TSTP Solution File: LCL638+1.005 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL638+1.005 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n014.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 08:11:51 EDT 2023
% Result : Theorem 32.80s 5.17s
% Output : Proof 33.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL638+1.005 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n014.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 : Thu Aug 24 18:03:04 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.15/1.26 Prover 4: Preprocessing ...
% 4.15/1.26 Prover 1: Preprocessing ...
% 4.15/1.29 Prover 3: Preprocessing ...
% 4.15/1.29 Prover 5: Preprocessing ...
% 4.15/1.29 Prover 0: Preprocessing ...
% 4.15/1.29 Prover 2: Preprocessing ...
% 4.15/1.29 Prover 6: Preprocessing ...
% 7.22/1.73 Prover 2: Constructing countermodel ...
% 8.48/1.85 Prover 5: Constructing countermodel ...
% 10.16/2.20 Prover 6: Proving ...
% 10.16/2.20 Prover 0: Proving ...
% 10.16/2.23 Prover 1: Constructing countermodel ...
% 10.16/2.24 Prover 3: Constructing countermodel ...
% 10.16/2.24 Prover 4: Constructing countermodel ...
% 32.80/5.16 Prover 1: Found proof (size 69)
% 32.80/5.16 Prover 1: proved (4539ms)
% 32.80/5.16 Prover 5: stopped
% 32.80/5.16 Prover 2: stopped
% 32.80/5.16 Prover 3: stopped
% 32.80/5.17 Prover 4: stopped
% 32.80/5.17 Prover 6: stopped
% 32.80/5.17 Prover 0: stopped
% 32.80/5.17
% 32.80/5.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.80/5.17
% 32.80/5.18 % SZS output start Proof for theBenchmark
% 32.80/5.18 Assumptions after simplification:
% 32.80/5.18 ---------------------------------
% 32.80/5.18
% 32.80/5.18 (main)
% 33.57/5.27 ? [v0: $i] : ($i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (p1(v1) =
% 33.57/5.27 v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & r1(v0, v1) = v3) | !
% 33.57/5.27 [v3: $i] : ( ~ (r1(v1, v3) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: int] :
% 33.57/5.27 ( ~ (v5 = 0) & r1(v3, v4) = 0 & p1(v4) = v5 & $i(v4)))) & ! [v1: $i] :
% 33.57/5.27 ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0)
% 33.57/5.27 & r1(v1, v2) = 0 & p1(v2) = v3 & $i(v2)) | ! [v2: $i] : ( ~ (r1(v1, v2)
% 33.57/5.27 = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (p1(v3) =
% 33.57/5.27 v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & r1(v2, v3) = v5))))
% 33.57/5.27 & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : (r1(v1, v2)
% 33.57/5.27 = 0 & $i(v2) & ! [v3: $i] : ( ~ (p1(v3) = 0) | ~ $i(v3) | ? [v4: int]
% 33.57/5.27 : ( ~ (v4 = 0) & r1(v2, v3) = v4))) | ! [v2: $i] : ( ~ (r1(v1, v2) =
% 33.57/5.27 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ?
% 33.57/5.27 [v4: $i] : (r1(v3, v4) = 0 & p1(v4) = 0 & $i(v4))))) & ! [v1: $i] : (
% 33.57/5.27 ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : (r1(v1, v2) = 0 & $i(v2)))
% 33.57/5.27 & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3:
% 33.57/5.27 int] : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 =
% 33.57/5.27 0) & r1(v1, v2) = v4) | ! [v4: $i] : ( ~ (r1(v2, v4) = 0) | ~
% 33.57/5.27 $i(v4) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & r1(v4, v5) = 0 &
% 33.57/5.27 p1(v5) = v6 & $i(v5))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~
% 33.57/5.27 $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ? [v3: $i] : ?
% 33.57/5.27 [v4: int] : ( ~ (v4 = 0) & r1(v2, v3) = 0 & p1(v3) = v4 & $i(v3)) | !
% 33.57/5.27 [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ! [v5: int]
% 33.57/5.27 : (v5 = 0 | ~ (p1(v4) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0)
% 33.57/5.27 & r1(v3, v4) = v6))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~
% 33.57/5.27 $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ? [v3: $i] :
% 33.57/5.27 (r1(v2, v3) = 0 & $i(v3) & ! [v4: $i] : ( ~ (p1(v4) = 0) | ~ $i(v4) |
% 33.57/5.28 ? [v5: int] : ( ~ (v5 = 0) & r1(v3, v4) = v5))) | ! [v3: $i] : ( ~
% 33.57/5.28 (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3, v4) = 0) | ~
% 33.57/5.28 $i(v4) | ? [v5: $i] : (r1(v4, v5) = 0 & p1(v5) = 0 & $i(v5)))))) &
% 33.57/5.28 ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1,
% 33.57/5.28 v2) = 0) | ~ $i(v2) | ? [v3: $i] : (r1(v2, v3) = 0 & $i(v3)))) &
% 33.57/5.28 ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1,
% 33.57/5.28 v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 33.57/5.28 (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & r1(v2, v3) =
% 33.57/5.28 v5) | ! [v5: $i] : ( ~ (r1(v3, v5) = 0) | ~ $i(v5) | ? [v6: $i] :
% 33.57/5.28 ? [v7: int] : ( ~ (v7 = 0) & r1(v5, v6) = 0 & p1(v6) = v7 &
% 33.57/5.28 $i(v6)))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | !
% 33.57/5.28 [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2,
% 33.57/5.28 v3) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 33.57/5.28 r1(v3, v4) = 0 & p1(v4) = v5 & $i(v4)) | ! [v4: $i] : ( ~ (r1(v3,
% 33.57/5.28 v4) = 0) | ~ $i(v4) | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~
% 33.57/5.28 (p1(v5) = v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & r1(v4,
% 33.57/5.28 v5) = v7)))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~
% 33.57/5.28 $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : (
% 33.57/5.28 ~ (r1(v2, v3) = 0) | ~ $i(v3) | ? [v4: $i] : (r1(v3, v4) = 0 &
% 33.57/5.28 $i(v4) & ! [v5: $i] : ( ~ (p1(v5) = 0) | ~ $i(v5) | ? [v6: int] :
% 33.57/5.28 ( ~ (v6 = 0) & r1(v4, v5) = v6))) | ! [v4: $i] : ( ~ (r1(v3, v4)
% 33.57/5.28 = 0) | ~ $i(v4) | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~ $i(v5)
% 33.57/5.28 | ? [v6: $i] : (r1(v5, v6) = 0 & p1(v6) = 0 & $i(v6))))))) & !
% 33.57/5.28 [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2)
% 33.57/5.28 = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ?
% 33.57/5.28 [v4: $i] : (r1(v3, v4) = 0 & $i(v4))))) & ! [v1: $i] : ( ~ (r1(v0,
% 33.57/5.28 v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2)
% 33.57/5.28 | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ! [v5:
% 33.57/5.28 int] : (v5 = 0 | ~ (p1(v4) = v5) | ~ $i(v4) | ? [v6: int] : ( ~
% 33.57/5.28 (v6 = 0) & r1(v3, v4) = v6) | ! [v6: $i] : ( ~ (r1(v4, v6) = 0) |
% 33.57/5.28 ~ $i(v6) | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & r1(v6, v7)
% 33.57/5.28 = 0 & p1(v7) = v8 & $i(v7))))))) & ! [v1: $i] : ( ~ (r1(v0, v1)
% 33.57/5.28 = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | !
% 33.57/5.28 [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3,
% 33.57/5.28 v4) = 0) | ~ $i(v4) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0)
% 33.57/5.28 & r1(v4, v5) = 0 & p1(v5) = v6 & $i(v5)) | ! [v5: $i] : ( ~
% 33.57/5.28 (r1(v4, v5) = 0) | ~ $i(v5) | ! [v6: $i] : ! [v7: int] : (v7 =
% 33.57/5.28 0 | ~ (p1(v6) = v7) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) &
% 33.57/5.28 r1(v5, v6) = v8))))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) |
% 33.57/5.28 ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] :
% 33.57/5.28 ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3, v4) = 0) |
% 33.57/5.28 ~ $i(v4) | ? [v5: $i] : (r1(v4, v5) = 0 & $i(v5) & ! [v6: $i] : (
% 33.57/5.28 ~ (p1(v6) = 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) &
% 33.57/5.28 r1(v5, v6) = v7))) | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~
% 33.57/5.28 $i(v5) | ! [v6: $i] : ( ~ (r1(v5, v6) = 0) | ~ $i(v6) | ? [v7:
% 33.57/5.28 $i] : (r1(v6, v7) = 0 & p1(v7) = 0 & $i(v7)))))))) & ! [v1:
% 33.57/5.28 $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) =
% 33.57/5.28 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | !
% 33.57/5.28 [v4: $i] : ( ~ (r1(v3, v4) = 0) | ~ $i(v4) | ? [v5: $i] : (r1(v4,
% 33.57/5.28 v5) = 0 & $i(v5)))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~
% 33.57/5.28 $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : (
% 33.57/5.28 ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3, v4) = 0) |
% 33.57/5.28 ~ $i(v4) | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (p1(v5) = v6) |
% 33.57/5.28 ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & r1(v4, v5) = v7) | !
% 33.57/5.28 [v7: $i] : ( ~ (r1(v5, v7) = 0) | ~ $i(v7) | ? [v8: $i] : ?
% 33.57/5.28 [v9: int] : ( ~ (v9 = 0) & r1(v7, v8) = 0 & p1(v8) = v9 &
% 33.57/5.28 $i(v8)))))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1)
% 33.57/5.28 | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~
% 33.57/5.28 (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3, v4) = 0) | ~
% 33.57/5.28 $i(v4) | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~ $i(v5) | ? [v6:
% 33.57/5.28 $i] : ? [v7: int] : ( ~ (v7 = 0) & r1(v5, v6) = 0 & p1(v6) = v7
% 33.57/5.28 & $i(v6)) | ! [v6: $i] : ( ~ (r1(v5, v6) = 0) | ~ $i(v6) | !
% 33.57/5.28 [v7: $i] : ! [v8: int] : (v8 = 0 | ~ (p1(v7) = v8) | ~ $i(v7)
% 33.57/5.28 | ? [v9: int] : ( ~ (v9 = 0) & r1(v6, v7) = v9)))))))) & !
% 33.57/5.28 [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2)
% 33.57/5.28 = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | !
% 33.57/5.28 [v4: $i] : ( ~ (r1(v3, v4) = 0) | ~ $i(v4) | ! [v5: $i] : ( ~
% 33.57/5.28 (r1(v4, v5) = 0) | ~ $i(v5) | ? [v6: $i] : (r1(v5, v6) = 0 &
% 33.57/5.28 $i(v6) & ! [v7: $i] : ( ~ (p1(v7) = 0) | ~ $i(v7) | ? [v8:
% 33.57/5.28 int] : ( ~ (v8 = 0) & r1(v6, v7) = v8))) | ! [v6: $i] : ( ~
% 33.57/5.28 (r1(v5, v6) = 0) | ~ $i(v6) | ! [v7: $i] : ( ~ (r1(v6, v7) =
% 33.57/5.28 0) | ~ $i(v7) | ? [v8: $i] : (r1(v7, v8) = 0 & p1(v8) = 0
% 33.57/5.28 & $i(v8))))))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~
% 33.57/5.28 $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : (
% 33.57/5.28 ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3, v4) = 0) |
% 33.57/5.28 ~ $i(v4) | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~ $i(v5) | ? [v6:
% 33.57/5.28 $i] : (r1(v5, v6) = 0 & $i(v6))))))) & ! [v1: $i] : ( ~ (r1(v0,
% 33.57/5.28 v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2)
% 33.57/5.28 | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~
% 33.57/5.28 (r1(v3, v4) = 0) | ~ $i(v4) | ! [v5: $i] : ( ~ (p1(v5) = 0) | ~
% 33.57/5.28 $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & r1(v4, v5) = v6) | ! [v6:
% 33.57/5.28 $i] : ( ~ (r1(v5, v6) = 0) | ~ $i(v6) | ? [v7: $i] : (r1(v6,
% 33.57/5.28 v7) = 0 & p1(v7) = 0 & $i(v7)))))))) & ! [v1: $i] : ( ~
% 33.57/5.28 (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~
% 33.57/5.28 $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] :
% 33.57/5.28 ( ~ (p1(v4) = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & r1(v3,
% 33.57/5.28 v4) = v5) | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~ $i(v5) | ?
% 33.57/5.28 [v6: $i] : (r1(v5, v6) = 0 & p1(v6) = 0 & $i(v6))))))) & ! [v1:
% 33.57/5.28 $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) =
% 33.57/5.28 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (p1(v3) = 0) | ~ $i(v3) | ? [v4:
% 33.57/5.28 int] : ( ~ (v4 = 0) & r1(v2, v3) = v4) | ! [v4: $i] : ( ~ (r1(v3,
% 33.57/5.28 v4) = 0) | ~ $i(v4) | ? [v5: $i] : (r1(v4, v5) = 0 & p1(v5) =
% 33.57/5.28 0 & $i(v5)))))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) |
% 33.57/5.28 ! [v2: $i] : ( ~ (p1(v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 33.57/5.28 r1(v1, v2) = v3) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ?
% 33.57/5.28 [v4: $i] : (r1(v3, v4) = 0 & p1(v4) = 0 & $i(v4))))) & ! [v1: $i] : (
% 33.57/5.28 ~ (p1(v1) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & r1(v0, v1) =
% 33.57/5.28 v2) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ? [v3: $i] :
% 33.57/5.28 (r1(v2, v3) = 0 & p1(v3) = 0 & $i(v3)))) & ? [v1: $i] : (r1(v0, v1) = 0
% 33.57/5.28 & $i(v1) & ? [v2: $i] : (r1(v1, v2) = 0 & $i(v2) & ? [v3: $i] : (r1(v2,
% 33.57/5.28 v3) = 0 & $i(v3) & ? [v4: $i] : (r1(v3, v4) = 0 & $i(v4) & ? [v5:
% 33.57/5.28 $i] : ? [v6: int] : ( ~ (v6 = 0) & r1(v4, v5) = 0 & p1(v5) = v6 &
% 33.57/5.28 $i(v5) & ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ (p1(v7) = v8) |
% 33.57/5.28 ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & r1(v5, v7) =
% 33.57/5.28 v9))))))))
% 33.57/5.28
% 33.57/5.28 (function-axioms)
% 33.57/5.29 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 33.57/5.29 [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) & ! [v0:
% 33.57/5.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 33.57/5.29 ~ (p1(v2) = v1) | ~ (p1(v2) = v0))
% 33.57/5.29
% 33.57/5.29 Those formulas are unsatisfiable:
% 33.57/5.29 ---------------------------------
% 33.57/5.29
% 33.57/5.29 Begin of proof
% 33.57/5.29 |
% 33.57/5.29 | ALPHA: (function-axioms) implies:
% 33.57/5.29 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 33.57/5.29 | ! [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0))
% 33.57/5.29 |
% 33.57/5.29 | DELTA: instantiating (main) with fresh symbol all_3_0 gives:
% 33.76/5.32 | (2) $i(all_3_0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) |
% 33.76/5.32 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & r1(all_3_0, v0) = v2) | !
