TSTP Solution File: LCL672+1.001 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL672+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n017.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 08:12:20 EDT 2023
% Result : Theorem 11.65s 2.30s
% Output : Proof 13.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : LCL672+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 07:00:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.65 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.24/1.07 Prover 4: Preprocessing ...
% 2.24/1.07 Prover 1: Preprocessing ...
% 3.03/1.10 Prover 3: Preprocessing ...
% 3.03/1.10 Prover 2: Preprocessing ...
% 3.03/1.10 Prover 5: Preprocessing ...
% 3.03/1.10 Prover 6: Preprocessing ...
% 3.03/1.11 Prover 0: Preprocessing ...
% 3.80/1.31 Prover 2: Proving ...
% 3.80/1.31 Prover 5: Proving ...
% 4.43/1.40 Prover 1: Constructing countermodel ...
% 4.43/1.42 Prover 6: Proving ...
% 4.43/1.42 Prover 3: Constructing countermodel ...
% 4.43/1.44 Prover 0: Proving ...
% 5.35/1.45 Prover 4: Constructing countermodel ...
% 11.65/2.30 Prover 3: proved (1631ms)
% 11.65/2.30
% 11.65/2.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.65/2.30
% 11.65/2.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.65/2.30 Prover 2: stopped
% 11.65/2.30 Prover 6: stopped
% 11.65/2.31 Prover 0: stopped
% 11.65/2.32 Prover 5: stopped
% 11.65/2.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.65/2.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.65/2.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.65/2.33 Prover 7: Preprocessing ...
% 11.65/2.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.65/2.34 Prover 8: Preprocessing ...
% 12.11/2.36 Prover 10: Preprocessing ...
% 12.11/2.36 Prover 11: Preprocessing ...
% 12.11/2.37 Prover 13: Preprocessing ...
% 12.11/2.37 Prover 7: Warning: ignoring some quantifiers
% 12.11/2.38 Prover 7: Constructing countermodel ...
% 12.11/2.38 Prover 10: Warning: ignoring some quantifiers
% 12.11/2.38 Prover 13: Warning: ignoring some quantifiers
% 12.11/2.39 Prover 10: Constructing countermodel ...
% 12.11/2.39 Prover 13: Constructing countermodel ...
% 12.58/2.42 Prover 1: Found proof (size 87)
% 12.58/2.42 Prover 1: proved (1767ms)
% 12.58/2.42 Prover 10: stopped
% 12.58/2.42 Prover 7: stopped
% 12.58/2.42 Prover 13: stopped
% 12.58/2.42 Prover 4: stopped
% 12.58/2.43 Prover 8: Warning: ignoring some quantifiers
% 12.58/2.43 Prover 11: Constructing countermodel ...
% 12.58/2.43 Prover 11: stopped
% 12.58/2.43 Prover 8: Constructing countermodel ...
% 12.58/2.44 Prover 8: stopped
% 12.58/2.44
% 12.58/2.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.58/2.44
% 12.58/2.44 % SZS output start Proof for theBenchmark
% 12.58/2.44 Assumptions after simplification:
% 12.58/2.44 ---------------------------------
% 12.58/2.44
% 12.58/2.44 (main)
% 12.85/2.48 ? [v0: $i] : ($i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & p1(v1) =
% 12.85/2.48 v2 & r1(v0, v1) = 0 & $i(v1)) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0)
% 12.85/2.48 & p2(v1) = v2 & r1(v0, v1) = 0 & $i(v1)) & ? [v1: $i] : (r1(v0, v1) = 0 &
% 12.85/2.48 $i(v1) & ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1,
% 12.85/2.48 v2) = 0 & $i(v2)) & ? [v2: $i] : (r1(v1, v2) = 0 & $i(v2) & ! [v3:
% 12.85/2.48 $i] : ! [v4: int] : (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5:
% 12.85/2.48 int] : ( ~ (v5 = 0) & r1(v2, v3) = v5)))) & ( ! [v1: $i] : ! [v2:
% 12.85/2.48 int] : (v2 = 0 | ~ (p1(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 =
% 12.85/2.48 0) & r1(v0, v1) = v3)) | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 12.85/2.48 (p2(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & r1(v0, v1) =
% 12.85/2.48 v3)) | ( ! [v1: $i] : ( ~ (p1(v1) = 0) | ~ $i(v1) | ? [v2: int] : (
% 12.85/2.48 ~ (v2 = 0) & r1(v0, v1) = v2) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) |
% 12.85/2.48 ~ $i(v2) | ? [v3: $i] : (p1(v3) = 0 & r1(v2, v3) = 0 & $i(v3)))) &
% 12.85/2.48 ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : (r1(v1,
% 12.85/2.48 v2) = 0 & $i(v2))) & ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~
% 12.85/2.48 $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ? [v3: $i]
% 12.85/2.48 : ? [v4: int] : ( ~ (v4 = 0) & p1(v3) = v4 & r1(v2, v3) = 0 &
% 12.85/2.48 $i(v3))) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | ?
% 12.85/2.48 [v3: $i] : (r1(v2, v3) = 0 & $i(v3) & ! [v4: $i] : ! [v5: int] :
% 12.85/2.48 (v5 = 0 | ~ (p1(v4) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 =
% 12.85/2.48 0) & r1(v3, v4) = v6))))) & ! [v1: $i] : ( ~ (r1(v0, v1) =
% 12.85/2.48 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~ $i(v2) | !
