TSTP Solution File: SET812+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET812+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n005.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 15:26:32 EDT 2023
% Result : Theorem 12.77s 2.40s
% Output : Proof 16.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET812+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n005.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 : Sat Aug 26 11:14:53 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
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 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
% 3.08/1.09 Prover 4: Preprocessing ...
% 3.08/1.11 Prover 1: Preprocessing ...
% 3.08/1.13 Prover 6: Preprocessing ...
% 3.08/1.13 Prover 3: Preprocessing ...
% 3.08/1.13 Prover 0: Preprocessing ...
% 3.08/1.13 Prover 2: Preprocessing ...
% 3.08/1.13 Prover 5: Preprocessing ...
% 7.21/1.66 Prover 5: Proving ...
% 7.21/1.67 Prover 6: Proving ...
% 7.51/1.70 Prover 2: Proving ...
% 7.51/1.72 Prover 1: Constructing countermodel ...
% 7.93/1.74 Prover 3: Constructing countermodel ...
% 8.77/1.88 Prover 4: Constructing countermodel ...
% 8.77/1.93 Prover 0: Proving ...
% 9.43/1.99 Prover 3: gave up
% 9.43/1.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.03/2.07 Prover 7: Preprocessing ...
% 10.03/2.07 Prover 6: gave up
% 10.03/2.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.03/2.09 Prover 1: gave up
% 10.03/2.09 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 10.03/2.10 Prover 8: Preprocessing ...
% 10.64/2.12 Prover 9: Preprocessing ...
% 10.76/2.15 Prover 7: Warning: ignoring some quantifiers
% 10.76/2.17 Prover 7: Constructing countermodel ...
% 11.42/2.26 Prover 8: Warning: ignoring some quantifiers
% 11.42/2.27 Prover 8: Constructing countermodel ...
% 12.66/2.37 Prover 9: Constructing countermodel ...
% 12.77/2.40 Prover 0: proved (1775ms)
% 12.77/2.40
% 12.77/2.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.77/2.40
% 12.77/2.41 Prover 9: stopped
% 12.77/2.41 Prover 5: stopped
% 12.96/2.42 Prover 2: stopped
% 13.07/2.43 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.07/2.43 Prover 7: gave up
% 13.07/2.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.07/2.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.07/2.43 Prover 8: gave up
% 13.07/2.44 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 13.07/2.44 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 13.07/2.47 Prover 10: Preprocessing ...
% 13.07/2.48 Prover 16: Preprocessing ...
% 13.07/2.48 Prover 11: Preprocessing ...
% 13.07/2.49 Prover 13: Preprocessing ...
% 13.07/2.51 Prover 19: Preprocessing ...
% 13.74/2.53 Prover 10: Warning: ignoring some quantifiers
% 13.74/2.54 Prover 10: Constructing countermodel ...
% 13.74/2.56 Prover 13: Warning: ignoring some quantifiers
% 13.74/2.58 Prover 16: Warning: ignoring some quantifiers
% 14.30/2.60 Prover 16: Constructing countermodel ...
% 14.30/2.60 Prover 13: Constructing countermodel ...
% 14.30/2.60 Prover 10: gave up
% 14.30/2.67 Prover 19: Warning: ignoring some quantifiers
% 14.30/2.69 Prover 19: Constructing countermodel ...
% 15.48/2.76 Prover 4: Found proof (size 102)
% 15.48/2.76 Prover 4: proved (2131ms)
% 15.48/2.76 Prover 16: stopped
% 15.48/2.76 Prover 13: stopped
% 15.48/2.76 Prover 19: stopped
% 15.48/2.77 Prover 11: Constructing countermodel ...
% 15.48/2.78 Prover 11: stopped
% 15.63/2.78
% 15.63/2.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.63/2.78
% 15.63/2.80 % SZS output start Proof for theBenchmark
% 15.63/2.80 Assumptions after simplification:
% 15.63/2.80 ---------------------------------
% 15.63/2.80
% 15.63/2.80 (equal_set)
% 15.89/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 15.89/2.84 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 15.89/2.84 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 15.89/2.84 $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) | ~ $i(v1) |
% 15.89/2.84 ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 &
% 15.89/2.84 subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] :
% 15.89/2.84 ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 15.89/2.84 | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) =
% 15.89/2.84 v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 15.89/2.84 (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | (subset(v1, v0) = 0 &
% 15.89/2.84 subset(v0, v1) = 0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v1, v0) =
% 15.89/2.84 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0,
% 15.89/2.84 v1) = v3 & subset(v0, v1) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i]
% 15.89/2.84 : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 15.89/2.85 any] : ? [v3: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) = v2 & ( ~
% 15.89/2.85 (v2 = 0) | v3 = 0)))
% 15.89/2.85
% 15.89/2.85 (intersection)
% 15.89/2.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 15.89/2.85 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~
% 15.89/2.85 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 &
% 15.89/2.85 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 15.89/2.85 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~
% 15.89/2.85 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) =
% 15.89/2.85 0 & member(v0, v1) = 0))
% 15.89/2.85
% 15.89/2.85 (ordinal_number)
% 15.89/2.85 $i(member_predicate) & $i(on) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2
% 15.89/2.85 = 0 | ~ (subset(v1, v0) = v2) | ~ (member(v0, on) = 0) | ~ $i(v1) | ~
% 15.89/2.85 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & member(v1, v0) = v3)) & ! [v0: $i] :
% 15.89/2.85 ! [v1: int] : (v1 = 0 | ~ (member(v0, on) = v1) | ~ $i(v0) | ? [v2: any] :
% 15.89/2.85 ? [v3: any] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : ($i(v4) & ((v5 =
% 15.89/2.85 0 & ~ (v6 = 0) & subset(v4, v0) = v6 & member(v4, v0) = 0) |
% 15.89/2.85 (strict_well_order(member_predicate, v0) = v3 & set(v0) = v2 & ( ~ (v3 =
% 15.89/2.85 0) | ~ (v2 = 0)))))) & ! [v0: $i] : ! [v1: any] : ( ~
% 15.89/2.85 (strict_well_order(member_predicate, v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 15.89/2.85 ? [v3: any] : (set(v0) = v3 & member(v0, on) = v2 & ( ~ (v2 = 0) | (v3 = 0 &
% 15.89/2.85 v1 = 0 & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (subset(v4, v0) =
% 15.89/2.85 v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & member(v4, v0) =
% 15.89/2.85 v6)) & ! [v4: $i] : ( ~ (member(v4, v0) = 0) | ~ $i(v4) |
% 15.89/2.85 subset(v4, v0) = 0))))) & ! [v0: $i] : ! [v1: any] : ( ~ (set(v0)
% 15.89/2.85 = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 15.89/2.85 (strict_well_order(member_predicate, v0) = v3 & member(v0, on) = v2 & ( ~
% 15.89/2.85 (v2 = 0) | (v3 = 0 & v1 = 0 & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~
% 15.89/2.85 (subset(v4, v0) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) &
% 15.89/2.85 member(v4, v0) = v6)) & ! [v4: $i] : ( ~ (member(v4, v0) = 0) |
% 15.89/2.85 ~ $i(v4) | subset(v4, v0) = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 15.89/2.85 (member(v1, v0) = 0) | ~ (member(v0, on) = 0) | ~ $i(v1) | ~ $i(v0) |
% 15.89/2.85 subset(v1, v0) = 0) & ! [v0: $i] : ( ~ (strict_well_order(member_predicate,
% 15.89/2.85 v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: $i] : ?
