TSTP Solution File: SEU234+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU234+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n007.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 17:43:32 EDT 2023
% Result : Theorem 29.34s 5.02s
% Output : Proof 65.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU234+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.31 % Computer : n007.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Wed Aug 23 17:59:09 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.15/0.61 ________ _____
% 0.15/0.61 ___ __ \_________(_)________________________________
% 0.15/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.15/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.15/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.15/0.61
% 0.15/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.15/0.61 (2023-06-19)
% 0.15/0.61
% 0.15/0.61 (c) Philipp Rümmer, 2009-2023
% 0.15/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.15/0.61 Amanda Stjerna.
% 0.15/0.61 Free software under BSD-3-Clause.
% 0.15/0.61
% 0.15/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.15/0.61
% 0.15/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.15/0.63 Running up to 7 provers in parallel.
% 0.15/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.15/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.15/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.15/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.15/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.15/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.15/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.01/1.21 Prover 4: Preprocessing ...
% 3.01/1.21 Prover 1: Preprocessing ...
% 3.35/1.28 Prover 0: Preprocessing ...
% 3.35/1.28 Prover 3: Preprocessing ...
% 3.35/1.28 Prover 5: Preprocessing ...
% 3.35/1.28 Prover 2: Preprocessing ...
% 3.35/1.28 Prover 6: Preprocessing ...
% 6.47/1.81 Prover 2: Proving ...
% 6.47/1.82 Prover 5: Proving ...
% 7.18/1.96 Prover 1: Warning: ignoring some quantifiers
% 7.53/1.99 Prover 1: Constructing countermodel ...
% 7.53/2.01 Prover 3: Warning: ignoring some quantifiers
% 7.53/2.04 Prover 3: Constructing countermodel ...
% 7.53/2.04 Prover 6: Proving ...
% 8.40/2.12 Prover 4: Warning: ignoring some quantifiers
% 8.40/2.22 Prover 4: Constructing countermodel ...
% 10.21/2.37 Prover 0: Proving ...
% 13.38/2.86 Prover 3: gave up
% 13.38/2.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.38/2.97 Prover 7: Preprocessing ...
% 14.88/3.06 Prover 7: Warning: ignoring some quantifiers
% 14.88/3.08 Prover 7: Constructing countermodel ...
% 17.60/3.45 Prover 1: gave up
% 17.60/3.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 18.02/3.52 Prover 8: Preprocessing ...
% 18.59/3.66 Prover 8: Warning: ignoring some quantifiers
% 18.59/3.70 Prover 8: Constructing countermodel ...
% 21.07/3.92 Prover 7: gave up
% 21.07/3.93 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 21.76/4.04 Prover 9: Preprocessing ...
% 23.34/4.41 Prover 8: gave up
% 23.34/4.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 23.34/4.47 Prover 9: Warning: ignoring some quantifiers
% 23.34/4.48 Prover 9: Constructing countermodel ...
% 25.24/4.53 Prover 10: Preprocessing ...
% 26.31/4.62 Prover 10: Warning: ignoring some quantifiers
% 26.31/4.65 Prover 10: Constructing countermodel ...
% 27.78/4.88 Prover 10: gave up
% 28.52/4.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 28.58/4.97 Prover 11: Preprocessing ...
% 29.34/5.01 Prover 0: proved (4367ms)
% 29.34/5.02
% 29.34/5.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.34/5.02
% 29.34/5.02 Prover 5: stopped
% 29.34/5.03 Prover 6: stopped
% 29.34/5.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 29.34/5.03 Prover 9: stopped
% 29.34/5.03 Prover 2: stopped
% 29.34/5.03 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 29.34/5.03 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 29.34/5.06 Prover 13: Preprocessing ...
% 29.34/5.08 Prover 19: Preprocessing ...
% 29.34/5.09 Prover 16: Preprocessing ...
% 29.34/5.15 Prover 11: Warning: ignoring some quantifiers
% 29.34/5.16 Prover 11: Constructing countermodel ...
% 29.34/5.17 Prover 16: Warning: ignoring some quantifiers
% 29.34/5.18 Prover 16: Constructing countermodel ...
% 29.34/5.18 Prover 13: Warning: ignoring some quantifiers
% 29.34/5.19 Prover 13: Constructing countermodel ...
% 29.34/5.26 Prover 19: Warning: ignoring some quantifiers
% 29.34/5.27 Prover 19: Constructing countermodel ...
% 32.40/5.44 Prover 13: gave up
% 34.39/5.79 Prover 19: gave up
% 43.39/7.21 Prover 16: gave up
% 64.26/11.33 Prover 4: Found proof (size 102)
% 64.26/11.33 Prover 4: proved (10692ms)
% 64.26/11.34 Prover 11: stopped
% 64.26/11.34
% 64.26/11.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 64.26/11.34
% 64.41/11.36 % SZS output start Proof for theBenchmark
% 64.41/11.36 Assumptions after simplification:
% 64.41/11.36 ---------------------------------
% 64.41/11.36
% 64.41/11.36 (d2_ordinal1)
% 64.41/11.41 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v1, v0) = v2)
% 64.41/11.41 | ~ (epsilon_transitive(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : (
% 64.41/11.41 ~ (v3 = 0) & in(v1, v0) = v3)) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 64.41/11.41 (epsilon_transitive(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~
% 64.41/11.41 (v3 = 0) & subset(v2, v0) = v3 & in(v2, v0) = 0 & $i(v2))) & ! [v0: $i] :
% 64.41/11.41 ! [v1: $i] : ( ~ (epsilon_transitive(v0) = 0) | ~ (in(v1, v0) = 0) | ~
% 64.41/11.41 $i(v1) | ~ $i(v0) | subset(v1, v0) = 0)
% 64.41/11.41
% 64.41/11.41 (d3_ordinal1)
% 64.41/11.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 = v1 |
% 64.41/11.42 ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 64.41/11.42 | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v2, v0) = v5
% 64.41/11.42 & in(v1, v2) = v6 & in(v1, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 =
% 64.41/11.42 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0
% 64.41/11.42 | v2 = v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v1, v2) = v3) | ~
% 64.41/11.42 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any]
% 64.41/11.42 : (in(v2, v1) = v6 & in(v2, v0) = v5 & in(v1, v0) = v4 & ( ~ (v5 = 0) | ~
% 64.41/11.43 (v4 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 64.41/11.43 (epsilon_connected(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ?
