TSTP Solution File: KRS082+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS082+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 : n027.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 05:51:10 EDT 2023
% Result : Unsatisfiable 6.41s 1.60s
% Output : Proof 7.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS082+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.34 % Computer : n027.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon Aug 28 02:42:06 EDT 2023
% 0.15/0.34 % 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/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.61 Running up to 7 provers in parallel.
% 0.18/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.21/0.99 Prover 1: Preprocessing ...
% 2.21/0.99 Prover 4: Preprocessing ...
% 2.21/1.03 Prover 3: Preprocessing ...
% 2.21/1.03 Prover 2: Preprocessing ...
% 2.75/1.04 Prover 6: Preprocessing ...
% 2.75/1.04 Prover 0: Preprocessing ...
% 2.75/1.04 Prover 5: Preprocessing ...
% 4.02/1.25 Prover 2: Proving ...
% 4.31/1.26 Prover 5: Proving ...
% 5.07/1.42 Prover 6: Proving ...
% 5.07/1.42 Prover 1: Constructing countermodel ...
% 5.07/1.44 Prover 3: Constructing countermodel ...
% 5.07/1.47 Prover 4: Constructing countermodel ...
% 5.07/1.49 Prover 0: Proving ...
% 5.07/1.56 Prover 3: gave up
% 5.07/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.07/1.57 Prover 1: gave up
% 5.07/1.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.41/1.60 Prover 7: Preprocessing ...
% 6.41/1.60 Prover 2: proved (981ms)
% 6.41/1.60
% 6.41/1.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.41/1.60
% 6.41/1.60 Prover 8: Preprocessing ...
% 6.41/1.60 Prover 5: stopped
% 6.41/1.60 Prover 0: stopped
% 6.41/1.60 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.41/1.60 Prover 6: stopped
% 6.41/1.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.41/1.60 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.41/1.60 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.62/1.63 Prover 11: Preprocessing ...
% 6.62/1.63 Prover 16: Preprocessing ...
% 6.62/1.63 Prover 13: Preprocessing ...
% 6.62/1.64 Prover 10: Preprocessing ...
% 6.62/1.64 Prover 7: Warning: ignoring some quantifiers
% 6.62/1.65 Prover 7: Constructing countermodel ...
% 6.62/1.67 Prover 16: Warning: ignoring some quantifiers
% 6.62/1.67 Prover 13: Warning: ignoring some quantifiers
% 7.07/1.67 Prover 13: Constructing countermodel ...
% 7.07/1.67 Prover 16: Constructing countermodel ...
% 7.07/1.70 Prover 10: Warning: ignoring some quantifiers
% 7.07/1.70 Prover 4: Found proof (size 24)
% 7.07/1.70 Prover 4: proved (1077ms)
% 7.07/1.70 Prover 11: stopped
% 7.07/1.70 Prover 16: stopped
% 7.07/1.70 Prover 13: stopped
% 7.07/1.70 Prover 7: stopped
% 7.07/1.70 Prover 10: Constructing countermodel ...
% 7.07/1.71 Prover 10: stopped
% 7.07/1.72 Prover 8: Warning: ignoring some quantifiers
% 7.07/1.73 Prover 8: Constructing countermodel ...
