TSTP Solution File: SEU248+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU248+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 : n018.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 11.06s 2.30s
% Output : Proof 16.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU248+1 : 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 : n018.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 : Wed Aug 23 16:49:57 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.54/1.03 Prover 4: Preprocessing ...
% 2.54/1.03 Prover 1: Preprocessing ...
% 2.54/1.07 Prover 0: Preprocessing ...
% 2.54/1.07 Prover 3: Preprocessing ...
% 2.54/1.07 Prover 6: Preprocessing ...
% 2.54/1.07 Prover 2: Preprocessing ...
% 2.54/1.07 Prover 5: Preprocessing ...
% 6.00/1.54 Prover 1: Warning: ignoring some quantifiers
% 6.64/1.60 Prover 1: Constructing countermodel ...
% 6.64/1.62 Prover 6: Proving ...
% 6.64/1.62 Prover 5: Proving ...
% 6.64/1.62 Prover 3: Warning: ignoring some quantifiers
% 6.64/1.63 Prover 4: Warning: ignoring some quantifiers
% 6.64/1.63 Prover 3: Constructing countermodel ...
% 6.64/1.64 Prover 2: Proving ...
% 6.64/1.65 Prover 4: Constructing countermodel ...
% 7.35/1.71 Prover 0: Proving ...
% 11.06/2.30 Prover 0: proved (1667ms)
% 11.06/2.30
% 11.06/2.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.06/2.30
% 11.06/2.30 Prover 3: stopped
% 11.06/2.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.06/2.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.06/2.30 Prover 2: stopped
% 11.06/2.30 Prover 5: stopped
% 11.06/2.31 Prover 6: stopped
% 11.81/2.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.81/2.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.81/2.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.81/2.35 Prover 10: Preprocessing ...
% 11.81/2.36 Prover 7: Preprocessing ...
% 11.81/2.36 Prover 13: Preprocessing ...
% 11.81/2.36 Prover 11: Preprocessing ...
% 11.81/2.37 Prover 8: Preprocessing ...
% 12.45/2.44 Prover 10: Warning: ignoring some quantifiers
% 12.45/2.44 Prover 7: Warning: ignoring some quantifiers
% 12.45/2.45 Prover 10: Constructing countermodel ...
% 12.45/2.47 Prover 7: Constructing countermodel ...
% 12.45/2.47 Prover 8: Warning: ignoring some quantifiers
% 13.16/2.48 Prover 13: Warning: ignoring some quantifiers
% 13.16/2.49 Prover 8: Constructing countermodel ...
% 13.16/2.50 Prover 13: Constructing countermodel ...
% 13.39/2.60 Prover 11: Warning: ignoring some quantifiers
% 14.12/2.62 Prover 11: Constructing countermodel ...
% 14.77/2.83 Prover 4: Found proof (size 98)
% 14.77/2.83 Prover 4: proved (2192ms)
% 14.77/2.83 Prover 8: stopped
% 14.77/2.83 Prover 7: stopped
% 14.77/2.83 Prover 10: stopped
% 14.77/2.83 Prover 11: stopped
% 14.77/2.83 Prover 1: stopped
% 14.77/2.83 Prover 13: stopped
% 14.77/2.83
% 14.77/2.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.77/2.83
% 14.77/2.84 % SZS output start Proof for theBenchmark
% 14.77/2.85 Assumptions after simplification:
% 14.77/2.85 ---------------------------------
% 14.77/2.85
% 14.77/2.85 (cc2_funct_1)
% 14.77/2.88 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 14.77/2.88 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) =
% 14.77/2.88 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 14.77/2.88 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 14.77/2.88 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0)
% 14.77/2.88 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 14.77/2.88 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any]
% 14.77/2.88 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) |
% 14.77/2.88 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0)
% 14.77/2.88 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 &
% 14.77/2.88 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 =
% 14.77/2.88 0)))
% 14.77/2.88
% 14.77/2.88 (d12_relat_1)
% 16.01/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.01/2.89 $i] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4)
% 16.01/2.89 = v5) | ~ (relation(v2) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 16.01/2.89 $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: any] : ? [v8: any] : (( ~ (v6 =
% 16.01/2.89 0) & relation(v1) = v6) | (in(v5, v2) = v8 & in(v5, v1) = v7 & in(v4,
% 16.01/2.89 v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0)))) & ! [v0: $i] : !
