TSTP Solution File: KRS162+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS162+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n024.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 05:51:30 EDT 2023
% Result : Theorem 11.61s 2.25s
% Output : Proof 13.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : KRS162+1 : TPTP v8.1.2. Released v3.1.0.
% 0.10/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 02:26:08 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.18/0.60 ________ _____
% 0.18/0.60 ___ __ \_________(_)________________________________
% 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.60
% 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.60 (2023-06-19)
% 0.18/0.60
% 0.18/0.60 (c) Philipp Rümmer, 2009-2023
% 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.60 Amanda Stjerna.
% 0.18/0.60 Free software under BSD-3-Clause.
% 0.18/0.60
% 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.60
% 0.18/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.58/0.61 Running up to 7 provers in parallel.
% 0.58/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.58/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.58/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.58/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.58/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.58/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.58/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.58/1.02 Prover 4: Preprocessing ...
% 2.58/1.02 Prover 1: Preprocessing ...
% 2.58/1.06 Prover 2: Preprocessing ...
% 2.58/1.06 Prover 0: Preprocessing ...
% 2.58/1.06 Prover 3: Preprocessing ...
% 2.58/1.06 Prover 5: Preprocessing ...
% 2.58/1.06 Prover 6: Preprocessing ...
% 3.87/1.27 Prover 5: Proving ...
% 3.87/1.28 Prover 2: Proving ...
% 4.62/1.31 Prover 6: Proving ...
% 4.91/1.36 Prover 0: Proving ...
% 5.09/1.37 Prover 3: Constructing countermodel ...
% 5.09/1.37 Prover 1: Constructing countermodel ...
% 5.09/1.38 Prover 4: Constructing countermodel ...
% 11.61/2.24 Prover 3: proved (1622ms)
% 11.61/2.25
% 11.61/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.61/2.25
% 11.61/2.25 Prover 0: stopped
% 11.61/2.25 Prover 2: stopped
% 11.61/2.25 Prover 6: stopped
% 11.61/2.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.61/2.25 Prover 5: stopped
% 11.61/2.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.61/2.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.87/2.27 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.87/2.27 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.87/2.30 Prover 10: Preprocessing ...
% 11.87/2.31 Prover 7: Preprocessing ...
% 11.87/2.31 Prover 8: Preprocessing ...
% 11.87/2.31 Prover 13: Preprocessing ...
% 11.87/2.31 Prover 11: Preprocessing ...
% 12.37/2.34 Prover 7: Warning: ignoring some quantifiers
% 12.37/2.35 Prover 7: Constructing countermodel ...
% 12.37/2.35 Prover 10: Warning: ignoring some quantifiers
% 12.37/2.35 Prover 13: Warning: ignoring some quantifiers
% 12.37/2.36 Prover 10: Constructing countermodel ...
% 12.61/2.36 Prover 13: Constructing countermodel ...
% 12.61/2.38 Prover 7: gave up
% 12.61/2.38 Prover 10: gave up
% 12.61/2.38 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 12.61/2.39 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 12.61/2.40 Prover 13: gave up
% 12.61/2.42 Prover 19: Preprocessing ...
% 12.61/2.42 Prover 16: Preprocessing ...
% 12.61/2.42 Prover 4: Found proof (size 112)
% 12.61/2.42 Prover 4: proved (1798ms)
% 12.61/2.42 Prover 1: stopped
% 12.61/2.42 Prover 8: Warning: ignoring some quantifiers
% 12.61/2.43 Prover 11: Constructing countermodel ...
% 13.11/2.43 Prover 8: Constructing countermodel ...
% 13.11/2.43 Prover 11: stopped
% 13.11/2.43 Prover 8: stopped
% 13.11/2.43 Prover 16: stopped
% 13.29/2.48 Prover 19: Warning: ignoring some quantifiers
% 13.29/2.48 Prover 19: Constructing countermodel ...
% 13.29/2.48 Prover 19: stopped
% 13.29/2.48
% 13.29/2.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.29/2.48
% 13.29/2.50 % SZS output start Proof for theBenchmark
% 13.29/2.50 Assumptions after simplification:
% 13.29/2.50 ---------------------------------
% 13.29/2.50
% 13.29/2.50 (axiom_0)
% 13.29/2.52 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ $i(v0)) &
% 13.29/2.52 ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0))
% 13.29/2.52
% 13.29/2.52 (axiom_1)
% 13.29/2.52 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ $i(v0) |
% 13.29/2.52 xsd_integer(v0) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 13.29/2.52 (xsd_integer(v0) = v1) | ~ $i(v0) | xsd_string(v0) = 0) & ! [v0: $i] : ( ~
% 13.29/2.52 (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 13.29/2.52 xsd_integer(v0) = v1)) & ! [v0: $i] : ( ~ (xsd_integer(v0) = 0) | ~
% 13.29/2.52 $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & xsd_string(v0) = v1))
% 13.29/2.52
% 13.29/2.52 (axiom_2)
% 13.29/2.53 ! [v0: $i] : ! [v1: $i] : ( ~ (rp(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 13.29/2.53 cA(v1) = 0)
% 13.29/2.53
% 13.29/2.53 (axiom_3)
% 13.29/2.53 ! [v0: $i] : ! [v1: $i] : ( ~ (rq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 13.29/2.53 cB(v1) = 0)
% 13.29/2.53
% 13.29/2.53 (axiom_4)
% 13.29/2.53 ! [v0: $i] : ( ~ (cB(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 13.29/2.53 cA(v0) = v1)) & ! [v0: $i] : ( ~ (cA(v0) = 0) | ~ $i(v0) | ? [v1: int]
% 13.29/2.53 : ( ~ (v1 = 0) & cB(v0) = v1))
% 13.29/2.53
% 13.29/2.53 (axiom_5)
% 13.29/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rr(v0, v1) = v2) | ~
% 13.29/2.53 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rq(v0, v1) = v3)) & !
% 13.29/2.53 [v0: $i] : ! [v1: $i] : ( ~ (rq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | rr(v0,
% 13.63/2.53 v1) = 0)
% 13.63/2.53
% 13.63/2.53 (axiom_6)
% 13.63/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rr(v0, v1) = v2) | ~
% 13.63/2.53 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rp(v0, v1) = v3)) & !
