TSTP Solution File: SWV401+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV401+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n006.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 22:56:11 EDT 2023
% Result : Theorem 8.52s 1.93s
% Output : Proof 10.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV401+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 03:23:06 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.47/0.60 ________ _____
% 0.47/0.60 ___ __ \_________(_)________________________________
% 0.47/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.47/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.47/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.47/0.60
% 0.47/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.47/0.60 (2023-06-19)
% 0.47/0.60
% 0.47/0.60 (c) Philipp Rümmer, 2009-2023
% 0.47/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.47/0.60 Amanda Stjerna.
% 0.47/0.60 Free software under BSD-3-Clause.
% 0.47/0.60
% 0.47/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.47/0.60
% 0.47/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.47/0.61 Running up to 7 provers in parallel.
% 0.47/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.47/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.47/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.47/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.47/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.47/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.47/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.81/1.09 Prover 4: Preprocessing ...
% 2.81/1.09 Prover 1: Preprocessing ...
% 2.81/1.13 Prover 0: Preprocessing ...
% 2.81/1.13 Prover 5: Preprocessing ...
% 2.81/1.13 Prover 6: Preprocessing ...
% 2.81/1.13 Prover 2: Preprocessing ...
% 2.81/1.13 Prover 3: Preprocessing ...
% 5.59/1.53 Prover 6: Proving ...
% 5.59/1.53 Prover 1: Constructing countermodel ...
% 6.04/1.54 Prover 3: Constructing countermodel ...
% 6.04/1.55 Prover 5: Proving ...
% 6.04/1.55 Prover 2: Proving ...
% 6.16/1.57 Prover 4: Constructing countermodel ...
% 6.16/1.58 Prover 0: Proving ...
% 8.52/1.93 Prover 3: proved (1303ms)
% 8.52/1.93
% 8.52/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.52/1.93
% 8.52/1.93 Prover 0: stopped
% 8.52/1.93 Prover 2: stopped
% 8.52/1.93 Prover 6: stopped
% 8.52/1.95 Prover 5: stopped
% 8.52/1.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.52/1.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.52/1.95 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.52/1.95 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.52/1.95 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.52/1.96 Prover 8: Preprocessing ...
% 9.19/1.99 Prover 7: Preprocessing ...
% 9.19/1.99 Prover 11: Preprocessing ...
% 9.19/1.99 Prover 13: Preprocessing ...
% 9.19/2.00 Prover 10: Preprocessing ...
% 9.67/2.06 Prover 7: Warning: ignoring some quantifiers
% 9.67/2.09 Prover 7: Constructing countermodel ...
% 9.67/2.09 Prover 10: Warning: ignoring some quantifiers
% 9.67/2.09 Prover 1: Found proof (size 101)
% 9.67/2.10 Prover 1: proved (1477ms)
% 9.67/2.10 Prover 4: stopped
% 9.67/2.10 Prover 7: stopped
% 9.67/2.10 Prover 13: Warning: ignoring some quantifiers
% 9.67/2.10 Prover 10: Constructing countermodel ...
% 9.67/2.10 Prover 8: Warning: ignoring some quantifiers
% 9.67/2.11 Prover 10: stopped
% 9.67/2.11 Prover 8: Constructing countermodel ...
% 9.67/2.11 Prover 13: Constructing countermodel ...
% 9.67/2.12 Prover 8: stopped
% 9.67/2.12 Prover 13: stopped
% 10.33/2.13 Prover 11: Constructing countermodel ...
% 10.33/2.14 Prover 11: stopped
% 10.33/2.14
% 10.33/2.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.33/2.14
% 10.33/2.16 % SZS output start Proof for theBenchmark
% 10.33/2.16 Assumptions after simplification:
% 10.33/2.16 ---------------------------------
% 10.33/2.16
% 10.33/2.16 (ax23)
% 10.63/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 10.63/2.19 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (pair_in_list(v6, v2, v4) =
% 10.63/2.19 v7) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ $i(v4) |
% 10.63/2.19 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ? [v8: int] : ( ~ (v8 = 0)
% 10.63/2.19 & pair_in_list(v0, v2, v4) = v8) & ( ~ (v4 = v3) | ~ (v2 = v1)))) & !
% 10.63/2.19 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 10.63/2.19 : ! [v6: $i] : ( ~ (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) |
% 10.63/2.19 ~ (insert_slb(v0, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 10.63/2.19 | ~ $i(v0) | pair_in_list(v0, v2, v4) = 0 | (v4 = v3 & v2 = v1))
% 10.63/2.19
% 10.63/2.19 (ax29)
% 10.63/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 10.63/2.19 $i] : ! [v6: $i] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) |
% 10.63/2.19 ~ (insert_slb(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 10.63/2.19 | ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : (update_slb(v0,
% 10.63/2.19 v2) = v8 & pair(v1, v2) = v9 & insert_slb(v8, v9) = v10 &
% 10.63/2.19 strictly_less_than(v3, v2) = v7 & $i(v10) & $i(v9) & $i(v8) & ( ~ (v7 = 0)
% 10.63/2.19 | v10 = v6)))
% 10.63/2.19
% 10.63/2.19 (ax30)
% 10.63/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 10.63/2.20 $i] : ! [v6: $i] : ( ~ (update_slb(v5, v2) = v6) | ~ (pair(v1, v3) = v4) |
% 10.63/2.20 ~ (insert_slb(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 10.63/2.20 | ? [v7: any] : ? [v8: $i] : ? [v9: $i] : (update_slb(v0, v2) = v8 &
% 10.63/2.20 insert_slb(v8, v4) = v9 & less_than(v2, v3) = v7 & $i(v9) & $i(v8) & ( ~
% 10.63/2.20 (v7 = 0) | v9 = v6)))
% 10.63/2.20
% 10.63/2.20 (l37_co)
% 10.63/2.20 ? [v0: $i] : ($i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 10.63/2.20 : ! [v5: int] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~
% 10.63/2.20 (pair_in_list(v4, v1, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ?