% 15.89/2.85 [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & subset(v3, v0)
% 15.89/2.85 = v5 & member(v3, v0) = 0) | (set(v0) = v1 & member(v0, on) = v2 & ( ~
% 15.89/2.85 (v1 = 0) | v2 = 0))))) & ! [v0: $i] : ( ~ (set(v0) = 0) | ~ $i(v0)
% 15.89/2.85 | ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: int] : ? [v5: int] :
% 15.89/2.85 ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & subset(v3, v0) = v5 & member(v3, v0) = 0)
% 15.89/2.85 | (strict_well_order(member_predicate, v0) = v1 & member(v0, on) = v2 &
% 15.89/2.85 ( ~ (v1 = 0) | v2 = 0))))) & ! [v0: $i] : ( ~ (member(v0, on) = 0) |
% 15.89/2.85 ~ $i(v0) | (strict_well_order(member_predicate, v0) = 0 & set(v0) = 0))
% 15.89/2.85
% 15.89/2.85 (power_set)
% 15.89/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 15.89/2.86 (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 15.89/2.86 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i]
% 15.89/2.86 : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 15.89/2.86 ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0,
% 15.89/2.86 v3) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 15.89/2.86 (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) |
% 15.89/2.86 subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) |
% 15.89/2.86 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (power_set(v1) = v2 & member(v0, v2) =
% 15.89/2.86 0 & $i(v2)))
% 15.89/2.86
% 15.89/2.86 (subset)
% 15.89/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 15.89/2.86 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 15.89/2.86 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] :
% 15.89/2.86 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) |
% 15.89/2.86 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 &
% 15.89/2.86 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 15.89/2.86 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 15.89/2.86 ~ $i(v0) | member(v2, v1) = 0)
% 15.89/2.86
% 15.89/2.86 (thV10)
% 15.89/2.86 $i(on) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0)
% 15.89/2.86 & intersection(v0, v1) = v2 & power_set(v0) = v1 & equal_set(v0, v2) = v3 &
% 15.89/2.86 member(v0, on) = 0 & $i(v2) & $i(v1) & $i(v0))
% 15.89/2.86
% 15.89/2.86 (function-axioms)
% 15.89/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 15.89/2.86 | ~ (initial_segment(v4, v3, v2) = v1) | ~ (initial_segment(v4, v3, v2) =
% 15.89/2.86 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 15.89/2.86 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 15.89/2.86 ~ (apply(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.89/2.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 15.89/2.86 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0:
% 15.89/2.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.89/2.86 : (v1 = v0 | ~ (strict_order(v3, v2) = v1) | ~ (strict_order(v3, v2) = v0))
% 15.89/2.86 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 15.89/2.86 [v3: $i] : (v1 = v0 | ~ (strict_well_order(v3, v2) = v1) | ~
% 15.89/2.86 (strict_well_order(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 15.89/2.86 : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~
% 15.89/2.86 (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 15.89/2.86 ! [v3: $i] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2)
% 15.89/2.86 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 15.89/2.86 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 15.89/2.86 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1)
% 15.89/2.86 | ~ (intersection(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.89/2.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.89/2.86 (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0:
% 15.89/2.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.89/2.86 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 15.89/2.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.89/2.86 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0:
% 15.89/2.86 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (suc(v2) = v1) | ~ (suc(v2)
% 15.89/2.86 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 15.89/2.86 $i] : (v1 = v0 | ~ (set(v2) = v1) | ~ (set(v2) = v0)) & ! [v0: $i] : !