% 7.07/1.73 Prover 8: stopped
% 7.07/1.73
% 7.07/1.73 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.07/1.73
% 7.07/1.74 % SZS output start Proof for theBenchmark
% 7.07/1.74 Assumptions after simplification:
% 7.07/1.74 ---------------------------------
% 7.07/1.74
% 7.07/1.74 (axiom_2)
% 7.61/1.77 ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 7.61/1.77 $i] : ? [v3: $i] : (rs(v0, v1) = 0 & rr(v1, v2) = 0 & rp(v1, v3) = 0 &
% 7.61/1.77 cowlThing(v3) = 0 & cowlThing(v2) = 0 & $i(v3) & $i(v2) & $i(v1) & ! [v4:
% 7.61/1.77 $i] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (cc(v5) = v6) | ~
% 7.61/1.77 (rp(v1, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v7: int] : ( ~ (v7 = 0) &
% 7.61/1.77 rr(v4, v5) = v7)) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (cc(v4)
% 7.61/1.77 = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & rr(v1, v4) = v6)) &
% 7.61/1.77 ! [v4: $i] : ! [v5: $i] : ( ~ (rr(v4, v5) = 0) | ~ (rp(v1, v4) = 0) | ~
% 7.61/1.77 $i(v5) | ~ $i(v4) | cc(v5) = 0) & ! [v4: $i] : ( ~ (rr(v1, v4) = 0) |
% 7.61/1.77 ~ $i(v4) | cc(v4) = 0) & ! [v4: $i] : ( ~ (rp(v1, v4) = 0) | ~ $i(v4)
% 7.61/1.77 | ? [v5: $i] : (rr(v4, v5) = 0 & cowlThing(v5) = 0 & $i(v5))) & ! [v4:
% 7.61/1.77 $i] : ( ~ (rp(v1, v4) = 0) | ~ $i(v4) | ? [v5: $i] : (rp(v4, v5) = 0 &
% 7.61/1.77 cowlThing(v5) = 0 & $i(v5)))))
% 7.61/1.77
% 7.61/1.77 (axiom_3)
% 7.61/1.77 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (ca(v0) = v1) | ~ $i(v0) | ? [v2:
% 7.61/1.77 int] : ( ~ (v2 = 0) & cUnsatisfiable(v0) = v2)) & ! [v0: $i] : ( ~
% 7.61/1.77 (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ca(v0) = 0)
% 7.61/1.77
% 7.61/1.77 (axiom_4)
% 7.61/1.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (rinvR(v0, v1) =
% 7.61/1.78 0) | ~ (rinvP(v1, v2) = 0) | ~ (rinvS(v2, v3) = 0) | ~ (cc(v0) = 0) |
% 7.61/1.78 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) &
% 7.61/1.78 ca(v3) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 7.61/1.78 ~ (rinvR(v0, v1) = 0) | ~ (rinvP(v1, v2) = 0) | ~ (ca(v3) = 0) | ~
% 7.61/1.78 (cc(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int]
% 7.61/1.78 : ( ~ (v4 = 0) & rinvS(v2, v3) = v4)) & ! [v0: $i] : ! [v1: int] : (v1 = 0
% 7.61/1.78 | ~ (cc(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 7.61/1.78 (rinvR(v0, v2) = 0 & rinvP(v2, v3) = 0 & rinvS(v3, v4) = 0 & ca(v4) = 0 &
% 7.61/1.78 $i(v4) & $i(v3) & $i(v2)))
% 7.61/1.78
% 7.61/1.78 (axiom_5)
% 7.61/1.78 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rinvP(v0, v1) = v2) |
% 7.61/1.78 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rp(v1, v0) = v3)) & !
% 7.61/1.78 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rp(v1, v0) = v2) | ~
% 7.61/1.78 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rinvP(v0, v1) = v3)) & !
% 7.61/1.78 [v0: $i] : ! [v1: $i] : ( ~ (rinvP(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 7.61/1.78 rp(v1, v0) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (rp(v1, v0) = 0) | ~
% 7.61/1.78 $i(v1) | ~ $i(v0) | rinvP(v0, v1) = 0)
% 7.61/1.78
% 7.61/1.78 (axiom_6)
% 7.74/1.79 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rinvR(v0, v1) = v2) |
% 7.74/1.79 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rr(v1, v0) = v3)) & !
% 7.74/1.79 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rr(v1, v0) = v2) | ~
% 7.74/1.79 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rinvR(v0, v1) = v3)) & !
% 7.74/1.79 [v0: $i] : ! [v1: $i] : ( ~ (rinvR(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 7.74/1.79 rr(v1, v0) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (rr(v1, v0) = 0) | ~
% 7.74/1.79 $i(v1) | ~ $i(v0) | rinvR(v0, v1) = 0)
% 7.74/1.79
% 7.74/1.79 (axiom_7)
% 7.74/1.79 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rinvS(v0, v1) = v2) |
% 7.74/1.79 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rs(v1, v0) = v3)) & !
% 7.74/1.79 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rs(v1, v0) = v2) | ~
% 7.74/1.79 $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & rinvS(v0, v1) = v3)) & !
% 7.74/1.79 [v0: $i] : ! [v1: $i] : ( ~ (rinvS(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 7.74/1.79 rs(v1, v0) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (rs(v1, v0) = 0) | ~
% 7.74/1.79 $i(v1) | ~ $i(v0) | rinvS(v0, v1) = 0)
% 7.74/1.79
% 7.74/1.79 (axiom_9)
% 7.74/1.79 cUnsatisfiable(i2003_11_14_17_19_28752) = 0 & $i(i2003_11_14_17_19_28752)
% 7.74/1.79
% 7.74/1.79 (function-axioms)
% 7.74/1.79 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.74/1.79 [v3: $i] : (v1 = v0 | ~ (rinvR(v3, v2) = v1) | ~ (rinvR(v3, v2) = v0)) & !
