 0) | ! [v0: $i] : ! [v1: $i] : (
% 89.03/12.78 | ~ (relation_rng(v0) = v1) | ~ (subset(all_738_0, v1) = 0) | ~
% 89.03/12.78 | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] :
% 89.03/12.78 | (relation_composition(v0, empty_set) = v3 & relation_rng(v3) = v4
% 89.03/12.78 | & relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v4 =
% 89.03/12.78 | empty_set))))
% 89.03/12.78 |
% 89.03/12.78 | ALPHA: (106) implies:
% 89.03/12.78 | (107) relation(empty_set) = all_738_1
% 89.03/12.78 |
% 89.03/12.78 | DELTA: instantiating (87) with fresh symbols all_764_0, all_764_1 gives:
% 89.03/12.78 | (108) relation_dom(empty_set) = all_764_0 & relation(empty_set) = all_764_1
% 89.03/12.78 | & $i(all_764_0) & ( ~ (all_764_1 = 0) | ! [v0: $i] : ! [v1: $i] :
% 89.03/12.78 | ! [v2: any] : ( ~ (relation_rng(v0) = v1) | ~ (subset(empty_set,
% 89.03/12.78 | v1) = v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5:
% 89.03/12.78 | $i] : ? [v6: any] : (relation_dom(v0) = v5 & subset(all_764_0,
% 89.03/12.78 | v5) = v6 & subset(empty_set, v0) = v4 & relation(v0) = v3 &
% 89.03/12.78 | $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v2 = 0)))))
% 89.03/12.78 |
% 89.03/12.78 | ALPHA: (108) implies:
% 89.03/12.78 | (109) relation(empty_set) = all_764_1
% 89.03/12.78 |
% 89.03/12.78 | DELTA: instantiating (84) with fresh symbols all_766_0, all_766_1, all_766_2
% 89.03/12.78 | gives:
% 89.03/12.78 | (110) relation_dom(all_309_0) = all_766_0 & relation(all_309_0) = all_766_2
% 89.03/12.78 | & function(all_309_0) = all_766_1 & $i(all_766_0) & ( ~ (all_766_1 =
% 89.03/12.78 | 0) | ~ (all_766_2 = 0) | ! [v0: $i] : ! [v1: $i] : (v1 = v0 |
% 89.03/12.78 | ~ (in(v1, all_766_0) = 0) | ~ (in(v0, all_766_0) = 0) | ~
% 89.03/12.78 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) &
% 89.03/12.78 | apply(all_309_0, v1) = v3 & apply(all_309_0, v0) = v2 & $i(v3)
% 89.03/12.78 | & $i(v2))))
% 89.03/12.78 |
% 89.03/12.78 | ALPHA: (110) implies:
% 89.03/12.78 | (111) function(all_309_0) = all_766_1
% 89.03/12.78 | (112) relation(all_309_0) = all_766_2
% 89.03/12.78 | (113) ~ (all_766_1 = 0) | ~ (all_766_2 = 0) | ! [v0: $i] : ! [v1: $i] :
% 89.03/12.78 | (v1 = v0 | ~ (in(v1, all_766_0) = 0) | ~ (in(v0, all_766_0) = 0) |
% 89.03/12.78 | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) &
% 89.03/12.78 | apply(all_309_0, v1) = v3 & apply(all_309_0, v0) = v2 & $i(v3) &
% 89.03/12.78 | $i(v2)))
% 89.03/12.78 |
% 89.03/12.78 | DELTA: instantiating (83) with fresh symbols all_770_0, all_770_1, all_770_2
% 89.03/12.78 | gives:
% 89.03/12.78 | (114) relation_dom(empty_set) = all_770_0 & relation(empty_set) = all_770_2
% 89.03/12.78 | & function(empty_set) = all_770_1 & $i(all_770_0) & ( ~ (all_770_1 =
% 89.03/12.78 | 0) | ~ (all_770_2 = 0) | ! [v0: $i] : ! [v1: $i] : (v1 = v0 |
% 89.03/12.78 | ~ (in(v1, all_770_0) = 0) | ~ (in(v0, all_770_0) = 0) | ~
% 89.03/12.78 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) &
% 89.03/12.78 | apply(empty_set, v1) = v3 & apply(empty_set, v0) = v2 & $i(v3)
% 89.03/12.78 | & $i(v2))))
% 89.03/12.78 |
% 89.03/12.78 | ALPHA: (114) implies:
% 89.03/12.78 | (115) function(empty_set) = all_770_1
% 89.03/12.78 | (116) relation(empty_set) = all_770_2
% 89.03/12.78 |
% 89.03/12.78 | DELTA: instantiating (86) with fresh symbols all_820_0, all_820_1, all_820_2,
% 89.03/12.78 | all_820_3, all_820_4, all_820_5 gives:
% 89.03/12.78 | (117) reflexive(all_342_1) = all_820_4 & well_founded_relation(all_342_1) =
% 89.03/12.78 | all_820_0 & transitive(all_342_1) = all_820_3 & connected(all_342_1)
% 89.03/12.78 | = all_820_1 & antisymmetric(all_342_1) = all_820_2 &
% 89.03/12.78 | relation(all_342_1) = all_820_5 & ( ~ (all_820_5 = 0) | (( ~
% 89.03/12.78 | (all_820_0 = 0) | ~ (all_820_1 = 0) | ~ (all_820_2 = 0) | ~
% 89.03/12.78 | (all_820_3 = 0) | ~ (all_820_4 = 0) | all_342_0 = 0) & ( ~
% 89.03/12.78 | (all_342_0 = 0) | (all_820_0 = 0 & all_820_1 = 0 & all_820_2 =
% 89.03/12.78 | 0 & all_820_3 = 0 & all_820_4 = 0))))
% 89.03/12.79 |
% 89.03/12.79 | ALPHA: (117) implies:
% 89.03/12.79 | (118) relation(all_342_1) = all_820_5
% 89.03/12.79 | (119) antisymmetric(all_342_1) = all_820_2
% 89.03/12.79 | (120) connected(all_342_1) = all_820_1
% 89.03/12.79 | (121) transitive(all_342_1) = all_820_3
% 89.03/12.79 | (122) well_founded_relation(all_342_1) = all_820_0
% 89.03/12.79 | (123) reflexive(all_342_1) = all_820_4
% 89.03/12.79 | (124) ~ (all_820_5 = 0) | (( ~ (all_820_0 = 0) | ~ (all_820_1 = 0) | ~
% 89.03/12.79 | (all_820_2 = 0) | ~ (all_820_3 = 0) | ~ (all_820_4 = 0) |
% 89.03/12.79 | all_342_0 = 0) & ( ~ (all_342_0 = 0) | (all_820_0 = 0 & all_820_1
% 89.03/12.79 | = 0 & all_820_2 = 0 & all_820_3 = 0 & all_820_4 = 0)))
% 89.03/12.79 |
% 89.03/12.79 | DELTA: instantiating (80) with fresh symbols all_822_0, all_822_1 gives:
% 89.03/12.79 | (125) relation_dom(all_344_0) = all_822_0 & relation(all_344_0) = all_822_1
% 89.03/12.79 | & $i(all_822_0) & ( ~ (all_822_1 = 0) | ( ! [v0: $i] : ! [v1: $i] :
% 89.03/12.79 | ! [v2: $i] : ! [v3: any] : ( ~ (ordered_pair(v0, v1) = v2) | ~
% 89.03/12.79 | (in(v2, all_344_0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any]
% 89.03/12.79 | : ? [v5: $i] : (apply(all_344_0, v0) = v5 & in(v0, all_822_0)
% 89.03/12.79 | = v4 & $i(v5) & ( ~ (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~
% 89.03/12.79 | (v3 = 0) | v5 = v1))))) & ? [v0: $i] : ! [v1: $i] :
% 89.03/12.79 | ! [v2: int] : (v2 = 0 | ~ (in(v1, all_822_0) = v2) | ~ $i(v1) |
% 89.03/12.79 | ~ $i(v0) | ? [v3: $i] : (apply(all_344_0, v1) = v3 & $i(v3) &
% 89.03/12.79 | ( ~ (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 =
% 89.03/12.79 | empty_set)))))
% 89.03/12.79 |
% 89.03/12.79 | ALPHA: (125) implies:
% 89.03/12.79 | (126) relation(all_344_0) = all_822_1
% 89.03/12.79 |
% 89.03/12.79 | DELTA: instantiating (72) with fresh symbols all_826_0, all_826_1 gives:
% 89.03/12.79 | (127) relation_dom(all_294_0) = all_826_0 & relation(all_294_0) = all_826_1
% 89.03/12.79 | & $i(all_826_0) & ( ~ (all_826_1 = 0) | ( ! [v0: $i] : ! [v1: $i] :
% 89.03/12.79 | ! [v2: $i] : ! [v3: any] : ( ~ (ordered_pair(v0, v1) = v2) | ~
% 89.03/12.79 | (in(v2, all_294_0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any]
% 89.03/12.79 | : ? [v5: $i] : (apply(all_294_0, v0) = v5 & in(v0, all_826_0)
% 89.03/12.79 | = v4 & $i(v5) & ( ~ (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~
% 89.03/12.79 | (v3 = 0) | v5 = v1))))) & ? [v0: $i] : ! [v1: $i] :
% 89.03/12.79 | ! [v2: int] : (v2 = 0 | ~ (in(v1, all_826_0) = v2) | ~ $i(v1) |
% 89.03/12.79 | ~ $i(v0) | ? [v3: $i] : (apply(all_294_0, v1) = v3 & $i(v3) &
% 89.03/12.79 | ( ~ (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 =
% 89.03/12.79 | empty_set)))))
% 89.03/12.79 |
% 89.03/12.79 | ALPHA: (127) implies:
% 89.03/12.79 | (128) relation(all_294_0) = all_826_1
% 89.03/12.79 |
% 89.03/12.79 | DELTA: instantiating (68) with fresh symbols all_828_0, all_828_1 gives:
% 89.03/12.79 | (129) relation_dom(all_288_0) = all_828_0 & relation(all_288_0) = all_828_1
% 89.03/12.79 | & $i(all_828_0) & ( ~ (all_828_1 = 0) | ( ! [v0: $i] : ! [v1: $i] :
% 89.03/12.79 | ! [v2: $i] : ! [v3: any] : ( ~ (ordered_pair(v0, v1) = v2) | ~
% 89.03/12.79 | (in(v2, all_288_0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any]
% 89.03/12.79 | : ? [v5: $i] : (apply(all_288_0, v0) = v5 & in(v0, all_828_0)
% 89.03/12.79 | = v4 & $i(v5) & ( ~ (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~
% 89.03/12.79 | (v3 = 0) | v5 = v1))))) & ? [v0: $i] : ! [v1: $i] :
% 89.03/12.79 | ! [v2: int] : (v2 = 0 | ~ (in(v1, all_828_0) = v2) | ~ $i(v1) |
% 89.03/12.79 | ~ $i(v0) | ? [v3: $i] : (apply(all_288_0, v1) = v3 & $i(v3) &
% 89.03/12.79 | ( ~ (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 =
% 89.03/12.79 | empty_set)))))
% 89.03/12.79 |
% 89.03/12.79 | ALPHA: (129) implies:
% 89.03/12.79 | (130) relation(all_288_0) = all_828_1
% 89.03/12.79 |
% 89.03/12.79 | DELTA: instantiating (64) with fresh symbols all_832_0, all_832_1 gives:
% 89.03/12.79 | (131) relation_dom(empty_set) = all_832_0 & relation(empty_set) = all_832_1
% 89.03/12.79 | & $i(all_832_0) & ( ~ (all_832_1 = 0) | ( ! [v0: $i] : ! [v1: $i] :
% 89.03/12.79 | ! [v2: $i] : ! [v3: any] : ( ~ (ordered_pair(v0, v1) = v2) | ~
% 89.03/12.79 | (in(v2, empty_set) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any]
% 89.03/12.79 | : ? [v5: $i] : (apply(empty_set, v0) = v5 & in(v0, all_832_0)
% 89.03/12.79 | = v4 & $i(v5) & ( ~ (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~
% 89.03/12.79 | (v3 = 0) | v5 = v1))))) & ? [v0: $i] : ! [v1: $i] :
% 89.03/12.79 | ! [v2: int] : (v2 = 0 | ~ (in(v1, all_832_0) = v2) | ~ $i(v1) |
% 89.03/12.79 | ~ $i(v0) | ? [v3: $i] : (apply(empty_set, v1) = v3 & $i(v3) &
% 89.03/12.79 | ( ~ (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 =
% 89.03/12.79 | empty_set)))))
% 89.03/12.79 |
% 89.03/12.79 | ALPHA: (131) implies:
% 89.03/12.79 | (132) relation(empty_set) = all_832_1
% 89.03/12.79 |
% 89.03/12.79 | DELTA: instantiating (76) with fresh symbols all_834_0, all_834_1 gives:
% 89.03/12.79 | (133) relation_dom(all_309_0) = all_834_0 & relation(all_309_0) = all_834_1
% 89.03/12.79 | & $i(all_834_0) & ( ~ (all_834_1 = 0) | ( ! [v0: $i] : ! [v1: $i] :
% 89.03/12.79 | ! [v2: $i] : ! [v3: any] : ( ~ (ordered_pair(v0, v1) = v2) | ~
% 89.03/12.79 | (in(v2, all_309_0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any]
% 89.03/12.79 | : ? [v5: $i] : (apply(all_309_0, v0) = v5 & in(v0, all_834_0)
% 89.03/12.79 | = v4 & $i(v5) & ( ~ (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~
% 89.03/12.79 | (v3 = 0) | v5 = v1))))) & ? [v0: $i] : ! [v1: $i] :
% 89.03/12.79 | ! [v2: int] : (v2 = 0 | ~ (in(v1, all_834_0) = v2) | ~ $i(v1) |
% 89.03/12.79 | ~ $i(v0) | ? [v3: $i] : (apply(all_309_0, v1) = v3 & $i(v3) &
% 89.03/12.79 | ( ~ (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 =
% 89.03/12.79 | empty_set)))))
% 89.03/12.79 |
% 89.03/12.79 | ALPHA: (133) implies:
% 89.03/12.79 | (134) relation(all_309_0) = all_834_1
% 89.03/12.79 |
% 89.03/12.79 | DELTA: instantiating (75) with fresh symbols all_836_0, all_836_1, all_836_2
% 89.03/12.79 | gives:
% 89.03/12.80 | (135) relation_rng(all_309_0) = all_836_1 & relation_dom(all_309_0) =
% 89.03/12.80 | all_836_0 & relation(all_309_0) = all_836_2 & $i(all_836_0) &
% 89.03/12.80 | $i(all_836_1) & ( ~ (all_836_2 = 0) | ( ! [v0: $i] : ! [v1: int] :
% 89.03/12.80 | (v1 = 0 | ~ (in(v0, all_836_1) = v1) | ~ $i(v0) | ! [v2: $i] :
% 89.03/12.80 | ( ~ (in(v2, all_836_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ (v3
% 89.03/12.80 | = v0) & apply(all_309_0, v2) = v3 & $i(v3)))) & ! [v0:
% 89.03/12.80 | $i] : ( ~ (in(v0, all_836_1) = 0) | ~ $i(v0) | ? [v1: $i] :
% 89.03/12.80 | (apply(all_309_0, v1) = v0 & in(v1, all_836_0) = 0 & $i(v1))) &
% 89.03/12.80 | ? [v0: any] : (v0 = all_836_1 | ~ $i(v0) | ? [v1: $i] : ?
% 89.03/12.80 | [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3:
% 89.03/12.80 | $i] : ( ~ (in(v3, all_836_0) = 0) | ~ $i(v3) | ? [v4:
% 89.03/12.80 | $i] : ( ~ (v4 = v1) & apply(all_309_0, v3) = v4 &
% 89.03/12.80 | $i(v4)))) & (v2 = 0 | ? [v3: $i] : (apply(all_309_0,
% 89.03/12.80 | v3) = v1 & in(v3, all_836_0) = 0 & $i(v3)))))))
% 89.03/12.80 |
% 89.03/12.80 | ALPHA: (135) implies:
% 89.03/12.80 | (136) relation(all_309_0) = all_836_2
% 89.03/12.80 |
% 89.03/12.80 | DELTA: instantiating (67) with fresh symbols all_838_0, all_838_1, all_838_2
% 89.03/12.80 | gives:
% 89.03/12.80 | (137) relation_rng(all_288_0) = all_838_1 & relation_dom(all_288_0) =
% 89.03/12.80 | all_838_0 & relation(all_288_0) = all_838_2 & $i(all_838_0) &
% 89.03/12.80 | $i(all_838_1) & ( ~ (all_838_2 = 0) | ( ! [v0: $i] : ! [v1: int] :
% 89.03/12.80 | (v1 = 0 | ~ (in(v0, all_838_1) = v1) | ~ $i(v0) | ! [v2: $i] :
% 89.03/12.80 | ( ~ (in(v2, all_838_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ (v3
% 89.03/12.80 | = v0) & apply(all_288_0, v2) = v3 & $i(v3)))) & ! [v0:
% 89.03/12.80 | $i] : ( ~ (in(v0, all_838_1) = 0) | ~ $i(v0) | ? [v1: $i] :
% 89.03/12.80 | (apply(all_288_0, v1) = v0 & in(v1, all_838_0) = 0 & $i(v1))) &
% 89.03/12.80 | ? [v0: any] : (v0 = all_838_1 | ~ $i(v0) | ? [v1: $i] : ?
% 89.03/12.80 | [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3:
% 89.03/12.80 | $i] : ( ~ (in(v3, all_838_0) = 0) | ~ $i(v3) | ? [v4:
% 89.03/12.80 | $i] : ( ~ (v4 = v1) & apply(all_288_0, v3) = v4 &
% 89.03/12.80 | $i(v4)))) & (v2 = 0 | ? [v3: $i] : (apply(all_288_0,
% 89.03/12.80 | v3) = v1 & in(v3, all_838_0) = 0 & $i(v3)))))))
% 89.03/12.80 |
% 89.03/12.80 | ALPHA: (137) implies:
% 89.03/12.80 | (138) relation(all_288_0) = all_838_2
% 89.03/12.80 | (139) relation_rng(all_288_0) = all_838_1
% 89.03/12.80 |
% 89.03/12.80 | DELTA: instantiating (63) with fresh symbols all_842_0, all_842_1, all_842_2
% 89.03/12.80 | gives:
% 89.03/12.80 | (140) relation_rng(empty_set) = all_842_1 & relation_dom(empty_set) =
% 89.03/12.80 | all_842_0 & relation(empty_set) = all_842_2 & $i(all_842_0) &
% 89.03/12.80 | $i(all_842_1) & ( ~ (all_842_2 = 0) | ( ! [v0: $i] : ! [v1: int] :
% 89.03/12.80 | (v1 = 0 | ~ (in(v0, all_842_1) = v1) | ~ $i(v0) | ! [v2: $i] :
% 89.03/12.80 | ( ~ (in(v2, all_842_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ (v3
% 89.03/12.80 | = v0) & apply(empty_set, v2) = v3 & $i(v3)))) & ! [v0:
% 89.03/12.80 | $i] : ( ~ (in(v0, all_842_1) = 0) | ~ $i(v0) | ? [v1: $i] :
% 89.03/12.80 | (apply(empty_set, v1) = v0 & in(v1, all_842_0) = 0 & $i(v1))) &
% 89.03/12.80 | ? [v0: any] : (v0 = all_842_1 | ~ $i(v0) | ? [v1: $i] : ?