% 15.89/2.86 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 15.89/2.86 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 15.89/2.86 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 15.89/2.86 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 15.89/2.86 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 15.89/2.86 (power_set(v2) = v0))
% 15.89/2.86
% 15.89/2.86 Further assumptions not needed in the proof:
% 15.89/2.86 --------------------------------------------
% 15.89/2.86 difference, empty_set, initial_segment, least, product, rel_member, set_member,
% 15.89/2.86 singleton, strict_order, strict_well_order, successor, sum, union,
% 15.89/2.86 unordered_pair
% 15.89/2.86
% 15.89/2.86 Those formulas are unsatisfiable:
% 15.89/2.86 ---------------------------------
% 15.89/2.86
% 15.89/2.86 Begin of proof
% 15.89/2.86 |
% 15.89/2.86 | ALPHA: (subset) implies:
% 15.89/2.87 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 15.89/2.87 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 15.89/2.87 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 15.89/2.87 |
% 15.89/2.87 | ALPHA: (equal_set) implies:
% 15.89/2.87 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) |
% 15.89/2.87 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0,
% 15.89/2.87 | v1) = v3 & subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 =
% 15.89/2.87 | 0))))
% 15.89/2.87 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 15.89/2.87 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 15.89/2.87 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 15.89/2.87 | 0))))
% 15.89/2.87 |
% 15.89/2.87 | ALPHA: (power_set) implies:
% 15.89/2.87 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 15.89/2.87 | $i(v0) | ? [v2: $i] : (power_set(v1) = v2 & member(v0, v2) = 0 &
% 15.89/2.87 | $i(v2)))
% 15.89/2.87 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 15.89/2.87 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 15.89/2.87 | (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4 & $i(v3)))
% 15.89/2.87 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 15.89/2.87 | (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~
% 15.89/2.87 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 15.89/2.87 |
% 15.89/2.87 | ALPHA: (intersection) implies:
% 15.89/2.87 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 15.89/2.87 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) |
% 15.89/2.87 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 15.89/2.87 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 15.89/2.87 | (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) |
% 15.89/2.87 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 15.89/2.87 | (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 15.89/2.87 | 0))))
% 15.89/2.87 |
% 15.89/2.87 | ALPHA: (ordinal_number) implies:
% 15.89/2.87 | (9) ! [v0: $i] : ( ~ (member(v0, on) = 0) | ~ $i(v0) |
% 15.89/2.87 | (strict_well_order(member_predicate, v0) = 0 & set(v0) = 0))
% 15.89/2.87 | (10) ! [v0: $i] : ! [v1: any] : ( ~ (set(v0) = v1) | ~ $i(v0) | ? [v2:
% 15.89/2.87 | any] : ? [v3: any] : (strict_well_order(member_predicate, v0) =
% 15.89/2.87 | v3 & member(v0, on) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0 & !
% 15.89/2.87 | [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (subset(v4, v0) = v5) |
% 15.89/2.87 | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & member(v4, v0) =
% 15.89/2.87 | v6)) & ! [v4: $i] : ( ~ (member(v4, v0) = 0) | ~ $i(v4)
% 15.89/2.87 | | subset(v4, v0) = 0)))))
% 15.89/2.87 | (11) ! [v0: $i] : ! [v1: any] : ( ~ (strict_well_order(member_predicate,
% 15.89/2.87 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (set(v0) =
% 15.89/2.87 | v3 & member(v0, on) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0 & !
% 15.89/2.87 | [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (subset(v4, v0) = v5) |
% 15.89/2.87 | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & member(v4, v0) =
% 15.89/2.87 | v6)) & ! [v4: $i] : ( ~ (member(v4, v0) = 0) | ~ $i(v4)
% 15.89/2.87 | | subset(v4, v0) = 0)))))
% 15.89/2.87 |
% 15.89/2.87 | ALPHA: (thV10) implies:
% 15.89/2.87 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0)
% 15.89/2.87 | & intersection(v0, v1) = v2 & power_set(v0) = v1 & equal_set(v0, v2)
% 15.89/2.87 | = v3 & member(v0, on) = 0 & $i(v2) & $i(v1) & $i(v0))
% 15.89/2.87 |
% 15.89/2.87 | ALPHA: (function-axioms) implies:
% 15.89/2.87 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2)
% 15.89/2.87 | = v1) | ~ (power_set(v2) = v0))
% 15.89/2.88 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.89/2.88 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3,
% 15.89/2.88 | v2) = v0))
% 15.89/2.88 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.89/2.88 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3,
% 15.89/2.88 | v2) = v0))
% 15.89/2.88 |
% 15.89/2.88 | DELTA: instantiating (12) with fresh symbols all_23_0, all_23_1, all_23_2,
% 15.89/2.88 | all_23_3 gives:
% 15.89/2.88 | (16) ~ (all_23_0 = 0) & intersection(all_23_3, all_23_2) = all_23_1 &
% 15.89/2.88 | power_set(all_23_3) = all_23_2 & equal_set(all_23_3, all_23_1) =
% 15.89/2.88 | all_23_0 & member(all_23_3, on) = 0 & $i(all_23_1) & $i(all_23_2) &
% 15.89/2.88 | $i(all_23_3)
% 15.89/2.88 |
% 15.89/2.88 | ALPHA: (16) implies:
% 15.89/2.88 | (17) ~ (all_23_0 = 0)
% 15.89/2.88 | (18) $i(all_23_3)
% 15.89/2.88 | (19) $i(all_23_2)
% 15.89/2.88 | (20) $i(all_23_1)
% 15.89/2.88 | (21) member(all_23_3, on) = 0
% 15.89/2.88 | (22) equal_set(all_23_3, all_23_1) = all_23_0
% 15.89/2.88 | (23) power_set(all_23_3) = all_23_2
% 15.89/2.88 | (24) intersection(all_23_3, all_23_2) = all_23_1
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (9) with all_23_3, simplifying with (18), (21)
% 15.89/2.88 | gives:
% 15.89/2.88 | (25) strict_well_order(member_predicate, all_23_3) = 0 & set(all_23_3) = 0
% 15.89/2.88 |
% 15.89/2.88 | ALPHA: (25) implies:
% 15.89/2.88 | (26) set(all_23_3) = 0
% 15.89/2.88 | (27) strict_well_order(member_predicate, all_23_3) = 0
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (3) with all_23_3, all_23_1, all_23_0, simplifying
% 15.89/2.88 | with (18), (20), (22) gives:
% 15.89/2.88 | (28) all_23_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_23_1,
% 15.89/2.88 | all_23_3) = v1 & subset(all_23_3, all_23_1) = v0 & ( ~ (v1 = 0) |
% 15.89/2.88 | ~ (v0 = 0)))
% 15.89/2.88 |
% 15.89/2.88 | BETA: splitting (28) gives:
% 15.89/2.88 |
% 15.89/2.88 | Case 1:
% 15.89/2.88 | |
% 15.89/2.88 | | (29) all_23_0 = 0
% 15.89/2.88 | |
% 15.89/2.88 | | REDUCE: (17), (29) imply:
% 15.89/2.88 | | (30) $false
% 15.89/2.88 | |
% 15.89/2.88 | | CLOSE: (30) is inconsistent.
