TSTP Solution File: SET758+4 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET758+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 15:26:19 EDT 2023
% Result : Theorem 10.82s 2.22s
% Output : Proof 14.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET758+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 15:53:35 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.42/1.16 Prover 4: Preprocessing ...
% 3.42/1.16 Prover 1: Preprocessing ...
% 3.72/1.19 Prover 6: Preprocessing ...
% 3.72/1.19 Prover 0: Preprocessing ...
% 3.72/1.19 Prover 3: Preprocessing ...
% 3.72/1.19 Prover 2: Preprocessing ...
% 3.72/1.19 Prover 5: Preprocessing ...
% 8.75/1.92 Prover 5: Proving ...
% 9.20/1.94 Prover 2: Proving ...
% 9.20/1.98 Prover 6: Proving ...
% 9.20/2.02 Prover 1: Constructing countermodel ...
% 9.20/2.04 Prover 3: Constructing countermodel ...
% 10.82/2.22 Prover 3: proved (1594ms)
% 10.82/2.22
% 10.82/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.82/2.22
% 10.82/2.22 Prover 2: stopped
% 10.82/2.22 Prover 6: stopped
% 10.82/2.23 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.82/2.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.82/2.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.82/2.23 Prover 5: stopped
% 11.39/2.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.58/2.31 Prover 10: Preprocessing ...
% 11.58/2.32 Prover 1: Found proof (size 45)
% 11.97/2.35 Prover 7: Preprocessing ...
% 11.97/2.35 Prover 1: proved (1713ms)
% 11.97/2.35 Prover 11: Preprocessing ...
% 12.14/2.36 Prover 8: Preprocessing ...
% 12.14/2.36 Prover 10: stopped
% 12.14/2.38 Prover 7: stopped
% 12.98/2.47 Prover 11: stopped
% 12.98/2.53 Prover 4: Constructing countermodel ...
% 13.52/2.54 Prover 0: Proving ...
% 13.52/2.54 Prover 0: stopped
% 13.52/2.55 Prover 4: stopped
% 13.69/2.61 Prover 8: Warning: ignoring some quantifiers
% 13.69/2.62 Prover 8: Constructing countermodel ...
% 13.69/2.63 Prover 8: stopped
% 13.69/2.63
% 13.69/2.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.69/2.63
% 13.69/2.64 % SZS output start Proof for theBenchmark
% 13.69/2.64 Assumptions after simplification:
% 13.69/2.64 ---------------------------------
% 13.69/2.64
% 13.69/2.64 (image3)
% 13.69/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 13.69/2.67 int] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = v5) |
% 13.69/2.67 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ (v6 = 0) &
% 13.69/2.67 member(v3, v2) = v6) | ! [v6: $i] : ( ~ (apply(v0, v6, v3) = 0) | ~
% 13.69/2.67 $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & member(v6, v1) = v7))) & ! [v0:
% 13.69/2.67 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 13.69/2.67 (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ $i(v3) | ~ $i(v2)
% 13.69/2.67 | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? [v5: $i] : (apply(v0, v5,
% 13.69/2.67 v3) = 0 & member(v5, v1) = 0 & $i(v5))))
% 13.69/2.67
% 13.69/2.67 (inverse_image3)
% 13.69/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 13.69/2.67 int] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) =
% 13.69/2.68 v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~
% 13.69/2.68 (v6 = 0) & member(v3, v2) = v6) | ! [v6: $i] : ( ~ (apply(v0, v3, v6) =
% 13.69/2.68 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & member(v6, v1) = v7))) &
% 13.69/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 13.69/2.68 (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ $i(v3) | ~
% 13.69/2.68 $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? [v5: $i] :
% 13.69/2.68 (apply(v0, v3, v5) = 0 & member(v5, v1) = 0 & $i(v5))))
% 13.69/2.68
% 13.69/2.68 (maps)
% 13.69/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.69/2.68 (maps(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 13.69/2.68 ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0,
% 13.69/2.68 v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) =
% 13.69/2.68 0 & $i(v6) & $i(v5) & $i(v4)) | ? [v4: $i] : (member(v4, v1) = 0 & $i(v4)
% 13.69/2.68 & ! [v5: $i] : ( ~ (apply(v0, v4, v5) = 0) | ~ $i(v5) | ? [v6: int] : (
% 13.69/2.68 ~ (v6 = 0) & member(v5, v2) = v6)))) & ! [v0: $i] : ! [v1: $i] : !