% 89.03/12.80 | [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3:
% 89.03/12.80 | $i] : ( ~ (in(v3, all_842_0) = 0) | ~ $i(v3) | ? [v4:
% 89.03/12.80 | $i] : ( ~ (v4 = v1) & apply(empty_set, v3) = v4 &
% 89.03/12.80 | $i(v4)))) & (v2 = 0 | ? [v3: $i] : (apply(empty_set,
% 89.03/12.80 | v3) = v1 & in(v3, all_842_0) = 0 & $i(v3)))))))
% 89.03/12.80 |
% 89.03/12.80 | ALPHA: (140) implies:
% 89.03/12.80 | (141) relation(empty_set) = all_842_2
% 89.03/12.80 |
% 89.03/12.80 | DELTA: instantiating (79) with fresh symbols all_844_0, all_844_1, all_844_2
% 89.03/12.80 | gives:
% 89.03/12.80 | (142) relation_rng(all_344_0) = all_844_1 & relation_dom(all_344_0) =
% 89.03/12.80 | all_844_0 & relation(all_344_0) = all_844_2 & $i(all_844_0) &
% 89.03/12.80 | $i(all_844_1) & ( ~ (all_844_2 = 0) | ( ! [v0: $i] : ! [v1: int] :
% 89.03/12.80 | (v1 = 0 | ~ (in(v0, all_844_1) = v1) | ~ $i(v0) | ! [v2: $i] :
% 89.03/12.80 | ( ~ (in(v2, all_844_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ (v3
% 89.03/12.80 | = v0) & apply(all_344_0, v2) = v3 & $i(v3)))) & ! [v0:
% 89.03/12.80 | $i] : ( ~ (in(v0, all_844_1) = 0) | ~ $i(v0) | ? [v1: $i] :
% 89.03/12.80 | (apply(all_344_0, v1) = v0 & in(v1, all_844_0) = 0 & $i(v1))) &
% 89.03/12.80 | ? [v0: any] : (v0 = all_844_1 | ~ $i(v0) | ? [v1: $i] : ?
% 89.03/12.80 | [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3:
% 89.03/12.80 | $i] : ( ~ (in(v3, all_844_0) = 0) | ~ $i(v3) | ? [v4:
% 89.03/12.80 | $i] : ( ~ (v4 = v1) & apply(all_344_0, v3) = v4 &
% 89.03/12.80 | $i(v4)))) & (v2 = 0 | ? [v3: $i] : (apply(all_344_0,
% 89.03/12.80 | v3) = v1 & in(v3, all_844_0) = 0 & $i(v3)))))))
% 89.03/12.80 |
% 89.03/12.80 | ALPHA: (142) implies:
% 89.03/12.80 | (143) $i(all_844_1)
% 89.03/12.80 | (144) relation(all_344_0) = all_844_2
% 89.03/12.80 | (145) relation_rng(all_344_0) = all_844_1
% 89.03/12.80 |
% 89.03/12.80 | DELTA: instantiating (71) with fresh symbols all_846_0, all_846_1, all_846_2
% 89.03/12.80 | gives:
% 89.03/12.81 | (146) relation_rng(all_294_0) = all_846_1 & relation_dom(all_294_0) =
% 89.03/12.81 | all_846_0 & relation(all_294_0) = all_846_2 & $i(all_846_0) &
% 89.03/12.81 | $i(all_846_1) & ( ~ (all_846_2 = 0) | ( ! [v0: $i] : ! [v1: int] :
% 89.03/12.81 | (v1 = 0 | ~ (in(v0, all_846_1) = v1) | ~ $i(v0) | ! [v2: $i] :
% 89.03/12.81 | ( ~ (in(v2, all_846_0) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ (v3
% 89.03/12.81 | = v0) & apply(all_294_0, v2) = v3 & $i(v3)))) & ! [v0:
% 89.03/12.81 | $i] : ( ~ (in(v0, all_846_1) = 0) | ~ $i(v0) | ? [v1: $i] :
% 89.03/12.81 | (apply(all_294_0, v1) = v0 & in(v1, all_846_0) = 0 & $i(v1))) &
% 89.03/12.81 | ? [v0: any] : (v0 = all_846_1 | ~ $i(v0) | ? [v1: $i] : ?
% 89.03/12.81 | [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3:
% 89.03/12.81 | $i] : ( ~ (in(v3, all_846_0) = 0) | ~ $i(v3) | ? [v4:
% 89.03/12.81 | $i] : ( ~ (v4 = v1) & apply(all_294_0, v3) = v4 &
% 89.03/12.81 | $i(v4)))) & (v2 = 0 | ? [v3: $i] : (apply(all_294_0,
% 89.03/12.81 | v3) = v1 & in(v3, all_846_0) = 0 & $i(v3)))))))
% 89.03/12.81 |
% 89.03/12.81 | ALPHA: (146) implies:
% 89.03/12.81 | (147) relation(all_294_0) = all_846_2
% 89.03/12.81 |
% 89.03/12.81 | DELTA: instantiating (77) with fresh symbols all_850_0, all_850_1 gives:
% 89.03/12.81 | (148) relation_dom(all_309_0) = all_850_0 & relation(all_309_0) = all_850_1
% 89.03/12.81 | & $i(all_850_0) & ( ~ (all_850_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 89.03/12.81 | ! [v2: $i] : (v2 = v0 | ~ (relation_inverse_image(all_309_0, v1)
% 89.03/12.81 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] :
% 89.03/12.81 | ? [v5: any] : ? [v6: $i] : ? [v7: any] : (apply(all_309_0,
% 89.03/12.81 | v3) = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3,
% 89.03/12.81 | all_850_0) = v5 & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 =
% 89.03/12.81 | 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))) & !
% 89.03/12.81 | [v0: $i] : ! [v1: $i] : ( ~ (relation_inverse_image(all_309_0,
% 89.03/12.81 | v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3:
% 89.03/12.81 | $i] : ! [v4: any] : ( ~ (apply(all_309_0, v2) = v3) | ~
% 89.03/12.81 | (in(v3, v0) = v4) | ~ $i(v2) | ? [v5: any] : ? [v6: any]
% 89.03/12.81 | : (in(v2, v1) = v5 & in(v2, all_850_0) = v6 & ( ~ (v5 = 0)
% 89.03/12.81 | | (v6 = 0 & v4 = 0)))) & ! [v2: $i] : ! [v3: $i] : (
% 89.03/12.81 | ~ (apply(all_309_0, v2) = v3) | ~ (in(v3, v0) = 0) | ~
% 89.03/12.81 | $i(v2) | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 &
% 89.03/12.81 | in(v2, all_850_0) = v4 & ( ~ (v4 = 0) | v5 = 0)))))))
% 89.03/12.81 |
% 89.03/12.81 | ALPHA: (148) implies:
% 89.03/12.81 | (149) relation(all_309_0) = all_850_1
% 89.03/12.81 |
% 89.03/12.81 | DELTA: instantiating (81) with fresh symbols all_854_0, all_854_1 gives:
% 89.03/12.81 | (150) relation_dom(all_344_0) = all_854_0 & relation(all_344_0) = all_854_1
% 89.03/12.81 | & $i(all_854_0) & ( ~ (all_854_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 89.03/12.81 | ! [v2: $i] : (v2 = v0 | ~ (relation_inverse_image(all_344_0, v1)
% 89.03/12.81 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] :
% 89.03/12.81 | ? [v5: any] : ? [v6: $i] : ? [v7: any] : (apply(all_344_0,
% 89.03/12.81 | v3) = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3,
% 89.03/12.81 | all_854_0) = v5 & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 =
% 89.03/12.81 | 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))) & !
% 89.03/12.81 | [v0: $i] : ! [v1: $i] : ( ~ (relation_inverse_image(all_344_0,
% 89.03/12.81 | v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3:
% 89.03/12.81 | $i] : ! [v4: any] : ( ~ (apply(all_344_0, v2) = v3) | ~
% 89.03/12.81 | (in(v3, v0) = v4) | ~ $i(v2) | ? [v5: any] : ? [v6: any]
% 89.03/12.81 | : (in(v2, v1) = v5 & in(v2, all_854_0) = v6 & ( ~ (v5 = 0)
% 89.03/12.81 | | (v6 = 0 & v4 = 0)))) & ! [v2: $i] : ! [v3: $i] : (
% 89.03/12.81 | ~ (apply(all_344_0, v2) = v3) | ~ (in(v3, v0) = 0) | ~
% 89.03/12.81 | $i(v2) | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 &
% 89.03/12.81 | in(v2, all_854_0) = v4 & ( ~ (v4 = 0) | v5 = 0)))))))
% 89.03/12.81 |
% 89.03/12.81 | ALPHA: (150) implies:
% 89.03/12.81 | (151) relation(all_344_0) = all_854_1
% 89.03/12.81 |
% 89.03/12.81 | DELTA: instantiating (65) with fresh symbols all_858_0, all_858_1 gives:
% 89.03/12.81 | (152) relation_dom(empty_set) = all_858_0 & relation(empty_set) = all_858_1
% 89.03/12.81 | & $i(all_858_0) & ( ~ (all_858_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 89.03/12.81 | ! [v2: $i] : (v2 = v0 | ~ (relation_inverse_image(empty_set, v1)
% 89.03/12.81 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] :
% 89.03/12.81 | ? [v5: any] : ? [v6: $i] : ? [v7: any] : (apply(empty_set,
% 89.03/12.81 | v3) = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3,
% 89.03/12.81 | all_858_0) = v5 & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 =
% 89.03/12.81 | 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))) & !
% 89.03/12.81 | [v0: $i] : ! [v1: $i] : ( ~ (relation_inverse_image(empty_set,
% 89.03/12.81 | v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3:
% 89.03/12.81 | $i] : ! [v4: any] : ( ~ (apply(empty_set, v2) = v3) | ~
% 89.03/12.81 | (in(v3, v0) = v4) | ~ $i(v2) | ? [v5: any] : ? [v6: any]
% 89.03/12.81 | : (in(v2, v1) = v5 & in(v2, all_858_0) = v6 & ( ~ (v5 = 0)
% 89.03/12.81 | | (v6 = 0 & v4 = 0)))) & ! [v2: $i] : ! [v3: $i] : (
% 89.03/12.81 | ~ (apply(empty_set, v2) = v3) | ~ (in(v3, v0) = 0) | ~
% 89.03/12.81 | $i(v2) | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 &
% 89.03/12.81 | in(v2, all_858_0) = v4 & ( ~ (v4 = 0) | v5 = 0)))))))
% 89.03/12.81 |
% 89.03/12.81 | ALPHA: (152) implies:
% 89.03/12.81 | (153) relation(empty_set) = all_858_1
% 89.03/12.81 |
% 89.03/12.81 | DELTA: instantiating (73) with fresh symbols all_860_0, all_860_1 gives:
% 89.03/12.81 | (154) relation_dom(all_294_0) = all_860_0 & relation(all_294_0) = all_860_1
% 89.03/12.81 | & $i(all_860_0) & ( ~ (all_860_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 89.03/12.81 | ! [v2: $i] : (v2 = v0 | ~ (relation_inverse_image(all_294_0, v1)
% 89.03/12.81 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] :
% 89.03/12.81 | ? [v5: any] : ? [v6: $i] : ? [v7: any] : (apply(all_294_0,
% 89.03/12.81 | v3) = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3,
% 89.03/12.81 | all_860_0) = v5 & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 =
% 89.03/12.81 | 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))) & !
% 89.03/12.81 | [v0: $i] : ! [v1: $i] : ( ~ (relation_inverse_image(all_294_0,
% 89.03/12.81 | v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3:
% 89.03/12.81 | $i] : ! [v4: any] : ( ~ (apply(all_294_0, v2) = v3) | ~
% 89.03/12.81 | (in(v3, v0) = v4) | ~ $i(v2) | ? [v5: any] : ? [v6: any]
% 89.03/12.81 | : (in(v2, v1) = v5 & in(v2, all_860_0) = v6 & ( ~ (v5 = 0)
% 89.03/12.81 | | (v6 = 0 & v4 = 0)))) & ! [v2: $i] : ! [v3: $i] : (
% 89.03/12.81 | ~ (apply(all_294_0, v2) = v3) | ~ (in(v3, v0) = 0) | ~
% 89.03/12.81 | $i(v2) | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 &
% 89.03/12.81 | in(v2, all_860_0) = v4 & ( ~ (v4 = 0) | v5 = 0)))))))
% 89.03/12.81 |
% 89.03/12.81 | ALPHA: (154) implies:
% 89.03/12.81 | (155) relation(all_294_0) = all_860_1
% 89.03/12.81 |
% 89.03/12.81 | DELTA: instantiating (69) with fresh symbols all_862_0, all_862_1 gives:
% 89.03/12.82 | (156) relation_dom(all_288_0) = all_862_0 & relation(all_288_0) = all_862_1
% 89.03/12.82 | & $i(all_862_0) & ( ~ (all_862_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 89.03/12.82 | ! [v2: $i] : (v2 = v0 | ~ (relation_inverse_image(all_288_0, v1)
% 89.03/12.82 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] :
% 89.03/12.82 | ? [v5: any] : ? [v6: $i] : ? [v7: any] : (apply(all_288_0,
% 89.03/12.82 | v3) = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3,
% 89.03/12.82 | all_862_0) = v5 & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 =
% 89.03/12.82 | 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))) & !
% 89.03/12.82 | [v0: $i] : ! [v1: $i] : ( ~ (relation_inverse_image(all_288_0,
% 89.03/12.82 | v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3:
% 89.03/12.82 | $i] : ! [v4: any] : ( ~ (apply(all_288_0, v2) = v3) | ~
% 89.03/12.82 | (in(v3, v0) = v4) | ~ $i(v2) | ? [v5: any] : ? [v6: any]
% 89.03/12.82 | : (in(v2, v1) = v5 & in(v2, all_862_0) = v6 & ( ~ (v5 = 0)
% 89.03/12.82 | | (v6 = 0 & v4 = 0)))) & ! [v2: $i] : ! [v3: $i] : (
% 89.03/12.82 | ~ (apply(all_288_0, v2) = v3) | ~ (in(v3, v0) = 0) | ~
% 89.03/12.82 | $i(v2) | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 &
% 89.03/12.82 | in(v2, all_862_0) = v4 & ( ~ (v4 = 0) | v5 = 0)))))))
% 89.03/12.82 |
% 89.03/12.82 | ALPHA: (156) implies:
% 89.03/12.82 | (157) relation(all_288_0) = all_862_1
% 89.03/12.82 |
% 89.03/12.82 | DELTA: instantiating (70) with fresh symbols all_864_0, all_864_1 gives:
% 89.03/12.82 | (158) relation_dom(all_288_0) = all_864_0 & relation(all_288_0) = all_864_1
% 89.03/12.82 | & $i(all_864_0) & ( ~ (all_864_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 89.03/12.82 | ! [v2: $i] : (v2 = v0 | ~ (relation_image(all_288_0, v1) = v2) |
% 89.03/12.82 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3,
% 89.03/12.82 | v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ! [v5: $i] : ( ~
% 89.03/12.82 | (in(v5, all_864_0) = 0) | ~ $i(v5) | ? [v6: any] : ?
% 89.03/12.82 | [v7: $i] : (apply(all_288_0, v5) = v7 & in(v5, v1) = v6 &
% 89.03/12.82 | $i(v7) & ( ~ (v7 = v3) | ~ (v6 = 0))))) & (v4 = 0 | ?
% 89.03/12.82 | [v5: $i] : (apply(all_288_0, v5) = v3 & in(v5, v1) = 0 &
% 89.03/12.82 | in(v5, all_864_0) = 0 & $i(v5))))) & ! [v0: $i] : !
% 89.03/12.82 | [v1: $i] : ( ~ (relation_image(all_288_0, v0) = v1) | ~ $i(v1) |
% 89.03/12.82 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2,
% 89.03/12.82 | v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4,
% 89.03/12.82 | all_864_0) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 89.03/12.82 | $i] : (apply(all_288_0, v4) = v6 & in(v4, v0) = v5 &
% 89.03/12.82 | $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i]
% 89.03/12.82 | : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] :
% 89.03/12.82 | (apply(all_288_0, v3) = v2 & in(v3, v0) = 0 & in(v3,
% 89.03/12.82 | all_864_0) = 0 & $i(v3)))))))
% 89.03/12.82 |
% 89.03/12.82 | ALPHA: (158) implies:
% 89.03/12.82 | (159) relation(all_288_0) = all_864_1
% 89.03/12.82 |
% 89.03/12.82 | DELTA: instantiating (82) with fresh symbols all_866_0, all_866_1 gives:
% 89.03/12.82 | (160) relation_dom(all_344_0) = all_866_0 & relation(all_344_0) = all_866_1
% 89.03/12.82 | & $i(all_866_0) & ( ~ (all_866_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 89.03/12.82 | ! [v2: $i] : (v2 = v0 | ~ (relation_image(all_344_0, v1) = v2) |
% 89.03/12.82 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3,
% 89.03/12.82 | v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ! [v5: $i] : ( ~
% 89.03/12.82 | (in(v5, all_866_0) = 0) | ~ $i(v5) | ? [v6: any] : ?
% 89.03/12.82 | [v7: $i] : (apply(all_344_0, v5) = v7 & in(v5, v1) = v6 &
% 89.03/12.82 | $i(v7) & ( ~ (v7 = v3) | ~ (v6 = 0))))) & (v4 = 0 | ?
% 89.03/12.82 | [v5: $i] : (apply(all_344_0, v5) = v3 & in(v5, v1) = 0 &
% 89.03/12.82 | in(v5, all_866_0) = 0 & $i(v5))))) & ! [v0: $i] : !