% 33.76/5.32 | [v2: $i] : ( ~ (r1(v0, v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 33.76/5.32 | int] : ( ~ (v4 = 0) & r1(v2, v3) = 0 & p1(v3) = v4 & $i(v3)))) &
% 33.76/5.32 | ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 33.76/5.32 | [v2: int] : ( ~ (v2 = 0) & r1(v0, v1) = 0 & p1(v1) = v2 & $i(v1)) |
% 33.76/5.32 | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3:
% 33.76/5.32 | int] : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : (
% 33.76/5.32 | ~ (v4 = 0) & r1(v1, v2) = v4)))) & ! [v0: $i] : ( ~
% 33.76/5.32 | (r1(all_3_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] : (r1(v0, v1) = 0 &
% 33.76/5.32 | $i(v1) & ! [v2: $i] : ( ~ (p1(v2) = 0) | ~ $i(v2) | ? [v3: int]
% 33.76/5.32 | : ( ~ (v3 = 0) & r1(v1, v2) = v3))) | ! [v1: $i] : ( ~ (r1(v0,
% 33.76/5.32 | v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~
% 33.76/5.32 | $i(v2) | ? [v3: $i] : (r1(v2, v3) = 0 & p1(v3) = 0 & $i(v3)))))
% 33.76/5.32 | & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 33.76/5.32 | (r1(v0, v1) = 0 & $i(v1))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0)
% 33.76/5.32 | | ~ $i(v0) | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (p1(v1) = v2)
% 33.76/5.32 | | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & r1(v0, v1) = v3) | !
% 33.76/5.32 | [v3: $i] : ( ~ (r1(v1, v3) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5:
% 33.76/5.32 | int] : ( ~ (v5 = 0) & r1(v3, v4) = 0 & p1(v4) = v5 & $i(v4)))))
% 33.76/5.32 | & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : (
% 33.76/5.32 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] : ( ~
% 33.76/5.32 | (v3 = 0) & r1(v1, v2) = 0 & p1(v2) = v3 & $i(v2)) | ! [v2: $i] :
% 33.76/5.32 | ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: int] : (v4
% 33.76/5.32 | = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 =
% 33.76/5.32 | 0) & r1(v2, v3) = v5))))) & ! [v0: $i] : ( ~ (r1(all_3_0,
% 33.76/5.32 | v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~
% 33.76/5.32 | $i(v1) | ? [v2: $i] : (r1(v1, v2) = 0 & $i(v2) & ! [v3: $i] : ( ~
% 33.76/5.32 | (p1(v3) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & r1(v2,
% 33.76/5.32 | v3) = v4))) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~
% 33.76/5.32 | $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ? [v4:
% 33.76/5.32 | $i] : (r1(v3, v4) = 0 & p1(v4) = 0 & $i(v4)))))) & ! [v0:
% 33.76/5.32 | $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~
% 33.76/5.32 | (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : (r1(v1, v2) = 0 &
% 33.76/5.32 | $i(v2)))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) |
% 33.76/5.32 | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : !
% 33.76/5.32 | [v3: int] : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] :
% 33.76/5.32 | ( ~ (v4 = 0) & r1(v1, v2) = v4) | ! [v4: $i] : ( ~ (r1(v2, v4) =
% 33.76/5.32 | 0) | ~ $i(v4) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) &
% 33.76/5.32 | r1(v4, v5) = 0 & p1(v5) = v6 & $i(v5)))))) & ! [v0: $i] : (
% 33.76/5.32 | ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) =
% 33.76/5.32 | 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) |
% 33.76/5.32 | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & r1(v2, v3) = 0 &
% 33.76/5.32 | p1(v3) = v4 & $i(v3)) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~
% 33.76/5.32 | $i(v3) | ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (p1(v4) =
% 33.76/5.32 | v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & r1(v3, v4)
% 33.76/5.32 | = v6)))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~
% 33.76/5.32 | $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i]
% 33.76/5.32 | : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ? [v3: $i] : (r1(v2, v3) = 0
% 33.76/5.32 | & $i(v3) & ! [v4: $i] : ( ~ (p1(v4) = 0) | ~ $i(v4) | ? [v5:
% 33.76/5.32 | int] : ( ~ (v5 = 0) & r1(v3, v4) = v5))) | ! [v3: $i] : (
% 33.76/5.32 | ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3, v4)
% 33.76/5.32 | = 0) | ~ $i(v4) | ? [v5: $i] : (r1(v4, v5) = 0 & p1(v5) =
% 33.76/5.32 | 0 & $i(v5))))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0)
% 33.76/5.32 | | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | !
% 33.76/5.32 | [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ? [v3: $i] : (r1(v2,
% 33.76/5.32 | v3) = 0 & $i(v3))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) =
% 33.76/5.32 | 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) |
% 33.76/5.32 | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : !
% 33.76/5.32 | [v4: int] : (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int]
% 33.76/5.32 | : ( ~ (v5 = 0) & r1(v2, v3) = v5) | ! [v5: $i] : ( ~ (r1(v3,
% 33.76/5.32 | v5) = 0) | ~ $i(v5) | ? [v6: $i] : ? [v7: int] : ( ~
% 33.76/5.32 | (v7 = 0) & r1(v5, v6) = 0 & p1(v6) = v7 & $i(v6))))))) & !
% 33.76/5.32 | [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~
% 33.76/5.32 | (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) |
% 33.76/5.32 | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ?
% 33.76/5.32 | [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & r1(v3, v4) = 0 &
% 33.76/5.32 | p1(v4) = v5 & $i(v4)) | ! [v4: $i] : ( ~ (r1(v3, v4) = 0) |
% 33.76/5.32 | ~ $i(v4) | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (p1(v5)
% 33.76/5.32 | = v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & r1(v4,
% 33.76/5.32 | v5) = v7))))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) =
% 33.76/5.32 | 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) |
% 33.76/5.32 | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~
% 33.76/5.32 | (r1(v2, v3) = 0) | ~ $i(v3) | ? [v4: $i] : (r1(v3, v4) = 0 &
% 33.76/5.32 | $i(v4) & ! [v5: $i] : ( ~ (p1(v5) = 0) | ~ $i(v5) | ? [v6:
% 33.76/5.32 | int] : ( ~ (v6 = 0) & r1(v4, v5) = v6))) | ! [v4: $i] :
% 33.76/5.32 | ( ~ (r1(v3, v4) = 0) | ~ $i(v4) | ! [v5: $i] : ( ~ (r1(v4,
% 33.76/5.32 | v5) = 0) | ~ $i(v5) | ? [v6: $i] : (r1(v5, v6) = 0 &
% 33.76/5.32 | p1(v6) = 0 & $i(v6)))))))) & ! [v0: $i] : ( ~
% 33.76/5.32 | (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) =
% 33.76/5.33 | 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) |
% 33.76/5.33 | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ? [v4: $i] :
% 33.76/5.33 | (r1(v3, v4) = 0 & $i(v4)))))) & ! [v0: $i] : ( ~ (r1(all_3_0,
% 33.76/5.33 | v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~
% 33.76/5.33 | $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3:
% 33.76/5.33 | $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ! [v5:
% 33.76/5.33 | int] : (v5 = 0 | ~ (p1(v4) = v5) | ~ $i(v4) | ? [v6: int]
% 33.76/5.33 | : ( ~ (v6 = 0) & r1(v3, v4) = v6) | ! [v6: $i] : ( ~ (r1(v4,
% 33.76/5.33 | v6) = 0) | ~ $i(v6) | ? [v7: $i] : ? [v8: int] : ( ~
% 33.76/5.33 | (v8 = 0) & r1(v6, v7) = 0 & p1(v7) = v8 & $i(v7)))))))) &
% 33.76/5.33 | ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~
% 33.76/5.33 | (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) |
% 33.76/5.33 | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | !
% 33.76/5.33 | [v4: $i] : ( ~ (r1(v3, v4) = 0) | ~ $i(v4) | ? [v5: $i] : ?
% 33.76/5.33 | [v6: int] : ( ~ (v6 = 0) & r1(v4, v5) = 0 & p1(v5) = v6 &
% 33.76/5.33 | $i(v5)) | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~ $i(v5) |
% 33.76/5.33 | ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (p1(v6) = v7) | ~
% 33.76/5.33 | $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & r1(v5, v6) =
% 33.76/5.33 | v8)))))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) |
% 33.76/5.33 | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2:
% 33.76/5.33 | $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~
% 33.76/5.33 | (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (r1(v3, v4) =
% 33.76/5.33 | 0) | ~ $i(v4) | ? [v5: $i] : (r1(v4, v5) = 0 & $i(v5) &
% 33.76/5.33 | ! [v6: $i] : ( ~ (p1(v6) = 0) | ~ $i(v6) | ? [v7: int] :
% 33.76/5.33 | ( ~ (v7 = 0) & r1(v5, v6) = v7))) | ! [v5: $i] : ( ~
% 33.76/5.33 | (r1(v4, v5) = 0) | ~ $i(v5) | ! [v6: $i] : ( ~ (r1(v5,
% 33.76/5.33 | v6) = 0) | ~ $i(v6) | ? [v7: $i] : (r1(v6, v7) = 0
% 33.76/5.33 | & p1(v7) = 0 & $i(v7))))))))) & ! [v0: $i] : ( ~
% 33.76/5.33 | (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) =
% 33.76/5.33 | 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) |
% 33.76/5.33 | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : (
% 33.76/5.33 | ~ (r1(v3, v4) = 0) | ~ $i(v4) | ? [v5: $i] : (r1(v4, v5) =
% 33.76/5.33 | 0 & $i(v5))))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0)
% 33.76/5.33 | | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | !
% 33.76/5.33 | [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~
% 33.76/5.33 | (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ( ~ (p1(v4) = 0) |
% 33.76/5.33 | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & r1(v3, v4) = v5) |
% 33.76/5.33 | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~ $i(v5) | ? [v6: $i] :
% 33.76/5.33 | (r1(v5, v6) = 0 & p1(v6) = 0 & $i(v6)))))))) & ! [v0: $i]
% 33.76/5.33 | : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1)
% 33.76/5.33 | = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2)
% 33.76/5.33 | | ! [v3: $i] : ( ~ (p1(v3) = 0) | ~ $i(v3) | ? [v4: int] : ( ~
% 33.76/5.33 | (v4 = 0) & r1(v2, v3) = v4) | ! [v4: $i] : ( ~ (r1(v3, v4) =
% 33.76/5.33 | 0) | ~ $i(v4) | ? [v5: $i] : (r1(v4, v5) = 0 & p1(v5) = 0
% 33.76/5.33 | & $i(v5))))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) |
% 33.76/5.33 | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2:
% 33.76/5.33 | $i] : ( ~ (p1(v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0)
% 33.76/5.33 | & r1(v1, v2) = v3) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~
% 33.76/5.33 | $i(v3) | ? [v4: $i] : (r1(v3, v4) = 0 & p1(v4) = 0 &
% 33.76/5.33 | $i(v4)))))) & ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~
% 33.76/5.33 | $i(v0) | ! [v1: $i] : ( ~ (p1(v1) = 0) | ~ $i(v1) | ? [v2: int] :
% 33.76/5.33 | ( ~ (v2 = 0) & r1(v0, v1) = v2) | ! [v2: $i] : ( ~ (r1(v1, v2) =
% 33.76/5.33 | 0) | ~ $i(v2) | ? [v3: $i] : (r1(v2, v3) = 0 & p1(v3) = 0 &
% 33.76/5.33 | $i(v3))))) & ! [v0: $i] : ( ~ (p1(v0) = 0) | ~ $i(v0) | ?
% 33.76/5.33 | [v1: int] : ( ~ (v1 = 0) & r1(all_3_0, v0) = v1) | ! [v1: $i] : ( ~
% 33.76/5.33 | (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : (r1(v1, v2) = 0 &
% 33.76/5.33 | p1(v2) = 0 & $i(v2)))) & ? [v0: $i] : (r1(all_3_0, v0) = 0 &
% 33.76/5.33 | $i(v0) & ? [v1: $i] : (r1(v0, v1) = 0 & $i(v1) & ? [v2: $i] :
% 33.76/5.33 | (r1(v1, v2) = 0 & $i(v2) & ? [v3: $i] : (r1(v2, v3) = 0 & $i(v3) &
% 33.76/5.33 | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & r1(v3, v4) = 0 &
% 33.76/5.33 | p1(v4) = v5 & $i(v4) & ! [v6: $i] : ! [v7: int] : (v7 = 0 |
% 33.76/5.33 | ~ (p1(v6) = v7) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0)
% 33.76/5.33 | & r1(v4, v6) = v8)))))))
% 33.76/5.33 |
% 33.76/5.33 | ALPHA: (2) implies:
% 33.76/5.33 | (3) ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~
% 33.76/5.33 | (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) |
% 33.76/5.33 | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | !
% 33.76/5.33 | [v4: $i] : ( ~ (r1(v3, v4) = 0) | ~ $i(v4) | ? [v5: $i] :
% 33.76/5.33 | (r1(v4, v5) = 0 & $i(v5)))))))
% 33.76/5.33 | (4) ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~
% 33.76/5.33 | (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) |
% 33.76/5.33 | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | !
% 33.76/5.33 | [v4: $i] : ( ~ (r1(v3, v4) = 0) | ~ $i(v4) | ? [v5: $i] : ?
% 33.76/5.33 | [v6: int] : ( ~ (v6 = 0) & r1(v4, v5) = 0 & p1(v5) = v6 &
% 33.76/5.33 | $i(v5)) | ! [v5: $i] : ( ~ (r1(v4, v5) = 0) | ~ $i(v5) |
% 33.76/5.33 | ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (p1(v6) = v7) | ~
% 33.76/5.33 | $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & r1(v5, v6) =
% 33.76/5.33 | v8))))))))
% 33.76/5.33 | (5) ! [v0: $i] : ( ~ (r1(all_3_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~
% 33.76/5.33 | (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) |
% 33.76/5.33 | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~ $i(v3) | !