% 13.69/2.68 [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (
% 13.69/2.68 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5)
% 13.69/2.68 = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3)
% 13.69/2.68 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 &
% 13.69/2.68 member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0)
% 13.69/2.68 | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) = 0) | ~
% 13.69/2.68 $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0 &
% 13.69/2.68 $i(v4)))))
% 13.69/2.68
% 13.69/2.68 (subset)
% 13.69/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 13.69/2.68 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 13.69/2.68 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 13.69/2.68 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 13.69/2.68 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 13.69/2.68
% 13.69/2.68 (thIIa08)
% 13.69/2.69 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 13.69/2.69 $i] : ? [v6: int] : ( ~ (v6 = 0) & inverse_image3(v0, v3, v1) = v4 &
% 13.69/2.69 image3(v0, v4, v2) = v5 & maps(v0, v1, v2) = 0 & subset(v5, v3) = v6 &
% 13.69/2.69 subset(v3, v2) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.69/2.69
% 13.69/2.69 (function-axioms)
% 13.69/2.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.69/2.70 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 13.69/2.70 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~
% 13.69/2.70 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 13.69/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.69/2.70 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5,
% 13.69/2.70 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 13.69/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.69/2.70 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5,
% 13.69/2.70 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 13.69/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.69/2.70 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5,
% 13.69/2.70 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 13.69/2.70 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 13.69/2.70 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~
% 13.69/2.70 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 13.69/2.70 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 13.69/2.70 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~
% 13.69/2.70 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 13.69/2.70 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 13.69/2.70 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5,
% 13.69/2.70 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 13.69/2.70 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~
% 13.69/2.70 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 13.69/2.70 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~
% 13.69/2.70 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 13.69/2.70 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) |
% 13.69/2.70 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 13.69/2.70 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 13.69/2.70 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & !
% 13.69/2.70 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 13.69/2.70 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~
% 13.69/2.70 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.69/2.70 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 13.69/2.70 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0:
% 13.69/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.69/2.70 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) =
% 13.69/2.70 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.69/2.70 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 13.69/2.70 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 13.69/2.70 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~
% 13.69/2.70 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 13.69/2.70 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) &
% 13.69/2.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.69/2.70 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 13.69/2.70 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.69/2.70 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 13.69/2.70 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.69/2.70 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 13.69/2.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 13.69/2.70 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 13.69/2.70 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 13.69/2.70 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.69/2.70 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 13.69/2.70 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.69/2.70 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 13.69/2.70 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 13.69/2.70 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.69/2.70 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 13.69/2.70 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 13.69/2.70 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 13.69/2.70 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 13.69/2.70 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 13.69/2.70 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 13.69/2.70 (power_set(v2) = v0))
% 13.69/2.70
% 13.69/2.70 Further assumptions not needed in the proof:
% 13.69/2.70 --------------------------------------------
% 13.69/2.70 compose_function, compose_predicate, decreasing_function, difference, empty_set,
% 13.69/2.70 equal_maps, equal_set, identity, image2, increasing_function, injective,
% 13.69/2.70 intersection, inverse_function, inverse_image2, inverse_predicate, isomorphism,
% 13.69/2.70 one_to_one, power_set, product, singleton, sum, surjective, union,
% 13.69/2.70 unordered_pair
% 13.69/2.70
% 13.69/2.70 Those formulas are unsatisfiable:
% 13.69/2.70 ---------------------------------
% 13.69/2.70
% 13.69/2.70 Begin of proof
% 13.69/2.70 |
% 13.69/2.70 | ALPHA: (subset) implies:
% 13.69/2.70 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 13.69/2.70 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) |
% 13.69/2.70 | member(v2, v1) = 0))
% 13.69/2.70 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 13.69/2.70 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 13.69/2.70 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 13.69/2.71 |
% 13.69/2.71 | ALPHA: (maps) implies:
% 13.69/2.71 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) |
% 13.69/2.71 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: $i] : !