% 64.41/11.43 [v4: int] : ? [v5: int] : ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) &
% 64.41/11.43 in(v3, v2) = v5 & in(v3, v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 &
% 64.41/11.43 $i(v3) & $i(v2)))
% 64.41/11.43
% 64.41/11.43 (d4_ordinal1)
% 64.83/11.44 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (ordinal(v0) = v1) | ~ $i(v0) | ?
% 64.83/11.44 [v2: any] : ? [v3: any] : (epsilon_transitive(v0) = v2 &
% 64.83/11.44 epsilon_connected(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] :
% 64.83/11.44 ! [v1: any] : ( ~ (epsilon_transitive(v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 64.83/11.44 ? [v3: any] : (ordinal(v0) = v2 & epsilon_connected(v0) = v3 & ( ~ (v2 = 0)
% 64.83/11.44 | (v3 = 0 & v1 = 0)))) & ! [v0: $i] : ! [v1: any] : ( ~
% 64.83/11.44 (epsilon_connected(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 64.83/11.44 (epsilon_transitive(v0) = v3 & ordinal(v0) = v2 & ( ~ (v2 = 0) | (v3 = 0 &
% 64.83/11.44 v1 = 0)))) & ! [v0: $i] : ( ~ (epsilon_transitive(v0) = 0) | ~
% 64.83/11.44 $i(v0) | ? [v1: any] : ? [v2: any] : (ordinal(v0) = v2 &
% 64.83/11.44 epsilon_connected(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0: $i] : ( ~
% 64.83/11.44 (ordinal(v0) = 0) | ~ $i(v0) | (epsilon_transitive(v0) = 0 &
% 64.83/11.44 epsilon_connected(v0) = 0)) & ! [v0: $i] : ( ~ (epsilon_connected(v0) =
% 64.83/11.44 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (epsilon_transitive(v0) =
% 64.83/11.44 v1 & ordinal(v0) = v2 & ( ~ (v1 = 0) | v2 = 0)))
% 64.83/11.44
% 64.83/11.44 (fc2_ordinal1)
% 64.83/11.44 relation_empty_yielding(empty_set) = 0 & one_to_one(empty_set) = 0 &
% 64.83/11.44 relation(empty_set) = 0 & epsilon_transitive(empty_set) = 0 &
% 64.83/11.44 ordinal(empty_set) = 0 & epsilon_connected(empty_set) = 0 &
% 64.83/11.44 function(empty_set) = 0 & empty(empty_set) = 0 & $i(empty_set)
% 64.83/11.44
% 64.83/11.44 (rc1_relat_1)
% 64.83/11.44 ? [v0: $i] : (relation(v0) = 0 & empty(v0) = 0 & $i(v0))
% 64.83/11.44
% 64.83/11.44 (rc1_xboole_0)
% 64.83/11.44 ? [v0: $i] : (empty(v0) = 0 & $i(v0))
% 64.83/11.44
% 64.83/11.44 (rc2_funct_1)
% 64.83/11.44 ? [v0: $i] : (relation(v0) = 0 & function(v0) = 0 & empty(v0) = 0 & $i(v0))
% 64.83/11.44
% 64.83/11.44 (rc2_ordinal1)
% 64.83/11.45 ? [v0: $i] : (one_to_one(v0) = 0 & relation(v0) = 0 & epsilon_transitive(v0)
% 64.83/11.45 = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0 & function(v0) = 0 &
% 64.83/11.45 empty(v0) = 0 & $i(v0))
% 64.83/11.45
% 64.83/11.45 (rc3_ordinal1)
% 64.83/11.45 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & epsilon_transitive(v0) = 0 &
% 64.83/11.45 ordinal(v0) = 0 & epsilon_connected(v0) = 0 & empty(v0) = v1 & $i(v0))
% 64.83/11.45
% 64.83/11.45 (t24_ordinal1)
% 64.83/11.45 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (ordinal(v0)
% 64.83/11.45 = 0) | ~ (in(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ?
% 64.83/11.45 [v4: any] : (ordinal(v1) = v3 & in(v0, v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) &
% 64.83/11.45 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (ordinal(v0)
% 64.83/11.45 = 0) | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ?
% 64.83/11.45 [v4: any] : (ordinal(v1) = v3 & in(v1, v0) = v4 & ( ~ (v3 = 0) | v4 = 0))) &
% 64.83/11.45 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (ordinal(v1) = 0) | ~ (ordinal(v0)
% 64.83/11.45 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in(v1, v0) =
% 64.83/11.45 v3 & in(v0, v1) = v2 & (v3 = 0 | v2 = 0)))
% 64.83/11.45
% 64.83/11.45 (t31_ordinal1)
% 64.83/11.45 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & ordinal(v0) = v1 & $i(v0) & !
