TSTP Solution File: SEU177+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU177+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 17:43:04 EDT 2023
% Result : Theorem 17.01s 3.05s
% Output : Proof 23.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU177+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 02:04:01 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.42/1.30 Prover 4: Preprocessing ...
% 4.42/1.31 Prover 1: Preprocessing ...
% 4.42/1.34 Prover 5: Preprocessing ...
% 4.42/1.34 Prover 6: Preprocessing ...
% 4.42/1.34 Prover 3: Preprocessing ...
% 4.42/1.34 Prover 0: Preprocessing ...
% 4.42/1.35 Prover 2: Preprocessing ...
% 12.11/2.35 Prover 1: Warning: ignoring some quantifiers
% 12.80/2.44 Prover 3: Warning: ignoring some quantifiers
% 12.96/2.46 Prover 1: Constructing countermodel ...
% 12.96/2.46 Prover 5: Proving ...
% 12.96/2.48 Prover 3: Constructing countermodel ...
% 12.96/2.50 Prover 4: Warning: ignoring some quantifiers
% 12.96/2.51 Prover 6: Proving ...
% 13.74/2.60 Prover 2: Proving ...
% 13.74/2.63 Prover 4: Constructing countermodel ...
% 14.33/2.70 Prover 0: Proving ...
% 17.01/3.03 Prover 2: proved (2412ms)
% 17.01/3.04
% 17.01/3.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.01/3.05
% 17.01/3.05 Prover 3: stopped
% 17.01/3.05 Prover 5: stopped
% 17.01/3.05 Prover 6: stopped
% 17.01/3.05 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.01/3.05 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 17.01/3.05 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 17.01/3.05 Prover 0: stopped
% 17.01/3.05 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 17.01/3.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.64/3.22 Prover 8: Preprocessing ...
% 18.72/3.26 Prover 13: Preprocessing ...
% 18.72/3.28 Prover 7: Preprocessing ...
% 18.72/3.29 Prover 10: Preprocessing ...
% 18.72/3.29 Prover 11: Preprocessing ...
% 21.42/3.65 Prover 10: Warning: ignoring some quantifiers
% 21.42/3.67 Prover 4: Found proof (size 41)
% 21.42/3.68 Prover 4: proved (3051ms)
% 21.42/3.68 Prover 1: stopped
% 22.13/3.70 Prover 10: Constructing countermodel ...
% 22.13/3.71 Prover 13: Warning: ignoring some quantifiers
% 22.13/3.73 Prover 7: Warning: ignoring some quantifiers
% 22.13/3.74 Prover 10: stopped
% 22.13/3.74 Prover 8: Warning: ignoring some quantifiers
% 22.13/3.75 Prover 13: Constructing countermodel ...
% 22.13/3.77 Prover 7: Constructing countermodel ...
% 22.13/3.77 Prover 8: Constructing countermodel ...
% 22.13/3.78 Prover 13: stopped
% 22.90/3.79 Prover 8: stopped
% 22.95/3.80 Prover 7: stopped
% 23.42/3.92 Prover 11: Warning: ignoring some quantifiers
% 23.42/3.95 Prover 11: Constructing countermodel ...