% 16.01/2.89 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 16.01/2.89 (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) |
% 16.01/2.89 ~ (relation(v2) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.01/2.89 $i(v0) | ? [v6: int] : ? [v7: any] : ? [v8: any] : (( ~ (v6 = 0) &
% 16.01/2.89 relation(v1) = v6) | (in(v5, v2) = v6 & in(v5, v1) = v8 & in(v4, v0) =
% 16.01/2.89 v7 & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0))))) & ! [v0: $i] : ! [v1: $i] :
% 16.01/2.89 ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) =
% 16.01/2.89 v2) | ~ (relation(v3) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 16.01/2.89 int] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9:
% 16.01/2.89 any] : ? [v10: any] : ($i(v6) & $i(v5) & (( ~ (v4 = 0) & relation(v1) =
% 16.01/2.89 v4) | (ordered_pair(v5, v6) = v7 & in(v7, v3) = v8 & in(v7, v1) = v10
% 16.01/2.89 & in(v6, v0) = v9 & $i(v7) & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 =
% 16.01/2.89 0)) & (v8 = 0 | (v10 = 0 & v9 = 0))))))
% 16.01/2.89
% 16.01/2.89 (d3_tarski)
% 16.01/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 16.01/2.89 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.01/2.89 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 16.01/2.89 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 16.01/2.89 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 16.01/2.89 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 16.01/2.89 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 16.01/2.89 $i(v0) | in(v2, v1) = 0)
% 16.01/2.89
% 16.01/2.89 (d4_relat_1)
% 16.01/2.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : ! [v5:
% 16.01/2.90 $i] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5)
% 16.01/2.90 | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 16.01/2.90 [v6: int] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) =
% 16.01/2.90 v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0)
% 16.01/2.90 = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 16.01/2.90 int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ($i(v4) & ((v6 = 0 &
% 16.01/2.90 ordered_pair(v2, v4) = v5 & in(v5, v0) = 0 & $i(v5)) | ( ~ (v3 = 0) &
% 16.01/2.90 relation(v0) = v3)))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2
% 16.01/2.90 = v0 | ~ (relation_dom(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] :
% 16.01/2.90 ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] :
% 16.01/2.90 ($i(v6) & $i(v4) & (( ~ (v3 = 0) & relation(v1) = v3) | (in(v4, v0) = v5 & (
% 16.01/2.90 ~ (v5 = 0) | ! [v9: $i] : ! [v10: $i] : ( ~ (ordered_pair(v4, v9)
% 16.01/2.90 = v10) | ~ $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & in(v10, v1)
% 16.01/2.90 = v11))) & (v5 = 0 | (v8 = 0 & ordered_pair(v4, v6) = v7 &
% 16.10/2.90 in(v7, v1) = 0 & $i(v7))))))) & ! [v0: $i] : ( ~ (relation(v0) =
% 16.10/2.90 0) | ~ $i(v0) | ? [v1: $i] : (relation_dom(v0) = v1 & $i(v1) & ! [v2:
% 16.10/2.90 $i] : ! [v3: int] : ! [v4: $i] : ! [v5: $i] : (v3 = 0 | ~
% 16.10/2.90 (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~
% 16.10/2.90 $i(v2) | ? [v6: int] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2: $i] :
% 16.10/2.90 ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] :
% 16.10/2.90 (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) & $i(v3))) & ?
% 16.10/2.90 [v2: $i] : (v2 = v1 | ~ $i(v2) | ? [v3: $i] : ? [v4: any] : ? [v5: $i]
% 16.10/2.90 : ? [v6: $i] : ? [v7: int] : (in(v3, v2) = v4 & $i(v5) & $i(v3) & ( ~
% 16.10/2.90 (v4 = 0) | ! [v8: $i] : ! [v9: $i] : ( ~ (ordered_pair(v3, v8) =
% 16.10/2.90 v9) | ~ $i(v8) | ? [v10: int] : ( ~ (v10 = 0) & in(v9, v0) =
% 16.10/2.90 v10))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6,
% 16.10/2.90 v0) = 0 & $i(v6)))))))
% 16.10/2.90
% 16.10/2.90 (dt_k8_relat_1)
% 16.10/2.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 16.10/2.90 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 16.10/2.90 (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 16.10/2.90
% 16.10/2.90 (fc5_funct_1)
% 16.10/2.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 16.10/2.90 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 16.10/2.90 [v5: any] : ? [v6: any] : (relation(v2) = v5 & relation(v1) = v3 &
% 16.10/2.90 function(v2) = v6 & function(v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 =
% 16.10/2.90 0 & v5 = 0))))
% 16.10/2.90
% 16.10/2.90 (l29_wellord1)
% 16.10/2.90 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 16.10/2.90 int] : ( ~ (v5 = 0) & relation_dom(v2) = v3 & relation_dom(v1) = v4 &
% 16.10/2.90 subset(v3, v4) = v5 & relation_rng_restriction(v0, v1) = v2 & relation(v1) =
% 16.10/2.90 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 16.10/2.90
% 16.10/2.90 (function-axioms)
% 16.10/2.91 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 16.10/2.91 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 16.10/2.91 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 16.10/2.91 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 16.10/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.10/2.91 (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3,
% 16.10/2.91 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 16.10/2.91 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & !
% 16.10/2.91 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.10/2.91 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 16.10/2.91 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.10/2.91 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 16.10/2.91 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 16.10/2.91 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 16.10/2.91 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 16.10/2.91 : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) =
% 16.10/2.91 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 16.10/2.91 $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & !
% 16.10/2.91 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 16.10/2.91 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0:
% 16.10/2.91 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 16.10/2.91 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool]
% 16.10/2.91 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) |
% 16.10/2.91 ~ (empty(v2) = v0))
% 16.10/2.91
% 16.10/2.91 Further assumptions not needed in the proof:
% 16.10/2.91 --------------------------------------------
% 16.10/2.91 antisymmetry_r2_hidden, cc1_funct_1, commutativity_k2_tarski, d5_tarski,
% 16.10/2.91 dt_k1_relat_1, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski,
% 16.10/2.91 dt_k4_tarski, dt_m1_subset_1, existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1,
% 16.10/2.91 rc1_funct_1, rc1_xboole_0, rc2_funct_1, rc2_xboole_0, rc3_funct_1,
% 16.10/2.91 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 16.10/2.91 t6_boole, t7_boole, t8_boole
% 16.10/2.91
% 16.10/2.91 Those formulas are unsatisfiable:
% 16.10/2.91 ---------------------------------
% 16.10/2.91
% 16.10/2.91 Begin of proof
% 16.10/2.91 |
% 16.10/2.91 | ALPHA: (cc2_funct_1) implies:
% 16.10/2.91 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 16.10/2.91 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 &
% 16.10/2.91 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 16.10/2.91 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ?
