TSTP Solution File: SEU248+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU248+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 : n003.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 17:43:38 EDT 2023
% Result : Theorem 129.01s 17.82s
% Output : Proof 143.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU248+2 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.35 % Computer : n003.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 23 18:09:22 EDT 2023
% 0.15/0.35 % 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,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 7.02/1.73 Prover 4: Preprocessing ...
% 7.02/1.73 Prover 3: Preprocessing ...
% 7.02/1.75 Prover 5: Preprocessing ...
% 7.02/1.75 Prover 6: Preprocessing ...
% 7.02/1.75 Prover 0: Preprocessing ...
% 7.60/1.77 Prover 2: Preprocessing ...
% 8.01/1.83 Prover 1: Preprocessing ...
% 21.46/3.64 Prover 3: Warning: ignoring some quantifiers
% 21.60/3.64 Prover 1: Warning: ignoring some quantifiers
% 21.60/3.68 Prover 3: Constructing countermodel ...
% 22.14/3.74 Prover 1: Constructing countermodel ...
% 22.56/3.83 Prover 6: Proving ...
% 23.35/3.89 Prover 5: Proving ...
% 28.66/4.59 Prover 2: Proving ...
% 32.83/5.18 Prover 4: Warning: ignoring some quantifiers
% 34.32/5.32 Prover 4: Constructing countermodel ...
% 40.27/6.18 Prover 0: Proving ...
% 85.65/12.14 Prover 2: stopped
% 85.65/12.14 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 86.62/12.39 Prover 7: Preprocessing ...
% 91.18/12.89 Prover 7: Warning: ignoring some quantifiers
% 91.97/12.93 Prover 7: Constructing countermodel ...
% 99.34/13.98 Prover 5: stopped
% 99.34/13.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 102.05/14.27 Prover 8: Preprocessing ...
% 104.91/14.68 Prover 8: Warning: ignoring some quantifiers
% 106.07/14.76 Prover 8: Constructing countermodel ...
% 114.99/15.98 Prover 1: stopped
% 114.99/15.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 117.07/16.24 Prover 9: Preprocessing ...
% 125.52/17.45 Prover 9: Warning: ignoring some quantifiers
% 125.52/17.49 Prover 9: Constructing countermodel ...
% 128.85/17.82 Prover 9: proved (1833ms)
% 129.01/17.82
% 129.01/17.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 129.01/17.82
% 129.01/17.84 Prover 6: stopped
% 129.01/17.84 Prover 3: stopped
% 129.01/17.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 129.01/17.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 129.01/17.85 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 129.01/17.85 Prover 0: stopped
% 129.01/17.85 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 131.92/18.31 Prover 16: Preprocessing ...
% 132.68/18.32 Prover 11: Preprocessing ...
% 132.68/18.33 Prover 13: Preprocessing ...
% 132.68/18.36 Prover 10: Preprocessing ...
% 134.99/18.66 Prover 16: Warning: ignoring some quantifiers
% 134.99/18.68 Prover 10: Warning: ignoring some quantifiers
% 135.51/18.71 Prover 10: Constructing countermodel ...
% 135.51/18.72 Prover 16: Constructing countermodel ...
% 136.24/18.79 Prover 13: Warning: ignoring some quantifiers
% 136.24/18.85 Prover 13: Constructing countermodel ...
% 140.91/19.49 Prover 10: Found proof (size 59)
% 140.91/19.49 Prover 10: proved (1651ms)
% 140.91/19.49 Prover 16: stopped
% 140.91/19.49 Prover 13: stopped
% 140.91/19.49 Prover 7: stopped
% 140.91/19.49 Prover 4: stopped
% 140.91/19.52 Prover 8: stopped
% 142.68/19.78 Prover 11: Warning: ignoring some quantifiers
% 142.99/19.84 Prover 11: Constructing countermodel ...