% 13.63/2.53 [v0: $i] : ! [v1: $i] : ( ~ (rp(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | rr(v0,
% 13.63/2.53 v1) = 0)
% 13.63/2.53
% 13.63/2.53 (the_axiom)
% 13.63/2.54 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5:
% 13.63/2.54 int] : ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10:
% 13.63/2.54 int] : ? [v11: $i] : ? [v12: any] : ? [v13: any] : ? [v14: $i] : ?
% 13.63/2.54 [v15: any] : ? [v16: any] : ($i(v14) & $i(v11) & $i(v8) & $i(v7) & $i(v3) &
% 13.63/2.54 $i(v2) & $i(v1) & $i(v0) & ((v10 = 0 & v9 = 0 & v6 = 0 & v5 = 0 & v4 = 0 &
% 13.63/2.54 ~ (v8 = v7) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v2 = v1) & rq(v0, v3) =
% 13.63/2.54 0 & rq(v0, v2) = 0 & rq(v0, v1) = 0 & rp(v0, v8) = 0 & rp(v0, v7) = 0 &
% 13.63/2.54 ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i]
% 13.63/2.54 : (v21 = v20 | v21 = v19 | v21 = v18 | v21 = v17 | v20 = v19 | v20 = v18
% 13.63/2.54 | v20 = v17 | v19 = v18 | v19 = v17 | v18 = v17 | ~ (rr(v0, v21) = 0)
% 13.63/2.54 | ~ (rr(v0, v20) = 0) | ~ (rr(v0, v19) = 0) | ~ (rr(v0, v18) = 0) |
% 13.63/2.54 ~ (rr(v0, v17) = 0) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~
% 13.63/2.54 $i(v18) | ~ $i(v17))) | (xsd_string(v11) = v12 & xsd_integer(v11) =
% 13.63/2.54 v13 & ((v13 = 0 & v12 = 0) | ( ~ (v13 = 0) & ~ (v12 = 0)))) |
% 13.63/2.54 (cowlThing(v14) = v15 & cowlNothing(v14) = v16 & ( ~ (v15 = 0) | v16 =
% 13.63/2.54 0))))
% 13.63/2.54
% 13.63/2.54 (function-axioms)
% 13.63/2.54 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.63/2.54 [v3: $i] : (v1 = v0 | ~ (rr(v3, v2) = v1) | ~ (rr(v3, v2) = v0)) & ! [v0:
% 13.63/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.63/2.54 : (v1 = v0 | ~ (rq(v3, v2) = v1) | ~ (rq(v3, v2) = v0)) & ! [v0:
% 13.63/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.63/2.54 : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) & ! [v0:
% 13.63/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 13.63/2.54 ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0:
% 13.63/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 13.63/2.54 ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0:
% 13.63/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 13.63/2.54 ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0:
% 13.63/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 13.63/2.54 ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0:
% 13.63/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 13.63/2.54 ~ (cB(v2) = v1) | ~ (cB(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.63/2.54 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(v2)
% 13.63/2.54 = v0))
% 13.63/2.54
% 13.63/2.54 Further assumptions not needed in the proof:
% 13.63/2.54 --------------------------------------------
% 13.63/2.54 cA_substitution_1, cB_substitution_1, cowlNothing_substitution_1,
% 13.63/2.54 cowlThing_substitution_1, rp_substitution_1, rp_substitution_2,
% 13.63/2.54 rq_substitution_1, rq_substitution_2, rr_substitution_1, rr_substitution_2,
% 13.63/2.54 xsd_integer_substitution_1, xsd_string_substitution_1
% 13.63/2.54
% 13.63/2.54 Those formulas are unsatisfiable:
% 13.63/2.54 ---------------------------------
% 13.63/2.54
% 13.63/2.54 Begin of proof
% 13.63/2.54 |
% 13.63/2.54 | ALPHA: (axiom_0) implies:
% 13.63/2.54 | (1) ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) | ~ $i(v0))
% 13.63/2.54 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~
% 13.63/2.54 | $i(v0))
% 13.63/2.54 |
% 13.63/2.54 | ALPHA: (axiom_1) implies:
% 13.63/2.54 | (3) ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 13.63/2.54 | (v1 = 0) & xsd_integer(v0) = v1))
% 13.63/2.54 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~
% 13.63/2.54 | $i(v0) | xsd_string(v0) = 0)
% 13.63/2.55 | (5) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~
% 13.63/2.55 | $i(v0) | xsd_integer(v0) = 0)
% 13.63/2.55 |
% 13.63/2.55 | ALPHA: (axiom_4) implies:
% 13.63/2.55 | (6) ! [v0: $i] : ( ~ (cA(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 =
% 13.63/2.55 | 0) & cB(v0) = v1))
% 13.63/2.55 | (7) ! [v0: $i] : ( ~ (cB(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 =
% 13.63/2.55 | 0) & cA(v0) = v1))
% 13.63/2.55 |
% 13.63/2.55 | ALPHA: (axiom_5) implies:
% 13.63/2.55 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (rq(v0, v1) = 0) | ~ $i(v1) | ~
% 13.63/2.55 | $i(v0) | rr(v0, v1) = 0)
% 13.63/2.55 |
% 13.63/2.55 | ALPHA: (axiom_6) implies:
% 13.63/2.55 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (rp(v0, v1) = 0) | ~ $i(v1) | ~
% 13.63/2.55 | $i(v0) | rr(v0, v1) = 0)
% 13.63/2.55 |
% 13.63/2.55 | ALPHA: (function-axioms) implies:
% 13.63/2.55 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 13.63/2.55 | : (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(v2) = v0))
% 13.63/2.55 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 13.63/2.55 | : (v1 = v0 | ~ (cB(v2) = v1) | ~ (cB(v2) = v0))
% 13.63/2.55 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 13.63/2.55 | : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 13.63/2.55 |
% 13.63/2.55 | DELTA: instantiating (the_axiom) with fresh symbols all_10_0, all_10_1,
% 13.63/2.55 | all_10_2, all_10_3, all_10_4, all_10_5, all_10_6, all_10_7, all_10_8,
% 13.63/2.55 | all_10_9, all_10_10, all_10_11, all_10_12, all_10_13, all_10_14,
% 13.63/2.55 | all_10_15, all_10_16 gives:
% 13.63/2.55 | (13) $i(all_10_2) & $i(all_10_5) & $i(all_10_8) & $i(all_10_9) &
% 13.63/2.55 | $i(all_10_13) & $i(all_10_14) & $i(all_10_15) & $i(all_10_16) &
% 13.63/2.55 | ((all_10_6 = 0 & all_10_7 = 0 & all_10_10 = 0 & all_10_11 = 0 &
% 13.63/2.55 | all_10_12 = 0 & ~ (all_10_8 = all_10_9) & ~ (all_10_13 =
% 13.63/2.55 | all_10_14) & ~ (all_10_13 = all_10_15) & ~ (all_10_14 =
% 13.63/2.55 | all_10_15) & rq(all_10_16, all_10_13) = 0 & rq(all_10_16,
% 13.63/2.55 | all_10_14) = 0 & rq(all_10_16, all_10_15) = 0 & rp(all_10_16,
% 13.63/2.55 | all_10_8) = 0 & rp(all_10_16, all_10_9) = 0 & ! [v0: $i] : !