% 16.10/2.91 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 &
% 16.10/2.91 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 16.10/2.91 | ~ (v2 = 0) | v1 = 0)))
% 16.10/2.91 |
% 16.10/2.91 | ALPHA: (d12_relat_1) implies:
% 16.10/2.91 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.10/2.91 | ! [v5: $i] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~
% 16.10/2.91 | (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ $i(v4) | ~
% 16.10/2.91 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7:
% 16.10/2.91 | any] : ? [v8: any] : (( ~ (v6 = 0) & relation(v1) = v6) | (in(v5,
% 16.10/2.91 | v2) = v6 & in(v5, v1) = v8 & in(v4, v0) = v7 & ( ~ (v6 = 0) |
% 16.10/2.91 | (v8 = 0 & v7 = 0)))))
% 16.17/2.91 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.17/2.91 | ! [v5: $i] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~
% 16.17/2.91 | (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ $i(v4) | ~
% 16.17/2.91 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7:
% 16.17/2.91 | any] : ? [v8: any] : (( ~ (v6 = 0) & relation(v1) = v6) | (in(v5,
% 16.17/2.91 | v2) = v8 & in(v5, v1) = v7 & in(v4, v0) = v6 & ( ~ (v7 = 0) |
% 16.17/2.91 | ~ (v6 = 0) | v8 = 0))))
% 16.17/2.91 |
% 16.17/2.91 | ALPHA: (d3_tarski) implies:
% 16.17/2.92 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 16.17/2.92 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 16.17/2.92 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 16.17/2.92 |
% 16.17/2.92 | ALPHA: (d4_relat_1) implies:
% 16.17/2.92 | (6) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 16.17/2.92 | (relation_dom(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: int] : !
% 16.17/2.92 | [v4: $i] : ! [v5: $i] : (v3 = 0 | ~ (ordered_pair(v2, v4) = v5) |
% 16.17/2.92 | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ? [v6: int] : ( ~
% 16.17/2.92 | (v6 = 0) & in(v5, v0) = v6)) & ! [v2: $i] : ( ~ (in(v2, v1) =
% 16.17/2.92 | 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2,
% 16.17/2.92 | v3) = v4 & in(v4, v0) = 0 & $i(v4) & $i(v3))) & ? [v2: $i] :
% 16.17/2.92 | (v2 = v1 | ~ $i(v2) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] :
% 16.17/2.92 | ? [v6: $i] : ? [v7: int] : (in(v3, v2) = v4 & $i(v5) & $i(v3) &
% 16.17/2.92 | ( ~ (v4 = 0) | ! [v8: $i] : ! [v9: $i] : ( ~
% 16.17/2.92 | (ordered_pair(v3, v8) = v9) | ~ $i(v8) | ? [v10: int] : (
% 16.17/2.92 | ~ (v10 = 0) & in(v9, v0) = v10))) & (v4 = 0 | (v7 = 0 &
% 16.17/2.92 | ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6)))))))
% 16.17/2.92 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) = v1) |
% 16.17/2.92 | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 16.17/2.92 | int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ($i(v4) & ((v6 =
% 16.17/2.92 | 0 & ordered_pair(v2, v4) = v5 & in(v5, v0) = 0 & $i(v5)) | ( ~
% 16.17/2.92 | (v3 = 0) & relation(v0) = v3))))
% 16.17/2.92 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] :
% 16.17/2.92 | ! [v5: $i] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~
% 16.17/2.92 | (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~
% 16.17/2.92 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : (( ~ (v6 = 0) &
% 16.17/2.92 | relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = v6)))
% 16.17/2.92 |
% 16.17/2.92 | ALPHA: (function-axioms) implies:
% 16.17/2.92 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 16.17/2.92 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 16.17/2.92 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 16.17/2.92 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 16.17/2.92 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 16.17/2.92 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 16.17/2.92 | v0))
% 16.17/2.92 |
% 16.17/2.92 | DELTA: instantiating (l29_wellord1) with fresh symbols all_35_0, all_35_1,
% 16.17/2.92 | all_35_2, all_35_3, all_35_4, all_35_5 gives:
% 16.17/2.92 | (12) ~ (all_35_0 = 0) & relation_dom(all_35_3) = all_35_2 &
% 16.17/2.92 | relation_dom(all_35_4) = all_35_1 & subset(all_35_2, all_35_1) =
% 16.17/2.92 | all_35_0 & relation_rng_restriction(all_35_5, all_35_4) = all_35_3 &
% 16.17/2.92 | relation(all_35_4) = 0 & $i(all_35_1) & $i(all_35_2) & $i(all_35_3) &
% 16.17/2.92 | $i(all_35_4) & $i(all_35_5)
% 16.17/2.92 |
% 16.17/2.92 | ALPHA: (12) implies:
% 16.17/2.92 | (13) ~ (all_35_0 = 0)
% 16.17/2.92 | (14) $i(all_35_5)
% 16.17/2.92 | (15) $i(all_35_4)
% 16.17/2.92 | (16) $i(all_35_3)
% 16.17/2.92 | (17) $i(all_35_2)
% 16.17/2.92 | (18) $i(all_35_1)
% 16.17/2.92 | (19) relation(all_35_4) = 0
% 16.17/2.92 | (20) relation_rng_restriction(all_35_5, all_35_4) = all_35_3
% 16.17/2.92 | (21) subset(all_35_2, all_35_1) = all_35_0
% 16.17/2.92 | (22) relation_dom(all_35_4) = all_35_1
% 16.17/2.92 | (23) relation_dom(all_35_3) = all_35_2
% 16.17/2.92 |
% 16.17/2.93 | GROUND_INST: instantiating (1) with all_35_4, simplifying with (15), (19)
% 16.17/2.93 | gives:
% 16.17/2.93 | (24) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_35_4) =
% 16.17/2.93 | v2 & function(all_35_4) = v1 & empty(all_35_4) = v0 & ( ~ (v1 = 0) |
% 16.17/2.93 | ~ (v0 = 0) | v2 = 0))
% 16.17/2.93 |
% 16.17/2.93 | GROUND_INST: instantiating (6) with all_35_4, simplifying with (15), (19)
% 16.17/2.93 | gives:
% 16.17/2.93 | (25) ? [v0: $i] : (relation_dom(all_35_4) = v0 & $i(v0) & ! [v1: $i] : !
% 16.17/2.93 | [v2: int] : ! [v3: $i] : ! [v4: $i] : (v2 = 0 | ~
% 16.17/2.93 | (ordered_pair(v1, v3) = v4) | ~ (in(v1, v0) = v2) | ~ $i(v3) |
% 16.17/2.93 | ~ $i(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v4, all_35_4) = v5)) &
% 16.17/2.93 | ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ? [v2: $i] : ?