% 142.99/19.86 Prover 11: stopped
% 142.99/19.86
% 142.99/19.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 142.99/19.86
% 142.99/19.87 % SZS output start Proof for theBenchmark
% 143.31/19.89 Assumptions after simplification:
% 143.31/19.89 ---------------------------------
% 143.31/19.89
% 143.31/19.89 (d3_relat_1)
% 143.31/19.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 143.31/19.94 (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 143.31/19.94 | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) |
% 143.31/19.94 in(v4, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 143.31/19.94 relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i]
% 143.31/19.94 : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) &
% 143.31/19.94 in(v4, v0) & ~ in(v4, v1)))
% 143.31/19.94
% 143.31/19.94 (dt_k8_relat_1)
% 143.31/19.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 143.31/19.95 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | relation(v2))
% 143.31/19.95
% 143.31/19.95 (l29_wellord1)
% 143.31/19.95 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 143.31/19.95 (relation_rng_restriction(v0, v1) = v2 & relation_dom(v2) = v3 &
% 143.31/19.95 relation_dom(v1) = v4 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 143.31/19.95 relation(v1) & ~ subset(v3, v4))
% 143.31/19.95
% 143.31/19.95 (t116_relat_1)
% 143.31/19.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 143.31/19.95 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3: $i] :
% 143.31/19.95 (relation_rng(v2) = v3 & $i(v3) & subset(v3, v0)))
% 143.31/19.95
% 143.31/19.95 (t117_relat_1)
% 143.31/19.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 143.31/19.95 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | subset(v2, v1))
% 143.31/19.95
% 143.31/19.96 (t118_relat_1)
% 143.31/19.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 143.31/19.96 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3: $i] : ?
% 143.31/19.96 [v4: $i] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & $i(v4) & $i(v3)
% 143.31/19.96 & subset(v3, v4)))
% 143.31/19.96
% 143.31/19.96 (t25_relat_1)
% 143.31/19.96 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 143.31/19.96 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] :
% 143.31/19.96 ! [v4: $i] : ( ~ (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3)
% 143.31/19.96 | ~ relation(v3) | subset(v1, v4)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 143.31/19.96 (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3) | ~
% 143.31/19.96 relation(v3) | ? [v5: $i] : (relation_dom(v3) = v5 & $i(v5) &
% 143.31/19.96 subset(v2, v5)))))
% 143.31/19.96
% 143.31/19.96 (t46_relat_1)
% 143.31/19.96 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 143.31/19.96 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] :
% 143.31/19.96 ! [v4: $i] : ( ~ (relation_composition(v0, v3) = v4) | ~ $i(v3) | ~
% 143.31/19.96 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v2 & relation_dom(v4)
% 143.31/19.96 = v2) | (relation_dom(v3) = v5 & $i(v5) & ~ subset(v1, v5))))))
% 143.31/19.96
% 143.31/19.96 (t47_relat_1)
% 143.31/19.97 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 143.31/19.97 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] :
% 143.31/19.97 ! [v4: $i] : ( ~ (relation_composition(v3, v0) = v4) | ~ $i(v3) | ~
% 143.31/19.97 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v1 & relation_rng(v4)
% 143.31/19.97 = v1 & $i(v1)) | (relation_rng(v3) = v5 & $i(v5) & ~ subset(v2,
% 143.31/19.97 v5))))))
% 143.31/19.97
% 143.31/19.97 (function-axioms)
% 143.77/19.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 143.77/19.99 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3,
% 143.77/19.99 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 143.77/19.99 [v4: $i] : (v1 = v0 | ~ (unordered_triple(v4, v3, v2) = v1) | ~
% 143.77/19.99 (unordered_triple(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 143.77/19.99 $i] : ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~
% 143.77/19.99 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 143.77/19.99 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~
% 143.77/19.99 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 143.77/19.99 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~
% 143.77/19.99 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 143.77/19.99 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~
% 143.77/19.99 (relation_composition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 143.77/19.99 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~
% 143.77/19.99 (relation_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 143.77/19.99 $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~
% 143.77/19.99 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 143.77/19.99 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~
% 143.77/19.99 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 143.77/19.99 ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~
% 143.77/19.99 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 143.77/19.99 : ! [v3: $i] : (v1 = v0 | ~ (fiber(v3, v2) = v1) | ~ (fiber(v3, v2) = v0))
% 143.77/19.99 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 143.77/19.99 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) =
% 143.77/19.99 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 143.77/19.99 ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3,
% 143.77/19.99 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 143.77/19.99 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0))
% 143.77/19.99 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 143.77/19.99 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 143.77/19.99 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2)
% 143.77/19.99 = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: $i] : !
% 143.77/19.99 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) =
% 143.77/19.99 v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 143.77/19.99 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~
% 143.77/19.99 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 143.77/19.99 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3,
% 143.77/19.99 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 143.77/19.99 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 143.77/19.99 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.77/19.99 (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) & ! [v0: $i]
% 143.77/19.99 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~
% 143.77/19.99 (relation_inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 143.77/19.99 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0:
% 143.77/19.99 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~
% 143.77/19.99 (union(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.77/19.99 (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : !
% 143.77/19.99 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 143.77/19.99 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.77/19.99 (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 143.77/19.99 ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) &
% 143.77/19.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~
% 143.77/19.99 (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.77/19.99 (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0: $i] : !