% 10.63/2.20 [v6: any] : ? [v7: any] : (pair_in_list(v0, v1, v2) = v6 & less_than(v3,
% 10.63/2.20 v2) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ? [v1: $i] : ? [v2: $i] :
% 10.63/2.20 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 10.63/2.20 [v8: $i] : ? [v9: int] : ( ~ (v9 = 0) & update_slb(v7, v3) = v8 &
% 10.63/2.20 pair_in_list(v8, v1, v2) = v9 & pair_in_list(v7, v1, v2) = 0 & pair(v4,
% 10.63/2.20 v5) = v6 & insert_slb(v0, v6) = v7 & less_than(v3, v2) = 0 & $i(v8) &
% 10.63/2.20 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1)))
% 10.63/2.20
% 10.63/2.20 (stricly_smaller_definition)
% 10.63/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 10.63/2.21 (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 10.63/2.21 ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 =
% 10.63/2.21 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 10.63/2.21 (strictly_less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : (
% 10.63/2.21 ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0))
% 10.63/2.21
% 10.63/2.21 (totality)
% 10.63/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v0, v1) =
% 10.63/2.21 v2) | ~ $i(v1) | ~ $i(v0) | less_than(v1, v0) = 0)
% 10.63/2.21
% 10.63/2.21 (function-axioms)
% 10.63/2.21 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.63/2.21 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 10.63/2.21 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 10.63/2.21 ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2)
% 10.63/2.21 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 10.63/2.21 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) & ! [v0: $i]
% 10.63/2.21 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_slb(v3, v2)
% 10.63/2.21 = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 10.63/2.21 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.63/2.21 (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) & ! [v0: $i]
% 10.63/2.21 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (pair(v3, v2) = v1)
% 10.63/2.21 | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 10.63/2.21 [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) =
% 10.63/2.21 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.63/2.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~
% 10.63/2.21 (strictly_less_than(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.63/2.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.63/2.21 (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) & ! [v0:
% 10.63/2.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.63/2.21 ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0))
% 10.63/2.21
% 10.63/2.22 Further assumptions not needed in the proof:
% 10.63/2.22 --------------------------------------------
% 10.63/2.22 ax18, ax19, ax20, ax21, ax22, ax24, ax25, ax26, ax27, ax28, bottom_smallest,
% 10.63/2.22 reflexivity, transitivity
% 10.63/2.22
% 10.63/2.22 Those formulas are unsatisfiable:
% 10.63/2.22 ---------------------------------
% 10.63/2.22
% 10.63/2.22 Begin of proof
% 10.63/2.22 |
% 10.63/2.22 | ALPHA: (stricly_smaller_definition) implies:
% 10.63/2.22 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 10.63/2.22 | (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 10.63/2.22 | any] : ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) =
% 10.63/2.22 | v3 & ( ~ (v3 = 0) | v4 = 0)))
% 10.63/2.22 |
% 10.63/2.22 | ALPHA: (ax23) implies:
% 10.63/2.22 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 10.63/2.22 | ! [v5: $i] : ! [v6: $i] : ( ~ (pair_in_list(v6, v2, v4) = 0) | ~
% 10.63/2.22 | (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ $i(v4) | ~
% 10.63/2.22 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | pair_in_list(v0, v2, v4)
% 10.63/2.22 | = 0 | (v4 = v3 & v2 = v1))
% 10.63/2.22 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 10.63/2.22 | ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~
% 10.63/2.22 | (pair_in_list(v6, v2, v4) = v7) | ~ (pair(v1, v3) = v5) | ~
% 10.63/2.22 | (insert_slb(v0, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 10.63/2.22 | $i(v1) | ~ $i(v0) | ( ? [v8: int] : ( ~ (v8 = 0) & pair_in_list(v0,
% 10.63/2.22 | v2, v4) = v8) & ( ~ (v4 = v3) | ~ (v2 = v1))))
% 10.63/2.22 |
% 10.63/2.22 | ALPHA: (function-axioms) implies:
% 10.63/2.22 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.63/2.22 | ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~
% 10.63/2.22 | (less_than(v3, v2) = v0))
% 10.63/2.23 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.63/2.23 | (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0))
% 10.63/2.23 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.63/2.23 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) =
% 10.63/2.23 | v1) | ~ (pair_in_list(v4, v3, v2) = v0))
% 10.63/2.23 |
% 10.63/2.23 | DELTA: instantiating (l37_co) with fresh symbol all_23_0 gives:
% 10.63/2.23 | (7) $i(all_23_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 10.63/2.23 | ! [v4: int] : (v4 = 0 | ~ (update_slb(all_23_0, v2) = v3) | ~
% 10.63/2.23 | (pair_in_list(v3, v0, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 10.63/2.23 | ? [v5: any] : ? [v6: any] : (pair_in_list(all_23_0, v0, v1) = v5 &
% 10.63/2.23 | less_than(v2, v1) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ? [v0:
% 10.63/2.23 | $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 10.63/2.23 | $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 10.63/2.23 | update_slb(v6, v2) = v7 & pair_in_list(v7, v0, v1) = v8 &
% 10.63/2.23 | pair_in_list(v6, v0, v1) = 0 & pair(v3, v4) = v5 &
% 10.63/2.23 | insert_slb(all_23_0, v5) = v6 & less_than(v2, v1) = 0 & $i(v7) &
% 10.63/2.23 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.63/2.23 |
% 10.63/2.23 | ALPHA: (7) implies:
% 10.63/2.23 | (8) $i(all_23_0)
% 10.63/2.23 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 10.63/2.23 | (v4 = 0 | ~ (update_slb(all_23_0, v2) = v3) | ~ (pair_in_list(v3, v0,
% 10.63/2.23 | v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ?