% 13.69/2.71 | [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0,
% 13.69/2.71 | v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6:
% 13.69/2.71 | any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 &
% 13.69/2.71 | member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~
% 13.69/2.71 | (v7 = 0) | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1)
% 13.69/2.71 | = 0) | ~ $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 &
% 13.69/2.71 | member(v4, v2) = 0 & $i(v4)))))
% 13.69/2.71 |
% 13.69/2.71 | ALPHA: (image3) implies:
% 13.69/2.71 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 13.69/2.71 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ $i(v3) |
% 13.69/2.71 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? [v5: $i]
% 13.69/2.71 | : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0 & $i(v5))))
% 13.69/2.71 |
% 13.69/2.71 | ALPHA: (inverse_image3) implies:
% 13.69/2.71 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 13.69/2.71 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~
% 13.69/2.71 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ?
% 13.69/2.71 | [v5: $i] : (apply(v0, v3, v5) = 0 & member(v5, v1) = 0 & $i(v5))))
% 13.69/2.71 |
% 13.69/2.71 | ALPHA: (function-axioms) implies:
% 13.69/2.71 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.69/2.71 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 13.69/2.71 | = v0))
% 13.69/2.71 |
% 13.69/2.71 | DELTA: instantiating (thIIa08) with fresh symbols all_32_0, all_32_1,
% 13.69/2.71 | all_32_2, all_32_3, all_32_4, all_32_5, all_32_6 gives:
% 13.69/2.71 | (7) ~ (all_32_0 = 0) & inverse_image3(all_32_6, all_32_3, all_32_5) =
% 13.69/2.71 | all_32_2 & image3(all_32_6, all_32_2, all_32_4) = all_32_1 &
% 13.69/2.71 | maps(all_32_6, all_32_5, all_32_4) = 0 & subset(all_32_1, all_32_3) =
% 13.69/2.71 | all_32_0 & subset(all_32_3, all_32_4) = 0 & $i(all_32_1) & $i(all_32_2)
% 13.69/2.71 | & $i(all_32_3) & $i(all_32_4) & $i(all_32_5) & $i(all_32_6)
% 13.69/2.71 |
% 13.69/2.71 | ALPHA: (7) implies:
% 13.69/2.71 | (8) ~ (all_32_0 = 0)
% 13.69/2.71 | (9) $i(all_32_6)
% 13.69/2.71 | (10) $i(all_32_5)
% 13.69/2.71 | (11) $i(all_32_4)
% 13.69/2.71 | (12) $i(all_32_3)
% 13.69/2.72 | (13) $i(all_32_2)
% 13.69/2.72 | (14) $i(all_32_1)
% 14.37/2.72 | (15) subset(all_32_3, all_32_4) = 0
% 14.37/2.72 | (16) subset(all_32_1, all_32_3) = all_32_0
% 14.37/2.72 | (17) maps(all_32_6, all_32_5, all_32_4) = 0
% 14.37/2.72 | (18) image3(all_32_6, all_32_2, all_32_4) = all_32_1
% 14.37/2.72 | (19) inverse_image3(all_32_6, all_32_3, all_32_5) = all_32_2
% 14.37/2.72 |
% 14.37/2.72 | GROUND_INST: instantiating (1) with all_32_3, all_32_4, simplifying with (11),
% 14.37/2.72 | (12), (15) gives:
% 14.37/2.72 | (20) ! [v0: $i] : ( ~ (member(v0, all_32_3) = 0) | ~ $i(v0) | member(v0,
% 14.37/2.72 | all_32_4) = 0)
% 14.37/2.72 |