% 143.77/19.99 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 143.77/19.99 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 143.77/19.99 v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 143.77/19.99
% 143.77/19.99 Further assumptions not needed in the proof:
% 143.77/19.99 --------------------------------------------
% 143.77/19.99 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_funct_1, cc1_ordinal1,
% 143.77/19.99 cc1_relat_1, cc2_funct_1, cc2_ordinal1, cc3_ordinal1, commutativity_k2_tarski,
% 143.77/19.99 commutativity_k2_xboole_0, commutativity_k3_xboole_0, connectedness_r1_ordinal1,
% 143.77/19.99 d10_relat_1, d10_xboole_0, d11_relat_1, d12_funct_1, d12_relat_1, d12_relat_2,
% 143.77/19.99 d13_funct_1, d13_relat_1, d14_relat_1, d14_relat_2, d16_relat_2, d1_enumset1,
% 143.77/19.99 d1_ordinal1, d1_relat_1, d1_relat_2, d1_setfam_1, d1_tarski, d1_xboole_0,
% 143.77/19.99 d1_zfmisc_1, d2_ordinal1, d2_relat_1, d2_subset_1, d2_tarski, d2_wellord1,
% 143.77/19.99 d2_xboole_0, d2_zfmisc_1, d3_ordinal1, d3_tarski, d3_wellord1, d3_xboole_0,
% 143.77/19.99 d4_funct_1, d4_ordinal1, d4_relat_1, d4_relat_2, d4_subset_1, d4_tarski,
% 143.77/19.99 d4_wellord1, d4_xboole_0, d5_funct_1, d5_relat_1, d5_subset_1, d5_tarski,
% 143.77/19.99 d5_wellord1, d6_ordinal1, d6_relat_1, d6_relat_2, d6_wellord1, d7_relat_1,
% 143.77/19.99 d7_xboole_0, d8_funct_1, d8_relat_1, d8_relat_2, d8_setfam_1, d8_xboole_0,
% 143.77/19.99 d9_funct_1, d9_relat_2, dt_k10_relat_1, dt_k1_enumset1, dt_k1_funct_1,
% 143.77/19.99 dt_k1_ordinal1, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_wellord1,
% 143.77/19.99 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_funct_1, dt_k2_relat_1, dt_k2_subset_1,
% 143.77/19.99 dt_k2_tarski, dt_k2_wellord1, dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_relat_1,
% 143.77/19.99 dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_relat_1, dt_k4_tarski,
% 143.77/19.99 dt_k4_xboole_0, dt_k5_relat_1, dt_k5_setfam_1, dt_k6_relat_1, dt_k6_setfam_1,
% 143.77/19.99 dt_k6_subset_1, dt_k7_relat_1, dt_k7_setfam_1, dt_k9_relat_1, dt_m1_subset_1,
% 143.77/19.99 existence_m1_subset_1, fc10_relat_1, fc11_relat_1, fc12_relat_1, fc13_relat_1,
% 143.77/19.99 fc1_funct_1, fc1_ordinal1, fc1_relat_1, fc1_subset_1, fc1_xboole_0,
% 143.77/19.99 fc1_zfmisc_1, fc2_funct_1, fc2_ordinal1, fc2_relat_1, fc2_subset_1,
% 143.77/19.99 fc2_xboole_0, fc3_funct_1, fc3_ordinal1, fc3_relat_1, fc3_subset_1,
% 143.77/19.99 fc3_xboole_0, fc4_funct_1, fc4_ordinal1, fc4_relat_1, fc4_subset_1, fc5_funct_1,
% 143.77/19.99 fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1, fc9_relat_1,
% 143.77/19.99 idempotence_k2_xboole_0, idempotence_k3_xboole_0, involutiveness_k3_subset_1,
% 143.77/19.99 involutiveness_k4_relat_1, involutiveness_k7_setfam_1,
% 143.77/19.99 irreflexivity_r2_xboole_0, l1_wellord1, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1,
% 143.77/19.99 l28_zfmisc_1, l2_wellord1, l2_zfmisc_1, l32_xboole_1, l3_subset_1, l3_wellord1,
% 143.77/19.99 l3_zfmisc_1, l4_wellord1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1,
% 143.77/19.99 l82_funct_1, rc1_funct_1, rc1_ordinal1, rc1_relat_1, rc1_subset_1, rc1_xboole_0,
% 143.77/19.99 rc2_funct_1, rc2_ordinal1, rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1,
% 143.77/19.99 rc3_ordinal1, rc3_relat_1, rc4_funct_1, redefinition_k5_setfam_1,
% 143.77/19.99 redefinition_k6_setfam_1, redefinition_k6_subset_1, redefinition_r1_ordinal1,