% 15.89/2.88 | |
% 15.89/2.88 | Case 2:
% 15.89/2.88 | |
% 15.89/2.88 | | (31) ? [v0: any] : ? [v1: any] : (subset(all_23_1, all_23_3) = v1 &
% 15.89/2.88 | | subset(all_23_3, all_23_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 15.89/2.88 | |
% 15.89/2.88 | | DELTA: instantiating (31) with fresh symbols all_35_0, all_35_1 gives:
% 15.89/2.88 | | (32) subset(all_23_1, all_23_3) = all_35_0 & subset(all_23_3, all_23_1) =
% 15.89/2.88 | | all_35_1 & ( ~ (all_35_0 = 0) | ~ (all_35_1 = 0))
% 15.89/2.88 | |
% 15.89/2.88 | | ALPHA: (32) implies:
% 15.89/2.88 | | (33) subset(all_23_3, all_23_1) = all_35_1
% 15.89/2.88 | | (34) subset(all_23_1, all_23_3) = all_35_0
% 15.89/2.88 | | (35) ~ (all_35_0 = 0) | ~ (all_35_1 = 0)
% 15.89/2.88 | |
% 15.89/2.88 | | GROUND_INST: instantiating (5) with all_23_3, all_23_1, all_35_1,
% 15.89/2.88 | | simplifying with (18), (20), (33) gives:
% 15.89/2.88 | | (36) all_35_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 15.89/2.88 | | power_set(all_23_1) = v0 & member(all_23_3, v0) = v1 & $i(v0))
% 15.89/2.88 | |
% 15.89/2.88 | | GROUND_INST: instantiating (1) with all_23_3, all_23_1, all_35_1,
% 15.89/2.88 | | simplifying with (18), (20), (33) gives:
% 15.89/2.88 | | (37) all_35_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 15.89/2.88 | | member(v0, all_23_1) = v1 & member(v0, all_23_3) = 0 & $i(v0))
% 15.89/2.88 | |
% 15.89/2.88 | | GROUND_INST: instantiating (2) with all_23_1, all_23_3, all_35_1,
% 15.89/2.89 | | simplifying with (18), (20), (33) gives:
% 15.89/2.89 | | (38) ? [v0: any] : ? [v1: any] : (equal_set(all_23_1, all_23_3) = v0 &
% 15.89/2.89 | | subset(all_23_1, all_23_3) = v1 & ( ~ (v0 = 0) | (v1 = 0 &
% 15.89/2.89 | | all_35_1 = 0)))
% 15.89/2.89 | |
% 15.89/2.89 | | GROUND_INST: instantiating (5) with all_23_1, all_23_3, all_35_0,
% 15.89/2.89 | | simplifying with (18), (20), (34) gives:
% 15.89/2.89 | | (39) all_35_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 15.89/2.89 | | power_set(all_23_3) = v0 & member(all_23_1, v0) = v1 & $i(v0))
% 15.89/2.89 | |
% 15.89/2.89 | | GROUND_INST: instantiating (1) with all_23_1, all_23_3, all_35_0,
% 15.89/2.89 | | simplifying with (18), (20), (34) gives:
% 15.89/2.89 | | (40) all_35_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 15.89/2.89 | | member(v0, all_23_1) = 0 & member(v0, all_23_3) = v1 & $i(v0))
% 15.89/2.89 | |
% 15.89/2.89 | | GROUND_INST: instantiating (10) with all_23_3, 0, simplifying with (18),
% 15.89/2.89 | | (26) gives:
% 15.89/2.89 | | (41) ? [v0: any] : ? [v1: any] : (strict_well_order(member_predicate,
% 15.89/2.89 | | all_23_3) = v1 & member(all_23_3, on) = v0 & ( ~ (v0 = 0) | (v1
% 15.89/2.89 | | = 0 & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (subset(v2,
% 15.89/2.89 | | all_23_3) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 =
% 15.89/2.89 | | 0) & member(v2, all_23_3) = v4)) & ! [v2: $i] : ( ~
% 15.89/2.89 | | (member(v2, all_23_3) = 0) | ~ $i(v2) | subset(v2,
% 15.89/2.89 | | all_23_3) = 0))))
% 15.89/2.89 | |
% 15.89/2.89 | | GROUND_INST: instantiating (11) with all_23_3, 0, simplifying with (18),
% 15.89/2.89 | | (27) gives:
% 15.89/2.89 | | (42) ? [v0: any] : ? [v1: any] : (set(all_23_3) = v1 & member(all_23_3,
% 15.89/2.89 | | on) = v0 & ( ~ (v0 = 0) | (v1 = 0 & ! [v2: $i] : ! [v3: int] :
% 15.89/2.89 | | (v3 = 0 | ~ (subset(v2, all_23_3) = v3) | ~ $i(v2) | ? [v4:
% 15.89/2.89 | | int] : ( ~ (v4 = 0) & member(v2, all_23_3) = v4)) & !