% 14.37/2.72 | GROUND_INST: instantiating (2) with all_32_1, all_32_3, all_32_0, simplifying
% 14.37/2.72 | with (12), (14), (16) gives:
% 14.37/2.72 | (21) all_32_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 14.37/2.72 | all_32_1) = 0 & member(v0, all_32_3) = v1 & $i(v0))
% 14.37/2.72 |
% 14.37/2.72 | GROUND_INST: instantiating (3) with all_32_6, all_32_5, all_32_4, simplifying
% 14.37/2.72 | with (9), (10), (11), (17) gives:
% 14.37/2.72 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 14.37/2.72 | (apply(all_32_6, v0, v2) = 0) | ~ (apply(all_32_6, v0, v1) = 0) |
% 14.37/2.72 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 14.37/2.72 | [v5: any] : (member(v2, all_32_4) = v5 & member(v1, all_32_4) = v4 &
% 14.37/2.72 | member(v0, all_32_5) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 =
% 14.37/2.72 | 0)))) & ! [v0: $i] : ( ~ (member(v0, all_32_5) = 0) | ~
% 14.37/2.72 | $i(v0) | ? [v1: $i] : (apply(all_32_6, v0, v1) = 0 & member(v1,
% 14.37/2.72 | all_32_4) = 0 & $i(v1)))
% 14.37/2.72 |
% 14.37/2.72 | ALPHA: (22) implies:
% 14.37/2.72 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 14.37/2.72 | (apply(all_32_6, v0, v2) = 0) | ~ (apply(all_32_6, v0, v1) = 0) |
% 14.37/2.72 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 14.37/2.72 | [v5: any] : (member(v2, all_32_4) = v5 & member(v1, all_32_4) = v4 &
% 14.37/2.72 | member(v0, all_32_5) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 =
% 14.37/2.72 | 0))))
% 14.37/2.72 |
% 14.37/2.72 | BETA: splitting (21) gives:
% 14.37/2.72 |
% 14.37/2.72 | Case 1:
% 14.37/2.72 | |
% 14.37/2.72 | | (24) all_32_0 = 0
% 14.37/2.72 | |
% 14.37/2.72 | | REDUCE: (8), (24) imply:
% 14.37/2.72 | | (25) $false
% 14.37/2.73 | |
% 14.37/2.73 | | CLOSE: (25) is inconsistent.
% 14.37/2.73 | |
% 14.37/2.73 | Case 2:
% 14.37/2.73 | |
% 14.37/2.73 | | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1) = 0
% 14.37/2.73 | | & member(v0, all_32_3) = v1 & $i(v0))
% 14.37/2.73 | |
% 14.37/2.73 | | DELTA: instantiating (26) with fresh symbols all_44_0, all_44_1 gives:
% 14.37/2.73 | | (27) ~ (all_44_0 = 0) & member(all_44_1, all_32_1) = 0 &
% 14.37/2.73 | | member(all_44_1, all_32_3) = all_44_0 & $i(all_44_1)
% 14.37/2.73 | |
% 14.37/2.73 | | ALPHA: (27) implies:
% 14.37/2.73 | | (28) ~ (all_44_0 = 0)
% 14.37/2.73 | | (29) $i(all_44_1)
% 14.37/2.73 | | (30) member(all_44_1, all_32_3) = all_44_0
% 14.37/2.73 | | (31) member(all_44_1, all_32_1) = 0
% 14.37/2.73 | |
% 14.37/2.73 | | GROUND_INST: instantiating (4) with all_32_6, all_32_2, all_32_4, all_44_1,
% 14.37/2.73 | | all_32_1, simplifying with (9), (11), (13), (18), (29), (31)
% 14.37/2.73 | | gives:
% 14.37/2.73 | | (32) member(all_44_1, all_32_4) = 0 & ? [v0: $i] : (apply(all_32_6, v0,
% 14.37/2.73 | | all_44_1) = 0 & member(v0, all_32_2) = 0 & $i(v0))
% 14.37/2.73 | |
% 14.37/2.73 | | ALPHA: (32) implies:
% 14.37/2.73 | | (33) member(all_44_1, all_32_4) = 0