% 23.42/3.98 Prover 11: stopped
% 23.42/3.98
% 23.42/3.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.42/3.98
% 23.42/3.98 % SZS output start Proof for theBenchmark
% 23.42/3.99 Assumptions after simplification:
% 23.42/3.99 ---------------------------------
% 23.42/3.99
% 23.42/3.99 (d4_relat_1)
% 23.79/4.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : ! [v5:
% 23.79/4.03 $i] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5)
% 23.79/4.03 | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 23.79/4.03 [v6: int] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) =
% 23.79/4.03 v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0)
% 23.79/4.03 = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 23.79/4.03 int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ($i(v4) & ((v6 = 0 &
% 23.79/4.03 ordered_pair(v2, v4) = v5 & in(v5, v0) = 0 & $i(v5)) | ( ~ (v3 = 0) &
% 23.79/4.03 relation(v0) = v3)))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2
% 23.79/4.03 = v0 | ~ (relation_dom(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] :
% 23.79/4.03 ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] :
% 23.79/4.03 ($i(v6) & $i(v4) & (( ~ (v3 = 0) & relation(v1) = v3) | (in(v4, v0) = v5 & (
% 23.79/4.03 ~ (v5 = 0) | ! [v9: $i] : ! [v10: $i] : ( ~ (ordered_pair(v4, v9)
% 23.79/4.03 = v10) | ~ $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & in(v10, v1)
% 23.79/4.03 = v11))) & (v5 = 0 | (v8 = 0 & ordered_pair(v4, v6) = v7 &
% 23.79/4.03 in(v7, v1) = 0 & $i(v7))))))) & ! [v0: $i] : ( ~ (relation(v0) =
% 23.79/4.03 0) | ~ $i(v0) | ? [v1: $i] : (relation_dom(v0) = v1 & $i(v1) & ! [v2:
% 23.79/4.03 $i] : ! [v3: int] : ! [v4: $i] : ! [v5: $i] : (v3 = 0 | ~
% 23.79/4.03 (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~
% 23.79/4.03 $i(v2) | ? [v6: int] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2: $i] :
% 23.79/4.03 ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] :
% 23.79/4.03 (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) & $i(v3))) & ?
% 23.79/4.03 [v2: $i] : (v2 = v1 | ~ $i(v2) | ? [v3: $i] : ? [v4: any] : ? [v5: $i]
% 23.79/4.03 : ? [v6: $i] : ? [v7: int] : (in(v3, v2) = v4 & $i(v5) & $i(v3) & ( ~
% 23.79/4.03 (v4 = 0) | ! [v8: $i] : ! [v9: $i] : ( ~ (ordered_pair(v3, v8) =
% 23.79/4.03 v9) | ~ $i(v8) | ? [v10: int] : ( ~ (v10 = 0) & in(v9, v0) =
% 23.79/4.03 v10))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6,
% 23.79/4.03 v0) = 0 & $i(v6)))))))
% 23.79/4.03
% 23.79/4.03 (d5_relat_1)
% 23.79/4.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : ! [v5:
% 23.79/4.04 $i] : (v3 = 0 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v4, v2) = v5)
% 23.79/4.04 | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 23.79/4.04 [v6: int] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) =
% 23.79/4.04 v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v0)
% 23.79/4.04 = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 23.79/4.04 int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ($i(v4) & ((v6 = 0 &
% 23.79/4.04 ordered_pair(v4, v2) = v5 & in(v5, v0) = 0 & $i(v5)) | ( ~ (v3 = 0) &
% 23.79/4.04 relation(v0) = v3)))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2
% 23.79/4.04 = v0 | ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] :
% 23.79/4.04 ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] :
% 23.79/4.04 ($i(v6) & $i(v4) & (( ~ (v3 = 0) & relation(v1) = v3) | (in(v4, v0) = v5 & (
% 23.79/4.04 ~ (v5 = 0) | ! [v9: $i] : ! [v10: $i] : ( ~ (ordered_pair(v9, v4)
% 23.79/4.04 = v10) | ~ $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & in(v10, v1)
% 23.79/4.04 = v11))) & (v5 = 0 | (v8 = 0 & ordered_pair(v6, v4) = v7 &
% 23.79/4.04 in(v7, v1) = 0 & $i(v7))))))) & ! [v0: $i] : ( ~ (relation(v0) =
% 23.79/4.04 0) | ~ $i(v0) | ? [v1: $i] : (relation_rng(v0) = v1 & $i(v1) & ! [v2:
% 23.79/4.04 $i] : ! [v3: int] : ! [v4: $i] : ! [v5: $i] : (v3 = 0 | ~
% 23.79/4.04 (ordered_pair(v4, v2) = v5) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~
% 23.79/4.04 $i(v2) | ? [v6: int] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2: $i] :
% 23.79/4.04 ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] :
% 23.79/4.04 (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0 & $i(v4) & $i(v3))) & ?
