TSTP Solution File: SEU220+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU220+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 : n013.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 17:43:23 EDT 2023
% Result : Theorem 43.43s 6.66s
% Output : Proof 66.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU220+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 13:19:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.77/1.64 Prover 1: Preprocessing ...
% 6.54/1.65 Prover 4: Preprocessing ...
% 6.62/1.68 Prover 6: Preprocessing ...
% 6.62/1.68 Prover 2: Preprocessing ...
% 6.62/1.68 Prover 5: Preprocessing ...
% 6.62/1.68 Prover 3: Preprocessing ...
% 6.62/1.68 Prover 0: Preprocessing ...
% 18.20/3.28 Prover 1: Warning: ignoring some quantifiers
% 19.54/3.48 Prover 1: Constructing countermodel ...
% 20.01/3.57 Prover 6: Proving ...
% 20.01/3.61 Prover 3: Warning: ignoring some quantifiers
% 21.28/3.66 Prover 3: Constructing countermodel ...
% 21.28/3.69 Prover 5: Proving ...
% 23.96/4.01 Prover 2: Proving ...
% 25.02/4.20 Prover 4: Warning: ignoring some quantifiers
% 25.59/4.31 Prover 4: Constructing countermodel ...
% 29.39/4.83 Prover 0: Proving ...
% 43.43/6.66 Prover 3: proved (6013ms)
% 43.43/6.66
% 43.43/6.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.43/6.66
% 44.04/6.67 Prover 6: stopped
% 44.04/6.67 Prover 0: stopped
% 44.04/6.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 44.04/6.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 44.04/6.68 Prover 2: stopped
% 44.16/6.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 44.16/6.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 44.50/6.73 Prover 5: stopped
% 44.50/6.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 47.22/7.11 Prover 13: Preprocessing ...
% 47.51/7.12 Prover 11: Preprocessing ...
% 47.51/7.20 Prover 7: Preprocessing ...
% 47.51/7.21 Prover 10: Preprocessing ...
% 48.17/7.23 Prover 8: Preprocessing ...
% 50.49/7.64 Prover 10: Warning: ignoring some quantifiers
% 50.49/7.71 Prover 10: Constructing countermodel ...
% 51.23/7.80 Prover 7: Warning: ignoring some quantifiers
% 52.78/7.82 Prover 13: Warning: ignoring some quantifiers
% 52.78/7.83 Prover 8: Warning: ignoring some quantifiers
% 52.91/7.84 Prover 7: Constructing countermodel ...
% 52.91/7.86 Prover 13: Constructing countermodel ...
% 52.91/7.88 Prover 8: Constructing countermodel ...
% 60.37/8.81 Prover 11: Warning: ignoring some quantifiers
% 61.47/8.94 Prover 11: Constructing countermodel ...
% 65.33/9.45 Prover 10: Found proof (size 249)
% 65.33/9.45 Prover 10: proved (2763ms)
% 65.33/9.45 Prover 11: stopped
% 65.33/9.45 Prover 7: stopped
% 65.33/9.45 Prover 13: stopped
% 65.33/9.45 Prover 1: stopped
% 65.33/9.45 Prover 4: stopped
% 65.33/9.46 Prover 8: stopped
% 65.33/9.46
% 65.33/9.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 65.33/9.46
% 65.33/9.51 % SZS output start Proof for theBenchmark
% 65.33/9.52 Assumptions after simplification:
% 65.33/9.52 ---------------------------------
% 65.33/9.52
% 65.33/9.52 (d1_relat_1)
% 65.33/9.55 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~
% 65.33/9.55 in(v1, v0) | ? [v2: $i] : ? [v3: $i] : (ordered_pair(v2, v3) = v1 & $i(v3)
% 65.33/9.55 & $i(v2))) & ? [v0: $i] : ( ~ $i(v0) | relation(v0) | ? [v1: $i] :
% 65.33/9.55 ($i(v1) & in(v1, v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3)
% 65.33/9.55 = v1) | ~ $i(v3) | ~ $i(v2))))
% 65.33/9.55
% 65.33/9.55 (d3_relat_1)
% 65.76/9.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 65.76/9.55 (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 65.76/9.55 | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) |
% 65.76/9.55 in(v4, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 65.76/9.55 relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i]
% 65.76/9.55 : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) &
% 65.76/9.55 in(v4, v0) & ~ in(v4, v1)))
% 65.76/9.55
% 65.76/9.55 (d4_funct_1)
% 65.76/9.55 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 65.76/9.55 [v4: $i] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~
% 65.76/9.55 $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) | ~
% 65.76/9.55 in(v2, v1) | ? [v5: $i] : (( ~ in(v4, v0) | (v5 = v3 & apply(v0, v2) = v3))
% 65.76/9.55 & (in(v4, v0) | ( ~ (v5 = v3) & apply(v0, v2) = v5 & $i(v5))))) & ! [v0:
% 65.76/9.55 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~
% 65.76/9.55 (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ $i(v3) | ~ $i(v2) |
% 65.76/9.55 ~ $i(v0) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) & ! [v0: $i] :
% 65.76/9.55 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~
% 65.76/9.55 (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ $i(v2) | ~ $i(v0) |
% 65.76/9.55 ~ relation(v0) | ~ function(v0) | in(v2, v1))
% 65.76/9.55
% 65.76/9.56 (d4_relat_1)
% 65.76/9.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 65.76/9.56 (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~
% 65.76/9.56 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v2,
% 65.76/9.56 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) =
% 65.76/9.56 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1)
% 65.76/9.56 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) &
% 65.76/9.56 in(v4, v0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 65.76/9.56 (relation_dom(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3:
% 65.76/9.56 $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ in(v3, v0) | !
% 65.76/9.56 [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v3, v6) = v7) | ~ $i(v6) |
% 65.76/9.56 ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & $i(v5) &
% 65.76/9.56 in(v5, v1)))))
% 65.76/9.56
% 65.76/9.56 (d5_relat_1)
% 65.76/9.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 65.76/9.56 (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ $i(v3) | ~
% 65.76/9.56 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v2,
% 65.76/9.56 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v0) =
% 65.76/9.56 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1)
% 65.76/9.56 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v3, v2) = v4 & $i(v4) & $i(v3) &
% 65.76/9.56 in(v4, v0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 65.76/9.56 (relation_rng(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3:
% 65.76/9.56 $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ in(v3, v0) | !
% 65.76/9.56 [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v3) = v7) | ~ $i(v6) |
% 65.76/9.56 ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & $i(v5) &
% 65.76/9.56 in(v5, v1)))))
% 65.76/9.56
% 65.76/9.56 (d7_relat_1)
% 65.76/9.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 65.76/9.57 (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) |
% 65.76/9.57 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ relation(v0) | ~
% 65.76/9.57 in(v4, v1) | ? [v5: $i] : (ordered_pair(v3, v2) = v5 & $i(v5) & in(v5,
% 65.76/9.57 v0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 65.76/9.57 $i] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~
% 65.76/9.57 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~
% 65.76/9.57 relation(v0) | in(v4, v1) | ? [v5: $i] : (ordered_pair(v3, v2) = v5 &
% 65.76/9.57 $i(v5) & ~ in(v5, v0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 =
% 65.76/9.57 v1 | ~ (relation_inverse(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 65.76/9.57 relation(v2) | ~ relation(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 65.76/9.57 ? [v6: $i] : ($i(v4) & $i(v3) & ((ordered_pair(v4, v3) = v6 & $i(v6) &
% 65.76/9.57 in(v6, v0)) | (ordered_pair(v3, v4) = v5 & $i(v5) & in(v5, v2))) &
% 65.76/9.57 ((ordered_pair(v4, v3) = v6 & $i(v6) & ~ in(v6, v0)) | (ordered_pair(v3,
% 65.76/9.57 v4) = v5 & $i(v5) & ~ in(v5, v2)))))
% 65.76/9.57
% 65.76/9.57 (d9_funct_1)
% 65.76/9.57 ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~
% 65.76/9.57 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | (relation_inverse(v0) =
% 65.76/9.57 v1 & $i(v1)))
% 65.76/9.57
% 65.76/9.57 (dt_k2_funct_1)
% 65.76/9.57 ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~
% 65.76/9.57 relation(v0) | ~ function(v0) | relation(v1)) & ! [v0: $i] : ! [v1: $i] :
% 65.76/9.57 ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ relation(v0) | ~
% 65.76/9.57 function(v0) | function(v1))
% 65.76/9.57
% 65.76/9.57 (involutiveness_k4_relat_1)
% 65.76/9.57 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_inverse(v0) = v1) | ~ $i(v0) | ~
% 65.76/9.57 relation(v0) | relation_inverse(v1) = v0)
% 65.76/9.57
% 65.76/9.57 (t20_relat_1)
% 65.76/9.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 65.76/9.57 (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ $i(v2) | ~
% 65.76/9.57 $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) & ! [v0:
% 65.76/9.57 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 65.76/9.57 (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ $i(v2) | ~
% 65.76/9.57 $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ in(v3, v2) | ? [v5: $i] :
% 65.76/9.57 (relation_dom(v2) = v5 & $i(v5) & in(v0, v5)))
% 65.76/9.57
% 65.76/9.57 (t22_funct_1)
% 65.76/9.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 65.76/9.58 (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ $i(v2) |
% 65.76/9.58 ~ $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) |
% 65.76/9.58 ~ function(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v4 &
% 65.76/9.58 apply(v2, v0) = v6 & apply(v1, v6) = v4 & $i(v6) & $i(v4)) |
% 65.76/9.58 (relation_dom(v3) = v5 & $i(v5) & ~ in(v0, v5))))
% 65.76/9.58
% 65.76/9.58 (t23_funct_1)
% 65.76/9.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (apply(v1, v0) = v2) | ~ $i(v1)
% 65.76/9.58 | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ? [v3: $i] :
% 65.76/9.58 (relation_dom(v1) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 65.76/9.58 ( ~ (relation_composition(v1, v4) = v5) | ~ (apply(v5, v0) = v6) | ~
% 65.76/9.58 $i(v4) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | (apply(v4,
% 65.76/9.58 v2) = v6 & $i(v6)))))
% 65.76/9.58
% 65.76/9.58 (t25_relat_1)
% 65.76/9.58 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 65.76/9.58 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] :
% 65.76/9.58 ! [v4: $i] : ( ~ (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3)
% 65.76/9.58 | ~ relation(v3) | subset(v1, v4)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 65.76/9.58 (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3) | ~
% 65.76/9.58 relation(v3) | ? [v5: $i] : (relation_dom(v3) = v5 & $i(v5) &
% 65.76/9.58 subset(v2, v5)))))
% 65.76/9.58
% 65.76/9.58 (t33_zfmisc_1)
% 65.76/9.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1
% 65.76/9.58 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4) | ~
% 65.76/9.58 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : !
% 65.76/9.58 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (ordered_pair(v2, v3) =
% 65.76/9.58 v4) | ~ (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 65.76/9.58 ~ $i(v0))
% 65.76/9.58
% 65.76/9.58 (t44_relat_1)
% 65.76/9.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 65.76/9.58 (relation_composition(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ $i(v2)
% 65.76/9.58 | ~ $i(v0) | ~ relation(v2) | ~ relation(v0) | ? [v4: $i] :
% 65.76/9.58 (relation_dom(v3) = v4 & $i(v4) & subset(v4, v1)))
% 65.76/9.58
% 65.76/9.58 (t46_relat_1)
% 65.76/9.58 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 65.76/9.58 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] :
% 65.76/9.58 ! [v4: $i] : ( ~ (relation_composition(v0, v3) = v4) | ~ $i(v3) | ~
% 65.76/9.58 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v2 & relation_dom(v4)
% 65.76/9.58 = v2) | (relation_dom(v3) = v5 & $i(v5) & ~ subset(v1, v5))))))
% 65.76/9.58
% 65.76/9.58 (t47_relat_1)
% 65.76/9.58 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 65.76/9.58 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] :
% 65.76/9.58 ! [v4: $i] : ( ~ (relation_composition(v3, v0) = v4) | ~ $i(v3) | ~
% 65.76/9.58 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v1 & relation_rng(v4)
% 65.76/9.58 = v1 & $i(v1)) | (relation_rng(v3) = v5 & $i(v5) & ~ subset(v2,
% 65.76/9.58 v5))))))
% 65.76/9.58
% 65.76/9.58 (t54_funct_1)
% 65.76/9.59 ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~
% 65.76/9.59 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3:
% 65.76/9.59 $i] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & $i(v3) & $i(v2) &
% 65.76/9.59 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = v6 | ~
% 65.76/9.59 (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) =
% 65.76/9.59 v5) | ~ $i(v6) | ~ $i(v5) | ~ $i(v1) | ~ relation(v1) | ~
% 65.76/9.59 function(v1) | ~ in(v6, v3)) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 65.76/9.59 : ! [v7: $i] : (v7 = v5 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5)
% 65.76/9.59 = v6) | ~ (apply(v0, v6) = v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v1) |
% 65.76/9.59 ~ relation(v1) | ~ function(v1) | ~ in(v5, v2)) & ! [v4: $i] : !
