TSTP Solution File: SEU192+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU192+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 : n002.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 17:43:10 EDT 2023
% Result : Theorem 139.84s 19.76s
% Output : Proof 140.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU192+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.34 % Computer : n002.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Wed Aug 23 17:27:46 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.19/0.65 ________ _____
% 0.19/0.65 ___ __ \_________(_)________________________________
% 0.19/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.65
% 0.19/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.65 (2023-06-19)
% 0.19/0.65
% 0.19/0.65 (c) Philipp Rümmer, 2009-2023
% 0.19/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.65 Amanda Stjerna.
% 0.19/0.65 Free software under BSD-3-Clause.
% 0.19/0.65
% 0.19/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.65
% 0.19/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.67 Running up to 7 provers in parallel.
% 0.19/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 5.89/1.72 Prover 4: Preprocessing ...
% 5.89/1.72 Prover 1: Preprocessing ...
% 6.22/1.79 Prover 0: Preprocessing ...
% 6.22/1.79 Prover 3: Preprocessing ...
% 6.22/1.79 Prover 5: Preprocessing ...
% 6.22/1.79 Prover 2: Preprocessing ...
% 6.22/1.79 Prover 6: Preprocessing ...
% 21.90/4.01 Prover 1: Warning: ignoring some quantifiers
% 22.31/4.13 Prover 3: Warning: ignoring some quantifiers
% 23.00/4.18 Prover 1: Constructing countermodel ...
% 23.23/4.19 Prover 3: Constructing countermodel ...
% 23.23/4.21 Prover 6: Proving ...
% 23.63/4.29 Prover 5: Proving ...
% 24.53/4.47 Prover 4: Warning: ignoring some quantifiers
% 24.53/4.60 Prover 2: Proving ...
% 25.99/4.66 Prover 4: Constructing countermodel ...
% 28.79/4.98 Prover 0: Proving ...
% 70.71/10.59 Prover 2: stopped
% 70.97/10.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 73.69/11.03 Prover 7: Preprocessing ...
% 77.89/11.67 Prover 7: Warning: ignoring some quantifiers
% 79.76/11.80 Prover 7: Constructing countermodel ...
% 96.55/14.03 Prover 5: stopped
% 96.55/14.04 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 97.26/14.19 Prover 8: Preprocessing ...
% 100.35/14.58 Prover 8: Warning: ignoring some quantifiers
% 100.78/14.61 Prover 8: Constructing countermodel ...
% 111.45/16.03 Prover 1: stopped
% 111.45/16.04 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 112.53/16.12 Prover 9: Preprocessing ...
% 115.73/16.57 Prover 9: Warning: ignoring some quantifiers
% 115.73/16.58 Prover 9: Constructing countermodel ...
% 126.38/17.95 Prover 6: stopped
% 126.38/17.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 127.55/18.10 Prover 10: Preprocessing ...
% 128.46/18.26 Prover 10: Warning: ignoring some quantifiers
% 128.46/18.30 Prover 10: Constructing countermodel ...
% 138.76/19.75 Prover 10: Found proof (size 99)
% 138.76/19.75 Prover 10: proved (1783ms)
% 138.76/19.75 Prover 9: stopped
% 138.76/19.75 Prover 3: stopped
% 138.76/19.75 Prover 0: stopped
% 138.76/19.75 Prover 4: stopped
% 139.84/19.75 Prover 8: stopped
% 139.84/19.76 Prover 7: stopped
% 139.84/19.76
% 139.84/19.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 139.84/19.76
% 139.84/19.77 % SZS output start Proof for theBenchmark
% 139.84/19.78 Assumptions after simplification:
% 139.84/19.78 ---------------------------------
% 139.84/19.78
% 139.84/19.78 (d11_relat_1)
% 140.33/19.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 140.33/19.81 $i] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4)
% 140.33/19.81 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 140.33/19.81 relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v5, v0)) & ! [v0: $i] :
% 140.33/19.81 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 140.33/19.81 (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) |
% 140.33/19.81 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) |
% 140.33/19.81 ~ relation(v0) | ~ in(v5, v2) | in(v3, v1)) & ! [v0: $i] : ! [v1: $i] :
% 140.33/19.81 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 140.33/19.81 (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) |
% 140.33/19.81 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) |
% 140.33/19.81 ~ relation(v0) | ~ in(v5, v0) | ~ in(v3, v1) | in(v5, v2)) & ! [v0: $i]
% 140.33/19.81 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 140.33/19.81 (relation_dom_restriction(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 140.33/19.81 | ~ relation(v2) | ~ relation(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6:
% 140.33/19.81 $i] : (ordered_pair(v4, v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ( ~ in(v6,
% 140.33/19.81 v2) | ~ in(v6, v0) | ~ in(v4, v1)) & (in(v6, v2) | (in(v6, v0) &
% 140.33/19.81 in(v4, v1)))))
% 140.33/19.81
% 140.33/19.81 (d1_xboole_0)
% 140.33/19.81 $i(empty_set) & ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) & ? [v0: $i]
% 140.33/19.81 : (v0 = empty_set | ~ $i(v0) | ? [v1: $i] : ($i(v1) & in(v1, v0)))
% 140.33/19.81
% 140.33/19.81 (d4_relat_1)
% 140.33/19.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 140.33/19.82 (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~
% 140.33/19.82 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v2,
% 140.33/19.82 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) =
% 140.33/19.82 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1)
% 140.33/19.82 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) &
% 140.33/19.82 in(v4, v0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 140.33/19.82 (relation_dom(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3:
% 140.33/19.82 $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ in(v3, v0) | !