% 16.17/2.93 | [v3: $i] : (ordered_pair(v1, v2) = v3 & in(v3, all_35_4) = 0 &
% 16.17/2.93 | $i(v3) & $i(v2))) & ? [v1: $i] : (v1 = v0 | ~ $i(v1) | ? [v2:
% 16.17/2.93 | $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] :
% 16.17/2.93 | (in(v2, v1) = v3 & $i(v4) & $i(v2) & ( ~ (v3 = 0) | ! [v7: $i] :
% 16.17/2.93 | ! [v8: $i] : ( ~ (ordered_pair(v2, v7) = v8) | ~ $i(v7) | ?
% 16.17/2.93 | [v9: int] : ( ~ (v9 = 0) & in(v8, all_35_4) = v9))) & (v3 =
% 16.17/2.93 | 0 | (v6 = 0 & ordered_pair(v2, v4) = v5 & in(v5, all_35_4) = 0
% 16.17/2.93 | & $i(v5))))))
% 16.17/2.93 |
% 16.17/2.93 | GROUND_INST: instantiating (fc5_funct_1) with all_35_5, all_35_4, all_35_3,
% 16.17/2.93 | simplifying with (14), (15), (20) gives:
% 16.17/2.93 | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 16.17/2.93 | (relation(all_35_3) = v2 & relation(all_35_4) = v0 &
% 16.17/2.93 | function(all_35_3) = v3 & function(all_35_4) = v1 & ( ~ (v1 = 0) |
% 16.17/2.93 | ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 16.17/2.93 |
% 16.17/2.93 | GROUND_INST: instantiating (dt_k8_relat_1) with all_35_5, all_35_4, all_35_3,
% 16.17/2.93 | simplifying with (14), (15), (20) gives:
% 16.17/2.93 | (27) ? [v0: any] : ? [v1: any] : (relation(all_35_3) = v1 &
% 16.17/2.93 | relation(all_35_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 16.17/2.93 |
% 16.17/2.93 | GROUND_INST: instantiating (5) with all_35_2, all_35_1, all_35_0, simplifying
% 16.17/2.93 | with (17), (18), (21) gives:
% 16.17/2.93 | (28) all_35_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 16.17/2.93 | all_35_1) = v1 & in(v0, all_35_2) = 0 & $i(v0))
% 16.17/2.93 |
% 16.17/2.93 | DELTA: instantiating (27) with fresh symbols all_47_0, all_47_1 gives:
% 16.17/2.93 | (29) relation(all_35_3) = all_47_0 & relation(all_35_4) = all_47_1 & ( ~
% 16.17/2.93 | (all_47_1 = 0) | all_47_0 = 0)
% 16.17/2.93 |
% 16.17/2.93 | ALPHA: (29) implies:
% 16.17/2.93 | (30) relation(all_35_4) = all_47_1
% 16.17/2.93 | (31) relation(all_35_3) = all_47_0
% 16.17/2.93 | (32) ~ (all_47_1 = 0) | all_47_0 = 0
% 16.17/2.93 |
% 16.17/2.93 | DELTA: instantiating (24) with fresh symbols all_53_0, all_53_1, all_53_2
% 16.17/2.93 | gives:
% 16.17/2.93 | (33) one_to_one(all_35_4) = all_53_0 & function(all_35_4) = all_53_1 &
% 16.17/2.93 | empty(all_35_4) = all_53_2 & ( ~ (all_53_1 = 0) | ~ (all_53_2 = 0) |
% 16.17/2.93 | all_53_0 = 0)
% 16.17/2.93 |
% 16.17/2.93 | ALPHA: (33) implies:
% 16.17/2.93 | (34) one_to_one(all_35_4) = all_53_0
% 16.17/2.93 |
% 16.17/2.93 | DELTA: instantiating (26) with fresh symbols all_69_0, all_69_1, all_69_2,
% 16.17/2.93 | all_69_3 gives:
% 16.17/2.93 | (35) relation(all_35_3) = all_69_1 & relation(all_35_4) = all_69_3 &
% 16.17/2.93 | function(all_35_3) = all_69_0 & function(all_35_4) = all_69_2 & ( ~
% 16.17/2.93 | (all_69_2 = 0) | ~ (all_69_3 = 0) | (all_69_0 = 0 & all_69_1 = 0))
% 16.17/2.93 |
% 16.17/2.93 | ALPHA: (35) implies:
% 16.17/2.93 | (36) relation(all_35_4) = all_69_3
% 16.17/2.93 | (37) relation(all_35_3) = all_69_1
% 16.17/2.93 |
% 16.17/2.93 | DELTA: instantiating (25) with fresh symbol all_71_0 gives:
% 16.17/2.94 | (38) relation_dom(all_35_4) = all_71_0 & $i(all_71_0) & ! [v0: $i] : !
% 16.17/2.94 | [v1: int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~ (ordered_pair(v0,
% 16.17/2.94 | v2) = v3) | ~ (in(v0, all_71_0) = v1) | ~ $i(v2) | ~ $i(v0) |
% 16.17/2.94 | ? [v4: int] : ( ~ (v4 = 0) & in(v3, all_35_4) = v4)) & ! [v0: $i]
% 16.17/2.94 | : ( ~ (in(v0, all_71_0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 16.17/2.94 | (ordered_pair(v0, v1) = v2 & in(v2, all_35_4) = 0 & $i(v2) &
% 16.17/2.94 | $i(v1))) & ? [v0: any] : (v0 = all_71_0 | ~ $i(v0) | ? [v1: $i]
% 16.17/2.94 | : ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: int] : (in(v1,
% 16.17/2.94 | v0) = v2 & $i(v3) & $i(v1) & ( ~ (v2 = 0) | ! [v6: $i] : !