% 12.85/2.48 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) |
% 12.85/2.48 ? [v5: int] : ( ~ (v5 = 0) & r1(v2, v3) = v5)) | ! [v3: $i] : ( ~
% 12.85/2.48 (r1(v2, v3) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: int] : ( ~
% 12.85/2.48 (v5 = 0) & p1(v4) = v5 & r1(v3, v4) = 0 & $i(v4))))))))
% 12.85/2.48
% 12.85/2.49 (reflexivity)
% 12.85/2.49 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (r1(v0, v0) = v1) | ~ $i(v0))
% 12.85/2.49
% 12.85/2.49 (function-axioms)
% 12.85/2.49 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.85/2.49 [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) & ! [v0:
% 12.85/2.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 12.85/2.49 ~ (p1(v2) = v1) | ~ (p1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.85/2.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (p2(v2) = v1) | ~ (p2(v2)
% 12.85/2.49 = v0))
% 12.85/2.49
% 12.85/2.49 Further assumptions not needed in the proof:
% 12.85/2.49 --------------------------------------------
% 12.85/2.49 transitivity
% 12.85/2.49
% 12.85/2.49 Those formulas are unsatisfiable:
% 12.85/2.49 ---------------------------------
% 12.85/2.49
% 12.85/2.49 Begin of proof
% 12.85/2.49 |
% 12.85/2.49 | ALPHA: (function-axioms) implies:
% 12.85/2.49 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.85/2.49 | ! [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0))
% 12.85/2.49 |
% 12.85/2.49 | DELTA: instantiating (main) with fresh symbol all_5_0 gives:
% 12.85/2.50 | (2) $i(all_5_0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p1(v0) = v1 &
% 12.85/2.50 | r1(all_5_0, v0) = 0 & $i(v0)) & ? [v0: $i] : ? [v1: int] : ( ~ (v1
% 12.85/2.50 | = 0) & p2(v0) = v1 & r1(all_5_0, v0) = 0 & $i(v0)) & ? [v0: $i] :
% 12.85/2.50 | (r1(all_5_0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 =
% 12.85/2.50 | 0) & p1(v1) = v2 & r1(v0, v1) = 0 & $i(v1)) & ? [v1: $i] :
% 12.85/2.50 | (r1(v0, v1) = 0 & $i(v1) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.85/2.50 | (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & r1(v1,
% 12.85/2.50 | v2) = v4)))) & ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 12.85/2.50 | (p1(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 12.85/2.50 | r1(all_5_0, v0) = v2)) | ! [v0: $i] : ! [v1: int] : (v1 = 0 |
% 12.85/2.50 | ~ (p2(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 12.85/2.50 | r1(all_5_0, v0) = v2)) | ( ! [v0: $i] : ( ~ (p1(v0) = 0) | ~
% 12.85/2.50 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & r1(all_5_0, v0) = v1) | !
% 12.85/2.50 | [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] :
% 12.85/2.50 | (p1(v2) = 0 & r1(v1, v2) = 0 & $i(v2)))) & ! [v0: $i] : ( ~
% 12.85/2.50 | (r1(all_5_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] : (r1(v0, v1) = 0
% 12.85/2.50 | & $i(v1))) & ! [v0: $i] : ( ~ (r1(all_5_0, v0) = 0) | ~
% 12.85/2.50 | $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2:
% 12.85/2.50 | $i] : ? [v3: int] : ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2)
% 12.85/2.50 | = 0 & $i(v2))) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~
% 12.85/2.50 | $i(v1) | ? [v2: $i] : (r1(v1, v2) = 0 & $i(v2) & ! [v3: $i] :
% 12.85/2.50 | ! [v4: int] : (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ?
% 12.85/2.50 | [v5: int] : ( ~ (v5 = 0) & r1(v2, v3) = v5))))) & ! [v0:
% 12.85/2.50 | $i] : ( ~ (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~
% 12.85/2.50 | (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: int] : (v3
% 12.85/2.50 | = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 =
% 12.85/2.50 | 0) & r1(v1, v2) = v4)) | ! [v2: $i] : ( ~ (r1(v1, v2) =
% 12.85/2.51 | 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0)
% 12.85/2.51 | & p1(v3) = v4 & r1(v2, v3) = 0 & $i(v3)))))))
% 12.85/2.51 |
% 12.85/2.51 | ALPHA: (2) implies:
% 12.85/2.51 | (3) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ $i(v0) |
% 12.85/2.51 | ? [v2: int] : ( ~ (v2 = 0) & r1(all_5_0, v0) = v2)) | ! [v0: $i] :
% 12.85/2.51 | ! [v1: int] : (v1 = 0 | ~ (p2(v0) = v1) | ~ $i(v0) | ? [v2: int] : (
% 12.85/2.51 | ~ (v2 = 0) & r1(all_5_0, v0) = v2)) | ( ! [v0: $i] : ( ~ (p1(v0) =
% 12.85/2.51 | 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & r1(all_5_0, v0) =
% 12.85/2.51 | v1) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2:
% 12.85/2.51 | $i] : (p1(v2) = 0 & r1(v1, v2) = 0 & $i(v2)))) & ! [v0: $i] :
% 12.85/2.51 | ( ~ (r1(all_5_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] : (r1(v0, v1) = 0
% 12.85/2.51 | & $i(v1))) & ! [v0: $i] : ( ~ (r1(all_5_0, v0) = 0) | ~ $i(v0)
% 12.85/2.51 | | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ?