% 10.63/2.23 | [v6: any] : (pair_in_list(all_23_0, v0, v1) = v5 & less_than(v2, v1)
% 10.63/2.23 | = v6 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 10.63/2.23 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 10.63/2.23 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 10.63/2.23 | update_slb(v6, v2) = v7 & pair_in_list(v7, v0, v1) = v8 &
% 10.63/2.23 | pair_in_list(v6, v0, v1) = 0 & pair(v3, v4) = v5 &
% 10.63/2.23 | insert_slb(all_23_0, v5) = v6 & less_than(v2, v1) = 0 & $i(v7) &
% 10.63/2.23 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.63/2.23 |
% 10.63/2.23 | DELTA: instantiating (10) with fresh symbols all_26_0, all_26_1, all_26_2,
% 10.63/2.23 | all_26_3, all_26_4, all_26_5, all_26_6, all_26_7, all_26_8 gives:
% 10.63/2.23 | (11) ~ (all_26_0 = 0) & update_slb(all_26_2, all_26_6) = all_26_1 &
% 10.63/2.23 | pair_in_list(all_26_1, all_26_8, all_26_7) = all_26_0 &
% 10.63/2.23 | pair_in_list(all_26_2, all_26_8, all_26_7) = 0 & pair(all_26_5,
% 10.63/2.23 | all_26_4) = all_26_3 & insert_slb(all_23_0, all_26_3) = all_26_2 &
% 10.63/2.24 | less_than(all_26_6, all_26_7) = 0 & $i(all_26_1) & $i(all_26_2) &
% 10.63/2.24 | $i(all_26_3) & $i(all_26_4) & $i(all_26_5) & $i(all_26_6) &
% 10.63/2.24 | $i(all_26_7) & $i(all_26_8)
% 10.63/2.24 |
% 10.63/2.24 | ALPHA: (11) implies:
% 10.63/2.24 | (12) ~ (all_26_0 = 0)
% 10.63/2.24 | (13) $i(all_26_8)
% 10.63/2.24 | (14) $i(all_26_7)
% 10.63/2.24 | (15) $i(all_26_6)
% 10.63/2.24 | (16) $i(all_26_5)
% 10.63/2.24 | (17) $i(all_26_4)
% 10.63/2.24 | (18) less_than(all_26_6, all_26_7) = 0
% 10.63/2.24 | (19) insert_slb(all_23_0, all_26_3) = all_26_2
% 10.63/2.24 | (20) pair(all_26_5, all_26_4) = all_26_3
% 10.63/2.24 | (21) pair_in_list(all_26_2, all_26_8, all_26_7) = 0
% 10.63/2.24 | (22) pair_in_list(all_26_1, all_26_8, all_26_7) = all_26_0
% 10.63/2.24 | (23) update_slb(all_26_2, all_26_6) = all_26_1
% 10.63/2.24 |
% 10.63/2.24 | GROUND_INST: instantiating (2) with all_23_0, all_26_5, all_26_8, all_26_4,
% 10.63/2.24 | all_26_7, all_26_3, all_26_2, simplifying with (8), (13), (14),
% 10.63/2.24 | (16), (17), (19), (20), (21) gives:
% 10.63/2.24 | (24) pair_in_list(all_23_0, all_26_8, all_26_7) = 0 | (all_26_4 = all_26_7
% 10.63/2.24 | & all_26_5 = all_26_8)
% 10.63/2.24 |
% 10.63/2.24 | GROUND_INST: instantiating (ax29) with all_23_0, all_26_5, all_26_6, all_26_4,
% 10.63/2.24 | all_26_3, all_26_2, all_26_1, simplifying with (8), (15), (16),
% 10.63/2.24 | (17), (19), (20), (23) gives:
% 10.63/2.24 | (25) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 10.63/2.24 | (update_slb(all_23_0, all_26_6) = v1 & pair(all_26_5, all_26_6) = v2 &
% 10.63/2.24 | insert_slb(v1, v2) = v3 & strictly_less_than(all_26_4, all_26_6) =
% 10.63/2.24 | v0 & $i(v3) & $i(v2) & $i(v1) & ( ~ (v0 = 0) | v3 = all_26_1))
% 10.63/2.24 |
% 10.63/2.24 | GROUND_INST: instantiating (ax30) with all_23_0, all_26_5, all_26_6, all_26_4,
% 10.63/2.24 | all_26_3, all_26_2, all_26_1, simplifying with (8), (15), (16),
% 10.63/2.24 | (17), (19), (20), (23) gives:
% 10.63/2.24 | (26) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (update_slb(all_23_0,
% 10.63/2.24 | all_26_6) = v1 & insert_slb(v1, all_26_3) = v2 &
% 10.63/2.24 | less_than(all_26_6, all_26_4) = v0 & $i(v2) & $i(v1) & ( ~ (v0 = 0)
% 10.63/2.24 | | v2 = all_26_1))
% 10.63/2.24 |
% 10.63/2.24 | DELTA: instantiating (26) with fresh symbols all_34_0, all_34_1, all_34_2