% 89.03/12.82 | [v1: $i] : ( ~ (relation_image(all_344_0, v0) = v1) | ~ $i(v1) |
% 89.03/12.82 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2,
% 89.03/12.82 | v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4,
% 89.03/12.82 | all_866_0) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 89.03/12.82 | $i] : (apply(all_344_0, v4) = v6 & in(v4, v0) = v5 &
% 89.03/12.82 | $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i]
% 89.03/12.82 | : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] :
% 89.03/12.82 | (apply(all_344_0, v3) = v2 & in(v3, v0) = 0 & in(v3,
% 89.03/12.82 | all_866_0) = 0 & $i(v3)))))))
% 89.03/12.82 |
% 89.03/12.82 | ALPHA: (160) implies:
% 89.03/12.82 | (161) relation(all_344_0) = all_866_1
% 89.03/12.82 |
% 89.03/12.82 | DELTA: instantiating (78) with fresh symbols all_868_0, all_868_1 gives:
% 89.03/12.82 | (162) relation_dom(all_309_0) = all_868_0 & relation(all_309_0) = all_868_1
% 89.03/12.82 | & $i(all_868_0) & ( ~ (all_868_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 89.03/12.82 | ! [v2: $i] : (v2 = v0 | ~ (relation_image(all_309_0, v1) = v2) |
% 89.03/12.82 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3,
% 89.03/12.82 | v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ! [v5: $i] : ( ~
% 89.03/12.82 | (in(v5, all_868_0) = 0) | ~ $i(v5) | ? [v6: any] : ?
% 89.03/12.82 | [v7: $i] : (apply(all_309_0, v5) = v7 & in(v5, v1) = v6 &
% 89.03/12.82 | $i(v7) & ( ~ (v7 = v3) | ~ (v6 = 0))))) & (v4 = 0 | ?
% 89.03/12.82 | [v5: $i] : (apply(all_309_0, v5) = v3 & in(v5, v1) = 0 &
% 89.03/12.82 | in(v5, all_868_0) = 0 & $i(v5))))) & ! [v0: $i] : !
% 89.03/12.82 | [v1: $i] : ( ~ (relation_image(all_309_0, v0) = v1) | ~ $i(v1) |
% 89.03/12.82 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2,
% 89.03/12.82 | v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4,
% 89.03/12.82 | all_868_0) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 89.03/12.82 | $i] : (apply(all_309_0, v4) = v6 & in(v4, v0) = v5 &
% 89.03/12.82 | $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i]
% 89.03/12.82 | : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] :
% 89.03/12.82 | (apply(all_309_0, v3) = v2 & in(v3, v0) = 0 & in(v3,
% 89.03/12.82 | all_868_0) = 0 & $i(v3)))))))
% 89.03/12.82 |
% 89.03/12.82 | ALPHA: (162) implies:
% 89.03/12.82 | (163) relation(all_309_0) = all_868_1
% 89.03/12.82 |
% 89.03/12.82 | DELTA: instantiating (74) with fresh symbols all_874_0, all_874_1 gives:
% 89.46/12.83 | (164) relation_dom(all_294_0) = all_874_0 & relation(all_294_0) = all_874_1
% 89.46/12.83 | & $i(all_874_0) & ( ~ (all_874_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 89.46/12.83 | ! [v2: $i] : (v2 = v0 | ~ (relation_image(all_294_0, v1) = v2) |
% 89.46/12.83 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3,
% 89.46/12.83 | v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ! [v5: $i] : ( ~
% 89.46/12.83 | (in(v5, all_874_0) = 0) | ~ $i(v5) | ? [v6: any] : ?
% 89.46/12.83 | [v7: $i] : (apply(all_294_0, v5) = v7 & in(v5, v1) = v6 &
% 89.46/12.83 | $i(v7) & ( ~ (v7 = v3) | ~ (v6 = 0))))) & (v4 = 0 | ?
% 89.46/12.83 | [v5: $i] : (apply(all_294_0, v5) = v3 & in(v5, v1) = 0 &
% 89.46/12.83 | in(v5, all_874_0) = 0 & $i(v5))))) & ! [v0: $i] : !
% 89.46/12.83 | [v1: $i] : ( ~ (relation_image(all_294_0, v0) = v1) | ~ $i(v1) |
% 89.46/12.83 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2,
% 89.46/12.83 | v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4,
% 89.46/12.83 | all_874_0) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 89.46/12.83 | $i] : (apply(all_294_0, v4) = v6 & in(v4, v0) = v5 &
% 89.46/12.83 | $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i]
% 89.46/12.83 | : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] :
% 89.46/12.83 | (apply(all_294_0, v3) = v2 & in(v3, v0) = 0 & in(v3,
% 89.46/12.83 | all_874_0) = 0 & $i(v3)))))))
% 89.46/12.83 |
% 89.46/12.83 | ALPHA: (164) implies:
% 89.46/12.83 | (165) relation(all_294_0) = all_874_1
% 89.46/12.83 |
% 89.46/12.83 | DELTA: instantiating (66) with fresh symbols all_876_0, all_876_1 gives:
% 89.46/12.83 | (166) relation_dom(empty_set) = all_876_0 & relation(empty_set) = all_876_1
% 89.46/12.83 | & $i(all_876_0) & ( ~ (all_876_1 = 0) | ( ? [v0: $i] : ! [v1: $i] :
% 89.46/12.83 | ! [v2: $i] : (v2 = v0 | ~ (relation_image(empty_set, v1) = v2) |
% 89.46/12.83 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3,
% 89.46/12.83 | v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ! [v5: $i] : ( ~
% 89.46/12.83 | (in(v5, all_876_0) = 0) | ~ $i(v5) | ? [v6: any] : ?
% 89.46/12.83 | [v7: $i] : (apply(empty_set, v5) = v7 & in(v5, v1) = v6 &
% 89.46/12.83 | $i(v7) & ( ~ (v7 = v3) | ~ (v6 = 0))))) & (v4 = 0 | ?
% 89.46/12.83 | [v5: $i] : (apply(empty_set, v5) = v3 & in(v5, v1) = 0 &
% 89.46/12.83 | in(v5, all_876_0) = 0 & $i(v5))))) & ! [v0: $i] : !
% 89.46/12.83 | [v1: $i] : ( ~ (relation_image(empty_set, v0) = v1) | ~ $i(v1) |
% 89.46/12.83 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2,
% 89.46/12.83 | v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4,
% 89.46/12.83 | all_876_0) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 89.46/12.83 | $i] : (apply(empty_set, v4) = v6 & in(v4, v0) = v5 &
% 89.46/12.83 | $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i]
% 89.46/12.83 | : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] :
% 89.46/12.83 | (apply(empty_set, v3) = v2 & in(v3, v0) = 0 & in(v3,
% 89.46/12.83 | all_876_0) = 0 & $i(v3)))))))
% 89.46/12.83 |
% 89.46/12.83 | ALPHA: (166) implies:
% 89.46/12.83 | (167) relation(empty_set) = all_876_1
% 89.46/12.83 |
% 89.46/12.83 | REDUCE: (62), (163) imply:
% 89.46/12.83 | (168) relation(empty_set) = all_868_1
% 89.46/12.83 |
% 89.46/12.83 | REDUCE: (62), (149) imply:
% 89.46/12.83 | (169) relation(empty_set) = all_850_1
% 89.46/12.83 |
% 89.46/12.83 | REDUCE: (62), (136) imply:
% 89.46/12.83 | (170) relation(empty_set) = all_836_2
% 89.46/12.83 |
% 89.46/12.83 | REDUCE: (62), (134) imply:
% 89.46/12.83 | (171) relation(empty_set) = all_834_1
% 89.46/12.83 |
% 89.46/12.83 | REDUCE: (62), (112) imply:
% 89.46/12.83 | (172) relation(empty_set) = all_766_2
% 89.46/12.83 |
% 89.46/12.83 | REDUCE: (95), (165) imply:
% 89.46/12.83 | (173) relation(empty_set) = all_874_1
% 89.46/12.83 |
% 89.46/12.83 | REDUCE: (95), (155) imply:
% 89.46/12.83 | (174) relation(empty_set) = all_860_1
% 89.46/12.83 |
% 89.46/12.83 | REDUCE: (95), (147) imply:
% 89.46/12.83 | (175) relation(empty_set) = all_846_2
% 89.46/12.83 |
% 89.46/12.83 | REDUCE: (95), (128) imply:
% 89.46/12.83 | (176) relation(empty_set) = all_826_1
% 89.46/12.83 |
% 89.46/12.83 | REDUCE: (57), (94) imply:
% 89.46/12.83 | (177) relation(empty_set) = 0
% 89.46/12.83 |
% 89.46/12.83 | REDUCE: (62), (111) imply:
% 89.46/12.83 | (178) function(empty_set) = all_766_1
% 89.46/12.83 |
% 89.46/12.83 | BETA: splitting (58) gives:
% 89.46/12.83 |
% 89.46/12.83 | Case 1:
% 89.46/12.83 | |
% 89.46/12.83 | | (179) all_292_0 = 0
% 89.46/12.83 | |
% 89.46/12.83 | | REDUCE: (26), (179) imply:
% 89.46/12.83 | | (180) $false
% 89.46/12.83 | |
% 89.46/12.83 | | CLOSE: (180) is inconsistent.
% 89.46/12.83 | |
% 89.46/12.83 | Case 2:
% 89.46/12.83 | |
% 89.46/12.83 | | (181) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 89.46/12.83 | | (relation_dom(all_292_1) = v1 & relation(all_292_1) = v0 &
% 89.46/12.83 | | empty(v1) = v2 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 89.46/12.83 | |
% 89.46/12.83 | | DELTA: instantiating (181) with fresh symbols all_882_0, all_882_1,
% 89.46/12.83 | | all_882_2 gives:
% 89.46/12.83 | | (182) relation_dom(all_292_1) = all_882_1 & relation(all_292_1) =
% 89.46/12.83 | | all_882_2 & empty(all_882_1) = all_882_0 & $i(all_882_1) & ( ~
% 89.46/12.83 | | (all_882_0 = 0) | ~ (all_882_2 = 0))
% 89.46/12.83 | |
% 89.46/12.83 | | ALPHA: (182) implies:
% 89.46/12.83 | | (183) $i(all_882_1)
% 89.46/12.83 | | (184) empty(all_882_1) = all_882_0
% 89.46/12.83 | | (185) relation(all_292_1) = all_882_2
% 89.46/12.83 | | (186) ~ (all_882_0 = 0) | ~ (all_882_2 = 0)
% 89.46/12.83 | |
% 89.46/12.84 | | GROUND_INST: instantiating (9) with 0, all_770_1, empty_set, simplifying
% 89.46/12.84 | | with (3), (115) gives:
% 89.46/12.84 | | (187) all_770_1 = 0
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (9) with all_766_1, all_770_1, empty_set,
% 89.46/12.84 | | simplifying with (115), (178) gives:
% 89.46/12.84 | | (188) all_770_1 = all_766_1
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_738_1, all_764_1, empty_set,
% 89.46/12.84 | | simplifying with (107), (109) gives:
% 89.46/12.84 | | (189) all_764_1 = all_738_1
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_764_1, all_766_2, empty_set,
% 89.46/12.84 | | simplifying with (109), (172) gives:
% 89.46/12.84 | | (190) all_766_2 = all_764_1
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with 0, all_826_1, empty_set, simplifying
% 89.46/12.84 | | with (176), (177) gives:
% 89.46/12.84 | | (191) all_826_1 = 0
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_738_1, all_826_1, empty_set,
% 89.46/12.84 | | simplifying with (107), (176) gives:
% 89.46/12.84 | | (192) all_826_1 = all_738_1
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_832_1, all_834_1, empty_set,
% 89.46/12.84 | | simplifying with (132), (171) gives:
% 89.46/12.84 | | (193) all_834_1 = all_832_1
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_766_2, all_834_1, empty_set,
% 89.46/12.84 | | simplifying with (171), (172) gives:
% 89.46/12.84 | | (194) all_834_1 = all_766_2
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_834_1, all_836_2, empty_set,
% 89.46/12.84 | | simplifying with (170), (171) gives:
% 89.46/12.84 | | (195) all_836_2 = all_834_1
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_836_2, all_842_2, empty_set,
% 89.46/12.84 | | simplifying with (141), (170) gives:
% 89.46/12.84 | | (196) all_842_2 = all_836_2
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_842_2, all_846_2, empty_set,
% 89.46/12.84 | | simplifying with (141), (175) gives:
% 89.46/12.84 | | (197) all_846_2 = all_842_2
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_832_1, all_868_1, empty_set,
% 89.46/12.84 | | simplifying with (132), (168) gives:
% 89.46/12.84 | | (198) all_868_1 = all_832_1
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_736_1, all_868_1, empty_set,
% 89.46/12.84 | | simplifying with (105), (168) gives:
% 89.46/12.84 | | (199) all_868_1 = all_736_1
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_858_1, all_874_1, empty_set,
% 89.46/12.84 | | simplifying with (153), (173) gives:
% 89.46/12.84 | | (200) all_874_1 = all_858_1
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_770_2, all_874_1, empty_set,
% 89.46/12.84 | | simplifying with (116), (173) gives:
% 89.46/12.84 | | (201) all_874_1 = all_770_2
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_860_1, all_876_1, empty_set,
% 89.46/12.84 | | simplifying with (167), (174) gives:
% 89.46/12.84 | | (202) all_876_1 = all_860_1
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_858_1, all_876_1, empty_set,
% 89.46/12.84 | | simplifying with (153), (167) gives:
% 89.46/12.84 | | (203) all_876_1 = all_858_1
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_850_1, all_876_1, empty_set,
% 89.46/12.84 | | simplifying with (167), (169) gives:
% 89.46/12.84 | | (204) all_876_1 = all_850_1
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_846_2, all_876_1, empty_set,
% 89.46/12.84 | | simplifying with (167), (175) gives:
% 89.46/12.84 | | (205) all_876_1 = all_846_2
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_838_2, all_862_1, all_288_0,
% 89.46/12.84 | | simplifying with (138), (157) gives:
% 89.46/12.84 | | (206) all_862_1 = all_838_2
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_828_1, all_862_1, all_288_0,
% 89.46/12.84 | | simplifying with (130), (157) gives:
% 89.46/12.84 | | (207) all_862_1 = all_828_1
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with 0, all_864_1, all_288_0, simplifying
% 89.46/12.84 | | with (24), (159) gives:
% 89.46/12.84 | | (208) all_864_1 = 0
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_862_1, all_864_1, all_288_0,
% 89.46/12.84 | | simplifying with (157), (159) gives:
% 89.46/12.84 | | (209) all_864_1 = all_862_1
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with 0, all_882_2, all_292_1, simplifying
% 89.46/12.84 | | with (29), (185) gives:
% 89.46/12.84 | | (210) all_882_2 = 0
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with 0, all_734_5, all_316_1, simplifying
% 89.46/12.84 | | with (41), (97) gives:
% 89.46/12.84 | | (211) all_734_5 = 0
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with 0, all_820_5, all_342_1, simplifying
% 89.46/12.84 | | with (46), (118) gives:
% 89.46/12.84 | | (212) all_820_5 = 0
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with 0, all_854_1, all_344_0, simplifying
% 89.46/12.84 | | with (54), (151) gives:
% 89.46/12.84 | | (213) all_854_1 = 0
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_844_2, all_854_1, all_344_0,
% 89.46/12.84 | | simplifying with (144), (151) gives:
% 89.46/12.84 | | (214) all_854_1 = all_844_2
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_854_1, all_866_1, all_344_0,
% 89.46/12.84 | | simplifying with (151), (161) gives:
% 89.46/12.84 | | (215) all_866_1 = all_854_1
% 89.46/12.84 | |
% 89.46/12.84 | | GROUND_INST: instantiating (10) with all_822_1, all_866_1, all_344_0,
% 89.46/12.84 | | simplifying with (126), (161) gives:
% 89.46/12.84 | | (216) all_866_1 = all_822_1
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (202), (205) imply:
% 89.46/12.84 | | (217) all_860_1 = all_846_2
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (202), (204) imply:
% 89.46/12.84 | | (218) all_860_1 = all_850_1
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (202), (203) imply:
% 89.46/12.84 | | (219) all_860_1 = all_858_1
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (200), (201) imply:
% 89.46/12.84 | | (220) all_858_1 = all_770_2
% 89.46/12.84 | |
% 89.46/12.84 | | SIMP: (220) implies:
% 89.46/12.84 | | (221) all_858_1 = all_770_2
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (198), (199) imply:
% 89.46/12.84 | | (222) all_832_1 = all_736_1
% 89.46/12.84 | |
% 89.46/12.84 | | SIMP: (222) implies:
% 89.46/12.84 | | (223) all_832_1 = all_736_1
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (215), (216) imply:
% 89.46/12.84 | | (224) all_854_1 = all_822_1
% 89.46/12.84 | |
% 89.46/12.84 | | SIMP: (224) implies:
% 89.46/12.84 | | (225) all_854_1 = all_822_1
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (208), (209) imply:
% 89.46/12.84 | | (226) all_862_1 = 0
% 89.46/12.84 | |
% 89.46/12.84 | | SIMP: (226) implies:
% 89.46/12.84 | | (227) all_862_1 = 0
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (206), (207) imply:
% 89.46/12.84 | | (228) all_838_2 = all_828_1
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (206), (227) imply:
% 89.46/12.84 | | (229) all_838_2 = 0
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (217), (218) imply:
% 89.46/12.84 | | (230) all_850_1 = all_846_2
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (218), (219) imply:
% 89.46/12.84 | | (231) all_858_1 = all_850_1
% 89.46/12.84 | |
% 89.46/12.84 | | SIMP: (231) implies:
% 89.46/12.84 | | (232) all_858_1 = all_850_1
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (221), (232) imply:
% 89.46/12.84 | | (233) all_850_1 = all_770_2
% 89.46/12.84 | |
% 89.46/12.84 | | SIMP: (233) implies:
% 89.46/12.84 | | (234) all_850_1 = all_770_2
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (213), (214) imply:
% 89.46/12.84 | | (235) all_844_2 = 0
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (214), (225) imply:
% 89.46/12.84 | | (236) all_844_2 = all_822_1
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (230), (234) imply:
% 89.46/12.84 | | (237) all_846_2 = all_770_2
% 89.46/12.84 | |
% 89.46/12.84 | | SIMP: (237) implies:
% 89.46/12.84 | | (238) all_846_2 = all_770_2
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (197), (238) imply:
% 89.46/12.84 | | (239) all_842_2 = all_770_2
% 89.46/12.84 | |
% 89.46/12.84 | | SIMP: (239) implies:
% 89.46/12.84 | | (240) all_842_2 = all_770_2
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (235), (236) imply:
% 89.46/12.84 | | (241) all_822_1 = 0
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (196), (240) imply:
% 89.46/12.84 | | (242) all_836_2 = all_770_2
% 89.46/12.84 | |
% 89.46/12.84 | | SIMP: (242) implies:
% 89.46/12.84 | | (243) all_836_2 = all_770_2
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (228), (229) imply:
% 89.46/12.84 | | (244) all_828_1 = 0
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (195), (243) imply:
% 89.46/12.84 | | (245) all_834_1 = all_770_2
% 89.46/12.84 | |
% 89.46/12.84 | | SIMP: (245) implies:
% 89.46/12.84 | | (246) all_834_1 = all_770_2
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (193), (246) imply:
% 89.46/12.84 | | (247) all_832_1 = all_770_2
% 89.46/12.84 | |
% 89.46/12.84 | | SIMP: (247) implies:
% 89.46/12.84 | | (248) all_832_1 = all_770_2
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (194), (246) imply:
% 89.46/12.84 | | (249) all_770_2 = all_766_2
% 89.46/12.84 | |
% 89.46/12.84 | | COMBINE_EQS: (223), (248) imply:
% 89.46/12.84 | | (250) all_770_2 = all_736_1
% 89.46/12.84 | |
% 89.46/12.84 | | SIMP: (250) implies:
% 89.46/12.84 | | (251) all_770_2 = all_736_1
% 89.46/12.84 | |
% 89.46/12.85 | | COMBINE_EQS: (191), (192) imply:
% 89.46/12.85 | | (252) all_738_1 = 0
% 89.46/12.85 | |
% 89.46/12.85 | | SIMP: (252) implies:
% 89.46/12.85 | | (253) all_738_1 = 0
% 89.46/12.85 | |
% 89.46/12.85 | | COMBINE_EQS: (187), (188) imply:
% 89.46/12.85 | | (254) all_766_1 = 0
% 89.46/12.85 | |
% 89.46/12.85 | | SIMP: (254) implies:
% 89.46/12.85 | | (255) all_766_1 = 0
% 89.46/12.85 | |
% 89.46/12.85 | | COMBINE_EQS: (249), (251) imply:
% 89.46/12.85 | | (256) all_766_2 = all_736_1
% 89.46/12.85 | |
% 89.46/12.85 | | SIMP: (256) implies:
% 89.46/12.85 | | (257) all_766_2 = all_736_1
% 89.46/12.85 | |
% 89.46/12.85 | | COMBINE_EQS: (190), (257) imply:
% 89.46/12.85 | | (258) all_764_1 = all_736_1
% 89.46/12.85 | |
% 89.46/12.85 | | SIMP: (258) implies:
% 89.46/12.85 | | (259) all_764_1 = all_736_1
% 89.46/12.85 | |
% 89.46/12.85 | | COMBINE_EQS: (189), (259) imply:
% 89.46/12.85 | | (260) all_738_1 = all_736_1
% 89.46/12.85 | |
% 89.46/12.85 | | SIMP: (260) implies:
% 89.46/12.85 | | (261) all_738_1 = all_736_1
% 89.46/12.85 | |
% 89.46/12.85 | | COMBINE_EQS: (253), (261) imply:
% 89.46/12.85 | | (262) all_736_1 = 0
% 89.46/12.85 | |
% 89.46/12.85 | | COMBINE_EQS: (257), (262) imply:
% 89.46/12.85 | | (263) all_766_2 = 0
% 89.46/12.85 | |
% 89.46/12.85 | | BETA: splitting (186) gives:
% 89.46/12.85 | |
% 89.46/12.85 | | Case 1:
% 89.46/12.85 | | |
% 89.46/12.85 | | | (264) ~ (all_882_0 = 0)
% 89.46/12.85 | | |
% 89.46/12.85 | | | BETA: splitting (103) gives:
% 89.46/12.85 | | |
% 89.46/12.85 | | | Case 1:
% 89.46/12.85 | | | |
% 89.46/12.85 | | | | (265) ~ (all_734_5 = 0)
% 89.46/12.85 | | | |
% 89.46/12.85 | | | | REDUCE: (211), (265) imply:
% 89.46/12.85 | | | | (266) $false
% 89.46/12.85 | | | |
% 89.46/12.85 | | | | CLOSE: (266) is inconsistent.