% 14.37/2.73 | | (34) ? [v0: $i] : (apply(all_32_6, v0, all_44_1) = 0 & member(v0,
% 14.37/2.73 | | all_32_2) = 0 & $i(v0))
% 14.37/2.73 | |
% 14.37/2.73 | | DELTA: instantiating (34) with fresh symbol all_52_0 gives:
% 14.37/2.73 | | (35) apply(all_32_6, all_52_0, all_44_1) = 0 & member(all_52_0, all_32_2)
% 14.37/2.73 | | = 0 & $i(all_52_0)
% 14.37/2.73 | |
% 14.37/2.73 | | ALPHA: (35) implies:
% 14.37/2.73 | | (36) $i(all_52_0)
% 14.37/2.73 | | (37) member(all_52_0, all_32_2) = 0
% 14.37/2.73 | | (38) apply(all_32_6, all_52_0, all_44_1) = 0
% 14.37/2.73 | |
% 14.37/2.73 | | GROUND_INST: instantiating (5) with all_32_6, all_32_3, all_32_5, all_52_0,
% 14.37/2.73 | | all_32_2, simplifying with (9), (10), (12), (19), (36), (37)
% 14.37/2.73 | | gives:
% 14.37/2.73 | | (39) member(all_52_0, all_32_5) = 0 & ? [v0: $i] : (apply(all_32_6,
% 14.37/2.73 | | all_52_0, v0) = 0 & member(v0, all_32_3) = 0 & $i(v0))
% 14.37/2.73 | |
% 14.37/2.73 | | ALPHA: (39) implies:
% 14.37/2.73 | | (40) member(all_52_0, all_32_5) = 0
% 14.37/2.73 | | (41) ? [v0: $i] : (apply(all_32_6, all_52_0, v0) = 0 & member(v0,
% 14.37/2.73 | | all_32_3) = 0 & $i(v0))
% 14.37/2.73 | |
% 14.37/2.73 | | DELTA: instantiating (41) with fresh symbol all_60_0 gives:
% 14.37/2.73 | | (42) apply(all_32_6, all_52_0, all_60_0) = 0 & member(all_60_0, all_32_3)
% 14.37/2.73 | | = 0 & $i(all_60_0)
% 14.37/2.73 | |
% 14.37/2.73 | | ALPHA: (42) implies:
% 14.37/2.73 | | (43) $i(all_60_0)
% 14.37/2.73 | | (44) member(all_60_0, all_32_3) = 0
% 14.37/2.74 | | (45) apply(all_32_6, all_52_0, all_60_0) = 0
% 14.37/2.74 | |
% 14.37/2.74 | | GROUND_INST: instantiating (20) with all_60_0, simplifying with (43), (44)
% 14.37/2.74 | | gives:
% 14.37/2.74 | | (46) member(all_60_0, all_32_4) = 0
% 14.37/2.74 | |
% 14.37/2.74 | | GROUND_INST: instantiating (23) with all_52_0, all_60_0, all_44_1,
% 14.37/2.74 | | simplifying with (29), (36), (38), (43), (45) gives:
% 14.37/2.74 | | (47) all_60_0 = all_44_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 14.37/2.74 | | (member(all_60_0, all_32_4) = v1 & member(all_52_0, all_32_5) = v0 &
% 14.37/2.74 | | member(all_44_1, all_32_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 14.37/2.74 | | (v0 = 0)))
% 14.37/2.74 | |
% 14.37/2.74 | | BETA: splitting (47) gives:
% 14.37/2.74 | |
% 14.37/2.74 | | Case 1:
% 14.37/2.74 | | |
% 14.37/2.74 | | | (48) all_60_0 = all_44_1
% 14.37/2.74 | | |
% 14.37/2.74 | | | REDUCE: (44), (48) imply:
% 14.37/2.74 | | | (49) member(all_44_1, all_32_3) = 0
% 14.37/2.74 | | |
% 14.37/2.74 | | | GROUND_INST: instantiating (6) with all_44_0, 0, all_32_3, all_44_1,
% 14.37/2.74 | | | simplifying with (30), (49) gives:
% 14.37/2.74 | | | (50) all_44_0 = 0
% 14.37/2.74 | | |
% 14.37/2.74 | | | REDUCE: (28), (50) imply:
% 14.37/2.74 | | | (51) $false
% 14.37/2.74 | | |
% 14.37/2.74 | | | CLOSE: (51) is inconsistent.