% 10.63/2.24 | gives:
% 10.63/2.24 | (27) update_slb(all_23_0, all_26_6) = all_34_1 & insert_slb(all_34_1,
% 10.63/2.24 | all_26_3) = all_34_0 & less_than(all_26_6, all_26_4) = all_34_2 &
% 10.63/2.24 | $i(all_34_0) & $i(all_34_1) & ( ~ (all_34_2 = 0) | all_34_0 =
% 10.63/2.24 | all_26_1)
% 10.63/2.24 |
% 10.63/2.24 | ALPHA: (27) implies:
% 10.63/2.25 | (28) less_than(all_26_6, all_26_4) = all_34_2
% 10.63/2.25 | (29) insert_slb(all_34_1, all_26_3) = all_34_0
% 10.63/2.25 | (30) update_slb(all_23_0, all_26_6) = all_34_1
% 10.63/2.25 | (31) ~ (all_34_2 = 0) | all_34_0 = all_26_1
% 10.63/2.25 |
% 10.63/2.25 | DELTA: instantiating (25) with fresh symbols all_36_0, all_36_1, all_36_2,
% 10.63/2.25 | all_36_3 gives:
% 10.63/2.25 | (32) update_slb(all_23_0, all_26_6) = all_36_2 & pair(all_26_5, all_26_6) =
% 10.63/2.25 | all_36_1 & insert_slb(all_36_2, all_36_1) = all_36_0 &
% 10.63/2.25 | strictly_less_than(all_26_4, all_26_6) = all_36_3 & $i(all_36_0) &
% 10.63/2.25 | $i(all_36_1) & $i(all_36_2) & ( ~ (all_36_3 = 0) | all_36_0 =
% 10.63/2.25 | all_26_1)
% 10.63/2.25 |
% 10.63/2.25 | ALPHA: (32) implies:
% 10.63/2.25 | (33) $i(all_36_2)
% 10.63/2.25 | (34) strictly_less_than(all_26_4, all_26_6) = all_36_3
% 10.63/2.25 | (35) insert_slb(all_36_2, all_36_1) = all_36_0
% 10.63/2.25 | (36) pair(all_26_5, all_26_6) = all_36_1
% 10.63/2.25 | (37) update_slb(all_23_0, all_26_6) = all_36_2
% 10.63/2.25 | (38) ~ (all_36_3 = 0) | all_36_0 = all_26_1
% 10.63/2.25 |
% 10.63/2.25 | GROUND_INST: instantiating (5) with all_34_1, all_36_2, all_26_6, all_23_0,
% 10.63/2.25 | simplifying with (30), (37) gives:
% 10.63/2.25 | (39) all_36_2 = all_34_1
% 10.63/2.25 |
% 10.63/2.25 | REDUCE: (35), (39) imply:
% 10.63/2.25 | (40) insert_slb(all_34_1, all_36_1) = all_36_0
% 10.63/2.25 |
% 10.63/2.25 | REDUCE: (33), (39) imply:
% 10.63/2.25 | (41) $i(all_34_1)
% 10.63/2.25 |
% 10.63/2.25 | GROUND_INST: instantiating (totality) with all_26_6, all_26_4, all_34_2,
% 10.63/2.25 | simplifying with (15), (17), (28) gives:
% 10.63/2.25 | (42) all_34_2 = 0 | less_than(all_26_4, all_26_6) = 0
% 10.63/2.25 |
% 10.63/2.25 | GROUND_INST: instantiating (1) with all_26_4, all_26_6, all_36_3, simplifying
% 10.63/2.25 | with (15), (17), (34) gives:
% 10.63/2.25 | (43) all_36_3 = 0 | ? [v0: any] : ? [v1: any] : (less_than(all_26_4,
% 10.63/2.25 | all_26_6) = v0 & less_than(all_26_6, all_26_4) = v1 & ( ~ (v0 = 0)
% 10.63/2.25 | | v1 = 0))
% 10.63/2.25 |
% 10.63/2.25 | BETA: splitting (24) gives:
% 10.63/2.25 |
% 10.63/2.25 | Case 1:
% 10.63/2.25 | |
% 10.63/2.25 | | (44) pair_in_list(all_23_0, all_26_8, all_26_7) = 0
% 10.63/2.25 | |
% 10.63/2.25 | | BETA: splitting (31) gives:
% 10.63/2.25 | |
% 10.63/2.25 | | Case 1:
% 10.63/2.25 | | |
% 10.63/2.25 | | | (45) ~ (all_34_2 = 0)
% 10.63/2.25 | | |
% 10.63/2.25 | | | BETA: splitting (42) gives:
% 10.63/2.25 | | |
% 10.63/2.25 | | | Case 1:
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | (46) less_than(all_26_4, all_26_6) = 0
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | BETA: splitting (43) gives:
% 10.63/2.25 | | | |
% 10.63/2.25 | | | | Case 1:
% 10.63/2.25 | | | | |
% 10.63/2.25 | | | | | (47) all_36_3 = 0
% 10.63/2.25 | | | | |
% 10.63/2.25 | | | | | BETA: splitting (38) gives:
% 10.63/2.25 | | | | |
% 10.63/2.25 | | | | | Case 1:
% 10.63/2.25 | | | | | |