% 12.85/2.51 | [v3: int] : ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0 &
% 12.85/2.51 | $i(v2))) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ?
% 12.85/2.51 | [v2: $i] : (r1(v1, v2) = 0 & $i(v2) & ! [v3: $i] : ! [v4: int]
% 12.85/2.51 | : (v4 = 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~
% 12.85/2.51 | (v5 = 0) & r1(v2, v3) = v5))))) & ! [v0: $i] : ( ~
% 12.85/2.51 | (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0, v1) =
% 12.85/2.51 | 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.85/2.51 | (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) &
% 12.85/2.51 | r1(v1, v2) = v4)) | ! [v2: $i] : ( ~ (r1(v1, v2) = 0) | ~
% 12.85/2.51 | $i(v2) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & p1(v3) =
% 12.85/2.51 | v4 & r1(v2, v3) = 0 & $i(v3))))))
% 12.85/2.51 | (4) ? [v0: $i] : (r1(all_5_0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2:
% 12.85/2.51 | int] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1) = 0 & $i(v1)) & ?
% 12.85/2.51 | [v1: $i] : (r1(v0, v1) = 0 & $i(v1) & ! [v2: $i] : ! [v3: int] :
% 12.85/2.51 | (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 =
% 12.85/2.51 | 0) & r1(v1, v2) = v4))))
% 12.85/2.51 | (5) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p2(v0) = v1 & r1(all_5_0,
% 12.85/2.51 | v0) = 0 & $i(v0))
% 12.85/2.51 | (6) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p1(v0) = v1 & r1(all_5_0,
% 12.85/2.51 | v0) = 0 & $i(v0))
% 12.85/2.51 |
% 12.85/2.51 | DELTA: instantiating (5) with fresh symbols all_7_0, all_7_1 gives:
% 12.85/2.52 | (7) ~ (all_7_0 = 0) & p2(all_7_1) = all_7_0 & r1(all_5_0, all_7_1) = 0 &
% 12.85/2.52 | $i(all_7_1)
% 12.85/2.52 |
% 12.85/2.52 | ALPHA: (7) implies:
% 12.85/2.52 | (8) ~ (all_7_0 = 0)
% 12.85/2.52 | (9) $i(all_7_1)
% 12.85/2.52 | (10) r1(all_5_0, all_7_1) = 0
% 12.85/2.52 | (11) p2(all_7_1) = all_7_0
% 12.85/2.52 |
% 12.85/2.52 | DELTA: instantiating (6) with fresh symbols all_9_0, all_9_1 gives:
% 12.85/2.52 | (12) ~ (all_9_0 = 0) & p1(all_9_1) = all_9_0 & r1(all_5_0, all_9_1) = 0 &
% 12.85/2.52 | $i(all_9_1)
% 12.85/2.52 |
% 12.85/2.52 | ALPHA: (12) implies:
% 12.85/2.52 | (13) ~ (all_9_0 = 0)
% 12.85/2.52 | (14) $i(all_9_1)
% 12.85/2.52 | (15) r1(all_5_0, all_9_1) = 0
% 12.85/2.52 | (16) p1(all_9_1) = all_9_0
% 12.85/2.52 |
% 12.85/2.52 | DELTA: instantiating (4) with fresh symbol all_11_0 gives:
% 12.85/2.52 | (17) r1(all_5_0, all_11_0) = 0 & $i(all_11_0) & ? [v0: $i] : ? [v1: int]
% 12.85/2.52 | : ( ~ (v1 = 0) & p1(v0) = v1 & r1(all_11_0, v0) = 0 & $i(v0)) & ?