% 64.83/11.45 [v2: $i] : ! [v3: any] : ( ~ (subset(v2, v0) = v3) | ~ $i(v2) | ? [v4:
% 64.83/11.45 any] : ? [v5: any] : (ordinal(v2) = v5 & in(v2, v0) = v4 & ( ~ (v4 = 0)
% 64.83/11.45 | (v5 = 0 & v3 = 0)))) & ! [v2: $i] : ! [v3: any] : ( ~ (ordinal(v2)
% 64.83/11.45 = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : (subset(v2, v0) = v5 &
% 64.83/11.45 in(v2, v0) = v4 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v2: $i] : (
% 64.83/11.45 ~ (in(v2, v0) = 0) | ~ $i(v2) | (subset(v2, v0) = 0 & ordinal(v2) = 0)))
% 64.83/11.45
% 64.83/11.45 (t6_boole)
% 64.83/11.45 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~
% 64.83/11.45 $i(v0))
% 64.83/11.45
% 64.83/11.45 (t8_boole)
% 64.83/11.45 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)
% 64.83/11.45 | ~ $i(v1) | ~ $i(v0))
% 64.83/11.45
% 64.83/11.45 (function-axioms)
% 64.83/11.46 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 64.83/11.46 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 64.83/11.46 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 64.83/11.46 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 64.83/11.46 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 64.83/11.46 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i]
% 64.83/11.46 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 64.83/11.46 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 64.83/11.46 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 64.83/11.46 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 64.83/11.46 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 64.83/11.46 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0:
% 64.83/11.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 64.83/11.46 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool]
% 64.83/11.46 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 64.83/11.46 (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0:
% 64.83/11.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 64.83/11.46 ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] :
% 64.83/11.46 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 64.83/11.46 (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0:
% 64.83/11.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 64.83/11.46 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool]
% 64.83/11.46 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) |
% 64.83/11.46 ~ (empty(v2) = v0))
% 64.83/11.46
% 64.83/11.46 Further assumptions not needed in the proof:
% 64.83/11.46 --------------------------------------------
% 64.83/11.46 antisymmetry_r2_hidden, cc1_funct_1, cc1_ordinal1, cc1_relat_1, cc2_funct_1,
% 64.83/11.46 cc2_ordinal1, cc3_ordinal1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_m1_subset_1,
% 64.83/11.46 existence_m1_subset_1, fc12_relat_1, fc1_xboole_0, fc4_relat_1, rc1_funct_1,
% 64.83/11.46 rc1_ordinal1, rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, rc4_funct_1,
% 64.83/11.46 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 64.83/11.46 t7_boole
% 64.83/11.46
% 64.83/11.46 Those formulas are unsatisfiable:
% 64.83/11.46 ---------------------------------
% 64.83/11.46
% 64.83/11.46 Begin of proof
% 64.83/11.46 |
% 64.83/11.46 | ALPHA: (d2_ordinal1) implies:
% 64.83/11.46 | (1) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1)
% 64.83/11.46 | | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & subset(v2,
% 64.83/11.46 | v0) = v3 & in(v2, v0) = 0 & $i(v2)))
% 64.83/11.46 |
% 64.83/11.46 | ALPHA: (d3_ordinal1) implies:
% 64.83/11.47 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_connected(v0) = v1)
% 64.83/11.47 | | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: int]
% 64.83/11.47 | : ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) & in(v3, v2) = v5 &
% 64.83/11.47 | in(v3, v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 & $i(v3) &
% 64.83/11.47 | $i(v2)))
% 64.83/11.47 |
% 64.83/11.47 | ALPHA: (d4_ordinal1) implies:
% 64.83/11.47 | (3) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (ordinal(v0) = v1) | ~
% 64.83/11.47 | $i(v0) | ? [v2: any] : ? [v3: any] : (epsilon_transitive(v0) = v2 &
% 64.83/11.47 | epsilon_connected(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 64.83/11.47 |
% 64.83/11.47 | ALPHA: (fc2_ordinal1) implies:
% 64.83/11.47 | (4) ordinal(empty_set) = 0
% 64.83/11.47 |
% 64.83/11.47 | ALPHA: (t24_ordinal1) implies:
% 64.83/11.47 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (ordinal(v1) = 0) | ~
% 64.83/11.47 | (ordinal(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 64.83/11.47 | any] : (in(v1, v0) = v3 & in(v0, v1) = v2 & (v3 = 0 | v2 = 0)))
% 64.83/11.47 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~
% 64.83/11.47 | (ordinal(v0) = 0) | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 64.83/11.47 | [v3: any] : ? [v4: any] : (ordinal(v1) = v3 & in(v1, v0) = v4 & ( ~
% 64.83/11.47 | (v3 = 0) | v4 = 0)))
% 64.83/11.47 |
% 64.83/11.47 | ALPHA: (t6_boole) implies:
% 64.83/11.47 | (7) $i(empty_set)
