TSTP Solution File: KRS070+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS070+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 : n028.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 05:51:08 EDT 2023
% Result : Unsatisfiable 6.49s 1.93s
% Output : Proof 9.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : KRS070+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36 % Computer : n028.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 01:46:54 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.63 ________ _____
% 0.22/0.63 ___ __ \_________(_)________________________________
% 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.63
% 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.63 (2023-06-19)
% 0.22/0.63
% 0.22/0.63 (c) Philipp Rümmer, 2009-2023
% 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.63 Amanda Stjerna.
% 0.22/0.63 Free software under BSD-3-Clause.
% 0.22/0.63
% 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.63
% 0.22/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.65 Running up to 7 provers in parallel.
% 0.22/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.49/1.19 Prover 1: Preprocessing ...
% 2.49/1.19 Prover 4: Preprocessing ...
% 2.92/1.24 Prover 5: Preprocessing ...
% 2.92/1.24 Prover 2: Preprocessing ...
% 2.92/1.24 Prover 6: Preprocessing ...
% 2.92/1.24 Prover 0: Preprocessing ...
% 2.92/1.24 Prover 3: Preprocessing ...
% 5.21/1.72 Prover 5: Proving ...
% 5.21/1.73 Prover 2: Proving ...
% 6.03/1.88 Prover 1: Constructing countermodel ...
% 6.03/1.90 Prover 6: Proving ...
% 6.49/1.92 Prover 3: Constructing countermodel ...
% 6.49/1.93 Prover 5: proved (1260ms)
% 6.49/1.93
% 6.49/1.93 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.49/1.93
% 6.49/1.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.49/1.94 Prover 2: stopped
% 6.49/1.94 Prover 3: stopped
% 6.49/1.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.49/1.94 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.49/1.96 Prover 6: stopped
% 6.49/1.97 Prover 4: Constructing countermodel ...
% 6.49/1.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.84/2.05 Prover 10: Preprocessing ...
% 6.84/2.07 Prover 0: Proving ...
% 6.84/2.07 Prover 0: stopped
% 6.84/2.09 Prover 8: Preprocessing ...
% 6.84/2.09 Prover 7: Preprocessing ...
% 6.84/2.10 Prover 11: Preprocessing ...
% 6.84/2.12 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.84/2.17 Prover 1: gave up
% 6.84/2.18 Prover 13: Preprocessing ...
% 7.62/2.20 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.97/2.22 Prover 10: Warning: ignoring some quantifiers
% 7.97/2.22 Prover 10: Constructing countermodel ...
% 7.97/2.24 Prover 7: Warning: ignoring some quantifiers
% 8.15/2.27 Prover 7: Constructing countermodel ...
% 8.15/2.29 Prover 13: Warning: ignoring some quantifiers
% 8.15/2.31 Prover 13: Constructing countermodel ...
% 8.15/2.31 Prover 16: Preprocessing ...
% 8.63/2.35 Prover 10: Found proof (size 15)
% 8.63/2.35 Prover 4: Found proof (size 31)
% 8.63/2.35 Prover 4: proved (1678ms)
% 8.63/2.35 Prover 10: proved (404ms)
% 8.63/2.35 Prover 7: stopped
% 8.63/2.36 Prover 13: stopped
% 8.91/2.39 Prover 16: Warning: ignoring some quantifiers
% 8.91/2.39 Prover 16: Constructing countermodel ...
% 8.91/2.39 Prover 16: stopped
% 8.91/2.40 Prover 8: Warning: ignoring some quantifiers
% 8.91/2.43 Prover 8: Constructing countermodel ...
% 8.91/2.44 Prover 8: stopped
% 9.24/2.45 Prover 11: Constructing countermodel ...
