TSTP Solution File: SET755+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n010.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 15:26:18 EDT 2023
% Result : Theorem 11.13s 2.24s
% Output : Proof 13.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n010.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 09:45:05 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 ________ _____
% 0.19/0.58 ___ __ \_________(_)________________________________
% 0.19/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.58 (2023-06-19)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2023
% 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.58 Amanda Stjerna.
% 0.19/0.58 Free software under BSD-3-Clause.
% 0.19/0.58
% 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.59 Running up to 7 provers in parallel.
% 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.97/1.24 Prover 4: Preprocessing ...
% 3.97/1.25 Prover 1: Preprocessing ...
% 3.97/1.28 Prover 5: Preprocessing ...
% 3.97/1.28 Prover 3: Preprocessing ...
% 3.97/1.28 Prover 6: Preprocessing ...
% 3.97/1.28 Prover 2: Preprocessing ...
% 3.97/1.28 Prover 0: Preprocessing ...
% 8.93/1.94 Prover 5: Proving ...
% 8.93/1.99 Prover 2: Proving ...
% 10.04/2.07 Prover 6: Proving ...
% 10.04/2.08 Prover 3: Constructing countermodel ...
% 10.04/2.09 Prover 1: Constructing countermodel ...
% 11.13/2.23 Prover 3: proved (1631ms)
% 11.13/2.23
% 11.13/2.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.13/2.24
% 11.13/2.25 Prover 5: stopped
% 11.13/2.25 Prover 2: stopped
% 11.13/2.25 Prover 0: stopped
% 11.13/2.26 Prover 6: stopped
% 11.80/2.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.80/2.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.80/2.27 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.80/2.27 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.80/2.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.98/2.31 Prover 7: Preprocessing ...
% 11.98/2.31 Prover 1: Found proof (size 26)
% 11.98/2.31 Prover 1: proved (1712ms)
% 11.98/2.32 Prover 4: stopped
% 12.33/2.33 Prover 8: Preprocessing ...
% 12.33/2.34 Prover 10: Preprocessing ...
% 12.33/2.34 Prover 11: Preprocessing ...
% 12.33/2.35 Prover 13: Preprocessing ...
% 12.33/2.36 Prover 7: stopped
% 12.33/2.40 Prover 10: stopped
% 12.90/2.43 Prover 13: stopped
% 12.90/2.46 Prover 11: stopped
% 13.30/2.53 Prover 8: Warning: ignoring some quantifiers
% 13.30/2.54 Prover 8: Constructing countermodel ...
% 13.30/2.54 Prover 8: stopped
% 13.30/2.54
% 13.30/2.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.30/2.54
% 13.30/2.55 % SZS output start Proof for theBenchmark
% 13.30/2.55 Assumptions after simplification:
% 13.30/2.55 ---------------------------------
% 13.30/2.55
% 13.30/2.55 (inverse_image2)
% 13.73/2.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 13.73/2.57 | ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) |
% 13.73/2.57 ~ $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v2, v5) = 0) | ~ $i(v5)
% 13.73/2.57 | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6))) & ! [v0: $i] : !
% 13.73/2.57 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (inverse_image2(v0, v1) = v3) | ~
% 13.73/2.57 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 13.73/2.57 (apply(v0, v2, v4) = 0 & member(v4, v1) = 0 & $i(v4)))
% 13.73/2.57
% 13.73/2.57 (subset)
% 13.73/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 13.73/2.58 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 13.73/2.58 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 13.73/2.58 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 13.73/2.58 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 13.73/2.58
% 13.73/2.58 (thIIa05)
% 13.73/2.58 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 13.73/2.58 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & inverse_image2(v0, v4) =
% 13.73/2.58 v6 & inverse_image2(v0, v3) = v5 & maps(v0, v1, v2) = 0 & subset(v5, v6) =
% 13.73/2.58 v7 & subset(v4, v2) = 0 & subset(v3, v4) = 0 & subset(v3, v2) = 0 & $i(v6) &
% 13.73/2.58 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.73/2.58
% 13.73/2.58 (function-axioms)
% 13.73/2.59 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.73/2.59 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 13.73/2.59 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~
% 13.73/2.59 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 13.73/2.59 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.73/2.59 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5,
% 13.73/2.59 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 13.73/2.59 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.73/2.59 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5,
% 13.73/2.59 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 13.73/2.59 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.73/2.59 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5,
% 13.73/2.59 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 13.73/2.59 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 13.73/2.59 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~
% 13.73/2.59 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 13.73/2.59 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 13.73/2.59 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~
% 13.73/2.59 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 13.73/2.59 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 13.73/2.59 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5,
% 13.73/2.59 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 13.73/2.59 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~
% 13.73/2.59 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 13.73/2.59 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~
% 13.73/2.59 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 13.73/2.59 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) |
% 13.73/2.59 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 13.73/2.59 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 13.73/2.59 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & !
% 13.73/2.59 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 13.73/2.59 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~
% 13.73/2.59 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.73/2.59 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 13.73/2.59 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0:
% 13.73/2.59 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.73/2.59 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) =
% 13.73/2.59 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.73/2.59 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 13.73/2.59 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 13.73/2.59 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~
% 13.73/2.59 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 13.73/2.59 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) &
% 13.73/2.59 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.73/2.59 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 13.73/2.59 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.73/2.59 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 13.73/2.59 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.73/2.59 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 13.73/2.59 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 13.73/2.59 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 13.73/2.59 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 13.73/2.59 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.73/2.59 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 13.73/2.59 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.73/2.59 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 13.73/2.59 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 13.73/2.59 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.73/2.59 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 13.73/2.59 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 13.73/2.59 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 13.73/2.59 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 13.73/2.59 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 13.73/2.59 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 13.73/2.59 (power_set(v2) = v0))
% 13.73/2.59
% 13.73/2.59 Further assumptions not needed in the proof:
% 13.73/2.59 --------------------------------------------
% 13.73/2.59 compose_function, compose_predicate, decreasing_function, difference, empty_set,
% 13.73/2.59 equal_maps, equal_set, identity, image2, image3, increasing_function, injective,
% 13.73/2.59 intersection, inverse_function, inverse_image3, inverse_predicate, isomorphism,
% 13.73/2.59 maps, one_to_one, power_set, product, singleton, sum, surjective, union,
% 13.73/2.59 unordered_pair
% 13.73/2.59
% 13.73/2.59 Those formulas are unsatisfiable:
% 13.73/2.59 ---------------------------------
% 13.73/2.59
% 13.73/2.59 Begin of proof
% 13.73/2.59 |
% 13.73/2.59 | ALPHA: (subset) implies:
% 13.73/2.60 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 13.73/2.60 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) |
% 13.73/2.60 | member(v2, v1) = 0))
% 13.73/2.60 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 13.73/2.60 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 13.73/2.60 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 13.73/2.60 |