% 140.33/19.82 [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v3, v6) = v7) | ~ $i(v6) |
% 140.33/19.82 ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & $i(v5) &
% 140.33/19.82 in(v5, v1)))))
% 140.33/19.82
% 140.33/19.82 (d8_xboole_0)
% 140.33/19.82 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ subset(v0,
% 140.33/19.82 v1) | proper_subset(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 140.33/19.82 $i(v0) | ~ proper_subset(v0, v1) | subset(v0, v1)) & ! [v0: $i] : ( ~
% 140.33/19.82 $i(v0) | ~ proper_subset(v0, v0))
% 140.33/19.82
% 140.33/19.82 (dt_k7_relat_1)
% 140.33/19.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0,
% 140.33/19.82 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | relation(v2))
% 140.33/19.82
% 140.33/19.82 (fc1_subset_1)
% 140.33/19.82 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ~
% 140.33/19.82 empty(v1))
% 140.33/19.82
% 140.33/19.82 (fc4_relat_1)
% 140.33/19.82 $i(empty_set) & relation(empty_set) & empty(empty_set)
% 140.33/19.82
% 140.33/19.82 (l4_zfmisc_1)
% 140.33/19.83 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | v0 =
% 140.33/19.83 empty_set | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ subset(v0,
% 140.33/19.83 v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v1) = v0) | ~ $i(v1) |
% 140.33/19.83 ~ $i(v0) | subset(v0, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0)
% 140.33/19.83 = v1) | ~ $i(v0) | subset(empty_set, v1))
% 140.33/19.83
% 140.33/19.83 (rc2_subset_1)
% 140.33/19.83 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i]
% 140.33/19.83 : ($i(v2) & element(v2, v1) & empty(v2)))
% 140.33/19.83
% 140.33/19.83 (t1_zfmisc_1)
% 140.33/19.83 $i(empty_set) & ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set)
% 140.33/19.83 = v0 & $i(v0))
% 140.33/19.83
% 140.33/19.83 (t25_relat_1)
% 140.33/19.83 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 140.33/19.83 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] :
% 140.33/19.83 ! [v4: $i] : ( ~ (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3)
% 140.33/19.83 | ~ relation(v3) | subset(v1, v4)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 140.33/19.83 (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3) | ~
% 140.33/19.83 relation(v3) | ? [v5: $i] : (relation_dom(v3) = v5 & $i(v5) &
% 140.33/19.83 subset(v2, v5)))))
% 140.33/19.83
% 140.33/19.83 (t39_zfmisc_1)
% 140.33/19.83 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | v0 =
% 140.33/19.83 empty_set | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ subset(v0,
% 140.33/19.83 v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v1) = v0) | ~ $i(v1) |
% 140.33/19.83 ~ $i(v0) | subset(v0, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0)
% 140.33/19.83 = v1) | ~ $i(v0) | subset(empty_set, v1))
% 140.33/19.83
% 140.33/19.83 (t46_relat_1)
% 140.33/19.83 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 140.33/19.83 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] :
% 140.33/19.83 ! [v4: $i] : ( ~ (relation_composition(v0, v3) = v4) | ~ $i(v3) | ~
% 140.33/19.83 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v2 & relation_dom(v4)
% 140.33/19.83 = v2) | (relation_dom(v3) = v5 & $i(v5) & ~ subset(v1, v5))))))
% 140.33/19.83
% 140.33/19.83 (t47_relat_1)
% 140.33/19.83 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 140.33/19.83 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] :
% 140.33/19.83 ! [v4: $i] : ( ~ (relation_composition(v3, v0) = v4) | ~ $i(v3) | ~
% 140.33/19.83 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v1 & relation_rng(v4)
% 140.33/19.83 = v1 & $i(v1)) | (relation_rng(v3) = v5 & $i(v5) & ~ subset(v2,
% 140.33/19.83 v5))))))
% 140.33/19.83
% 140.33/19.83 (t56_relat_1)
% 140.33/19.83 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ relation(v0) |
% 140.33/19.83 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (ordered_pair(v1, v2) = v3 & $i(v3)
% 140.33/19.83 & $i(v2) & $i(v1) & in(v3, v0)))
% 140.33/19.83
% 140.33/19.83 (t60_relat_1)
% 140.33/19.83 relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set &
% 140.33/19.83 $i(empty_set)
% 140.33/19.83
% 140.33/19.83 (t6_boole)
% 140.33/19.84 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 140.33/19.84
% 140.33/19.84 (t86_relat_1)
% 140.33/19.84 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 140.33/19.84 $i] : (relation_dom(v3) = v4 & relation_dom_restriction(v2, v1) = v3 &
% 140.33/19.84 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & relation(v2) &
% 140.33/19.84 ((relation_dom(v2) = v5 & $i(v5) & in(v0, v5) & in(v0, v1) & ~ in(v0, v4))
% 140.33/19.84 | (in(v0, v4) & ( ~ in(v0, v1) | (relation_dom(v2) = v5 & $i(v5) & ~
% 140.33/19.84 in(v0, v5))))))
% 140.33/19.84
% 140.33/19.84 (function-axioms)
% 140.33/19.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 140.33/19.84 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3,
% 140.33/19.84 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 140.33/19.84 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) =
% 140.33/19.84 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 140.33/19.84 ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & !
% 140.33/19.84 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.33/19.84 (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) =
% 140.33/19.84 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 140.33/19.84 ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) =
% 140.33/19.84 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 140.33/19.84 ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) &
% 140.33/19.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.33/19.84 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 140.33/19.84 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.33/19.84 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 140.33/19.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.33/19.84 (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3,
% 140.33/19.84 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 140.33/19.84 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & !
% 140.33/19.84 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.33/19.84 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 140.33/19.84 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.33/19.84 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : !
% 140.33/19.84 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) =
% 140.33/19.84 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 140.33/19.84 [v2: $i] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~
% 140.33/19.84 (relation_inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 140.33/19.84 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & !
% 140.33/19.84 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) |
% 140.33/19.84 ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 140.33/19.84 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] : ! [v1:
% 140.33/19.84 $i] : ! [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~
% 140.33/19.84 (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 140.33/19.84 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i]
% 140.33/19.84 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 140.33/19.84 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 140.33/19.84 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1:
% 140.33/19.84 $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) =
% 140.33/19.84 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 140.33/19.84 (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 140.33/19.84
% 140.33/19.84 Further assumptions not needed in the proof:
% 140.33/19.84 --------------------------------------------
% 140.33/19.85 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_relat_1,
% 140.33/19.85 commutativity_k2_tarski, commutativity_k2_xboole_0, commutativity_k3_xboole_0,
% 140.33/19.85 d10_relat_1, d10_xboole_0, d1_relat_1, d1_setfam_1, d1_tarski, d1_zfmisc_1,
% 140.33/19.85 d2_subset_1, d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_tarski, d3_xboole_0,
% 140.33/19.85 d4_subset_1, d4_tarski, d4_xboole_0, d5_relat_1, d5_subset_1, d5_tarski,
% 140.33/19.85 d6_relat_1, d7_relat_1, d7_xboole_0, d8_relat_1, d8_setfam_1, dt_k1_relat_1,
% 140.33/19.85 dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1,
% 140.33/19.85 dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_relat_1,
% 140.33/19.85 dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_relat_1, dt_k4_tarski,
% 140.33/19.85 dt_k4_xboole_0, dt_k5_relat_1, dt_k5_setfam_1, dt_k6_relat_1, dt_k6_setfam_1,
% 140.33/19.85 dt_k6_subset_1, dt_k7_setfam_1, dt_m1_subset_1, existence_m1_subset_1,
% 140.33/19.85 fc10_relat_1, fc1_xboole_0, fc1_zfmisc_1, fc2_relat_1, fc2_subset_1,
% 140.33/19.85 fc2_xboole_0, fc3_subset_1, fc3_xboole_0, fc4_subset_1, fc5_relat_1,
% 140.33/19.85 fc6_relat_1, fc7_relat_1, fc8_relat_1, fc9_relat_1, idempotence_k2_xboole_0,
% 140.33/19.85 idempotence_k3_xboole_0, involutiveness_k3_subset_1, involutiveness_k4_relat_1,
% 140.33/19.85 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_zfmisc_1,
% 140.33/19.85 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1,
% 140.33/19.85 l3_subset_1, l3_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, rc1_relat_1,
% 140.33/19.85 rc1_subset_1, rc1_xboole_0, rc2_relat_1, rc2_xboole_0, redefinition_k5_setfam_1,
% 140.33/19.85 redefinition_k6_setfam_1, redefinition_k6_subset_1, reflexivity_r1_tarski,
% 140.33/19.85 symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, t118_zfmisc_1, t119_zfmisc_1,
% 140.33/19.85 t12_xboole_1, t136_zfmisc_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_subset,
% 140.33/19.85 t1_xboole_1, t20_relat_1, t21_relat_1, t26_xboole_1, t28_xboole_1, t2_boole,
% 140.33/19.85 t2_subset, t2_tarski, t2_xboole_1, t30_relat_1, t33_xboole_1, t33_zfmisc_1,
% 140.33/19.85 t36_xboole_1, t37_relat_1, t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1,
% 140.33/19.85 t39_xboole_1, t3_boole, t3_subset, t3_xboole_0, t3_xboole_1, t40_xboole_1,
% 140.33/19.85 t43_subset_1, t44_relat_1, t45_relat_1, t45_xboole_1, t46_setfam_1,
% 140.33/19.85 t46_zfmisc_1, t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole, t4_subset,
% 140.33/19.85 t4_xboole_0, t50_subset_1, t54_subset_1, t5_subset, t60_xboole_1, t63_xboole_1,
% 140.33/19.85 t64_relat_1, t65_relat_1, t65_zfmisc_1, t69_enumset1, t6_zfmisc_1, t71_relat_1,
% 140.33/19.85 t74_relat_1, t7_boole, t7_xboole_1, t83_xboole_1, t8_boole, t8_xboole_1,
% 140.33/19.85 t8_zfmisc_1, t92_zfmisc_1, t99_zfmisc_1, t9_tarski, t9_zfmisc_1
% 140.33/19.85
% 140.33/19.85 Those formulas are unsatisfiable:
% 140.33/19.85 ---------------------------------
% 140.33/19.85
% 140.33/19.85 Begin of proof
% 140.33/19.85 |
% 140.33/19.85 | ALPHA: (d11_relat_1) implies:
% 140.33/19.85 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 140.33/19.85 | (relation_dom_restriction(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 140.33/19.85 | $i(v0) | ~ relation(v2) | ~ relation(v0) | ? [v4: $i] : ? [v5:
% 140.33/19.85 | $i] : ? [v6: $i] : (ordered_pair(v4, v5) = v6 & $i(v6) & $i(v5) &
% 140.33/19.85 | $i(v4) & ( ~ in(v6, v2) | ~ in(v6, v0) | ~ in(v4, v1)) & (in(v6,
% 140.33/19.85 | v2) | (in(v6, v0) & in(v4, v1)))))
% 140.33/19.85 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 140.33/19.85 | ! [v5: $i] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~
% 140.33/19.85 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 140.33/19.85 | $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ relation(v0) | ~ in(v5,