% 23.79/4.04 [v2: $i] : (v2 = v1 | ~ $i(v2) | ? [v3: $i] : ? [v4: any] : ? [v5: $i]
% 23.79/4.04 : ? [v6: $i] : ? [v7: int] : (in(v3, v2) = v4 & $i(v5) & $i(v3) & ( ~
% 23.79/4.04 (v4 = 0) | ! [v8: $i] : ! [v9: $i] : ( ~ (ordered_pair(v8, v3) =
% 23.79/4.04 v9) | ~ $i(v8) | ? [v10: int] : ( ~ (v10 = 0) & in(v9, v0) =
% 23.79/4.04 v10))) & (v4 = 0 | (v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6,
% 23.79/4.04 v0) = 0 & $i(v6)))))))
% 23.79/4.04
% 23.79/4.04 (t20_relat_1)
% 23.79/4.04 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 23.79/4.04 any] : ? [v6: $i] : ? [v7: any] : (relation_rng(v2) = v6 &
% 23.79/4.04 relation_dom(v2) = v4 & relation(v2) = 0 & ordered_pair(v0, v1) = v3 &
% 23.79/4.04 in(v3, v2) = 0 & in(v1, v6) = v7 & in(v0, v4) = v5 & $i(v6) & $i(v4) &
% 23.79/4.04 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v7 = 0) | ~ (v5 = 0)))
% 23.79/4.04
% 23.79/4.04 (function-axioms)
% 23.79/4.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 23.79/4.05 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3,
% 23.79/4.05 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 23.79/4.05 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~
% 23.79/4.05 (are_equipotent(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 23.79/4.05 ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~
% 23.79/4.05 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 23.79/4.05 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~
% 23.79/4.05 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 23.79/4.05 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~
% 23.79/4.05 (complements_of_subsets(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 23.79/4.05 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.79/4.05 (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : !
% 23.79/4.05 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3,
% 23.79/4.05 v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 23.79/4.05 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) =
% 23.79/4.05 v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 23.79/4.05 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~
% 23.79/4.05 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 23.79/4.05 : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~
% 23.79/4.05 (ordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 23.79/4.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3,
% 23.79/4.05 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 23.79/4.05 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.79/4.05 (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 23.79/4.05 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) =
% 23.79/4.05 v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 23.79/4.05 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~
% 23.79/4.05 (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 23.79/4.05 [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~
% 23.79/4.05 (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 23.79/4.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.79/4.05 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0:
% 23.79/4.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 23.79/4.05 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 23.79/4.05 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~
% 23.79/4.05 (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 23.79/4.05 v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 23.79/4.05 : ! [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~