% 15.89/2.89 | | [v2: $i] : ( ~ (member(v2, all_23_3) = 0) | ~ $i(v2) |
% 15.89/2.89 | | subset(v2, all_23_3) = 0))))
% 15.89/2.89 | |
% 15.89/2.89 | | DELTA: instantiating (38) with fresh symbols all_45_0, all_45_1 gives:
% 15.89/2.89 | | (43) equal_set(all_23_1, all_23_3) = all_45_1 & subset(all_23_1,
% 15.89/2.89 | | all_23_3) = all_45_0 & ( ~ (all_45_1 = 0) | (all_45_0 = 0 &
% 15.89/2.89 | | all_35_1 = 0))
% 15.89/2.89 | |
% 15.89/2.89 | | ALPHA: (43) implies:
% 15.89/2.89 | | (44) subset(all_23_1, all_23_3) = all_45_0
% 15.89/2.89 | |
% 15.89/2.89 | | DELTA: instantiating (41) with fresh symbols all_51_0, all_51_1 gives:
% 15.89/2.89 | | (45) strict_well_order(member_predicate, all_23_3) = all_51_0 &
% 15.89/2.89 | | member(all_23_3, on) = all_51_1 & ( ~ (all_51_1 = 0) | (all_51_0 = 0
% 15.89/2.89 | | & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0,
% 15.89/2.89 | | all_23_3) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0)
% 15.89/2.89 | | & member(v0, all_23_3) = v2)) & ! [v0: $i] : ( ~
% 15.89/2.89 | | (member(v0, all_23_3) = 0) | ~ $i(v0) | subset(v0, all_23_3)
% 15.89/2.89 | | = 0)))
% 15.89/2.89 | |
% 15.89/2.89 | | ALPHA: (45) implies:
% 15.89/2.89 | | (46) member(all_23_3, on) = all_51_1
% 15.89/2.89 | | (47) ~ (all_51_1 = 0) | (all_51_0 = 0 & ! [v0: $i] : ! [v1: int] : (v1
% 15.89/2.89 | | = 0 | ~ (subset(v0, all_23_3) = v1) | ~ $i(v0) | ? [v2: int]
% 15.89/2.89 | | : ( ~ (v2 = 0) & member(v0, all_23_3) = v2)) & ! [v0: $i] : ( ~
% 15.89/2.89 | | (member(v0, all_23_3) = 0) | ~ $i(v0) | subset(v0, all_23_3) =
% 15.89/2.89 | | 0))
% 15.89/2.89 | |
% 15.89/2.89 | | DELTA: instantiating (42) with fresh symbols all_53_0, all_53_1 gives:
% 15.89/2.89 | | (48) set(all_23_3) = all_53_0 & member(all_23_3, on) = all_53_1 & ( ~
% 15.89/2.89 | | (all_53_1 = 0) | (all_53_0 = 0 & ! [v0: $i] : ! [v1: int] : (v1
% 15.89/2.89 | | = 0 | ~ (subset(v0, all_23_3) = v1) | ~ $i(v0) | ? [v2:
% 15.89/2.89 | | int] : ( ~ (v2 = 0) & member(v0, all_23_3) = v2)) & ! [v0:
% 15.89/2.89 | | $i] : ( ~ (member(v0, all_23_3) = 0) | ~ $i(v0) | subset(v0,
% 15.89/2.89 | | all_23_3) = 0)))
% 15.89/2.89 | |
% 15.89/2.89 | | ALPHA: (48) implies:
% 15.89/2.89 | | (49) member(all_23_3, on) = all_53_1
% 15.89/2.89 | |
% 15.89/2.89 | | GROUND_INST: instantiating (14) with 0, all_53_1, on, all_23_3, simplifying
% 15.89/2.89 | | with (21), (49) gives:
% 15.89/2.89 | | (50) all_53_1 = 0
% 15.89/2.89 | |
% 15.89/2.89 | | GROUND_INST: instantiating (14) with all_51_1, all_53_1, on, all_23_3,
% 15.89/2.89 | | simplifying with (46), (49) gives:
% 15.89/2.89 | | (51) all_53_1 = all_51_1
% 15.89/2.89 | |
% 15.89/2.89 | | GROUND_INST: instantiating (15) with all_35_0, all_45_0, all_23_3, all_23_1,
% 15.89/2.89 | | simplifying with (34), (44) gives:
% 15.89/2.89 | | (52) all_45_0 = all_35_0
% 15.89/2.89 | |
% 15.89/2.89 | | COMBINE_EQS: (50), (51) imply:
% 15.89/2.89 | | (53) all_51_1 = 0
% 15.89/2.90 | |
% 15.89/2.90 | | BETA: splitting (47) gives:
% 15.89/2.90 | |
% 15.89/2.90 | | Case 1:
% 15.89/2.90 | | |
% 15.89/2.90 | | | (54) ~ (all_51_1 = 0)
% 15.89/2.90 | | |
% 15.89/2.90 | | | REDUCE: (53), (54) imply:
% 15.89/2.90 | | | (55) $false
% 15.89/2.90 | | |
% 15.89/2.90 | | | CLOSE: (55) is inconsistent.
% 15.89/2.90 | | |
% 15.89/2.90 | | Case 2:
% 15.89/2.90 | | |
% 15.89/2.90 | | | (56) all_51_0 = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 15.89/2.90 | | | (subset(v0, all_23_3) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2
% 15.89/2.90 | | | = 0) & member(v0, all_23_3) = v2)) & ! [v0: $i] : ( ~
% 15.89/2.90 | | | (member(v0, all_23_3) = 0) | ~ $i(v0) | subset(v0, all_23_3) =
% 15.89/2.90 | | | 0)
% 15.89/2.90 | | |
% 15.89/2.90 | | | ALPHA: (56) implies:
% 15.89/2.90 | | | (57) ! [v0: $i] : ( ~ (member(v0, all_23_3) = 0) | ~ $i(v0) |
% 15.89/2.90 | | | subset(v0, all_23_3) = 0)
% 15.89/2.90 | | | (58) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, all_23_3) =
% 15.89/2.90 | | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0,
% 15.89/2.90 | | | all_23_3) = v2))
% 15.89/2.90 | | |
% 15.89/2.90 | | | GROUND_INST: instantiating (58) with all_23_1, all_35_0, simplifying with
% 15.89/2.90 | | | (20), (34) gives:
% 15.89/2.90 | | | (59) all_35_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_23_1,
% 15.89/2.90 | | | all_23_3) = v0)
% 15.89/2.90 | | |
% 15.89/2.90 | | | BETA: splitting (35) gives:
% 15.89/2.90 | | |
% 15.89/2.90 | | | Case 1:
% 15.89/2.90 | | | |
% 15.89/2.90 | | | | (60) ~ (all_35_0 = 0)
% 15.89/2.90 | | | |
% 15.89/2.90 | | | | BETA: splitting (40) gives:
% 15.89/2.90 | | | |
% 15.89/2.90 | | | | Case 1:
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | | (61) all_35_0 = 0
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | | REDUCE: (60), (61) imply:
% 15.89/2.90 | | | | | (62) $false
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | | CLOSE: (62) is inconsistent.