% 9.24/2.46 Prover 11: stopped
% 9.24/2.46
% 9.24/2.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.24/2.46
% 9.32/2.47 % SZS output start Proof for theBenchmark
% 9.32/2.48 Assumptions after simplification:
% 9.32/2.48 ---------------------------------
% 9.32/2.48
% 9.32/2.48 (axiom_16)
% 9.32/2.51 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rrx(v0, v1) = v2) |
% 9.32/2.51 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rrx4(v0, v1) = v3)) &
% 9.32/2.51 ! [v0: $i] : ! [v1: $i] : ( ~ (rrx4(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 9.32/2.51 rrx(v0, v1) = 0)
% 9.32/2.51
% 9.32/2.51 (axiom_2)
% 9.56/2.53 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~
% 9.56/2.53 (rrx4(v0, v3) = 0) | ~ (rrx3(v0, v2) = 0) | ~ (cUnsatisfiable(v0) = v1) |
% 9.56/2.53 ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: int]
% 9.56/2.53 : ? [v7: int] : ? [v8: int] : ? [v9: int] : ($i(v5) & ((v8 = 0 & v7 = 0 &
% 9.56/2.53 v6 = 0 & rrx3(v0, v5) = 0 & cc2(v5) = 0 & cc1(v5) = 0) | ( ~ (v9 = 0)
% 9.56/2.53 & cc2(v3) = v9) | ( ~ (v4 = 0) & cc1(v2) = v4)))) & ! [v0: $i] : !
% 9.56/2.53 [v1: int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~ (rrx4(v0, v3) = 0) | ~
% 9.56/2.53 (cc1(v2) = 0) | ~ (cUnsatisfiable(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~
% 9.56/2.53 $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8:
% 9.56/2.53 int] : ? [v9: int] : ($i(v5) & ((v8 = 0 & v7 = 0 & v6 = 0 & rrx3(v0, v5)
% 9.56/2.53 = 0 & cc2(v5) = 0 & cc1(v5) = 0) | ( ~ (v9 = 0) & cc2(v3) = v9) | ( ~
% 9.56/2.53 (v4 = 0) & rrx3(v0, v2) = v4)))) & ! [v0: $i] : ! [v1: int] : !
% 9.56/2.53 [v2: $i] : ! [v3: $i] : (v1 = 0 | ~ (rrx3(v0, v2) = 0) | ~ (cc2(v3) = 0) |
% 9.56/2.53 ~ (cUnsatisfiable(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v4:
% 9.56/2.53 int] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9:
% 9.56/2.53 int] : ($i(v5) & ((v8 = 0 & v7 = 0 & v6 = 0 & rrx3(v0, v5) = 0 & cc2(v5) =
% 9.56/2.53 0 & cc1(v5) = 0) | ( ~ (v9 = 0) & rrx4(v0, v3) = v9) | ( ~ (v4 = 0) &
% 9.56/2.53 cc1(v2) = v4)))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : ! [v3:
% 9.56/2.53 $i] : (v1 = 0 | ~ (cc2(v3) = 0) | ~ (cc1(v2) = 0) | ~ (cUnsatisfiable(v0)
% 9.56/2.53 = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: int] : ? [v5: $i] :
% 9.56/2.53 ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ($i(v5) & ((v8 =
% 9.56/2.53 0 & v7 = 0 & v6 = 0 & rrx3(v0, v5) = 0 & cc2(v5) = 0 & cc1(v5) = 0) |
% 9.56/2.53 ( ~ (v9 = 0) & rrx4(v0, v3) = v9) | ( ~ (v4 = 0) & rrx3(v0, v2) = v4))))
% 9.56/2.53 & ! [v0: $i] : ! [v1: $i] : ( ~ (rrx3(v0, v1) = 0) | ~ (cUnsatisfiable(v0)
% 9.56/2.53 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (cc2(v1) = v2
% 9.56/2.53 & cc1(v1) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i]