% 64.83/11.47 | (8) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 64.83/11.47 |
% 64.83/11.47 | ALPHA: (function-axioms) implies:
% 64.83/11.47 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 64.83/11.47 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 64.83/11.47 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 64.83/11.47 | : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 64.83/11.47 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 64.83/11.47 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 64.83/11.47 | v0))
% 64.83/11.47 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 64.83/11.47 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3,
% 64.83/11.47 | v2) = v0))
% 64.83/11.47 |
% 64.83/11.47 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_24_0 gives:
% 64.83/11.47 | (13) empty(all_24_0) = 0 & $i(all_24_0)
% 64.83/11.47 |
% 64.83/11.47 | ALPHA: (13) implies:
% 64.83/11.47 | (14) $i(all_24_0)
% 64.83/11.47 | (15) empty(all_24_0) = 0
% 64.83/11.47 |
% 64.83/11.47 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_26_0 gives:
% 64.83/11.48 | (16) relation(all_26_0) = 0 & empty(all_26_0) = 0 & $i(all_26_0)
% 64.83/11.48 |
% 64.83/11.48 | ALPHA: (16) implies:
% 64.83/11.48 | (17) $i(all_26_0)
% 64.83/11.48 | (18) empty(all_26_0) = 0
% 64.83/11.48 |
% 64.83/11.48 | DELTA: instantiating (rc2_funct_1) with fresh symbol all_43_0 gives:
% 64.83/11.48 | (19) relation(all_43_0) = 0 & function(all_43_0) = 0 & empty(all_43_0) = 0
% 64.83/11.48 | & $i(all_43_0)
% 64.83/11.48 |
% 64.83/11.48 | ALPHA: (19) implies:
% 64.83/11.48 | (20) $i(all_43_0)
% 64.83/11.48 | (21) empty(all_43_0) = 0
% 64.83/11.48 |
% 64.83/11.48 | DELTA: instantiating (rc3_ordinal1) with fresh symbols all_45_0, all_45_1
% 64.83/11.48 | gives:
% 64.83/11.48 | (22) ~ (all_45_0 = 0) & epsilon_transitive(all_45_1) = 0 &
% 64.83/11.48 | ordinal(all_45_1) = 0 & epsilon_connected(all_45_1) = 0 &
% 64.83/11.48 | empty(all_45_1) = all_45_0 & $i(all_45_1)
% 64.83/11.48 |
% 64.83/11.48 | ALPHA: (22) implies:
% 64.83/11.48 | (23) ~ (all_45_0 = 0)
% 64.83/11.48 | (24) $i(all_45_1)
% 64.83/11.48 | (25) empty(all_45_1) = all_45_0
% 64.83/11.48 | (26) ordinal(all_45_1) = 0
% 64.83/11.48 |
% 64.83/11.48 | DELTA: instantiating (rc2_ordinal1) with fresh symbol all_47_0 gives:
% 64.83/11.48 | (27) one_to_one(all_47_0) = 0 & relation(all_47_0) = 0 &
% 64.83/11.48 | epsilon_transitive(all_47_0) = 0 & ordinal(all_47_0) = 0 &
% 64.83/11.48 | epsilon_connected(all_47_0) = 0 & function(all_47_0) = 0 &
% 64.83/11.48 | empty(all_47_0) = 0 & $i(all_47_0)
% 64.83/11.48 |
% 64.83/11.48 | ALPHA: (27) implies:
% 64.83/11.48 | (28) $i(all_47_0)
% 64.83/11.48 | (29) empty(all_47_0) = 0
% 64.83/11.48 | (30) ordinal(all_47_0) = 0
% 64.83/11.48 |
% 64.83/11.48 | DELTA: instantiating (t31_ordinal1) with fresh symbols all_49_0, all_49_1
% 64.83/11.48 | gives:
% 64.83/11.48 | (31) ~ (all_49_0 = 0) & ordinal(all_49_1) = all_49_0 & $i(all_49_1) & !
% 64.83/11.48 | [v0: $i] : ! [v1: any] : ( ~ (subset(v0, all_49_1) = v1) | ~ $i(v0)
% 64.83/11.48 | | ? [v2: any] : ? [v3: any] : (ordinal(v0) = v3 & in(v0, all_49_1)
% 64.83/11.48 | = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: $i] : ! [v1:
% 64.83/11.48 | any] : ( ~ (ordinal(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 64.83/11.48 | any] : (subset(v0, all_49_1) = v3 & in(v0, all_49_1) = v2 & ( ~
% 64.83/11.48 | (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: $i] : ( ~ (in(v0,
% 64.83/11.48 | all_49_1) = 0) | ~ $i(v0) | (subset(v0, all_49_1) = 0 &
% 64.83/11.48 | ordinal(v0) = 0))
% 64.83/11.48 |
% 64.83/11.48 | ALPHA: (31) implies:
% 64.83/11.48 | (32) ~ (all_49_0 = 0)
% 64.83/11.48 | (33) $i(all_49_1)
% 64.83/11.48 | (34) ordinal(all_49_1) = all_49_0
% 64.83/11.48 | (35) ! [v0: $i] : ( ~ (in(v0, all_49_1) = 0) | ~ $i(v0) | (subset(v0,
% 64.83/11.48 | all_49_1) = 0 & ordinal(v0) = 0))
% 64.83/11.48 |
% 65.10/11.49 | GROUND_INST: instantiating (t8_boole) with all_24_0, all_26_0, simplifying
% 65.10/11.49 | with (14), (15), (17), (18) gives:
% 65.10/11.49 | (36) all_26_0 = all_24_0
% 65.10/11.49 |
% 65.10/11.49 | GROUND_INST: instantiating (t8_boole) with all_26_0, all_43_0, simplifying
% 65.10/11.49 | with (17), (18), (20), (21) gives:
% 65.10/11.49 | (37) all_43_0 = all_26_0
% 65.10/11.49 |
% 65.10/11.49 | GROUND_INST: instantiating (t8_boole) with all_43_0, all_47_0, simplifying
% 65.10/11.49 | with (20), (21), (28), (29) gives:
% 65.10/11.49 | (38) all_47_0 = all_43_0
% 65.10/11.49 |
% 65.10/11.49 | GROUND_INST: instantiating (8) with all_47_0, simplifying with (28), (29)
% 65.10/11.49 | gives:
% 65.10/11.49 | (39) all_47_0 = empty_set
% 65.10/11.49 |
% 65.10/11.49 | GROUND_INST: instantiating (5) with empty_set, all_45_1, simplifying with (4),
% 65.10/11.49 | (7), (24), (26) gives:
% 65.10/11.49 | (40) all_45_1 = empty_set | ? [v0: any] : ? [v1: any] : (in(all_45_1,
% 65.10/11.49 | empty_set) = v1 & in(empty_set, all_45_1) = v0 & (v1 = 0 | v0 =
% 65.10/11.49 | 0))
% 65.10/11.49 |