% 16.17/2.94 | [v7: $i] : ( ~ (ordered_pair(v1, v6) = v7) | ~ $i(v6) | ? [v8:
% 16.17/2.94 | int] : ( ~ (v8 = 0) & in(v7, all_35_4) = v8))) & (v2 = 0 |
% 16.17/2.94 | (v5 = 0 & ordered_pair(v1, v3) = v4 & in(v4, all_35_4) = 0 &
% 16.17/2.94 | $i(v4)))))
% 16.17/2.94 |
% 16.17/2.94 | ALPHA: (38) implies:
% 16.17/2.94 | (39) $i(all_71_0)
% 16.17/2.94 | (40) relation_dom(all_35_4) = all_71_0
% 16.17/2.94 |
% 16.17/2.94 | BETA: splitting (28) gives:
% 16.17/2.94 |
% 16.17/2.94 | Case 1:
% 16.17/2.94 | |
% 16.17/2.94 | | (41) all_35_0 = 0
% 16.17/2.94 | |
% 16.17/2.94 | | REDUCE: (13), (41) imply:
% 16.17/2.94 | | (42) $false
% 16.17/2.94 | |
% 16.17/2.94 | | CLOSE: (42) is inconsistent.
% 16.17/2.94 | |
% 16.17/2.94 | Case 2:
% 16.17/2.94 | |
% 16.17/2.94 | | (43) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_35_1) = v1 &
% 16.17/2.94 | | in(v0, all_35_2) = 0 & $i(v0))
% 16.17/2.94 | |
% 16.17/2.94 | | DELTA: instantiating (43) with fresh symbols all_91_0, all_91_1 gives:
% 16.17/2.94 | | (44) ~ (all_91_0 = 0) & in(all_91_1, all_35_1) = all_91_0 & in(all_91_1,
% 16.17/2.94 | | all_35_2) = 0 & $i(all_91_1)
% 16.17/2.94 | |
% 16.17/2.94 | | ALPHA: (44) implies:
% 16.17/2.94 | | (45) ~ (all_91_0 = 0)
% 16.17/2.94 | | (46) $i(all_91_1)
% 16.17/2.94 | | (47) in(all_91_1, all_35_2) = 0
% 16.17/2.94 | | (48) in(all_91_1, all_35_1) = all_91_0
% 16.17/2.94 | |
% 16.17/2.94 | | GROUND_INST: instantiating (9) with 0, all_69_3, all_35_4, simplifying with
% 16.17/2.94 | | (19), (36) gives:
% 16.17/2.94 | | (49) all_69_3 = 0
% 16.17/2.94 | |
% 16.17/2.94 | | GROUND_INST: instantiating (9) with all_47_1, all_69_3, all_35_4,
% 16.17/2.94 | | simplifying with (30), (36) gives:
% 16.17/2.94 | | (50) all_69_3 = all_47_1
% 16.17/2.94 | |
% 16.17/2.94 | | GROUND_INST: instantiating (9) with all_47_0, all_69_1, all_35_3,
% 16.17/2.94 | | simplifying with (31), (37) gives:
% 16.17/2.94 | | (51) all_69_1 = all_47_0
% 16.17/2.94 | |
% 16.17/2.94 | | GROUND_INST: instantiating (10) with all_35_1, all_71_0, all_35_4,
% 16.17/2.94 | | simplifying with (22), (40) gives:
% 16.17/2.94 | | (52) all_71_0 = all_35_1
% 16.17/2.94 | |
% 16.17/2.94 | | COMBINE_EQS: (49), (50) imply:
% 16.17/2.94 | | (53) all_47_1 = 0
% 16.17/2.94 | |
% 16.17/2.94 | | BETA: splitting (32) gives:
% 16.17/2.94 | |
% 16.17/2.94 | | Case 1:
% 16.17/2.94 | | |
% 16.17/2.94 | | | (54) ~ (all_47_1 = 0)
% 16.17/2.94 | | |
% 16.17/2.94 | | | REDUCE: (53), (54) imply:
% 16.17/2.94 | | | (55) $false
% 16.17/2.94 | | |
% 16.17/2.94 | | | CLOSE: (55) is inconsistent.
% 16.17/2.94 | | |
% 16.17/2.94 | | Case 2:
% 16.17/2.94 | | |
% 16.17/2.94 | | | (56) all_47_0 = 0
% 16.17/2.94 | | |
% 16.17/2.94 | | | REDUCE: (31), (56) imply:
% 16.17/2.94 | | | (57) relation(all_35_3) = 0
% 16.17/2.94 | | |
% 16.17/2.94 | | | GROUND_INST: instantiating (7) with all_35_3, all_35_2, all_91_1,
% 16.17/2.94 | | | simplifying with (16), (17), (23), (46), (47) gives:
% 16.17/2.94 | | | (58) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ($i(v1)
% 16.17/2.94 | | | & ((v3 = 0 & ordered_pair(all_91_1, v1) = v2 & in(v2, all_35_3)
% 16.17/2.94 | | | = 0 & $i(v2)) | ( ~ (v0 = 0) & relation(all_35_3) = v0)))
% 16.17/2.94 | | |
% 16.17/2.94 | | | GROUND_INST: instantiating (2) with all_35_4, all_53_0, simplifying with
% 16.17/2.94 | | | (15), (34) gives:
% 16.17/2.94 | | | (59) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_35_4) =
% 16.17/2.94 | | | v0 & function(all_35_4) = v2 & empty(all_35_4) = v1 & ( ~ (v2 =
% 16.17/2.94 | | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | all_53_0 = 0))
% 16.17/2.94 | | |
% 16.17/2.94 | | | DELTA: instantiating (59) with fresh symbols all_132_0, all_132_1,
% 16.17/2.94 | | | all_132_2 gives:
% 16.17/2.95 | | | (60) relation(all_35_4) = all_132_2 & function(all_35_4) = all_132_0 &
% 16.17/2.95 | | | empty(all_35_4) = all_132_1 & ( ~ (all_132_0 = 0) | ~ (all_132_1
% 16.17/2.95 | | | = 0) | ~ (all_132_2 = 0) | all_53_0 = 0)
% 16.17/2.95 | | |
% 16.17/2.95 | | | ALPHA: (60) implies:
% 16.17/2.95 | | | (61) relation(all_35_4) = all_132_2
% 16.17/2.95 | | |
% 16.17/2.95 | | | DELTA: instantiating (58) with fresh symbols all_134_0, all_134_1,
% 16.17/2.95 | | | all_134_2, all_134_3 gives:
% 16.17/2.95 | | | (62) $i(all_134_2) & ((all_134_0 = 0 & ordered_pair(all_91_1,
% 16.17/2.95 | | | all_134_2) = all_134_1 & in(all_134_1, all_35_3) = 0 &