% 13.63/2.55 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | v4
% 13.63/2.55 | = v2 | v4 = v1 | v4 = v0 | v3 = v2 | v3 = v1 | v3 = v0 | v2 = v1
% 13.63/2.55 | | v2 = v0 | v1 = v0 | ~ (rr(all_10_16, v4) = 0) | ~
% 13.63/2.55 | (rr(all_10_16, v3) = 0) | ~ (rr(all_10_16, v2) = 0) | ~
% 13.63/2.55 | (rr(all_10_16, v1) = 0) | ~ (rr(all_10_16, v0) = 0) | ~ $i(v4)
% 13.63/2.55 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))) |
% 13.63/2.55 | (xsd_string(all_10_5) = all_10_4 & xsd_integer(all_10_5) = all_10_3
% 13.63/2.55 | & ((all_10_3 = 0 & all_10_4 = 0) | ( ~ (all_10_3 = 0) & ~
% 13.63/2.55 | (all_10_4 = 0)))) | (cowlThing(all_10_2) = all_10_1 &
% 13.63/2.55 | cowlNothing(all_10_2) = all_10_0 & ( ~ (all_10_1 = 0) | all_10_0 =
% 13.63/2.55 | 0)))
% 13.63/2.55 |
% 13.63/2.55 | ALPHA: (13) implies:
% 13.63/2.55 | (14) $i(all_10_16)
% 13.63/2.55 | (15) $i(all_10_15)
% 13.63/2.55 | (16) $i(all_10_14)
% 13.63/2.55 | (17) $i(all_10_13)
% 13.63/2.55 | (18) $i(all_10_9)
% 13.63/2.55 | (19) $i(all_10_8)
% 13.63/2.55 | (20) $i(all_10_5)
% 13.63/2.55 | (21) $i(all_10_2)
% 13.63/2.56 | (22) (all_10_6 = 0 & all_10_7 = 0 & all_10_10 = 0 & all_10_11 = 0 &
% 13.63/2.56 | all_10_12 = 0 & ~ (all_10_8 = all_10_9) & ~ (all_10_13 =
% 13.63/2.56 | all_10_14) & ~ (all_10_13 = all_10_15) & ~ (all_10_14 =
% 13.63/2.56 | all_10_15) & rq(all_10_16, all_10_13) = 0 & rq(all_10_16,
% 13.63/2.56 | all_10_14) = 0 & rq(all_10_16, all_10_15) = 0 & rp(all_10_16,
% 13.63/2.56 | all_10_8) = 0 & rp(all_10_16, all_10_9) = 0 & ! [v0: $i] : !
% 13.63/2.56 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | v4 =
% 13.63/2.56 | v2 | v4 = v1 | v4 = v0 | v3 = v2 | v3 = v1 | v3 = v0 | v2 = v1 |
% 13.63/2.56 | v2 = v0 | v1 = v0 | ~ (rr(all_10_16, v4) = 0) | ~ (rr(all_10_16,
% 13.63/2.56 | v3) = 0) | ~ (rr(all_10_16, v2) = 0) | ~ (rr(all_10_16, v1)
% 13.63/2.56 | = 0) | ~ (rr(all_10_16, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~
% 13.63/2.56 | $i(v2) | ~ $i(v1) | ~ $i(v0))) | (xsd_string(all_10_5) =
% 13.63/2.56 | all_10_4 & xsd_integer(all_10_5) = all_10_3 & ((all_10_3 = 0 &
% 13.63/2.56 | all_10_4 = 0) | ( ~ (all_10_3 = 0) & ~ (all_10_4 = 0)))) |
% 13.63/2.56 | (cowlThing(all_10_2) = all_10_1 & cowlNothing(all_10_2) = all_10_0 & (
% 13.63/2.56 | ~ (all_10_1 = 0) | all_10_0 = 0))
% 13.63/2.56 |
% 13.63/2.56 | BETA: splitting (22) gives:
% 13.63/2.56 |
% 13.63/2.56 | Case 1:
% 13.63/2.56 | |
% 13.63/2.56 | | (23) all_10_6 = 0 & all_10_7 = 0 & all_10_10 = 0 & all_10_11 = 0 &
% 13.63/2.56 | | all_10_12 = 0 & ~ (all_10_8 = all_10_9) & ~ (all_10_13 =
% 13.63/2.56 | | all_10_14) & ~ (all_10_13 = all_10_15) & ~ (all_10_14 =
% 13.63/2.56 | | all_10_15) & rq(all_10_16, all_10_13) = 0 & rq(all_10_16,
% 13.63/2.56 | | all_10_14) = 0 & rq(all_10_16, all_10_15) = 0 & rp(all_10_16,
% 13.63/2.56 | | all_10_8) = 0 & rp(all_10_16, all_10_9) = 0 & ! [v0: $i] : !