% 65.10/11.49 | GROUND_INST: instantiating (5) with all_45_1, all_47_0, simplifying with (24),
% 65.10/11.49 | (26), (28), (30) gives:
% 65.10/11.49 | (41) all_47_0 = all_45_1 | ? [v0: any] : ? [v1: any] : (in(all_47_0,
% 65.10/11.49 | all_45_1) = v1 & in(all_45_1, all_47_0) = v0 & (v1 = 0 | v0 = 0))
% 65.10/11.49 |
% 65.10/11.49 | GROUND_INST: instantiating (3) with all_49_1, all_49_0, simplifying with (33),
% 65.10/11.49 | (34) gives:
% 65.10/11.49 | (42) all_49_0 = 0 | ? [v0: any] : ? [v1: any] :
% 65.10/11.49 | (epsilon_transitive(all_49_1) = v0 & epsilon_connected(all_49_1) = v1
% 65.10/11.49 | & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 65.10/11.49 |
% 65.10/11.49 | COMBINE_EQS: (38), (39) imply:
% 65.10/11.49 | (43) all_43_0 = empty_set
% 65.10/11.49 |
% 65.10/11.49 | SIMP: (43) implies:
% 65.10/11.49 | (44) all_43_0 = empty_set
% 65.10/11.49 |
% 65.10/11.49 | COMBINE_EQS: (37), (44) imply:
% 65.10/11.49 | (45) all_26_0 = empty_set
% 65.10/11.49 |
% 65.10/11.49 | SIMP: (45) implies:
% 65.10/11.49 | (46) all_26_0 = empty_set
% 65.10/11.49 |
% 65.10/11.49 | COMBINE_EQS: (36), (46) imply:
% 65.10/11.49 | (47) all_24_0 = empty_set
% 65.10/11.49 |
% 65.10/11.49 | REDUCE: (15), (47) imply:
% 65.10/11.49 | (48) empty(empty_set) = 0
% 65.10/11.49 |
% 65.10/11.49 | BETA: splitting (40) gives:
% 65.10/11.49 |
% 65.10/11.49 | Case 1:
% 65.10/11.49 | |
% 65.10/11.49 | | (49) all_45_1 = empty_set
% 65.10/11.49 | |
% 65.10/11.49 | | REDUCE: (25), (49) imply:
% 65.10/11.49 | | (50) empty(empty_set) = all_45_0
% 65.10/11.49 | |
% 65.10/11.49 | | GROUND_INST: instantiating (9) with 0, all_45_0, empty_set, simplifying with
% 65.10/11.49 | | (48), (50) gives:
% 65.10/11.49 | | (51) all_45_0 = 0
% 65.10/11.49 | |
% 65.10/11.49 | | REDUCE: (23), (51) imply:
% 65.10/11.49 | | (52) $false
% 65.10/11.50 | |
% 65.10/11.50 | | CLOSE: (52) is inconsistent.
% 65.10/11.50 | |
% 65.10/11.50 | Case 2:
% 65.10/11.50 | |
% 65.10/11.50 | | (53) ~ (all_45_1 = empty_set)
% 65.10/11.50 | |
% 65.10/11.50 | | BETA: splitting (42) gives:
% 65.10/11.50 | |
% 65.10/11.50 | | Case 1:
% 65.10/11.50 | | |
% 65.10/11.50 | | | (54) all_49_0 = 0
% 65.10/11.50 | | |
% 65.10/11.50 | | | REDUCE: (32), (54) imply:
% 65.10/11.50 | | | (55) $false
% 65.10/11.50 | | |
% 65.10/11.50 | | | CLOSE: (55) is inconsistent.
% 65.10/11.50 | | |
% 65.10/11.50 | | Case 2:
% 65.10/11.50 | | |
% 65.10/11.50 | | | (56) ? [v0: any] : ? [v1: any] : (epsilon_transitive(all_49_1) = v0 &
% 65.10/11.50 | | | epsilon_connected(all_49_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 65.10/11.50 | | |
% 65.10/11.50 | | | DELTA: instantiating (56) with fresh symbols all_213_0, all_213_1 gives:
% 65.10/11.50 | | | (57) epsilon_transitive(all_49_1) = all_213_1 &
% 65.10/11.50 | | | epsilon_connected(all_49_1) = all_213_0 & ( ~ (all_213_0 = 0) | ~
% 65.10/11.50 | | | (all_213_1 = 0))
% 65.10/11.50 | | |
% 65.10/11.50 | | | ALPHA: (57) implies:
% 65.10/11.50 | | | (58) epsilon_connected(all_49_1) = all_213_0
% 65.10/11.50 | | | (59) epsilon_transitive(all_49_1) = all_213_1
% 65.10/11.50 | | | (60) ~ (all_213_0 = 0) | ~ (all_213_1 = 0)
% 65.10/11.50 | | |
% 65.10/11.50 | | | BETA: splitting (41) gives:
% 65.10/11.50 | | |
% 65.10/11.50 | | | Case 1:
% 65.10/11.50 | | | |
% 65.10/11.50 | | | | (61) all_47_0 = all_45_1
% 65.10/11.50 | | | |
% 65.10/11.50 | | | | COMBINE_EQS: (39), (61) imply:
% 65.10/11.50 | | | | (62) all_45_1 = empty_set
% 65.10/11.50 | | | |
% 65.10/11.50 | | | | REDUCE: (53), (62) imply:
% 65.10/11.50 | | | | (63) $false
% 65.10/11.50 | | | |
% 65.10/11.50 | | | | CLOSE: (63) is inconsistent.
% 65.10/11.50 | | | |
% 65.10/11.50 | | | Case 2:
% 65.10/11.50 | | | |
% 65.10/11.50 | | | |
% 65.10/11.50 | | | | GROUND_INST: instantiating (2) with all_49_1, all_213_0, simplifying
% 65.10/11.50 | | | | with (33), (58) gives:
% 65.10/11.50 | | | | (64) all_213_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ?
% 65.10/11.50 | | | | [v3: int] : ( ~ (v3 = 0) & ~ (v2 = 0) & ~ (v1 = v0) & in(v1,
% 65.10/11.50 | | | | v0) = v3 & in(v1, all_49_1) = 0 & in(v0, v1) = v2 & in(v0,
% 65.10/11.50 | | | | all_49_1) = 0 & $i(v1) & $i(v0))
% 65.10/11.50 | | | |
% 65.10/11.50 | | | | GROUND_INST: instantiating (1) with all_49_1, all_213_1, simplifying
% 65.10/11.50 | | | | with (33), (59) gives:
% 65.10/11.51 | | | | (65) all_213_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 65.10/11.51 | | | | subset(v0, all_49_1) = v1 & in(v0, all_49_1) = 0 & $i(v0))
% 65.10/11.51 | | | |
% 65.10/11.51 | | | | BETA: splitting (60) gives:
% 65.10/11.51 | | | |
% 65.10/11.51 | | | | Case 1:
% 65.10/11.51 | | | | |
% 65.10/11.51 | | | | | (66) ~ (all_213_0 = 0)
% 65.10/11.51 | | | | |
% 65.10/11.51 | | | | | BETA: splitting (64) gives:
% 65.10/11.51 | | | | |
% 65.10/11.51 | | | | | Case 1:
% 65.10/11.51 | | | | | |
% 65.10/11.51 | | | | | | (67) all_213_0 = 0
% 65.10/11.51 | | | | | |
% 65.10/11.51 | | | | | | REDUCE: (66), (67) imply:
% 65.10/11.51 | | | | | | (68) $false
% 65.10/11.51 | | | | | |
% 65.10/11.51 | | | | | | CLOSE: (68) is inconsistent.