% 13.73/2.60 | ALPHA: (inverse_image2) implies:
% 13.73/2.60 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 13.73/2.60 | (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) |
% 13.73/2.60 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v2, v4) = 0 &
% 13.73/2.60 | member(v4, v1) = 0 & $i(v4)))
% 13.73/2.60 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 13.73/2.60 | (v4 = 0 | ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) |
% 13.73/2.60 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v2,
% 13.73/2.60 | v5) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5,
% 13.73/2.60 | v1) = v6)))
% 13.73/2.60 |
% 13.73/2.60 | ALPHA: (function-axioms) implies:
% 13.73/2.60 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.73/2.60 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 13.73/2.60 | = v0))
% 13.73/2.60 |
% 13.73/2.60 | DELTA: instantiating (thIIa05) with fresh symbols all_32_0, all_32_1,
% 13.73/2.60 | all_32_2, all_32_3, all_32_4, all_32_5, all_32_6, all_32_7 gives:
% 13.73/2.60 | (6) ~ (all_32_0 = 0) & inverse_image2(all_32_7, all_32_3) = all_32_1 &
% 13.73/2.60 | inverse_image2(all_32_7, all_32_4) = all_32_2 & maps(all_32_7,
% 13.73/2.60 | all_32_6, all_32_5) = 0 & subset(all_32_2, all_32_1) = all_32_0 &
% 13.73/2.60 | subset(all_32_3, all_32_5) = 0 & subset(all_32_4, all_32_3) = 0 &
% 13.73/2.60 | subset(all_32_4, all_32_5) = 0 & $i(all_32_1) & $i(all_32_2) &
% 13.73/2.60 | $i(all_32_3) & $i(all_32_4) & $i(all_32_5) & $i(all_32_6) &
% 13.73/2.60 | $i(all_32_7)
% 13.73/2.60 |
% 13.73/2.60 | ALPHA: (6) implies:
% 13.73/2.60 | (7) ~ (all_32_0 = 0)
% 13.73/2.60 | (8) $i(all_32_7)
% 13.73/2.60 | (9) $i(all_32_4)
% 13.73/2.60 | (10) $i(all_32_3)
% 13.73/2.60 | (11) $i(all_32_2)
% 13.73/2.60 | (12) $i(all_32_1)
% 13.73/2.60 | (13) subset(all_32_4, all_32_3) = 0
% 13.73/2.60 | (14) subset(all_32_2, all_32_1) = all_32_0
% 13.73/2.60 | (15) inverse_image2(all_32_7, all_32_4) = all_32_2
% 13.73/2.60 | (16) inverse_image2(all_32_7, all_32_3) = all_32_1
% 13.73/2.60 |
% 13.73/2.60 | GROUND_INST: instantiating (1) with all_32_4, all_32_3, simplifying with (9),
% 13.73/2.60 | (10), (13) gives:
% 13.73/2.60 | (17) ! [v0: $i] : ( ~ (member(v0, all_32_4) = 0) | ~ $i(v0) | member(v0,
% 13.73/2.60 | all_32_3) = 0)
% 13.73/2.60 |
% 13.73/2.60 | GROUND_INST: instantiating (2) with all_32_2, all_32_1, all_32_0, simplifying
% 13.73/2.60 | with (11), (12), (14) gives:
% 13.73/2.60 | (18) all_32_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 13.73/2.60 | all_32_1) = v1 & member(v0, all_32_2) = 0 & $i(v0))
% 13.73/2.60 |
% 13.73/2.60 | BETA: splitting (18) gives:
% 13.73/2.60 |
% 13.73/2.60 | Case 1:
% 13.73/2.60 | |
% 13.73/2.60 | | (19) all_32_0 = 0
% 13.73/2.60 | |
% 13.73/2.61 | | REDUCE: (7), (19) imply:
% 13.73/2.61 | | (20) $false
% 13.73/2.61 | |
% 13.73/2.61 | | CLOSE: (20) is inconsistent.
% 13.73/2.61 | |
% 13.73/2.61 | Case 2:
% 13.73/2.61 | |
% 13.73/2.61 | | (21) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1) =
% 13.73/2.61 | | v1 & member(v0, all_32_2) = 0 & $i(v0))
% 13.73/2.61 | |
% 13.73/2.61 | | DELTA: instantiating (21) with fresh symbols all_46_0, all_46_1 gives:
% 13.73/2.61 | | (22) ~ (all_46_0 = 0) & member(all_46_1, all_32_1) = all_46_0 &
% 13.73/2.61 | | member(all_46_1, all_32_2) = 0 & $i(all_46_1)