% 143.77/19.99 reflexivity_r1_ordinal1, reflexivity_r1_tarski, symmetry_r1_xboole_0,
% 143.77/19.99 t106_zfmisc_1, t10_ordinal1, t10_zfmisc_1, t115_relat_1, t118_zfmisc_1,
% 143.77/19.99 t119_relat_1, t119_zfmisc_1, t12_xboole_1, t136_zfmisc_1, t140_relat_1,
% 143.77/19.99 t143_relat_1, t144_relat_1, t145_funct_1, t145_relat_1, t146_funct_1,
% 143.77/19.99 t146_relat_1, t147_funct_1, t160_relat_1, t166_relat_1, t167_relat_1,
% 143.77/19.99 t16_wellord1, t174_relat_1, t178_relat_1, t17_wellord1, t17_xboole_1,
% 143.77/19.99 t18_wellord1, t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, t1_zfmisc_1,
% 143.77/19.99 t20_relat_1, t21_funct_1, t21_ordinal1, t21_relat_1, t22_funct_1, t23_funct_1,
% 143.77/19.99 t23_ordinal1, t24_ordinal1, t26_xboole_1, t28_xboole_1, t2_boole, t2_subset,
% 143.77/19.99 t2_tarski, t2_xboole_1, t30_relat_1, t31_ordinal1, t32_ordinal1, t33_ordinal1,
% 143.77/19.99 t33_xboole_1, t33_zfmisc_1, t34_funct_1, t35_funct_1, t36_xboole_1, t37_relat_1,
% 143.77/19.99 t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole,
% 143.77/19.99 t3_ordinal1, t3_subset, t3_xboole_0, t3_xboole_1, t40_xboole_1, t41_ordinal1,
% 143.77/19.99 t42_ordinal1, t43_subset_1, t44_relat_1, t45_relat_1, t45_xboole_1,
% 143.77/19.99 t46_setfam_1, t46_zfmisc_1, t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole,
% 143.77/19.99 t4_subset, t4_xboole_0, t50_subset_1, t54_funct_1, t54_subset_1, t55_funct_1,
% 143.77/19.99 t56_relat_1, t57_funct_1, t5_subset, t5_wellord1, t60_relat_1, t60_xboole_1,
% 143.77/19.99 t62_funct_1, t63_xboole_1, t64_relat_1, t65_relat_1, t65_zfmisc_1, t68_funct_1,
% 143.77/19.99 t69_enumset1, t6_boole, t6_zfmisc_1, t70_funct_1, t71_relat_1, t72_funct_1,
% 143.77/19.99 t74_relat_1, t7_boole, t7_tarski, t7_xboole_1, t83_xboole_1, t86_relat_1,
% 143.77/19.99 t88_relat_1, t8_boole, t8_funct_1, t8_wellord1, t8_xboole_1, t8_zfmisc_1,
% 143.77/19.99 t90_relat_1, t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1, t9_tarski,
% 143.77/19.99 t9_zfmisc_1
% 143.77/19.99
% 143.77/19.99 Those formulas are unsatisfiable:
% 143.77/19.99 ---------------------------------
% 143.77/19.99
% 143.77/19.99 Begin of proof
% 143.77/19.99 |
% 143.77/19.99 | ALPHA: (d3_relat_1) implies:
% 143.77/19.99 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) |
% 143.77/19.99 | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 143.77/19.99 | $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) &
% 143.77/19.99 | in(v4, v0) & ~ in(v4, v1)))
% 143.77/19.99 |
% 143.77/19.99 | ALPHA: (function-axioms) implies:
% 143.77/20.00 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.77/20.00 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 143.77/20.00 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 143.77/20.00 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 143.77/20.00 |
% 143.77/20.00 | DELTA: instantiating (l29_wellord1) with fresh symbols all_304_0, all_304_1,
% 143.77/20.00 | all_304_2, all_304_3, all_304_4 gives:
% 143.88/20.00 | (4) relation_rng_restriction(all_304_4, all_304_3) = all_304_2 &
% 143.88/20.00 | relation_dom(all_304_2) = all_304_1 & relation_dom(all_304_3) =
% 143.88/20.00 | all_304_0 & $i(all_304_0) & $i(all_304_1) & $i(all_304_2) &
% 143.88/20.00 | $i(all_304_3) & $i(all_304_4) & relation(all_304_3) & ~
% 143.88/20.00 | subset(all_304_1, all_304_0)
% 143.88/20.00 |
% 143.88/20.00 | ALPHA: (4) implies:
% 143.88/20.00 | (5) ~ subset(all_304_1, all_304_0)