% 65.10/11.51 | | | | | |
% 65.10/11.51 | | | | | Case 2:
% 65.10/11.51 | | | | | |
% 65.10/11.51 | | | | | | (69) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : (
% 65.10/11.51 | | | | | | ~ (v3 = 0) & ~ (v2 = 0) & ~ (v1 = v0) & in(v1, v0) = v3
% 65.10/11.51 | | | | | | & in(v1, all_49_1) = 0 & in(v0, v1) = v2 & in(v0,
% 65.10/11.51 | | | | | | all_49_1) = 0 & $i(v1) & $i(v0))
% 65.10/11.51 | | | | | |
% 65.10/11.51 | | | | | | DELTA: instantiating (69) with fresh symbols all_563_0, all_563_1,
% 65.10/11.51 | | | | | | all_563_2, all_563_3 gives:
% 65.10/11.51 | | | | | | (70) ~ (all_563_0 = 0) & ~ (all_563_1 = 0) & ~ (all_563_2 =
% 65.10/11.51 | | | | | | all_563_3) & in(all_563_2, all_563_3) = all_563_0 &
% 65.10/11.51 | | | | | | in(all_563_2, all_49_1) = 0 & in(all_563_3, all_563_2) =
% 65.10/11.51 | | | | | | all_563_1 & in(all_563_3, all_49_1) = 0 & $i(all_563_2) &
% 65.10/11.51 | | | | | | $i(all_563_3)
% 65.10/11.51 | | | | | |
% 65.10/11.51 | | | | | | ALPHA: (70) implies:
% 65.10/11.51 | | | | | | (71) ~ (all_563_2 = all_563_3)
% 65.10/11.51 | | | | | | (72) ~ (all_563_1 = 0)
% 65.10/11.51 | | | | | | (73) ~ (all_563_0 = 0)
% 65.10/11.51 | | | | | | (74) $i(all_563_3)
% 65.10/11.51 | | | | | | (75) $i(all_563_2)
% 65.10/11.51 | | | | | | (76) in(all_563_3, all_49_1) = 0
% 65.10/11.51 | | | | | | (77) in(all_563_3, all_563_2) = all_563_1
% 65.10/11.51 | | | | | | (78) in(all_563_2, all_49_1) = 0
% 65.10/11.51 | | | | | | (79) in(all_563_2, all_563_3) = all_563_0
% 65.10/11.51 | | | | | |
% 65.10/11.51 | | | | | | GROUND_INST: instantiating (35) with all_563_3, simplifying with
% 65.10/11.51 | | | | | | (74), (76) gives:
% 65.10/11.51 | | | | | | (80) subset(all_563_3, all_49_1) = 0 & ordinal(all_563_3) = 0
% 65.10/11.51 | | | | | |
% 65.10/11.51 | | | | | | ALPHA: (80) implies:
% 65.10/11.51 | | | | | | (81) ordinal(all_563_3) = 0
% 65.10/11.51 | | | | | |
% 65.10/11.51 | | | | | | GROUND_INST: instantiating (35) with all_563_2, simplifying with
% 65.10/11.51 | | | | | | (75), (78) gives:
% 65.10/11.52 | | | | | | (82) subset(all_563_2, all_49_1) = 0 & ordinal(all_563_2) = 0
% 65.10/11.52 | | | | | |
% 65.10/11.52 | | | | | | ALPHA: (82) implies:
% 65.10/11.52 | | | | | | (83) ordinal(all_563_2) = 0
% 65.10/11.52 | | | | | |
% 65.10/11.52 | | | | | | GROUND_INST: instantiating (6) with all_563_2, all_563_3, all_563_0,
% 65.10/11.52 | | | | | | simplifying with (74), (75), (79), (83) gives:
% 65.10/11.52 | | | | | | (84) all_563_0 = 0 | all_563_2 = all_563_3 | ? [v0: any] : ?
% 65.10/11.52 | | | | | | [v1: any] : (ordinal(all_563_3) = v0 & in(all_563_3,
% 65.10/11.52 | | | | | | all_563_2) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 65.10/11.52 | | | | | |
% 65.10/11.52 | | | | | | GROUND_INST: instantiating (5) with all_563_2, all_563_3,
% 65.10/11.52 | | | | | | simplifying with (74), (75), (81), (83) gives:
% 65.10/11.52 | | | | | | (85) all_563_2 = all_563_3 | ? [v0: any] : ? [v1: any] :
% 65.10/11.52 | | | | | | (in(all_563_2, all_563_3) = v0 & in(all_563_3, all_563_2) =
% 65.10/11.52 | | | | | | v1 & (v1 = 0 | v0 = 0))
% 65.10/11.52 | | | | | |
% 65.10/11.52 | | | | | | BETA: splitting (85) gives:
% 65.10/11.52 | | | | | |
% 65.10/11.52 | | | | | | Case 1:
% 65.10/11.52 | | | | | | |
% 65.10/11.52 | | | | | | | (86) all_563_2 = all_563_3
% 65.10/11.52 | | | | | | |
% 65.10/11.52 | | | | | | | REDUCE: (71), (86) imply:
% 65.10/11.52 | | | | | | | (87) $false
% 65.10/11.52 | | | | | | |
% 65.10/11.52 | | | | | | | CLOSE: (87) is inconsistent.