% 23.79/4.05 (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 23.79/4.05 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0:
% 23.79/4.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 23.79/4.05 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool]
% 23.79/4.05 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) |
% 23.79/4.05 ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 23.79/4.05 ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 23.79/4.05 : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 23.79/4.05 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1)
% 23.79/4.05 | ~ (set_meet(v2) = v0))
% 23.79/4.05
% 23.79/4.05 Further assumptions not needed in the proof:
% 23.79/4.05 --------------------------------------------
% 23.79/4.05 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski,
% 23.79/4.05 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_setfam_1,
% 23.79/4.05 d1_tarski, d1_xboole_0, d1_zfmisc_1, d2_subset_1, d2_tarski, d2_xboole_0,
% 23.79/4.05 d2_zfmisc_1, d3_tarski, d3_xboole_0, d4_subset_1, d4_tarski, d4_xboole_0,
% 23.79/4.05 d5_subset_1, d5_tarski, d7_xboole_0, d8_setfam_1, d8_xboole_0, dt_k1_relat_1,
% 23.79/4.05 dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1,
% 23.79/4.05 dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_subset_1,
% 23.79/4.05 dt_k3_tarski, dt_k3_xboole_0, dt_k4_tarski, dt_k4_xboole_0, dt_k5_setfam_1,
% 23.79/4.05 dt_k6_setfam_1, dt_k6_subset_1, dt_k7_setfam_1, dt_m1_subset_1,
% 23.79/4.05 existence_m1_subset_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_subset_1,
% 23.79/4.05 fc2_xboole_0, fc3_subset_1, fc3_xboole_0, idempotence_k2_xboole_0,
% 23.79/4.05 idempotence_k3_xboole_0, involutiveness_k3_subset_1, involutiveness_k7_setfam_1,
% 23.79/4.05 irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1,
% 23.79/4.05 l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_subset_1, l3_zfmisc_1, l4_zfmisc_1,
% 23.79/4.05 l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, rc1_relat_1, rc1_subset_1,
% 23.79/4.05 rc1_xboole_0, rc2_subset_1, rc2_xboole_0, redefinition_k5_setfam_1,
% 23.79/4.05 redefinition_k6_setfam_1, redefinition_k6_subset_1, reflexivity_r1_tarski,
% 23.79/4.05 symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, t118_zfmisc_1, t119_zfmisc_1,
% 23.79/4.05 t12_xboole_1, t136_zfmisc_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_subset,
% 23.79/4.05 t1_xboole_1, t1_zfmisc_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_subset,
% 23.79/4.05 t2_tarski, t2_xboole_1, t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_xboole_1,
% 23.79/4.05 t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_subset,
% 23.79/4.05 t3_xboole_0, t3_xboole_1, t40_xboole_1, t43_subset_1, t45_xboole_1,
% 23.79/4.05 t46_setfam_1, t46_zfmisc_1, t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole,
% 23.79/4.05 t4_subset, t4_xboole_0, t50_subset_1, t54_subset_1, t5_subset, t60_xboole_1,
% 23.79/4.05 t63_xboole_1, t65_zfmisc_1, t69_enumset1, t6_boole, t6_zfmisc_1, t7_boole,
% 23.79/4.05 t7_xboole_1, t83_xboole_1, t8_boole, t8_xboole_1, t8_zfmisc_1, t92_zfmisc_1,
% 23.79/4.05 t99_zfmisc_1, t9_tarski, t9_zfmisc_1
% 23.79/4.05
% 23.79/4.05 Those formulas are unsatisfiable:
% 23.79/4.05 ---------------------------------
% 23.79/4.05
% 23.79/4.05 Begin of proof
% 23.79/4.05 |
% 23.79/4.05 | ALPHA: (d4_relat_1) implies:
% 23.79/4.06 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] :
% 23.79/4.06 | ! [v5: $i] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~
% 23.79/4.06 | (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~