% 13.63/2.56 | | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | v4 =
% 13.63/2.56 | | v2 | v4 = v1 | v4 = v0 | v3 = v2 | v3 = v1 | v3 = v0 | v2 = v1 |
% 13.63/2.56 | | v2 = v0 | v1 = v0 | ~ (rr(all_10_16, v4) = 0) | ~ (rr(all_10_16,
% 13.63/2.56 | | v3) = 0) | ~ (rr(all_10_16, v2) = 0) | ~ (rr(all_10_16, v1)
% 13.63/2.56 | | = 0) | ~ (rr(all_10_16, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~
% 13.63/2.56 | | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 13.63/2.56 | |
% 13.63/2.56 | | ALPHA: (23) implies:
% 13.63/2.56 | | (24) ~ (all_10_14 = all_10_15)
% 13.63/2.56 | | (25) ~ (all_10_13 = all_10_15)
% 13.63/2.56 | | (26) ~ (all_10_13 = all_10_14)
% 13.63/2.56 | | (27) ~ (all_10_8 = all_10_9)
% 13.63/2.56 | | (28) rp(all_10_16, all_10_9) = 0
% 13.63/2.56 | | (29) rp(all_10_16, all_10_8) = 0
% 13.63/2.56 | | (30) rq(all_10_16, all_10_15) = 0
% 13.63/2.56 | | (31) rq(all_10_16, all_10_14) = 0
% 13.63/2.56 | | (32) rq(all_10_16, all_10_13) = 0
% 13.63/2.56 | | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 13.63/2.56 | | : (v4 = v3 | v4 = v2 | v4 = v1 | v4 = v0 | v3 = v2 | v3 = v1 | v3 =
% 13.63/2.56 | | v0 | v2 = v1 | v2 = v0 | v1 = v0 | ~ (rr(all_10_16, v4) = 0) | ~
% 13.63/2.56 | | (rr(all_10_16, v3) = 0) | ~ (rr(all_10_16, v2) = 0) | ~
% 13.63/2.56 | | (rr(all_10_16, v1) = 0) | ~ (rr(all_10_16, v0) = 0) | ~ $i(v4) |
% 13.63/2.56 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 13.63/2.56 | |
% 13.63/2.56 | | GROUND_INST: instantiating (9) with all_10_16, all_10_9, simplifying with
% 13.63/2.56 | | (14), (18), (28) gives:
% 13.63/2.56 | | (34) rr(all_10_16, all_10_9) = 0
% 13.63/2.56 | |
% 13.63/2.56 | | GROUND_INST: instantiating (axiom_2) with all_10_16, all_10_9, simplifying
% 13.63/2.56 | | with (14), (18), (28) gives:
% 13.63/2.56 | | (35) cA(all_10_9) = 0
% 13.63/2.56 | |
% 13.63/2.56 | | GROUND_INST: instantiating (9) with all_10_16, all_10_8, simplifying with
% 13.63/2.56 | | (14), (19), (29) gives:
% 13.63/2.58 | | (36) rr(all_10_16, all_10_8) = 0
% 13.63/2.58 | |
% 13.63/2.58 | | GROUND_INST: instantiating (axiom_2) with all_10_16, all_10_8, simplifying
% 13.63/2.58 | | with (14), (19), (29) gives:
% 13.63/2.58 | | (37) cA(all_10_8) = 0
% 13.63/2.58 | |
% 13.63/2.58 | | GROUND_INST: instantiating (8) with all_10_16, all_10_15, simplifying with
% 13.63/2.58 | | (14), (15), (30) gives:
% 13.63/2.58 | | (38) rr(all_10_16, all_10_15) = 0
% 13.63/2.58 | |
% 13.63/2.58 | | GROUND_INST: instantiating (axiom_3) with all_10_16, all_10_15, simplifying
% 13.63/2.58 | | with (14), (15), (30) gives:
% 13.63/2.58 | | (39) cB(all_10_15) = 0
% 13.63/2.58 | |
% 13.63/2.58 | | GROUND_INST: instantiating (8) with all_10_16, all_10_14, simplifying with
% 13.63/2.58 | | (14), (16), (31) gives:
% 13.63/2.58 | | (40) rr(all_10_16, all_10_14) = 0
% 13.63/2.59 | |
% 13.63/2.59 | | GROUND_INST: instantiating (axiom_3) with all_10_16, all_10_14, simplifying
% 13.63/2.59 | | with (14), (16), (31) gives:
% 13.63/2.59 | | (41) cB(all_10_14) = 0
% 13.63/2.59 | |
% 13.63/2.59 | | GROUND_INST: instantiating (8) with all_10_16, all_10_13, simplifying with
% 13.63/2.59 | | (14), (17), (32) gives:
% 13.63/2.59 | | (42) rr(all_10_16, all_10_13) = 0
% 13.63/2.59 | |
% 13.63/2.59 | | GROUND_INST: instantiating (axiom_3) with all_10_16, all_10_13, simplifying
% 13.63/2.59 | | with (14), (17), (32) gives:
% 13.63/2.59 | | (43) cB(all_10_13) = 0
% 13.63/2.59 | |
% 13.63/2.59 | | GROUND_INST: instantiating (6) with all_10_9, simplifying with (18), (35)
% 13.63/2.59 | | gives:
% 13.63/2.59 | | (44) ? [v0: int] : ( ~ (v0 = 0) & cB(all_10_9) = v0)
% 13.63/2.59 | |
% 13.63/2.59 | | GROUND_INST: instantiating (6) with all_10_8, simplifying with (19), (37)
% 13.63/2.59 | | gives:
% 13.63/2.59 | | (45) ? [v0: int] : ( ~ (v0 = 0) & cB(all_10_8) = v0)
% 13.63/2.59 | |
% 13.63/2.59 | | GROUND_INST: instantiating (7) with all_10_14, simplifying with (16), (41)
% 13.63/2.59 | | gives:
% 13.63/2.59 | | (46) ? [v0: int] : ( ~ (v0 = 0) & cA(all_10_14) = v0)
% 13.63/2.59 | |
% 13.63/2.59 | | GROUND_INST: instantiating (7) with all_10_13, simplifying with (17), (43)
% 13.63/2.59 | | gives:
% 13.63/2.59 | | (47) ? [v0: int] : ( ~ (v0 = 0) & cA(all_10_13) = v0)
% 13.63/2.59 | |
% 13.63/2.59 | | GROUND_INST: instantiating (33) with all_10_15, all_10_14, all_10_13,
% 13.63/2.59 | | all_10_9, all_10_8, simplifying with (15), (16), (17), (18),
% 13.63/2.59 | | (19), (34), (36), (38), (40), (42) gives:
% 13.63/2.59 | | (48) all_10_8 = all_10_9 | all_10_8 = all_10_13 | all_10_8 = all_10_14 |
% 13.63/2.59 | | all_10_8 = all_10_15 | all_10_9 = all_10_13 | all_10_9 = all_10_14 |
% 13.63/2.59 | | all_10_9 = all_10_15 | all_10_13 = all_10_14 | all_10_13 = all_10_15
% 13.63/2.59 | | | all_10_14 = all_10_15
% 13.63/2.59 | |
% 13.63/2.59 | | DELTA: instantiating (47) with fresh symbol all_31_0 gives:
% 13.63/2.59 | | (49) ~ (all_31_0 = 0) & cA(all_10_13) = all_31_0
% 13.63/2.59 | |
% 13.63/2.59 | | ALPHA: (49) implies:
% 13.63/2.59 | | (50) ~ (all_31_0 = 0)
% 13.63/2.59 | | (51) cA(all_10_13) = all_31_0
% 13.63/2.59 | |
% 13.63/2.59 | | DELTA: instantiating (46) with fresh symbol all_33_0 gives:
% 13.63/2.59 | | (52) ~ (all_33_0 = 0) & cA(all_10_14) = all_33_0
% 13.63/2.59 | |
% 13.63/2.59 | | ALPHA: (52) implies:
% 13.63/2.59 | | (53) ~ (all_33_0 = 0)
% 13.63/2.59 | | (54) cA(all_10_14) = all_33_0
% 13.63/2.59 | |
% 13.63/2.59 | | DELTA: instantiating (45) with fresh symbol all_35_0 gives:
% 13.63/2.59 | | (55) ~ (all_35_0 = 0) & cB(all_10_8) = all_35_0
% 13.63/2.59 | |
% 13.63/2.59 | | ALPHA: (55) implies:
% 13.63/2.59 | | (56) ~ (all_35_0 = 0)
% 13.63/2.59 | | (57) cB(all_10_8) = all_35_0
% 13.63/2.59 | |
% 13.63/2.59 | | DELTA: instantiating (44) with fresh symbol all_37_0 gives:
% 13.63/2.59 | | (58) ~ (all_37_0 = 0) & cB(all_10_9) = all_37_0
% 13.63/2.59 | |
% 13.63/2.59 | | ALPHA: (58) implies:
% 13.63/2.59 | | (59) ~ (all_37_0 = 0)
% 13.63/2.59 | | (60) cB(all_10_9) = all_37_0
% 13.63/2.59 | |
% 13.63/2.59 | | BETA: splitting (48) gives:
% 13.63/2.59 | |
% 13.63/2.59 | | Case 1:
% 13.63/2.59 | | |
% 13.63/2.59 | | | (61) all_10_8 = all_10_9
% 13.63/2.59 | | |
% 13.63/2.59 | | | REDUCE: (27), (61) imply:
% 13.63/2.59 | | | (62) $false
% 13.63/2.59 | | |
% 13.63/2.59 | | | CLOSE: (62) is inconsistent.
% 13.63/2.59 | | |
% 13.63/2.59 | | Case 2:
% 13.63/2.59 | | |
% 13.63/2.59 | | | (63) all_10_8 = all_10_13 | all_10_8 = all_10_14 | all_10_8 = all_10_15
% 13.63/2.59 | | | | all_10_9 = all_10_13 | all_10_9 = all_10_14 | all_10_9 =
% 13.63/2.59 | | | all_10_15 | all_10_13 = all_10_14 | all_10_13 = all_10_15 |
% 13.63/2.59 | | | all_10_14 = all_10_15
% 13.63/2.59 | | |
% 13.63/2.59 | | | BETA: splitting (63) gives:
% 13.63/2.59 | | |
% 13.63/2.59 | | | Case 1:
% 13.63/2.59 | | | |
% 13.63/2.60 | | | | (64) all_10_8 = all_10_13
% 13.63/2.60 | | | |
% 13.63/2.60 | | | | REDUCE: (37), (64) imply:
% 13.63/2.60 | | | | (65) cA(all_10_13) = 0
% 13.63/2.60 | | | |
% 13.63/2.60 | | | | GROUND_INST: instantiating (10) with all_31_0, 0, all_10_13, simplifying
% 13.63/2.60 | | | | with (51), (65) gives:
% 13.63/2.60 | | | | (66) all_31_0 = 0
% 13.63/2.60 | | | |
% 13.63/2.60 | | | | REDUCE: (50), (66) imply:
% 13.63/2.60 | | | | (67) $false
% 13.63/2.60 | | | |
% 13.63/2.60 | | | | CLOSE: (67) is inconsistent.
% 13.63/2.60 | | | |
% 13.63/2.60 | | | Case 2:
% 13.63/2.60 | | | |
% 13.63/2.60 | | | | (68) all_10_8 = all_10_14 | all_10_8 = all_10_15 | all_10_9 =
% 13.63/2.60 | | | | all_10_13 | all_10_9 = all_10_14 | all_10_9 = all_10_15 |
% 13.63/2.60 | | | | all_10_13 = all_10_14 | all_10_13 = all_10_15 | all_10_14 =
% 13.63/2.60 | | | | all_10_15
% 13.63/2.60 | | | |
% 13.63/2.60 | | | | BETA: splitting (68) gives:
% 13.63/2.60 | | | |
% 13.63/2.60 | | | | Case 1:
% 13.63/2.60 | | | | |
% 13.63/2.60 | | | | | (69) all_10_8 = all_10_14
% 13.63/2.60 | | | | |
% 13.63/2.60 | | | | | REDUCE: (37), (69) imply:
% 13.63/2.60 | | | | | (70) cA(all_10_14) = 0
% 13.63/2.60 | | | | |
% 13.63/2.60 | | | | | GROUND_INST: instantiating (10) with all_33_0, 0, all_10_14,
% 13.63/2.60 | | | | | simplifying with (54), (70) gives:
% 13.63/2.60 | | | | | (71) all_33_0 = 0
% 13.63/2.60 | | | | |
% 13.63/2.60 | | | | | REDUCE: (53), (71) imply:
% 13.63/2.60 | | | | | (72) $false
% 13.63/2.60 | | | | |
% 13.63/2.60 | | | | | CLOSE: (72) is inconsistent.