% 140.33/19.85 | v0) | ~ in(v3, v1) | in(v5, v2))
% 140.33/19.85 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 140.33/19.85 | ! [v5: $i] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~
% 140.33/19.85 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 140.33/19.85 | $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ relation(v0) | ~ in(v5,
% 140.33/19.85 | v2) | in(v3, v1))
% 140.33/19.85 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 140.33/19.85 | ! [v5: $i] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~
% 140.33/19.85 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 140.33/19.85 | $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ relation(v0) | ~ in(v5,
% 140.33/19.85 | v2) | in(v5, v0))
% 140.33/19.85 |
% 140.33/19.85 | ALPHA: (d1_xboole_0) implies:
% 140.33/19.85 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set))
% 140.33/19.85 |
% 140.33/19.85 | ALPHA: (d4_relat_1) implies:
% 140.33/19.85 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) = v1) |
% 140.33/19.85 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1) |
% 140.33/19.85 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) &
% 140.33/19.85 | $i(v3) & in(v4, v0)))
% 140.33/19.85 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 140.33/19.85 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~
% 140.33/19.85 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~
% 140.33/19.85 | in(v4, v0) | in(v2, v1))
% 140.33/19.85 |
% 140.33/19.85 | ALPHA: (d8_xboole_0) implies:
% 140.33/19.86 | (8) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 140.33/19.86 | subset(v0, v1) | proper_subset(v0, v1))
% 140.33/19.86 |
% 140.33/19.86 | ALPHA: (fc4_relat_1) implies:
% 140.33/19.86 | (9) relation(empty_set)
% 140.33/19.86 |
% 140.33/19.86 | ALPHA: (t1_zfmisc_1) implies:
% 140.33/19.86 | (10) ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) = v0 &
% 140.33/19.86 | $i(v0))
% 140.33/19.86 |
% 140.33/19.86 | ALPHA: (t39_zfmisc_1) implies:
% 140.33/19.86 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 140.33/19.86 | subset(empty_set, v1))
% 140.33/19.86 |
% 140.33/19.86 | ALPHA: (t56_relat_1) implies:
% 140.33/19.86 | (12) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ relation(v0) | ? [v1:
% 140.33/19.86 | $i] : ? [v2: $i] : ? [v3: $i] : (ordered_pair(v1, v2) = v3 &
% 140.33/19.86 | $i(v3) & $i(v2) & $i(v1) & in(v3, v0)))
% 140.33/19.86 |
% 140.33/19.86 | ALPHA: (t60_relat_1) implies:
% 140.33/19.86 | (13) relation_dom(empty_set) = empty_set
% 140.33/19.86 | (14) relation_rng(empty_set) = empty_set
% 140.33/19.86 |
% 140.33/19.86 | ALPHA: (t6_boole) implies:
% 140.33/19.86 | (15) $i(empty_set)
% 140.33/19.86 | (16) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 140.33/19.86 |
% 140.33/19.86 | ALPHA: (function-axioms) implies:
% 140.33/19.86 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 140.33/19.86 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 140.33/19.86 |
% 140.33/19.86 | DELTA: instantiating (10) with fresh symbol all_160_0 gives:
% 140.33/19.86 | (18) powerset(empty_set) = all_160_0 & singleton(empty_set) = all_160_0 &
% 140.33/19.86 | $i(all_160_0)
% 140.33/19.86 |
% 140.33/19.86 | ALPHA: (18) implies:
% 140.33/19.86 | (19) $i(all_160_0)
% 140.33/19.86 | (20) singleton(empty_set) = all_160_0
% 140.33/19.86 | (21) powerset(empty_set) = all_160_0
% 140.33/19.86 |
% 140.33/19.86 | DELTA: instantiating (t86_relat_1) with fresh symbols all_198_0, all_198_1,
% 140.33/19.86 | all_198_2, all_198_3, all_198_4, all_198_5 gives:
% 140.33/19.86 | (22) relation_dom(all_198_2) = all_198_1 &
% 140.33/19.86 | relation_dom_restriction(all_198_3, all_198_4) = all_198_2 &
% 140.33/19.86 | $i(all_198_1) & $i(all_198_2) & $i(all_198_3) & $i(all_198_4) &
% 140.33/19.86 | $i(all_198_5) & relation(all_198_3) & ((relation_dom(all_198_3) =
% 140.33/19.86 | all_198_0 & $i(all_198_0) & in(all_198_5, all_198_0) &
% 140.33/19.86 | in(all_198_5, all_198_4) & ~ in(all_198_5, all_198_1)) |
% 140.33/19.86 | (in(all_198_5, all_198_1) & ( ~ in(all_198_5, all_198_4) |
% 140.33/19.86 | (relation_dom(all_198_3) = all_198_0 & $i(all_198_0) & ~
% 140.33/19.86 | in(all_198_5, all_198_0)))))
% 140.33/19.86 |
% 140.33/19.86 | ALPHA: (22) implies:
% 140.33/19.86 | (23) relation(all_198_3)
% 140.33/19.86 | (24) $i(all_198_5)
% 140.33/19.86 | (25) $i(all_198_4)
% 140.33/19.86 | (26) $i(all_198_3)
% 140.33/19.86 | (27) $i(all_198_2)
% 140.33/19.86 | (28) $i(all_198_1)
% 140.33/19.86 | (29) relation_dom_restriction(all_198_3, all_198_4) = all_198_2
% 140.33/19.86 | (30) relation_dom(all_198_2) = all_198_1
% 140.33/19.86 | (31) (relation_dom(all_198_3) = all_198_0 & $i(all_198_0) & in(all_198_5,
% 140.33/19.86 | all_198_0) & in(all_198_5, all_198_4) & ~ in(all_198_5,
% 140.33/19.86 | all_198_1)) | (in(all_198_5, all_198_1) & ( ~ in(all_198_5,
% 140.33/19.86 | all_198_4) | (relation_dom(all_198_3) = all_198_0 &