% 9.56/2.53 : ( ~ (cc2(v1) = 0) | ~ (cUnsatisfiable(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 9.56/2.53 [v2: any] : ? [v3: any] : (rrx3(v0, v1) = v2 & cc1(v1) = v3 & ( ~ (v3 = 0)
% 9.56/2.53 | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (cc1(v1) = 0) | ~
% 9.56/2.53 (cUnsatisfiable(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 9.56/2.53 any] : (rrx3(v0, v1) = v2 & cc2(v1) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) &
% 9.56/2.53 ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 9.56/2.53 (rrx4(v0, v1) = 0 & cc2(v1) = 0 & $i(v1))) & ! [v0: $i] : ( ~
% 9.56/2.53 (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (rrx3(v0, v1) = 0 &
% 9.56/2.53 cc1(v1) = 0 & $i(v1)))
% 9.56/2.53
% 9.56/2.53 (axiom_3)
% 9.56/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (rrx(v0, v2) = 0) | ~
% 9.56/2.53 (rrx(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 9.56/2.53
% 9.56/2.53 (axiom_8)
% 9.56/2.53 cUnsatisfiable(i2003_11_14_17_18_32242) = 0 & $i(i2003_11_14_17_18_32242)
% 9.56/2.53
% 9.56/2.53 (axiom_9)
% 9.56/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rrx(v0, v1) = v2) |
% 9.56/2.53 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rrx3(v0, v1) = v3)) &
% 9.56/2.53 ! [v0: $i] : ! [v1: $i] : ( ~ (rrx3(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 9.56/2.53 rrx(v0, v1) = 0)
% 9.56/2.53
% 9.56/2.53 (function-axioms)
% 9.56/2.54 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 9.56/2.54 [v3: $i] : (v1 = v0 | ~ (rrxa(v3, v2) = v1) | ~ (rrxa(v3, v2) = v0)) & !
% 9.56/2.54 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 9.56/2.54 $i] : (v1 = v0 | ~ (rrx4a(v3, v2) = v1) | ~ (rrx4a(v3, v2) = v0)) & !
% 9.56/2.54 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 9.56/2.54 $i] : (v1 = v0 | ~ (rrx4(v3, v2) = v1) | ~ (rrx4(v3, v2) = v0)) & ! [v0:
% 9.56/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.56/2.54 : (v1 = v0 | ~ (rrx3a(v3, v2) = v1) | ~ (rrx3a(v3, v2) = v0)) & ! [v0:
% 9.56/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.56/2.54 : (v1 = v0 | ~ (rrx3(v3, v2) = v1) | ~ (rrx3(v3, v2) = v0)) & ! [v0:
% 9.56/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.56/2.54 : (v1 = v0 | ~ (rrx2a(v3, v2) = v1) | ~ (rrx2a(v3, v2) = v0)) & ! [v0:
% 9.56/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.56/2.54 : (v1 = v0 | ~ (rrx2(v3, v2) = v1) | ~ (rrx2(v3, v2) = v0)) & ! [v0:
% 9.56/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.56/2.54 : (v1 = v0 | ~ (rrx1a(v3, v2) = v1) | ~ (rrx1a(v3, v2) = v0)) & ! [v0:
% 9.56/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.56/2.54 : (v1 = v0 | ~ (rrx1(v3, v2) = v1) | ~ (rrx1(v3, v2) = v0)) & ! [v0:
% 9.56/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.56/2.54 : (v1 = v0 | ~ (rrx(v3, v2) = v1) | ~ (rrx(v3, v2) = v0)) & ! [v0:
% 9.56/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.56/2.54 ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0:
% 9.56/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.56/2.54 ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0:
% 9.56/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.56/2.54 ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0:
% 9.56/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.56/2.54 ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0:
% 9.56/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.56/2.54 ~ (cc2(v2) = v1) | ~ (cc2(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.56/2.54 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cc1(v2) = v1) | ~
% 9.56/2.54 (cc1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 9.56/2.54 ! [v2: $i] : (v1 = v0 | ~ (cUnsatisfiable(v2) = v1) | ~ (cUnsatisfiable(v2)
% 9.56/2.54 = v0))
% 9.56/2.54
% 9.56/2.54 Further assumptions not needed in the proof:
% 9.56/2.54 --------------------------------------------
% 9.56/2.54 axiom_0, axiom_1, axiom_10, axiom_11, axiom_12, axiom_13, axiom_14, axiom_15,
% 9.56/2.54 axiom_4, axiom_5, axiom_6, axiom_7, cUnsatisfiable_substitution_1,
% 9.56/2.54 cc1_substitution_1, cc2_substitution_1, cowlNothing_substitution_1,
% 9.56/2.54 cowlThing_substitution_1, rrx1_substitution_1, rrx1_substitution_2,
% 9.56/2.54 rrx1a_substitution_1, rrx1a_substitution_2, rrx2_substitution_1,
% 9.56/2.54 rrx2_substitution_2, rrx2a_substitution_1, rrx2a_substitution_2,
% 9.56/2.54 rrx3_substitution_1, rrx3_substitution_2, rrx3a_substitution_1,
% 9.56/2.54 rrx3a_substitution_2, rrx4_substitution_1, rrx4_substitution_2,
% 9.56/2.54 rrx4a_substitution_1, rrx4a_substitution_2, rrx_substitution_1,
% 9.56/2.54 rrx_substitution_2, rrxa_substitution_1, rrxa_substitution_2,
% 9.56/2.54 xsd_integer_substitution_1, xsd_string_substitution_1
% 9.56/2.54
% 9.56/2.54 Those formulas are unsatisfiable:
% 9.56/2.54 ---------------------------------
% 9.56/2.54
% 9.56/2.54 Begin of proof
% 9.56/2.54 |
% 9.56/2.54 | ALPHA: (axiom_2) implies:
% 9.56/2.54 | (1) ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 9.56/2.54 | (rrx3(v0, v1) = 0 & cc1(v1) = 0 & $i(v1)))
% 9.56/2.54 | (2) ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 9.56/2.54 | (rrx4(v0, v1) = 0 & cc2(v1) = 0 & $i(v1)))
% 9.70/2.55 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (cc1(v1) = 0) | ~ (cUnsatisfiable(v0)
% 9.70/2.55 | = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 9.70/2.55 | (rrx3(v0, v1) = v2 & cc2(v1) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 9.70/2.55 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (rrx3(v0, v1) = 0) | ~
% 9.70/2.55 | (cUnsatisfiable(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ?
% 9.70/2.55 | [v3: any] : (cc2(v1) = v2 & cc1(v1) = v3 & ( ~ (v3 = 0) | ~ (v2 =
% 9.70/2.55 | 0))))
% 9.70/2.55 |
% 9.70/2.55 | ALPHA: (axiom_8) implies:
% 9.70/2.55 | (5) $i(i2003_11_14_17_18_32242)
% 9.70/2.55 | (6) cUnsatisfiable(i2003_11_14_17_18_32242) = 0
% 9.70/2.55 |
% 9.70/2.55 | ALPHA: (axiom_9) implies:
% 9.70/2.55 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (rrx3(v0, v1) = 0) | ~ $i(v1) | ~
% 9.70/2.55 | $i(v0) | rrx(v0, v1) = 0)
% 9.70/2.55 |
% 9.70/2.55 | ALPHA: (axiom_16) implies:
% 9.70/2.55 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (rrx4(v0, v1) = 0) | ~ $i(v1) | ~
% 9.70/2.55 | $i(v0) | rrx(v0, v1) = 0)
% 9.70/2.55 |
% 9.70/2.55 | ALPHA: (function-axioms) implies:
% 9.70/2.55 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.70/2.55 | (v1 = v0 | ~ (cc2(v2) = v1) | ~ (cc2(v2) = v0))
% 9.70/2.55 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 9.70/2.55 | : ! [v3: $i] : (v1 = v0 | ~ (rrx3(v3, v2) = v1) | ~ (rrx3(v3, v2) =
% 9.70/2.55 | v0))
% 9.70/2.55 |
% 9.70/2.55 | GROUND_INST: instantiating (2) with i2003_11_14_17_18_32242, simplifying with
% 9.70/2.55 | (5), (6) gives:
% 9.70/2.55 | (11) ? [v0: $i] : (rrx4(i2003_11_14_17_18_32242, v0) = 0 & cc2(v0) = 0 &
% 9.70/2.55 | $i(v0))
% 9.70/2.55 |
% 9.70/2.55 | GROUND_INST: instantiating (1) with i2003_11_14_17_18_32242, simplifying with
% 9.70/2.55 | (5), (6) gives:
% 9.70/2.55 | (12) ? [v0: $i] : (rrx3(i2003_11_14_17_18_32242, v0) = 0 & cc1(v0) = 0 &
% 9.70/2.55 | $i(v0))
% 9.70/2.55 |
% 9.70/2.55 | DELTA: instantiating (12) with fresh symbol all_25_0 gives:
% 9.70/2.55 | (13) rrx3(i2003_11_14_17_18_32242, all_25_0) = 0 & cc1(all_25_0) = 0 &
% 9.70/2.55 | $i(all_25_0)
% 9.70/2.55 |
% 9.70/2.55 | ALPHA: (13) implies:
% 9.70/2.56 | (14) $i(all_25_0)
% 9.70/2.56 | (15) cc1(all_25_0) = 0
% 9.70/2.56 | (16) rrx3(i2003_11_14_17_18_32242, all_25_0) = 0
% 9.70/2.56 |
% 9.70/2.56 | DELTA: instantiating (11) with fresh symbol all_27_0 gives:
% 9.70/2.56 | (17) rrx4(i2003_11_14_17_18_32242, all_27_0) = 0 & cc2(all_27_0) = 0 &
% 9.70/2.56 | $i(all_27_0)
% 9.70/2.56 |
% 9.70/2.56 | ALPHA: (17) implies:
% 9.70/2.56 | (18) $i(all_27_0)
% 9.70/2.56 | (19) cc2(all_27_0) = 0
% 9.70/2.56 | (20) rrx4(i2003_11_14_17_18_32242, all_27_0) = 0
% 9.70/2.56 |
% 9.70/2.56 | GROUND_INST: instantiating (3) with i2003_11_14_17_18_32242, all_25_0,
% 9.70/2.56 | simplifying with (5), (6), (14), (15) gives:
% 9.70/2.56 | (21) ? [v0: any] : ? [v1: any] : (rrx3(i2003_11_14_17_18_32242, all_25_0)
% 9.70/2.56 | = v0 & cc2(all_25_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 9.70/2.56 |
% 9.70/2.56 | GROUND_INST: instantiating (4) with i2003_11_14_17_18_32242, all_25_0,
% 9.70/2.56 | simplifying with (5), (6), (14), (16) gives:
% 9.70/2.56 | (22) ? [v0: any] : ? [v1: any] : (cc2(all_25_0) = v0 & cc1(all_25_0) = v1
% 9.70/2.56 | & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 9.70/2.56 |
% 9.70/2.56 | GROUND_INST: instantiating (7) with i2003_11_14_17_18_32242, all_25_0,