% 16.17/2.95 | | | $i(all_134_1)) | ( ~ (all_134_3 = 0) & relation(all_35_3) =
% 16.17/2.95 | | | all_134_3))
% 16.17/2.95 | | |
% 16.17/2.95 | | | ALPHA: (62) implies:
% 16.17/2.95 | | | (63) $i(all_134_2)
% 16.17/2.95 | | | (64) (all_134_0 = 0 & ordered_pair(all_91_1, all_134_2) = all_134_1 &
% 16.17/2.95 | | | in(all_134_1, all_35_3) = 0 & $i(all_134_1)) | ( ~ (all_134_3 =
% 16.17/2.95 | | | 0) & relation(all_35_3) = all_134_3)
% 16.17/2.95 | | |
% 16.17/2.95 | | | BETA: splitting (64) gives:
% 16.17/2.95 | | |
% 16.17/2.95 | | | Case 1:
% 16.17/2.95 | | | |
% 16.17/2.95 | | | | (65) all_134_0 = 0 & ordered_pair(all_91_1, all_134_2) = all_134_1 &
% 16.17/2.95 | | | | in(all_134_1, all_35_3) = 0 & $i(all_134_1)
% 16.17/2.95 | | | |
% 16.17/2.95 | | | | ALPHA: (65) implies:
% 16.17/2.95 | | | | (66) in(all_134_1, all_35_3) = 0
% 16.17/2.95 | | | | (67) ordered_pair(all_91_1, all_134_2) = all_134_1
% 16.17/2.95 | | | |
% 16.17/2.95 | | | | GROUND_INST: instantiating (9) with 0, all_132_2, all_35_4, simplifying
% 16.17/2.95 | | | | with (19), (61) gives:
% 16.17/2.95 | | | | (68) all_132_2 = 0
% 16.17/2.95 | | | |
% 16.17/2.95 | | | | GROUND_INST: instantiating (8) with all_35_4, all_35_1, all_91_1,
% 16.17/2.95 | | | | all_91_0, all_134_2, all_134_1, simplifying with (15),
% 16.17/2.95 | | | | (18), (22), (46), (48), (63), (67) gives:
% 16.17/2.95 | | | | (69) all_91_0 = 0 | ? [v0: int] : (( ~ (v0 = 0) & relation(all_35_4)
% 16.17/2.95 | | | | = v0) | ( ~ (v0 = 0) & in(all_134_1, all_35_4) = v0))
% 16.17/2.95 | | | |
% 16.17/2.95 | | | | GROUND_INST: instantiating (4) with all_35_5, all_35_4, all_35_3,
% 16.17/2.95 | | | | all_91_1, all_134_2, all_134_1, simplifying with (14),
% 16.17/2.95 | | | | (15), (16), (20), (46), (57), (63), (67) gives:
% 16.17/2.95 | | | | (70) ? [v0: int] : ? [v1: any] : ? [v2: any] : (( ~ (v0 = 0) &
% 16.17/2.95 | | | | relation(all_35_4) = v0) | (in(all_134_1, all_35_3) = v2 &
% 16.17/2.95 | | | | in(all_134_1, all_35_4) = v1 & in(all_134_2, all_35_5) = v0
% 16.17/2.95 | | | | & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)))
% 16.17/2.95 | | | |
% 16.17/2.95 | | | | GROUND_INST: instantiating (3) with all_35_5, all_35_4, all_35_3,
% 16.17/2.95 | | | | all_91_1, all_134_2, all_134_1, simplifying with (14),
% 16.17/2.95 | | | | (15), (16), (20), (46), (57), (63), (67) gives:
% 16.17/2.95 | | | | (71) ? [v0: int] : ? [v1: any] : ? [v2: any] : (( ~ (v0 = 0) &
% 16.17/2.95 | | | | relation(all_35_4) = v0) | (in(all_134_1, all_35_3) = v0 &
% 16.17/2.95 | | | | in(all_134_1, all_35_4) = v2 & in(all_134_2, all_35_5) = v1
% 16.17/2.95 | | | | & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))))
% 16.17/2.95 | | | |
% 16.17/2.95 | | | | DELTA: instantiating (71) with fresh symbols all_179_0, all_179_1,
% 16.17/2.95 | | | | all_179_2 gives:
% 16.17/2.95 | | | | (72) ( ~ (all_179_2 = 0) & relation(all_35_4) = all_179_2) |
% 16.17/2.95 | | | | (in(all_134_1, all_35_3) = all_179_2 & in(all_134_1, all_35_4) =
% 16.17/2.95 | | | | all_179_0 & in(all_134_2, all_35_5) = all_179_1 & ( ~
% 16.17/2.95 | | | | (all_179_2 = 0) | (all_179_0 = 0 & all_179_1 = 0)))
% 16.17/2.95 | | | |
% 16.17/2.95 | | | | DELTA: instantiating (70) with fresh symbols all_180_0, all_180_1,
% 16.17/2.95 | | | | all_180_2 gives:
% 16.17/2.95 | | | | (73) ( ~ (all_180_2 = 0) & relation(all_35_4) = all_180_2) |
% 16.17/2.95 | | | | (in(all_134_1, all_35_3) = all_180_0 & in(all_134_1, all_35_4) =
% 16.17/2.95 | | | | all_180_1 & in(all_134_2, all_35_5) = all_180_2 & ( ~
% 16.17/2.95 | | | | (all_180_1 = 0) | ~ (all_180_2 = 0) | all_180_0 = 0))
% 16.17/2.95 | | | |
% 16.17/2.95 | | | | BETA: splitting (73) gives:
% 16.17/2.95 | | | |
% 16.17/2.95 | | | | Case 1:
% 16.17/2.95 | | | | |
% 16.17/2.96 | | | | | (74) ~ (all_180_2 = 0) & relation(all_35_4) = all_180_2
% 16.17/2.96 | | | | |
% 16.17/2.96 | | | | | ALPHA: (74) implies:
% 16.17/2.96 | | | | | (75) ~ (all_180_2 = 0)
% 16.17/2.96 | | | | | (76) relation(all_35_4) = all_180_2
% 16.17/2.96 | | | | |
% 16.17/2.96 | | | | | GROUND_INST: instantiating (9) with 0, all_180_2, all_35_4,
% 16.17/2.96 | | | | | simplifying with (19), (76) gives:
% 16.17/2.96 | | | | | (77) all_180_2 = 0
% 16.17/2.96 | | | | |
% 16.17/2.96 | | | | | REDUCE: (75), (77) imply:
% 16.17/2.96 | | | | | (78) $false
% 16.17/2.96 | | | | |
% 16.17/2.96 | | | | | CLOSE: (78) is inconsistent.