% 140.33/19.86 | $i(all_198_0) & ~ in(all_198_5, all_198_0))))
% 140.33/19.86 |
% 140.67/19.86 | GROUND_INST: instantiating (12) with all_198_3, simplifying with (23), (26)
% 140.67/19.86 | gives:
% 140.67/19.87 | (32) all_198_3 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 140.67/19.87 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2,
% 140.67/19.87 | all_198_3))
% 140.67/19.87 |
% 140.67/19.87 | GROUND_INST: instantiating (1) with all_198_3, all_198_4, all_198_3,
% 140.67/19.87 | all_198_2, simplifying with (23), (25), (26), (29) gives:
% 140.68/19.87 | (33) all_198_2 = all_198_3 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 140.68/19.87 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2,
% 140.68/19.87 | all_198_3) & ~ in(v0, all_198_4))
% 140.68/19.87 |
% 140.68/19.87 | GROUND_INST: instantiating (dt_k7_relat_1) with all_198_3, all_198_4,
% 140.68/19.87 | all_198_2, simplifying with (23), (25), (26), (29) gives:
% 140.68/19.87 | (34) relation(all_198_2)
% 140.68/19.87 |
% 140.68/19.87 | GROUND_INST: instantiating (11) with empty_set, all_160_0, simplifying with
% 140.68/19.87 | (15), (20) gives:
% 140.68/19.87 | (35) subset(empty_set, all_160_0)
% 140.68/19.87 |
% 140.68/19.87 | GROUND_INST: instantiating (rc2_subset_1) with empty_set, all_160_0,
% 140.68/19.87 | simplifying with (15), (21) gives:
% 140.68/19.87 | (36) ? [v0: $i] : ($i(v0) & element(v0, all_160_0) & empty(v0))
% 140.68/19.87 |
% 140.68/19.87 | GROUND_INST: instantiating (t47_relat_1) with empty_set, empty_set,
% 140.68/19.87 | simplifying with (9), (14), (15) gives:
% 140.68/19.87 | (37) ? [v0: $i] : (relation_dom(empty_set) = v0 & $i(v0) & ! [v1: $i] :
% 140.68/19.87 | ! [v2: $i] : ( ~ (relation_composition(v1, empty_set) = v2) | ~
% 140.68/19.87 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 =
% 140.68/19.87 | empty_set & relation_rng(v2) = empty_set) | (relation_rng(v1)
% 140.68/19.87 | = v3 & $i(v3) & ~ subset(v0, v3)))))
% 140.68/19.87 |
% 140.68/19.87 | GROUND_INST: instantiating (t46_relat_1) with empty_set, empty_set,
% 140.68/19.87 | simplifying with (9), (14), (15) gives:
% 140.68/19.87 | (38) ? [v0: $i] : (relation_dom(empty_set) = v0 & $i(v0) & ! [v1: $i] :
% 140.68/19.87 | ! [v2: $i] : ( ~ (relation_composition(empty_set, v1) = v2) | ~
% 140.68/19.87 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = v0 &
% 140.68/19.87 | relation_dom(v2) = v0) | (relation_dom(v1) = v3 & $i(v3) & ~
% 140.68/19.87 | subset(empty_set, v3)))))
% 140.68/19.87 |
% 140.68/19.87 | GROUND_INST: instantiating (t25_relat_1) with empty_set, empty_set,
% 140.68/19.87 | simplifying with (9), (14), (15) gives:
% 140.68/19.87 | (39) ? [v0: $i] : (relation_dom(empty_set) = v0 & $i(v0) & ! [v1: $i] :
% 140.68/19.87 | ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~
% 140.68/19.87 | subset(empty_set, v1) | ~ relation(v1) | subset(empty_set, v2)) &
% 140.68/19.87 | ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1)
% 140.68/19.87 | | ~ subset(empty_set, v1) | ~ relation(v1) | ? [v3: $i] :
% 140.68/19.87 | (relation_dom(v1) = v3 & $i(v3) & subset(v0, v3))))
% 140.68/19.87 |
% 140.68/19.87 | DELTA: instantiating (36) with fresh symbol all_209_0 gives:
% 140.68/19.87 | (40) $i(all_209_0) & element(all_209_0, all_160_0) & empty(all_209_0)
% 140.68/19.87 |
% 140.68/19.87 | ALPHA: (40) implies:
% 140.68/19.87 | (41) empty(all_209_0)
% 140.68/19.87 | (42) $i(all_209_0)
% 140.68/19.87 |
% 140.68/19.87 | DELTA: instantiating (38) with fresh symbol all_211_0 gives:
% 140.68/19.87 | (43) relation_dom(empty_set) = all_211_0 & $i(all_211_0) & ! [v0: $i] : !
% 140.68/19.87 | [v1: $i] : ( ~ (relation_composition(empty_set, v0) = v1) | ~ $i(v0)
% 140.68/19.87 | | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = all_211_0 &
% 140.68/19.87 | relation_dom(v1) = all_211_0) | (relation_dom(v0) = v2 & $i(v2)
% 140.68/19.87 | & ~ subset(empty_set, v2))))
% 140.68/19.87 |
% 140.68/19.87 | ALPHA: (43) implies:
% 140.68/19.87 | (44) $i(all_211_0)
% 140.68/19.87 | (45) relation_dom(empty_set) = all_211_0
% 140.68/19.87 |
% 140.68/19.87 | DELTA: instantiating (37) with fresh symbol all_214_0 gives:
% 140.68/19.88 | (46) relation_dom(empty_set) = all_214_0 & $i(all_214_0) & ! [v0: $i] : !
% 140.68/19.88 | [v1: $i] : ( ~ (relation_composition(v0, empty_set) = v1) | ~ $i(v0)
% 140.68/19.88 | | ~ relation(v0) | ? [v2: $i] : ? [v3: $i] : ((v3 = empty_set &
% 140.68/19.88 | relation_rng(v1) = empty_set) | (relation_rng(v0) = v2 & $i(v2)
% 140.68/19.88 | & ~ subset(all_214_0, v2))))
% 140.68/19.88 |
% 140.68/19.88 | ALPHA: (46) implies:
% 140.68/19.88 | (47) relation_dom(empty_set) = all_214_0
% 140.68/19.88 |
% 140.68/19.88 | DELTA: instantiating (39) with fresh symbol all_217_0 gives:
% 140.68/19.88 | (48) relation_dom(empty_set) = all_217_0 & $i(all_217_0) & ! [v0: $i] : !