% 13.73/2.61 | |
% 13.73/2.61 | | ALPHA: (22) implies:
% 13.73/2.61 | | (23) ~ (all_46_0 = 0)
% 13.73/2.61 | | (24) $i(all_46_1)
% 13.73/2.61 | | (25) member(all_46_1, all_32_2) = 0
% 13.73/2.61 | | (26) member(all_46_1, all_32_1) = all_46_0
% 13.73/2.61 | |
% 13.73/2.61 | | GROUND_INST: instantiating (3) with all_32_7, all_32_4, all_46_1, all_32_2,
% 13.73/2.61 | | simplifying with (8), (9), (15), (24), (25) gives:
% 13.73/2.61 | | (27) ? [v0: $i] : (apply(all_32_7, all_46_1, v0) = 0 & member(v0,
% 13.73/2.61 | | all_32_4) = 0 & $i(v0))
% 13.73/2.61 | |
% 13.73/2.61 | | GROUND_INST: instantiating (4) with all_32_7, all_32_3, all_46_1, all_32_1,
% 13.73/2.61 | | all_46_0, simplifying with (8), (10), (16), (24), (26) gives:
% 13.73/2.61 | | (28) all_46_0 = 0 | ! [v0: $i] : ( ~ (apply(all_32_7, all_46_1, v0) = 0)
% 13.73/2.61 | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_3) =
% 13.73/2.61 | | v1))
% 13.73/2.61 | |
% 13.73/2.61 | | DELTA: instantiating (27) with fresh symbol all_53_0 gives:
% 13.73/2.61 | | (29) apply(all_32_7, all_46_1, all_53_0) = 0 & member(all_53_0, all_32_4)
% 13.73/2.61 | | = 0 & $i(all_53_0)
% 13.73/2.61 | |
% 13.73/2.61 | | ALPHA: (29) implies:
% 13.73/2.61 | | (30) $i(all_53_0)
% 13.73/2.61 | | (31) member(all_53_0, all_32_4) = 0
% 13.73/2.61 | | (32) apply(all_32_7, all_46_1, all_53_0) = 0
% 13.73/2.61 | |
% 13.73/2.61 | | BETA: splitting (28) gives:
% 13.73/2.61 | |
% 13.73/2.61 | | Case 1:
% 13.73/2.61 | | |
% 13.73/2.61 | | | (33) all_46_0 = 0
% 13.73/2.61 | | |
% 13.73/2.61 | | | REDUCE: (23), (33) imply:
% 13.73/2.61 | | | (34) $false
% 13.73/2.61 | | |
% 13.73/2.61 | | | CLOSE: (34) is inconsistent.
% 13.73/2.61 | | |
% 13.73/2.61 | | Case 2:
% 13.73/2.61 | | |
% 13.73/2.61 | | | (35) ! [v0: $i] : ( ~ (apply(all_32_7, all_46_1, v0) = 0) | ~ $i(v0)
% 13.73/2.61 | | | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_3) = v1))
% 13.73/2.61 | | |
% 13.73/2.61 | | | GROUND_INST: instantiating (17) with all_53_0, simplifying with (30), (31)
% 13.73/2.61 | | | gives:
% 13.73/2.61 | | | (36) member(all_53_0, all_32_3) = 0
% 13.73/2.61 | | |
% 13.73/2.61 | | | GROUND_INST: instantiating (35) with all_53_0, simplifying with (30), (32)
% 13.73/2.61 | | | gives:
% 13.73/2.61 | | | (37) ? [v0: int] : ( ~ (v0 = 0) & member(all_53_0, all_32_3) = v0)
% 13.73/2.61 | | |
% 13.73/2.61 | | | DELTA: instantiating (37) with fresh symbol all_66_0 gives:
% 13.73/2.61 | | | (38) ~ (all_66_0 = 0) & member(all_53_0, all_32_3) = all_66_0
% 13.73/2.61 | | |
% 13.73/2.61 | | | ALPHA: (38) implies:
% 13.73/2.61 | | | (39) ~ (all_66_0 = 0)
% 13.73/2.61 | | | (40) member(all_53_0, all_32_3) = all_66_0
% 13.73/2.61 | | |
% 13.73/2.61 | | | GROUND_INST: instantiating (5) with 0, all_66_0, all_32_3, all_53_0,
% 13.73/2.61 | | | simplifying with (36), (40) gives:
% 13.73/2.62 | | | (41) all_66_0 = 0
% 13.73/2.62 | | |
% 13.73/2.62 | | | REDUCE: (39), (41) imply:
% 13.73/2.62 | | | (42) $false
% 13.73/2.62 | | |
% 13.73/2.62 | | | CLOSE: (42) is inconsistent.
% 13.73/2.62 | | |
% 13.73/2.62 | | End of split
% 13.73/2.62 | |
% 13.73/2.62 | End of split
% 13.73/2.62 |
% 13.73/2.62 End of proof
% 13.73/2.62 % SZS output end Proof for theBenchmark
% 13.73/2.62
% 13.73/2.62 2035ms
%------------------------------------------------------------------------------