% 89.46/12.85 | | | |
% 89.46/12.85 | | | Case 2:
% 89.46/12.85 | | | |
% 89.46/12.85 | | | | (267) all_734_0 = 0 & all_734_1 = 0 & all_734_2 = 0 & all_734_3 = 0 &
% 89.46/12.85 | | | | all_734_4 = 0
% 89.46/12.85 | | | |
% 89.46/12.85 | | | | ALPHA: (267) implies:
% 89.46/12.85 | | | | (268) all_734_4 = 0
% 89.46/12.85 | | | | (269) all_734_3 = 0
% 89.46/12.85 | | | | (270) all_734_2 = 0
% 89.46/12.85 | | | | (271) all_734_1 = 0
% 89.46/12.85 | | | | (272) all_734_0 = 0
% 89.46/12.85 | | | |
% 89.46/12.85 | | | | REDUCE: (102), (268) imply:
% 89.46/12.85 | | | | (273) reflexive(all_316_1) = 0
% 89.46/12.85 | | | |
% 89.46/12.85 | | | | REDUCE: (101), (272) imply:
% 89.46/12.85 | | | | (274) well_founded_relation(all_316_1) = 0
% 89.46/12.85 | | | |
% 89.46/12.85 | | | | REDUCE: (100), (269) imply:
% 89.46/12.85 | | | | (275) transitive(all_316_1) = 0
% 89.46/12.85 | | | |
% 89.46/12.85 | | | | REDUCE: (99), (271) imply:
% 89.46/12.85 | | | | (276) connected(all_316_1) = 0
% 89.46/12.85 | | | |
% 89.46/12.85 | | | | REDUCE: (98), (270) imply:
% 89.46/12.85 | | | | (277) antisymmetric(all_316_1) = 0
% 89.46/12.85 | | | |
% 89.46/12.85 | | | | BETA: splitting (113) gives:
% 89.46/12.85 | | | |
% 89.46/12.85 | | | | Case 1:
% 89.46/12.85 | | | | |
% 89.46/12.85 | | | | | (278) ~ (all_766_1 = 0)
% 89.46/12.85 | | | | |
% 89.46/12.85 | | | | | REDUCE: (255), (278) imply:
% 89.46/12.85 | | | | | (279) $false
% 89.46/12.85 | | | | |
% 89.46/12.85 | | | | | CLOSE: (279) is inconsistent.
% 89.46/12.85 | | | | |
% 89.46/12.85 | | | | Case 2:
% 89.46/12.85 | | | | |
% 89.46/12.85 | | | | | (280) ~ (all_766_2 = 0) | ! [v0: $i] : ! [v1: $i] : (v1 = v0 |
% 89.46/12.85 | | | | | ~ (in(v1, all_766_0) = 0) | ~ (in(v0, all_766_0) = 0) | ~
% 89.46/12.85 | | | | | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 89.46/12.85 | | | | | v2) & apply(all_309_0, v1) = v3 & apply(all_309_0, v0)
% 89.46/12.85 | | | | | = v2 & $i(v3) & $i(v2)))
% 89.46/12.85 | | | | |
% 89.46/12.85 | | | | | BETA: splitting (280) gives:
% 89.46/12.85 | | | | |
% 89.46/12.85 | | | | | Case 1:
% 89.46/12.85 | | | | | |
% 89.46/12.85 | | | | | | (281) ~ (all_766_2 = 0)
% 89.46/12.85 | | | | | |
% 89.46/12.85 | | | | | | REDUCE: (263), (281) imply:
% 89.46/12.85 | | | | | | (282) $false
% 89.46/12.85 | | | | | |
% 89.46/12.85 | | | | | | CLOSE: (282) is inconsistent.
% 89.46/12.85 | | | | | |
% 89.46/12.85 | | | | | Case 2:
% 89.46/12.85 | | | | | |
% 89.46/12.85 | | | | | |
% 89.46/12.85 | | | | | | GROUND_INST: instantiating (rc1_subset_1) with all_882_1, all_882_0,
% 89.46/12.85 | | | | | | simplifying with (183), (184) gives:
% 89.46/12.85 | | | | | | (283) all_882_0 = 0 | ? [v0: $i] : (powerset(all_882_1) = v0 &
% 89.46/12.85 | | | | | | $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 89.46/12.85 | | | | | | element(v1, v0) = 0 & empty(v1) = v2 & $i(v1)))
% 89.46/12.85 | | | | | |
% 89.46/12.85 | | | | | | GROUND_INST: instantiating (l4_wellord1) with all_342_1, all_820_1,
% 89.46/12.85 | | | | | | simplifying with (45), (120) gives:
% 89.46/12.85 | | | | | | (284) ? [v0: any] : ? [v1: $i] : (relation_field(all_342_1) =
% 89.46/12.85 | | | | | | v1 & relation(all_342_1) = v0 & $i(v1) & ( ~ (v0 = 0) |
% 89.46/12.85 | | | | | | (( ~ (all_820_1 = 0) | ! [v2: $i] : ! [v3: $i] : (v3
% 89.46/12.85 | | | | | | = v2 | ~ (in(v3, v1) = 0) | ~ (in(v2, v1) = 0)
% 89.46/12.85 | | | | | | | ~ $i(v3) | ~ $i(v2) | ? [v4: $i] : ? [v5:
% 89.46/12.85 | | | | | | any] : ? [v6: $i] : ? [v7: any] :
% 89.46/12.85 | | | | | | (ordered_pair(v3, v2) = v6 & ordered_pair(v2, v3)
% 89.46/12.85 | | | | | | = v4 & in(v6, all_342_1) = v7 & in(v4,
% 89.46/12.85 | | | | | | all_342_1) = v5 & $i(v6) & $i(v4) & (v7 = 0 |
% 89.46/12.85 | | | | | | v5 = 0)))) & (all_820_1 = 0 | ? [v2: $i] :
% 89.46/12.85 | | | | | | ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ? [v6:
% 89.46/12.85 | | | | | | $i] : ? [v7: int] : ( ~ (v7 = 0) & ~ (v5 = 0) &
% 89.46/12.85 | | | | | | ~ (v3 = v2) & ordered_pair(v3, v2) = v6 &
% 89.46/12.85 | | | | | | ordered_pair(v2, v3) = v4 & in(v6, all_342_1) =
% 89.46/12.85 | | | | | | v7 & in(v4, all_342_1) = v5 & in(v3, v1) = 0 &
% 89.46/12.85 | | | | | | in(v2, v1) = 0 & $i(v6) & $i(v4) & $i(v3) &
% 89.46/12.85 | | | | | | $i(v2))))))
% 89.46/12.85 | | | | | |
% 89.46/12.85 | | | | | | GROUND_INST: instantiating (t53_wellord1) with all_316_1, 0,
% 89.46/12.85 | | | | | | simplifying with (40), (274) gives:
% 89.46/12.85 | | | | | | (285) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 89.46/12.85 | | | | | | ? [v4: any] : (reflexive(all_316_1) = v1 &
% 89.46/12.85 | | | | | | transitive(all_316_1) = v2 & connected(all_316_1) = v3 &
% 89.46/12.85 | | | | | | antisymmetric(all_316_1) = v4 & relation(all_316_1) = v0
% 89.46/12.85 | | | | | | & ( ~ (v0 = 0) | ! [v5: $i] : ! [v6: any] : ( ~
% 89.46/12.85 | | | | | | (well_founded_relation(v5) = v6) | ~ $i(v5) | ?
% 89.46/12.85 | | | | | | [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10:
% 89.46/12.85 | | | | | | any] : ? [v11: any] : (reflexive(v5) = v8 &
% 89.46/12.85 | | | | | | transitive(v5) = v9 & connected(v5) = v10 &
% 89.46/12.85 | | | | | | antisymmetric(v5) = v11 & relation(v5) = v7 & ( ~
% 89.46/12.85 | | | | | | (v7 = 0) | ! [v12: $i] : ( ~
% 89.46/12.85 | | | | | | (relation_isomorphism(all_316_1, v5, v12) = 0)
% 89.46/12.85 | | | | | | | ~ $i(v12) | ? [v13: any] : ? [v14: any] :
% 89.46/12.85 | | | | | | (relation(v12) = v13 & function(v12) = v14 & (
% 89.46/12.85 | | | | | | ~ (v14 = 0) | ~ (v13 = 0))) | (v6 = 0 & (
% 89.46/12.85 | | | | | | ~ (v4 = 0) | v11 = 0) & ( ~ (v3 = 0) | v10
% 89.46/12.85 | | | | | | = 0) & ( ~ (v2 = 0) | v9 = 0) & ( ~ (v1 =
% 89.46/12.85 | | | | | | 0) | v8 = 0))))))))
% 89.46/12.85 | | | | | |
% 89.46/12.85 | | | | | | GROUND_INST: instantiating (t53_wellord1) with all_342_1, all_820_0,
% 89.46/12.85 | | | | | | simplifying with (45), (122) gives:
% 89.46/12.86 | | | | | | (286) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 89.46/12.86 | | | | | | ? [v4: any] : (reflexive(all_342_1) = v1 &
% 89.46/12.86 | | | | | | transitive(all_342_1) = v2 & connected(all_342_1) = v3 &
% 89.46/12.86 | | | | | | antisymmetric(all_342_1) = v4 & relation(all_342_1) = v0
% 89.46/12.86 | | | | | | & ( ~ (v0 = 0) | ! [v5: $i] : ! [v6: any] : ( ~
% 89.46/12.86 | | | | | | (well_founded_relation(v5) = v6) | ~ $i(v5) | ?
% 89.46/12.86 | | | | | | [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10:
% 89.46/12.86 | | | | | | any] : ? [v11: any] : (reflexive(v5) = v8 &
% 89.46/12.86 | | | | | | transitive(v5) = v9 & connected(v5) = v10 &
% 89.46/12.86 | | | | | | antisymmetric(v5) = v11 & relation(v5) = v7 & ( ~
% 89.46/12.86 | | | | | | (v7 = 0) | ! [v12: $i] : ( ~
% 89.46/12.86 | | | | | | (relation_isomorphism(all_342_1, v5, v12) = 0)
% 89.46/12.86 | | | | | | | ~ $i(v12) | ? [v13: any] : ? [v14: any] :
% 89.46/12.86 | | | | | | (relation(v12) = v13 & function(v12) = v14 & (
% 89.46/12.86 | | | | | | ~ (v14 = 0) | ~ (v13 = 0))) | (( ~ (v4 =
% 89.46/12.86 | | | | | | 0) | v11 = 0) & ( ~ (v3 = 0) | v10 = 0) &
% 89.46/12.86 | | | | | | ( ~ (v2 = 0) | v9 = 0) & ( ~ (v1 = 0) | v8 =
% 89.46/12.86 | | | | | | 0) & ( ~ (all_820_0 = 0) | v6 = 0))))))))
% 89.46/12.86 | | | | | |
% 89.46/12.86 | | | | | | GROUND_INST: instantiating (1) with all_342_1, all_820_0,
% 89.46/12.86 | | | | | | simplifying with (45), (122) gives:
% 89.46/12.86 | | | | | | (287) ? [v0: any] : ? [v1: $i] : (relation_field(all_342_1) =
% 89.46/12.86 | | | | | | v1 & relation(all_342_1) = v0 & $i(v1) & ( ~ (v0 = 0) |
% 89.46/12.86 | | | | | | (( ~ (all_820_0 = 0) | ! [v2: $i] : (v2 = empty_set |
% 89.46/12.86 | | | | | | ~ (subset(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i]
% 89.46/12.86 | | | | | | : ? [v4: $i] : (disjoint(v4, v2) = 0 &
% 89.46/12.86 | | | | | | fiber(all_342_1, v3) = v4 & in(v3, v2) = 0 &
% 89.46/12.86 | | | | | | $i(v4) & $i(v3)))) & (all_820_0 = 0 | ? [v2:
% 89.46/12.86 | | | | | | $i] : ( ~ (v2 = empty_set) & subset(v2, v1) = 0 &
% 89.46/12.86 | | | | | | $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~
% 89.46/12.86 | | | | | | (disjoint(v4, v2) = 0) | ~ (fiber(all_342_1,
% 89.46/12.86 | | | | | | v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~
% 89.46/12.86 | | | | | | (v5 = 0) & in(v3, v2) = v5)))))))
% 89.46/12.86 | | | | | |
% 89.46/12.86 | | | | | | GROUND_INST: instantiating (l1_wellord1) with all_342_1, all_820_4,
% 89.46/12.86 | | | | | | simplifying with (45), (123) gives:
% 89.46/12.86 | | | | | | (288) ? [v0: any] : ? [v1: $i] : (relation_field(all_342_1) =
% 89.46/12.86 | | | | | | v1 & relation(all_342_1) = v0 & $i(v1) & ( ~ (v0 = 0) |
% 89.46/12.86 | | | | | | (( ~ (all_820_4 = 0) | ! [v2: $i] : ( ~ (in(v2, v1) =
% 89.46/12.86 | | | | | | 0) | ~ $i(v2) | ? [v3: $i] :
% 89.46/12.86 | | | | | | (ordered_pair(v2, v2) = v3 & in(v3, all_342_1) =
% 89.46/12.86 | | | | | | 0 & $i(v3)))) & (all_820_4 = 0 | ? [v2: $i] :
% 89.46/12.86 | | | | | | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 89.46/12.86 | | | | | | ordered_pair(v2, v2) = v3 & in(v3, all_342_1) =
% 89.46/12.86 | | | | | | v4 & in(v2, v1) = 0 & $i(v3) & $i(v2))))))
% 89.46/12.86 | | | | | |
% 89.46/12.86 | | | | | | GROUND_INST: instantiating (fc6_relat_1) with all_288_0, all_838_1,
% 89.46/12.86 | | | | | | simplifying with (22), (139) gives:
% 89.46/12.86 | | | | | | (289) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 89.46/12.86 | | | | | | (relation(all_288_0) = v1 & empty(all_838_1) = v2 &
% 89.46/12.86 | | | | | | empty(all_288_0) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 =
% 89.46/12.86 | | | | | | 0))
% 89.46/12.86 | | | | | |
% 89.46/12.86 | | | | | | GROUND_INST: instantiating (t25_relat_1) with all_288_0, all_838_1,
% 89.46/12.86 | | | | | | simplifying with (22), (139) gives:
% 89.46/12.86 | | | | | | (290) ? [v0: any] : ? [v1: $i] : (relation_dom(all_288_0) = v1
% 89.46/12.86 | | | | | | & relation(all_288_0) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 89.46/12.86 | | | | | | [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 89.46/12.86 | | | | | | (relation_rng(v2) = v3) | ~ (subset(all_838_1, v3) =
% 89.46/12.86 | | | | | | v4) | ~ $i(v2) | ? [v5: any] : ? [v6: any] : ?