% 140.68/19.88 | [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 140.68/19.88 | subset(empty_set, v0) | ~ relation(v0) | subset(empty_set, v1)) &
% 140.68/19.88 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 140.68/19.88 | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2: $i] :
% 140.68/19.88 | (relation_dom(v0) = v2 & $i(v2) & subset(all_217_0, v2)))
% 140.68/19.88 |
% 140.68/19.88 | ALPHA: (48) implies:
% 140.68/19.88 | (49) relation_dom(empty_set) = all_217_0
% 140.68/19.88 |
% 140.68/19.88 | GROUND_INST: instantiating (17) with empty_set, all_214_0, empty_set,
% 140.68/19.88 | simplifying with (13), (47) gives:
% 140.68/19.88 | (50) all_214_0 = empty_set
% 140.68/19.88 |
% 140.68/19.88 | GROUND_INST: instantiating (17) with all_214_0, all_217_0, empty_set,
% 140.68/19.88 | simplifying with (47), (49) gives:
% 140.68/19.88 | (51) all_217_0 = all_214_0
% 140.68/19.88 |
% 140.68/19.88 | GROUND_INST: instantiating (17) with all_211_0, all_217_0, empty_set,
% 140.68/19.88 | simplifying with (45), (49) gives:
% 140.68/19.88 | (52) all_217_0 = all_211_0
% 140.68/19.88 |
% 140.68/19.88 | COMBINE_EQS: (51), (52) imply:
% 140.68/19.88 | (53) all_214_0 = all_211_0
% 140.68/19.88 |
% 140.68/19.88 | SIMP: (53) implies:
% 140.68/19.88 | (54) all_214_0 = all_211_0
% 140.68/19.88 |
% 140.68/19.88 | COMBINE_EQS: (50), (54) imply:
% 140.68/19.88 | (55) all_211_0 = empty_set
% 140.68/19.88 |
% 140.68/19.88 | GROUND_INST: instantiating (16) with all_209_0, simplifying with (41), (42)
% 140.68/19.88 | gives:
% 140.68/19.88 | (56) all_209_0 = empty_set
% 140.68/19.88 |
% 140.68/19.88 | GROUND_INST: instantiating (8) with empty_set, all_160_0, simplifying with
% 140.68/19.88 | (15), (19), (35) gives:
% 140.68/19.88 | (57) all_160_0 = empty_set | proper_subset(empty_set, all_160_0)
% 140.68/19.88 |
% 140.68/19.88 | REDUCE: (41), (56) imply:
% 140.68/19.88 | (58) empty(empty_set)
% 140.68/19.88 |
% 140.68/19.88 | BETA: splitting (31) gives:
% 140.68/19.88 |
% 140.68/19.88 | Case 1:
% 140.68/19.88 | |
% 140.68/19.88 | | (59) relation_dom(all_198_3) = all_198_0 & $i(all_198_0) & in(all_198_5,
% 140.68/19.88 | | all_198_0) & in(all_198_5, all_198_4) & ~ in(all_198_5,
% 140.68/19.88 | | all_198_1)
% 140.68/19.88 | |
% 140.68/19.88 | | ALPHA: (59) implies:
% 140.68/19.88 | | (60) ~ in(all_198_5, all_198_1)
% 140.68/19.88 | | (61) in(all_198_5, all_198_4)
% 140.68/19.88 | | (62) in(all_198_5, all_198_0)
% 140.68/19.88 | | (63) $i(all_198_0)
% 140.68/19.88 | | (64) relation_dom(all_198_3) = all_198_0
% 140.68/19.88 | |
% 140.68/19.88 | | GROUND_INST: instantiating (6) with all_198_3, all_198_0, all_198_5,
% 140.68/19.88 | | simplifying with (23), (24), (26), (62), (63), (64) gives:
% 140.68/19.88 | | (65) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_198_5, v0) = v1 &
% 140.68/19.88 | | $i(v1) & $i(v0) & in(v1, all_198_3))
% 140.68/19.88 | |
% 140.68/19.88 | | DELTA: instantiating (65) with fresh symbols all_420_0, all_420_1 gives:
% 140.68/19.88 | | (66) ordered_pair(all_198_5, all_420_1) = all_420_0 & $i(all_420_0) &
% 140.68/19.88 | | $i(all_420_1) & in(all_420_0, all_198_3)
% 140.68/19.88 | |
% 140.68/19.88 | | ALPHA: (66) implies:
% 140.68/19.88 | | (67) in(all_420_0, all_198_3)
% 140.68/19.88 | | (68) $i(all_420_1)
% 140.68/19.88 | | (69) ordered_pair(all_198_5, all_420_1) = all_420_0
% 140.68/19.88 | |
% 140.68/19.88 | | BETA: splitting (57) gives:
% 140.68/19.88 | |
% 140.68/19.88 | | Case 1:
% 140.68/19.88 | | |
% 140.68/19.88 | | |
% 140.68/19.88 | | | GROUND_INST: instantiating (2) with all_198_3, all_198_4, all_198_2,
% 140.68/19.88 | | | all_198_5, all_420_1, all_420_0, simplifying with (23), (24),
% 140.68/19.88 | | | (25), (26), (27), (29), (34), (61), (67), (68), (69) gives:
% 140.68/19.88 | | | (70) in(all_420_0, all_198_2)
% 140.68/19.88 | | |
% 140.68/19.89 | | | GROUND_INST: instantiating (7) with all_198_2, all_198_1, all_198_5,
% 140.68/19.89 | | | all_420_1, all_420_0, simplifying with (24), (27), (28),
% 140.68/19.89 | | | (30), (34), (60), (68), (69), (70) gives:
% 140.68/19.89 | | | (71) $false
% 140.68/19.89 | | |
% 140.68/19.89 | | | CLOSE: (71) is inconsistent.
% 140.68/19.89 | | |
% 140.68/19.89 | | Case 2:
% 140.68/19.89 | | |
% 140.68/19.89 | | | (72) all_160_0 = empty_set
% 140.68/19.89 | | |
% 140.68/19.89 | | | REDUCE: (21), (72) imply:
% 140.68/19.89 | | | (73) powerset(empty_set) = empty_set
% 140.68/19.89 | | |
% 140.68/19.89 | | | GROUND_INST: instantiating (fc1_subset_1) with empty_set, empty_set,
% 140.68/19.89 | | | simplifying with (15), (58), (73) gives:
% 140.68/19.89 | | | (74) $false
% 140.68/19.89 | | |
% 140.68/19.89 | | | CLOSE: (74) is inconsistent.