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | Case 2:
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | | (63) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 15.89/2.90 | | | | | all_23_1) = 0 & member(v0, all_23_3) = v1 & $i(v0))
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | | DELTA: instantiating (63) with fresh symbols all_97_0, all_97_1 gives:
% 15.89/2.90 | | | | | (64) ~ (all_97_0 = 0) & member(all_97_1, all_23_1) = 0 &
% 15.89/2.90 | | | | | member(all_97_1, all_23_3) = all_97_0 & $i(all_97_1)
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | | ALPHA: (64) implies:
% 15.89/2.90 | | | | | (65) ~ (all_97_0 = 0)
% 15.89/2.90 | | | | | (66) $i(all_97_1)
% 15.89/2.90 | | | | | (67) member(all_97_1, all_23_3) = all_97_0
% 15.89/2.90 | | | | | (68) member(all_97_1, all_23_1) = 0
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | | BETA: splitting (39) gives:
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | | Case 1:
% 15.89/2.90 | | | | | |
% 15.89/2.90 | | | | | | (69) all_35_0 = 0
% 15.89/2.90 | | | | | |
% 15.89/2.90 | | | | | | REDUCE: (60), (69) imply:
% 15.89/2.90 | | | | | | (70) $false
% 15.89/2.90 | | | | | |
% 15.89/2.90 | | | | | | CLOSE: (70) is inconsistent.
% 15.89/2.90 | | | | | |
% 15.89/2.90 | | | | | Case 2:
% 15.89/2.90 | | | | | |
% 15.89/2.90 | | | | | | (71) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 15.89/2.90 | | | | | | power_set(all_23_3) = v0 & member(all_23_1, v0) = v1 &
% 15.89/2.90 | | | | | | $i(v0))
% 15.89/2.90 | | | | | |
% 15.89/2.90 | | | | | | DELTA: instantiating (71) with fresh symbols all_103_0, all_103_1
% 15.89/2.90 | | | | | | gives:
% 15.89/2.90 | | | | | | (72) ~ (all_103_0 = 0) & power_set(all_23_3) = all_103_1 &
% 15.89/2.90 | | | | | | member(all_23_1, all_103_1) = all_103_0 & $i(all_103_1)
% 15.89/2.90 | | | | | |
% 15.89/2.90 | | | | | | ALPHA: (72) implies:
% 15.89/2.90 | | | | | | (73) $i(all_103_1)
% 15.89/2.90 | | | | | | (74) power_set(all_23_3) = all_103_1
% 15.89/2.90 | | | | | |
% 15.89/2.90 | | | | | | BETA: splitting (59) gives:
% 15.89/2.90 | | | | | |
% 15.89/2.90 | | | | | | Case 1:
% 15.89/2.90 | | | | | | |
% 15.89/2.90 | | | | | | | (75) all_35_0 = 0
% 15.89/2.90 | | | | | | |
% 15.89/2.90 | | | | | | | REDUCE: (60), (75) imply:
% 15.89/2.90 | | | | | | | (76) $false
% 15.89/2.90 | | | | | | |
% 15.89/2.90 | | | | | | | CLOSE: (76) is inconsistent.
% 15.89/2.90 | | | | | | |
% 15.89/2.90 | | | | | | Case 2:
% 15.89/2.90 | | | | | | |
% 15.89/2.90 | | | | | | |
% 15.89/2.90 | | | | | | | GROUND_INST: instantiating (13) with all_23_2, all_103_1,
% 15.89/2.90 | | | | | | | all_23_3, simplifying with (23), (74) gives:
% 15.89/2.90 | | | | | | | (77) all_103_1 = all_23_2
% 15.89/2.90 | | | | | | |
% 15.89/2.90 | | | | | | | GROUND_INST: instantiating (7) with all_97_1, all_23_3, all_23_2,
% 15.89/2.90 | | | | | | | all_23_1, simplifying with (18), (19), (24), (66),
% 15.89/2.90 | | | | | | | (68) gives:
% 15.89/2.90 | | | | | | | (78) member(all_97_1, all_23_2) = 0 & member(all_97_1,
% 15.89/2.90 | | | | | | | all_23_3) = 0
% 15.89/2.90 | | | | | | |
% 15.89/2.90 | | | | | | | ALPHA: (78) implies:
% 15.89/2.90 | | | | | | | (79) member(all_97_1, all_23_3) = 0
% 15.89/2.90 | | | | | | |
% 15.89/2.90 | | | | | | | GROUND_INST: instantiating (14) with all_97_0, 0, all_23_3,
% 15.89/2.90 | | | | | | | all_97_1, simplifying with (67), (79) gives:
% 15.89/2.90 | | | | | | | (80) all_97_0 = 0
% 15.89/2.90 | | | | | | |
% 15.89/2.90 | | | | | | | REDUCE: (65), (80) imply:
% 15.89/2.90 | | | | | | | (81) $false
% 15.89/2.90 | | | | | | |
% 15.89/2.90 | | | | | | | CLOSE: (81) is inconsistent.