% 143.88/20.00 | (6) relation(all_304_3)
% 143.88/20.00 | (7) $i(all_304_4)
% 143.88/20.00 | (8) $i(all_304_3)
% 143.88/20.00 | (9) $i(all_304_2)
% 143.88/20.00 | (10) relation_dom(all_304_3) = all_304_0
% 143.88/20.00 | (11) relation_dom(all_304_2) = all_304_1
% 143.88/20.00 | (12) relation_rng_restriction(all_304_4, all_304_3) = all_304_2
% 143.88/20.00 |
% 143.88/20.00 | GROUND_INST: instantiating (1) with all_304_3, all_304_3, simplifying with
% 143.88/20.00 | (6), (8) gives:
% 143.88/20.00 | (13) subset(all_304_3, all_304_3)
% 143.88/20.00 |
% 143.88/20.00 | GROUND_INST: instantiating (t117_relat_1) with all_304_4, all_304_3,
% 143.88/20.00 | all_304_2, simplifying with (6), (7), (8), (12) gives:
% 143.88/20.00 | (14) subset(all_304_2, all_304_3)
% 143.88/20.00 |
% 143.88/20.00 | GROUND_INST: instantiating (dt_k8_relat_1) with all_304_4, all_304_3,
% 143.88/20.00 | all_304_2, simplifying with (6), (7), (8), (12) gives:
% 143.88/20.00 | (15) relation(all_304_2)
% 143.88/20.00 |
% 143.88/20.00 | GROUND_INST: instantiating (t118_relat_1) with all_304_4, all_304_3,
% 143.88/20.00 | all_304_2, simplifying with (6), (7), (8), (12) gives:
% 143.88/20.00 | (16) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_304_2) = v0 &
% 143.88/20.00 | relation_rng(all_304_3) = v1 & $i(v1) & $i(v0) & subset(v0, v1))
% 143.88/20.00 |
% 143.88/20.00 | GROUND_INST: instantiating (t116_relat_1) with all_304_4, all_304_3,
% 143.88/20.00 | all_304_2, simplifying with (6), (7), (8), (12) gives:
% 143.88/20.00 | (17) ? [v0: $i] : (relation_rng(all_304_2) = v0 & $i(v0) & subset(v0,
% 143.88/20.00 | all_304_4))
% 143.88/20.00 |
% 143.88/20.00 | DELTA: instantiating (17) with fresh symbol all_366_0 gives:
% 143.88/20.00 | (18) relation_rng(all_304_2) = all_366_0 & $i(all_366_0) &
% 143.88/20.00 | subset(all_366_0, all_304_4)
% 143.88/20.00 |
% 143.88/20.00 | ALPHA: (18) implies:
% 143.88/20.00 | (19) relation_rng(all_304_2) = all_366_0
% 143.88/20.00 |
% 143.88/20.00 | DELTA: instantiating (16) with fresh symbols all_368_0, all_368_1 gives:
% 143.88/20.00 | (20) relation_rng(all_304_2) = all_368_1 & relation_rng(all_304_3) =
% 143.88/20.00 | all_368_0 & $i(all_368_0) & $i(all_368_1) & subset(all_368_1,
% 143.88/20.00 | all_368_0)
% 143.88/20.00 |
% 143.88/20.00 | ALPHA: (20) implies:
% 143.88/20.00 | (21) relation_rng(all_304_3) = all_368_0
% 143.88/20.00 | (22) relation_rng(all_304_2) = all_368_1
% 143.88/20.00 |
% 143.88/20.00 | GROUND_INST: instantiating (3) with all_366_0, all_368_1, all_304_2,
% 143.88/20.00 | simplifying with (19), (22) gives:
% 143.88/20.00 | (23) all_368_1 = all_366_0
% 143.88/20.00 |
% 143.88/20.01 | GROUND_INST: instantiating (t47_relat_1) with all_304_3, all_368_0,
% 143.88/20.01 | simplifying with (6), (8), (21) gives:
% 143.88/20.01 | (24) ? [v0: $i] : (relation_dom(all_304_3) = v0 & $i(v0) & ! [v1: $i] :
% 143.88/20.01 | ! [v2: $i] : ( ~ (relation_composition(v1, all_304_3) = v2) | ~
% 143.88/20.01 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: int] : ((v4 =
% 143.88/20.01 | all_368_0 & relation_rng(v2) = all_368_0 & $i(all_368_0)) |
% 143.88/20.01 | (relation_rng(v1) = v3 & $i(v3) & ~ subset(v0, v3)))))
% 143.88/20.01 |
% 143.88/20.01 | GROUND_INST: instantiating (t46_relat_1) with all_304_3, all_368_0,
% 143.88/20.01 | simplifying with (6), (8), (21) gives:
% 143.88/20.01 | (25) ? [v0: $i] : (relation_dom(all_304_3) = v0 & $i(v0) & ! [v1: $i] :