% 16.17/2.96 | | | | |
% 16.17/2.96 | | | | Case 2:
% 16.17/2.96 | | | | |
% 16.17/2.96 | | | | | (79) in(all_134_1, all_35_3) = all_180_0 & in(all_134_1, all_35_4)
% 16.17/2.96 | | | | | = all_180_1 & in(all_134_2, all_35_5) = all_180_2 & ( ~
% 16.17/2.96 | | | | | (all_180_1 = 0) | ~ (all_180_2 = 0) | all_180_0 = 0)
% 16.17/2.96 | | | | |
% 16.17/2.96 | | | | | ALPHA: (79) implies:
% 16.17/2.96 | | | | | (80) in(all_134_1, all_35_3) = all_180_0
% 16.17/2.96 | | | | |
% 16.17/2.96 | | | | | BETA: splitting (72) gives:
% 16.17/2.96 | | | | |
% 16.17/2.96 | | | | | Case 1:
% 16.17/2.96 | | | | | |
% 16.17/2.96 | | | | | | (81) ~ (all_179_2 = 0) & relation(all_35_4) = all_179_2
% 16.17/2.96 | | | | | |
% 16.17/2.96 | | | | | | ALPHA: (81) implies:
% 16.17/2.96 | | | | | | (82) ~ (all_179_2 = 0)
% 16.17/2.96 | | | | | | (83) relation(all_35_4) = all_179_2
% 16.17/2.96 | | | | | |
% 16.17/2.96 | | | | | | GROUND_INST: instantiating (9) with 0, all_179_2, all_35_4,
% 16.17/2.96 | | | | | | simplifying with (19), (83) gives:
% 16.17/2.96 | | | | | | (84) all_179_2 = 0
% 16.17/2.96 | | | | | |
% 16.17/2.96 | | | | | | REDUCE: (82), (84) imply:
% 16.17/2.96 | | | | | | (85) $false
% 16.17/2.96 | | | | | |
% 16.17/2.96 | | | | | | CLOSE: (85) is inconsistent.
% 16.17/2.96 | | | | | |
% 16.17/2.96 | | | | | Case 2:
% 16.17/2.96 | | | | | |
% 16.17/2.96 | | | | | | (86) in(all_134_1, all_35_3) = all_179_2 & in(all_134_1,
% 16.17/2.96 | | | | | | all_35_4) = all_179_0 & in(all_134_2, all_35_5) =
% 16.17/2.96 | | | | | | all_179_1 & ( ~ (all_179_2 = 0) | (all_179_0 = 0 & all_179_1
% 16.17/2.96 | | | | | | = 0))
% 16.17/2.96 | | | | | |
% 16.17/2.96 | | | | | | ALPHA: (86) implies:
% 16.17/2.96 | | | | | | (87) in(all_134_1, all_35_4) = all_179_0
% 16.17/2.96 | | | | | | (88) in(all_134_1, all_35_3) = all_179_2
% 16.17/2.96 | | | | | | (89) ~ (all_179_2 = 0) | (all_179_0 = 0 & all_179_1 = 0)
% 16.17/2.96 | | | | | |
% 16.17/2.96 | | | | | | BETA: splitting (69) gives:
% 16.17/2.96 | | | | | |
% 16.17/2.96 | | | | | | Case 1:
% 16.17/2.96 | | | | | | |
% 16.17/2.96 | | | | | | | (90) all_91_0 = 0
% 16.17/2.96 | | | | | | |
% 16.17/2.96 | | | | | | | REDUCE: (45), (90) imply:
% 16.17/2.96 | | | | | | | (91) $false
% 16.17/2.96 | | | | | | |
% 16.17/2.96 | | | | | | | CLOSE: (91) is inconsistent.