% 15.89/2.90 | | | | | | |
% 15.89/2.90 | | | | | | End of split
% 15.89/2.90 | | | | | |
% 15.89/2.90 | | | | | End of split
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | End of split
% 15.89/2.90 | | | |
% 15.89/2.90 | | | Case 2:
% 15.89/2.90 | | | |
% 15.89/2.90 | | | | (82) all_35_0 = 0
% 15.89/2.90 | | | | (83) ~ (all_35_1 = 0)
% 15.89/2.90 | | | |
% 15.89/2.90 | | | | REDUCE: (34), (82) imply:
% 15.89/2.90 | | | | (84) subset(all_23_1, all_23_3) = 0
% 15.89/2.90 | | | |
% 15.89/2.90 | | | | BETA: splitting (37) gives:
% 15.89/2.90 | | | |
% 15.89/2.90 | | | | Case 1:
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | | (85) all_35_1 = 0
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | | REDUCE: (83), (85) imply:
% 15.89/2.90 | | | | | (86) $false
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | | CLOSE: (86) is inconsistent.
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | Case 2:
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | | (87) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 15.89/2.90 | | | | | all_23_1) = v1 & member(v0, all_23_3) = 0 & $i(v0))
% 15.89/2.90 | | | | |
% 15.89/2.90 | | | | | DELTA: instantiating (87) with fresh symbols all_97_0, all_97_1 gives:
% 15.89/2.91 | | | | | (88) ~ (all_97_0 = 0) & member(all_97_1, all_23_1) = all_97_0 &
% 15.89/2.91 | | | | | member(all_97_1, all_23_3) = 0 & $i(all_97_1)
% 15.89/2.91 | | | | |
% 15.89/2.91 | | | | | ALPHA: (88) implies:
% 15.89/2.91 | | | | | (89) ~ (all_97_0 = 0)
% 15.89/2.91 | | | | | (90) $i(all_97_1)
% 15.89/2.91 | | | | | (91) member(all_97_1, all_23_3) = 0
% 15.89/2.91 | | | | | (92) member(all_97_1, all_23_1) = all_97_0
% 15.89/2.91 | | | | |
% 15.89/2.91 | | | | | BETA: splitting (36) gives:
% 15.89/2.91 | | | | |
% 15.89/2.91 | | | | | Case 1:
% 15.89/2.91 | | | | | |
% 15.89/2.91 | | | | | | (93) all_35_1 = 0
% 15.89/2.91 | | | | | |
% 15.89/2.91 | | | | | | REDUCE: (83), (93) imply:
% 15.89/2.91 | | | | | | (94) $false
% 15.89/2.91 | | | | | |
% 15.89/2.91 | | | | | | CLOSE: (94) is inconsistent.
% 15.89/2.91 | | | | | |
% 15.89/2.91 | | | | | Case 2:
% 15.89/2.91 | | | | | |
% 15.89/2.91 | | | | | |
% 15.89/2.91 | | | | | | GROUND_INST: instantiating (57) with all_97_1, simplifying with
% 15.89/2.91 | | | | | | (90), (91) gives:
% 15.89/2.91 | | | | | | (95) subset(all_97_1, all_23_3) = 0
% 15.89/2.91 | | | | | |
% 15.89/2.91 | | | | | | GROUND_INST: instantiating (8) with all_97_1, all_23_3, all_23_2,
% 15.89/2.91 | | | | | | all_23_1, all_97_0, simplifying with (18), (19), (24),
% 15.89/2.91 | | | | | | (90), (92) gives:
% 15.89/2.91 | | | | | | (96) all_97_0 = 0 | ? [v0: any] : ? [v1: any] :
% 15.89/2.91 | | | | | | (member(all_97_1, all_23_2) = v1 & member(all_97_1,
% 15.89/2.91 | | | | | | all_23_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 15.89/2.91 | | | | | |
% 15.89/2.91 | | | | | | GROUND_INST: instantiating (4) with all_23_1, all_23_3, simplifying
% 15.89/2.91 | | | | | | with (18), (20), (84) gives:
% 15.89/2.91 | | | | | | (97) ? [v0: $i] : (power_set(all_23_3) = v0 & member(all_23_1,
% 15.89/2.91 | | | | | | v0) = 0 & $i(v0))
% 15.89/2.91 | | | | | |
% 15.89/2.91 | | | | | | DELTA: instantiating (97) with fresh symbol all_110_0 gives:
% 15.89/2.91 | | | | | | (98) power_set(all_23_3) = all_110_0 & member(all_23_1,
% 15.89/2.91 | | | | | | all_110_0) = 0 & $i(all_110_0)
% 15.89/2.91 | | | | | |
% 15.89/2.91 | | | | | | ALPHA: (98) implies:
% 15.89/2.91 | | | | | | (99) power_set(all_23_3) = all_110_0
% 15.89/2.91 | | | | | |
% 15.89/2.91 | | | | | | BETA: splitting (96) gives:
% 15.89/2.91 | | | | | |
% 15.89/2.91 | | | | | | Case 1:
% 15.89/2.91 | | | | | | |
% 15.89/2.91 | | | | | | | (100) all_97_0 = 0
% 15.89/2.91 | | | | | | |
% 15.89/2.91 | | | | | | | REDUCE: (89), (100) imply:
% 15.89/2.91 | | | | | | | (101) $false
% 15.89/2.91 | | | | | | |
% 15.89/2.91 | | | | | | | CLOSE: (101) is inconsistent.