% 23.79/4.06 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : (( ~ (v6 = 0) &
% 23.79/4.06 | relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = v6)))
% 23.79/4.06 |
% 23.79/4.06 | ALPHA: (d5_relat_1) implies:
% 23.79/4.06 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] :
% 23.79/4.06 | ! [v5: $i] : (v3 = 0 | ~ (relation_rng(v0) = v1) | ~
% 23.79/4.06 | (ordered_pair(v4, v2) = v5) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~
% 23.79/4.06 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : (( ~ (v6 = 0) &
% 23.79/4.06 | relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = v6)))
% 23.79/4.06 |
% 23.79/4.06 | ALPHA: (function-axioms) implies:
% 23.79/4.06 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 23.79/4.06 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 23.79/4.06 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 23.79/4.06 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 23.79/4.06 |
% 23.79/4.06 | DELTA: instantiating (t20_relat_1) with fresh symbols all_141_0, all_141_1,
% 23.79/4.06 | all_141_2, all_141_3, all_141_4, all_141_5, all_141_6, all_141_7 gives:
% 23.79/4.06 | (5) relation_rng(all_141_5) = all_141_1 & relation_dom(all_141_5) =
% 23.79/4.06 | all_141_3 & relation(all_141_5) = 0 & ordered_pair(all_141_7,
% 23.79/4.06 | all_141_6) = all_141_4 & in(all_141_4, all_141_5) = 0 & in(all_141_6,
% 23.79/4.06 | all_141_1) = all_141_0 & in(all_141_7, all_141_3) = all_141_2 &
% 23.79/4.06 | $i(all_141_1) & $i(all_141_3) & $i(all_141_4) & $i(all_141_5) &
% 23.79/4.06 | $i(all_141_6) & $i(all_141_7) & ( ~ (all_141_0 = 0) | ~ (all_141_2 =
% 23.79/4.06 | 0))
% 23.79/4.06 |
% 23.79/4.06 | ALPHA: (5) implies:
% 23.79/4.06 | (6) $i(all_141_7)
% 23.79/4.06 | (7) $i(all_141_6)
% 23.79/4.06 | (8) $i(all_141_5)
% 23.79/4.06 | (9) $i(all_141_3)
% 23.79/4.06 | (10) $i(all_141_1)
% 23.79/4.06 | (11) in(all_141_7, all_141_3) = all_141_2
% 23.79/4.06 | (12) in(all_141_6, all_141_1) = all_141_0
% 23.79/4.06 | (13) in(all_141_4, all_141_5) = 0
% 23.79/4.06 | (14) ordered_pair(all_141_7, all_141_6) = all_141_4
% 23.79/4.06 | (15) relation(all_141_5) = 0
% 23.79/4.06 | (16) relation_dom(all_141_5) = all_141_3
% 23.79/4.06 | (17) relation_rng(all_141_5) = all_141_1
% 23.79/4.06 | (18) ~ (all_141_0 = 0) | ~ (all_141_2 = 0)
% 23.79/4.06 |
% 23.79/4.06 | GROUND_INST: instantiating (1) with all_141_5, all_141_3, all_141_7,
% 23.79/4.06 | all_141_2, all_141_6, all_141_4, simplifying with (6), (7), (8),
% 23.79/4.06 | (9), (11), (14), (16) gives:
% 23.79/4.06 | (19) all_141_2 = 0 | ? [v0: int] : (( ~ (v0 = 0) & relation(all_141_5) =
% 23.79/4.06 | v0) | ( ~ (v0 = 0) & in(all_141_4, all_141_5) = v0))
% 23.79/4.06 |
% 23.79/4.07 | GROUND_INST: instantiating (2) with all_141_5, all_141_1, all_141_6,
% 23.79/4.07 | all_141_0, all_141_7, all_141_4, simplifying with (6), (7), (8),
% 23.79/4.07 | (10), (12), (14), (17) gives:
% 23.79/4.07 | (20) all_141_0 = 0 | ? [v0: int] : (( ~ (v0 = 0) & relation(all_141_5) =
% 23.79/4.07 | v0) | ( ~ (v0 = 0) & in(all_141_4, all_141_5) = v0))
% 23.79/4.07 |
% 23.79/4.07 | BETA: splitting (20) gives:
% 23.79/4.07 |
% 23.79/4.07 | Case 1:
% 23.79/4.07 | |
% 23.79/4.07 | | (21) all_141_0 = 0
% 23.79/4.07 | |
% 23.79/4.07 | | BETA: splitting (18) gives:
% 23.79/4.07 | |
% 23.79/4.07 | | Case 1:
% 23.79/4.07 | | |
% 23.79/4.07 | | | (22) ~ (all_141_0 = 0)
% 23.79/4.07 | | |
% 23.79/4.07 | | | REDUCE: (21), (22) imply:
% 23.79/4.07 | | | (23) $false
% 23.79/4.07 | | |
% 23.79/4.07 | | | CLOSE: (23) is inconsistent.