% 12.85/2.52 | [v0: $i] : (r1(all_11_0, v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: int]
% 12.85/2.52 | : (v2 = 0 | ~ (p1(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 =
% 12.85/2.52 | 0) & r1(v0, v1) = v3)))
% 12.85/2.52 |
% 12.85/2.52 | ALPHA: (17) implies:
% 12.85/2.52 | (18) $i(all_11_0)
% 12.85/2.52 | (19) r1(all_5_0, all_11_0) = 0
% 12.85/2.52 | (20) ? [v0: $i] : (r1(all_11_0, v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2:
% 12.85/2.52 | int] : (v2 = 0 | ~ (p1(v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~
% 12.85/2.52 | (v3 = 0) & r1(v0, v1) = v3)))
% 12.85/2.52 | (21) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p1(v0) = v1 & r1(all_11_0,
% 12.85/2.52 | v0) = 0 & $i(v0))
% 12.85/2.52 |
% 12.85/2.52 | DELTA: instantiating (21) with fresh symbols all_13_0, all_13_1 gives:
% 12.85/2.52 | (22) ~ (all_13_0 = 0) & p1(all_13_1) = all_13_0 & r1(all_11_0, all_13_1) =
% 12.85/2.52 | 0 & $i(all_13_1)
% 12.85/2.52 |
% 12.85/2.52 | ALPHA: (22) implies:
% 12.85/2.52 | (23) ~ (all_13_0 = 0)
% 12.85/2.52 | (24) $i(all_13_1)
% 12.85/2.52 | (25) r1(all_11_0, all_13_1) = 0
% 12.85/2.52 | (26) p1(all_13_1) = all_13_0
% 12.85/2.52 |
% 12.85/2.52 | DELTA: instantiating (20) with fresh symbol all_15_0 gives:
% 12.85/2.52 | (27) r1(all_11_0, all_15_0) = 0 & $i(all_15_0) & ! [v0: $i] : ! [v1: int]
% 12.85/2.52 | : (v1 = 0 | ~ (p1(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0)
% 12.85/2.52 | & r1(all_15_0, v0) = v2))
% 12.85/2.52 |
% 12.85/2.52 | ALPHA: (27) implies:
% 12.85/2.52 | (28) $i(all_15_0)
% 12.85/2.52 | (29) r1(all_11_0, all_15_0) = 0
% 12.85/2.52 | (30) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ $i(v0) |
% 12.85/2.52 | ? [v2: int] : ( ~ (v2 = 0) & r1(all_15_0, v0) = v2))
% 12.85/2.52 |
% 12.85/2.52 | BETA: splitting (3) gives:
% 12.85/2.52 |
% 12.85/2.52 | Case 1:
% 12.85/2.52 | |
% 12.85/2.53 | | (31) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ $i(v0)
% 12.85/2.53 | | | ? [v2: int] : ( ~ (v2 = 0) & r1(all_5_0, v0) = v2))
% 12.85/2.53 | |
% 12.85/2.53 | | GROUND_INST: instantiating (31) with all_9_1, all_9_0, simplifying with
% 12.85/2.53 | | (14), (16) gives:
% 12.85/2.53 | | (32) all_9_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_5_0, all_9_1) =
% 12.85/2.53 | | v0)
% 12.85/2.53 | |
% 12.85/2.53 | | BETA: splitting (32) gives:
% 12.85/2.53 | |
% 12.85/2.53 | | Case 1:
% 12.85/2.53 | | |
% 12.85/2.53 | | | (33) all_9_0 = 0
% 12.85/2.53 | | |
% 12.85/2.53 | | | REDUCE: (13), (33) imply:
% 12.85/2.53 | | | (34) $false
% 12.85/2.53 | | |
% 12.85/2.53 | | | CLOSE: (34) is inconsistent.
% 12.85/2.53 | | |
% 12.85/2.53 | | Case 2:
% 12.85/2.53 | | |
% 12.85/2.53 | | | (35) ? [v0: int] : ( ~ (v0 = 0) & r1(all_5_0, all_9_1) = v0)
% 12.85/2.53 | | |
% 12.85/2.53 | | | DELTA: instantiating (35) with fresh symbol all_35_0 gives:
% 12.85/2.53 | | | (36) ~ (all_35_0 = 0) & r1(all_5_0, all_9_1) = all_35_0
% 12.85/2.53 | | |
% 12.85/2.53 | | | ALPHA: (36) implies:
% 12.85/2.53 | | | (37) ~ (all_35_0 = 0)
% 12.85/2.53 | | | (38) r1(all_5_0, all_9_1) = all_35_0
% 12.85/2.53 | | |
% 12.85/2.53 | | | GROUND_INST: instantiating (1) with 0, all_35_0, all_9_1, all_5_0,
% 12.85/2.53 | | | simplifying with (15), (38) gives:
% 12.85/2.53 | | | (39) all_35_0 = 0
% 12.85/2.53 | | |
% 12.85/2.53 | | | REDUCE: (37), (39) imply:
% 12.85/2.53 | | | (40) $false
% 12.85/2.53 | | |
% 12.85/2.53 | | | CLOSE: (40) is inconsistent.
% 12.85/2.53 | | |
% 12.85/2.53 | | End of split
% 12.85/2.53 | |
% 12.85/2.53 | Case 2:
% 12.85/2.53 | |
% 12.85/2.53 | | (41) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p2(v0) = v1) | ~ $i(v0)
% 12.85/2.53 | | | ? [v2: int] : ( ~ (v2 = 0) & r1(all_5_0, v0) = v2)) | ( ! [v0:
% 12.85/2.53 | | $i] : ( ~ (p1(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0)
% 12.85/2.53 | | & r1(all_5_0, v0) = v1) | ! [v1: $i] : ( ~ (r1(v0, v1) = 0) |
% 12.85/2.53 | | ~ $i(v1) | ? [v2: $i] : (p1(v2) = 0 & r1(v1, v2) = 0 &
% 12.85/2.53 | | $i(v2)))) & ! [v0: $i] : ( ~ (r1(all_5_0, v0) = 0) | ~
% 12.85/2.53 | | $i(v0) | ? [v1: $i] : (r1(v0, v1) = 0 & $i(v1))) & ! [v0: $i]
% 12.85/2.53 | | : ( ~ (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~
% 12.85/2.53 | | (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] : (
% 12.85/2.53 | | ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0 & $i(v2))) | !