% 9.70/2.56 | simplifying with (5), (14), (16) gives:
% 9.70/2.56 | (23) rrx(i2003_11_14_17_18_32242, all_25_0) = 0
% 9.70/2.56 |
% 9.70/2.56 | GROUND_INST: instantiating (8) with i2003_11_14_17_18_32242, all_27_0,
% 9.70/2.56 | simplifying with (5), (18), (20) gives:
% 9.70/2.56 | (24) rrx(i2003_11_14_17_18_32242, all_27_0) = 0
% 9.70/2.56 |
% 9.70/2.56 | DELTA: instantiating (22) with fresh symbols all_35_0, all_35_1 gives:
% 9.70/2.56 | (25) cc2(all_25_0) = all_35_1 & cc1(all_25_0) = all_35_0 & ( ~ (all_35_0 =
% 9.70/2.56 | 0) | ~ (all_35_1 = 0))
% 9.70/2.56 |
% 9.70/2.56 | ALPHA: (25) implies:
% 9.70/2.56 | (26) cc2(all_25_0) = all_35_1
% 9.70/2.56 |
% 9.70/2.56 | DELTA: instantiating (21) with fresh symbols all_39_0, all_39_1 gives:
% 9.70/2.56 | (27) rrx3(i2003_11_14_17_18_32242, all_25_0) = all_39_1 & cc2(all_25_0) =
% 9.70/2.56 | all_39_0 & ( ~ (all_39_0 = 0) | ~ (all_39_1 = 0))
% 9.70/2.56 |
% 9.70/2.56 | ALPHA: (27) implies:
% 9.70/2.56 | (28) cc2(all_25_0) = all_39_0
% 9.70/2.56 | (29) rrx3(i2003_11_14_17_18_32242, all_25_0) = all_39_1
% 9.70/2.56 | (30) ~ (all_39_0 = 0) | ~ (all_39_1 = 0)
% 9.70/2.56 |
% 9.70/2.56 | GROUND_INST: instantiating (9) with all_35_1, all_39_0, all_25_0, simplifying
% 9.70/2.56 | with (26), (28) gives:
% 9.70/2.56 | (31) all_39_0 = all_35_1
% 9.70/2.56 |
% 9.70/2.56 | GROUND_INST: instantiating (10) with 0, all_39_1, all_25_0,
% 9.70/2.56 | i2003_11_14_17_18_32242, simplifying with (16), (29) gives:
% 9.70/2.56 | (32) all_39_1 = 0
% 9.70/2.56 |
% 9.70/2.56 | BETA: splitting (30) gives:
% 9.70/2.56 |
% 9.70/2.57 | Case 1:
% 9.70/2.57 | |
% 9.70/2.57 | | (33) ~ (all_39_0 = 0)
% 9.70/2.57 | |
% 9.70/2.57 | | REDUCE: (31), (33) imply:
% 9.70/2.57 | | (34) ~ (all_35_1 = 0)
% 9.70/2.57 | |
% 9.70/2.57 | | GROUND_INST: instantiating (axiom_3) with i2003_11_14_17_18_32242, all_25_0,
% 9.70/2.57 | | all_27_0, simplifying with (5), (14), (18), (23), (24) gives:
% 9.70/2.57 | | (35) all_27_0 = all_25_0
% 9.70/2.57 | |
% 9.70/2.57 | | REDUCE: (19), (35) imply:
% 9.70/2.57 | | (36) cc2(all_25_0) = 0
% 9.70/2.57 | |
% 9.70/2.57 | | GROUND_INST: instantiating (9) with all_35_1, 0, all_25_0, simplifying with
% 9.70/2.57 | | (26), (36) gives:
% 9.70/2.57 | | (37) all_35_1 = 0
% 9.70/2.57 | |
% 9.70/2.57 | | REDUCE: (34), (37) imply:
% 9.70/2.57 | | (38) $false
% 9.70/2.57 | |
% 9.70/2.57 | | CLOSE: (38) is inconsistent.
% 9.70/2.57 | |
% 9.70/2.57 | Case 2:
% 9.70/2.57 | |
% 9.70/2.57 | | (39) ~ (all_39_1 = 0)
% 9.70/2.57 | |
% 9.70/2.57 | | REDUCE: (32), (39) imply:
% 9.70/2.57 | | (40) $false
% 9.70/2.57 | |
% 9.70/2.57 | | CLOSE: (40) is inconsistent.
% 9.70/2.57 | |
% 9.70/2.57 | End of split
% 9.70/2.57 |
% 9.70/2.57 End of proof
% 9.70/2.57 % SZS output end Proof for theBenchmark
% 9.70/2.57
% 9.70/2.57 1934ms
%------------------------------------------------------------------------------