% 15.89/2.91 | | | | | | |
% 15.89/2.91 | | | | | | Case 2:
% 15.89/2.91 | | | | | | |
% 15.89/2.91 | | | | | | | (102) ? [v0: any] : ? [v1: any] : (member(all_97_1, all_23_2)
% 15.89/2.91 | | | | | | | = v1 & member(all_97_1, all_23_3) = v0 & ( ~ (v1 = 0) |
% 15.89/2.91 | | | | | | | ~ (v0 = 0)))
% 15.89/2.91 | | | | | | |
% 15.89/2.91 | | | | | | | DELTA: instantiating (102) with fresh symbols all_132_0, all_132_1
% 15.89/2.91 | | | | | | | gives:
% 15.89/2.91 | | | | | | | (103) member(all_97_1, all_23_2) = all_132_0 & member(all_97_1,
% 15.89/2.91 | | | | | | | all_23_3) = all_132_1 & ( ~ (all_132_0 = 0) | ~
% 15.89/2.91 | | | | | | | (all_132_1 = 0))
% 15.89/2.91 | | | | | | |
% 15.89/2.91 | | | | | | | ALPHA: (103) implies:
% 16.25/2.91 | | | | | | | (104) member(all_97_1, all_23_3) = all_132_1
% 16.25/2.91 | | | | | | | (105) member(all_97_1, all_23_2) = all_132_0
% 16.25/2.91 | | | | | | | (106) ~ (all_132_0 = 0) | ~ (all_132_1 = 0)
% 16.25/2.91 | | | | | | |
% 16.25/2.91 | | | | | | | GROUND_INST: instantiating (14) with 0, all_132_1, all_23_3,
% 16.25/2.91 | | | | | | | all_97_1, simplifying with (91), (104) gives:
% 16.25/2.91 | | | | | | | (107) all_132_1 = 0
% 16.25/2.91 | | | | | | |
% 16.25/2.91 | | | | | | | GROUND_INST: instantiating (13) with all_23_2, all_110_0,
% 16.25/2.91 | | | | | | | all_23_3, simplifying with (23), (99) gives:
% 16.25/2.91 | | | | | | | (108) all_110_0 = all_23_2
% 16.25/2.91 | | | | | | |
% 16.25/2.91 | | | | | | | BETA: splitting (106) gives:
% 16.25/2.91 | | | | | | |
% 16.25/2.91 | | | | | | | Case 1:
% 16.25/2.91 | | | | | | | |
% 16.25/2.91 | | | | | | | | (109) ~ (all_132_0 = 0)
% 16.25/2.91 | | | | | | | |
% 16.25/2.91 | | | | | | | | GROUND_INST: instantiating (6) with all_97_1, all_23_3,
% 16.25/2.91 | | | | | | | | all_23_2, all_132_0, simplifying with (18), (23),
% 16.25/2.91 | | | | | | | | (90), (105) gives:
% 16.25/2.91 | | | | | | | | (110) all_132_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 16.25/2.91 | | | | | | | | subset(all_97_1, all_23_3) = v0)
% 16.25/2.91 | | | | | | | |
% 16.25/2.91 | | | | | | | | BETA: splitting (110) gives:
% 16.25/2.91 | | | | | | | |
% 16.25/2.91 | | | | | | | | Case 1:
% 16.25/2.91 | | | | | | | | |
% 16.25/2.91 | | | | | | | | | (111) all_132_0 = 0
% 16.25/2.91 | | | | | | | | |
% 16.25/2.91 | | | | | | | | | REDUCE: (109), (111) imply:
% 16.25/2.91 | | | | | | | | | (112) $false
% 16.25/2.91 | | | | | | | | |
% 16.25/2.91 | | | | | | | | | CLOSE: (112) is inconsistent.
% 16.25/2.91 | | | | | | | | |
% 16.25/2.91 | | | | | | | | Case 2:
% 16.25/2.91 | | | | | | | | |
% 16.25/2.91 | | | | | | | | | (113) ? [v0: int] : ( ~ (v0 = 0) & subset(all_97_1,
% 16.25/2.91 | | | | | | | | | all_23_3) = v0)
% 16.25/2.91 | | | | | | | | |
% 16.25/2.91 | | | | | | | | | DELTA: instantiating (113) with fresh symbol all_176_0 gives:
% 16.25/2.91 | | | | | | | | | (114) ~ (all_176_0 = 0) & subset(all_97_1, all_23_3) =
% 16.25/2.91 | | | | | | | | | all_176_0
% 16.25/2.91 | | | | | | | | |
% 16.25/2.91 | | | | | | | | | ALPHA: (114) implies:
% 16.25/2.91 | | | | | | | | | (115) ~ (all_176_0 = 0)
% 16.25/2.91 | | | | | | | | | (116) subset(all_97_1, all_23_3) = all_176_0
% 16.25/2.91 | | | | | | | | |
% 16.25/2.91 | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_176_0, all_23_3,
% 16.25/2.91 | | | | | | | | | all_97_1, simplifying with (95), (116) gives:
% 16.25/2.91 | | | | | | | | | (117) all_176_0 = 0
% 16.25/2.91 | | | | | | | | |
% 16.25/2.91 | | | | | | | | | REDUCE: (115), (117) imply:
% 16.25/2.91 | | | | | | | | | (118) $false
% 16.25/2.91 | | | | | | | | |
% 16.25/2.91 | | | | | | | | | CLOSE: (118) is inconsistent.
% 16.25/2.91 | | | | | | | | |
% 16.25/2.91 | | | | | | | | End of split
% 16.25/2.91 | | | | | | | |
% 16.25/2.91 | | | | | | | Case 2:
% 16.25/2.91 | | | | | | | |
% 16.25/2.91 | | | | | | | | (119) ~ (all_132_1 = 0)
% 16.25/2.91 | | | | | | | |
% 16.25/2.91 | | | | | | | | REDUCE: (107), (119) imply:
% 16.25/2.91 | | | | | | | | (120) $false
% 16.25/2.91 | | | | | | | |
% 16.25/2.91 | | | | | | | | CLOSE: (120) is inconsistent.
% 16.25/2.91 | | | | | | | |
% 16.25/2.91 | | | | | | | End of split
% 16.25/2.91 | | | | | | |
% 16.25/2.91 | | | | | | End of split
% 16.25/2.91 | | | | | |
% 16.25/2.91 | | | | | End of split
% 16.25/2.91 | | | | |
% 16.25/2.91 | | | | End of split
% 16.25/2.91 | | | |
% 16.25/2.91 | | | End of split
% 16.25/2.91 | | |
% 16.25/2.91 | | End of split
% 16.25/2.91 | |
% 16.25/2.91 | End of split
% 16.25/2.91 |
% 16.25/2.91 End of proof
% 16.25/2.91 % SZS output end Proof for theBenchmark
% 16.25/2.91
% 16.25/2.91 2308ms
%------------------------------------------------------------------------------