% 12.85/2.53 | | [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] :
% 12.85/2.53 | | (r1(v1, v2) = 0 & $i(v2) & ! [v3: $i] : ! [v4: int] : (v4 =
% 12.85/2.53 | | 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5
% 12.85/2.53 | | = 0) & r1(v2, v3) = v5))))) & ! [v0: $i] : ( ~
% 12.85/2.53 | | (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0,
% 12.85/2.53 | | v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: int] : (v3 =
% 12.85/2.53 | | 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 =
% 12.85/2.53 | | 0) & r1(v1, v2) = v4)) | ! [v2: $i] : ( ~ (r1(v1, v2) =
% 12.85/2.54 | | 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0)
% 12.85/2.54 | | & p1(v3) = v4 & r1(v2, v3) = 0 & $i(v3))))))
% 12.85/2.54 | |
% 12.85/2.54 | | BETA: splitting (41) gives:
% 12.85/2.54 | |
% 12.85/2.54 | | Case 1:
% 12.85/2.54 | | |
% 12.85/2.54 | | | (42) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p2(v0) = v1) | ~
% 12.85/2.54 | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & r1(all_5_0, v0) = v2))
% 12.85/2.54 | | |
% 12.85/2.54 | | | GROUND_INST: instantiating (42) with all_7_1, all_7_0, simplifying with
% 12.85/2.54 | | | (9), (11) gives:
% 12.85/2.54 | | | (43) all_7_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_5_0, all_7_1) =
% 12.85/2.54 | | | v0)
% 12.85/2.54 | | |
% 12.85/2.54 | | | BETA: splitting (43) gives:
% 12.85/2.54 | | |
% 12.85/2.54 | | | Case 1:
% 12.85/2.54 | | | |
% 12.85/2.54 | | | | (44) all_7_0 = 0
% 12.85/2.54 | | | |
% 12.85/2.54 | | | | REDUCE: (8), (44) imply:
% 12.85/2.54 | | | | (45) $false
% 12.85/2.54 | | | |
% 12.85/2.54 | | | | CLOSE: (45) is inconsistent.
% 12.85/2.54 | | | |
% 12.85/2.54 | | | Case 2:
% 12.85/2.54 | | | |
% 12.85/2.54 | | | | (46) ? [v0: int] : ( ~ (v0 = 0) & r1(all_5_0, all_7_1) = v0)
% 12.85/2.54 | | | |
% 12.85/2.54 | | | | DELTA: instantiating (46) with fresh symbol all_35_0 gives:
% 12.85/2.54 | | | | (47) ~ (all_35_0 = 0) & r1(all_5_0, all_7_1) = all_35_0
% 12.85/2.54 | | | |
% 12.85/2.54 | | | | ALPHA: (47) implies:
% 12.85/2.54 | | | | (48) ~ (all_35_0 = 0)
% 12.85/2.54 | | | | (49) r1(all_5_0, all_7_1) = all_35_0
% 12.85/2.54 | | | |
% 12.85/2.54 | | | | GROUND_INST: instantiating (1) with 0, all_35_0, all_7_1, all_5_0,
% 12.85/2.54 | | | | simplifying with (10), (49) gives:
% 12.85/2.54 | | | | (50) all_35_0 = 0
% 12.85/2.54 | | | |
% 12.85/2.54 | | | | REDUCE: (48), (50) imply:
% 12.85/2.54 | | | | (51) $false
% 12.85/2.54 | | | |
% 12.85/2.54 | | | | CLOSE: (51) is inconsistent.
% 12.85/2.54 | | | |
% 12.85/2.54 | | | End of split
% 12.85/2.54 | | |
% 12.85/2.54 | | Case 2:
% 12.85/2.54 | | |
% 12.85/2.54 | | | (52) ! [v0: $i] : ( ~ (p1(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 12.85/2.54 | | | (v1 = 0) & r1(all_5_0, v0) = v1) | ! [v1: $i] : ( ~ (r1(v0,
% 12.85/2.54 | | | v1) = 0) | ~ $i(v1) | ? [v2: $i] : (p1(v2) = 0 & r1(v1,
% 12.85/2.54 | | | v2) = 0 & $i(v2)))) & ! [v0: $i] : ( ~ (r1(all_5_0, v0) =
% 12.85/2.54 | | | 0) | ~ $i(v0) | ? [v1: $i] : (r1(v0, v1) = 0 & $i(v1))) & !
% 12.85/2.54 | | | [v0: $i] : ( ~ (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : (
% 12.85/2.54 | | | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] :
% 12.85/2.54 | | | ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0 & $i(v2))) | !
% 12.85/2.54 | | | [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] :
% 12.85/2.54 | | | (r1(v1, v2) = 0 & $i(v2) & ! [v3: $i] : ! [v4: int] : (v4 =
% 12.85/2.54 | | | 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5
% 12.85/2.54 | | | = 0) & r1(v2, v3) = v5))))) & ! [v0: $i] : ( ~
% 12.85/2.54 | | | (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (r1(v0,
% 12.85/2.54 | | | v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: int] : (v3 =
% 12.85/2.54 | | | 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 =
% 12.85/2.54 | | | 0) & r1(v1, v2) = v4)) | ! [v2: $i] : ( ~ (r1(v1, v2) =
% 12.85/2.54 | | | 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0)
% 12.85/2.54 | | | & p1(v3) = v4 & r1(v2, v3) = 0 & $i(v3)))))
% 12.85/2.54 | | |
% 12.85/2.54 | | | ALPHA: (52) implies:
% 13.27/2.55 | | | (53) ! [v0: $i] : ( ~ (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i]
% 13.27/2.55 | | | : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: int]
% 13.27/2.55 | | | : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~
% 13.27/2.55 | | | (v4 = 0) & r1(v1, v2) = v4)) | ! [v2: $i] : ( ~ (r1(v1,
% 13.27/2.55 | | | v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: int] : ( ~
% 13.27/2.55 | | | (v4 = 0) & p1(v3) = v4 & r1(v2, v3) = 0 & $i(v3)))))
% 13.27/2.55 | | | (54) ! [v0: $i] : ( ~ (r1(all_5_0, v0) = 0) | ~ $i(v0) | ! [v1: $i]
% 13.27/2.55 | | | : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int]
% 13.27/2.55 | | | : ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0 & $i(v2))) | !