% 13.63/2.60 | | | | |
% 13.63/2.60 | | | | Case 2:
% 13.63/2.60 | | | | |
% 13.63/2.60 | | | | | (73) all_10_8 = all_10_15 | all_10_9 = all_10_13 | all_10_9 =
% 13.63/2.60 | | | | | all_10_14 | all_10_9 = all_10_15 | all_10_13 = all_10_14 |
% 13.63/2.60 | | | | | all_10_13 = all_10_15 | all_10_14 = all_10_15
% 13.63/2.60 | | | | |
% 13.63/2.60 | | | | | BETA: splitting (73) gives:
% 13.63/2.60 | | | | |
% 13.63/2.60 | | | | | Case 1:
% 13.63/2.60 | | | | | |
% 13.63/2.60 | | | | | | (74) all_10_8 = all_10_15
% 13.63/2.60 | | | | | |
% 13.63/2.60 | | | | | | REDUCE: (57), (74) imply:
% 13.63/2.60 | | | | | | (75) cB(all_10_15) = all_35_0
% 13.63/2.60 | | | | | |
% 13.63/2.60 | | | | | | GROUND_INST: instantiating (11) with 0, all_35_0, all_10_15,
% 13.63/2.60 | | | | | | simplifying with (39), (75) gives:
% 13.63/2.60 | | | | | | (76) all_35_0 = 0
% 13.63/2.60 | | | | | |
% 13.63/2.60 | | | | | | REDUCE: (56), (76) imply:
% 13.63/2.60 | | | | | | (77) $false
% 13.63/2.60 | | | | | |
% 13.63/2.60 | | | | | | CLOSE: (77) is inconsistent.
% 13.63/2.60 | | | | | |
% 13.63/2.60 | | | | | Case 2:
% 13.63/2.60 | | | | | |
% 13.63/2.60 | | | | | | (78) all_10_9 = all_10_13 | all_10_9 = all_10_14 | all_10_9 =
% 13.63/2.60 | | | | | | all_10_15 | all_10_13 = all_10_14 | all_10_13 = all_10_15 |
% 13.63/2.60 | | | | | | all_10_14 = all_10_15
% 13.63/2.60 | | | | | |
% 13.63/2.60 | | | | | | BETA: splitting (78) gives:
% 13.63/2.60 | | | | | |
% 13.63/2.60 | | | | | | Case 1:
% 13.63/2.60 | | | | | | |
% 13.63/2.60 | | | | | | | (79) all_10_9 = all_10_13
% 13.63/2.60 | | | | | | |
% 13.63/2.60 | | | | | | | REDUCE: (35), (79) imply:
% 13.63/2.60 | | | | | | | (80) cA(all_10_13) = 0
% 13.63/2.60 | | | | | | |
% 13.63/2.60 | | | | | | | GROUND_INST: instantiating (10) with all_31_0, 0, all_10_13,
% 13.63/2.60 | | | | | | | simplifying with (51), (80) gives:
% 13.63/2.60 | | | | | | | (81) all_31_0 = 0
% 13.63/2.60 | | | | | | |
% 13.63/2.60 | | | | | | | REDUCE: (50), (81) imply:
% 13.63/2.60 | | | | | | | (82) $false
% 13.63/2.60 | | | | | | |
% 13.63/2.60 | | | | | | | CLOSE: (82) is inconsistent.
% 13.63/2.60 | | | | | | |
% 13.63/2.60 | | | | | | Case 2:
% 13.63/2.60 | | | | | | |
% 13.63/2.60 | | | | | | | (83) all_10_9 = all_10_14 | all_10_9 = all_10_15 | all_10_13 =
% 13.63/2.60 | | | | | | | all_10_14 | all_10_13 = all_10_15 | all_10_14 = all_10_15
% 13.63/2.60 | | | | | | |
% 13.63/2.60 | | | | | | | BETA: splitting (83) gives:
% 13.63/2.60 | | | | | | |
% 13.63/2.60 | | | | | | | Case 1:
% 13.63/2.60 | | | | | | | |
% 13.63/2.60 | | | | | | | | (84) all_10_9 = all_10_14
% 13.63/2.60 | | | | | | | |
% 13.63/2.60 | | | | | | | | REDUCE: (35), (84) imply:
% 13.63/2.60 | | | | | | | | (85) cA(all_10_14) = 0
% 13.63/2.60 | | | | | | | |
% 13.63/2.60 | | | | | | | | GROUND_INST: instantiating (10) with all_33_0, 0, all_10_14,
% 13.63/2.60 | | | | | | | | simplifying with (54), (85) gives:
% 13.63/2.60 | | | | | | | | (86) all_33_0 = 0
% 13.63/2.60 | | | | | | | |
% 13.63/2.60 | | | | | | | | REDUCE: (53), (86) imply:
% 13.63/2.60 | | | | | | | | (87) $false
% 13.63/2.60 | | | | | | | |
% 13.63/2.60 | | | | | | | | CLOSE: (87) is inconsistent.
% 13.63/2.60 | | | | | | | |
% 13.63/2.60 | | | | | | | Case 2:
% 13.63/2.60 | | | | | | | |
% 13.63/2.60 | | | | | | | | (88) all_10_9 = all_10_15 | all_10_13 = all_10_14 | all_10_13
% 13.63/2.60 | | | | | | | | = all_10_15 | all_10_14 = all_10_15
% 13.63/2.60 | | | | | | | |
% 13.63/2.60 | | | | | | | | BETA: splitting (88) gives:
% 13.63/2.60 | | | | | | | |
% 13.63/2.60 | | | | | | | | Case 1:
% 13.63/2.60 | | | | | | | | |
% 13.63/2.60 | | | | | | | | | (89) all_10_9 = all_10_15
% 13.63/2.60 | | | | | | | | |
% 13.63/2.60 | | | | | | | | | REDUCE: (60), (89) imply:
% 13.63/2.60 | | | | | | | | | (90) cB(all_10_15) = all_37_0
% 13.63/2.60 | | | | | | | | |
% 13.63/2.60 | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_37_0, all_10_15,
% 13.63/2.60 | | | | | | | | | simplifying with (39), (90) gives:
% 13.63/2.60 | | | | | | | | | (91) all_37_0 = 0
% 13.63/2.60 | | | | | | | | |
% 13.63/2.60 | | | | | | | | | REDUCE: (59), (91) imply:
% 13.63/2.60 | | | | | | | | | (92) $false
% 13.63/2.60 | | | | | | | | |
% 13.63/2.60 | | | | | | | | | CLOSE: (92) is inconsistent.