% 65.76/9.59 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (relation_dom(v1) = v4) | ~
% 65.76/9.59 (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ $i(v6) | ~ $i(v5) |
% 65.76/9.59 ~ $i(v1) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3) | in(v5,
% 65.76/9.59 v2)) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 65.76/9.59 (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) =
% 65.76/9.59 v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v1) | ~ relation(v1) | ~
% 65.76/9.59 function(v1) | ~ in(v5, v2) | in(v6, v3)) & ! [v4: $i] : (v4 = v2 | ~
% 65.76/9.59 (relation_dom(v1) = v4) | ~ $i(v1) | ~ relation(v1) | ~ function(v1))
% 65.76/9.59 & ! [v4: $i] : (v4 = v1 | ~ (relation_dom(v4) = v2) | ~ $i(v4) | ~
% 65.76/9.59 relation(v4) | ~ function(v4) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 65.76/9.59 : ? [v8: $i] : ($i(v6) & $i(v5) & ((v8 = v5 & apply(v0, v6) = v5 &
% 65.76/9.59 in(v6, v3) & ( ~ in(v5, v2) | ( ~ (v7 = v6) & apply(v4, v5) = v7 &
% 65.76/9.59 $i(v7)))) | (v7 = v6 & apply(v4, v5) = v6 & in(v5, v2) & ( ~
% 65.76/9.59 in(v6, v3) | ( ~ (v8 = v5) & apply(v0, v6) = v8 & $i(v8)))))))))
% 65.76/9.59
% 65.76/9.59 (t55_funct_1)
% 65.76/9.59 ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~
% 65.76/9.59 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3:
% 65.76/9.59 $i] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) =
% 65.76/9.59 v2 & relation_dom(v0) = v3 & $i(v3) & $i(v2)))
% 65.76/9.59
% 65.76/9.59 (t57_funct_1)
% 65.76/9.59 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 65.76/9.59 $i] : ? [v6: $i] : ? [v7: $i] : (function_inverse(v1) = v3 &
% 65.76/9.59 relation_rng(v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & one_to_one(v1) &
% 65.76/9.59 relation(v1) & function(v1) & in(v0, v2) & (( ~ (v7 = v0) &
% 65.76/9.59 relation_composition(v3, v1) = v6 & apply(v6, v0) = v7 & $i(v7) &
% 65.76/9.59 $i(v6)) | ( ~ (v5 = v0) & apply(v3, v0) = v4 & apply(v1, v4) = v5 &
% 65.76/9.59 $i(v5) & $i(v4))))
% 65.76/9.59
% 65.76/9.59 (t8_funct_1)
% 65.76/9.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 65.76/9.59 (apply(v2, v0) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ $i(v2) | ~
% 65.76/9.59 $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ function(v2) | ? [v5: $i] : (( ~
% 65.76/9.59 (v4 = v1) | in(v3, v2) | (relation_dom(v2) = v5 & $i(v5) & ~ in(v0,
% 65.76/9.59 v5))) & ( ~ in(v3, v2) | (v4 = v1 & relation_dom(v2) = v5 & $i(v5) &
% 65.76/9.59 in(v0, v5)))))
% 65.76/9.59
% 65.76/9.59 (function-axioms)
% 66.01/9.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 66.01/9.60 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3,
% 66.01/9.60 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 66.01/9.60 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) =
% 66.01/9.60 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 66.01/9.60 ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & !
% 66.01/9.60 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.01/9.60 (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) =
% 66.01/9.60 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 66.01/9.60 ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) =
% 66.01/9.60 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 66.01/9.60 ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) &
% 66.01/9.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.01/9.60 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 66.01/9.60 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2)
% 66.01/9.60 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 66.01/9.60 : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~
% 66.01/9.60 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 66.01/9.60 : ! [v3: $i] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~
% 66.01/9.60 (relation_inverse_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 66.01/9.60 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~
% 66.01/9.60 (relation_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 66.01/9.60 ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~
% 66.01/9.60 (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 66.01/9.60 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1)
% 66.01/9.60 | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 66.01/9.60 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~
% 66.01/9.60 (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 66.01/9.60 [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~
% 66.01/9.60 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 66.01/9.60 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3,
% 66.01/9.60 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 66.01/9.60 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 66.01/9.60 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 66.01/9.60 (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) & ! [v0: $i]
% 66.01/9.60 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~
% 66.01/9.60 (relation_inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 66.01/9.60 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & !
% 66.01/9.60 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) |
% 66.01/9.60 ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 66.01/9.60 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] : ! [v1:
% 66.01/9.60 $i] : ! [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~
% 66.01/9.60 (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 66.01/9.60 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i]
% 66.01/9.60 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 66.01/9.60 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 66.01/9.60 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1:
% 66.01/9.60 $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) =
% 66.01/9.60 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 66.01/9.60 (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 66.01/9.60
% 66.01/9.60 Further assumptions not needed in the proof:
% 66.01/9.60 --------------------------------------------
% 66.01/9.60 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_funct_1, cc1_relat_1,
% 66.01/9.60 cc2_funct_1, commutativity_k2_tarski, commutativity_k2_xboole_0,
% 66.01/9.60 commutativity_k3_xboole_0, d10_relat_1, d10_xboole_0, d11_relat_1, d12_relat_1,
% 66.01/9.60 d13_relat_1, d14_relat_1, d1_setfam_1, d1_tarski, d1_xboole_0, d1_zfmisc_1,
% 66.01/9.60 d2_relat_1, d2_subset_1, d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_tarski,
% 66.01/9.60 d3_xboole_0, d4_subset_1, d4_tarski, d4_xboole_0, d5_subset_1, d5_tarski,
% 66.01/9.60 d6_relat_1, d7_xboole_0, d8_relat_1, d8_setfam_1, d8_xboole_0, dt_k10_relat_1,
% 66.01/9.60 dt_k1_funct_1, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0,
% 66.01/9.60 dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0,
% 66.01/9.60 dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0,
% 66.01/9.60 dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, dt_k5_relat_1, dt_k5_setfam_1,
% 66.01/9.60 dt_k6_relat_1, dt_k6_setfam_1, dt_k6_subset_1, dt_k7_relat_1, dt_k7_setfam_1,
% 66.01/9.60 dt_k8_relat_1, dt_k9_relat_1, dt_m1_subset_1, existence_m1_subset_1,
% 66.01/9.60 fc10_relat_1, fc11_relat_1, fc12_relat_1, fc1_funct_1, fc1_relat_1,
% 66.01/9.60 fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_funct_1, fc2_relat_1,
% 66.01/9.60 fc2_subset_1, fc2_xboole_0, fc3_funct_1, fc3_subset_1, fc3_xboole_0,
% 66.01/9.60 fc4_relat_1, fc4_subset_1, fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1,
% 66.01/9.60 fc9_relat_1, idempotence_k2_xboole_0, idempotence_k3_xboole_0,
% 66.01/9.60 involutiveness_k3_subset_1, involutiveness_k7_setfam_1,
% 66.01/9.60 irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1,
% 66.01/9.60 l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_subset_1, l3_zfmisc_1, l4_zfmisc_1,
% 66.01/9.60 l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, rc1_funct_1, rc1_relat_1,
% 66.01/9.60 rc1_subset_1, rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_subset_1,
% 66.01/9.60 rc2_xboole_0, rc3_funct_1, rc3_relat_1, redefinition_k5_setfam_1,
% 66.01/9.60 redefinition_k6_setfam_1, redefinition_k6_subset_1, reflexivity_r1_tarski,
% 66.01/9.60 symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, t115_relat_1, t116_relat_1,
% 66.01/9.60 t117_relat_1, t118_relat_1, t118_zfmisc_1, t119_relat_1, t119_zfmisc_1,
% 66.01/9.60 t12_xboole_1, t136_zfmisc_1, t140_relat_1, t143_relat_1, t144_relat_1,
% 66.01/9.60 t145_relat_1, t146_relat_1, t160_relat_1, t166_relat_1, t167_relat_1,
% 66.01/9.60 t174_relat_1, t178_relat_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_subset,
% 66.01/9.60 t1_xboole_1, t1_zfmisc_1, t21_funct_1, t21_relat_1, t26_xboole_1, t28_xboole_1,
% 66.01/9.60 t2_boole, t2_subset, t2_tarski, t2_xboole_1, t30_relat_1, t33_xboole_1,
% 66.01/9.60 t34_funct_1, t35_funct_1, t36_xboole_1, t37_relat_1, t37_xboole_1, t37_zfmisc_1,
% 66.01/9.60 t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_subset, t3_xboole_0,
% 66.01/9.60 t3_xboole_1, t40_xboole_1, t43_subset_1, t45_relat_1, t45_xboole_1,
% 66.01/9.60 t46_setfam_1, t46_zfmisc_1, t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole,
% 66.01/9.60 t4_subset, t4_xboole_0, t50_subset_1, t54_subset_1, t56_relat_1, t5_subset,
% 66.01/9.60 t60_relat_1, t60_xboole_1, t63_xboole_1, t64_relat_1, t65_relat_1, t65_zfmisc_1,
% 66.01/9.60 t69_enumset1, t6_boole, t6_zfmisc_1, t71_relat_1, t74_relat_1, t7_boole,
% 66.01/9.60 t7_xboole_1, t83_xboole_1, t86_relat_1, t88_relat_1, t8_boole, t8_xboole_1,
% 66.01/9.60 t8_zfmisc_1, t90_relat_1, t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1,
% 66.01/9.60 t9_tarski, t9_zfmisc_1
% 66.01/9.60
% 66.01/9.60 Those formulas are unsatisfiable:
% 66.01/9.60 ---------------------------------
% 66.01/9.60
% 66.01/9.60 Begin of proof
% 66.01/9.60 |
% 66.01/9.60 | ALPHA: (d1_relat_1) implies:
% 66.01/9.60 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v0) |
% 66.01/9.60 | ~ in(v1, v0) | ? [v2: $i] : ? [v3: $i] : (ordered_pair(v2, v3) = v1
% 66.01/9.60 | & $i(v3) & $i(v2)))
% 66.01/9.60 |
% 66.01/9.61 | ALPHA: (d3_relat_1) implies:
% 66.01/9.61 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) |
% 66.01/9.61 | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 66.01/9.61 | $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) &
% 66.01/9.61 | in(v4, v0) & ~ in(v4, v1)))
% 66.01/9.61 |
% 66.01/9.61 | ALPHA: (d4_funct_1) implies:
% 66.01/9.61 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 66.01/9.61 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~
% 66.01/9.61 | $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) |
% 66.01/9.61 | ~ in(v2, v1) | ? [v5: $i] : (( ~ in(v4, v0) | (v5 = v3 & apply(v0,
% 66.01/9.61 | v2) = v3)) & (in(v4, v0) | ( ~ (v5 = v3) & apply(v0, v2) = v5
% 66.01/9.61 | & $i(v5)))))
% 66.01/9.61 |
% 66.01/9.61 | ALPHA: (d4_relat_1) implies:
% 66.01/9.61 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) = v1) |
% 66.01/9.61 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1) |
% 66.01/9.61 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) &
% 66.01/9.61 | $i(v3) & in(v4, v0)))
% 66.01/9.61 |
% 66.01/9.61 | ALPHA: (d5_relat_1) implies:
% 66.01/9.61 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v0) = v1) |
% 66.01/9.61 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1) |
% 66.01/9.61 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v3, v2) = v4 & $i(v4) &
% 66.01/9.61 | $i(v3) & in(v4, v0)))
% 66.01/9.61 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 66.01/9.61 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~
% 66.01/9.61 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~
% 66.01/9.61 | in(v4, v0) | in(v2, v1))
% 66.01/9.61 |
% 66.01/9.61 | ALPHA: (d7_relat_1) implies:
% 66.01/9.61 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 66.01/9.61 | ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~
% 66.01/9.61 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~
% 66.01/9.61 | relation(v0) | ~ in(v4, v1) | ? [v5: $i] : (ordered_pair(v3, v2) =
% 66.01/9.61 | v5 & $i(v5) & in(v5, v0)))
% 66.01/9.61 |
% 66.01/9.61 | ALPHA: (dt_k2_funct_1) implies:
% 66.01/9.61 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0)
% 66.01/9.61 | | ~ relation(v0) | ~ function(v0) | function(v1))
% 66.01/9.61 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0)
% 66.01/9.61 | | ~ relation(v0) | ~ function(v0) | relation(v1))
% 66.01/9.61 |
% 66.01/9.61 | ALPHA: (t20_relat_1) implies:
% 66.01/9.61 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 66.01/9.61 | ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~
% 66.01/9.61 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ in(v3, v2) |
% 66.01/9.61 | ? [v5: $i] : (relation_dom(v2) = v5 & $i(v5) & in(v0, v5)))
% 66.01/9.61 |
% 66.01/9.61 | ALPHA: (t33_zfmisc_1) implies:
% 66.01/9.61 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 66.01/9.61 | (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) =
% 66.01/9.61 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 66.01/9.61 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 66.01/9.61 | (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) =
% 66.01/9.61 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 66.01/9.61 |
% 66.01/9.61 | ALPHA: (function-axioms) implies:
% 66.01/9.62 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 66.01/9.62 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 66.01/9.62 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 66.01/9.62 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 66.01/9.62 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.01/9.62 | (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 66.01/9.62 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.01/9.62 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 66.01/9.62 |
% 66.01/9.62 | DELTA: instantiating (t57_funct_1) with fresh symbols all_256_0, all_256_1,
% 66.01/9.62 | all_256_2, all_256_3, all_256_4, all_256_5, all_256_6, all_256_7 gives:
% 66.01/9.62 | (17) function_inverse(all_256_6) = all_256_4 & relation_rng(all_256_6) =
% 66.01/9.62 | all_256_5 & $i(all_256_4) & $i(all_256_5) & $i(all_256_6) &
% 66.01/9.62 | $i(all_256_7) & one_to_one(all_256_6) & relation(all_256_6) &
% 66.01/9.62 | function(all_256_6) & in(all_256_7, all_256_5) & (( ~ (all_256_0 =
% 66.01/9.62 | all_256_7) & relation_composition(all_256_4, all_256_6) =
% 66.01/9.62 | all_256_1 & apply(all_256_1, all_256_7) = all_256_0 &
% 66.01/9.62 | $i(all_256_0) & $i(all_256_1)) | ( ~ (all_256_2 = all_256_7) &
% 66.01/9.62 | apply(all_256_4, all_256_7) = all_256_3 & apply(all_256_6,
% 66.01/9.62 | all_256_3) = all_256_2 & $i(all_256_2) & $i(all_256_3)))
% 66.01/9.62 |
% 66.01/9.62 | ALPHA: (17) implies:
% 66.01/9.62 | (18) in(all_256_7, all_256_5)
% 66.01/9.62 | (19) function(all_256_6)
% 66.01/9.62 | (20) relation(all_256_6)
% 66.01/9.62 | (21) one_to_one(all_256_6)
% 66.01/9.62 | (22) $i(all_256_7)
% 66.01/9.62 | (23) $i(all_256_6)
% 66.01/9.62 | (24) $i(all_256_5)
% 66.01/9.62 | (25) relation_rng(all_256_6) = all_256_5
% 66.01/9.62 | (26) function_inverse(all_256_6) = all_256_4
% 66.01/9.62 | (27) ( ~ (all_256_0 = all_256_7) & relation_composition(all_256_4,
% 66.01/9.62 | all_256_6) = all_256_1 & apply(all_256_1, all_256_7) = all_256_0 &
% 66.01/9.62 | $i(all_256_0) & $i(all_256_1)) | ( ~ (all_256_2 = all_256_7) &
% 66.01/9.62 | apply(all_256_4, all_256_7) = all_256_3 & apply(all_256_6,
% 66.01/9.62 | all_256_3) = all_256_2 & $i(all_256_2) & $i(all_256_3))
% 66.01/9.62 |
% 66.01/9.62 | GROUND_INST: instantiating (2) with all_256_6, all_256_6, simplifying with
% 66.01/9.62 | (20), (23) gives:
% 66.01/9.62 | (28) subset(all_256_6, all_256_6)
% 66.01/9.62 |
% 66.01/9.62 | GROUND_INST: instantiating (5) with all_256_6, all_256_5, all_256_7,
% 66.01/9.62 | simplifying with (18), (20), (22), (23), (24), (25) gives:
% 66.01/9.62 | (29) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, all_256_7) = v1 & $i(v1)
% 66.01/9.62 | & $i(v0) & in(v1, all_256_6))
% 66.01/9.62 |
% 66.01/9.62 | GROUND_INST: instantiating (t47_relat_1) with all_256_6, all_256_5,
% 66.01/9.62 | simplifying with (20), (23), (25) gives:
% 66.01/9.62 | (30) ? [v0: $i] : (relation_dom(all_256_6) = v0 & $i(v0) & ! [v1: $i] :
% 66.01/9.62 | ! [v2: $i] : ( ~ (relation_composition(v1, all_256_6) = v2) | ~
% 66.01/9.62 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: int] : ((v4 =
% 66.01/9.62 | all_256_5 & relation_rng(v2) = all_256_5 & $i(all_256_5)) |
% 66.01/9.62 | (relation_rng(v1) = v3 & $i(v3) & ~ subset(v0, v3)))))
% 66.01/9.62 |
% 66.01/9.63 | GROUND_INST: instantiating (t46_relat_1) with all_256_6, all_256_5,
% 66.01/9.63 | simplifying with (20), (23), (25) gives:
% 66.01/9.63 | (31) ? [v0: $i] : (relation_dom(all_256_6) = v0 & $i(v0) & ! [v1: $i] :
% 66.01/9.63 | ! [v2: $i] : ( ~ (relation_composition(all_256_6, v1) = v2) | ~
% 66.01/9.63 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = v0 &
% 66.01/9.63 | relation_dom(v2) = v0) | (relation_dom(v1) = v3 & $i(v3) & ~
% 66.01/9.63 | subset(all_256_5, v3)))))
% 66.01/9.63 |
% 66.01/9.63 | GROUND_INST: instantiating (t25_relat_1) with all_256_6, all_256_5,
% 66.01/9.63 | simplifying with (20), (23), (25) gives:
% 66.01/9.63 | (32) ? [v0: $i] : (relation_dom(all_256_6) = v0 & $i(v0) & ! [v1: $i] :
% 66.01/9.63 | ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~
% 66.01/9.63 | subset(all_256_6, v1) | ~ relation(v1) | subset(all_256_5, v2)) &
% 66.01/9.63 | ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1)
% 66.01/9.63 | | ~ subset(all_256_6, v1) | ~ relation(v1) | ? [v3: $i] :
% 66.01/9.63 | (relation_dom(v1) = v3 & $i(v3) & subset(v0, v3))))
% 66.01/9.63 |
% 66.01/9.63 | GROUND_INST: instantiating (t55_funct_1) with all_256_6, all_256_4,
% 66.01/9.63 | simplifying with (19), (20), (21), (23), (26) gives:
% 66.01/9.63 | (33) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_256_4) = v1 &
% 66.01/9.63 | relation_rng(all_256_6) = v0 & relation_dom(all_256_4) = v0 &
% 66.01/9.63 | relation_dom(all_256_6) = v1 & $i(v1) & $i(v0))
% 66.01/9.63 |
% 66.01/9.63 | GROUND_INST: instantiating (t54_funct_1) with all_256_6, all_256_4,
% 66.01/9.63 | simplifying with (19), (20), (21), (23), (26) gives:
% 66.01/9.63 | (34) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_256_6) = v0 &
% 66.01/9.63 | relation_dom(all_256_6) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 66.01/9.63 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 66.01/9.63 | (relation_dom(all_256_4) = v2) | ~ (apply(all_256_4, v3) = v5) |
% 66.01/9.63 | ~ (apply(all_256_6, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~
% 66.01/9.63 | $i(all_256_4) | ~ relation(all_256_4) | ~ function(all_256_4) |
% 66.01/9.63 | ~ in(v4, v1)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 66.01/9.63 | $i] : (v5 = v3 | ~ (relation_dom(all_256_4) = v2) | ~
% 66.01/9.63 | (apply(all_256_4, v3) = v4) | ~ (apply(all_256_6, v4) = v5) | ~
% 66.01/9.63 | $i(v4) | ~ $i(v3) | ~ $i(all_256_4) | ~ relation(all_256_4) |
% 66.01/9.63 | ~ function(all_256_4) | ~ in(v3, v0)) & ! [v2: $i] : ! [v3: $i]
% 66.01/9.63 | : ! [v4: $i] : ! [v5: $i] : ( ~ (relation_dom(all_256_4) = v2) |
% 66.01/9.63 | ~ (apply(all_256_4, v3) = v5) | ~ (apply(all_256_6, v4) = v3) |
% 66.01/9.63 | ~ $i(v4) | ~ $i(v3) | ~ $i(all_256_4) | ~ relation(all_256_4) |
% 66.01/9.63 | ~ function(all_256_4) | ~ in(v4, v1) | in(v3, v0)) & ! [v2: $i]
% 66.01/9.63 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 66.01/9.63 | (relation_dom(all_256_4) = v2) | ~ (apply(all_256_4, v3) = v4) |
% 66.01/9.63 | ~ (apply(all_256_6, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 66.01/9.63 | $i(all_256_4) | ~ relation(all_256_4) | ~ function(all_256_4) |
% 66.01/9.63 | ~ in(v3, v0) | in(v4, v1)) & ! [v2: $i] : (v2 = v0 | ~
% 66.01/9.63 | (relation_dom(all_256_4) = v2) | ~ $i(all_256_4) | ~
% 66.01/9.63 | relation(all_256_4) | ~ function(all_256_4)) & ! [v2: any] : (v2
% 66.01/9.63 | = all_256_4 | ~ (relation_dom(v2) = v0) | ~ $i(v2) | ~
% 66.01/9.63 | relation(v2) | ~ function(v2) | ? [v3: $i] : ? [v4: $i] : ?
% 66.01/9.63 | [v5: $i] : ? [v6: $i] : ($i(v4) & $i(v3) & ((v6 = v3 &
% 66.01/9.63 | apply(all_256_6, v4) = v3 & in(v4, v1) & ( ~ in(v3, v0) | (
% 66.01/9.63 | ~ (v5 = v4) & apply(v2, v3) = v5 & $i(v5)))) | (v5 = v4
% 66.01/9.63 | & apply(v2, v3) = v4 & in(v3, v0) & ( ~ in(v4, v1) | ( ~ (v6
% 66.01/9.63 | = v3) & apply(all_256_6, v4) = v6 & $i(v6))))))))
% 66.01/9.63 |
% 66.01/9.63 | GROUND_INST: instantiating (d9_funct_1) with all_256_6, all_256_4, simplifying
% 66.01/9.63 | with (19), (20), (21), (23), (26) gives:
% 66.01/9.63 | (35) relation_inverse(all_256_6) = all_256_4 & $i(all_256_4)
% 66.01/9.63 |
% 66.01/9.63 | ALPHA: (35) implies:
% 66.01/9.63 | (36) $i(all_256_4)
% 66.01/9.63 | (37) relation_inverse(all_256_6) = all_256_4
% 66.01/9.63 |
% 66.01/9.63 | GROUND_INST: instantiating (9) with all_256_6, all_256_4, simplifying with
% 66.01/9.63 | (19), (20), (23), (26) gives:
% 66.01/9.63 | (38) relation(all_256_4)
% 66.01/9.63 |
% 66.01/9.63 | GROUND_INST: instantiating (8) with all_256_6, all_256_4, simplifying with
% 66.01/9.63 | (19), (20), (23), (26) gives:
% 66.01/9.63 | (39) function(all_256_4)
% 66.01/9.63 |
% 66.01/9.63 | DELTA: instantiating (29) with fresh symbols all_272_0, all_272_1 gives:
% 66.01/9.63 | (40) ordered_pair(all_272_1, all_256_7) = all_272_0 & $i(all_272_0) &
% 66.01/9.63 | $i(all_272_1) & in(all_272_0, all_256_6)
% 66.01/9.63 |
% 66.01/9.63 | ALPHA: (40) implies:
% 66.01/9.63 | (41) in(all_272_0, all_256_6)
% 66.01/9.63 | (42) $i(all_272_1)
% 66.01/9.63 | (43) $i(all_272_0)
% 66.01/9.63 | (44) ordered_pair(all_272_1, all_256_7) = all_272_0
% 66.01/9.63 |
% 66.01/9.63 | DELTA: instantiating (33) with fresh symbols all_274_0, all_274_1 gives:
% 66.01/9.64 | (45) relation_rng(all_256_4) = all_274_0 & relation_rng(all_256_6) =
% 66.01/9.64 | all_274_1 & relation_dom(all_256_4) = all_274_1 &
% 66.01/9.64 | relation_dom(all_256_6) = all_274_0 & $i(all_274_0) & $i(all_274_1)
% 66.01/9.64 |
% 66.01/9.64 | ALPHA: (45) implies:
% 66.01/9.64 | (46) $i(all_274_1)
% 66.01/9.64 | (47) relation_dom(all_256_6) = all_274_0
% 66.01/9.64 | (48) relation_dom(all_256_4) = all_274_1
% 66.01/9.64 | (49) relation_rng(all_256_6) = all_274_1
% 66.01/9.64 | (50) relation_rng(all_256_4) = all_274_0
% 66.01/9.64 |
% 66.01/9.64 | DELTA: instantiating (31) with fresh symbol all_280_0 gives:
% 66.01/9.64 | (51) relation_dom(all_256_6) = all_280_0 & $i(all_280_0) & ! [v0: $i] : !
% 66.01/9.64 | [v1: $i] : ( ~ (relation_composition(all_256_6, v0) = v1) | ~ $i(v0)
% 66.01/9.64 | | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = all_280_0 &
% 66.01/9.64 | relation_dom(v1) = all_280_0) | (relation_dom(v0) = v2 & $i(v2)
% 66.01/9.64 | & ~ subset(all_256_5, v2))))
% 66.01/9.64 |
% 66.01/9.64 | ALPHA: (51) implies:
% 66.01/9.64 | (52) relation_dom(all_256_6) = all_280_0
% 66.01/9.64 |
% 66.01/9.64 | DELTA: instantiating (30) with fresh symbol all_286_0 gives:
% 66.01/9.64 | (53) relation_dom(all_256_6) = all_286_0 & $i(all_286_0) & ! [v0: $i] : !
% 66.01/9.64 | [v1: $i] : ( ~ (relation_composition(v0, all_256_6) = v1) | ~ $i(v0)
% 66.01/9.64 | | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = all_256_5 &
% 66.01/9.64 | relation_rng(v1) = all_256_5 & $i(all_256_5)) |
% 66.01/9.64 | (relation_rng(v0) = v2 & $i(v2) & ~ subset(all_286_0, v2))))
% 66.01/9.64 |
% 66.01/9.64 | ALPHA: (53) implies:
% 66.01/9.64 | (54) relation_dom(all_256_6) = all_286_0
% 66.01/9.64 |
% 66.01/9.64 | DELTA: instantiating (32) with fresh symbol all_289_0 gives:
% 66.01/9.64 | (55) relation_dom(all_256_6) = all_289_0 & $i(all_289_0) & ! [v0: $i] : !