% 13.27/2.55 | | | [v1: $i] : ( ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] :
% 13.27/2.55 | | | (r1(v1, v2) = 0 & $i(v2) & ! [v3: $i] : ! [v4: int] : (v4 =
% 13.27/2.55 | | | 0 | ~ (p1(v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5
% 13.27/2.55 | | | = 0) & r1(v2, v3) = v5)))))
% 13.27/2.55 | | |
% 13.27/2.55 | | | GROUND_INST: instantiating (54) with all_11_0, simplifying with (18), (19)
% 13.27/2.55 | | | gives:
% 13.27/2.55 | | | (55) ! [v0: $i] : ( ~ (r1(all_11_0, v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 13.27/2.55 | | | : ? [v2: int] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1) = 0 &
% 13.27/2.55 | | | $i(v1))) | ! [v0: $i] : ( ~ (r1(all_11_0, v0) = 0) | ~
% 13.27/2.55 | | | $i(v0) | ? [v1: $i] : (r1(v0, v1) = 0 & $i(v1) & ! [v2: $i] :
% 13.27/2.55 | | | ! [v3: int] : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4:
% 13.27/2.55 | | | int] : ( ~ (v4 = 0) & r1(v1, v2) = v4))))
% 13.27/2.55 | | |
% 13.27/2.55 | | | GROUND_INST: instantiating (53) with all_11_0, simplifying with (18), (19)
% 13.27/2.55 | | | gives:
% 13.27/2.55 | | | (56) ! [v0: $i] : ( ~ (r1(all_11_0, v0) = 0) | ~ $i(v0) | ! [v1: $i]
% 13.27/2.55 | | | : ! [v2: int] : (v2 = 0 | ~ (p1(v1) = v2) | ~ $i(v1) | ?
% 13.27/2.55 | | | [v3: int] : ( ~ (v3 = 0) & r1(v0, v1) = v3)) | ! [v1: $i] : (
% 13.27/2.55 | | | ~ (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] :
% 13.27/2.55 | | | ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0 & $i(v2))))
% 13.27/2.55 | | |
% 13.27/2.55 | | | GROUND_INST: instantiating (56) with all_13_1, simplifying with (24), (25)
% 13.27/2.55 | | | gives:
% 13.27/2.55 | | | (57) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~
% 13.27/2.55 | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & r1(all_13_1, v0) = v2)) |
% 13.27/2.55 | | | ! [v0: $i] : ( ~ (r1(all_13_1, v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 13.27/2.55 | | | : ? [v2: int] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1) = 0 &
% 13.27/2.55 | | | $i(v1)))
% 13.27/2.55 | | |
% 13.27/2.55 | | | BETA: splitting (55) gives:
% 13.27/2.55 | | |
% 13.27/2.55 | | | Case 1:
% 13.27/2.55 | | | |
% 13.27/2.55 | | | | (58) ! [v0: $i] : ( ~ (r1(all_11_0, v0) = 0) | ~ $i(v0) | ? [v1:
% 13.27/2.55 | | | | $i] : ? [v2: int] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1)
% 13.27/2.55 | | | | = 0 & $i(v1)))
% 13.27/2.55 | | | |
% 13.27/2.55 | | | | GROUND_INST: instantiating (58) with all_15_0, simplifying with (28),
% 13.27/2.55 | | | | (29) gives:
% 13.27/2.56 | | | | (59) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p1(v0) = v1 &
% 13.27/2.56 | | | | r1(all_15_0, v0) = 0 & $i(v0))
% 13.27/2.56 | | | |
% 13.27/2.56 | | | | DELTA: instantiating (59) with fresh symbols all_54_0, all_54_1 gives:
% 13.27/2.56 | | | | (60) ~ (all_54_0 = 0) & p1(all_54_1) = all_54_0 & r1(all_15_0,
% 13.27/2.56 | | | | all_54_1) = 0 & $i(all_54_1)
% 13.27/2.56 | | | |
% 13.27/2.56 | | | | ALPHA: (60) implies:
% 13.27/2.56 | | | | (61) ~ (all_54_0 = 0)
% 13.27/2.56 | | | | (62) $i(all_54_1)
% 13.27/2.56 | | | | (63) r1(all_15_0, all_54_1) = 0
% 13.27/2.56 | | | | (64) p1(all_54_1) = all_54_0
% 13.27/2.56 | | | |
% 13.27/2.56 | | | | GROUND_INST: instantiating (30) with all_54_1, all_54_0, simplifying
% 13.27/2.56 | | | | with (62), (64) gives:
% 13.27/2.56 | | | | (65) all_54_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_15_0,
% 13.27/2.56 | | | | all_54_1) = v0)
% 13.27/2.56 | | | |
% 13.27/2.56 | | | | BETA: splitting (65) gives:
% 13.27/2.56 | | | |
% 13.27/2.56 | | | | Case 1:
% 13.27/2.56 | | | | |
% 13.27/2.56 | | | | | (66) all_54_0 = 0
% 13.27/2.56 | | | | |
% 13.27/2.56 | | | | | REDUCE: (61), (66) imply:
% 13.27/2.56 | | | | | (67) $false
% 13.27/2.56 | | | | |
% 13.27/2.56 | | | | | CLOSE: (67) is inconsistent.