% 10.63/2.25 | | | | | | (48) ~ (all_36_3 = 0)
% 10.63/2.25 | | | | | |
% 10.63/2.25 | | | | | | REDUCE: (47), (48) imply:
% 10.63/2.25 | | | | | | (49) $false
% 10.63/2.25 | | | | | |
% 10.63/2.25 | | | | | | CLOSE: (49) is inconsistent.
% 10.63/2.25 | | | | | |
% 10.63/2.25 | | | | | Case 2:
% 10.63/2.25 | | | | | |
% 10.63/2.25 | | | | | | (50) all_36_0 = all_26_1
% 10.63/2.25 | | | | | |
% 10.63/2.26 | | | | | | REDUCE: (40), (50) imply:
% 10.63/2.26 | | | | | | (51) insert_slb(all_34_1, all_36_1) = all_26_1
% 10.63/2.26 | | | | | |
% 10.96/2.26 | | | | | | GROUND_INST: instantiating (3) with all_34_1, all_26_5, all_26_8,
% 10.96/2.26 | | | | | | all_26_6, all_26_7, all_36_1, all_26_1, all_26_0,
% 10.96/2.26 | | | | | | simplifying with (13), (14), (15), (16), (22), (36),
% 10.96/2.26 | | | | | | (41), (51) gives:
% 10.96/2.26 | | | | | | (52) all_26_0 = 0 | ( ? [v0: int] : ( ~ (v0 = 0) &
% 10.96/2.26 | | | | | | pair_in_list(all_34_1, all_26_8, all_26_7) = v0) & ( ~
% 10.96/2.26 | | | | | | (all_26_5 = all_26_8) | ~ (all_26_6 = all_26_7)))
% 10.96/2.26 | | | | | |
% 10.96/2.26 | | | | | | BETA: splitting (52) gives:
% 10.96/2.26 | | | | | |
% 10.96/2.26 | | | | | | Case 1:
% 10.96/2.26 | | | | | | |
% 10.96/2.26 | | | | | | | (53) all_26_0 = 0
% 10.96/2.26 | | | | | | |
% 10.96/2.26 | | | | | | | REDUCE: (12), (53) imply:
% 10.96/2.26 | | | | | | | (54) $false
% 10.96/2.26 | | | | | | |
% 10.96/2.26 | | | | | | | CLOSE: (54) is inconsistent.
% 10.96/2.26 | | | | | | |
% 10.96/2.26 | | | | | | Case 2:
% 10.96/2.26 | | | | | | |
% 10.96/2.26 | | | | | | | (55) ? [v0: int] : ( ~ (v0 = 0) & pair_in_list(all_34_1,
% 10.96/2.26 | | | | | | | all_26_8, all_26_7) = v0) & ( ~ (all_26_5 = all_26_8)
% 10.96/2.26 | | | | | | | | ~ (all_26_6 = all_26_7))
% 10.96/2.26 | | | | | | |
% 10.96/2.26 | | | | | | | ALPHA: (55) implies:
% 10.96/2.26 | | | | | | | (56) ? [v0: int] : ( ~ (v0 = 0) & pair_in_list(all_34_1,
% 10.96/2.26 | | | | | | | all_26_8, all_26_7) = v0)
% 10.96/2.26 | | | | | | |
% 10.96/2.26 | | | | | | | DELTA: instantiating (56) with fresh symbol all_90_0 gives:
% 10.96/2.26 | | | | | | | (57) ~ (all_90_0 = 0) & pair_in_list(all_34_1, all_26_8,
% 10.96/2.26 | | | | | | | all_26_7) = all_90_0
% 10.96/2.26 | | | | | | |
% 10.96/2.26 | | | | | | | ALPHA: (57) implies:
% 10.96/2.26 | | | | | | | (58) ~ (all_90_0 = 0)
% 10.96/2.26 | | | | | | | (59) pair_in_list(all_34_1, all_26_8, all_26_7) = all_90_0
% 10.96/2.26 | | | | | | |
% 10.96/2.26 | | | | | | | GROUND_INST: instantiating (9) with all_26_8, all_26_7, all_26_6,
% 10.96/2.26 | | | | | | | all_34_1, all_90_0, simplifying with (13), (14),
% 10.96/2.26 | | | | | | | (15), (30), (59) gives:
% 10.96/2.26 | | | | | | | (60) all_90_0 = 0 | ? [v0: any] : ? [v1: any] :
% 10.96/2.26 | | | | | | | (pair_in_list(all_23_0, all_26_8, all_26_7) = v0 &
% 10.96/2.26 | | | | | | | less_than(all_26_6, all_26_7) = v1 & ( ~ (v1 = 0) | ~
% 10.96/2.26 | | | | | | | (v0 = 0)))
% 10.96/2.26 | | | | | | |
% 10.96/2.26 | | | | | | | BETA: splitting (60) gives:
% 10.96/2.26 | | | | | | |
% 10.96/2.26 | | | | | | | Case 1:
% 10.96/2.26 | | | | | | | |
% 10.96/2.26 | | | | | | | | (61) all_90_0 = 0
% 10.96/2.26 | | | | | | | |
% 10.96/2.26 | | | | | | | | REDUCE: (58), (61) imply:
% 10.96/2.26 | | | | | | | | (62) $false
% 10.96/2.26 | | | | | | | |
% 10.96/2.26 | | | | | | | | CLOSE: (62) is inconsistent.