% 33.76/5.33 | [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (p1(v4) = v5) | ~
% 33.76/5.33 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & r1(v3, v4) = v6) | !
% 33.76/5.33 | [v6: $i] : ( ~ (r1(v4, v6) = 0) | ~ $i(v6) | ? [v7: $i] :
% 33.76/5.33 | ? [v8: int] : ( ~ (v8 = 0) & r1(v6, v7) = 0 & p1(v7) = v8 &
% 33.76/5.33 | $i(v7))))))))
% 33.93/5.33 | (6) ? [v0: $i] : (r1(all_3_0, v0) = 0 & $i(v0) & ? [v1: $i] : (r1(v0, v1)
% 33.93/5.33 | = 0 & $i(v1) & ? [v2: $i] : (r1(v1, v2) = 0 & $i(v2) & ? [v3: $i]
% 33.93/5.33 | : (r1(v2, v3) = 0 & $i(v3) & ? [v4: $i] : ? [v5: int] : ( ~ (v5
% 33.93/5.33 | = 0) & r1(v3, v4) = 0 & p1(v4) = v5 & $i(v4) & ! [v6: $i]
% 33.93/5.33 | : ! [v7: int] : (v7 = 0 | ~ (p1(v6) = v7) | ~ $i(v6) | ?
% 33.93/5.33 | [v8: int] : ( ~ (v8 = 0) & r1(v4, v6) = v8)))))))
% 33.93/5.33 |
% 33.93/5.33 | DELTA: instantiating (6) with fresh symbol all_6_0 gives:
% 33.93/5.34 | (7) r1(all_3_0, all_6_0) = 0 & $i(all_6_0) & ? [v0: $i] : (r1(all_6_0, v0)
% 33.93/5.34 | = 0 & $i(v0) & ? [v1: $i] : (r1(v0, v1) = 0 & $i(v1) & ? [v2: $i] :
% 33.93/5.34 | (r1(v1, v2) = 0 & $i(v2) & ? [v3: $i] : ? [v4: int] : ( ~ (v4 =
% 33.93/5.34 | 0) & r1(v2, v3) = 0 & p1(v3) = v4 & $i(v3) & ! [v5: $i] : !
% 33.93/5.34 | [v6: int] : (v6 = 0 | ~ (p1(v5) = v6) | ~ $i(v5) | ? [v7:
% 33.93/5.34 | int] : ( ~ (v7 = 0) & r1(v3, v5) = v7))))))
% 33.93/5.34 |
% 33.93/5.34 | ALPHA: (7) implies:
% 33.93/5.34 | (8) $i(all_6_0)
% 33.93/5.34 | (9) r1(all_3_0, all_6_0) = 0
% 33.93/5.34 | (10) ? [v0: $i] : (r1(all_6_0, v0) = 0 & $i(v0) & ? [v1: $i] : (r1(v0,
% 33.93/5.34 | v1) = 0 & $i(v1) & ? [v2: $i] : (r1(v1, v2) = 0 & $i(v2) & ?
% 33.93/5.34 | [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & r1(v2, v3) = 0 & p1(v3)
% 33.93/5.34 | = v4 & $i(v3) & ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~
% 33.93/5.34 | (p1(v5) = v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) &
% 33.93/5.34 | r1(v3, v5) = v7))))))
% 33.93/5.34 |
% 33.93/5.34 | DELTA: instantiating (10) with fresh symbol all_8_0 gives:
% 33.93/5.34 | (11) r1(all_6_0, all_8_0) = 0 & $i(all_8_0) & ? [v0: $i] : (r1(all_8_0,
% 33.93/5.34 | v0) = 0 & $i(v0) & ? [v1: $i] : (r1(v0, v1) = 0 & $i(v1) & ?
% 33.93/5.34 | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & r1(v1, v2) = 0 & p1(v2) =
% 33.93/5.34 | v3 & $i(v2) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (p1(v4)
% 33.93/5.34 | = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & r1(v2, v4)
% 33.93/5.34 | = v6)))))
% 33.93/5.34 |
% 33.93/5.34 | ALPHA: (11) implies:
% 33.93/5.34 | (12) $i(all_8_0)
% 33.93/5.34 | (13) r1(all_6_0, all_8_0) = 0
% 33.93/5.34 | (14) ? [v0: $i] : (r1(all_8_0, v0) = 0 & $i(v0) & ? [v1: $i] : (r1(v0,
% 33.93/5.34 | v1) = 0 & $i(v1) & ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 33.93/5.34 | r1(v1, v2) = 0 & p1(v2) = v3 & $i(v2) & ! [v4: $i] : ! [v5:
% 33.93/5.34 | int] : (v5 = 0 | ~ (p1(v4) = v5) | ~ $i(v4) | ? [v6: int] :
% 33.93/5.34 | ( ~ (v6 = 0) & r1(v2, v4) = v6)))))
% 33.93/5.34 |
% 33.93/5.34 | DELTA: instantiating (14) with fresh symbol all_10_0 gives:
% 33.93/5.34 | (15) r1(all_8_0, all_10_0) = 0 & $i(all_10_0) & ? [v0: $i] : (r1(all_10_0,
% 33.93/5.34 | v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 33.93/5.34 | r1(v0, v1) = 0 & p1(v1) = v2 & $i(v1) & ! [v3: $i] : ! [v4: int]
% 33.93/5.34 | : (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5
% 33.93/5.34 | = 0) & r1(v1, v3) = v5))))
% 33.93/5.34 |
% 33.93/5.34 | ALPHA: (15) implies:
% 33.93/5.34 | (16) $i(all_10_0)
% 33.93/5.34 | (17) r1(all_8_0, all_10_0) = 0
% 33.93/5.34 | (18) ? [v0: $i] : (r1(all_10_0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2:
% 33.93/5.34 | int] : ( ~ (v2 = 0) & r1(v0, v1) = 0 & p1(v1) = v2 & $i(v1) & !
% 33.93/5.34 | [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) |
% 33.93/5.34 | ? [v5: int] : ( ~ (v5 = 0) & r1(v1, v3) = v5))))
% 33.93/5.34 |
% 33.93/5.34 | DELTA: instantiating (18) with fresh symbol all_12_0 gives:
% 33.93/5.34 | (19) r1(all_10_0, all_12_0) = 0 & $i(all_12_0) & ? [v0: $i] : ? [v1: int]
% 33.93/5.34 | : ( ~ (v1 = 0) & r1(all_12_0, v0) = 0 & p1(v0) = v1 & $i(v0) & ! [v2:
% 33.93/5.34 | $i] : ! [v3: int] : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ?