% 13.27/2.56 | | | | |
% 13.27/2.56 | | | | Case 2:
% 13.27/2.56 | | | | |
% 13.27/2.56 | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & r1(all_15_0, all_54_1) = v0)
% 13.27/2.56 | | | | |
% 13.27/2.56 | | | | | DELTA: instantiating (68) with fresh symbol all_72_0 gives:
% 13.27/2.56 | | | | | (69) ~ (all_72_0 = 0) & r1(all_15_0, all_54_1) = all_72_0
% 13.27/2.56 | | | | |
% 13.27/2.56 | | | | | ALPHA: (69) implies:
% 13.27/2.56 | | | | | (70) ~ (all_72_0 = 0)
% 13.27/2.56 | | | | | (71) r1(all_15_0, all_54_1) = all_72_0
% 13.27/2.56 | | | | |
% 13.27/2.56 | | | | | GROUND_INST: instantiating (1) with 0, all_72_0, all_54_1, all_15_0,
% 13.27/2.56 | | | | | simplifying with (63), (71) gives:
% 13.27/2.56 | | | | | (72) all_72_0 = 0
% 13.27/2.56 | | | | |
% 13.27/2.56 | | | | | REDUCE: (70), (72) imply:
% 13.27/2.56 | | | | | (73) $false
% 13.27/2.56 | | | | |
% 13.27/2.56 | | | | | CLOSE: (73) is inconsistent.
% 13.27/2.56 | | | | |
% 13.27/2.56 | | | | End of split
% 13.27/2.56 | | | |
% 13.27/2.56 | | | Case 2:
% 13.27/2.56 | | | |
% 13.27/2.56 | | | | (74) ! [v0: $i] : ( ~ (r1(all_11_0, v0) = 0) | ~ $i(v0) | ? [v1:
% 13.27/2.56 | | | | $i] : (r1(v0, v1) = 0 & $i(v1) & ! [v2: $i] : ! [v3: int]
% 13.27/2.56 | | | | : (v3 = 0 | ~ (p1(v2) = v3) | ~ $i(v2) | ? [v4: int] : (
% 13.27/2.56 | | | | ~ (v4 = 0) & r1(v1, v2) = v4))))
% 13.27/2.56 | | | |
% 13.27/2.56 | | | | GROUND_INST: instantiating (74) with all_13_1, simplifying with (24),
% 13.27/2.56 | | | | (25) gives:
% 13.27/2.56 | | | | (75) ? [v0: $i] : (r1(all_13_1, v0) = 0 & $i(v0) & ! [v1: $i] : !
% 13.27/2.56 | | | | [v2: int] : (v2 = 0 | ~ (p1(v1) = v2) | ~ $i(v1) | ? [v3:
% 13.27/2.56 | | | | int] : ( ~ (v3 = 0) & r1(v0, v1) = v3)))
% 13.27/2.56 | | | |
% 13.27/2.56 | | | | DELTA: instantiating (75) with fresh symbol all_58_0 gives:
% 13.27/2.56 | | | | (76) r1(all_13_1, all_58_0) = 0 & $i(all_58_0) & ! [v0: $i] : !
% 13.27/2.56 | | | | [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~ $i(v0) | ? [v2:
% 13.27/2.56 | | | | int] : ( ~ (v2 = 0) & r1(all_58_0, v0) = v2))
% 13.27/2.56 | | | |
% 13.27/2.56 | | | | ALPHA: (76) implies:
% 13.27/2.56 | | | | (77) $i(all_58_0)
% 13.27/2.56 | | | | (78) r1(all_13_1, all_58_0) = 0
% 13.27/2.56 | | | | (79) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~
% 13.27/2.56 | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & r1(all_58_0, v0) = v2))
% 13.27/2.56 | | | |
% 13.27/2.56 | | | | BETA: splitting (57) gives:
% 13.27/2.56 | | | |
% 13.27/2.56 | | | | Case 1:
% 13.27/2.56 | | | | |
% 13.27/2.56 | | | | | (80) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ~
% 13.27/2.56 | | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & r1(all_13_1, v0) =
% 13.27/2.56 | | | | | v2))
% 13.27/2.56 | | | | |
% 13.27/2.56 | | | | | GROUND_INST: instantiating (80) with all_13_1, all_13_0, simplifying
% 13.27/2.56 | | | | | with (24), (26) gives:
% 13.27/2.56 | | | | | (81) all_13_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_13_1,
% 13.27/2.57 | | | | | all_13_1) = v0)
% 13.27/2.57 | | | | |
% 13.27/2.57 | | | | | BETA: splitting (81) gives:
% 13.27/2.57 | | | | |
% 13.27/2.57 | | | | | Case 1:
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | (82) all_13_0 = 0
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | REDUCE: (23), (82) imply:
% 13.27/2.57 | | | | | | (83) $false
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | CLOSE: (83) is inconsistent.