% 10.96/2.26 | | | | | | | |
% 10.96/2.26 | | | | | | | Case 2:
% 10.96/2.26 | | | | | | | |
% 10.96/2.26 | | | | | | | | (63) ? [v0: any] : ? [v1: any] : (pair_in_list(all_23_0,
% 10.96/2.26 | | | | | | | | all_26_8, all_26_7) = v0 & less_than(all_26_6,
% 10.96/2.26 | | | | | | | | all_26_7) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 10.96/2.26 | | | | | | | |
% 10.96/2.26 | | | | | | | | DELTA: instantiating (63) with fresh symbols all_95_0, all_95_1
% 10.96/2.26 | | | | | | | | gives:
% 10.96/2.26 | | | | | | | | (64) pair_in_list(all_23_0, all_26_8, all_26_7) = all_95_1 &
% 10.96/2.26 | | | | | | | | less_than(all_26_6, all_26_7) = all_95_0 & ( ~ (all_95_0
% 10.96/2.26 | | | | | | | | = 0) | ~ (all_95_1 = 0))
% 10.96/2.26 | | | | | | | |
% 10.96/2.26 | | | | | | | | REF_CLOSE: (4), (6), (18), (44), (64) are inconsistent by
% 10.96/2.26 | | | | | | | | sub-proof #1.
% 10.96/2.26 | | | | | | | |
% 10.96/2.26 | | | | | | | End of split
% 10.96/2.26 | | | | | | |
% 10.96/2.26 | | | | | | End of split
% 10.96/2.26 | | | | | |
% 10.96/2.26 | | | | | End of split
% 10.96/2.26 | | | | |
% 10.96/2.26 | | | | Case 2:
% 10.96/2.26 | | | | |
% 10.96/2.27 | | | | | (65) ? [v0: any] : ? [v1: any] : (less_than(all_26_4, all_26_6) =
% 10.96/2.27 | | | | | v0 & less_than(all_26_6, all_26_4) = v1 & ( ~ (v0 = 0) | v1
% 10.96/2.27 | | | | | = 0))
% 10.96/2.27 | | | | |
% 10.96/2.27 | | | | | DELTA: instantiating (65) with fresh symbols all_70_0, all_70_1 gives:
% 10.99/2.27 | | | | | (66) less_than(all_26_4, all_26_6) = all_70_1 & less_than(all_26_6,
% 10.99/2.27 | | | | | all_26_4) = all_70_0 & ( ~ (all_70_1 = 0) | all_70_0 = 0)
% 10.99/2.27 | | | | |
% 10.99/2.27 | | | | | ALPHA: (66) implies:
% 10.99/2.27 | | | | | (67) less_than(all_26_6, all_26_4) = all_70_0
% 10.99/2.27 | | | | | (68) less_than(all_26_4, all_26_6) = all_70_1
% 10.99/2.27 | | | | | (69) ~ (all_70_1 = 0) | all_70_0 = 0
% 10.99/2.27 | | | | |
% 10.99/2.27 | | | | | GROUND_INST: instantiating (4) with all_34_2, all_70_0, all_26_4,
% 10.99/2.27 | | | | | all_26_6, simplifying with (28), (67) gives:
% 10.99/2.27 | | | | | (70) all_70_0 = all_34_2
% 10.99/2.27 | | | | |
% 10.99/2.27 | | | | | GROUND_INST: instantiating (4) with 0, all_70_1, all_26_6, all_26_4,
% 10.99/2.27 | | | | | simplifying with (46), (68) gives:
% 10.99/2.27 | | | | | (71) all_70_1 = 0
% 10.99/2.27 | | | | |
% 10.99/2.27 | | | | | BETA: splitting (69) gives:
% 10.99/2.27 | | | | |
% 10.99/2.27 | | | | | Case 1:
% 10.99/2.27 | | | | | |
% 10.99/2.27 | | | | | | (72) ~ (all_70_1 = 0)
% 10.99/2.27 | | | | | |
% 10.99/2.27 | | | | | | REDUCE: (71), (72) imply:
% 10.99/2.27 | | | | | | (73) $false
% 10.99/2.27 | | | | | |
% 10.99/2.27 | | | | | | CLOSE: (73) is inconsistent.