% 65.10/11.52 | | | | | | |
% 65.10/11.52 | | | | | | Case 2:
% 65.10/11.52 | | | | | | |
% 65.10/11.52 | | | | | | | (88) ? [v0: any] : ? [v1: any] : (in(all_563_2, all_563_3) =
% 65.10/11.52 | | | | | | | v0 & in(all_563_3, all_563_2) = v1 & (v1 = 0 | v0 = 0))
% 65.10/11.52 | | | | | | |
% 65.10/11.52 | | | | | | | DELTA: instantiating (88) with fresh symbols all_732_0, all_732_1
% 65.10/11.52 | | | | | | | gives:
% 65.10/11.52 | | | | | | | (89) in(all_563_2, all_563_3) = all_732_1 & in(all_563_3,
% 65.10/11.52 | | | | | | | all_563_2) = all_732_0 & (all_732_0 = 0 | all_732_1 = 0)
% 65.10/11.52 | | | | | | |
% 65.10/11.52 | | | | | | | ALPHA: (89) implies:
% 65.10/11.52 | | | | | | | (90) in(all_563_3, all_563_2) = all_732_0
% 65.10/11.52 | | | | | | |
% 65.10/11.52 | | | | | | | BETA: splitting (84) gives:
% 65.10/11.52 | | | | | | |
% 65.10/11.52 | | | | | | | Case 1:
% 65.10/11.52 | | | | | | | |
% 65.10/11.52 | | | | | | | | (91) all_563_0 = 0
% 65.10/11.52 | | | | | | | |
% 65.10/11.52 | | | | | | | | REDUCE: (73), (91) imply:
% 65.10/11.52 | | | | | | | | (92) $false
% 65.10/11.52 | | | | | | | |
% 65.10/11.52 | | | | | | | | CLOSE: (92) is inconsistent.
% 65.10/11.52 | | | | | | | |
% 65.10/11.52 | | | | | | | Case 2:
% 65.10/11.52 | | | | | | | |
% 65.10/11.52 | | | | | | | | (93) all_563_2 = all_563_3 | ? [v0: any] : ? [v1: any] :
% 65.10/11.52 | | | | | | | | (ordinal(all_563_3) = v0 & in(all_563_3, all_563_2) = v1
% 65.10/11.52 | | | | | | | | & ( ~ (v0 = 0) | v1 = 0))
% 65.10/11.53 | | | | | | | |
% 65.10/11.53 | | | | | | | | BETA: splitting (93) gives:
% 65.10/11.53 | | | | | | | |
% 65.10/11.53 | | | | | | | | Case 1:
% 65.10/11.53 | | | | | | | | |
% 65.10/11.53 | | | | | | | | | (94) all_563_2 = all_563_3
% 65.10/11.53 | | | | | | | | |
% 65.10/11.53 | | | | | | | | | REDUCE: (71), (94) imply:
% 65.10/11.53 | | | | | | | | | (95) $false
% 65.10/11.53 | | | | | | | | |
% 65.10/11.53 | | | | | | | | | CLOSE: (95) is inconsistent.
% 65.10/11.53 | | | | | | | | |
% 65.10/11.53 | | | | | | | | Case 2:
% 65.10/11.53 | | | | | | | | |
% 65.10/11.53 | | | | | | | | | (96) ? [v0: any] : ? [v1: any] : (ordinal(all_563_3) = v0
% 65.10/11.53 | | | | | | | | | & in(all_563_3, all_563_2) = v1 & ( ~ (v0 = 0) | v1
% 65.10/11.53 | | | | | | | | | = 0))
% 65.10/11.53 | | | | | | | | |
% 65.10/11.53 | | | | | | | | | DELTA: instantiating (96) with fresh symbols all_742_0,
% 65.10/11.53 | | | | | | | | | all_742_1 gives:
% 65.10/11.53 | | | | | | | | | (97) ordinal(all_563_3) = all_742_1 & in(all_563_3,
% 65.10/11.53 | | | | | | | | | all_563_2) = all_742_0 & ( ~ (all_742_1 = 0) |
% 65.10/11.53 | | | | | | | | | all_742_0 = 0)
% 65.10/11.53 | | | | | | | | |
% 65.10/11.53 | | | | | | | | | ALPHA: (97) implies:
% 65.10/11.53 | | | | | | | | | (98) in(all_563_3, all_563_2) = all_742_0
% 65.10/11.53 | | | | | | | | | (99) ordinal(all_563_3) = all_742_1
% 65.10/11.53 | | | | | | | | | (100) ~ (all_742_1 = 0) | all_742_0 = 0
% 65.10/11.53 | | | | | | | | |
% 65.10/11.53 | | | | | | | | | GROUND_INST: instantiating (11) with all_563_1, all_742_0,
% 65.10/11.53 | | | | | | | | | all_563_2, all_563_3, simplifying with (77), (98)
% 65.10/11.53 | | | | | | | | | gives:
% 65.10/11.53 | | | | | | | | | (101) all_742_0 = all_563_1
% 65.10/11.53 | | | | | | | | |
% 65.10/11.53 | | | | | | | | | GROUND_INST: instantiating (11) with all_732_0, all_742_0,
% 65.10/11.53 | | | | | | | | | all_563_2, all_563_3, simplifying with (90), (98)
% 65.10/11.53 | | | | | | | | | gives:
% 65.10/11.53 | | | | | | | | | (102) all_742_0 = all_732_0
% 65.10/11.53 | | | | | | | | |
% 65.10/11.53 | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_742_1, all_563_3,
% 65.10/11.53 | | | | | | | | | simplifying with (81), (99) gives:
% 65.10/11.53 | | | | | | | | | (103) all_742_1 = 0
% 65.10/11.53 | | | | | | | | |
% 65.10/11.53 | | | | | | | | | COMBINE_EQS: (101), (102) imply:
% 65.10/11.53 | | | | | | | | | (104) all_732_0 = all_563_1
% 65.10/11.53 | | | | | | | | |
% 65.10/11.53 | | | | | | | | | BETA: splitting (100) gives:
% 65.10/11.53 | | | | | | | | |
% 65.10/11.53 | | | | | | | | | Case 1:
% 65.10/11.53 | | | | | | | | | |
% 65.10/11.53 | | | | | | | | | | (105) ~ (all_742_1 = 0)
% 65.10/11.53 | | | | | | | | | |
% 65.10/11.53 | | | | | | | | | | REDUCE: (103), (105) imply:
% 65.10/11.53 | | | | | | | | | | (106) $false
% 65.10/11.53 | | | | | | | | | |
% 65.10/11.53 | | | | | | | | | | CLOSE: (106) is inconsistent.