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | Case 2:
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & r1(all_13_1, all_13_1) = v0)
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | DELTA: instantiating (84) with fresh symbol all_155_0 gives:
% 13.27/2.57 | | | | | | (85) ~ (all_155_0 = 0) & r1(all_13_1, all_13_1) = all_155_0
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | ALPHA: (85) implies:
% 13.27/2.57 | | | | | | (86) ~ (all_155_0 = 0)
% 13.27/2.57 | | | | | | (87) r1(all_13_1, all_13_1) = all_155_0
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | GROUND_INST: instantiating (reflexivity) with all_13_1, all_155_0,
% 13.27/2.57 | | | | | | simplifying with (24), (87) gives:
% 13.27/2.57 | | | | | | (88) all_155_0 = 0
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | REDUCE: (86), (88) imply:
% 13.27/2.57 | | | | | | (89) $false
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | CLOSE: (89) is inconsistent.
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | End of split
% 13.27/2.57 | | | | |
% 13.27/2.57 | | | | Case 2:
% 13.27/2.57 | | | | |
% 13.27/2.57 | | | | | (90) ! [v0: $i] : ( ~ (r1(all_13_1, v0) = 0) | ~ $i(v0) | ? [v1:
% 13.27/2.57 | | | | | $i] : ? [v2: int] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0,
% 13.27/2.57 | | | | | v1) = 0 & $i(v1)))
% 13.27/2.57 | | | | |
% 13.27/2.57 | | | | | GROUND_INST: instantiating (90) with all_58_0, simplifying with (77),
% 13.27/2.57 | | | | | (78) gives:
% 13.27/2.57 | | | | | (91) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p1(v0) = v1 &
% 13.27/2.57 | | | | | r1(all_58_0, v0) = 0 & $i(v0))
% 13.27/2.57 | | | | |
% 13.27/2.57 | | | | | DELTA: instantiating (91) with fresh symbols all_145_0, all_145_1
% 13.27/2.57 | | | | | gives:
% 13.27/2.57 | | | | | (92) ~ (all_145_0 = 0) & p1(all_145_1) = all_145_0 & r1(all_58_0,
% 13.27/2.57 | | | | | all_145_1) = 0 & $i(all_145_1)
% 13.27/2.57 | | | | |
% 13.27/2.57 | | | | | ALPHA: (92) implies:
% 13.27/2.57 | | | | | (93) ~ (all_145_0 = 0)
% 13.27/2.57 | | | | | (94) $i(all_145_1)
% 13.27/2.57 | | | | | (95) r1(all_58_0, all_145_1) = 0
% 13.27/2.57 | | | | | (96) p1(all_145_1) = all_145_0
% 13.27/2.57 | | | | |
% 13.27/2.57 | | | | | GROUND_INST: instantiating (79) with all_145_1, all_145_0, simplifying
% 13.27/2.57 | | | | | with (94), (96) gives:
% 13.27/2.57 | | | | | (97) all_145_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & r1(all_58_0,
% 13.27/2.57 | | | | | all_145_1) = v0)
% 13.27/2.57 | | | | |
% 13.27/2.57 | | | | | BETA: splitting (97) gives:
% 13.27/2.57 | | | | |
% 13.27/2.57 | | | | | Case 1:
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | (98) all_145_0 = 0
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | REDUCE: (93), (98) imply:
% 13.27/2.57 | | | | | | (99) $false
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | CLOSE: (99) is inconsistent.
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | Case 2:
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | (100) ? [v0: int] : ( ~ (v0 = 0) & r1(all_58_0, all_145_1) = v0)
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | DELTA: instantiating (100) with fresh symbol all_164_0 gives:
% 13.27/2.57 | | | | | | (101) ~ (all_164_0 = 0) & r1(all_58_0, all_145_1) = all_164_0
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | ALPHA: (101) implies:
% 13.27/2.57 | | | | | | (102) ~ (all_164_0 = 0)
% 13.27/2.57 | | | | | | (103) r1(all_58_0, all_145_1) = all_164_0
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | GROUND_INST: instantiating (1) with 0, all_164_0, all_145_1,
% 13.27/2.57 | | | | | | all_58_0, simplifying with (95), (103) gives:
% 13.27/2.57 | | | | | | (104) all_164_0 = 0
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | REDUCE: (102), (104) imply:
% 13.27/2.57 | | | | | | (105) $false
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | | CLOSE: (105) is inconsistent.
% 13.27/2.57 | | | | | |
% 13.27/2.57 | | | | | End of split
% 13.27/2.57 | | | | |
% 13.27/2.57 | | | | End of split
% 13.27/2.57 | | | |
% 13.27/2.57 | | | End of split
% 13.27/2.57 | | |
% 13.27/2.57 | | End of split
% 13.27/2.57 | |
% 13.27/2.57 | End of split
% 13.27/2.57 |
% 13.27/2.57 End of proof
% 13.27/2.57 % SZS output end Proof for theBenchmark
% 13.27/2.57
% 13.27/2.57 1939ms
%------------------------------------------------------------------------------