% 89.46/12.86 | | | | | | [v7: $i] : ? [v8: any] : (relation_dom(v2) = v7 &
% 89.46/12.86 | | | | | | subset(v1, v7) = v8 & subset(all_288_0, v2) = v6 &
% 89.46/12.86 | | | | | | relation(v2) = v5 & $i(v7) & ( ~ (v6 = 0) | ~ (v5
% 89.46/12.86 | | | | | | = 0) | (v8 = 0 & v4 = 0))))))
% 89.46/12.86 | | | | | |
% 89.46/12.86 | | | | | | GROUND_INST: instantiating (t47_relat_1) with all_288_0, all_838_1,
% 89.46/12.86 | | | | | | simplifying with (22), (139) gives:
% 89.46/12.86 | | | | | | (291) ? [v0: any] : ? [v1: $i] : (relation_dom(all_288_0) = v1
% 89.46/12.86 | | | | | | & relation(all_288_0) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 89.46/12.86 | | | | | | [v2: $i] : ! [v3: $i] : ( ~ (relation_rng(v2) = v3) |
% 89.46/12.86 | | | | | | ~ (subset(v1, v3) = 0) | ~ $i(v2) | ? [v4: any] :
% 89.46/12.86 | | | | | | ? [v5: $i] : ? [v6: $i] : (relation_composition(v2,
% 89.46/12.86 | | | | | | all_288_0) = v5 & relation_rng(v5) = v6 &
% 89.46/12.86 | | | | | | relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0)
% 89.46/12.86 | | | | | | | v6 = all_838_1)))))
% 89.46/12.86 | | | | | |
% 89.46/12.86 | | | | | | GROUND_INST: instantiating (t46_relat_1) with all_288_0, all_838_1,
% 89.46/12.86 | | | | | | simplifying with (22), (139) gives:
% 89.46/12.86 | | | | | | (292) ? [v0: any] : ? [v1: $i] : (relation_dom(all_288_0) = v1
% 89.46/12.86 | | | | | | & relation(all_288_0) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 89.46/12.86 | | | | | | [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v2) = v3) |
% 89.46/12.86 | | | | | | ~ (subset(all_838_1, v3) = 0) | ~ $i(v2) | ? [v4:
% 89.46/12.86 | | | | | | any] : ? [v5: $i] : ? [v6: $i] :
% 89.46/12.86 | | | | | | (relation_composition(all_288_0, v2) = v5 &
% 89.46/12.86 | | | | | | relation_dom(v5) = v6 & relation(v2) = v4 & $i(v6)
% 89.46/12.86 | | | | | | & $i(v5) & ( ~ (v4 = 0) | v6 = v1)))))
% 89.46/12.86 | | | | | |
% 89.46/12.86 | | | | | | GROUND_INST: instantiating (6) with all_288_0, all_838_1,
% 89.46/12.86 | | | | | | simplifying with (22), (139) gives:
% 89.46/12.86 | | | | | | (293) ? [v0: any] : ? [v1: $i] : (relation_dom(all_288_0) = v1
% 89.46/12.86 | | | | | | & relation(all_288_0) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~
% 89.46/12.86 | | | | | | (v1 = empty_set) | all_838_1 = empty_set) & ( ~
% 89.46/12.86 | | | | | | (all_838_1 = empty_set) | v1 = empty_set))))
% 89.46/12.86 | | | | | |
% 89.46/12.86 | | | | | | GROUND_INST: instantiating (fc6_relat_1) with all_344_0, all_844_1,
% 89.46/12.86 | | | | | | simplifying with (52), (145) gives:
% 89.46/12.86 | | | | | | (294) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 89.46/12.86 | | | | | | (relation(all_344_0) = v1 & empty(all_844_1) = v2 &
% 89.46/12.86 | | | | | | empty(all_344_0) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 =
% 89.46/12.86 | | | | | | 0))
% 89.46/12.86 | | | | | |
% 89.46/12.86 | | | | | | GROUND_INST: instantiating (t25_relat_1) with all_344_0, all_844_1,
% 89.46/12.86 | | | | | | simplifying with (52), (145) gives:
% 89.46/12.86 | | | | | | (295) ? [v0: any] : ? [v1: $i] : (relation_dom(all_344_0) = v1
% 89.46/12.86 | | | | | | & relation(all_344_0) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 89.46/12.86 | | | | | | [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 89.46/12.86 | | | | | | (relation_rng(v2) = v3) | ~ (subset(all_844_1, v3) =
% 89.46/12.86 | | | | | | v4) | ~ $i(v2) | ? [v5: any] : ? [v6: any] : ?
% 89.46/12.86 | | | | | | [v7: $i] : ? [v8: any] : (relation_dom(v2) = v7 &
% 89.46/12.86 | | | | | | subset(v1, v7) = v8 & subset(all_344_0, v2) = v6 &
% 89.46/12.86 | | | | | | relation(v2) = v5 & $i(v7) & ( ~ (v6 = 0) | ~ (v5
% 89.46/12.86 | | | | | | = 0) | (v8 = 0 & v4 = 0))))))
% 89.46/12.86 | | | | | |
% 89.46/12.86 | | | | | | GROUND_INST: instantiating (t47_relat_1) with all_344_0, all_844_1,
% 89.46/12.86 | | | | | | simplifying with (52), (145) gives:
% 89.46/12.86 | | | | | | (296) ? [v0: any] : ? [v1: $i] : (relation_dom(all_344_0) = v1
% 89.46/12.86 | | | | | | & relation(all_344_0) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 89.46/12.86 | | | | | | [v2: $i] : ! [v3: $i] : ( ~ (relation_rng(v2) = v3) |
% 89.46/12.86 | | | | | | ~ (subset(v1, v3) = 0) | ~ $i(v2) | ? [v4: any] :
% 89.46/12.86 | | | | | | ? [v5: $i] : ? [v6: $i] : (relation_composition(v2,
% 89.46/12.86 | | | | | | all_344_0) = v5 & relation_rng(v5) = v6 &
% 89.46/12.86 | | | | | | relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0)
% 89.46/12.86 | | | | | | | v6 = all_844_1)))))
% 89.46/12.86 | | | | | |
% 89.46/12.86 | | | | | | GROUND_INST: instantiating (t46_relat_1) with all_344_0, all_844_1,
% 89.46/12.86 | | | | | | simplifying with (52), (145) gives:
% 89.46/12.87 | | | | | | (297) ? [v0: any] : ? [v1: $i] : (relation_dom(all_344_0) = v1
% 89.46/12.87 | | | | | | & relation(all_344_0) = v0 & $i(v1) & ( ~ (v0 = 0) | !
% 89.46/12.87 | | | | | | [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v2) = v3) |
% 89.46/12.87 | | | | | | ~ (subset(all_844_1, v3) = 0) | ~ $i(v2) | ? [v4:
% 89.46/12.87 | | | | | | any] : ? [v5: $i] : ? [v6: $i] :
% 89.46/12.87 | | | | | | (relation_composition(all_344_0, v2) = v5 &
% 89.46/12.87 | | | | | | relation_dom(v5) = v6 & relation(v2) = v4 & $i(v6)
% 89.46/12.87 | | | | | | & $i(v5) & ( ~ (v4 = 0) | v6 = v1)))))
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | GROUND_INST: instantiating (6) with all_344_0, all_844_1,
% 89.46/12.87 | | | | | | simplifying with (52), (145) gives:
% 89.46/12.87 | | | | | | (298) ? [v0: any] : ? [v1: $i] : (relation_dom(all_344_0) = v1
% 89.46/12.87 | | | | | | & relation(all_344_0) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~
% 89.46/12.87 | | | | | | (v1 = empty_set) | all_844_1 = empty_set) & ( ~
% 89.46/12.87 | | | | | | (all_844_1 = empty_set) | v1 = empty_set))))
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | GROUND_INST: instantiating (d5_relat_1) with all_344_0, all_844_1,
% 89.46/12.87 | | | | | | simplifying with (52), (145) gives:
% 89.46/12.87 | | | | | | (299) ? [v0: int] : ( ~ (v0 = 0) & relation(all_344_0) = v0) | (
% 89.46/12.87 | | | | | | ? [v0: any] : (v0 = all_844_1 | ~ $i(v0) | ? [v1: $i] :
% 89.46/12.87 | | | | | | ? [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0)
% 89.46/12.87 | | | | | | | ! [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v3,
% 89.46/12.87 | | | | | | v1) = v4) | ~ (in(v4, all_344_0) = 0) | ~
% 89.46/12.87 | | | | | | $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] :
% 89.46/12.87 | | | | | | (ordered_pair(v3, v1) = v4 & in(v4, all_344_0) = 0
% 89.46/12.87 | | | | | | & $i(v4) & $i(v3))))) & ( ~ $i(all_844_1) | ( !
% 89.46/12.87 | | | | | | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 89.46/12.87 | | | | | | all_844_1) = v1) | ~ $i(v0) | ! [v2: $i] : !
% 89.46/12.87 | | | | | | [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~
% 89.46/12.87 | | | | | | (in(v3, all_344_0) = 0) | ~ $i(v2))) & ! [v0:
% 89.46/12.87 | | | | | | $i] : ( ~ (in(v0, all_844_1) = 0) | ~ $i(v0) | ?
% 89.46/12.87 | | | | | | [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) = v2
% 89.46/12.87 | | | | | | & in(v2, all_344_0) = 0 & $i(v2) & $i(v1))))))
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | DELTA: instantiating (294) with fresh symbols all_1194_0,
% 89.46/12.87 | | | | | | all_1194_1, all_1194_2 gives:
% 89.46/12.87 | | | | | | (300) relation(all_344_0) = all_1194_1 & empty(all_844_1) =
% 89.46/12.87 | | | | | | all_1194_0 & empty(all_344_0) = all_1194_2 & ( ~
% 89.46/12.87 | | | | | | (all_1194_0 = 0) | ~ (all_1194_1 = 0) | all_1194_2 = 0)
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | ALPHA: (300) implies:
% 89.46/12.87 | | | | | | (301) relation(all_344_0) = all_1194_1
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | DELTA: instantiating (289) with fresh symbols all_1196_0,
% 89.46/12.87 | | | | | | all_1196_1, all_1196_2 gives:
% 89.46/12.87 | | | | | | (302) relation(all_288_0) = all_1196_1 & empty(all_838_1) =
% 89.46/12.87 | | | | | | all_1196_0 & empty(all_288_0) = all_1196_2 & ( ~
% 89.46/12.87 | | | | | | (all_1196_0 = 0) | ~ (all_1196_1 = 0) | all_1196_2 = 0)
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | ALPHA: (302) implies:
% 89.46/12.87 | | | | | | (303) relation(all_288_0) = all_1196_1
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | DELTA: instantiating (298) with fresh symbols all_1212_0, all_1212_1
% 89.46/12.87 | | | | | | gives:
% 89.46/12.87 | | | | | | (304) relation_dom(all_344_0) = all_1212_0 & relation(all_344_0)
% 89.46/12.87 | | | | | | = all_1212_1 & $i(all_1212_0) & ( ~ (all_1212_1 = 0) | (( ~
% 89.46/12.87 | | | | | | (all_1212_0 = empty_set) | all_844_1 = empty_set) & (
% 89.46/12.87 | | | | | | ~ (all_844_1 = empty_set) | all_1212_0 = empty_set)))
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | ALPHA: (304) implies:
% 89.46/12.87 | | | | | | (305) relation(all_344_0) = all_1212_1
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | DELTA: instantiating (293) with fresh symbols all_1216_0, all_1216_1
% 89.46/12.87 | | | | | | gives:
% 89.46/12.87 | | | | | | (306) relation_dom(all_288_0) = all_1216_0 & relation(all_288_0)
% 89.46/12.87 | | | | | | = all_1216_1 & $i(all_1216_0) & ( ~ (all_1216_1 = 0) | (( ~
% 89.46/12.87 | | | | | | (all_1216_0 = empty_set) | all_838_1 = empty_set) & (
% 89.46/12.87 | | | | | | ~ (all_838_1 = empty_set) | all_1216_0 = empty_set)))
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | ALPHA: (306) implies:
% 89.46/12.87 | | | | | | (307) relation(all_288_0) = all_1216_1
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | DELTA: instantiating (292) with fresh symbols all_1226_0, all_1226_1
% 89.46/12.87 | | | | | | gives:
% 89.46/12.87 | | | | | | (308) relation_dom(all_288_0) = all_1226_0 & relation(all_288_0)
% 89.46/12.87 | | | | | | = all_1226_1 & $i(all_1226_0) & ( ~ (all_1226_1 = 0) | !
% 89.46/12.87 | | | | | | [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~
% 89.46/12.87 | | | | | | (subset(all_838_1, v1) = 0) | ~ $i(v0) | ? [v2: any]
% 89.46/12.87 | | | | | | : ? [v3: $i] : ? [v4: $i] :
% 89.46/12.87 | | | | | | (relation_composition(all_288_0, v0) = v3 &
% 89.46/12.87 | | | | | | relation_dom(v3) = v4 & relation(v0) = v2 & $i(v4) &
% 89.46/12.87 | | | | | | $i(v3) & ( ~ (v2 = 0) | v4 = all_1226_0))))
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | ALPHA: (308) implies:
% 89.46/12.87 | | | | | | (309) relation(all_288_0) = all_1226_1
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | DELTA: instantiating (297) with fresh symbols all_1228_0, all_1228_1
% 89.46/12.87 | | | | | | gives:
% 89.46/12.87 | | | | | | (310) relation_dom(all_344_0) = all_1228_0 & relation(all_344_0)
% 89.46/12.87 | | | | | | = all_1228_1 & $i(all_1228_0) & ( ~ (all_1228_1 = 0) | !
% 89.46/12.87 | | | | | | [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~
% 89.46/12.87 | | | | | | (subset(all_844_1, v1) = 0) | ~ $i(v0) | ? [v2: any]
% 89.46/12.87 | | | | | | : ? [v3: $i] : ? [v4: $i] :
% 89.46/12.87 | | | | | | (relation_composition(all_344_0, v0) = v3 &
% 89.46/12.87 | | | | | | relation_dom(v3) = v4 & relation(v0) = v2 & $i(v4) &
% 89.46/12.87 | | | | | | $i(v3) & ( ~ (v2 = 0) | v4 = all_1228_0))))
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | ALPHA: (310) implies:
% 89.46/12.87 | | | | | | (311) relation(all_344_0) = all_1228_1
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | DELTA: instantiating (296) with fresh symbols all_1232_0, all_1232_1
% 89.46/12.87 | | | | | | gives:
% 89.46/12.87 | | | | | | (312) relation_dom(all_344_0) = all_1232_0 & relation(all_344_0)
% 89.46/12.87 | | | | | | = all_1232_1 & $i(all_1232_0) & ( ~ (all_1232_1 = 0) | !
% 89.46/12.87 | | | | | | [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~
% 89.46/12.87 | | | | | | (subset(all_1232_0, v1) = 0) | ~ $i(v0) | ? [v2: any]
% 89.46/12.87 | | | | | | : ? [v3: $i] : ? [v4: $i] : (relation_composition(v0,
% 89.46/12.87 | | | | | | all_344_0) = v3 & relation_rng(v3) = v4 &
% 89.46/12.87 | | | | | | relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) |
% 89.46/12.87 | | | | | | v4 = all_844_1))))
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | ALPHA: (312) implies:
% 89.46/12.87 | | | | | | (313) relation(all_344_0) = all_1232_1
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | DELTA: instantiating (291) with fresh symbols all_1234_0, all_1234_1
% 89.46/12.87 | | | | | | gives:
% 89.46/12.87 | | | | | | (314) relation_dom(all_288_0) = all_1234_0 & relation(all_288_0)
% 89.46/12.87 | | | | | | = all_1234_1 & $i(all_1234_0) & ( ~ (all_1234_1 = 0) | !
% 89.46/12.87 | | | | | | [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~
% 89.46/12.87 | | | | | | (subset(all_1234_0, v1) = 0) | ~ $i(v0) | ? [v2: any]
% 89.46/12.87 | | | | | | : ? [v3: $i] : ? [v4: $i] : (relation_composition(v0,
% 89.46/12.87 | | | | | | all_288_0) = v3 & relation_rng(v3) = v4 &
% 89.46/12.87 | | | | | | relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) |
% 89.46/12.87 | | | | | | v4 = all_838_1))))
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | ALPHA: (314) implies:
% 89.46/12.87 | | | | | | (315) relation(all_288_0) = all_1234_1
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | DELTA: instantiating (295) with fresh symbols all_1250_0, all_1250_1
% 89.46/12.87 | | | | | | gives:
% 89.46/12.87 | | | | | | (316) relation_dom(all_344_0) = all_1250_0 & relation(all_344_0)
% 89.46/12.87 | | | | | | = all_1250_1 & $i(all_1250_0) & ( ~ (all_1250_1 = 0) | !
% 89.46/12.87 | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 89.46/12.87 | | | | | | (relation_rng(v0) = v1) | ~ (subset(all_844_1, v1) =
% 89.46/12.87 | | | | | | v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 89.46/12.87 | | | | | | [v5: $i] : ? [v6: any] : (relation_dom(v0) = v5 &
% 89.46/12.87 | | | | | | subset(all_1250_0, v5) = v6 & subset(all_344_0, v0) =
% 89.46/12.87 | | | | | | v4 & relation(v0) = v3 & $i(v5) & ( ~ (v4 = 0) | ~
% 89.46/12.87 | | | | | | (v3 = 0) | (v6 = 0 & v2 = 0)))))
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | ALPHA: (316) implies:
% 89.46/12.87 | | | | | | (317) relation(all_344_0) = all_1250_1
% 89.46/12.87 | | | | | |
% 89.46/12.87 | | | | | | DELTA: instantiating (290) with fresh symbols all_1252_0, all_1252_1
% 89.46/12.87 | | | | | | gives:
% 89.46/12.87 | | | | | | (318) relation_dom(all_288_0) = all_1252_0 & relation(all_288_0)
% 89.46/12.87 | | | | | | = all_1252_1 & $i(all_1252_0) & ( ~ (all_1252_1 = 0) | !