% 66.01/9.64 | [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 66.01/9.64 | subset(all_256_6, v0) | ~ relation(v0) | subset(all_256_5, v1)) &
% 66.01/9.64 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 66.01/9.64 | ~ subset(all_256_6, v0) | ~ relation(v0) | ? [v2: $i] :
% 66.01/9.64 | (relation_dom(v0) = v2 & $i(v2) & subset(all_289_0, v2)))
% 66.01/9.64 |
% 66.01/9.64 | ALPHA: (55) implies:
% 66.01/9.64 | (56) relation_dom(all_256_6) = all_289_0
% 66.01/9.64 | (57) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 66.01/9.64 | ~ subset(all_256_6, v0) | ~ relation(v0) | ? [v2: $i] :
% 66.01/9.64 | (relation_dom(v0) = v2 & $i(v2) & subset(all_289_0, v2)))
% 66.01/9.64 |
% 66.01/9.64 | DELTA: instantiating (34) with fresh symbols all_295_0, all_295_1 gives:
% 66.01/9.64 | (58) relation_rng(all_256_6) = all_295_1 & relation_dom(all_256_6) =
% 66.01/9.64 | all_295_0 & $i(all_295_0) & $i(all_295_1) & ! [v0: $i] : ! [v1: $i]
% 66.01/9.64 | : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (relation_dom(all_256_4) =
% 66.01/9.64 | v0) | ~ (apply(all_256_4, v1) = v3) | ~ (apply(all_256_6, v2) =
% 66.01/9.64 | v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(all_256_4) | ~
% 66.01/9.64 | relation(all_256_4) | ~ function(all_256_4) | ~ in(v2, all_295_0))
% 66.01/9.64 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 |
% 66.01/9.64 | ~ (relation_dom(all_256_4) = v0) | ~ (apply(all_256_4, v1) = v2) |
% 66.01/9.64 | ~ (apply(all_256_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 66.01/9.64 | $i(all_256_4) | ~ relation(all_256_4) | ~ function(all_256_4) | ~
% 66.01/9.64 | in(v1, all_295_1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 66.01/9.64 | [v3: $i] : ( ~ (relation_dom(all_256_4) = v0) | ~ (apply(all_256_4,
% 66.01/9.64 | v1) = v3) | ~ (apply(all_256_6, v2) = v1) | ~ $i(v2) | ~
% 66.01/9.64 | $i(v1) | ~ $i(all_256_4) | ~ relation(all_256_4) | ~
% 66.01/9.64 | function(all_256_4) | ~ in(v2, all_295_0) | in(v1, all_295_1)) & !
% 66.01/9.64 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 66.01/9.64 | (relation_dom(all_256_4) = v0) | ~ (apply(all_256_4, v1) = v2) | ~
% 66.01/9.64 | (apply(all_256_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 66.01/9.64 | $i(all_256_4) | ~ relation(all_256_4) | ~ function(all_256_4) | ~
% 66.01/9.64 | in(v1, all_295_1) | in(v2, all_295_0)) & ! [v0: int] : (v0 =
% 66.01/9.64 | all_295_1 | ~ (relation_dom(all_256_4) = v0) | ~ $i(all_256_4) |
% 66.01/9.64 | ~ relation(all_256_4) | ~ function(all_256_4)) & ! [v0: any] : (v0
% 66.01/9.64 | = all_256_4 | ~ (relation_dom(v0) = all_295_1) | ~ $i(v0) | ~
% 66.01/9.64 | relation(v0) | ~ function(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3:
% 66.01/9.64 | $i] : ? [v4: $i] : ($i(v2) & $i(v1) & ((v4 = v1 &
% 66.01/9.64 | apply(all_256_6, v2) = v1 & in(v2, all_295_0) & ( ~ in(v1,
% 66.01/9.64 | all_295_1) | ( ~ (v3 = v2) & apply(v0, v1) = v3 &
% 66.01/9.64 | $i(v3)))) | (v3 = v2 & apply(v0, v1) = v2 & in(v1,
% 66.01/9.64 | all_295_1) & ( ~ in(v2, all_295_0) | ( ~ (v4 = v1) &
% 66.01/9.64 | apply(all_256_6, v2) = v4 & $i(v4)))))))
% 66.01/9.64 |
% 66.01/9.64 | ALPHA: (58) implies:
% 66.01/9.64 | (59) relation_dom(all_256_6) = all_295_0
% 66.01/9.64 | (60) relation_rng(all_256_6) = all_295_1
% 66.01/9.64 |
% 66.01/9.64 | GROUND_INST: instantiating (13) with all_286_0, all_289_0, all_256_6,
% 66.01/9.64 | simplifying with (54), (56) gives:
% 66.01/9.64 | (61) all_289_0 = all_286_0
% 66.01/9.64 |
% 66.01/9.64 | GROUND_INST: instantiating (13) with all_280_0, all_289_0, all_256_6,
% 66.01/9.64 | simplifying with (52), (56) gives:
% 66.01/9.64 | (62) all_289_0 = all_280_0
% 66.01/9.64 |
% 66.01/9.64 | GROUND_INST: instantiating (13) with all_286_0, all_295_0, all_256_6,
% 66.01/9.64 | simplifying with (54), (59) gives:
% 66.24/9.64 | (63) all_295_0 = all_286_0
% 66.24/9.64 |
% 66.24/9.64 | GROUND_INST: instantiating (13) with all_274_0, all_295_0, all_256_6,
% 66.24/9.64 | simplifying with (47), (59) gives:
% 66.24/9.64 | (64) all_295_0 = all_274_0
% 66.24/9.64 |
% 66.24/9.64 | GROUND_INST: instantiating (14) with all_256_5, all_295_1, all_256_6,
% 66.24/9.64 | simplifying with (25), (60) gives:
% 66.24/9.64 | (65) all_295_1 = all_256_5
% 66.24/9.64 |
% 66.25/9.64 | GROUND_INST: instantiating (14) with all_274_1, all_295_1, all_256_6,
% 66.25/9.64 | simplifying with (49), (60) gives:
% 66.25/9.64 | (66) all_295_1 = all_274_1
% 66.25/9.64 |
% 66.25/9.64 | COMBINE_EQS: (63), (64) imply:
% 66.25/9.65 | (67) all_286_0 = all_274_0
% 66.25/9.65 |
% 66.25/9.65 | SIMP: (67) implies:
% 66.25/9.65 | (68) all_286_0 = all_274_0
% 66.25/9.65 |
% 66.25/9.65 | COMBINE_EQS: (65), (66) imply:
% 66.25/9.65 | (69) all_274_1 = all_256_5
% 66.25/9.65 |
% 66.25/9.65 | SIMP: (69) implies:
% 66.25/9.65 | (70) all_274_1 = all_256_5
% 66.25/9.65 |
% 66.25/9.65 | COMBINE_EQS: (61), (62) imply:
% 66.25/9.65 | (71) all_286_0 = all_280_0
% 66.25/9.65 |
% 66.25/9.65 | SIMP: (71) implies:
% 66.25/9.65 | (72) all_286_0 = all_280_0
% 66.25/9.65 |
% 66.25/9.65 | COMBINE_EQS: (68), (72) imply:
% 66.25/9.65 | (73) all_280_0 = all_274_0
% 66.25/9.65 |
% 66.25/9.65 | COMBINE_EQS: (62), (73) imply:
% 66.25/9.65 | (74) all_289_0 = all_274_0
% 66.25/9.65 |
% 66.25/9.65 | REDUCE: (48), (70) imply:
% 66.25/9.65 | (75) relation_dom(all_256_4) = all_256_5
% 66.25/9.65 |
% 66.25/9.65 | GROUND_INST: instantiating (1) with all_256_6, all_272_0, simplifying with
% 66.25/9.65 | (20), (23), (41), (43) gives:
% 66.25/9.65 | (76) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_272_0 & $i(v1)
% 66.25/9.65 | & $i(v0))
% 66.25/9.65 |
% 66.25/9.65 | GROUND_INST: instantiating (57) with all_256_6, all_256_5, simplifying with
% 66.25/9.65 | (20), (23), (25), (28) gives:
% 66.25/9.65 | (77) ? [v0: $i] : (relation_dom(all_256_6) = v0 & $i(v0) &
% 66.25/9.65 | subset(all_289_0, v0))
% 66.25/9.65 |
% 66.25/9.65 | GROUND_INST: instantiating (10) with all_272_1, all_256_7, all_256_6,
% 66.25/9.65 | all_272_0, all_256_5, simplifying with (20), (22), (23), (25),
% 66.25/9.65 | (41), (42), (44) gives:
% 66.25/9.65 | (78) ? [v0: $i] : (relation_dom(all_256_6) = v0 & $i(v0) & in(all_272_1,
% 66.25/9.65 | v0))
% 66.25/9.65 |
% 66.25/9.65 | GROUND_INST: instantiating (4) with all_256_4, all_256_5, all_256_7,
% 66.25/9.65 | simplifying with (18), (22), (24), (36), (38), (75) gives:
% 66.25/9.65 | (79) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_256_7, v0) = v1 & $i(v1)
% 66.25/9.65 | & $i(v0) & in(v1, all_256_4))
% 66.25/9.65 |
% 66.25/9.65 | GROUND_INST: instantiating (t47_relat_1) with all_256_4, all_274_0,
% 66.25/9.65 | simplifying with (36), (38), (50) gives:
% 66.25/9.65 | (80) ? [v0: $i] : (relation_dom(all_256_4) = v0 & $i(v0) & ! [v1: $i] :
% 66.25/9.65 | ! [v2: $i] : ( ~ (relation_composition(v1, all_256_4) = v2) | ~
% 66.25/9.65 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: int] : ((v4 =
% 66.25/9.65 | all_274_0 & relation_rng(v2) = all_274_0 & $i(all_274_0)) |
% 66.25/9.65 | (relation_rng(v1) = v3 & $i(v3) & ~ subset(v0, v3)))))
% 66.25/9.65 |
% 66.25/9.65 | GROUND_INST: instantiating (t46_relat_1) with all_256_4, all_274_0,
% 66.25/9.65 | simplifying with (36), (38), (50) gives:
% 66.25/9.65 | (81) ? [v0: $i] : (relation_dom(all_256_4) = v0 & $i(v0) & ! [v1: $i] :
% 66.25/9.65 | ! [v2: $i] : ( ~ (relation_composition(all_256_4, v1) = v2) | ~
% 66.25/9.65 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = v0 &
% 66.25/9.65 | relation_dom(v2) = v0) | (relation_dom(v1) = v3 & $i(v3) & ~
% 66.25/9.65 | subset(all_274_0, v3)))))
% 66.25/9.65 |
% 66.25/9.65 | GROUND_INST: instantiating (t25_relat_1) with all_256_4, all_274_0,
% 66.25/9.65 | simplifying with (36), (38), (50) gives:
% 66.25/9.65 | (82) ? [v0: $i] : (relation_dom(all_256_4) = v0 & $i(v0) & ! [v1: $i] :
% 66.25/9.65 | ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~
% 66.25/9.65 | subset(all_256_4, v1) | ~ relation(v1) | subset(all_274_0, v2)) &
% 66.25/9.65 | ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1)
% 66.25/9.65 | | ~ subset(all_256_4, v1) | ~ relation(v1) | ? [v3: $i] :
% 66.25/9.65 | (relation_dom(v1) = v3 & $i(v3) & subset(v0, v3))))
% 66.25/9.65 |
% 66.25/9.65 | GROUND_INST: instantiating (involutiveness_k4_relat_1) with all_256_6,
% 66.25/9.65 | all_256_4, simplifying with (20), (23), (37) gives:
% 66.25/9.65 | (83) relation_inverse(all_256_4) = all_256_6
% 66.25/9.65 |
% 66.25/9.65 | DELTA: instantiating (76) with fresh symbols all_308_0, all_308_1 gives:
% 66.25/9.65 | (84) ordered_pair(all_308_1, all_308_0) = all_272_0 & $i(all_308_0) &
% 66.25/9.65 | $i(all_308_1)
% 66.25/9.65 |
% 66.25/9.65 | ALPHA: (84) implies:
% 66.25/9.65 | (85) $i(all_308_1)
% 66.25/9.65 | (86) $i(all_308_0)
% 66.25/9.65 | (87) ordered_pair(all_308_1, all_308_0) = all_272_0
% 66.25/9.65 |
% 66.25/9.65 | DELTA: instantiating (77) with fresh symbol all_310_0 gives:
% 66.25/9.65 | (88) relation_dom(all_256_6) = all_310_0 & $i(all_310_0) &
% 66.25/9.65 | subset(all_289_0, all_310_0)
% 66.25/9.65 |
% 66.25/9.65 | ALPHA: (88) implies:
% 66.25/9.65 | (89) subset(all_289_0, all_310_0)
% 66.25/9.65 | (90) $i(all_310_0)
% 66.25/9.65 | (91) relation_dom(all_256_6) = all_310_0
% 66.25/9.65 |
% 66.25/9.65 | DELTA: instantiating (78) with fresh symbol all_312_0 gives:
% 66.25/9.65 | (92) relation_dom(all_256_6) = all_312_0 & $i(all_312_0) & in(all_272_1,
% 66.25/9.65 | all_312_0)
% 66.25/9.65 |
% 66.25/9.65 | ALPHA: (92) implies:
% 66.25/9.65 | (93) in(all_272_1, all_312_0)
% 66.25/9.65 | (94) relation_dom(all_256_6) = all_312_0
% 66.25/9.65 |
% 66.25/9.65 | DELTA: instantiating (79) with fresh symbols all_314_0, all_314_1 gives:
% 66.25/9.65 | (95) ordered_pair(all_256_7, all_314_1) = all_314_0 & $i(all_314_0) &
% 66.25/9.65 | $i(all_314_1) & in(all_314_0, all_256_4)
% 66.25/9.65 |
% 66.25/9.65 | ALPHA: (95) implies:
% 66.25/9.65 | (96) in(all_314_0, all_256_4)
% 66.25/9.65 | (97) $i(all_314_1)
% 66.25/9.65 | (98) $i(all_314_0)
% 66.25/9.65 | (99) ordered_pair(all_256_7, all_314_1) = all_314_0
% 66.25/9.65 |
% 66.25/9.65 | DELTA: instantiating (81) with fresh symbol all_317_0 gives:
% 66.25/9.65 | (100) relation_dom(all_256_4) = all_317_0 & $i(all_317_0) & ! [v0: $i] :
% 66.25/9.65 | ! [v1: $i] : ( ~ (relation_composition(all_256_4, v0) = v1) | ~
% 66.25/9.65 | $i(v0) | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 =
% 66.25/9.65 | all_317_0 & relation_dom(v1) = all_317_0) | (relation_dom(v0) =
% 66.25/9.65 | v2 & $i(v2) & ~ subset(all_274_0, v2))))
% 66.25/9.65 |
% 66.25/9.65 | ALPHA: (100) implies:
% 66.25/9.65 | (101) relation_dom(all_256_4) = all_317_0
% 66.25/9.65 | (102) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_composition(all_256_4, v0)
% 66.25/9.65 | = v1) | ~ $i(v0) | ~ relation(v0) | ? [v2: $i] : ? [v3: int]
% 66.25/9.65 | : ((v3 = all_317_0 & relation_dom(v1) = all_317_0) |
% 66.25/9.65 | (relation_dom(v0) = v2 & $i(v2) & ~ subset(all_274_0, v2))))
% 66.25/9.65 |
% 66.25/9.65 | DELTA: instantiating (80) with fresh symbol all_320_0 gives:
% 66.25/9.65 | (103) relation_dom(all_256_4) = all_320_0 & $i(all_320_0) & ! [v0: $i] :