% 10.99/2.27 | | | | | |
% 10.99/2.27 | | | | | Case 2:
% 10.99/2.27 | | | | | |
% 10.99/2.27 | | | | | | (74) all_70_0 = 0
% 10.99/2.27 | | | | | |
% 10.99/2.27 | | | | | | COMBINE_EQS: (70), (74) imply:
% 10.99/2.27 | | | | | | (75) all_34_2 = 0
% 10.99/2.27 | | | | | |
% 10.99/2.27 | | | | | | REDUCE: (45), (75) imply:
% 10.99/2.27 | | | | | | (76) $false
% 10.99/2.27 | | | | | |
% 10.99/2.27 | | | | | | CLOSE: (76) is inconsistent.
% 10.99/2.27 | | | | | |
% 10.99/2.27 | | | | | End of split
% 10.99/2.27 | | | | |
% 10.99/2.27 | | | | End of split
% 10.99/2.27 | | | |
% 10.99/2.27 | | | Case 2:
% 10.99/2.27 | | | |
% 10.99/2.27 | | | | (77) all_34_2 = 0
% 10.99/2.27 | | | |
% 10.99/2.27 | | | | REDUCE: (45), (77) imply:
% 10.99/2.27 | | | | (78) $false
% 10.99/2.27 | | | |
% 10.99/2.27 | | | | CLOSE: (78) is inconsistent.
% 10.99/2.27 | | | |
% 10.99/2.27 | | | End of split
% 10.99/2.27 | | |
% 10.99/2.27 | | Case 2:
% 10.99/2.27 | | |
% 10.99/2.27 | | | (79) all_34_0 = all_26_1
% 10.99/2.27 | | |
% 10.99/2.27 | | | REDUCE: (29), (79) imply:
% 10.99/2.27 | | | (80) insert_slb(all_34_1, all_26_3) = all_26_1
% 10.99/2.27 | | |
% 10.99/2.27 | | | GROUND_INST: instantiating (3) with all_34_1, all_26_5, all_26_8,
% 10.99/2.27 | | | all_26_4, all_26_7, all_26_3, all_26_1, all_26_0, simplifying
% 10.99/2.27 | | | with (13), (14), (16), (17), (20), (22), (41), (80) gives:
% 10.99/2.27 | | | (81) all_26_0 = 0 | ( ? [v0: int] : ( ~ (v0 = 0) &
% 10.99/2.27 | | | pair_in_list(all_34_1, all_26_8, all_26_7) = v0) & ( ~
% 10.99/2.27 | | | (all_26_4 = all_26_7) | ~ (all_26_5 = all_26_8)))
% 10.99/2.27 | | |
% 10.99/2.27 | | | BETA: splitting (81) gives:
% 10.99/2.27 | | |
% 10.99/2.27 | | | Case 1:
% 10.99/2.27 | | | |
% 10.99/2.27 | | | | (82) all_26_0 = 0
% 10.99/2.27 | | | |
% 10.99/2.27 | | | | REDUCE: (12), (82) imply:
% 10.99/2.27 | | | | (83) $false
% 10.99/2.27 | | | |
% 10.99/2.27 | | | | CLOSE: (83) is inconsistent.
% 10.99/2.27 | | | |
% 10.99/2.27 | | | Case 2:
% 10.99/2.27 | | | |
% 10.99/2.27 | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & pair_in_list(all_34_1, all_26_8,
% 10.99/2.27 | | | | all_26_7) = v0) & ( ~ (all_26_4 = all_26_7) | ~ (all_26_5 =
% 10.99/2.27 | | | | all_26_8))
% 10.99/2.27 | | | |
% 10.99/2.27 | | | | ALPHA: (84) implies:
% 10.99/2.27 | | | | (85) ? [v0: int] : ( ~ (v0 = 0) & pair_in_list(all_34_1, all_26_8,
% 10.99/2.27 | | | | all_26_7) = v0)
% 10.99/2.27 | | | |
% 10.99/2.27 | | | | DELTA: instantiating (85) with fresh symbol all_78_0 gives:
% 10.99/2.27 | | | | (86) ~ (all_78_0 = 0) & pair_in_list(all_34_1, all_26_8, all_26_7) =
% 10.99/2.27 | | | | all_78_0
% 10.99/2.27 | | | |
% 10.99/2.27 | | | | ALPHA: (86) implies:
% 10.99/2.27 | | | | (87) ~ (all_78_0 = 0)
% 10.99/2.27 | | | | (88) pair_in_list(all_34_1, all_26_8, all_26_7) = all_78_0
% 10.99/2.27 | | | |
% 10.99/2.28 | | | | GROUND_INST: instantiating (9) with all_26_8, all_26_7, all_26_6,
% 10.99/2.28 | | | | all_34_1, all_78_0, simplifying with (13), (14), (15),
% 10.99/2.28 | | | | (30), (88) gives:
% 10.99/2.28 | | | | (89) all_78_0 = 0 | ? [v0: any] : ? [v1: any] :
% 10.99/2.28 | | | | (pair_in_list(all_23_0, all_26_8, all_26_7) = v0 &
% 10.99/2.28 | | | | less_than(all_26_6, all_26_7) = v1 & ( ~ (v1 = 0) | ~ (v0 =
% 10.99/2.28 | | | | 0)))
% 10.99/2.28 | | | |
% 10.99/2.28 | | | | BETA: splitting (89) gives:
% 10.99/2.28 | | | |
% 10.99/2.28 | | | | Case 1:
% 10.99/2.28 | | | | |
% 10.99/2.28 | | | | | (90) all_78_0 = 0
% 10.99/2.28 | | | | |
% 10.99/2.28 | | | | | REDUCE: (87), (90) imply:
% 10.99/2.28 | | | | | (91) $false
% 10.99/2.28 | | | | |
% 10.99/2.28 | | | | | CLOSE: (91) is inconsistent.