% 33.93/5.34 | [v4: int] : ( ~ (v4 = 0) & r1(v0, v2) = v4)))
% 33.93/5.34 |
% 33.93/5.34 | ALPHA: (19) implies:
% 33.93/5.34 | (20) $i(all_12_0)
% 33.93/5.34 | (21) r1(all_10_0, all_12_0) = 0
% 33.93/5.34 | (22) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & r1(all_12_0, v0) = 0 &
% 33.93/5.34 | p1(v0) = v1 & $i(v0) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 33.93/5.34 | (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & r1(v0,
% 33.93/5.34 | v2) = v4)))
% 33.93/5.34 |
% 33.93/5.34 | DELTA: instantiating (22) with fresh symbols all_14_0, all_14_1 gives:
% 33.93/5.34 | (23) ~ (all_14_0 = 0) & r1(all_12_0, all_14_1) = 0 & p1(all_14_1) =
% 33.93/5.34 | all_14_0 & $i(all_14_1) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 33.93/5.34 | (p1(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 33.93/5.34 | r1(all_14_1, v0) = v2))
% 33.93/5.34 |
% 33.93/5.34 | ALPHA: (23) implies:
% 33.93/5.34 | (24) ~ (all_14_0 = 0)
% 33.93/5.34 | (25) $i(all_14_1)
% 33.93/5.34 | (26) p1(all_14_1) = all_14_0
% 33.93/5.34 | (27) r1(all_12_0, all_14_1) = 0
% 33.93/5.34 | (28) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ $i(v0) |
% 33.93/5.34 | ? [v2: int] : ( ~ (v2 = 0) & r1(all_14_1, v0) = v2))
% 33.93/5.34 |
% 33.93/5.34 | GROUND_INST: instantiating (5) with all_6_0, simplifying with (8), (9) gives:
% 33.93/5.35 | (29) ! [v0: $i] : ( ~ (r1(all_6_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : (
% 33.93/5.35 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) =
% 33.93/5.35 | 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 33.93/5.35 | (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) &
% 33.93/5.35 | r1(v2, v3) = v5) | ! [v5: $i] : ( ~ (r1(v3, v5) = 0) | ~
% 33.93/5.35 | $i(v5) | ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & r1(v5,
% 33.93/5.35 | v6) = 0 & p1(v6) = v7 & $i(v6)))))))
% 33.93/5.35 |
% 33.93/5.35 | GROUND_INST: instantiating (4) with all_6_0, simplifying with (8), (9) gives:
% 33.93/5.35 | (30) ! [v0: $i] : ( ~ (r1(all_6_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : (
% 33.93/5.35 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) =
% 33.93/5.35 | 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~
% 33.93/5.35 | $i(v3) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & r1(v3,
% 33.93/5.35 | v4) = 0 & p1(v4) = v5 & $i(v4)) | ! [v4: $i] : ( ~
% 33.93/5.35 | (r1(v3, v4) = 0) | ~ $i(v4) | ! [v5: $i] : ! [v6: int] :
% 33.93/5.35 | (v6 = 0 | ~ (p1(v5) = v6) | ~ $i(v5) | ? [v7: int] : ( ~
% 33.93/5.35 | (v7 = 0) & r1(v4, v5) = v7)))))))
% 33.93/5.35 |
% 33.93/5.35 | GROUND_INST: instantiating (3) with all_6_0, simplifying with (8), (9) gives:
% 33.93/5.35 | (31) ! [v0: $i] : ( ~ (r1(all_6_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : (
% 33.93/5.35 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) =
% 33.93/5.35 | 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (r1(v2, v3) = 0) | ~
% 33.93/5.35 | $i(v3) | ? [v4: $i] : (r1(v3, v4) = 0 & $i(v4))))))
% 33.93/5.35 |
% 33.93/5.35 | GROUND_INST: instantiating (30) with all_8_0, simplifying with (12), (13)
% 33.93/5.35 | gives:
% 33.93/5.35 | (32) ! [v0: $i] : ( ~ (r1(all_8_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : (
% 33.93/5.35 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) =
% 33.93/5.35 | 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 33.93/5.35 | r1(v2, v3) = 0 & p1(v3) = v4 & $i(v3)) | ! [v3: $i] : ( ~
% 33.93/5.35 | (r1(v2, v3) = 0) | ~ $i(v3) | ! [v4: $i] : ! [v5: int] :
% 33.93/5.35 | (v5 = 0 | ~ (p1(v4) = v5) | ~ $i(v4) | ? [v6: int] : ( ~
% 33.93/5.35 | (v6 = 0) & r1(v3, v4) = v6))))))
% 33.93/5.35 |
% 33.93/5.35 | GROUND_INST: instantiating (29) with all_8_0, simplifying with (12), (13)
% 33.93/5.35 | gives:
% 33.93/5.35 | (33) ! [v0: $i] : ( ~ (r1(all_8_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : (
% 33.93/5.35 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: int] : (v3
% 33.93/5.35 | = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0)
% 33.93/5.35 | & r1(v1, v2) = v4) | ! [v4: $i] : ( ~ (r1(v2, v4) = 0) | ~
% 33.93/5.35 | $i(v4) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & r1(v4,
% 33.93/5.35 | v5) = 0 & p1(v5) = v6 & $i(v5))))))
% 33.93/5.35 |
% 33.93/5.35 | GROUND_INST: instantiating (31) with all_8_0, simplifying with (12), (13)
% 33.93/5.35 | gives:
% 33.93/5.35 | (34) ! [v0: $i] : ( ~ (r1(all_8_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : (
% 33.93/5.35 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) =
% 33.93/5.35 | 0) | ~ $i(v2) | ? [v3: $i] : (r1(v2, v3) = 0 & $i(v3)))))
% 33.93/5.35 |
% 33.93/5.35 | GROUND_INST: instantiating (32) with all_10_0, simplifying with (16), (17)
% 33.93/5.35 | gives:
% 33.93/5.35 | (35) ! [v0: $i] : ( ~ (r1(all_10_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : (
% 33.93/5.35 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] : ( ~
% 33.93/5.35 | (v3 = 0) & r1(v1, v2) = 0 & p1(v2) = v3 & $i(v2)) | ! [v2: $i]
% 33.93/5.35 | : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: int] :
% 33.93/5.35 | (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5
% 33.93/5.35 | = 0) & r1(v2, v3) = v5)))))
% 33.93/5.35 |
% 33.93/5.35 | GROUND_INST: instantiating (33) with all_10_0, simplifying with (16), (17)
% 33.93/5.35 | gives:
% 33.93/5.35 | (36) ! [v0: $i] : ( ~ (r1(all_10_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] :
% 33.93/5.35 | ! [v2: int] : (v2 = 0 | ~ (p1(v1) = v2) | ~ $i(v1) | ? [v3: int]
% 33.93/5.35 | : ( ~ (v3 = 0) & r1(v0, v1) = v3) | ! [v3: $i] : ( ~ (r1(v1, v3)
% 33.93/5.35 | = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 33.93/5.35 | r1(v3, v4) = 0 & p1(v4) = v5 & $i(v4)))))
% 33.93/5.35 |
% 33.93/5.35 | GROUND_INST: instantiating (34) with all_10_0, simplifying with (16), (17)
% 33.93/5.35 | gives:
% 33.93/5.35 | (37) ! [v0: $i] : ( ~ (r1(all_10_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : (
% 33.93/5.35 | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : (r1(v1, v2) = 0 &
% 33.93/5.35 | $i(v2))))
% 33.93/5.35 |
% 33.93/5.35 | GROUND_INST: instantiating (35) with all_12_0, simplifying with (20), (21)
% 33.93/5.35 | gives:
% 33.93/5.35 | (38) ! [v0: $i] : ( ~ (r1(all_12_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 33.93/5.35 | ? [v2: int] : ( ~ (v2 = 0) & r1(v0, v1) = 0 & p1(v1) = v2 & $i(v1))
% 33.93/5.35 | | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : !
% 33.93/5.35 | [v3: int] : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int]
% 33.93/5.35 | : ( ~ (v4 = 0) & r1(v1, v2) = v4))))
% 33.93/5.35 |
% 33.93/5.35 | GROUND_INST: instantiating (36) with all_12_0, simplifying with (20), (21)
% 33.93/5.35 | gives:
% 33.93/5.35 | (39) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ $i(v0) |
% 33.93/5.35 | ? [v2: int] : ( ~ (v2 = 0) & r1(all_12_0, v0) = v2) | ! [v2: $i] :
% 33.93/5.35 | ( ~ (r1(v0, v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: int] : ( ~
% 33.93/5.35 | (v4 = 0) & r1(v2, v3) = 0 & p1(v3) = v4 & $i(v3))))
% 33.93/5.35 |
% 33.93/5.35 | GROUND_INST: instantiating (37) with all_12_0, simplifying with (20), (21)
% 33.93/5.35 | gives:
% 33.93/5.36 | (40) ! [v0: $i] : ( ~ (r1(all_12_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 33.93/5.36 | (r1(v0, v1) = 0 & $i(v1)))
% 33.93/5.36 |
% 33.93/5.36 | GROUND_INST: instantiating (38) with all_14_1, simplifying with (25), (27)
% 33.93/5.36 | gives:
% 33.93/5.36 | (41) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & r1(all_14_1, v0) = 0 &
% 33.93/5.36 | p1(v0) = v1 & $i(v0)) | ! [v0: $i] : ( ~ (r1(all_14_1, v0) = 0) |
% 33.93/5.36 | ~ $i(v0) | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (p1(v1) = v2) |
% 33.93/5.36 | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & r1(v0, v1) = v3)))
% 33.93/5.36 |
% 33.93/5.36 | GROUND_INST: instantiating (39) with all_14_1, all_14_0, simplifying with
% 33.93/5.36 | (25), (26) gives:
% 33.93/5.36 | (42) all_14_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_12_0, all_14_1) =
% 33.93/5.36 | v0) | ! [v0: $i] : ( ~ (r1(all_14_1, v0) = 0) | ~ $i(v0) | ? [v1:
% 33.93/5.36 | $i] : ? [v2: int] : ( ~ (v2 = 0) & r1(v0, v1) = 0 & p1(v1) = v2 &
% 33.93/5.36 | $i(v1)))
% 33.93/5.36 |
% 33.93/5.36 | GROUND_INST: instantiating (40) with all_14_1, simplifying with (25), (27)
% 33.93/5.36 | gives:
% 33.93/5.36 | (43) ? [v0: $i] : (r1(all_14_1, v0) = 0 & $i(v0))
% 33.93/5.36 |
% 33.93/5.36 | DELTA: instantiating (43) with fresh symbol all_80_0 gives:
% 33.93/5.36 | (44) r1(all_14_1, all_80_0) = 0 & $i(all_80_0)
% 33.93/5.36 |
% 33.93/5.36 | ALPHA: (44) implies:
% 33.93/5.36 | (45) $i(all_80_0)
% 33.93/5.36 | (46) r1(all_14_1, all_80_0) = 0
% 33.93/5.36 |
% 33.93/5.36 | BETA: splitting (42) gives:
% 33.93/5.36 |
% 33.93/5.36 | Case 1:
% 33.93/5.36 | |
% 33.93/5.36 | | (47) all_14_0 = 0
% 33.93/5.36 | |
% 33.93/5.36 | | REDUCE: (24), (47) imply:
% 33.93/5.36 | | (48) $false
% 33.93/5.36 | |
% 33.93/5.36 | | CLOSE: (48) is inconsistent.
% 33.93/5.36 | |
% 33.93/5.36 | Case 2:
% 33.93/5.36 | |
% 33.93/5.36 | | (49) ? [v0: int] : ( ~ (v0 = 0) & r1(all_12_0, all_14_1) = v0) | ! [v0:
% 33.93/5.36 | | $i] : ( ~ (r1(all_14_1, v0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 33.93/5.36 | | [v2: int] : ( ~ (v2 = 0) & r1(v0, v1) = 0 & p1(v1) = v2 & $i(v1)))
% 33.93/5.36 | |
% 33.93/5.36 | | BETA: splitting (49) gives:
% 33.93/5.36 | |
% 33.93/5.36 | | Case 1:
% 33.93/5.36 | | |
% 33.93/5.36 | | | (50) ? [v0: int] : ( ~ (v0 = 0) & r1(all_12_0, all_14_1) = v0)
% 33.93/5.36 | | |
% 33.93/5.36 | | | DELTA: instantiating (50) with fresh symbol all_94_0 gives:
% 33.93/5.36 | | | (51) ~ (all_94_0 = 0) & r1(all_12_0, all_14_1) = all_94_0
% 33.93/5.36 | | |
% 33.93/5.36 | | | ALPHA: (51) implies:
% 33.93/5.36 | | | (52) ~ (all_94_0 = 0)
% 33.93/5.36 | | | (53) r1(all_12_0, all_14_1) = all_94_0
% 33.93/5.36 | | |
% 33.93/5.36 | | | GROUND_INST: instantiating (1) with 0, all_94_0, all_14_1, all_12_0,
% 33.93/5.36 | | | simplifying with (27), (53) gives:
% 33.93/5.36 | | | (54) all_94_0 = 0
% 33.93/5.36 | | |
% 33.93/5.36 | | | REDUCE: (52), (54) imply:
% 33.93/5.36 | | | (55) $false
% 33.93/5.36 | | |
% 33.93/5.36 | | | CLOSE: (55) is inconsistent.