% 66.25/9.65 | ! [v1: $i] : ( ~ (relation_composition(v0, all_256_4) = v1) | ~
% 66.25/9.65 | $i(v0) | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 =
% 66.25/9.65 | all_274_0 & relation_rng(v1) = all_274_0 & $i(all_274_0)) |
% 66.25/9.65 | (relation_rng(v0) = v2 & $i(v2) & ~ subset(all_320_0, v2))))
% 66.25/9.65 |
% 66.25/9.65 | ALPHA: (103) implies:
% 66.25/9.65 | (104) relation_dom(all_256_4) = all_320_0
% 66.25/9.65 |
% 66.25/9.65 | DELTA: instantiating (82) with fresh symbol all_323_0 gives:
% 66.25/9.66 | (105) relation_dom(all_256_4) = all_323_0 & $i(all_323_0) & ! [v0: $i] :
% 66.25/9.66 | ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 66.25/9.66 | subset(all_256_4, v0) | ~ relation(v0) | subset(all_274_0, v1)) &
% 66.25/9.66 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 66.25/9.66 | ~ subset(all_256_4, v0) | ~ relation(v0) | ? [v2: $i] :
% 66.25/9.66 | (relation_dom(v0) = v2 & $i(v2) & subset(all_323_0, v2)))
% 66.25/9.66 |
% 66.25/9.66 | ALPHA: (105) implies:
% 66.25/9.66 | (106) relation_dom(all_256_4) = all_323_0
% 66.25/9.66 |
% 66.25/9.66 | REDUCE: (74), (89) imply:
% 66.25/9.66 | (107) subset(all_274_0, all_310_0)
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (13) with all_274_0, all_312_0, all_256_6,
% 66.25/9.66 | simplifying with (47), (94) gives:
% 66.25/9.66 | (108) all_312_0 = all_274_0
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (13) with all_310_0, all_312_0, all_256_6,
% 66.25/9.66 | simplifying with (91), (94) gives:
% 66.25/9.66 | (109) all_312_0 = all_310_0
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (13) with all_256_5, all_320_0, all_256_4,
% 66.25/9.66 | simplifying with (75), (104) gives:
% 66.25/9.66 | (110) all_320_0 = all_256_5
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (13) with all_320_0, all_323_0, all_256_4,
% 66.25/9.66 | simplifying with (104), (106) gives:
% 66.25/9.66 | (111) all_323_0 = all_320_0
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (13) with all_317_0, all_323_0, all_256_4,
% 66.25/9.66 | simplifying with (101), (106) gives:
% 66.25/9.66 | (112) all_323_0 = all_317_0
% 66.25/9.66 |
% 66.25/9.66 | COMBINE_EQS: (111), (112) imply:
% 66.25/9.66 | (113) all_320_0 = all_317_0
% 66.25/9.66 |
% 66.25/9.66 | SIMP: (113) implies:
% 66.25/9.66 | (114) all_320_0 = all_317_0
% 66.25/9.66 |
% 66.25/9.66 | COMBINE_EQS: (110), (114) imply:
% 66.25/9.66 | (115) all_317_0 = all_256_5
% 66.25/9.66 |
% 66.25/9.66 | COMBINE_EQS: (108), (109) imply:
% 66.25/9.66 | (116) all_310_0 = all_274_0
% 66.25/9.66 |
% 66.25/9.66 | REDUCE: (90), (116) imply:
% 66.25/9.66 | (117) $i(all_274_0)
% 66.25/9.66 |
% 66.25/9.66 | REDUCE: (107), (116) imply:
% 66.25/9.66 | (118) subset(all_274_0, all_274_0)
% 66.25/9.66 |
% 66.25/9.66 | REDUCE: (93), (108) imply:
% 66.25/9.66 | (119) in(all_272_1, all_274_0)
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (3) with all_256_6, all_274_0, all_272_1,
% 66.25/9.66 | all_256_7, all_272_0, simplifying with (19), (20), (22), (23),
% 66.25/9.66 | (42), (44), (47), (119) gives:
% 66.25/9.66 | (120) ? [v0: any] : (( ~ in(all_272_0, all_256_6) | (v0 = all_256_7 &
% 66.25/9.66 | apply(all_256_6, all_272_1) = all_256_7)) & (in(all_272_0,
% 66.25/9.66 | all_256_6) | ( ~ (v0 = all_256_7) & apply(all_256_6, all_272_1)
% 66.25/9.66 | = v0 & $i(v0))))
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (4) with all_256_6, all_274_0, all_272_1,
% 66.25/9.66 | simplifying with (20), (23), (42), (47), (117), (119) gives:
% 66.25/9.66 | (121) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_272_1, v0) = v1 &
% 66.25/9.66 | $i(v1) & $i(v0) & in(v1, all_256_6))
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (5) with all_256_4, all_274_0, all_272_1,
% 66.25/9.66 | simplifying with (36), (38), (42), (50), (117), (119) gives:
% 66.25/9.66 | (122) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, all_272_1) = v1 &
% 66.25/9.66 | $i(v1) & $i(v0) & in(v1, all_256_4))
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (1) with all_256_4, all_314_0, simplifying with
% 66.25/9.66 | (36), (38), (96), (98) gives:
% 66.25/9.66 | (123) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_314_0 &
% 66.25/9.66 | $i(v1) & $i(v0))
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (7) with all_256_6, all_256_4, all_256_7,
% 66.25/9.66 | all_314_1, all_314_0, simplifying with (20), (22), (23), (36),
% 66.25/9.66 | (37), (38), (96), (97), (99) gives:
% 66.25/9.66 | (124) ? [v0: $i] : (ordered_pair(all_314_1, all_256_7) = v0 & $i(v0) &
% 66.25/9.66 | in(v0, all_256_6))
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (6) with all_256_4, all_274_0, all_314_1,
% 66.25/9.66 | all_256_7, all_314_0, simplifying with (22), (36), (38), (50),
% 66.25/9.66 | (96), (97), (99), (117) gives:
% 66.25/9.66 | (125) in(all_314_1, all_274_0)
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (3) with all_256_4, all_256_5, all_256_7,
% 66.25/9.66 | all_314_1, all_314_0, simplifying with (18), (22), (36), (38),
% 66.25/9.66 | (39), (75), (97), (99) gives:
% 66.25/9.66 | (126) ? [v0: any] : (( ~ in(all_314_0, all_256_4) | (v0 = all_314_1 &
% 66.25/9.66 | apply(all_256_4, all_256_7) = all_314_1)) & (in(all_314_0,
% 66.25/9.66 | all_256_4) | ( ~ (v0 = all_314_1) & apply(all_256_4, all_256_7)
% 66.25/9.66 | = v0 & $i(v0))))
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (12) with all_272_1, all_256_7, all_308_1,
% 66.25/9.66 | all_308_0, all_272_0, simplifying with (22), (42), (44), (85),
% 66.25/9.66 | (86), (87) gives:
% 66.25/9.66 | (127) all_308_0 = all_256_7
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (11) with all_272_1, all_256_7, all_308_1,
% 66.25/9.66 | all_308_0, all_272_0, simplifying with (22), (42), (44), (85),
% 66.25/9.66 | (86), (87) gives:
% 66.25/9.66 | (128) all_308_1 = all_272_1
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (10) with all_308_1, all_308_0, all_256_6,
% 66.25/9.66 | all_272_0, all_256_5, simplifying with (20), (23), (25), (41),
% 66.25/9.66 | (85), (86), (87) gives:
% 66.25/9.66 | (129) ? [v0: $i] : (relation_dom(all_256_6) = v0 & $i(v0) & in(all_308_1,
% 66.25/9.66 | v0))
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (7) with all_256_4, all_256_6, all_272_1,
% 66.25/9.66 | all_256_7, all_272_0, simplifying with (20), (22), (23), (36),
% 66.25/9.66 | (38), (41), (42), (44), (83) gives:
% 66.25/9.66 | (130) ? [v0: $i] : (ordered_pair(all_256_7, all_272_1) = v0 & $i(v0) &
% 66.25/9.66 | in(v0, all_256_4))
% 66.25/9.66 |
% 66.25/9.66 | GROUND_INST: instantiating (7) with all_256_4, all_256_6, all_308_1,
% 66.25/9.66 | all_308_0, all_272_0, simplifying with (20), (23), (36), (38),
% 66.25/9.66 | (41), (83), (85), (86), (87) gives:
% 66.25/9.66 | (131) ? [v0: $i] : (ordered_pair(all_308_0, all_308_1) = v0 & $i(v0) &
% 66.25/9.66 | in(v0, all_256_4))
% 66.25/9.66 |
% 66.25/9.66 | DELTA: instantiating (131) with fresh symbol all_360_0 gives:
% 66.25/9.66 | (132) ordered_pair(all_308_0, all_308_1) = all_360_0 & $i(all_360_0) &
% 66.25/9.66 | in(all_360_0, all_256_4)
% 66.25/9.66 |
% 66.25/9.66 | ALPHA: (132) implies:
% 66.25/9.66 | (133) ordered_pair(all_308_0, all_308_1) = all_360_0
% 66.25/9.66 |
% 66.25/9.66 | DELTA: instantiating (123) with fresh symbols all_362_0, all_362_1 gives:
% 66.25/9.66 | (134) ordered_pair(all_362_1, all_362_0) = all_314_0 & $i(all_362_0) &
% 66.25/9.66 | $i(all_362_1)
% 66.25/9.66 |
% 66.25/9.66 | ALPHA: (134) implies:
% 66.25/9.66 | (135) $i(all_362_1)
% 66.25/9.66 | (136) $i(all_362_0)
% 66.25/9.66 | (137) ordered_pair(all_362_1, all_362_0) = all_314_0
% 66.25/9.66 |
% 66.25/9.66 | DELTA: instantiating (129) with fresh symbol all_364_0 gives:
% 66.25/9.66 | (138) relation_dom(all_256_6) = all_364_0 & $i(all_364_0) & in(all_308_1,
% 66.25/9.66 | all_364_0)
% 66.25/9.66 |
% 66.25/9.67 | ALPHA: (138) implies:
% 66.25/9.67 | (139) relation_dom(all_256_6) = all_364_0
% 66.25/9.67 |
% 66.25/9.67 | DELTA: instantiating (130) with fresh symbol all_366_0 gives:
% 66.25/9.67 | (140) ordered_pair(all_256_7, all_272_1) = all_366_0 & $i(all_366_0) &
% 66.25/9.67 | in(all_366_0, all_256_4)
% 66.25/9.67 |
% 66.25/9.67 | ALPHA: (140) implies:
% 66.25/9.67 | (141) in(all_366_0, all_256_4)
% 66.25/9.67 | (142) ordered_pair(all_256_7, all_272_1) = all_366_0
% 66.25/9.67 |
% 66.25/9.67 | DELTA: instantiating (124) with fresh symbol all_368_0 gives:
% 66.25/9.67 | (143) ordered_pair(all_314_1, all_256_7) = all_368_0 & $i(all_368_0) &
% 66.25/9.67 | in(all_368_0, all_256_6)
% 66.25/9.67 |
% 66.25/9.67 | ALPHA: (143) implies:
% 66.25/9.67 | (144) in(all_368_0, all_256_6)
% 66.25/9.67 | (145) ordered_pair(all_314_1, all_256_7) = all_368_0
% 66.25/9.67 |
% 66.25/9.67 | DELTA: instantiating (122) with fresh symbols all_370_0, all_370_1 gives:
% 66.25/9.67 | (146) ordered_pair(all_370_1, all_272_1) = all_370_0 & $i(all_370_0) &
% 66.25/9.67 | $i(all_370_1) & in(all_370_0, all_256_4)
% 66.25/9.67 |
% 66.25/9.67 | ALPHA: (146) implies:
% 66.25/9.67 | (147) in(all_370_0, all_256_4)
% 66.25/9.67 | (148) $i(all_370_1)
% 66.25/9.67 | (149) ordered_pair(all_370_1, all_272_1) = all_370_0
% 66.25/9.67 |
% 66.25/9.67 | DELTA: instantiating (121) with fresh symbols all_372_0, all_372_1 gives:
% 66.25/9.67 | (150) ordered_pair(all_272_1, all_372_1) = all_372_0 & $i(all_372_0) &
% 66.25/9.67 | $i(all_372_1) & in(all_372_0, all_256_6)
% 66.25/9.67 |
% 66.25/9.67 | ALPHA: (150) implies:
% 66.25/9.67 | (151) in(all_372_0, all_256_6)
% 66.25/9.67 | (152) $i(all_372_1)
% 66.25/9.67 | (153) ordered_pair(all_272_1, all_372_1) = all_372_0
% 66.25/9.67 |
% 66.25/9.67 | DELTA: instantiating (126) with fresh symbol all_374_0 gives:
% 66.25/9.67 | (154) ( ~ in(all_314_0, all_256_4) | (all_374_0 = all_314_1 &
% 66.25/9.67 | apply(all_256_4, all_256_7) = all_314_1)) & (in(all_314_0,
% 66.25/9.67 | all_256_4) | ( ~ (all_374_0 = all_314_1) & apply(all_256_4,
% 66.25/9.67 | all_256_7) = all_374_0 & $i(all_374_0)))
% 66.25/9.67 |
% 66.25/9.67 | ALPHA: (154) implies:
% 66.25/9.67 | (155) ~ in(all_314_0, all_256_4) | (all_374_0 = all_314_1 &
% 66.25/9.67 | apply(all_256_4, all_256_7) = all_314_1)
% 66.25/9.67 |
% 66.25/9.67 | DELTA: instantiating (120) with fresh symbol all_375_0 gives:
% 66.25/9.67 | (156) ( ~ in(all_272_0, all_256_6) | (all_375_0 = all_256_7 &
% 66.25/9.67 | apply(all_256_6, all_272_1) = all_256_7)) & (in(all_272_0,
% 66.25/9.67 | all_256_6) | ( ~ (all_375_0 = all_256_7) & apply(all_256_6,
% 66.25/9.67 | all_272_1) = all_375_0 & $i(all_375_0)))
% 66.25/9.67 |
% 66.25/9.67 | ALPHA: (156) implies:
% 66.25/9.67 | (157) ~ in(all_272_0, all_256_6) | (all_375_0 = all_256_7 &
% 66.25/9.67 | apply(all_256_6, all_272_1) = all_256_7)
% 66.25/9.67 |
% 66.25/9.67 | REDUCE: (127), (128), (133) imply:
% 66.25/9.67 | (158) ordered_pair(all_256_7, all_272_1) = all_360_0
% 66.25/9.67 |
% 66.25/9.67 | BETA: splitting (157) gives:
% 66.25/9.67 |
% 66.25/9.67 | Case 1:
% 66.25/9.67 | |
% 66.25/9.67 | | (159) ~ in(all_272_0, all_256_6)
% 66.25/9.67 | |
% 66.25/9.67 | | PRED_UNIFY: (41), (159) imply:
% 66.25/9.67 | | (160) $false
% 66.25/9.67 | |
% 66.25/9.67 | | CLOSE: (160) is inconsistent.