% 143.88/20.01 | ! [v2: $i] : ( ~ (relation_composition(all_304_3, v1) = v2) | ~
% 143.88/20.01 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = v0 &
% 143.88/20.01 | relation_dom(v2) = v0) | (relation_dom(v1) = v3 & $i(v3) & ~
% 143.88/20.01 | subset(all_368_0, v3)))))
% 143.88/20.01 |
% 143.88/20.01 | GROUND_INST: instantiating (t25_relat_1) with all_304_3, all_368_0,
% 143.88/20.01 | simplifying with (6), (8), (21) gives:
% 143.88/20.01 | (26) ? [v0: $i] : (relation_dom(all_304_3) = v0 & $i(v0) & ! [v1: $i] :
% 143.88/20.01 | ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~
% 143.88/20.01 | subset(all_304_3, v1) | ~ relation(v1) | subset(all_368_0, v2)) &
% 143.88/20.01 | ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1)
% 143.88/20.01 | | ~ subset(all_304_3, v1) | ~ relation(v1) | ? [v3: $i] :
% 143.88/20.01 | (relation_dom(v1) = v3 & $i(v3) & subset(v0, v3))))
% 143.88/20.01 |
% 143.88/20.01 | GROUND_INST: instantiating (t47_relat_1) with all_304_2, all_366_0,
% 143.88/20.01 | simplifying with (9), (15), (19) gives:
% 143.88/20.01 | (27) ? [v0: $i] : (relation_dom(all_304_2) = v0 & $i(v0) & ! [v1: $i] :
% 143.88/20.01 | ! [v2: $i] : ( ~ (relation_composition(v1, all_304_2) = v2) | ~
% 143.88/20.01 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: int] : ((v4 =
% 143.88/20.01 | all_366_0 & relation_rng(v2) = all_366_0 & $i(all_366_0)) |
% 143.88/20.01 | (relation_rng(v1) = v3 & $i(v3) & ~ subset(v0, v3)))))
% 143.88/20.01 |
% 143.88/20.01 | GROUND_INST: instantiating (t25_relat_1) with all_304_2, all_366_0,
% 143.88/20.01 | simplifying with (9), (15), (19) gives:
% 143.88/20.01 | (28) ? [v0: $i] : (relation_dom(all_304_2) = v0 & $i(v0) & ! [v1: $i] :
% 143.88/20.01 | ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~
% 143.88/20.01 | subset(all_304_2, v1) | ~ relation(v1) | subset(all_366_0, v2)) &
% 143.88/20.01 | ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1)
% 143.88/20.01 | | ~ subset(all_304_2, v1) | ~ relation(v1) | ? [v3: $i] :
% 143.88/20.01 | (relation_dom(v1) = v3 & $i(v3) & subset(v0, v3))))
% 143.88/20.01 |
% 143.88/20.01 | DELTA: instantiating (25) with fresh symbol all_422_0 gives:
% 143.88/20.01 | (29) relation_dom(all_304_3) = all_422_0 & $i(all_422_0) & ! [v0: $i] : !
% 143.88/20.01 | [v1: $i] : ( ~ (relation_composition(all_304_3, v0) = v1) | ~ $i(v0)
% 143.88/20.01 | | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = all_422_0 &
% 143.88/20.01 | relation_dom(v1) = all_422_0) | (relation_dom(v0) = v2 & $i(v2)
% 143.88/20.01 | & ~ subset(all_368_0, v2))))
% 143.88/20.01 |
% 143.88/20.01 | ALPHA: (29) implies:
% 143.88/20.01 | (30) relation_dom(all_304_3) = all_422_0
% 143.88/20.01 |
% 143.88/20.01 | DELTA: instantiating (24) with fresh symbol all_428_0 gives:
% 143.88/20.02 | (31) relation_dom(all_304_3) = all_428_0 & $i(all_428_0) & ! [v0: $i] : !
% 143.88/20.02 | [v1: $i] : ( ~ (relation_composition(v0, all_304_3) = v1) | ~ $i(v0)
% 143.88/20.02 | | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = all_368_0 &
% 143.88/20.02 | relation_rng(v1) = all_368_0 & $i(all_368_0)) |
% 143.88/20.02 | (relation_rng(v0) = v2 & $i(v2) & ~ subset(all_428_0, v2))))
% 143.88/20.02 |
% 143.88/20.02 | ALPHA: (31) implies:
% 143.88/20.02 | (32) relation_dom(all_304_3) = all_428_0
% 143.88/20.02 |
% 143.88/20.02 | DELTA: instantiating (27) with fresh symbol all_431_0 gives:
% 143.88/20.02 | (33) relation_dom(all_304_2) = all_431_0 & $i(all_431_0) & ! [v0: $i] : !