% 33.93/5.36 | | |
% 33.93/5.36 | | Case 2:
% 33.93/5.36 | | |
% 33.93/5.36 | | | (56) ! [v0: $i] : ( ~ (r1(all_14_1, v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 33.93/5.36 | | | : ? [v2: int] : ( ~ (v2 = 0) & r1(v0, v1) = 0 & p1(v1) = v2 &
% 33.93/5.36 | | | $i(v1)))
% 33.93/5.36 | | |
% 33.93/5.36 | | | GROUND_INST: instantiating (56) with all_80_0, simplifying with (45), (46)
% 33.93/5.36 | | | gives:
% 33.93/5.36 | | | (57) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & r1(all_80_0, v0) = 0 &
% 33.93/5.36 | | | p1(v0) = v1 & $i(v0))
% 33.93/5.36 | | |
% 33.93/5.36 | | | DELTA: instantiating (57) with fresh symbols all_137_0, all_137_1 gives:
% 33.93/5.36 | | | (58) ~ (all_137_0 = 0) & r1(all_80_0, all_137_1) = 0 & p1(all_137_1) =
% 33.93/5.36 | | | all_137_0 & $i(all_137_1)
% 33.93/5.36 | | |
% 33.93/5.36 | | | ALPHA: (58) implies:
% 33.93/5.36 | | | (59) ~ (all_137_0 = 0)
% 33.93/5.36 | | | (60) $i(all_137_1)
% 33.93/5.36 | | | (61) p1(all_137_1) = all_137_0
% 33.93/5.36 | | | (62) r1(all_80_0, all_137_1) = 0
% 33.93/5.36 | | |
% 33.93/5.36 | | | BETA: splitting (41) gives:
% 33.93/5.36 | | |
% 33.93/5.36 | | | Case 1:
% 33.93/5.36 | | | |
% 33.93/5.36 | | | | (63) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & r1(all_14_1, v0) = 0
% 33.93/5.36 | | | | & p1(v0) = v1 & $i(v0))
% 33.93/5.36 | | | |
% 33.93/5.36 | | | | DELTA: instantiating (63) with fresh symbols all_358_0, all_358_1 gives:
% 33.93/5.36 | | | | (64) ~ (all_358_0 = 0) & r1(all_14_1, all_358_1) = 0 & p1(all_358_1)
% 33.93/5.36 | | | | = all_358_0 & $i(all_358_1)
% 33.93/5.36 | | | |
% 33.93/5.36 | | | | ALPHA: (64) implies:
% 33.93/5.36 | | | | (65) ~ (all_358_0 = 0)
% 33.93/5.36 | | | | (66) $i(all_358_1)
% 33.93/5.36 | | | | (67) p1(all_358_1) = all_358_0
% 33.93/5.36 | | | | (68) r1(all_14_1, all_358_1) = 0
% 33.93/5.36 | | | |
% 33.93/5.36 | | | | GROUND_INST: instantiating (28) with all_358_1, all_358_0, simplifying
% 33.93/5.36 | | | | with (66), (67) gives:
% 33.93/5.36 | | | | (69) all_358_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_14_1,
% 33.93/5.36 | | | | all_358_1) = v0)
% 33.93/5.36 | | | |
% 33.93/5.36 | | | | BETA: splitting (69) gives:
% 33.93/5.36 | | | |
% 33.93/5.36 | | | | Case 1:
% 33.93/5.36 | | | | |
% 33.93/5.36 | | | | | (70) all_358_0 = 0
% 33.93/5.36 | | | | |
% 33.93/5.36 | | | | | REDUCE: (65), (70) imply:
% 33.93/5.36 | | | | | (71) $false
% 33.93/5.36 | | | | |
% 33.93/5.36 | | | | | CLOSE: (71) is inconsistent.
% 33.93/5.36 | | | | |
% 33.93/5.36 | | | | Case 2:
% 33.93/5.36 | | | | |
% 33.93/5.36 | | | | | (72) ? [v0: int] : ( ~ (v0 = 0) & r1(all_14_1, all_358_1) = v0)
% 33.93/5.36 | | | | |
% 33.93/5.36 | | | | | DELTA: instantiating (72) with fresh symbol all_609_0 gives:
% 33.93/5.36 | | | | | (73) ~ (all_609_0 = 0) & r1(all_14_1, all_358_1) = all_609_0
% 33.93/5.36 | | | | |
% 33.93/5.36 | | | | | ALPHA: (73) implies:
% 33.93/5.36 | | | | | (74) ~ (all_609_0 = 0)
% 33.93/5.36 | | | | | (75) r1(all_14_1, all_358_1) = all_609_0
% 33.93/5.36 | | | | |
% 33.93/5.36 | | | | | GROUND_INST: instantiating (1) with 0, all_609_0, all_358_1, all_14_1,
% 33.93/5.36 | | | | | simplifying with (68), (75) gives:
% 33.93/5.36 | | | | | (76) all_609_0 = 0
% 33.93/5.36 | | | | |
% 33.93/5.36 | | | | | REDUCE: (74), (76) imply:
% 33.93/5.36 | | | | | (77) $false
% 33.93/5.36 | | | | |
% 33.93/5.36 | | | | | CLOSE: (77) is inconsistent.
% 33.93/5.36 | | | | |
% 33.93/5.36 | | | | End of split
% 33.93/5.36 | | | |
% 33.93/5.37 | | | Case 2:
% 33.93/5.37 | | | |
% 33.93/5.37 | | | | (78) ! [v0: $i] : ( ~ (r1(all_14_1, v0) = 0) | ~ $i(v0) | ! [v1:
% 33.93/5.37 | | | | $i] : ! [v2: int] : (v2 = 0 | ~ (p1(v1) = v2) | ~ $i(v1)
% 33.93/5.37 | | | | | ? [v3: int] : ( ~ (v3 = 0) & r1(v0, v1) = v3)))
% 33.93/5.37 | | | |
% 33.93/5.37 | | | | GROUND_INST: instantiating (78) with all_80_0, simplifying with (45),
% 33.93/5.37 | | | | (46) gives:
% 33.93/5.37 | | | | (79) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~
% 33.93/5.37 | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & r1(all_80_0, v0) = v2))
% 33.93/5.37 | | | |
% 33.93/5.37 | | | | GROUND_INST: instantiating (79) with all_137_1, all_137_0, simplifying
% 33.93/5.37 | | | | with (60), (61) gives:
% 33.93/5.37 | | | | (80) all_137_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_80_0,
% 33.93/5.37 | | | | all_137_1) = v0)
% 33.93/5.37 | | | |
% 33.93/5.37 | | | | BETA: splitting (80) gives:
% 33.93/5.37 | | | |
% 33.93/5.37 | | | | Case 1:
% 33.93/5.37 | | | | |
% 33.93/5.37 | | | | | (81) all_137_0 = 0
% 33.93/5.37 | | | | |
% 33.93/5.37 | | | | | REDUCE: (59), (81) imply:
% 33.93/5.37 | | | | | (82) $false
% 33.93/5.37 | | | | |
% 33.93/5.37 | | | | | CLOSE: (82) is inconsistent.
% 33.93/5.37 | | | | |
% 33.93/5.37 | | | | Case 2:
% 33.93/5.37 | | | | |
% 33.93/5.37 | | | | | (83) ? [v0: int] : ( ~ (v0 = 0) & r1(all_80_0, all_137_1) = v0)
% 33.93/5.37 | | | | |
% 33.93/5.37 | | | | | DELTA: instantiating (83) with fresh symbol all_363_0 gives:
% 33.93/5.37 | | | | | (84) ~ (all_363_0 = 0) & r1(all_80_0, all_137_1) = all_363_0
% 33.93/5.37 | | | | |
% 33.93/5.37 | | | | | ALPHA: (84) implies:
% 33.93/5.37 | | | | | (85) ~ (all_363_0 = 0)
% 33.93/5.37 | | | | | (86) r1(all_80_0, all_137_1) = all_363_0
% 33.93/5.37 | | | | |
% 33.93/5.37 | | | | | GROUND_INST: instantiating (1) with 0, all_363_0, all_137_1, all_80_0,
% 33.93/5.37 | | | | | simplifying with (62), (86) gives:
% 33.93/5.37 | | | | | (87) all_363_0 = 0
% 33.93/5.37 | | | | |
% 33.93/5.37 | | | | | REDUCE: (85), (87) imply:
% 33.93/5.37 | | | | | (88) $false
% 33.93/5.37 | | | | |
% 33.93/5.37 | | | | | CLOSE: (88) is inconsistent.
% 33.93/5.37 | | | | |
% 33.93/5.37 | | | | End of split
% 33.93/5.37 | | | |
% 33.93/5.37 | | | End of split
% 33.93/5.37 | | |
% 33.93/5.37 | | End of split
% 33.93/5.37 | |
% 33.93/5.37 | End of split
% 33.93/5.37 |
% 33.93/5.37 End of proof
% 33.93/5.37 % SZS output end Proof for theBenchmark
% 33.93/5.37
% 33.93/5.37 4765ms
%------------------------------------------------------------------------------