% 140.68/19.89 | | |
% 140.68/19.89 | | End of split
% 140.68/19.89 | |
% 140.68/19.89 | Case 2:
% 140.68/19.89 | |
% 140.68/19.89 | | (75) in(all_198_5, all_198_1) & ( ~ in(all_198_5, all_198_4) |
% 140.68/19.89 | | (relation_dom(all_198_3) = all_198_0 & $i(all_198_0) & ~
% 140.68/19.89 | | in(all_198_5, all_198_0)))
% 140.68/19.89 | |
% 140.68/19.89 | | ALPHA: (75) implies:
% 140.68/19.89 | | (76) in(all_198_5, all_198_1)
% 140.68/19.89 | | (77) ~ in(all_198_5, all_198_4) | (relation_dom(all_198_3) = all_198_0 &
% 140.68/19.89 | | $i(all_198_0) & ~ in(all_198_5, all_198_0))
% 140.68/19.89 | |
% 140.68/19.89 | | BETA: splitting (33) gives:
% 140.68/19.89 | |
% 140.68/19.89 | | Case 1:
% 140.68/19.89 | | |
% 140.68/19.89 | | | (78) all_198_2 = all_198_3
% 140.68/19.89 | | |
% 140.68/19.89 | | | REDUCE: (30), (78) imply:
% 140.68/19.89 | | | (79) relation_dom(all_198_3) = all_198_1
% 140.68/19.89 | | |
% 140.68/19.89 | | | REDUCE: (29), (78) imply:
% 140.68/19.89 | | | (80) relation_dom_restriction(all_198_3, all_198_4) = all_198_3
% 140.68/19.89 | | |
% 140.68/19.89 | | | BETA: splitting (77) gives:
% 140.68/19.89 | | |
% 140.68/19.89 | | | Case 1:
% 140.68/19.89 | | | |
% 140.68/19.89 | | | | (81) ~ in(all_198_5, all_198_4)
% 140.68/19.89 | | | |
% 140.68/19.89 | | | | GROUND_INST: instantiating (6) with all_198_3, all_198_1, all_198_5,
% 140.68/19.89 | | | | simplifying with (23), (24), (26), (28), (76), (79) gives:
% 140.68/19.89 | | | | (82) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_198_5, v0) = v1 &
% 140.68/19.89 | | | | $i(v1) & $i(v0) & in(v1, all_198_3))
% 140.68/19.89 | | | |
% 140.68/19.89 | | | | DELTA: instantiating (82) with fresh symbols all_417_0, all_417_1 gives:
% 140.68/19.89 | | | | (83) ordered_pair(all_198_5, all_417_1) = all_417_0 & $i(all_417_0) &
% 140.68/19.89 | | | | $i(all_417_1) & in(all_417_0, all_198_3)
% 140.68/19.89 | | | |
% 140.68/19.89 | | | | ALPHA: (83) implies:
% 140.68/19.89 | | | | (84) in(all_417_0, all_198_3)
% 140.68/19.89 | | | | (85) $i(all_417_1)
% 140.68/19.89 | | | | (86) ordered_pair(all_198_5, all_417_1) = all_417_0
% 140.68/19.89 | | | |
% 140.68/19.89 | | | | GROUND_INST: instantiating (3) with all_198_3, all_198_4, all_198_3,
% 140.68/19.89 | | | | all_198_5, all_417_1, all_417_0, simplifying with (23),
% 140.68/19.89 | | | | (24), (25), (26), (80), (81), (84), (85), (86) gives:
% 140.68/19.89 | | | | (87) $false
% 140.68/19.89 | | | |
% 140.68/19.89 | | | | CLOSE: (87) is inconsistent.
% 140.68/19.89 | | | |
% 140.68/19.89 | | | Case 2:
% 140.68/19.89 | | | |
% 140.68/19.89 | | | | (88) relation_dom(all_198_3) = all_198_0 & $i(all_198_0) & ~
% 140.68/19.89 | | | | in(all_198_5, all_198_0)
% 140.68/19.89 | | | |
% 140.68/19.89 | | | | ALPHA: (88) implies:
% 140.68/19.90 | | | | (89) ~ in(all_198_5, all_198_0)
% 140.68/19.90 | | | | (90) relation_dom(all_198_3) = all_198_0
% 140.68/19.90 | | | |
% 140.68/19.90 | | | | GROUND_INST: instantiating (17) with all_198_1, all_198_0, all_198_3,
% 140.68/19.90 | | | | simplifying with (79), (90) gives:
% 140.68/19.90 | | | | (91) all_198_0 = all_198_1
% 140.68/19.90 | | | |
% 140.68/19.90 | | | | REDUCE: (89), (91) imply:
% 140.68/19.90 | | | | (92) ~ in(all_198_5, all_198_1)
% 140.68/19.90 | | | |
% 140.68/19.90 | | | | PRED_UNIFY: (76), (92) imply:
% 140.68/19.90 | | | | (93) $false
% 140.68/19.90 | | | |
% 140.68/19.90 | | | | CLOSE: (93) is inconsistent.