% 143.88/20.02 | [v1: $i] : ( ~ (relation_composition(v0, all_304_2) = v1) | ~ $i(v0)
% 143.88/20.02 | | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = all_366_0 &
% 143.88/20.02 | relation_rng(v1) = all_366_0 & $i(all_366_0)) |
% 143.88/20.02 | (relation_rng(v0) = v2 & $i(v2) & ~ subset(all_431_0, v2))))
% 143.88/20.02 |
% 143.88/20.02 | ALPHA: (33) implies:
% 143.88/20.02 | (34) relation_dom(all_304_2) = all_431_0
% 143.88/20.02 |
% 143.88/20.02 | DELTA: instantiating (26) with fresh symbol all_434_0 gives:
% 143.88/20.02 | (35) relation_dom(all_304_3) = all_434_0 & $i(all_434_0) & ! [v0: $i] : !
% 143.99/20.02 | [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 143.99/20.02 | subset(all_304_3, v0) | ~ relation(v0) | subset(all_368_0, v1)) &
% 143.99/20.02 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 143.99/20.02 | ~ subset(all_304_3, v0) | ~ relation(v0) | ? [v2: $i] :
% 143.99/20.02 | (relation_dom(v0) = v2 & $i(v2) & subset(all_434_0, v2)))
% 143.99/20.02 |
% 143.99/20.02 | ALPHA: (35) implies:
% 143.99/20.02 | (36) relation_dom(all_304_3) = all_434_0
% 143.99/20.02 | (37) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 143.99/20.02 | ~ subset(all_304_3, v0) | ~ relation(v0) | ? [v2: $i] :
% 143.99/20.02 | (relation_dom(v0) = v2 & $i(v2) & subset(all_434_0, v2)))
% 143.99/20.02 |
% 143.99/20.02 | GROUND_INST: instantiating (37) with all_304_3, all_368_0, simplifying with
% 143.99/20.02 | (6), (8), (13), (21) gives:
% 143.99/20.02 | (38) ? [v0: $i] : (relation_dom(all_304_3) = v0 & $i(v0) &
% 143.99/20.02 | subset(all_434_0, v0))
% 143.99/20.02 |
% 143.99/20.02 | DELTA: instantiating (28) with fresh symbol all_438_0 gives:
% 143.99/20.02 | (39) relation_dom(all_304_2) = all_438_0 & $i(all_438_0) & ! [v0: $i] : !
% 143.99/20.02 | [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 143.99/20.02 | subset(all_304_2, v0) | ~ relation(v0) | subset(all_366_0, v1)) &
% 143.99/20.02 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 143.99/20.02 | ~ subset(all_304_2, v0) | ~ relation(v0) | ? [v2: $i] :
% 143.99/20.02 | (relation_dom(v0) = v2 & $i(v2) & subset(all_438_0, v2)))
% 143.99/20.02 |
% 143.99/20.02 | ALPHA: (39) implies:
% 143.99/20.02 | (40) relation_dom(all_304_2) = all_438_0
% 143.99/20.02 | (41) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 143.99/20.02 | ~ subset(all_304_2, v0) | ~ relation(v0) | ? [v2: $i] :
% 143.99/20.02 | (relation_dom(v0) = v2 & $i(v2) & subset(all_438_0, v2)))
% 143.99/20.02 |
% 143.99/20.02 | GROUND_INST: instantiating (41) with all_304_3, all_368_0, simplifying with
% 143.99/20.02 | (6), (8), (14), (21) gives:
% 143.99/20.02 | (42) ? [v0: $i] : (relation_dom(all_304_3) = v0 & $i(v0) &
% 143.99/20.02 | subset(all_438_0, v0))
% 143.99/20.02 |
% 143.99/20.02 | DELTA: instantiating (38) with fresh symbol all_441_0 gives:
% 143.99/20.02 | (43) relation_dom(all_304_3) = all_441_0 & $i(all_441_0) &
% 143.99/20.02 | subset(all_434_0, all_441_0)
% 143.99/20.02 |
% 143.99/20.02 | ALPHA: (43) implies:
% 143.99/20.03 | (44) relation_dom(all_304_3) = all_441_0
% 143.99/20.03 |
% 143.99/20.03 | DELTA: instantiating (42) with fresh symbol all_443_0 gives:
% 143.99/20.03 | (45) relation_dom(all_304_3) = all_443_0 & $i(all_443_0) &