% 66.25/9.67 | |
% 66.25/9.67 | Case 2:
% 66.25/9.67 | |
% 66.25/9.67 | | (161) all_375_0 = all_256_7 & apply(all_256_6, all_272_1) = all_256_7
% 66.25/9.67 | |
% 66.25/9.67 | | ALPHA: (161) implies:
% 66.25/9.67 | | (162) apply(all_256_6, all_272_1) = all_256_7
% 66.25/9.67 | |
% 66.25/9.67 | | BETA: splitting (155) gives:
% 66.25/9.67 | |
% 66.25/9.67 | | Case 1:
% 66.25/9.67 | | |
% 66.25/9.67 | | | (163) ~ in(all_314_0, all_256_4)
% 66.25/9.67 | | |
% 66.25/9.67 | | | PRED_UNIFY: (96), (163) imply:
% 66.25/9.67 | | | (164) $false
% 66.25/9.67 | | |
% 66.25/9.67 | | | CLOSE: (164) is inconsistent.
% 66.25/9.67 | | |
% 66.25/9.67 | | Case 2:
% 66.25/9.67 | | |
% 66.25/9.67 | | | (165) all_374_0 = all_314_1 & apply(all_256_4, all_256_7) = all_314_1
% 66.25/9.67 | | |
% 66.25/9.67 | | | ALPHA: (165) implies:
% 66.25/9.67 | | | (166) apply(all_256_4, all_256_7) = all_314_1
% 66.25/9.67 | | |
% 66.25/9.67 | | | GROUND_INST: instantiating (15) with all_360_0, all_366_0, all_272_1,
% 66.25/9.67 | | | all_256_7, simplifying with (142), (158) gives:
% 66.25/9.67 | | | (167) all_366_0 = all_360_0
% 66.25/9.67 | | |
% 66.25/9.67 | | | GROUND_INST: instantiating (13) with all_274_0, all_364_0, all_256_6,
% 66.25/9.67 | | | simplifying with (47), (139) gives:
% 66.25/9.67 | | | (168) all_364_0 = all_274_0
% 66.25/9.67 | | |
% 66.25/9.67 | | | REDUCE: (141), (167) imply:
% 66.25/9.67 | | | (169) in(all_360_0, all_256_4)
% 66.25/9.67 | | |
% 66.25/9.67 | | | BETA: splitting (27) gives:
% 66.25/9.67 | | |
% 66.25/9.67 | | | Case 1:
% 66.25/9.67 | | | |
% 66.25/9.67 | | | | (170) ~ (all_256_0 = all_256_7) & relation_composition(all_256_4,
% 66.25/9.67 | | | | all_256_6) = all_256_1 & apply(all_256_1, all_256_7) =
% 66.25/9.67 | | | | all_256_0 & $i(all_256_0) & $i(all_256_1)
% 66.25/9.67 | | | |
% 66.25/9.67 | | | | ALPHA: (170) implies:
% 66.25/9.67 | | | | (171) ~ (all_256_0 = all_256_7)
% 66.25/9.67 | | | | (172) apply(all_256_1, all_256_7) = all_256_0
% 66.25/9.67 | | | | (173) relation_composition(all_256_4, all_256_6) = all_256_1
% 66.25/9.67 | | | |
% 66.25/9.67 | | | | GROUND_INST: instantiating (3) with all_256_6, all_274_0, all_314_1,
% 66.25/9.67 | | | | all_256_7, all_368_0, simplifying with (19), (20), (22),
% 66.25/9.67 | | | | (23), (47), (97), (125), (145) gives:
% 66.25/9.67 | | | | (174) ? [v0: any] : (( ~ in(all_368_0, all_256_6) | (v0 = all_256_7
% 66.25/9.67 | | | | & apply(all_256_6, all_314_1) = all_256_7)) &
% 66.25/9.67 | | | | (in(all_368_0, all_256_6) | ( ~ (v0 = all_256_7) &
% 66.25/9.67 | | | | apply(all_256_6, all_314_1) = v0 & $i(v0))))
% 66.25/9.67 | | | |
% 66.25/9.67 | | | | GROUND_INST: instantiating (11) with all_256_7, all_314_1, all_362_1,
% 66.25/9.67 | | | | all_362_0, all_314_0, simplifying with (22), (97), (99),
% 66.25/9.67 | | | | (135), (136), (137) gives:
% 66.25/9.67 | | | | (175) all_362_1 = all_256_7
% 66.25/9.67 | | | |
% 66.25/9.67 | | | | GROUND_INST: instantiating (10) with all_362_1, all_362_0, all_256_4,
% 66.25/9.67 | | | | all_314_0, all_274_0, simplifying with (36), (38), (50),
% 66.25/9.67 | | | | (96), (135), (136), (137) gives:
% 66.25/9.67 | | | | (176) ? [v0: $i] : (relation_dom(all_256_4) = v0 & $i(v0) &
% 66.25/9.67 | | | | in(all_362_1, v0))
% 66.25/9.67 | | | |
% 66.25/9.67 | | | | GROUND_INST: instantiating (10) with all_370_1, all_272_1, all_256_4,
% 66.25/9.67 | | | | all_370_0, all_274_0, simplifying with (36), (38), (42),
% 66.25/9.67 | | | | (50), (147), (148), (149) gives:
% 66.25/9.67 | | | | (177) ? [v0: $i] : (relation_dom(all_256_4) = v0 & $i(v0) &
% 66.25/9.67 | | | | in(all_370_1, v0))
% 66.25/9.67 | | | |
% 66.25/9.67 | | | | GROUND_INST: instantiating (t8_funct_1) with all_272_1, all_372_1,
% 66.25/9.67 | | | | all_256_6, all_372_0, all_256_7, simplifying with (19),
% 66.25/9.67 | | | | (20), (23), (42), (152), (153), (162) gives:
% 66.25/9.67 | | | | (178) ? [v0: $i] : (( ~ (all_372_1 = all_256_7) | in(all_372_0,
% 66.25/9.67 | | | | all_256_6) | (relation_dom(all_256_6) = v0 & $i(v0) & ~
% 66.25/9.67 | | | | in(all_272_1, v0))) & ( ~ in(all_372_0, all_256_6) |
% 66.25/9.67 | | | | (all_372_1 = all_256_7 & relation_dom(all_256_6) = v0 &
% 66.25/9.67 | | | | $i(v0) & in(all_272_1, v0))))
% 66.25/9.67 | | | |
% 66.25/9.68 | | | | GROUND_INST: instantiating (t23_funct_1) with all_272_1, all_256_6,
% 66.25/9.68 | | | | all_256_7, simplifying with (19), (20), (23), (42), (162)
% 66.25/9.68 | | | | gives:
% 66.25/9.68 | | | | (179) ? [v0: $i] : (relation_dom(all_256_6) = v0 & $i(v0) & ! [v1:
% 66.25/9.68 | | | | $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 66.25/9.68 | | | | (relation_composition(all_256_6, v1) = v2) | ~ (apply(v2,
% 66.25/9.68 | | | | all_272_1) = v3) | ~ $i(v1) | ~ relation(v1) | ~
% 66.25/9.68 | | | | function(v1) | ~ in(all_272_1, v0) | (apply(v1, all_256_7)
% 66.25/9.68 | | | | = v3 & $i(v3))))
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | GROUND_INST: instantiating (t8_funct_1) with all_256_7, all_272_1,
% 66.25/9.68 | | | | all_256_4, all_360_0, all_314_1, simplifying with (22),
% 66.25/9.68 | | | | (36), (38), (39), (42), (158), (166) gives:
% 66.25/9.68 | | | | (180) ? [v0: $i] : (( ~ (all_314_1 = all_272_1) | in(all_360_0,
% 66.25/9.68 | | | | all_256_4) | (relation_dom(all_256_4) = v0 & $i(v0) & ~
% 66.25/9.68 | | | | in(all_256_7, v0))) & ( ~ in(all_360_0, all_256_4) |
% 66.25/9.68 | | | | (all_314_1 = all_272_1 & relation_dom(all_256_4) = v0 &
% 66.25/9.68 | | | | $i(v0) & in(all_256_7, v0))))
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | GROUND_INST: instantiating (t23_funct_1) with all_256_7, all_256_4,
% 66.25/9.68 | | | | all_314_1, simplifying with (22), (36), (38), (39), (166)
% 66.25/9.68 | | | | gives:
% 66.25/9.68 | | | | (181) ? [v0: $i] : (relation_dom(all_256_4) = v0 & $i(v0) & ! [v1:
% 66.25/9.68 | | | | $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 66.25/9.68 | | | | (relation_composition(all_256_4, v1) = v2) | ~ (apply(v2,
% 66.25/9.68 | | | | all_256_7) = v3) | ~ $i(v1) | ~ relation(v1) | ~
% 66.25/9.68 | | | | function(v1) | ~ in(all_256_7, v0) | (apply(v1, all_314_1)
% 66.25/9.68 | | | | = v3 & $i(v3))))
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | GROUND_INST: instantiating (t22_funct_1) with all_256_7, all_256_6,
% 66.25/9.68 | | | | all_256_4, all_256_1, all_256_0, simplifying with (19),
% 66.25/9.68 | | | | (20), (22), (23), (36), (38), (39), (172), (173) gives:
% 66.25/9.68 | | | | (182) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ((v2 = all_256_0 &
% 66.25/9.68 | | | | apply(all_256_4, all_256_7) = v1 & apply(all_256_6, v1) =
% 66.25/9.68 | | | | all_256_0 & $i(v1) & $i(all_256_0)) |
% 66.25/9.68 | | | | (relation_dom(all_256_1) = v0 & $i(v0) & ~ in(all_256_7,
% 66.25/9.68 | | | | v0)))
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | GROUND_INST: instantiating (t44_relat_1) with all_256_4, all_256_5,
% 66.25/9.68 | | | | all_256_6, all_256_1, simplifying with (20), (23), (36),
% 66.25/9.68 | | | | (38), (75), (173) gives:
% 66.25/9.68 | | | | (183) ? [v0: $i] : (relation_dom(all_256_1) = v0 & $i(v0) &
% 66.25/9.68 | | | | subset(v0, all_256_5))
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | GROUND_INST: instantiating (102) with all_256_6, all_256_1, simplifying
% 66.25/9.68 | | | | with (20), (23), (173) gives:
% 66.25/9.68 | | | | (184) ? [v0: $i] : ? [v1: int] : ((v1 = all_317_0 &
% 66.25/9.68 | | | | relation_dom(all_256_1) = all_317_0) |
% 66.25/9.68 | | | | (relation_dom(all_256_6) = v0 & $i(v0) & ~ subset(all_274_0,
% 66.25/9.68 | | | | v0)))
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | DELTA: instantiating (183) with fresh symbol all_445_0 gives:
% 66.25/9.68 | | | | (185) relation_dom(all_256_1) = all_445_0 & $i(all_445_0) &
% 66.25/9.68 | | | | subset(all_445_0, all_256_5)
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | ALPHA: (185) implies:
% 66.25/9.68 | | | | (186) relation_dom(all_256_1) = all_445_0
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | DELTA: instantiating (176) with fresh symbol all_457_0 gives:
% 66.25/9.68 | | | | (187) relation_dom(all_256_4) = all_457_0 & $i(all_457_0) &
% 66.25/9.68 | | | | in(all_362_1, all_457_0)
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | ALPHA: (187) implies:
% 66.25/9.68 | | | | (188) in(all_362_1, all_457_0)
% 66.25/9.68 | | | | (189) relation_dom(all_256_4) = all_457_0
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | DELTA: instantiating (177) with fresh symbol all_461_0 gives:
% 66.25/9.68 | | | | (190) relation_dom(all_256_4) = all_461_0 & $i(all_461_0) &
% 66.25/9.68 | | | | in(all_370_1, all_461_0)
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | ALPHA: (190) implies:
% 66.25/9.68 | | | | (191) relation_dom(all_256_4) = all_461_0
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | DELTA: instantiating (184) with fresh symbols all_469_0, all_469_1
% 66.25/9.68 | | | | gives:
% 66.25/9.68 | | | | (192) (all_469_0 = all_317_0 & relation_dom(all_256_1) = all_317_0) |
% 66.25/9.68 | | | | (relation_dom(all_256_6) = all_469_1 & $i(all_469_1) & ~
% 66.25/9.68 | | | | subset(all_274_0, all_469_1))
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | DELTA: instantiating (174) with fresh symbol all_474_0 gives:
% 66.25/9.68 | | | | (193) ( ~ in(all_368_0, all_256_6) | (all_474_0 = all_256_7 &
% 66.25/9.68 | | | | apply(all_256_6, all_314_1) = all_256_7)) & (in(all_368_0,
% 66.25/9.68 | | | | all_256_6) | ( ~ (all_474_0 = all_256_7) & apply(all_256_6,
% 66.25/9.68 | | | | all_314_1) = all_474_0 & $i(all_474_0)))
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | ALPHA: (193) implies:
% 66.25/9.68 | | | | (194) ~ in(all_368_0, all_256_6) | (all_474_0 = all_256_7 &
% 66.25/9.68 | | | | apply(all_256_6, all_314_1) = all_256_7)
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | DELTA: instantiating (182) with fresh symbols all_476_0, all_476_1,
% 66.25/9.68 | | | | all_476_2 gives:
% 66.25/9.68 | | | | (195) (all_476_0 = all_256_0 & apply(all_256_4, all_256_7) =
% 66.25/9.68 | | | | all_476_1 & apply(all_256_6, all_476_1) = all_256_0 &
% 66.25/9.68 | | | | $i(all_476_1) & $i(all_256_0)) | (relation_dom(all_256_1) =
% 66.25/9.68 | | | | all_476_2 & $i(all_476_2) & ~ in(all_256_7, all_476_2))
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | DELTA: instantiating (181) with fresh symbol all_477_0 gives:
% 66.25/9.68 | | | | (196) relation_dom(all_256_4) = all_477_0 & $i(all_477_0) & ! [v0:
% 66.25/9.68 | | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 66.25/9.68 | | | | (relation_composition(all_256_4, v0) = v1) | ~ (apply(v1,
% 66.25/9.68 | | | | all_256_7) = v2) | ~ $i(v0) | ~ relation(v0) | ~
% 66.25/9.68 | | | | function(v0) | ~ in(all_256_7, all_477_0) | (apply(v0,
% 66.25/9.68 | | | | all_314_1) = v2 & $i(v2)))
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | ALPHA: (196) implies:
% 66.25/9.68 | | | | (197) relation_dom(all_256_4) = all_477_0
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | DELTA: instantiating (178) with fresh symbol all_480_0 gives:
% 66.25/9.68 | | | | (198) ( ~ (all_372_1 = all_256_7) | in(all_372_0, all_256_6) |
% 66.25/9.68 | | | | (relation_dom(all_256_6) = all_480_0 & $i(all_480_0) & ~
% 66.25/9.68 | | | | in(all_272_1, all_480_0))) & ( ~ in(all_372_0, all_256_6) |
% 66.25/9.68 | | | | (all_372_1 = all_256_7 & relation_dom(all_256_6) = all_480_0
% 66.25/9.68 | | | | & $i(all_480_0) & in(all_272_1, all_480_0)))
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | ALPHA: (198) implies:
% 66.25/9.68 | | | | (199) ~ in(all_372_0, all_256_6) | (all_372_1 = all_256_7 &
% 66.25/9.68 | | | | relation_dom(all_256_6) = all_480_0 & $i(all_480_0) &
% 66.25/9.68 | | | | in(all_272_1, all_480_0))
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | DELTA: instantiating (180) with fresh symbol all_481_0 gives:
% 66.25/9.68 | | | | (200) ( ~ (all_314_1 = all_272_1) | in(all_360_0, all_256_4) |
% 66.25/9.68 | | | | (relation_dom(all_256_4) = all_481_0 & $i(all_481_0) & ~
% 66.25/9.68 | | | | in(all_256_7, all_481_0))) & ( ~ in(all_360_0, all_256_4) |
% 66.25/9.68 | | | | (all_314_1 = all_272_1 & relation_dom(all_256_4) = all_481_0
% 66.25/9.68 | | | | & $i(all_481_0) & in(all_256_7, all_481_0)))
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | ALPHA: (200) implies:
% 66.25/9.68 | | | | (201) ~ in(all_360_0, all_256_4) | (all_314_1 = all_272_1 &
% 66.25/9.68 | | | | relation_dom(all_256_4) = all_481_0 & $i(all_481_0) &
% 66.25/9.68 | | | | in(all_256_7, all_481_0))
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | DELTA: instantiating (179) with fresh symbol all_482_0 gives:
% 66.25/9.68 | | | | (202) relation_dom(all_256_6) = all_482_0 & $i(all_482_0) & ! [v0:
% 66.25/9.68 | | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 66.25/9.68 | | | | (relation_composition(all_256_6, v0) = v1) | ~ (apply(v1,
% 66.25/9.68 | | | | all_272_1) = v2) | ~ $i(v0) | ~ relation(v0) | ~
% 66.25/9.68 | | | | function(v0) | ~ in(all_272_1, all_482_0) | (apply(v0,
% 66.25/9.68 | | | | all_256_7) = v2 & $i(v2)))
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | ALPHA: (202) implies:
% 66.25/9.68 | | | | (203) relation_dom(all_256_6) = all_482_0
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | REDUCE: (175), (188) imply:
% 66.25/9.68 | | | | (204) in(all_256_7, all_457_0)
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | BETA: splitting (194) gives:
% 66.25/9.68 | | | |
% 66.25/9.68 | | | | Case 1:
% 66.25/9.68 | | | | |
% 66.25/9.68 | | | | | (205) ~ in(all_368_0, all_256_6)
% 66.25/9.68 | | | | |
% 66.25/9.68 | | | | | PRED_UNIFY: (144), (205) imply:
% 66.25/9.68 | | | | | (206) $false
% 66.25/9.68 | | | | |
% 66.25/9.68 | | | | | CLOSE: (206) is inconsistent.
% 66.25/9.68 | | | | |
% 66.25/9.68 | | | | Case 2:
% 66.25/9.68 | | | | |
% 66.25/9.68 | | | | | (207) all_474_0 = all_256_7 & apply(all_256_6, all_314_1) =
% 66.25/9.68 | | | | | all_256_7
% 66.25/9.68 | | | | |
% 66.25/9.68 | | | | | ALPHA: (207) implies:
% 66.25/9.68 | | | | | (208) apply(all_256_6, all_314_1) = all_256_7
% 66.25/9.68 | | | | |
% 66.25/9.68 | | | | | BETA: splitting (195) gives:
% 66.25/9.68 | | | | |
% 66.25/9.68 | | | | | Case 1:
% 66.25/9.68 | | | | | |
% 66.25/9.68 | | | | | | (209) all_476_0 = all_256_0 & apply(all_256_4, all_256_7) =
% 66.25/9.68 | | | | | | all_476_1 & apply(all_256_6, all_476_1) = all_256_0 &
% 66.25/9.68 | | | | | | $i(all_476_1) & $i(all_256_0)
% 66.25/9.68 | | | | | |
% 66.25/9.68 | | | | | | ALPHA: (209) implies:
% 66.25/9.68 | | | | | | (210) apply(all_256_6, all_476_1) = all_256_0
% 66.25/9.68 | | | | | | (211) apply(all_256_4, all_256_7) = all_476_1
% 66.25/9.68 | | | | | |
% 66.25/9.68 | | | | | | BETA: splitting (201) gives:
% 66.25/9.68 | | | | | |
% 66.25/9.68 | | | | | | Case 1:
% 66.25/9.68 | | | | | | |
% 66.25/9.68 | | | | | | | (212) ~ in(all_360_0, all_256_4)
% 66.25/9.68 | | | | | | |
% 66.25/9.68 | | | | | | | PRED_UNIFY: (169), (212) imply:
% 66.25/9.68 | | | | | | | (213) $false
% 66.25/9.68 | | | | | | |
% 66.25/9.68 | | | | | | | CLOSE: (213) is inconsistent.
% 66.25/9.68 | | | | | | |
% 66.25/9.68 | | | | | | Case 2:
% 66.25/9.68 | | | | | | |
% 66.25/9.68 | | | | | | | (214) all_314_1 = all_272_1 & relation_dom(all_256_4) =
% 66.25/9.68 | | | | | | | all_481_0 & $i(all_481_0) & in(all_256_7, all_481_0)
% 66.25/9.68 | | | | | | |
% 66.25/9.68 | | | | | | | ALPHA: (214) implies:
% 66.25/9.68 | | | | | | | (215) all_314_1 = all_272_1
% 66.25/9.68 | | | | | | |
% 66.25/9.68 | | | | | | | REDUCE: (166), (215) imply:
% 66.25/9.68 | | | | | | | (216) apply(all_256_4, all_256_7) = all_272_1
% 66.25/9.68 | | | | | | |
% 66.25/9.68 | | | | | | | GROUND_INST: instantiating (16) with all_272_1, all_476_1,
% 66.25/9.68 | | | | | | | all_256_7, all_256_4, simplifying with (211), (216)
% 66.25/9.68 | | | | | | | gives:
% 66.25/9.68 | | | | | | | (217) all_476_1 = all_272_1
% 66.25/9.68 | | | | | | |
% 66.25/9.68 | | | | | | | REDUCE: (210), (217) imply:
% 66.25/9.68 | | | | | | | (218) apply(all_256_6, all_272_1) = all_256_0
% 66.25/9.68 | | | | | | |
% 66.25/9.68 | | | | | | | GROUND_INST: instantiating (16) with all_256_7, all_256_0,
% 66.25/9.68 | | | | | | | all_272_1, all_256_6, simplifying with (162), (218)
% 66.25/9.68 | | | | | | | gives:
% 66.25/9.69 | | | | | | | (219) all_256_0 = all_256_7
% 66.25/9.69 | | | | | | |
% 66.25/9.69 | | | | | | | REDUCE: (171), (219) imply:
% 66.25/9.69 | | | | | | | (220) $false
% 66.25/9.69 | | | | | | |
% 66.25/9.69 | | | | | | | CLOSE: (220) is inconsistent.
% 66.25/9.69 | | | | | | |
% 66.25/9.69 | | | | | | End of split
% 66.25/9.69 | | | | | |
% 66.25/9.69 | | | | | Case 2:
% 66.25/9.69 | | | | | |
% 66.25/9.69 | | | | | | (221) relation_dom(all_256_1) = all_476_2 & $i(all_476_2) & ~
% 66.25/9.69 | | | | | | in(all_256_7, all_476_2)
% 66.25/9.69 | | | | | |
% 66.25/9.69 | | | | | | ALPHA: (221) implies:
% 66.25/9.69 | | | | | | (222) ~ in(all_256_7, all_476_2)
% 66.25/9.69 | | | | | | (223) relation_dom(all_256_1) = all_476_2
% 66.25/9.69 | | | | | |
% 66.25/9.69 | | | | | | BETA: splitting (199) gives:
% 66.25/9.69 | | | | | |
% 66.25/9.69 | | | | | | Case 1:
% 66.25/9.69 | | | | | | |
% 66.25/9.69 | | | | | | | (224) ~ in(all_372_0, all_256_6)
% 66.25/9.69 | | | | | | |
% 66.25/9.69 | | | | | | | PRED_UNIFY: (151), (224) imply:
% 66.25/9.69 | | | | | | | (225) $false
% 66.25/9.69 | | | | | | |
% 66.25/9.69 | | | | | | | CLOSE: (225) is inconsistent.