% 13.63/2.60 | | | | | | | | |
% 13.63/2.60 | | | | | | | | Case 2:
% 13.63/2.60 | | | | | | | | |
% 13.63/2.60 | | | | | | | | | (93) all_10_13 = all_10_14 | all_10_13 = all_10_15 |
% 13.63/2.60 | | | | | | | | | all_10_14 = all_10_15
% 13.63/2.60 | | | | | | | | |
% 13.63/2.60 | | | | | | | | | BETA: splitting (93) gives:
% 13.63/2.60 | | | | | | | | |
% 13.63/2.60 | | | | | | | | | Case 1:
% 13.63/2.60 | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | | (94) all_10_13 = all_10_14
% 13.63/2.60 | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | | REDUCE: (26), (94) imply:
% 13.63/2.60 | | | | | | | | | | (95) $false
% 13.63/2.60 | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | | CLOSE: (95) is inconsistent.
% 13.63/2.60 | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | Case 2:
% 13.63/2.60 | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | | (96) all_10_13 = all_10_15 | all_10_14 = all_10_15
% 13.63/2.60 | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | | BETA: splitting (96) gives:
% 13.63/2.60 | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | | Case 1:
% 13.63/2.60 | | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | | | (97) all_10_13 = all_10_15
% 13.63/2.60 | | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | | | REDUCE: (25), (97) imply:
% 13.63/2.60 | | | | | | | | | | | (98) $false
% 13.63/2.60 | | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | | | CLOSE: (98) is inconsistent.
% 13.63/2.60 | | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | | Case 2:
% 13.63/2.60 | | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | | | (99) all_10_14 = all_10_15
% 13.63/2.60 | | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | | | REDUCE: (24), (99) imply:
% 13.63/2.60 | | | | | | | | | | | (100) $false
% 13.63/2.60 | | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | | | CLOSE: (100) is inconsistent.
% 13.63/2.60 | | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | | End of split
% 13.63/2.60 | | | | | | | | | |
% 13.63/2.60 | | | | | | | | | End of split
% 13.63/2.60 | | | | | | | | |
% 13.63/2.60 | | | | | | | | End of split
% 13.63/2.60 | | | | | | | |
% 13.63/2.60 | | | | | | | End of split
% 13.63/2.60 | | | | | | |
% 13.63/2.60 | | | | | | End of split
% 13.63/2.60 | | | | | |
% 13.63/2.60 | | | | | End of split
% 13.63/2.60 | | | | |
% 13.63/2.60 | | | | End of split
% 13.63/2.60 | | | |
% 13.63/2.60 | | | End of split
% 13.63/2.60 | | |
% 13.63/2.60 | | End of split
% 13.63/2.60 | |
% 13.63/2.60 | Case 2:
% 13.63/2.60 | |
% 13.63/2.60 | | (101) (xsd_string(all_10_5) = all_10_4 & xsd_integer(all_10_5) = all_10_3
% 13.63/2.60 | | & ((all_10_3 = 0 & all_10_4 = 0) | ( ~ (all_10_3 = 0) & ~
% 13.63/2.61 | | (all_10_4 = 0)))) | (cowlThing(all_10_2) = all_10_1 &
% 13.63/2.61 | | cowlNothing(all_10_2) = all_10_0 & ( ~ (all_10_1 = 0) | all_10_0
% 13.63/2.61 | | = 0))
% 13.63/2.61 | |
% 13.63/2.61 | | BETA: splitting (101) gives:
% 13.63/2.61 | |
% 13.63/2.61 | | Case 1:
% 13.63/2.61 | | |
% 13.63/2.61 | | | (102) xsd_string(all_10_5) = all_10_4 & xsd_integer(all_10_5) =
% 13.63/2.61 | | | all_10_3 & ((all_10_3 = 0 & all_10_4 = 0) | ( ~ (all_10_3 = 0) &
% 13.63/2.61 | | | ~ (all_10_4 = 0)))
% 13.63/2.61 | | |
% 13.63/2.61 | | | ALPHA: (102) implies:
% 13.63/2.61 | | | (103) xsd_integer(all_10_5) = all_10_3
% 13.63/2.61 | | | (104) xsd_string(all_10_5) = all_10_4
% 13.63/2.61 | | | (105) (all_10_3 = 0 & all_10_4 = 0) | ( ~ (all_10_3 = 0) & ~ (all_10_4
% 13.63/2.61 | | | = 0))
% 13.63/2.61 | | |
% 13.63/2.61 | | | GROUND_INST: instantiating (4) with all_10_5, all_10_3, simplifying with
% 13.63/2.61 | | | (20), (103) gives:
% 13.63/2.61 | | | (106) all_10_3 = 0 | xsd_string(all_10_5) = 0
% 13.63/2.61 | | |
% 13.63/2.61 | | | GROUND_INST: instantiating (5) with all_10_5, all_10_4, simplifying with
% 13.63/2.61 | | | (20), (104) gives:
% 13.63/2.61 | | | (107) all_10_4 = 0 | xsd_integer(all_10_5) = 0
% 13.63/2.61 | | |
% 13.63/2.61 | | | BETA: splitting (105) gives:
% 13.63/2.61 | | |
% 13.63/2.61 | | | Case 1:
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | (108) all_10_3 = 0 & all_10_4 = 0
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | ALPHA: (108) implies:
% 13.63/2.61 | | | | (109) all_10_4 = 0
% 13.63/2.61 | | | | (110) all_10_3 = 0
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | REDUCE: (104), (109) imply:
% 13.63/2.61 | | | | (111) xsd_string(all_10_5) = 0
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | REDUCE: (103), (110) imply:
% 13.63/2.61 | | | | (112) xsd_integer(all_10_5) = 0
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | REF_CLOSE: (3), (12), (20), (111), (112) are inconsistent by sub-proof
% 13.63/2.61 | | | | #1.