% 16.17/2.96 | | | | | | |
% 16.17/2.96 | | | | | | Case 2:
% 16.17/2.96 | | | | | | |
% 16.17/2.96 | | | | | | | (92) ? [v0: int] : (( ~ (v0 = 0) & relation(all_35_4) = v0) |
% 16.17/2.96 | | | | | | | ( ~ (v0 = 0) & in(all_134_1, all_35_4) = v0))
% 16.17/2.96 | | | | | | |
% 16.17/2.96 | | | | | | | DELTA: instantiating (92) with fresh symbol all_198_0 gives:
% 16.17/2.96 | | | | | | | (93) ( ~ (all_198_0 = 0) & relation(all_35_4) = all_198_0) | (
% 16.17/2.96 | | | | | | | ~ (all_198_0 = 0) & in(all_134_1, all_35_4) = all_198_0)
% 16.17/2.96 | | | | | | |
% 16.17/2.96 | | | | | | | BETA: splitting (93) gives:
% 16.17/2.96 | | | | | | |
% 16.17/2.96 | | | | | | | Case 1:
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | | (94) ~ (all_198_0 = 0) & relation(all_35_4) = all_198_0
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | | ALPHA: (94) implies:
% 16.17/2.96 | | | | | | | | (95) ~ (all_198_0 = 0)
% 16.17/2.96 | | | | | | | | (96) relation(all_35_4) = all_198_0
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_198_0, all_35_4,
% 16.17/2.96 | | | | | | | | simplifying with (19), (96) gives:
% 16.17/2.96 | | | | | | | | (97) all_198_0 = 0
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | | REDUCE: (95), (97) imply:
% 16.17/2.96 | | | | | | | | (98) $false
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | | CLOSE: (98) is inconsistent.
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | Case 2:
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | | (99) ~ (all_198_0 = 0) & in(all_134_1, all_35_4) = all_198_0
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | | ALPHA: (99) implies:
% 16.17/2.96 | | | | | | | | (100) ~ (all_198_0 = 0)
% 16.17/2.96 | | | | | | | | (101) in(all_134_1, all_35_4) = all_198_0
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | | GROUND_INST: instantiating (11) with all_179_0, all_198_0,
% 16.17/2.96 | | | | | | | | all_35_4, all_134_1, simplifying with (87), (101)
% 16.17/2.96 | | | | | | | | gives:
% 16.17/2.96 | | | | | | | | (102) all_198_0 = all_179_0
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | | GROUND_INST: instantiating (11) with 0, all_180_0, all_35_3,
% 16.17/2.96 | | | | | | | | all_134_1, simplifying with (66), (80) gives:
% 16.17/2.96 | | | | | | | | (103) all_180_0 = 0
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | | GROUND_INST: instantiating (11) with all_179_2, all_180_0,
% 16.17/2.96 | | | | | | | | all_35_3, all_134_1, simplifying with (80), (88)
% 16.17/2.96 | | | | | | | | gives:
% 16.17/2.96 | | | | | | | | (104) all_180_0 = all_179_2
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | | COMBINE_EQS: (103), (104) imply:
% 16.17/2.96 | | | | | | | | (105) all_179_2 = 0
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | | REDUCE: (100), (102) imply:
% 16.17/2.96 | | | | | | | | (106) ~ (all_179_0 = 0)
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | | BETA: splitting (89) gives:
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | | Case 1:
% 16.17/2.96 | | | | | | | | |
% 16.17/2.96 | | | | | | | | | (107) ~ (all_179_2 = 0)
% 16.17/2.96 | | | | | | | | |
% 16.17/2.96 | | | | | | | | | REDUCE: (105), (107) imply:
% 16.17/2.96 | | | | | | | | | (108) $false
% 16.17/2.96 | | | | | | | | |
% 16.17/2.96 | | | | | | | | | CLOSE: (108) is inconsistent.
% 16.17/2.96 | | | | | | | | |
% 16.17/2.96 | | | | | | | | Case 2:
% 16.17/2.96 | | | | | | | | |
% 16.17/2.96 | | | | | | | | | (109) all_179_0 = 0 & all_179_1 = 0
% 16.17/2.96 | | | | | | | | |
% 16.17/2.96 | | | | | | | | | ALPHA: (109) implies:
% 16.17/2.96 | | | | | | | | | (110) all_179_0 = 0
% 16.17/2.96 | | | | | | | | |
% 16.17/2.96 | | | | | | | | | REDUCE: (106), (110) imply:
% 16.17/2.96 | | | | | | | | | (111) $false
% 16.17/2.96 | | | | | | | | |
% 16.17/2.96 | | | | | | | | | CLOSE: (111) is inconsistent.
% 16.17/2.96 | | | | | | | | |
% 16.17/2.96 | | | | | | | | End of split
% 16.17/2.96 | | | | | | | |
% 16.17/2.96 | | | | | | | End of split
% 16.17/2.96 | | | | | | |
% 16.17/2.96 | | | | | | End of split
% 16.17/2.96 | | | | | |
% 16.17/2.96 | | | | | End of split
% 16.17/2.96 | | | | |
% 16.17/2.96 | | | | End of split
% 16.17/2.96 | | | |
% 16.17/2.96 | | | Case 2:
% 16.17/2.96 | | | |
% 16.17/2.96 | | | | (112) ~ (all_134_3 = 0) & relation(all_35_3) = all_134_3
% 16.17/2.96 | | | |
% 16.17/2.96 | | | | ALPHA: (112) implies:
% 16.17/2.96 | | | | (113) ~ (all_134_3 = 0)
% 16.17/2.96 | | | | (114) relation(all_35_3) = all_134_3
% 16.17/2.96 | | | |
% 16.17/2.96 | | | | GROUND_INST: instantiating (9) with 0, all_134_3, all_35_3, simplifying
% 16.17/2.96 | | | | with (57), (114) gives:
% 16.17/2.96 | | | | (115) all_134_3 = 0
% 16.17/2.96 | | | |
% 16.17/2.96 | | | | REDUCE: (113), (115) imply:
% 16.17/2.96 | | | | (116) $false
% 16.17/2.96 | | | |
% 16.17/2.96 | | | | CLOSE: (116) is inconsistent.
% 16.17/2.96 | | | |
% 16.17/2.96 | | | End of split
% 16.17/2.96 | | |
% 16.17/2.97 | | End of split
% 16.17/2.97 | |
% 16.17/2.97 | End of split
% 16.17/2.97 |
% 16.17/2.97 End of proof
% 16.17/2.97 % SZS output end Proof for theBenchmark
% 16.17/2.97
% 16.17/2.97 2352ms
%------------------------------------------------------------------------------