% 7.74/1.79 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.74/1.79 $i] : (v1 = v0 | ~ (rinvP(v3, v2) = v1) | ~ (rinvP(v3, v2) = v0)) & !
% 7.74/1.79 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.74/1.79 $i] : (v1 = v0 | ~ (rinvS(v3, v2) = v1) | ~ (rinvS(v3, v2) = v0)) & !
% 7.74/1.79 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.74/1.79 $i] : (v1 = v0 | ~ (rs(v3, v2) = v1) | ~ (rs(v3, v2) = v0)) & ! [v0:
% 7.74/1.79 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.74/1.79 : (v1 = v0 | ~ (rr(v3, v2) = v1) | ~ (rr(v3, v2) = v0)) & ! [v0:
% 7.74/1.79 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.74/1.79 : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) & ! [v0:
% 7.74/1.79 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.74/1.79 ~ (ca(v2) = v1) | ~ (ca(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.74/1.79 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cUnsatisfiable(v2) = v1) |
% 7.74/1.79 ~ (cUnsatisfiable(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.74/1.79 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cc(v2) = v1) | ~ (cc(v2)
% 7.74/1.79 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 7.74/1.79 $i] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & !
% 7.74/1.79 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 7.74/1.79 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0:
% 7.74/1.79 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.74/1.79 ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0:
% 7.74/1.79 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.74/1.79 ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 7.74/1.79
% 7.74/1.79 Further assumptions not needed in the proof:
% 7.74/1.79 --------------------------------------------
% 7.74/1.79 axiom_0, axiom_1, axiom_8
% 7.74/1.79
% 7.74/1.79 Those formulas are unsatisfiable:
% 7.74/1.79 ---------------------------------
% 7.74/1.79
% 7.74/1.79 Begin of proof
% 7.74/1.80 |
% 7.74/1.80 | ALPHA: (axiom_3) implies:
% 7.74/1.80 | (1) ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) | ~ $i(v0) | ca(v0) = 0)
% 7.74/1.80 |
% 7.74/1.80 | ALPHA: (axiom_4) implies:
% 7.74/1.80 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (rinvR(v0,
% 7.74/1.80 | v1) = 0) | ~ (rinvP(v1, v2) = 0) | ~ (ca(v3) = 0) | ~ (cc(v0)
% 7.74/1.80 | = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int]
% 7.74/1.80 | : ( ~ (v4 = 0) & rinvS(v2, v3) = v4))
% 7.74/1.80 |
% 7.74/1.80 | ALPHA: (axiom_5) implies:
% 7.74/1.80 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (rp(v1, v0) = 0) | ~ $i(v1) | ~
% 7.74/1.80 | $i(v0) | rinvP(v0, v1) = 0)
% 7.74/1.80 |
% 7.74/1.80 | ALPHA: (axiom_6) implies:
% 7.74/1.80 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (rr(v1, v0) = 0) | ~ $i(v1) | ~
% 7.74/1.80 | $i(v0) | rinvR(v0, v1) = 0)
% 7.74/1.80 |
% 7.74/1.80 | ALPHA: (axiom_7) implies:
% 7.74/1.80 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (rs(v1, v0) = 0) | ~ $i(v1) | ~