% 140.68/19.90 | | | |
% 140.68/19.90 | | | End of split
% 140.68/19.90 | | |
% 140.68/19.90 | | Case 2:
% 140.68/19.90 | | |
% 140.68/19.90 | | | (94) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) =
% 140.68/19.90 | | | v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, all_198_3) & ~ in(v0,
% 140.84/19.90 | | | all_198_4))
% 140.84/19.90 | | |
% 140.84/19.90 | | | DELTA: instantiating (94) with fresh symbols all_364_0, all_364_1,
% 140.84/19.90 | | | all_364_2 gives:
% 140.84/19.90 | | | (95) ordered_pair(all_364_2, all_364_1) = all_364_0 & $i(all_364_0) &
% 140.84/19.90 | | | $i(all_364_1) & $i(all_364_2) & in(all_364_0, all_198_3) & ~
% 140.84/19.90 | | | in(all_364_2, all_198_4)
% 140.84/19.90 | | |
% 140.84/19.90 | | | ALPHA: (95) implies:
% 140.84/19.90 | | | (96) in(all_364_0, all_198_3)
% 140.84/19.90 | | | (97) $i(all_364_0)
% 140.84/19.90 | | |
% 140.84/19.90 | | | BETA: splitting (32) gives:
% 140.84/19.90 | | |
% 140.84/19.90 | | | Case 1:
% 140.84/19.90 | | | |
% 140.84/19.90 | | | | (98) all_198_3 = empty_set
% 140.84/19.90 | | | |
% 140.84/19.90 | | | | REDUCE: (96), (98) imply:
% 140.84/19.90 | | | | (99) in(all_364_0, empty_set)
% 140.84/19.90 | | | |
% 140.84/19.90 | | | | GROUND_INST: instantiating (5) with all_364_0, simplifying with (97),
% 140.84/19.90 | | | | (99) gives:
% 140.84/19.90 | | | | (100) $false
% 140.84/19.90 | | | |
% 140.84/19.90 | | | | CLOSE: (100) is inconsistent.
% 140.84/19.90 | | | |
% 140.84/19.90 | | | Case 2:
% 140.84/19.90 | | | |
% 140.84/19.90 | | | |
% 140.84/19.90 | | | | GROUND_INST: instantiating (6) with all_198_2, all_198_1, all_198_5,
% 140.84/19.90 | | | | simplifying with (24), (27), (28), (30), (34), (76) gives:
% 140.84/19.90 | | | | (101) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_198_5, v0) = v1 &
% 140.84/19.90 | | | | $i(v1) & $i(v0) & in(v1, all_198_2))
% 140.84/19.90 | | | |
% 140.84/19.90 | | | | DELTA: instantiating (101) with fresh symbols all_420_0, all_420_1
% 140.84/19.90 | | | | gives:
% 140.84/19.90 | | | | (102) ordered_pair(all_198_5, all_420_1) = all_420_0 & $i(all_420_0)
% 140.84/19.90 | | | | & $i(all_420_1) & in(all_420_0, all_198_2)
% 140.84/19.90 | | | |
% 140.84/19.90 | | | | ALPHA: (102) implies:
% 140.84/19.90 | | | | (103) in(all_420_0, all_198_2)
% 140.84/19.90 | | | | (104) $i(all_420_1)
% 140.84/19.90 | | | | (105) ordered_pair(all_198_5, all_420_1) = all_420_0
% 140.84/19.90 | | | |
% 140.84/19.90 | | | | GROUND_INST: instantiating (4) with all_198_3, all_198_4, all_198_2,
% 140.84/19.90 | | | | all_198_5, all_420_1, all_420_0, simplifying with (23),
% 140.84/19.90 | | | | (24), (25), (26), (27), (29), (34), (103), (104), (105)
% 140.84/19.90 | | | | gives:
% 140.84/19.90 | | | | (106) in(all_420_0, all_198_3)
% 140.84/19.90 | | | |
% 140.84/19.90 | | | | GROUND_INST: instantiating (3) with all_198_3, all_198_4, all_198_2,
% 140.84/19.90 | | | | all_198_5, all_420_1, all_420_0, simplifying with (23),
% 140.84/19.90 | | | | (24), (25), (26), (27), (29), (34), (103), (104), (105)
% 140.84/19.90 | | | | gives:
% 140.84/19.90 | | | | (107) in(all_198_5, all_198_4)
% 140.84/19.90 | | | |
% 140.84/19.91 | | | | BETA: splitting (77) gives:
% 140.84/19.91 | | | |
% 140.84/19.91 | | | | Case 1:
% 140.84/19.91 | | | | |
% 140.84/19.91 | | | | | (108) ~ in(all_198_5, all_198_4)
% 140.84/19.91 | | | | |
% 140.84/19.91 | | | | | PRED_UNIFY: (107), (108) imply:
% 140.84/19.91 | | | | | (109) $false
% 140.84/19.91 | | | | |
% 140.84/19.91 | | | | | CLOSE: (109) is inconsistent.
% 140.84/19.91 | | | | |
% 140.84/19.91 | | | | Case 2:
% 140.84/19.91 | | | | |
% 140.84/19.91 | | | | | (110) relation_dom(all_198_3) = all_198_0 & $i(all_198_0) & ~
% 140.84/19.91 | | | | | in(all_198_5, all_198_0)
% 140.84/19.91 | | | | |
% 140.84/19.91 | | | | | ALPHA: (110) implies:
% 140.84/19.91 | | | | | (111) ~ in(all_198_5, all_198_0)
% 140.84/19.91 | | | | | (112) $i(all_198_0)
% 140.84/19.91 | | | | | (113) relation_dom(all_198_3) = all_198_0
% 140.84/19.91 | | | | |
% 140.84/19.91 | | | | | GROUND_INST: instantiating (7) with all_198_3, all_198_0, all_198_5,
% 140.84/19.91 | | | | | all_420_1, all_420_0, simplifying with (23), (24), (26),
% 140.84/19.91 | | | | | (104), (105), (106), (111), (112), (113) gives:
% 140.84/19.91 | | | | | (114) $false
% 140.84/19.91 | | | | |
% 140.84/19.91 | | | | | CLOSE: (114) is inconsistent.
% 140.84/19.91 | | | | |
% 140.84/19.91 | | | | End of split
% 140.84/19.91 | | | |
% 140.84/19.91 | | | End of split
% 140.84/19.91 | | |
% 140.84/19.91 | | End of split
% 140.84/19.91 | |
% 140.84/19.91 | End of split
% 140.84/19.91 |
% 140.84/19.91 End of proof
% 140.84/19.91 % SZS output end Proof for theBenchmark
% 140.84/19.91
% 140.84/19.91 19257ms
%------------------------------------------------------------------------------