% 143.99/20.03 | subset(all_438_0, all_443_0)
% 143.99/20.03 |
% 143.99/20.03 | ALPHA: (45) implies:
% 143.99/20.03 | (46) subset(all_438_0, all_443_0)
% 143.99/20.03 | (47) relation_dom(all_304_3) = all_443_0
% 143.99/20.03 |
% 143.99/20.03 | GROUND_INST: instantiating (2) with all_304_0, all_441_0, all_304_3,
% 143.99/20.03 | simplifying with (10), (44) gives:
% 143.99/20.03 | (48) all_441_0 = all_304_0
% 143.99/20.03 |
% 143.99/20.03 | GROUND_INST: instantiating (2) with all_434_0, all_441_0, all_304_3,
% 143.99/20.03 | simplifying with (36), (44) gives:
% 143.99/20.03 | (49) all_441_0 = all_434_0
% 143.99/20.03 |
% 143.99/20.03 | GROUND_INST: instantiating (2) with all_428_0, all_441_0, all_304_3,
% 143.99/20.03 | simplifying with (32), (44) gives:
% 143.99/20.03 | (50) all_441_0 = all_428_0
% 143.99/20.03 |
% 143.99/20.03 | GROUND_INST: instantiating (2) with all_441_0, all_443_0, all_304_3,
% 143.99/20.03 | simplifying with (44), (47) gives:
% 143.99/20.03 | (51) all_443_0 = all_441_0
% 143.99/20.03 |
% 143.99/20.03 | GROUND_INST: instantiating (2) with all_422_0, all_443_0, all_304_3,
% 143.99/20.03 | simplifying with (30), (47) gives:
% 143.99/20.03 | (52) all_443_0 = all_422_0
% 143.99/20.03 |
% 143.99/20.03 | GROUND_INST: instantiating (2) with all_304_1, all_438_0, all_304_2,
% 143.99/20.03 | simplifying with (11), (40) gives:
% 143.99/20.03 | (53) all_438_0 = all_304_1
% 143.99/20.03 |
% 143.99/20.03 | GROUND_INST: instantiating (2) with all_431_0, all_438_0, all_304_2,
% 143.99/20.03 | simplifying with (34), (40) gives:
% 143.99/20.03 | (54) all_438_0 = all_431_0
% 143.99/20.03 |
% 143.99/20.03 | COMBINE_EQS: (51), (52) imply:
% 143.99/20.03 | (55) all_441_0 = all_422_0
% 143.99/20.03 |
% 143.99/20.03 | SIMP: (55) implies:
% 143.99/20.03 | (56) all_441_0 = all_422_0
% 143.99/20.03 |
% 143.99/20.03 | COMBINE_EQS: (48), (49) imply:
% 143.99/20.03 | (57) all_434_0 = all_304_0
% 143.99/20.03 |
% 143.99/20.03 | COMBINE_EQS: (49), (50) imply:
% 143.99/20.03 | (58) all_434_0 = all_428_0
% 143.99/20.03 |
% 143.99/20.03 | COMBINE_EQS: (49), (56) imply:
% 143.99/20.03 | (59) all_434_0 = all_422_0
% 143.99/20.03 |
% 143.99/20.03 | COMBINE_EQS: (53), (54) imply:
% 143.99/20.03 | (60) all_431_0 = all_304_1
% 143.99/20.03 |
% 143.99/20.03 | COMBINE_EQS: (57), (58) imply:
% 143.99/20.03 | (61) all_428_0 = all_304_0
% 143.99/20.03 |
% 143.99/20.03 | COMBINE_EQS: (58), (59) imply:
% 143.99/20.03 | (62) all_428_0 = all_422_0
% 143.99/20.03 |
% 143.99/20.03 | COMBINE_EQS: (61), (62) imply:
% 143.99/20.03 | (63) all_422_0 = all_304_0
% 143.99/20.03 |
% 143.99/20.03 | SIMP: (63) implies:
% 143.99/20.03 | (64) all_422_0 = all_304_0
% 143.99/20.03 |
% 143.99/20.03 | COMBINE_EQS: (52), (64) imply:
% 143.99/20.03 | (65) all_443_0 = all_304_0
% 143.99/20.03 |
% 143.99/20.03 | REDUCE: (46), (53), (65) imply:
% 143.99/20.03 | (66) subset(all_304_1, all_304_0)
% 143.99/20.03 |
% 143.99/20.03 | PRED_UNIFY: (5), (66) imply:
% 143.99/20.03 | (67) $false
% 143.99/20.03 |
% 143.99/20.03 | CLOSE: (67) is inconsistent.
% 143.99/20.03 |
% 143.99/20.03 End of proof
% 143.99/20.03 % SZS output end Proof for theBenchmark
% 143.99/20.03
% 143.99/20.03 19420ms
%------------------------------------------------------------------------------