% 65.10/11.53 | | | | | | | | | |
% 65.10/11.53 | | | | | | | | | Case 2:
% 65.10/11.53 | | | | | | | | | |
% 65.10/11.53 | | | | | | | | | | (107) all_742_0 = 0
% 65.10/11.53 | | | | | | | | | |
% 65.10/11.53 | | | | | | | | | | COMBINE_EQS: (101), (107) imply:
% 65.10/11.53 | | | | | | | | | | (108) all_563_1 = 0
% 65.10/11.53 | | | | | | | | | |
% 65.10/11.53 | | | | | | | | | | SIMP: (108) implies:
% 65.10/11.53 | | | | | | | | | | (109) all_563_1 = 0
% 65.10/11.53 | | | | | | | | | |
% 65.10/11.53 | | | | | | | | | | REDUCE: (72), (109) imply:
% 65.10/11.53 | | | | | | | | | | (110) $false
% 65.10/11.53 | | | | | | | | | |
% 65.10/11.53 | | | | | | | | | | CLOSE: (110) is inconsistent.
% 65.10/11.53 | | | | | | | | | |
% 65.10/11.53 | | | | | | | | | End of split
% 65.10/11.53 | | | | | | | | |
% 65.10/11.53 | | | | | | | | End of split
% 65.10/11.53 | | | | | | | |
% 65.10/11.53 | | | | | | | End of split
% 65.10/11.53 | | | | | | |
% 65.10/11.53 | | | | | | End of split
% 65.10/11.53 | | | | | |
% 65.10/11.53 | | | | | End of split
% 65.10/11.53 | | | | |
% 65.10/11.53 | | | | Case 2:
% 65.10/11.53 | | | | |
% 65.10/11.54 | | | | | (111) ~ (all_213_1 = 0)
% 65.10/11.54 | | | | |
% 65.10/11.54 | | | | | BETA: splitting (65) gives:
% 65.10/11.54 | | | | |
% 65.10/11.54 | | | | | Case 1:
% 65.10/11.54 | | | | | |
% 65.10/11.54 | | | | | | (112) all_213_1 = 0
% 65.10/11.54 | | | | | |
% 65.10/11.54 | | | | | | REDUCE: (111), (112) imply:
% 65.10/11.54 | | | | | | (113) $false
% 65.10/11.54 | | | | | |
% 65.10/11.54 | | | | | | CLOSE: (113) is inconsistent.
% 65.10/11.54 | | | | | |
% 65.10/11.54 | | | | | Case 2:
% 65.10/11.54 | | | | | |
% 65.10/11.54 | | | | | | (114) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0,
% 65.10/11.54 | | | | | | all_49_1) = v1 & in(v0, all_49_1) = 0 & $i(v0))
% 65.10/11.54 | | | | | |
% 65.10/11.54 | | | | | | DELTA: instantiating (114) with fresh symbols all_563_0, all_563_1
% 65.10/11.54 | | | | | | gives:
% 65.10/11.54 | | | | | | (115) ~ (all_563_0 = 0) & subset(all_563_1, all_49_1) =
% 65.10/11.54 | | | | | | all_563_0 & in(all_563_1, all_49_1) = 0 & $i(all_563_1)
% 65.10/11.54 | | | | | |
% 65.10/11.54 | | | | | | ALPHA: (115) implies:
% 65.10/11.54 | | | | | | (116) ~ (all_563_0 = 0)
% 65.10/11.54 | | | | | | (117) $i(all_563_1)
% 65.10/11.54 | | | | | | (118) in(all_563_1, all_49_1) = 0
% 65.10/11.54 | | | | | | (119) subset(all_563_1, all_49_1) = all_563_0
% 65.10/11.54 | | | | | |
% 65.10/11.54 | | | | | | GROUND_INST: instantiating (35) with all_563_1, simplifying with
% 65.10/11.54 | | | | | | (117), (118) gives:
% 65.10/11.54 | | | | | | (120) subset(all_563_1, all_49_1) = 0 & ordinal(all_563_1) = 0
% 65.10/11.54 | | | | | |
% 65.10/11.54 | | | | | | ALPHA: (120) implies:
% 65.10/11.54 | | | | | | (121) subset(all_563_1, all_49_1) = 0
% 65.10/11.54 | | | | | |
% 65.10/11.54 | | | | | | GROUND_INST: instantiating (12) with all_563_0, 0, all_49_1,
% 65.10/11.54 | | | | | | all_563_1, simplifying with (119), (121) gives:
% 65.10/11.54 | | | | | | (122) all_563_0 = 0
% 65.10/11.54 | | | | | |
% 65.10/11.54 | | | | | | REDUCE: (116), (122) imply:
% 65.10/11.54 | | | | | | (123) $false
% 65.10/11.54 | | | | | |
% 65.10/11.54 | | | | | | CLOSE: (123) is inconsistent.
% 65.10/11.54 | | | | | |
% 65.10/11.54 | | | | | End of split
% 65.10/11.54 | | | | |
% 65.10/11.54 | | | | End of split
% 65.10/11.54 | | | |
% 65.10/11.54 | | | End of split
% 65.10/11.54 | | |
% 65.10/11.54 | | End of split
% 65.10/11.54 | |
% 65.10/11.54 | End of split
% 65.10/11.54 |
% 65.10/11.54 End of proof
% 65.10/11.54 % SZS output end Proof for theBenchmark
% 65.10/11.54
% 65.10/11.54 10928ms
%------------------------------------------------------------------------------