% 23.79/4.07 | | |
% 23.79/4.07 | | Case 2:
% 23.79/4.07 | | |
% 23.79/4.07 | | | (24) ~ (all_141_2 = 0)
% 23.79/4.07 | | |
% 23.79/4.07 | | | BETA: splitting (19) gives:
% 23.79/4.07 | | |
% 23.79/4.07 | | | Case 1:
% 23.79/4.07 | | | |
% 23.79/4.07 | | | | (25) all_141_2 = 0
% 23.79/4.07 | | | |
% 23.79/4.07 | | | | REDUCE: (24), (25) imply:
% 23.79/4.07 | | | | (26) $false
% 23.79/4.07 | | | |
% 23.79/4.07 | | | | CLOSE: (26) is inconsistent.
% 23.79/4.07 | | | |
% 23.79/4.07 | | | Case 2:
% 23.79/4.07 | | | |
% 23.79/4.07 | | | | (27) ? [v0: int] : (( ~ (v0 = 0) & relation(all_141_5) = v0) | ( ~
% 23.79/4.07 | | | | (v0 = 0) & in(all_141_4, all_141_5) = v0))
% 23.79/4.07 | | | |
% 23.79/4.07 | | | | DELTA: instantiating (27) with fresh symbol all_242_0 gives:
% 23.79/4.07 | | | | (28) ( ~ (all_242_0 = 0) & relation(all_141_5) = all_242_0) | ( ~
% 23.79/4.07 | | | | (all_242_0 = 0) & in(all_141_4, all_141_5) = all_242_0)
% 23.79/4.07 | | | |
% 23.79/4.07 | | | | BETA: splitting (28) gives:
% 23.79/4.07 | | | |
% 23.79/4.07 | | | | Case 1:
% 23.79/4.07 | | | | |
% 23.79/4.07 | | | | | (29) ~ (all_242_0 = 0) & relation(all_141_5) = all_242_0
% 23.79/4.07 | | | | |
% 23.79/4.07 | | | | | ALPHA: (29) implies:
% 23.79/4.07 | | | | | (30) ~ (all_242_0 = 0)
% 23.79/4.07 | | | | | (31) relation(all_141_5) = all_242_0
% 23.79/4.07 | | | | |
% 23.79/4.07 | | | | | GROUND_INST: instantiating (3) with 0, all_242_0, all_141_5,
% 23.79/4.07 | | | | | simplifying with (15), (31) gives:
% 23.79/4.07 | | | | | (32) all_242_0 = 0
% 23.79/4.07 | | | | |
% 23.79/4.07 | | | | | REDUCE: (30), (32) imply:
% 23.79/4.07 | | | | | (33) $false
% 23.79/4.07 | | | | |
% 23.79/4.07 | | | | | CLOSE: (33) is inconsistent.
% 23.79/4.07 | | | | |
% 23.79/4.07 | | | | Case 2:
% 23.79/4.07 | | | | |
% 23.79/4.07 | | | | | (34) ~ (all_242_0 = 0) & in(all_141_4, all_141_5) = all_242_0
% 23.79/4.07 | | | | |
% 23.79/4.07 | | | | | ALPHA: (34) implies:
% 23.79/4.07 | | | | | (35) ~ (all_242_0 = 0)
% 23.79/4.07 | | | | | (36) in(all_141_4, all_141_5) = all_242_0
% 23.79/4.07 | | | | |
% 23.79/4.07 | | | | | GROUND_INST: instantiating (4) with 0, all_242_0, all_141_5,
% 23.79/4.07 | | | | | all_141_4, simplifying with (13), (36) gives:
% 23.79/4.07 | | | | | (37) all_242_0 = 0
% 23.79/4.07 | | | | |
% 23.79/4.07 | | | | | REDUCE: (35), (37) imply:
% 23.79/4.07 | | | | | (38) $false
% 23.79/4.07 | | | | |
% 23.79/4.07 | | | | | CLOSE: (38) is inconsistent.