% 14.37/2.74 | | |
% 14.37/2.74 | | Case 2:
% 14.37/2.74 | | |
% 14.49/2.74 | | | (52) ? [v0: any] : ? [v1: any] : ? [v2: any] : (member(all_60_0,
% 14.49/2.74 | | | all_32_4) = v1 & member(all_52_0, all_32_5) = v0 &
% 14.49/2.74 | | | member(all_44_1, all_32_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) |
% 14.49/2.74 | | | ~ (v0 = 0)))
% 14.49/2.74 | | |
% 14.49/2.74 | | | DELTA: instantiating (52) with fresh symbols all_74_0, all_74_1, all_74_2
% 14.49/2.74 | | | gives:
% 14.49/2.74 | | | (53) member(all_60_0, all_32_4) = all_74_1 & member(all_52_0, all_32_5)
% 14.49/2.74 | | | = all_74_2 & member(all_44_1, all_32_4) = all_74_0 & ( ~ (all_74_0
% 14.49/2.74 | | | = 0) | ~ (all_74_1 = 0) | ~ (all_74_2 = 0))
% 14.49/2.74 | | |
% 14.49/2.74 | | | ALPHA: (53) implies:
% 14.49/2.74 | | | (54) member(all_44_1, all_32_4) = all_74_0
% 14.49/2.74 | | | (55) member(all_52_0, all_32_5) = all_74_2
% 14.49/2.74 | | | (56) member(all_60_0, all_32_4) = all_74_1
% 14.49/2.74 | | | (57) ~ (all_74_0 = 0) | ~ (all_74_1 = 0) | ~ (all_74_2 = 0)
% 14.49/2.74 | | |
% 14.49/2.74 | | | GROUND_INST: instantiating (6) with 0, all_74_0, all_32_4, all_44_1,
% 14.49/2.74 | | | simplifying with (33), (54) gives:
% 14.49/2.74 | | | (58) all_74_0 = 0
% 14.49/2.74 | | |
% 14.49/2.74 | | | GROUND_INST: instantiating (6) with 0, all_74_2, all_32_5, all_52_0,
% 14.49/2.74 | | | simplifying with (40), (55) gives:
% 14.49/2.74 | | | (59) all_74_2 = 0
% 14.49/2.74 | | |
% 14.49/2.74 | | | GROUND_INST: instantiating (6) with 0, all_74_1, all_32_4, all_60_0,
% 14.49/2.74 | | | simplifying with (46), (56) gives:
% 14.49/2.74 | | | (60) all_74_1 = 0
% 14.49/2.74 | | |
% 14.49/2.74 | | | BETA: splitting (57) gives:
% 14.49/2.74 | | |
% 14.49/2.74 | | | Case 1:
% 14.49/2.74 | | | |
% 14.49/2.74 | | | | (61) ~ (all_74_0 = 0)
% 14.49/2.74 | | | |
% 14.49/2.74 | | | | REDUCE: (58), (61) imply:
% 14.49/2.74 | | | | (62) $false
% 14.49/2.74 | | | |
% 14.49/2.74 | | | | CLOSE: (62) is inconsistent.
% 14.49/2.74 | | | |
% 14.49/2.74 | | | Case 2:
% 14.49/2.74 | | | |
% 14.49/2.74 | | | | (63) ~ (all_74_1 = 0) | ~ (all_74_2 = 0)
% 14.49/2.74 | | | |
% 14.49/2.74 | | | | BETA: splitting (63) gives:
% 14.49/2.74 | | | |
% 14.49/2.74 | | | | Case 1:
% 14.49/2.74 | | | | |
% 14.49/2.74 | | | | | (64) ~ (all_74_1 = 0)
% 14.49/2.74 | | | | |
% 14.49/2.74 | | | | | REDUCE: (60), (64) imply:
% 14.49/2.74 | | | | | (65) $false
% 14.49/2.74 | | | | |
% 14.49/2.74 | | | | | CLOSE: (65) is inconsistent.
% 14.49/2.74 | | | | |
% 14.49/2.74 | | | | Case 2:
% 14.49/2.74 | | | | |
% 14.49/2.74 | | | | | (66) ~ (all_74_2 = 0)
% 14.49/2.74 | | | | |
% 14.49/2.74 | | | | | REDUCE: (59), (66) imply:
% 14.49/2.74 | | | | | (67) $false
% 14.49/2.74 | | | | |
% 14.49/2.74 | | | | | CLOSE: (67) is inconsistent.
% 14.49/2.74 | | | | |
% 14.49/2.75 | | | | End of split
% 14.49/2.75 | | | |
% 14.49/2.75 | | | End of split
% 14.49/2.75 | | |
% 14.49/2.75 | | End of split
% 14.49/2.75 | |
% 14.49/2.75 | End of split
% 14.49/2.75 |
% 14.49/2.75 End of proof
% 14.49/2.75 % SZS output end Proof for theBenchmark
% 14.49/2.75
% 14.49/2.75 2146ms
%------------------------------------------------------------------------------