% 7.74/1.80 | $i(v0) | rinvS(v0, v1) = 0)
% 7.74/1.80 |
% 7.74/1.80 | ALPHA: (axiom_9) implies:
% 7.74/1.80 | (6) $i(i2003_11_14_17_19_28752)
% 7.74/1.80 | (7) cUnsatisfiable(i2003_11_14_17_19_28752) = 0
% 7.74/1.80 |
% 7.74/1.80 | ALPHA: (function-axioms) implies:
% 7.74/1.80 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.74/1.80 | ! [v3: $i] : (v1 = v0 | ~ (rinvS(v3, v2) = v1) | ~ (rinvS(v3, v2) =
% 7.74/1.80 | v0))
% 7.74/1.80 |
% 7.74/1.81 | GROUND_INST: instantiating (1) with i2003_11_14_17_19_28752, simplifying with
% 7.74/1.81 | (6), (7) gives:
% 7.74/1.81 | (9) ca(i2003_11_14_17_19_28752) = 0
% 7.74/1.81 |
% 7.74/1.81 | GROUND_INST: instantiating (axiom_2) with i2003_11_14_17_19_28752, simplifying
% 7.74/1.81 | with (6), (7) gives:
% 7.74/1.81 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (rs(i2003_11_14_17_19_28752,
% 7.74/1.81 | v0) = 0 & rr(v0, v1) = 0 & rp(v0, v2) = 0 & cowlThing(v2) = 0 &
% 7.74/1.81 | cowlThing(v1) = 0 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4:
% 7.74/1.81 | $i] : ! [v5: int] : (v5 = 0 | ~ (cc(v4) = v5) | ~ (rp(v0, v3) =
% 7.74/1.81 | 0) | ~ $i(v4) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = 0) &
% 7.74/1.81 | rr(v3, v4) = v6)) & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 7.74/1.81 | (cc(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & rr(v0,
% 7.74/1.81 | v3) = v5)) & ! [v3: $i] : ! [v4: $i] : ( ~ (rr(v3, v4) = 0)
% 7.74/1.81 | | ~ (rp(v0, v3) = 0) | ~ $i(v4) | ~ $i(v3) | cc(v4) = 0) & !
% 7.74/1.81 | [v3: $i] : ( ~ (rr(v0, v3) = 0) | ~ $i(v3) | cc(v3) = 0) & ! [v3:
% 7.74/1.81 | $i] : ( ~ (rp(v0, v3) = 0) | ~ $i(v3) | ? [v4: $i] : (rr(v3, v4)
% 7.74/1.81 | = 0 & cowlThing(v4) = 0 & $i(v4))) & ! [v3: $i] : ( ~ (rp(v0,
% 7.74/1.81 | v3) = 0) | ~ $i(v3) | ? [v4: $i] : (rp(v3, v4) = 0 &
% 7.74/1.81 | cowlThing(v4) = 0 & $i(v4))))
% 7.74/1.81 |
% 7.74/1.81 | DELTA: instantiating (10) with fresh symbols all_19_0, all_19_1, all_19_2
% 7.74/1.81 | gives:
% 7.74/1.81 | (11) rs(i2003_11_14_17_19_28752, all_19_2) = 0 & rr(all_19_2, all_19_1) = 0
% 7.74/1.81 | & rp(all_19_2, all_19_0) = 0 & cowlThing(all_19_0) = 0 &
% 7.74/1.81 | cowlThing(all_19_1) = 0 & $i(all_19_0) & $i(all_19_1) & $i(all_19_2) &
% 7.74/1.81 | ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (cc(v1) = v2)
% 7.74/1.81 | | ~ (rp(all_19_2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] :
% 7.74/1.81 | ( ~ (v3 = 0) & rr(v0, v1) = v3)) & ! [v0: $i] : ! [v1: int] : (v1
% 7.74/1.81 | = 0 | ~ (cc(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 7.74/1.81 | rr(all_19_2, v0) = v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ (rr(v0,
% 7.74/1.81 | v1) = 0) | ~ (rp(all_19_2, v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 7.74/1.81 | cc(v1) = 0) & ! [v0: $i] : ( ~ (rr(all_19_2, v0) = 0) | ~ $i(v0) |
% 7.74/1.81 | cc(v0) = 0) & ! [v0: $i] : ( ~ (rp(all_19_2, v0) = 0) | ~ $i(v0) |
% 7.74/1.81 | ? [v1: $i] : (rr(v0, v1) = 0 & cowlThing(v1) = 0 & $i(v1))) & !