% 13.63/2.61 | | | |
% 13.63/2.61 | | | Case 2:
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | (113) ~ (all_10_3 = 0) & ~ (all_10_4 = 0)
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | ALPHA: (113) implies:
% 13.63/2.61 | | | | (114) ~ (all_10_4 = 0)
% 13.63/2.61 | | | | (115) ~ (all_10_3 = 0)
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | BETA: splitting (107) gives:
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | Case 1:
% 13.63/2.61 | | | | |
% 13.63/2.61 | | | | | (116) xsd_integer(all_10_5) = 0
% 13.63/2.61 | | | | |
% 13.63/2.61 | | | | | BETA: splitting (106) gives:
% 13.63/2.61 | | | | |
% 13.63/2.61 | | | | | Case 1:
% 13.63/2.61 | | | | | |
% 13.63/2.61 | | | | | | (117) xsd_string(all_10_5) = 0
% 13.63/2.61 | | | | | |
% 13.63/2.61 | | | | | | REF_CLOSE: (3), (12), (20), (116), (117) are inconsistent by
% 13.63/2.61 | | | | | | sub-proof #1.
% 13.63/2.61 | | | | | |
% 13.63/2.61 | | | | | Case 2:
% 13.63/2.61 | | | | | |
% 13.63/2.61 | | | | | | (118) all_10_3 = 0
% 13.63/2.61 | | | | | |
% 13.63/2.61 | | | | | | REDUCE: (115), (118) imply:
% 13.63/2.61 | | | | | | (119) $false
% 13.63/2.61 | | | | | |
% 13.63/2.61 | | | | | | CLOSE: (119) is inconsistent.
% 13.63/2.61 | | | | | |
% 13.63/2.61 | | | | | End of split
% 13.63/2.61 | | | | |
% 13.63/2.61 | | | | Case 2:
% 13.63/2.61 | | | | |
% 13.63/2.61 | | | | | (120) all_10_4 = 0
% 13.63/2.61 | | | | |
% 13.63/2.61 | | | | | REDUCE: (114), (120) imply:
% 13.63/2.61 | | | | | (121) $false
% 13.63/2.61 | | | | |
% 13.63/2.61 | | | | | CLOSE: (121) is inconsistent.
% 13.63/2.61 | | | | |
% 13.63/2.61 | | | | End of split
% 13.63/2.61 | | | |
% 13.63/2.61 | | | End of split
% 13.63/2.61 | | |
% 13.63/2.61 | | Case 2:
% 13.63/2.61 | | |
% 13.63/2.61 | | | (122) cowlThing(all_10_2) = all_10_1 & cowlNothing(all_10_2) = all_10_0
% 13.63/2.61 | | | & ( ~ (all_10_1 = 0) | all_10_0 = 0)
% 13.63/2.61 | | |
% 13.63/2.61 | | | ALPHA: (122) implies:
% 13.63/2.61 | | | (123) cowlNothing(all_10_2) = all_10_0
% 13.63/2.61 | | | (124) cowlThing(all_10_2) = all_10_1
% 13.63/2.61 | | | (125) ~ (all_10_1 = 0) | all_10_0 = 0
% 13.63/2.61 | | |
% 13.63/2.61 | | | GROUND_INST: instantiating (2) with all_10_2, all_10_1, simplifying with
% 13.63/2.61 | | | (21), (124) gives:
% 13.63/2.61 | | | (126) all_10_1 = 0
% 13.63/2.61 | | |
% 13.63/2.61 | | | BETA: splitting (125) gives:
% 13.63/2.61 | | |
% 13.63/2.61 | | | Case 1:
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | (127) ~ (all_10_1 = 0)
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | REDUCE: (126), (127) imply:
% 13.63/2.61 | | | | (128) $false
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | CLOSE: (128) is inconsistent.
% 13.63/2.61 | | | |
% 13.63/2.61 | | | Case 2:
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | (129) all_10_0 = 0
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | REDUCE: (123), (129) imply:
% 13.63/2.61 | | | | (130) cowlNothing(all_10_2) = 0
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | GROUND_INST: instantiating (1) with all_10_2, simplifying with (21),
% 13.63/2.61 | | | | (130) gives:
% 13.63/2.61 | | | | (131) $false
% 13.63/2.61 | | | |
% 13.63/2.61 | | | | CLOSE: (131) is inconsistent.
% 13.63/2.61 | | | |
% 13.63/2.61 | | | End of split
% 13.63/2.61 | | |
% 13.63/2.61 | | End of split
% 13.63/2.61 | |
% 13.63/2.61 | End of split
% 13.63/2.61 |
% 13.63/2.61 End of proof
% 13.63/2.61
% 13.63/2.61 Sub-proof #1 shows that the following formulas are inconsistent:
% 13.63/2.61 ----------------------------------------------------------------
% 13.63/2.61 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.63/2.61 (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 13.63/2.61 (2) ! [v0: $i] : ( ~ (xsd_string(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 13.63/2.61 (v1 = 0) & xsd_integer(v0) = v1))
% 13.63/2.61 (3) xsd_integer(all_10_5) = 0
% 13.63/2.61 (4) $i(all_10_5)
% 13.63/2.61 (5) xsd_string(all_10_5) = 0
% 13.63/2.61
% 13.63/2.61 Begin of proof
% 13.63/2.61 |
% 13.63/2.61 | GROUND_INST: instantiating (2) with all_10_5, simplifying with (4), (5) gives:
% 13.63/2.61 | (6) ? [v0: int] : ( ~ (v0 = 0) & xsd_integer(all_10_5) = v0)
% 13.63/2.61 |
% 13.63/2.61 | DELTA: instantiating (6) with fresh symbol all_31_0 gives:
% 13.63/2.61 | (7) ~ (all_31_0 = 0) & xsd_integer(all_10_5) = all_31_0
% 13.63/2.61 |
% 13.63/2.61 | ALPHA: (7) implies:
% 13.63/2.61 | (8) ~ (all_31_0 = 0)
% 13.63/2.61 | (9) xsd_integer(all_10_5) = all_31_0
% 13.63/2.61 |
% 13.63/2.61 | GROUND_INST: instantiating (1) with 0, all_31_0, all_10_5, simplifying with
% 13.63/2.61 | (3), (9) gives:
% 13.63/2.61 | (10) all_31_0 = 0
% 13.63/2.61 |
% 13.63/2.61 | REDUCE: (8), (10) imply:
% 13.63/2.62 | (11) $false
% 13.63/2.62 |
% 13.63/2.62 | CLOSE: (11) is inconsistent.
% 13.63/2.62 |
% 13.63/2.62 End of proof
% 13.63/2.62 % SZS output end Proof for theBenchmark
% 13.63/2.62
% 13.63/2.62 2016ms
%------------------------------------------------------------------------------