% 89.46/12.87 | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 89.46/12.87 | | | | | | (relation_rng(v0) = v1) | ~ (subset(all_838_1, v1) =
% 89.46/12.87 | | | | | | v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 89.46/12.87 | | | | | | [v5: $i] : ? [v6: any] : (relation_dom(v0) = v5 &
% 89.46/12.88 | | | | | | subset(all_1252_0, v5) = v6 & subset(all_288_0, v0) =
% 89.46/12.88 | | | | | | v4 & relation(v0) = v3 & $i(v5) & ( ~ (v4 = 0) | ~
% 89.46/12.88 | | | | | | (v3 = 0) | (v6 = 0 & v2 = 0)))))
% 89.46/12.88 | | | | | |
% 89.46/12.88 | | | | | | ALPHA: (318) implies:
% 89.46/12.88 | | | | | | (319) relation(all_288_0) = all_1252_1
% 89.46/12.88 | | | | | | (320) ~ (all_1252_1 = 0) | ! [v0: $i] : ! [v1: $i] : ! [v2:
% 89.46/12.88 | | | | | | any] : ( ~ (relation_rng(v0) = v1) | ~
% 89.46/12.88 | | | | | | (subset(all_838_1, v1) = v2) | ~ $i(v0) | ? [v3: any] :
% 89.46/12.88 | | | | | | ? [v4: any] : ? [v5: $i] : ? [v6: any] :
% 89.46/12.88 | | | | | | (relation_dom(v0) = v5 & subset(all_1252_0, v5) = v6 &
% 89.46/12.88 | | | | | | subset(all_288_0, v0) = v4 & relation(v0) = v3 & $i(v5)
% 89.46/12.88 | | | | | | & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v2 = 0))))
% 89.46/12.88 | | | | | |
% 89.46/12.88 | | | | | | DELTA: instantiating (288) with fresh symbols all_1254_0, all_1254_1
% 89.46/12.88 | | | | | | gives:
% 89.46/12.88 | | | | | | (321) relation_field(all_342_1) = all_1254_0 &
% 89.46/12.88 | | | | | | relation(all_342_1) = all_1254_1 & $i(all_1254_0) & ( ~
% 89.46/12.88 | | | | | | (all_1254_1 = 0) | (( ~ (all_820_4 = 0) | ! [v0: $i] : (
% 89.46/12.88 | | | | | | ~ (in(v0, all_1254_0) = 0) | ~ $i(v0) | ? [v1:
% 89.46/12.88 | | | | | | $i] : (ordered_pair(v0, v0) = v1 & in(v1,
% 89.46/12.88 | | | | | | all_342_1) = 0 & $i(v1)))) & (all_820_4 = 0 |
% 89.46/12.88 | | | | | | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 =
% 89.46/12.88 | | | | | | 0) & ordered_pair(v0, v0) = v1 & in(v1,
% 89.46/12.88 | | | | | | all_342_1) = v2 & in(v0, all_1254_0) = 0 & $i(v1)
% 89.46/12.88 | | | | | | & $i(v0)))))
% 89.46/12.88 | | | | | |
% 89.46/12.88 | | | | | | ALPHA: (321) implies:
% 89.46/12.88 | | | | | | (322) relation(all_342_1) = all_1254_1
% 89.46/12.88 | | | | | |
% 89.46/12.88 | | | | | | DELTA: instantiating (287) with fresh symbols all_1260_0, all_1260_1
% 89.46/12.88 | | | | | | gives:
% 89.46/12.88 | | | | | | (323) relation_field(all_342_1) = all_1260_0 &
% 89.46/12.88 | | | | | | relation(all_342_1) = all_1260_1 & $i(all_1260_0) & ( ~
% 89.46/12.88 | | | | | | (all_1260_1 = 0) | (( ~ (all_820_0 = 0) | ! [v0: $i] :
% 89.46/12.88 | | | | | | (v0 = empty_set | ~ (subset(v0, all_1260_0) = 0) |
% 89.46/12.88 | | | | | | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 89.46/12.88 | | | | | | (disjoint(v2, v0) = 0 & fiber(all_342_1, v1) = v2 &
% 89.46/12.88 | | | | | | in(v1, v0) = 0 & $i(v2) & $i(v1)))) & (all_820_0
% 89.46/12.88 | | | | | | = 0 | ? [v0: $i] : ( ~ (v0 = empty_set) & subset(v0,
% 89.46/12.88 | | | | | | all_1260_0) = 0 & $i(v0) & ! [v1: $i] : ! [v2:
% 89.46/12.88 | | | | | | $i] : ( ~ (disjoint(v2, v0) = 0) | ~
% 89.46/12.88 | | | | | | (fiber(all_342_1, v1) = v2) | ~ $i(v1) | ? [v3:
% 89.46/12.88 | | | | | | int] : ( ~ (v3 = 0) & in(v1, v0) = v3))))))
% 89.46/12.88 | | | | | |
% 89.46/12.88 | | | | | | ALPHA: (323) implies:
% 89.46/12.88 | | | | | | (324) relation(all_342_1) = all_1260_1
% 89.46/12.88 | | | | | |
% 89.46/12.88 | | | | | | DELTA: instantiating (285) with fresh symbols all_1262_0,
% 89.46/12.88 | | | | | | all_1262_1, all_1262_2, all_1262_3, all_1262_4 gives:
% 89.46/12.88 | | | | | | (325) reflexive(all_316_1) = all_1262_3 & transitive(all_316_1) =
% 89.46/12.88 | | | | | | all_1262_2 & connected(all_316_1) = all_1262_1 &
% 89.46/12.88 | | | | | | antisymmetric(all_316_1) = all_1262_0 & relation(all_316_1)
% 89.46/12.88 | | | | | | = all_1262_4 & ( ~ (all_1262_4 = 0) | ! [v0: $i] : ! [v1:
% 89.46/12.88 | | | | | | any] : ( ~ (well_founded_relation(v0) = v1) | ~ $i(v0)
% 89.46/12.88 | | | | | | | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5:
% 89.46/12.88 | | | | | | any] : ? [v6: any] : (reflexive(v0) = v3 &
% 89.46/12.88 | | | | | | transitive(v0) = v4 & connected(v0) = v5 &
% 89.46/12.88 | | | | | | antisymmetric(v0) = v6 & relation(v0) = v2 & ( ~ (v2
% 89.46/12.88 | | | | | | = 0) | ! [v7: $i] : ( ~
% 89.46/12.88 | | | | | | (relation_isomorphism(all_316_1, v0, v7) = 0) |
% 89.46/12.88 | | | | | | ~ $i(v7) | ? [v8: any] : ? [v9: any] :
% 89.46/12.88 | | | | | | (relation(v7) = v8 & function(v7) = v9 & ( ~ (v9
% 89.46/12.88 | | | | | | = 0) | ~ (v8 = 0))) | (v1 = 0 & ( ~
% 89.46/12.88 | | | | | | (all_1262_0 = 0) | v6 = 0) & ( ~ (all_1262_1
% 89.46/12.88 | | | | | | = 0) | v5 = 0) & ( ~ (all_1262_2 = 0) | v4
% 89.46/12.88 | | | | | | = 0) & ( ~ (all_1262_3 = 0) | v3 = 0)))))))
% 89.46/12.88 | | | | | |
% 89.46/12.88 | | | | | | ALPHA: (325) implies:
% 89.46/12.88 | | | | | | (326) relation(all_316_1) = all_1262_4
% 89.46/12.88 | | | | | | (327) antisymmetric(all_316_1) = all_1262_0
% 89.46/12.88 | | | | | | (328) connected(all_316_1) = all_1262_1
% 89.46/12.88 | | | | | | (329) transitive(all_316_1) = all_1262_2
% 89.46/12.88 | | | | | | (330) reflexive(all_316_1) = all_1262_3
% 89.46/12.88 | | | | | | (331) ~ (all_1262_4 = 0) | ! [v0: $i] : ! [v1: any] : ( ~
% 89.46/12.88 | | | | | | (well_founded_relation(v0) = v1) | ~ $i(v0) | ? [v2:
% 89.46/12.88 | | | | | | any] : ? [v3: any] : ? [v4: any] : ? [v5: any] : ?
% 89.46/12.88 | | | | | | [v6: any] : (reflexive(v0) = v3 & transitive(v0) = v4 &
% 89.46/12.88 | | | | | | connected(v0) = v5 & antisymmetric(v0) = v6 &
% 89.46/12.88 | | | | | | relation(v0) = v2 & ( ~ (v2 = 0) | ! [v7: $i] : ( ~
% 89.46/12.88 | | | | | | (relation_isomorphism(all_316_1, v0, v7) = 0) | ~
% 89.46/12.88 | | | | | | $i(v7) | ? [v8: any] : ? [v9: any] :
% 89.46/12.88 | | | | | | (relation(v7) = v8 & function(v7) = v9 & ( ~ (v9 =
% 89.46/12.88 | | | | | | 0) | ~ (v8 = 0))) | (v1 = 0 & ( ~
% 89.46/12.88 | | | | | | (all_1262_0 = 0) | v6 = 0) & ( ~ (all_1262_1 =
% 89.46/12.88 | | | | | | 0) | v5 = 0) & ( ~ (all_1262_2 = 0) | v4 = 0)
% 89.46/12.88 | | | | | | & ( ~ (all_1262_3 = 0) | v3 = 0))))))
% 89.46/12.88 | | | | | |
% 89.46/12.88 | | | | | | DELTA: instantiating (286) with fresh symbols all_1264_0,
% 89.46/12.88 | | | | | | all_1264_1, all_1264_2, all_1264_3, all_1264_4 gives:
% 89.46/12.88 | | | | | | (332) reflexive(all_342_1) = all_1264_3 & transitive(all_342_1) =
% 89.46/12.88 | | | | | | all_1264_2 & connected(all_342_1) = all_1264_1 &
% 89.46/12.88 | | | | | | antisymmetric(all_342_1) = all_1264_0 & relation(all_342_1)
% 89.46/12.88 | | | | | | = all_1264_4 & ( ~ (all_1264_4 = 0) | ! [v0: $i] : ! [v1:
% 89.46/12.88 | | | | | | any] : ( ~ (well_founded_relation(v0) = v1) | ~ $i(v0)
% 89.46/12.88 | | | | | | | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5:
% 89.46/12.88 | | | | | | any] : ? [v6: any] : (reflexive(v0) = v3 &
% 89.46/12.88 | | | | | | transitive(v0) = v4 & connected(v0) = v5 &
% 89.46/12.88 | | | | | | antisymmetric(v0) = v6 & relation(v0) = v2 & ( ~ (v2
% 89.46/12.88 | | | | | | = 0) | ! [v7: $i] : ( ~
% 89.46/12.88 | | | | | | (relation_isomorphism(all_342_1, v0, v7) = 0) |
% 89.46/12.88 | | | | | | ~ $i(v7) | ? [v8: any] : ? [v9: any] :
% 89.46/12.88 | | | | | | (relation(v7) = v8 & function(v7) = v9 & ( ~ (v9
% 89.46/12.88 | | | | | | = 0) | ~ (v8 = 0))) | (( ~ (all_1264_0 =
% 89.46/12.88 | | | | | | 0) | v6 = 0) & ( ~ (all_1264_1 = 0) | v5 =
% 89.46/12.88 | | | | | | 0) & ( ~ (all_1264_2 = 0) | v4 = 0) & ( ~
% 89.46/12.88 | | | | | | (all_1264_3 = 0) | v3 = 0) & ( ~ (all_820_0 =
% 89.46/12.88 | | | | | | 0) | v1 = 0)))))))
% 89.46/12.88 | | | | | |
% 89.46/12.88 | | | | | | ALPHA: (332) implies:
% 89.46/12.88 | | | | | | (333) relation(all_342_1) = all_1264_4
% 89.46/12.88 | | | | | | (334) antisymmetric(all_342_1) = all_1264_0
% 89.46/12.88 | | | | | | (335) connected(all_342_1) = all_1264_1
% 89.46/12.88 | | | | | | (336) transitive(all_342_1) = all_1264_2
% 89.46/12.88 | | | | | | (337) reflexive(all_342_1) = all_1264_3
% 89.46/12.88 | | | | | | (338) ~ (all_1264_4 = 0) | ! [v0: $i] : ! [v1: any] : ( ~
% 89.46/12.88 | | | | | | (well_founded_relation(v0) = v1) | ~ $i(v0) | ? [v2:
% 89.46/12.88 | | | | | | any] : ? [v3: any] : ? [v4: any] : ? [v5: any] : ?
% 89.46/12.88 | | | | | | [v6: any] : (reflexive(v0) = v3 & transitive(v0) = v4 &
% 89.46/12.88 | | | | | | connected(v0) = v5 & antisymmetric(v0) = v6 &
% 89.46/12.88 | | | | | | relation(v0) = v2 & ( ~ (v2 = 0) | ! [v7: $i] : ( ~
% 89.46/12.88 | | | | | | (relation_isomorphism(all_342_1, v0, v7) = 0) | ~
% 89.46/12.88 | | | | | | $i(v7) | ? [v8: any] : ? [v9: any] :
% 89.46/12.88 | | | | | | (relation(v7) = v8 & function(v7) = v9 & ( ~ (v9 =
% 89.46/12.88 | | | | | | 0) | ~ (v8 = 0))) | (( ~ (all_1264_0 = 0) |
% 89.46/12.88 | | | | | | v6 = 0) & ( ~ (all_1264_1 = 0) | v5 = 0) & ( ~
% 89.46/12.88 | | | | | | (all_1264_2 = 0) | v4 = 0) & ( ~ (all_1264_3 =
% 89.46/12.88 | | | | | | 0) | v3 = 0) & ( ~ (all_820_0 = 0) | v1 =
% 89.46/12.88 | | | | | | 0))))))
% 89.46/12.89 | | | | | |
% 89.46/12.89 | | | | | | DELTA: instantiating (284) with fresh symbols all_1266_0, all_1266_1
% 89.46/12.89 | | | | | | gives:
% 89.46/12.89 | | | | | | (339) relation_field(all_342_1) = all_1266_0 &
% 89.46/12.89 | | | | | | relation(all_342_1) = all_1266_1 & $i(all_1266_0) & ( ~
% 89.46/12.89 | | | | | | (all_1266_1 = 0) | (( ~ (all_820_1 = 0) | ! [v0: $i] :
% 89.46/12.89 | | | | | | ! [v1: $i] : (v1 = v0 | ~ (in(v1, all_1266_0) = 0) |
% 89.46/12.89 | | | | | | ~ (in(v0, all_1266_0) = 0) | ~ $i(v1) | ~ $i(v0)
% 89.46/12.89 | | | | | | | ? [v2: $i] : ? [v3: any] : ? [v4: $i] : ?
% 89.46/12.89 | | | | | | [v5: any] : (ordered_pair(v1, v0) = v4 &
% 89.46/12.89 | | | | | | ordered_pair(v0, v1) = v2 & in(v4, all_342_1) =
% 89.46/12.89 | | | | | | v5 & in(v2, all_342_1) = v3 & $i(v4) & $i(v2) &
% 89.46/12.89 | | | | | | (v5 = 0 | v3 = 0)))) & (all_820_1 = 0 | ? [v0:
% 89.46/12.89 | | | | | | $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ?
% 89.46/12.89 | | | | | | [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & ~ (v3 = 0)
% 89.46/12.89 | | | | | | & ~ (v1 = v0) & ordered_pair(v1, v0) = v4 &
% 89.46/12.89 | | | | | | ordered_pair(v0, v1) = v2 & in(v4, all_342_1) = v5
% 89.46/12.89 | | | | | | & in(v2, all_342_1) = v3 & in(v1, all_1266_0) = 0 &
% 89.46/12.89 | | | | | | in(v0, all_1266_0) = 0 & $i(v4) & $i(v2) & $i(v1) &
% 89.46/12.89 | | | | | | $i(v0)))))
% 89.46/12.89 | | | | | |
% 89.46/12.89 | | | | | | ALPHA: (339) implies:
% 89.46/12.89 | | | | | | (340) relation(all_342_1) = all_1266_1
% 89.46/12.89 | | | | | |
% 89.46/12.89 | | | | | | BETA: splitting (283) gives:
% 89.46/12.89 | | | | | |
% 89.46/12.89 | | | | | | Case 1:
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | (341) all_882_0 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | REDUCE: (264), (341) imply:
% 89.46/12.89 | | | | | | | (342) $false
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | CLOSE: (342) is inconsistent.