% 23.79/4.07 | | | | |
% 23.79/4.07 | | | | End of split
% 23.79/4.07 | | | |
% 23.79/4.07 | | | End of split
% 23.79/4.07 | | |
% 23.79/4.07 | | End of split
% 23.79/4.07 | |
% 23.79/4.07 | Case 2:
% 23.79/4.07 | |
% 23.79/4.07 | | (39) ? [v0: int] : (( ~ (v0 = 0) & relation(all_141_5) = v0) | ( ~ (v0 =
% 23.79/4.07 | | 0) & in(all_141_4, all_141_5) = v0))
% 23.79/4.07 | |
% 23.79/4.07 | | DELTA: instantiating (39) with fresh symbol all_223_0 gives:
% 23.79/4.07 | | (40) ( ~ (all_223_0 = 0) & relation(all_141_5) = all_223_0) | ( ~
% 23.79/4.07 | | (all_223_0 = 0) & in(all_141_4, all_141_5) = all_223_0)
% 23.79/4.07 | |
% 23.79/4.07 | | BETA: splitting (40) gives:
% 23.79/4.07 | |
% 23.79/4.07 | | Case 1:
% 23.79/4.07 | | |
% 23.79/4.07 | | | (41) ~ (all_223_0 = 0) & relation(all_141_5) = all_223_0
% 23.79/4.07 | | |
% 23.79/4.07 | | | ALPHA: (41) implies:
% 23.79/4.07 | | | (42) ~ (all_223_0 = 0)
% 23.79/4.07 | | | (43) relation(all_141_5) = all_223_0
% 23.79/4.07 | | |
% 23.79/4.07 | | | GROUND_INST: instantiating (3) with 0, all_223_0, all_141_5, simplifying
% 23.79/4.07 | | | with (15), (43) gives:
% 23.79/4.07 | | | (44) all_223_0 = 0
% 23.79/4.07 | | |
% 23.79/4.07 | | | REDUCE: (42), (44) imply:
% 23.79/4.07 | | | (45) $false
% 23.79/4.07 | | |
% 23.79/4.07 | | | CLOSE: (45) is inconsistent.
% 23.79/4.07 | | |
% 23.79/4.07 | | Case 2:
% 23.79/4.07 | | |
% 23.79/4.07 | | | (46) ~ (all_223_0 = 0) & in(all_141_4, all_141_5) = all_223_0
% 23.79/4.07 | | |
% 23.79/4.07 | | | ALPHA: (46) implies:
% 23.79/4.07 | | | (47) ~ (all_223_0 = 0)
% 23.79/4.07 | | | (48) in(all_141_4, all_141_5) = all_223_0
% 23.79/4.07 | | |
% 23.79/4.08 | | | GROUND_INST: instantiating (4) with 0, all_223_0, all_141_5, all_141_4,
% 23.79/4.08 | | | simplifying with (13), (48) gives:
% 23.79/4.08 | | | (49) all_223_0 = 0
% 23.79/4.08 | | |
% 23.79/4.08 | | | REDUCE: (47), (49) imply:
% 23.79/4.08 | | | (50) $false
% 23.79/4.08 | | |
% 23.79/4.08 | | | CLOSE: (50) is inconsistent.
% 23.79/4.08 | | |
% 23.79/4.08 | | End of split
% 23.79/4.08 | |
% 23.79/4.08 | End of split
% 23.79/4.08 |
% 23.79/4.08 End of proof
% 23.79/4.08 % SZS output end Proof for theBenchmark
% 23.79/4.08
% 23.79/4.08 3474ms
%------------------------------------------------------------------------------