% 66.25/9.69 | | | | | | |
% 66.25/9.69 | | | | | | Case 2:
% 66.25/9.69 | | | | | | |
% 66.25/9.69 | | | | | | | (226) all_372_1 = all_256_7 & relation_dom(all_256_6) =
% 66.25/9.69 | | | | | | | all_480_0 & $i(all_480_0) & in(all_272_1, all_480_0)
% 66.25/9.69 | | | | | | |
% 66.25/9.69 | | | | | | | ALPHA: (226) implies:
% 66.25/9.69 | | | | | | | (227) relation_dom(all_256_6) = all_480_0
% 66.25/9.69 | | | | | | |
% 66.25/9.69 | | | | | | | BETA: splitting (201) gives:
% 66.25/9.69 | | | | | | |
% 66.25/9.69 | | | | | | | Case 1:
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | (228) ~ in(all_360_0, all_256_4)
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | PRED_UNIFY: (169), (228) imply:
% 66.25/9.69 | | | | | | | | (229) $false
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | CLOSE: (229) is inconsistent.
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | Case 2:
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | (230) all_314_1 = all_272_1 & relation_dom(all_256_4) =
% 66.25/9.69 | | | | | | | | all_481_0 & $i(all_481_0) & in(all_256_7, all_481_0)
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | ALPHA: (230) implies:
% 66.25/9.69 | | | | | | | | (231) relation_dom(all_256_4) = all_481_0
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | GROUND_INST: instantiating (13) with all_274_0, all_482_0,
% 66.25/9.69 | | | | | | | | all_256_6, simplifying with (47), (203) gives:
% 66.25/9.69 | | | | | | | | (232) all_482_0 = all_274_0
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | GROUND_INST: instantiating (13) with all_480_0, all_482_0,
% 66.25/9.69 | | | | | | | | all_256_6, simplifying with (203), (227) gives:
% 66.25/9.69 | | | | | | | | (233) all_482_0 = all_480_0
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | GROUND_INST: instantiating (13) with all_457_0, all_461_0,
% 66.25/9.69 | | | | | | | | all_256_4, simplifying with (189), (191) gives:
% 66.25/9.69 | | | | | | | | (234) all_461_0 = all_457_0
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | GROUND_INST: instantiating (13) with all_461_0, all_477_0,
% 66.25/9.69 | | | | | | | | all_256_4, simplifying with (191), (197) gives:
% 66.25/9.69 | | | | | | | | (235) all_477_0 = all_461_0
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | GROUND_INST: instantiating (13) with all_256_5, all_481_0,
% 66.25/9.69 | | | | | | | | all_256_4, simplifying with (75), (231) gives:
% 66.25/9.69 | | | | | | | | (236) all_481_0 = all_256_5
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | GROUND_INST: instantiating (13) with all_477_0, all_481_0,
% 66.25/9.69 | | | | | | | | all_256_4, simplifying with (197), (231) gives:
% 66.25/9.69 | | | | | | | | (237) all_481_0 = all_477_0
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | GROUND_INST: instantiating (13) with all_445_0, all_476_2,
% 66.25/9.69 | | | | | | | | all_256_1, simplifying with (186), (223) gives:
% 66.25/9.69 | | | | | | | | (238) all_476_2 = all_445_0
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | COMBINE_EQS: (232), (233) imply:
% 66.25/9.69 | | | | | | | | (239) all_480_0 = all_274_0
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | COMBINE_EQS: (236), (237) imply:
% 66.25/9.69 | | | | | | | | (240) all_477_0 = all_256_5
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | SIMP: (240) implies:
% 66.25/9.69 | | | | | | | | (241) all_477_0 = all_256_5
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | COMBINE_EQS: (235), (241) imply:
% 66.25/9.69 | | | | | | | | (242) all_461_0 = all_256_5
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | SIMP: (242) implies:
% 66.25/9.69 | | | | | | | | (243) all_461_0 = all_256_5
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | COMBINE_EQS: (234), (243) imply:
% 66.25/9.69 | | | | | | | | (244) all_457_0 = all_256_5
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | SIMP: (244) implies:
% 66.25/9.69 | | | | | | | | (245) all_457_0 = all_256_5
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | REDUCE: (222), (238) imply:
% 66.25/9.69 | | | | | | | | (246) ~ in(all_256_7, all_445_0)
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | BETA: splitting (192) gives:
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | | Case 1:
% 66.25/9.69 | | | | | | | | |
% 66.25/9.69 | | | | | | | | | (247) all_469_0 = all_317_0 & relation_dom(all_256_1) =
% 66.25/9.69 | | | | | | | | | all_317_0
% 66.25/9.69 | | | | | | | | |
% 66.25/9.69 | | | | | | | | | ALPHA: (247) implies:
% 66.25/9.69 | | | | | | | | | (248) relation_dom(all_256_1) = all_317_0
% 66.25/9.69 | | | | | | | | |
% 66.25/9.69 | | | | | | | | | REDUCE: (115), (248) imply:
% 66.25/9.69 | | | | | | | | | (249) relation_dom(all_256_1) = all_256_5
% 66.25/9.69 | | | | | | | | |
% 66.25/9.69 | | | | | | | | | GROUND_INST: instantiating (13) with all_445_0, all_256_5,
% 66.25/9.69 | | | | | | | | | all_256_1, simplifying with (186), (249) gives:
% 66.25/9.69 | | | | | | | | | (250) all_445_0 = all_256_5
% 66.25/9.69 | | | | | | | | |
% 66.25/9.69 | | | | | | | | | REDUCE: (246), (250) imply:
% 66.25/9.69 | | | | | | | | | (251) ~ in(all_256_7, all_256_5)
% 66.25/9.69 | | | | | | | | |
% 66.25/9.69 | | | | | | | | | PRED_UNIFY: (18), (251) imply:
% 66.25/9.69 | | | | | | | | | (252) $false
% 66.25/9.69 | | | | | | | | |
% 66.25/9.69 | | | | | | | | | CLOSE: (252) is inconsistent.
% 66.25/9.69 | | | | | | | | |
% 66.25/9.69 | | | | | | | | Case 2:
% 66.25/9.69 | | | | | | | | |
% 66.25/9.69 | | | | | | | | | (253) relation_dom(all_256_6) = all_469_1 & $i(all_469_1) &
% 66.25/9.69 | | | | | | | | | ~ subset(all_274_0, all_469_1)
% 66.25/9.69 | | | | | | | | |
% 66.25/9.69 | | | | | | | | | ALPHA: (253) implies:
% 66.25/9.69 | | | | | | | | | (254) ~ subset(all_274_0, all_469_1)
% 66.25/9.69 | | | | | | | | | (255) relation_dom(all_256_6) = all_469_1
% 66.25/9.69 | | | | | | | | |
% 66.25/9.69 | | | | | | | | | GROUND_INST: instantiating (13) with all_274_0, all_469_1,
% 66.25/9.69 | | | | | | | | | all_256_6, simplifying with (47), (255) gives:
% 66.25/9.69 | | | | | | | | | (256) all_469_1 = all_274_0
% 66.25/9.69 | | | | | | | | |
% 66.25/9.69 | | | | | | | | | REDUCE: (254), (256) imply:
% 66.25/9.69 | | | | | | | | | (257) ~ subset(all_274_0, all_274_0)
% 66.25/9.69 | | | | | | | | |
% 66.25/9.69 | | | | | | | | | PRED_UNIFY: (118), (257) imply:
% 66.25/9.69 | | | | | | | | | (258) $false
% 66.25/9.69 | | | | | | | | |
% 66.25/9.69 | | | | | | | | | CLOSE: (258) is inconsistent.
% 66.25/9.69 | | | | | | | | |
% 66.25/9.69 | | | | | | | | End of split
% 66.25/9.69 | | | | | | | |
% 66.25/9.69 | | | | | | | End of split
% 66.25/9.69 | | | | | | |
% 66.25/9.69 | | | | | | End of split
% 66.25/9.69 | | | | | |
% 66.25/9.69 | | | | | End of split
% 66.25/9.69 | | | | |
% 66.25/9.69 | | | | End of split
% 66.25/9.69 | | | |
% 66.25/9.69 | | | Case 2:
% 66.25/9.69 | | | |
% 66.25/9.69 | | | | (259) ~ (all_256_2 = all_256_7) & apply(all_256_4, all_256_7) =
% 66.25/9.69 | | | | all_256_3 & apply(all_256_6, all_256_3) = all_256_2 &
% 66.25/9.69 | | | | $i(all_256_2) & $i(all_256_3)
% 66.25/9.69 | | | |
% 66.25/9.69 | | | | ALPHA: (259) implies:
% 66.25/9.69 | | | | (260) ~ (all_256_2 = all_256_7)
% 66.25/9.69 | | | | (261) apply(all_256_6, all_256_3) = all_256_2
% 66.25/9.69 | | | | (262) apply(all_256_4, all_256_7) = all_256_3
% 66.25/9.69 | | | |
% 66.25/9.69 | | | | GROUND_INST: instantiating (16) with all_314_1, all_256_3, all_256_7,
% 66.25/9.69 | | | | all_256_4, simplifying with (166), (262) gives:
% 66.25/9.69 | | | | (263) all_314_1 = all_256_3
% 66.25/9.69 | | | |
% 66.25/9.69 | | | | REDUCE: (145), (263) imply:
% 66.25/9.69 | | | | (264) ordered_pair(all_256_3, all_256_7) = all_368_0
% 66.25/9.69 | | | |
% 66.25/9.69 | | | | REDUCE: (97), (263) imply:
% 66.25/9.69 | | | | (265) $i(all_256_3)
% 66.25/9.69 | | | |
% 66.25/9.69 | | | | GROUND_INST: instantiating (t8_funct_1) with all_256_3, all_256_7,
% 66.25/9.69 | | | | all_256_6, all_368_0, all_256_2, simplifying with (19),
% 66.25/9.69 | | | | (20), (22), (23), (261), (264), (265) gives:
% 66.25/9.69 | | | | (266) ? [v0: $i] : (( ~ (all_256_2 = all_256_7) | in(all_368_0,
% 66.25/9.69 | | | | all_256_6) | (relation_dom(all_256_6) = v0 & $i(v0) & ~
% 66.25/9.69 | | | | in(all_256_3, v0))) & ( ~ in(all_368_0, all_256_6) |
% 66.25/9.69 | | | | (all_256_2 = all_256_7 & relation_dom(all_256_6) = v0 &
% 66.25/9.69 | | | | $i(v0) & in(all_256_3, v0))))
% 66.25/9.69 | | | |
% 66.25/9.69 | | | | DELTA: instantiating (266) with fresh symbol all_485_0 gives:
% 66.25/9.69 | | | | (267) ( ~ (all_256_2 = all_256_7) | in(all_368_0, all_256_6) |
% 66.25/9.69 | | | | (relation_dom(all_256_6) = all_485_0 & $i(all_485_0) & ~
% 66.25/9.69 | | | | in(all_256_3, all_485_0))) & ( ~ in(all_368_0, all_256_6) |
% 66.25/9.69 | | | | (all_256_2 = all_256_7 & relation_dom(all_256_6) = all_485_0
% 66.25/9.69 | | | | & $i(all_485_0) & in(all_256_3, all_485_0)))
% 66.25/9.69 | | | |
% 66.25/9.69 | | | | ALPHA: (267) implies:
% 66.25/9.69 | | | | (268) ~ in(all_368_0, all_256_6) | (all_256_2 = all_256_7 &
% 66.25/9.69 | | | | relation_dom(all_256_6) = all_485_0 & $i(all_485_0) &
% 66.25/9.69 | | | | in(all_256_3, all_485_0))
% 66.25/9.69 | | | |
% 66.25/9.69 | | | | BETA: splitting (268) gives:
% 66.25/9.69 | | | |
% 66.25/9.69 | | | | Case 1:
% 66.25/9.69 | | | | |
% 66.25/9.69 | | | | | (269) ~ in(all_368_0, all_256_6)
% 66.25/9.69 | | | | |
% 66.25/9.69 | | | | | PRED_UNIFY: (144), (269) imply:
% 66.25/9.69 | | | | | (270) $false
% 66.25/9.69 | | | | |
% 66.25/9.69 | | | | | CLOSE: (270) is inconsistent.
% 66.25/9.69 | | | | |
% 66.25/9.69 | | | | Case 2:
% 66.25/9.69 | | | | |
% 66.25/9.69 | | | | | (271) all_256_2 = all_256_7 & relation_dom(all_256_6) = all_485_0 &
% 66.25/9.69 | | | | | $i(all_485_0) & in(all_256_3, all_485_0)
% 66.25/9.69 | | | | |
% 66.25/9.69 | | | | | ALPHA: (271) implies:
% 66.25/9.69 | | | | | (272) all_256_2 = all_256_7
% 66.25/9.69 | | | | |
% 66.25/9.69 | | | | | REDUCE: (260), (272) imply:
% 66.25/9.70 | | | | | (273) $false
% 66.25/9.70 | | | | |
% 66.25/9.70 | | | | | CLOSE: (273) is inconsistent.
% 66.25/9.70 | | | | |
% 66.25/9.70 | | | | End of split
% 66.25/9.70 | | | |
% 66.25/9.70 | | | End of split
% 66.25/9.70 | | |
% 66.25/9.70 | | End of split
% 66.25/9.70 | |
% 66.25/9.70 | End of split
% 66.25/9.70 |
% 66.25/9.70 End of proof
% 66.25/9.70 % SZS output end Proof for theBenchmark
% 66.25/9.70
% 66.25/9.70 9078ms
%------------------------------------------------------------------------------