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | Case 2:
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (10) with 0, all_1216_1, all_288_0,
% 89.46/12.89 | | | | | | | simplifying with (24), (307) gives:
% 89.46/12.89 | | | | | | | (343) all_1216_1 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (10) with all_1216_1, all_1226_1,
% 89.46/12.89 | | | | | | | all_288_0, simplifying with (307), (309) gives:
% 89.46/12.89 | | | | | | | (344) all_1226_1 = all_1216_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (10) with all_1234_1, all_1252_1,
% 89.46/12.89 | | | | | | | all_288_0, simplifying with (315), (319) gives:
% 89.46/12.89 | | | | | | | (345) all_1252_1 = all_1234_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (10) with all_1226_1, all_1252_1,
% 89.46/12.89 | | | | | | | all_288_0, simplifying with (309), (319) gives:
% 89.46/12.89 | | | | | | | (346) all_1252_1 = all_1226_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (10) with all_1196_1, all_1252_1,
% 89.46/12.89 | | | | | | | all_288_0, simplifying with (303), (319) gives:
% 89.46/12.89 | | | | | | | (347) all_1252_1 = all_1196_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (10) with 0, all_1262_4, all_316_1,
% 89.46/12.89 | | | | | | | simplifying with (41), (326) gives:
% 89.46/12.89 | | | | | | | (348) all_1262_4 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (10) with 0, all_1260_1, all_342_1,
% 89.46/12.89 | | | | | | | simplifying with (46), (324) gives:
% 89.46/12.89 | | | | | | | (349) all_1260_1 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (10) with all_1264_4, all_1266_1,
% 89.46/12.89 | | | | | | | all_342_1, simplifying with (333), (340) gives:
% 89.46/12.89 | | | | | | | (350) all_1266_1 = all_1264_4
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (10) with all_1260_1, all_1266_1,
% 89.46/12.89 | | | | | | | all_342_1, simplifying with (324), (340) gives:
% 89.46/12.89 | | | | | | | (351) all_1266_1 = all_1260_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (10) with all_1254_1, all_1266_1,
% 89.46/12.89 | | | | | | | all_342_1, simplifying with (322), (340) gives:
% 89.46/12.89 | | | | | | | (352) all_1266_1 = all_1254_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (10) with all_1228_1, all_1232_1,
% 89.46/12.89 | | | | | | | all_344_0, simplifying with (311), (313) gives:
% 89.46/12.89 | | | | | | | (353) all_1232_1 = all_1228_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (10) with all_1194_1, all_1232_1,
% 89.46/12.89 | | | | | | | all_344_0, simplifying with (301), (313) gives:
% 89.46/12.89 | | | | | | | (354) all_1232_1 = all_1194_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (10) with 0, all_1250_1, all_344_0,
% 89.46/12.89 | | | | | | | simplifying with (54), (317) gives:
% 89.46/12.89 | | | | | | | (355) all_1250_1 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (10) with all_1228_1, all_1250_1,
% 89.46/12.89 | | | | | | | all_344_0, simplifying with (311), (317) gives:
% 89.46/12.89 | | | | | | | (356) all_1250_1 = all_1228_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (10) with all_1212_1, all_1250_1,
% 89.46/12.89 | | | | | | | all_344_0, simplifying with (305), (317) gives:
% 89.46/12.89 | | | | | | | (357) all_1250_1 = all_1212_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (11) with 0, all_1262_0, all_316_1,
% 89.46/12.89 | | | | | | | simplifying with (277), (327) gives:
% 89.46/12.89 | | | | | | | (358) all_1262_0 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (11) with all_820_2, all_1264_0,
% 89.46/12.89 | | | | | | | all_342_1, simplifying with (119), (334) gives:
% 89.46/12.89 | | | | | | | (359) all_1264_0 = all_820_2
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (12) with 0, all_1262_1, all_316_1,
% 89.46/12.89 | | | | | | | simplifying with (276), (328) gives:
% 89.46/12.89 | | | | | | | (360) all_1262_1 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (12) with all_820_1, all_1264_1,
% 89.46/12.89 | | | | | | | all_342_1, simplifying with (120), (335) gives:
% 89.46/12.89 | | | | | | | (361) all_1264_1 = all_820_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (13) with 0, all_1262_2, all_316_1,
% 89.46/12.89 | | | | | | | simplifying with (275), (329) gives:
% 89.46/12.89 | | | | | | | (362) all_1262_2 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (13) with all_820_3, all_1264_2,
% 89.46/12.89 | | | | | | | all_342_1, simplifying with (121), (336) gives:
% 89.46/12.89 | | | | | | | (363) all_1264_2 = all_820_3
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (14) with 0, all_1262_3, all_316_1,
% 89.46/12.89 | | | | | | | simplifying with (273), (330) gives:
% 89.46/12.89 | | | | | | | (364) all_1262_3 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | GROUND_INST: instantiating (14) with all_820_4, all_1264_3,
% 89.46/12.89 | | | | | | | all_342_1, simplifying with (123), (337) gives:
% 89.46/12.89 | | | | | | | (365) all_1264_3 = all_820_4
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (350), (352) imply:
% 89.46/12.89 | | | | | | | (366) all_1264_4 = all_1254_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (350), (351) imply:
% 89.46/12.89 | | | | | | | (367) all_1264_4 = all_1260_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (366), (367) imply:
% 89.46/12.89 | | | | | | | (368) all_1260_1 = all_1254_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | SIMP: (368) implies:
% 89.46/12.89 | | | | | | | (369) all_1260_1 = all_1254_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (349), (369) imply:
% 89.46/12.89 | | | | | | | (370) all_1254_1 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | SIMP: (370) implies:
% 89.46/12.89 | | | | | | | (371) all_1254_1 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (345), (347) imply:
% 89.46/12.89 | | | | | | | (372) all_1234_1 = all_1196_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (345), (346) imply:
% 89.46/12.89 | | | | | | | (373) all_1234_1 = all_1226_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (356), (357) imply:
% 89.46/12.89 | | | | | | | (374) all_1228_1 = all_1212_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | SIMP: (374) implies:
% 89.46/12.89 | | | | | | | (375) all_1228_1 = all_1212_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (355), (357) imply:
% 89.46/12.89 | | | | | | | (376) all_1212_1 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (372), (373) imply:
% 89.46/12.89 | | | | | | | (377) all_1226_1 = all_1196_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | SIMP: (377) implies:
% 89.46/12.89 | | | | | | | (378) all_1226_1 = all_1196_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (353), (354) imply:
% 89.46/12.89 | | | | | | | (379) all_1228_1 = all_1194_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | SIMP: (379) implies:
% 89.46/12.89 | | | | | | | (380) all_1228_1 = all_1194_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (375), (380) imply:
% 89.46/12.89 | | | | | | | (381) all_1212_1 = all_1194_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | SIMP: (381) implies:
% 89.46/12.89 | | | | | | | (382) all_1212_1 = all_1194_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (344), (378) imply:
% 89.46/12.89 | | | | | | | (383) all_1216_1 = all_1196_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | SIMP: (383) implies:
% 89.46/12.89 | | | | | | | (384) all_1216_1 = all_1196_1
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (343), (384) imply:
% 89.46/12.89 | | | | | | | (385) all_1196_1 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (376), (382) imply:
% 89.46/12.89 | | | | | | | (386) all_1194_1 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | SIMP: (386) implies:
% 89.46/12.89 | | | | | | | (387) all_1194_1 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (372), (385) imply:
% 89.46/12.89 | | | | | | | (388) all_1234_1 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (345), (388) imply:
% 89.46/12.89 | | | | | | | (389) all_1252_1 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | COMBINE_EQS: (366), (371) imply:
% 89.46/12.89 | | | | | | | (390) all_1264_4 = 0
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | BETA: splitting (299) gives:
% 89.46/12.89 | | | | | | |
% 89.46/12.89 | | | | | | | Case 1:
% 89.46/12.89 | | | | | | | |
% 89.46/12.89 | | | | | | | | (391) ? [v0: int] : ( ~ (v0 = 0) & relation(all_344_0) = v0)
% 89.46/12.89 | | | | | | | |
% 89.46/12.89 | | | | | | | | BETA: splitting (338) gives:
% 89.46/12.89 | | | | | | | |
% 89.46/12.89 | | | | | | | | Case 1:
% 89.46/12.89 | | | | | | | | |
% 89.46/12.89 | | | | | | | | | (392) ~ (all_1264_4 = 0)
% 89.46/12.89 | | | | | | | | |
% 89.46/12.89 | | | | | | | | | REDUCE: (390), (392) imply:
% 89.46/12.89 | | | | | | | | | (393) $false
% 89.46/12.89 | | | | | | | | |
% 89.46/12.89 | | | | | | | | | CLOSE: (393) is inconsistent.
% 89.46/12.89 | | | | | | | | |
% 89.46/12.89 | | | | | | | | Case 2:
% 89.46/12.89 | | | | | | | | |
% 89.46/12.89 | | | | | | | | |
% 89.46/12.89 | | | | | | | | | DELTA: instantiating (391) with fresh symbol all_1366_0 gives:
% 89.46/12.89 | | | | | | | | | (394) ~ (all_1366_0 = 0) & relation(all_344_0) =
% 89.46/12.89 | | | | | | | | | all_1366_0
% 89.46/12.89 | | | | | | | | |
% 89.46/12.89 | | | | | | | | | ALPHA: (394) implies:
% 89.46/12.89 | | | | | | | | | (395) ~ (all_1366_0 = 0)
% 89.46/12.89 | | | | | | | | | (396) relation(all_344_0) = all_1366_0
% 89.46/12.89 | | | | | | | | |
% 89.46/12.89 | | | | | | | | | BETA: splitting (320) gives:
% 89.46/12.89 | | | | | | | | |
% 89.46/12.89 | | | | | | | | | Case 1:
% 89.46/12.89 | | | | | | | | | |
% 89.46/12.89 | | | | | | | | | | (397) ~ (all_1252_1 = 0)
% 89.46/12.89 | | | | | | | | | |
% 89.46/12.89 | | | | | | | | | | REDUCE: (389), (397) imply:
% 89.46/12.89 | | | | | | | | | | (398) $false
% 89.46/12.89 | | | | | | | | | |
% 89.46/12.89 | | | | | | | | | | CLOSE: (398) is inconsistent.
% 89.46/12.89 | | | | | | | | | |
% 89.46/12.89 | | | | | | | | | Case 2:
% 89.46/12.89 | | | | | | | | | |
% 89.46/12.89 | | | | | | | | | |
% 89.46/12.89 | | | | | | | | | | DELTA: instantiating (391) with fresh symbol all_1438_0
% 89.46/12.89 | | | | | | | | | | gives:
% 89.46/12.90 | | | | | | | | | | (399) ~ (all_1438_0 = 0) & relation(all_344_0) =
% 89.46/12.90 | | | | | | | | | | all_1438_0
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | ALPHA: (399) implies:
% 89.46/12.90 | | | | | | | | | | (400) relation(all_344_0) = all_1438_0
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | DELTA: instantiating (391) with fresh symbol all_1440_0
% 89.46/12.90 | | | | | | | | | | gives:
% 89.46/12.90 | | | | | | | | | | (401) ~ (all_1440_0 = 0) & relation(all_344_0) =
% 89.46/12.90 | | | | | | | | | | all_1440_0
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | ALPHA: (401) implies:
% 89.46/12.90 | | | | | | | | | | (402) relation(all_344_0) = all_1440_0
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_1440_0, all_344_0,
% 89.46/12.90 | | | | | | | | | | simplifying with (54), (402) gives:
% 89.46/12.90 | | | | | | | | | | (403) all_1440_0 = 0
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | GROUND_INST: instantiating (10) with all_1438_0, all_1440_0,
% 89.46/12.90 | | | | | | | | | | all_344_0, simplifying with (400), (402) gives:
% 89.46/12.90 | | | | | | | | | | (404) all_1440_0 = all_1438_0
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | GROUND_INST: instantiating (10) with all_1366_0, all_1440_0,
% 89.46/12.90 | | | | | | | | | | all_344_0, simplifying with (396), (402) gives:
% 89.46/12.90 | | | | | | | | | | (405) all_1440_0 = all_1366_0
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | COMBINE_EQS: (403), (404) imply:
% 89.46/12.90 | | | | | | | | | | (406) all_1438_0 = 0
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | COMBINE_EQS: (404), (405) imply:
% 89.46/12.90 | | | | | | | | | | (407) all_1438_0 = all_1366_0
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | COMBINE_EQS: (406), (407) imply:
% 89.46/12.90 | | | | | | | | | | (408) all_1366_0 = 0
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | SIMP: (408) implies:
% 89.46/12.90 | | | | | | | | | | (409) all_1366_0 = 0
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | REDUCE: (395), (409) imply:
% 89.46/12.90 | | | | | | | | | | (410) $false
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | CLOSE: (410) is inconsistent.
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | End of split
% 89.46/12.90 | | | | | | | | |
% 89.46/12.90 | | | | | | | | End of split
% 89.46/12.90 | | | | | | | |
% 89.46/12.90 | | | | | | | Case 2:
% 89.46/12.90 | | | | | | | |
% 89.46/12.90 | | | | | | | | (411) ? [v0: any] : (v0 = all_844_1 | ~ $i(v0) | ? [v1:
% 89.46/12.90 | | | | | | | | $i] : ? [v2: any] : (in(v1, v0) = v2 & $i(v1) & (
% 89.46/12.90 | | | | | | | | ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] : ( ~
% 89.46/12.90 | | | | | | | | (ordered_pair(v3, v1) = v4) | ~ (in(v4,
% 89.46/12.90 | | | | | | | | all_344_0) = 0) | ~ $i(v3))) & (v2 = 0 |
% 89.46/12.90 | | | | | | | | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v3, v1)
% 89.46/12.90 | | | | | | | | = v4 & in(v4, all_344_0) = 0 & $i(v4) &
% 89.46/12.90 | | | | | | | | $i(v3))))) & ( ~ $i(all_844_1) | ( ! [v0: $i] :
% 89.46/12.90 | | | | | | | | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_844_1) =
% 89.46/12.90 | | | | | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : (
% 89.46/12.90 | | | | | | | | ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3,
% 89.46/12.90 | | | | | | | | all_344_0) = 0) | ~ $i(v2))) & ! [v0: $i]
% 89.46/12.90 | | | | | | | | : ( ~ (in(v0, all_844_1) = 0) | ~ $i(v0) | ? [v1:
% 89.46/12.90 | | | | | | | | $i] : ? [v2: $i] : (ordered_pair(v1, v0) = v2
% 89.46/12.90 | | | | | | | | & in(v2, all_344_0) = 0 & $i(v2) & $i(v1)))))
% 89.46/12.90 | | | | | | | |
% 89.46/12.90 | | | | | | | | ALPHA: (411) implies:
% 89.46/12.90 | | | | | | | | (412) ~ $i(all_844_1) | ( ! [v0: $i] : ! [v1: int] : (v1 =
% 89.46/12.90 | | | | | | | | 0 | ~ (in(v0, all_844_1) = v1) | ~ $i(v0) | !
% 89.46/12.90 | | | | | | | | [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v0)
% 89.46/12.90 | | | | | | | | = v3) | ~ (in(v3, all_344_0) = 0) | ~
% 89.46/12.90 | | | | | | | | $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_844_1) =
% 89.46/12.90 | | | | | | | | 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 89.46/12.90 | | | | | | | | (ordered_pair(v1, v0) = v2 & in(v2, all_344_0) = 0
% 89.46/12.90 | | | | | | | | & $i(v2) & $i(v1))))
% 89.46/12.90 | | | | | | | |
% 89.46/12.90 | | | | | | | | BETA: splitting (331) gives:
% 89.46/12.90 | | | | | | | |
% 89.46/12.90 | | | | | | | | Case 1:
% 89.46/12.90 | | | | | | | | |
% 89.46/12.90 | | | | | | | | | (413) ~ (all_1262_4 = 0)
% 89.46/12.90 | | | | | | | | |
% 89.46/12.90 | | | | | | | | | REDUCE: (348), (413) imply:
% 89.46/12.90 | | | | | | | | | (414) $false
% 89.46/12.90 | | | | | | | | |
% 89.46/12.90 | | | | | | | | | CLOSE: (414) is inconsistent.
% 89.46/12.90 | | | | | | | | |
% 89.46/12.90 | | | | | | | | Case 2:
% 89.46/12.90 | | | | | | | | |
% 89.46/12.90 | | | | | | | | | (415) ! [v0: $i] : ! [v1: any] : ( ~
% 89.46/12.90 | | | | | | | | | (well_founded_relation(v0) = v1) | ~ $i(v0) | ?
% 89.46/12.90 | | | | | | | | | [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5:
% 89.46/12.90 | | | | | | | | | any] : ? [v6: any] : (reflexive(v0) = v3 &
% 89.46/12.90 | | | | | | | | | transitive(v0) = v4 & connected(v0) = v5 &
% 89.46/12.90 | | | | | | | | | antisymmetric(v0) = v6 & relation(v0) = v2 & ( ~
% 89.46/12.90 | | | | | | | | | (v2 = 0) | ! [v7: $i] : ( ~
% 89.46/12.90 | | | | | | | | | (relation_isomorphism(all_316_1, v0, v7) = 0)
% 89.46/12.90 | | | | | | | | | | ~ $i(v7) | ? [v8: any] : ? [v9: any] :
% 89.46/12.90 | | | | | | | | | (relation(v7) = v8 & function(v7) = v9 & ( ~
% 89.46/12.90 | | | | | | | | | (v9 = 0) | ~ (v8 = 0))) | (v1 = 0 & ( ~
% 89.46/12.90 | | | | | | | | | (all_1262_0 = 0) | v6 = 0) & ( ~
% 89.46/12.90 | | | | | | | | | (all_1262_1 = 0) | v5 = 0) & ( ~
% 89.46/12.90 | | | | | | | | | (all_1262_2 = 0) | v4 = 0) & ( ~
% 89.46/12.90 | | | | | | | | | (all_1262_3 = 0) | v3 = 0))))))
% 89.46/12.90 | | | | | | | | |
% 89.46/12.90 | | | | | | | | | GROUND_INST: instantiating (415) with all_342_1, all_820_0,
% 89.46/12.90 | | | | | | | | | simplifying with (45), (122) gives:
% 89.46/12.90 | | | | | | | | | (416) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 89.46/12.90 | | | | | | | | | any] : ? [v4: any] : (reflexive(all_342_1) = v1 &
% 89.46/12.90 | | | | | | | | | transitive(all_342_1) = v2 & connected(all_342_1) =
% 89.46/12.90 | | | | | | | | | v3 & antisymmetric(all_342_1) = v4 &
% 89.46/12.90 | | | | | | | | | relation(all_342_1) = v0 & ( ~ (v0 = 0) | ! [v5:
% 89.46/12.90 | | | | | | | | | $i] : ( ~ (relation_isomorphism(all_316_1,
% 89.46/12.90 | | | | | | | | | all_342_1, v5) = 0) | ~ $i(v5) | ? [v6:
% 89.46/12.90 | | | | | | | | | any] : ? [v7: any] : (relation(v5) = v6 &
% 89.46/12.90 | | | | | | | | | function(v5) = v7 & ( ~ (v7 = 0) | ~ (v6 =
% 89.46/12.90 | | | | | | | | | 0))) | (all_820_0 = 0 & ( ~ (all_1262_0 =
% 89.46/12.90 | | | | | | | | | 0) | v4 = 0) & ( ~ (all_1262_1 = 0) | v3
% 89.46/12.90 | | | | | | | | | = 0) & ( ~ (all_1262_2 = 0) | v2 = 0) & ( ~
% 89.46/12.90 | | | | | | | | | (all_1262_3 = 0) | v1 = 0)))))
% 89.46/12.90 | | | | | | | | |
% 89.46/12.90 | | | | | | | | | BETA: splitting (412) gives:
% 89.46/12.90 | | | | | | | | |
% 89.46/12.90 | | | | | | | | | Case 1:
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | (417) ~ $i(all_844_1)
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | PRED_UNIFY: (143), (417) imply:
% 89.46/12.90 | | | | | | | | | | (418) $false
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | CLOSE: (418) is inconsistent.