% 7.74/1.81 | [v0: $i] : ( ~ (rp(all_19_2, v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 7.74/1.81 | (rp(v0, v1) = 0 & cowlThing(v1) = 0 & $i(v1)))
% 7.74/1.81 |
% 7.74/1.81 | ALPHA: (11) implies:
% 7.74/1.81 | (12) $i(all_19_2)
% 7.74/1.81 | (13) $i(all_19_0)
% 7.74/1.81 | (14) rp(all_19_2, all_19_0) = 0
% 7.74/1.81 | (15) rs(i2003_11_14_17_19_28752, all_19_2) = 0
% 7.74/1.82 | (16) ! [v0: $i] : ( ~ (rp(all_19_2, v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 7.74/1.82 | (rr(v0, v1) = 0 & cowlThing(v1) = 0 & $i(v1)))
% 7.74/1.82 | (17) ! [v0: $i] : ! [v1: $i] : ( ~ (rr(v0, v1) = 0) | ~ (rp(all_19_2,
% 7.74/1.82 | v0) = 0) | ~ $i(v1) | ~ $i(v0) | cc(v1) = 0)
% 7.74/1.82 |
% 7.74/1.82 | GROUND_INST: instantiating (16) with all_19_0, simplifying with (13), (14)
% 7.74/1.82 | gives:
% 7.74/1.82 | (18) ? [v0: $i] : (rr(all_19_0, v0) = 0 & cowlThing(v0) = 0 & $i(v0))
% 7.74/1.82 |
% 7.74/1.82 | GROUND_INST: instantiating (3) with all_19_0, all_19_2, simplifying with (12),
% 7.74/1.82 | (13), (14) gives:
% 7.74/1.82 | (19) rinvP(all_19_0, all_19_2) = 0
% 7.74/1.82 |
% 7.74/1.82 | GROUND_INST: instantiating (5) with all_19_2, i2003_11_14_17_19_28752,
% 7.74/1.82 | simplifying with (6), (12), (15) gives:
% 7.74/1.82 | (20) rinvS(all_19_2, i2003_11_14_17_19_28752) = 0
% 7.74/1.82 |
% 7.74/1.82 | DELTA: instantiating (18) with fresh symbol all_30_0 gives:
% 7.74/1.82 | (21) rr(all_19_0, all_30_0) = 0 & cowlThing(all_30_0) = 0 & $i(all_30_0)
% 7.74/1.82 |
% 7.74/1.82 | ALPHA: (21) implies:
% 7.74/1.82 | (22) $i(all_30_0)
% 7.74/1.82 | (23) rr(all_19_0, all_30_0) = 0
% 7.74/1.82 |
% 7.74/1.82 | GROUND_INST: instantiating (17) with all_19_0, all_30_0, simplifying with
% 7.74/1.82 | (13), (14), (22), (23) gives:
% 7.74/1.82 | (24) cc(all_30_0) = 0
% 7.74/1.82 |
% 7.74/1.82 | GROUND_INST: instantiating (4) with all_30_0, all_19_0, simplifying with (13),
% 7.74/1.82 | (22), (23) gives:
% 7.74/1.82 | (25) rinvR(all_30_0, all_19_0) = 0
% 7.74/1.82 |
% 7.74/1.82 | GROUND_INST: instantiating (2) with all_30_0, all_19_0, all_19_2,
% 7.74/1.82 | i2003_11_14_17_19_28752, simplifying with (6), (9), (12), (13),
% 7.74/1.82 | (19), (22), (24), (25) gives:
% 7.74/1.82 | (26) ? [v0: int] : ( ~ (v0 = 0) & rinvS(all_19_2, i2003_11_14_17_19_28752)
% 7.74/1.82 | = v0)
% 7.74/1.82 |
% 7.74/1.82 | DELTA: instantiating (26) with fresh symbol all_44_0 gives:
% 7.74/1.82 | (27) ~ (all_44_0 = 0) & rinvS(all_19_2, i2003_11_14_17_19_28752) =
% 7.74/1.82 | all_44_0
% 7.74/1.82 |
% 7.74/1.82 | ALPHA: (27) implies:
% 7.74/1.82 | (28) ~ (all_44_0 = 0)
% 7.74/1.82 | (29) rinvS(all_19_2, i2003_11_14_17_19_28752) = all_44_0
% 7.74/1.82 |
% 7.74/1.82 | GROUND_INST: instantiating (8) with 0, all_44_0, i2003_11_14_17_19_28752,
% 7.74/1.82 | all_19_2, simplifying with (20), (29) gives:
% 7.74/1.82 | (30) all_44_0 = 0
% 7.74/1.82 |
% 7.74/1.82 | REDUCE: (28), (30) imply:
% 7.74/1.82 | (31) $false
% 7.74/1.82 |
% 7.74/1.82 | CLOSE: (31) is inconsistent.
% 7.74/1.82 |
% 7.74/1.82 End of proof
% 7.74/1.82 % SZS output end Proof for theBenchmark
% 7.74/1.82
% 7.74/1.82 1225ms
%------------------------------------------------------------------------------