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | Case 2:
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | DELTA: instantiating (416) with fresh symbols all_1444_0,
% 89.46/12.90 | | | | | | | | | | all_1444_1, all_1444_2, all_1444_3, all_1444_4 gives:
% 89.46/12.90 | | | | | | | | | | (419) reflexive(all_342_1) = all_1444_3 &
% 89.46/12.90 | | | | | | | | | | transitive(all_342_1) = all_1444_2 &
% 89.46/12.90 | | | | | | | | | | connected(all_342_1) = all_1444_1 &
% 89.46/12.90 | | | | | | | | | | antisymmetric(all_342_1) = all_1444_0 &
% 89.46/12.90 | | | | | | | | | | relation(all_342_1) = all_1444_4 & ( ~ (all_1444_4
% 89.46/12.90 | | | | | | | | | | = 0) | ! [v0: $i] : ( ~
% 89.46/12.90 | | | | | | | | | | (relation_isomorphism(all_316_1, all_342_1, v0)
% 89.46/12.90 | | | | | | | | | | = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 89.46/12.90 | | | | | | | | | | any] : (relation(v0) = v1 & function(v0) = v2
% 89.46/12.90 | | | | | | | | | | & ( ~ (v2 = 0) | ~ (v1 = 0))) | (all_820_0 =
% 89.46/12.90 | | | | | | | | | | 0 & ( ~ (all_1262_0 = 0) | all_1444_0 = 0) &
% 89.46/12.90 | | | | | | | | | | ( ~ (all_1262_1 = 0) | all_1444_1 = 0) & ( ~
% 89.46/12.90 | | | | | | | | | | (all_1262_2 = 0) | all_1444_2 = 0) & ( ~
% 89.46/12.90 | | | | | | | | | | (all_1262_3 = 0) | all_1444_3 = 0))))
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | ALPHA: (419) implies:
% 89.46/12.90 | | | | | | | | | | (420) relation(all_342_1) = all_1444_4
% 89.46/12.90 | | | | | | | | | | (421) antisymmetric(all_342_1) = all_1444_0
% 89.46/12.90 | | | | | | | | | | (422) connected(all_342_1) = all_1444_1
% 89.46/12.90 | | | | | | | | | | (423) transitive(all_342_1) = all_1444_2
% 89.46/12.90 | | | | | | | | | | (424) reflexive(all_342_1) = all_1444_3
% 89.46/12.90 | | | | | | | | | | (425) ~ (all_1444_4 = 0) | ! [v0: $i] : ( ~
% 89.46/12.90 | | | | | | | | | | (relation_isomorphism(all_316_1, all_342_1, v0) =
% 89.46/12.90 | | | | | | | | | | 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] :
% 89.46/12.90 | | | | | | | | | | (relation(v0) = v1 & function(v0) = v2 & ( ~ (v2
% 89.46/12.90 | | | | | | | | | | = 0) | ~ (v1 = 0))) | (all_820_0 = 0 & ( ~
% 89.46/12.90 | | | | | | | | | | (all_1262_0 = 0) | all_1444_0 = 0) & ( ~
% 89.46/12.90 | | | | | | | | | | (all_1262_1 = 0) | all_1444_1 = 0) & ( ~
% 89.46/12.90 | | | | | | | | | | (all_1262_2 = 0) | all_1444_2 = 0) & ( ~
% 89.46/12.90 | | | | | | | | | | (all_1262_3 = 0) | all_1444_3 = 0)))
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_1444_4, all_342_1,
% 89.46/12.90 | | | | | | | | | | simplifying with (46), (420) gives:
% 89.46/12.90 | | | | | | | | | | (426) all_1444_4 = 0
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.90 | | | | | | | | | | GROUND_INST: instantiating (11) with all_820_2, all_1444_0,
% 89.46/12.90 | | | | | | | | | | all_342_1, simplifying with (119), (421) gives:
% 89.46/12.90 | | | | | | | | | | (427) all_1444_0 = all_820_2
% 89.46/12.90 | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | GROUND_INST: instantiating (12) with all_820_1, all_1444_1,
% 89.46/12.91 | | | | | | | | | | all_342_1, simplifying with (120), (422) gives:
% 89.46/12.91 | | | | | | | | | | (428) all_1444_1 = all_820_1
% 89.46/12.91 | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | GROUND_INST: instantiating (13) with all_820_3, all_1444_2,
% 89.46/12.91 | | | | | | | | | | all_342_1, simplifying with (121), (423) gives:
% 89.46/12.91 | | | | | | | | | | (429) all_1444_2 = all_820_3
% 89.46/12.91 | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | GROUND_INST: instantiating (14) with all_820_4, all_1444_3,
% 89.46/12.91 | | | | | | | | | | all_342_1, simplifying with (123), (424) gives:
% 89.46/12.91 | | | | | | | | | | (430) all_1444_3 = all_820_4
% 89.46/12.91 | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | BETA: splitting (425) gives:
% 89.46/12.91 | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | Case 1:
% 89.46/12.91 | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | (431) ~ (all_1444_4 = 0)
% 89.46/12.91 | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | REDUCE: (426), (431) imply:
% 89.46/12.91 | | | | | | | | | | | (432) $false
% 89.46/12.91 | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | CLOSE: (432) is inconsistent.
% 89.46/12.91 | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | Case 2:
% 89.46/12.91 | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | (433) ! [v0: $i] : ( ~ (relation_isomorphism(all_316_1,
% 89.46/12.91 | | | | | | | | | | | all_342_1, v0) = 0) | ~ $i(v0) | ? [v1:
% 89.46/12.91 | | | | | | | | | | | any] : ? [v2: any] : (relation(v0) = v1 &
% 89.46/12.91 | | | | | | | | | | | function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 =
% 89.46/12.91 | | | | | | | | | | | 0))) | (all_820_0 = 0 & ( ~ (all_1262_0 =
% 89.46/12.91 | | | | | | | | | | | 0) | all_1444_0 = 0) & ( ~ (all_1262_1 =
% 89.46/12.91 | | | | | | | | | | | 0) | all_1444_1 = 0) & ( ~ (all_1262_2 =
% 89.46/12.91 | | | | | | | | | | | 0) | all_1444_2 = 0) & ( ~ (all_1262_3 =
% 89.46/12.91 | | | | | | | | | | | 0) | all_1444_3 = 0)))
% 89.46/12.91 | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | GROUND_INST: instantiating (433) with all_344_0, simplifying
% 89.46/12.91 | | | | | | | | | | | with (52), (55) gives:
% 89.46/12.91 | | | | | | | | | | | (434) ? [v0: any] : ? [v1: any] : (relation(all_344_0)
% 89.46/12.91 | | | | | | | | | | | = v0 & function(all_344_0) = v1 & ( ~ (v1 = 0) |
% 89.46/12.91 | | | | | | | | | | | ~ (v0 = 0))) | (all_820_0 = 0 & ( ~
% 89.46/12.91 | | | | | | | | | | | (all_1262_0 = 0) | all_1444_0 = 0) & ( ~
% 89.46/12.91 | | | | | | | | | | | (all_1262_1 = 0) | all_1444_1 = 0) & ( ~
% 89.46/12.91 | | | | | | | | | | | (all_1262_2 = 0) | all_1444_2 = 0) & ( ~
% 89.46/12.91 | | | | | | | | | | | (all_1262_3 = 0) | all_1444_3 = 0))
% 89.46/12.91 | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | BETA: splitting (434) gives:
% 89.46/12.91 | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | Case 1:
% 89.46/12.91 | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | (435) ? [v0: any] : ? [v1: any] : (relation(all_344_0)
% 89.46/12.91 | | | | | | | | | | | | = v0 & function(all_344_0) = v1 & ( ~ (v1 = 0) |
% 89.46/12.91 | | | | | | | | | | | | ~ (v0 = 0)))
% 89.46/12.91 | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | DELTA: instantiating (435) with fresh symbols all_1505_0,
% 89.46/12.91 | | | | | | | | | | | | all_1505_1 gives:
% 89.46/12.91 | | | | | | | | | | | | (436) relation(all_344_0) = all_1505_1 &
% 89.46/12.91 | | | | | | | | | | | | function(all_344_0) = all_1505_0 & ( ~ (all_1505_0
% 89.46/12.91 | | | | | | | | | | | | = 0) | ~ (all_1505_1 = 0))
% 89.46/12.91 | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | ALPHA: (436) implies:
% 89.46/12.91 | | | | | | | | | | | | (437) function(all_344_0) = all_1505_0
% 89.46/12.91 | | | | | | | | | | | | (438) relation(all_344_0) = all_1505_1
% 89.46/12.91 | | | | | | | | | | | | (439) ~ (all_1505_0 = 0) | ~ (all_1505_1 = 0)
% 89.46/12.91 | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_1505_0, all_344_0,
% 89.46/12.91 | | | | | | | | | | | | simplifying with (53), (437) gives:
% 89.46/12.91 | | | | | | | | | | | | (440) all_1505_0 = 0
% 89.46/12.91 | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_1505_1, all_344_0,
% 89.46/12.91 | | | | | | | | | | | | simplifying with (54), (438) gives:
% 89.46/12.91 | | | | | | | | | | | | (441) all_1505_1 = 0
% 89.46/12.91 | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | BETA: splitting (439) gives:
% 89.46/12.91 | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | Case 1:
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | (442) ~ (all_1505_0 = 0)
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | REDUCE: (440), (442) imply:
% 89.46/12.91 | | | | | | | | | | | | | (443) $false
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | CLOSE: (443) is inconsistent.
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | Case 2:
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | (444) ~ (all_1505_1 = 0)
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | REDUCE: (441), (444) imply:
% 89.46/12.91 | | | | | | | | | | | | | (445) $false
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | CLOSE: (445) is inconsistent.
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | End of split
% 89.46/12.91 | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | Case 2:
% 89.46/12.91 | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | (446) all_820_0 = 0 & ( ~ (all_1262_0 = 0) | all_1444_0
% 89.46/12.91 | | | | | | | | | | | | = 0) & ( ~ (all_1262_1 = 0) | all_1444_1 = 0) &
% 89.46/12.91 | | | | | | | | | | | | ( ~ (all_1262_2 = 0) | all_1444_2 = 0) & ( ~
% 89.46/12.91 | | | | | | | | | | | | (all_1262_3 = 0) | all_1444_3 = 0)
% 89.46/12.91 | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | ALPHA: (446) implies:
% 89.46/12.91 | | | | | | | | | | | | (447) all_820_0 = 0
% 89.46/12.91 | | | | | | | | | | | | (448) ~ (all_1262_3 = 0) | all_1444_3 = 0
% 89.46/12.91 | | | | | | | | | | | | (449) ~ (all_1262_2 = 0) | all_1444_2 = 0
% 89.46/12.91 | | | | | | | | | | | | (450) ~ (all_1262_1 = 0) | all_1444_1 = 0
% 89.46/12.91 | | | | | | | | | | | | (451) ~ (all_1262_0 = 0) | all_1444_0 = 0
% 89.46/12.91 | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | BETA: splitting (448) gives:
% 89.46/12.91 | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | Case 1:
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | (452) ~ (all_1262_3 = 0)
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | REDUCE: (364), (452) imply:
% 89.46/12.91 | | | | | | | | | | | | | (453) $false
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | CLOSE: (453) is inconsistent.
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | Case 2:
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | (454) all_1444_3 = 0
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | COMBINE_EQS: (430), (454) imply:
% 89.46/12.91 | | | | | | | | | | | | | (455) all_820_4 = 0
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | BETA: splitting (449) gives:
% 89.46/12.91 | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | Case 1:
% 89.46/12.91 | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | (456) ~ (all_1262_2 = 0)
% 89.46/12.91 | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | REDUCE: (362), (456) imply:
% 89.46/12.91 | | | | | | | | | | | | | | (457) $false
% 89.46/12.91 | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | CLOSE: (457) is inconsistent.
% 89.46/12.91 | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | Case 2:
% 89.46/12.91 | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | (458) all_1444_2 = 0
% 89.46/12.91 | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | COMBINE_EQS: (429), (458) imply:
% 89.46/12.91 | | | | | | | | | | | | | | (459) all_820_3 = 0
% 89.46/12.91 | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | SIMP: (459) implies:
% 89.46/12.91 | | | | | | | | | | | | | | (460) all_820_3 = 0
% 89.46/12.91 | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | BETA: splitting (450) gives:
% 89.46/12.91 | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | Case 1:
% 89.46/12.91 | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | (461) ~ (all_1262_1 = 0)
% 89.46/12.91 | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | REDUCE: (360), (461) imply:
% 89.46/12.91 | | | | | | | | | | | | | | | (462) $false
% 89.46/12.91 | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | CLOSE: (462) is inconsistent.
% 89.46/12.91 | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | Case 2:
% 89.46/12.91 | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | (463) all_1444_1 = 0
% 89.46/12.91 | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | COMBINE_EQS: (428), (463) imply:
% 89.46/12.91 | | | | | | | | | | | | | | | (464) all_820_1 = 0
% 89.46/12.91 | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 89.46/12.91 | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | Case 1:
% 89.46/12.91 | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | (465) ~ (all_820_5 = 0)
% 89.46/12.91 | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | REDUCE: (212), (465) imply:
% 89.46/12.91 | | | | | | | | | | | | | | | | (466) $false
% 89.46/12.91 | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | CLOSE: (466) is inconsistent.
% 89.46/12.91 | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | Case 2:
% 89.46/12.91 | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | (467) ( ~ (all_820_0 = 0) | ~ (all_820_1 = 0) | ~
% 89.46/12.91 | | | | | | | | | | | | | | | | (all_820_2 = 0) | ~ (all_820_3 = 0) | ~
% 89.46/12.91 | | | | | | | | | | | | | | | | (all_820_4 = 0) | all_342_0 = 0) & ( ~
% 89.46/12.91 | | | | | | | | | | | | | | | | (all_342_0 = 0) | (all_820_0 = 0 & all_820_1 = 0
% 89.46/12.91 | | | | | | | | | | | | | | | | & all_820_2 = 0 & all_820_3 = 0 & all_820_4 =
% 89.46/12.91 | | | | | | | | | | | | | | | | 0))
% 89.46/12.91 | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | ALPHA: (467) implies:
% 89.46/12.91 | | | | | | | | | | | | | | | | (468) ~ (all_820_0 = 0) | ~ (all_820_1 = 0) | ~
% 89.46/12.91 | | | | | | | | | | | | | | | | (all_820_2 = 0) | ~ (all_820_3 = 0) | ~
% 89.46/12.91 | | | | | | | | | | | | | | | | (all_820_4 = 0) | all_342_0 = 0
% 89.46/12.91 | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | BETA: splitting (468) gives:
% 89.46/12.91 | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | Case 1:
% 89.46/12.91 | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | (469) ~ (all_820_0 = 0)
% 89.46/12.91 | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | REDUCE: (447), (469) imply:
% 89.46/12.91 | | | | | | | | | | | | | | | | | (470) $false
% 89.46/12.91 | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | CLOSE: (470) is inconsistent.
% 89.46/12.91 | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | Case 2:
% 89.46/12.91 | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | (471) ~ (all_820_1 = 0) | ~ (all_820_2 = 0) | ~
% 89.46/12.91 | | | | | | | | | | | | | | | | | (all_820_3 = 0) | ~ (all_820_4 = 0) | all_342_0 =
% 89.46/12.91 | | | | | | | | | | | | | | | | | 0
% 89.46/12.91 | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | BETA: splitting (471) gives:
% 89.46/12.91 | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | Case 1:
% 89.46/12.91 | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | (472) ~ (all_820_1 = 0)
% 89.46/12.91 | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | REDUCE: (464), (472) imply:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | (473) $false
% 89.46/12.91 | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | CLOSE: (473) is inconsistent.
% 89.46/12.91 | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | Case 2:
% 89.46/12.91 | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | (474) ~ (all_820_2 = 0) | ~ (all_820_3 = 0) | ~
% 89.46/12.91 | | | | | | | | | | | | | | | | | | (all_820_4 = 0) | all_342_0 = 0
% 89.46/12.91 | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | BETA: splitting (451) gives:
% 89.46/12.91 | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | Case 1:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | (475) ~ (all_1262_0 = 0)
% 89.46/12.91 | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | REDUCE: (358), (475) imply:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | (476) $false
% 89.46/12.91 | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | CLOSE: (476) is inconsistent.
% 89.46/12.91 | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | Case 2:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | (477) all_1444_0 = 0
% 89.46/12.91 | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (477) imply:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | (478) all_820_2 = 0
% 89.46/12.91 | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | BETA: splitting (474) gives:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | Case 1:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | (479) ~ (all_820_2 = 0)
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | REDUCE: (478), (479) imply:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | (480) $false
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | CLOSE: (480) is inconsistent.
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | Case 2:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | (481) ~ (all_820_3 = 0) | ~ (all_820_4 = 0) |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | all_342_0 = 0
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | BETA: splitting (481) gives:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | Case 1:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | (482) ~ (all_820_3 = 0)
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | REDUCE: (460), (482) imply:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | (483) $false
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | CLOSE: (483) is inconsistent.
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | Case 2:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | (484) ~ (all_820_4 = 0) | all_342_0 = 0
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (484) gives:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | | (485) ~ (all_820_4 = 0)
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (455), (485) imply:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | | (486) $false
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (486) is inconsistent.
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | | (487) all_342_0 = 0
% 89.46/12.91 | | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.92 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (487) imply:
% 89.46/12.92 | | | | | | | | | | | | | | | | | | | | | | (488) $false
% 89.46/12.92 | | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.92 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (488) is inconsistent.
% 89.46/12.92 | | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.92 | | | | | | | | | | | | | | | | | | | | | End of split
% 89.46/12.92 | | | | | | | | | | | | | | | | | | | | |
% 89.46/12.92 | | | | | | | | | | | | | | | | | | | | End of split
% 89.46/12.92 | | | | | | | | | | | | | | | | | | | |
% 89.46/12.92 | | | | | | | | | | | | | | | | | | | End of split
% 89.46/12.92 | | | | | | | | | | | | | | | | | | |
% 89.46/12.92 | | | | | | | | | | | | | | | | | | End of split
% 89.46/12.92 | | | | | | | | | | | | | | | | | |
% 89.46/12.92 | | | | | | | | | | | | | | | | | End of split
% 89.46/12.92 | | | | | | | | | | | | | | | | |
% 89.46/12.92 | | | | | | | | | | | | | | | | End of split
% 89.46/12.92 | | | | | | | | | | | | | | | |
% 89.46/12.92 | | | | | | | | | | | | | | | End of split
% 89.46/12.92 | | | | | | | | | | | | | | |
% 89.46/12.92 | | | | | | | | | | | | | | End of split
% 89.46/12.92 | | | | | | | | | | | | | |
% 89.46/12.92 | | | | | | | | | | | | | End of split
% 89.46/12.92 | | | | | | | | | | | | |
% 89.46/12.92 | | | | | | | | | | | | End of split
% 89.46/12.92 | | | | | | | | | | | |
% 89.46/12.92 | | | | | | | | | | | End of split
% 89.46/12.92 | | | | | | | | | | |
% 89.46/12.92 | | | | | | | | | | End of split
% 89.46/12.92 | | | | | | | | | |
% 89.46/12.92 | | | | | | | | | End of split
% 89.46/12.92 | | | | | | | | |
% 89.46/12.92 | | | | | | | | End of split
% 89.46/12.92 | | | | | | | |
% 89.46/12.92 | | | | | | | End of split
% 89.46/12.92 | | | | | | |
% 89.46/12.92 | | | | | | End of split
% 89.46/12.92 | | | | | |
% 89.46/12.92 | | | | | End of split
% 89.46/12.92 | | | | |
% 89.46/12.92 | | | | End of split
% 89.46/12.92 | | | |
% 89.46/12.92 | | | End of split
% 89.46/12.92 | | |
% 89.46/12.92 | | Case 2:
% 89.46/12.92 | | |
% 89.46/12.92 | | | (489) ~ (all_882_2 = 0)
% 89.46/12.92 | | |
% 89.46/12.92 | | | REDUCE: (210), (489) imply:
% 89.46/12.92 | | | (490) $false
% 89.46/12.92 | | |
% 89.46/12.92 | | | CLOSE: (490) is inconsistent.
% 89.46/12.92 | | |
% 89.46/12.92 | | End of split
% 89.46/12.92 | |
% 89.46/12.92 | End of split
% 89.46/12.92 |
% 89.46/12.92 End of proof
% 89.46/12.92 % SZS output end Proof for theBenchmark
% 89.46/12.92
% 89.46/12.92 12315ms
%------------------------------------------------------------------------------