% 10.99/2.28 | | | | |
% 10.99/2.28 | | | | Case 2:
% 10.99/2.28 | | | | |
% 10.99/2.28 | | | | | (92) ? [v0: any] : ? [v1: any] : (pair_in_list(all_23_0,
% 10.99/2.28 | | | | | all_26_8, all_26_7) = v0 & less_than(all_26_6, all_26_7) =
% 10.99/2.28 | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 10.99/2.28 | | | | |
% 10.99/2.28 | | | | | DELTA: instantiating (92) with fresh symbols all_95_0, all_95_1 gives:
% 10.99/2.28 | | | | | (93) pair_in_list(all_23_0, all_26_8, all_26_7) = all_95_1 &
% 10.99/2.28 | | | | | less_than(all_26_6, all_26_7) = all_95_0 & ( ~ (all_95_0 = 0)
% 10.99/2.28 | | | | | | ~ (all_95_1 = 0))
% 10.99/2.28 | | | | |
% 10.99/2.28 | | | | | REF_CLOSE: (4), (6), (18), (44), (93) are inconsistent by sub-proof
% 10.99/2.28 | | | | | #1.
% 10.99/2.28 | | | | |
% 10.99/2.28 | | | | End of split
% 10.99/2.28 | | | |
% 10.99/2.28 | | | End of split
% 10.99/2.28 | | |
% 10.99/2.28 | | End of split
% 10.99/2.28 | |
% 10.99/2.28 | Case 2:
% 10.99/2.28 | |
% 10.99/2.28 | | (94) all_26_4 = all_26_7 & all_26_5 = all_26_8
% 10.99/2.28 | |
% 10.99/2.28 | | ALPHA: (94) implies:
% 10.99/2.28 | | (95) all_26_5 = all_26_8
% 10.99/2.28 | | (96) all_26_4 = all_26_7
% 10.99/2.28 | |
% 10.99/2.28 | | REDUCE: (20), (95), (96) imply:
% 10.99/2.28 | | (97) pair(all_26_8, all_26_7) = all_26_3
% 10.99/2.28 | |
% 10.99/2.28 | | REDUCE: (28), (96) imply:
% 10.99/2.28 | | (98) less_than(all_26_6, all_26_7) = all_34_2
% 10.99/2.28 | |
% 10.99/2.28 | | GROUND_INST: instantiating (4) with 0, all_34_2, all_26_7, all_26_6,
% 10.99/2.28 | | simplifying with (18), (98) gives:
% 10.99/2.28 | | (99) all_34_2 = 0
% 10.99/2.28 | |
% 10.99/2.28 | | BETA: splitting (31) gives:
% 10.99/2.28 | |
% 10.99/2.28 | | Case 1:
% 10.99/2.28 | | |
% 10.99/2.28 | | | (100) ~ (all_34_2 = 0)
% 10.99/2.28 | | |
% 10.99/2.28 | | | REDUCE: (99), (100) imply:
% 10.99/2.28 | | | (101) $false
% 10.99/2.28 | | |
% 10.99/2.28 | | | CLOSE: (101) is inconsistent.
% 10.99/2.28 | | |
% 10.99/2.28 | | Case 2:
% 10.99/2.28 | | |
% 10.99/2.28 | | | (102) all_34_0 = all_26_1
% 10.99/2.28 | | |
% 10.99/2.29 | | | REDUCE: (29), (102) imply:
% 10.99/2.29 | | | (103) insert_slb(all_34_1, all_26_3) = all_26_1
% 10.99/2.29 | | |
% 10.99/2.29 | | | GROUND_INST: instantiating (3) with all_34_1, all_26_8, all_26_8,
% 10.99/2.29 | | | all_26_7, all_26_7, all_26_3, all_26_1, all_26_0, simplifying
% 10.99/2.29 | | | with (13), (14), (22), (41), (97), (103) gives:
% 10.99/2.29 | | | (104) all_26_0 = 0
% 10.99/2.29 | | |
% 10.99/2.29 | | | REDUCE: (12), (104) imply:
% 10.99/2.29 | | | (105) $false
% 10.99/2.29 | | |
% 10.99/2.29 | | | CLOSE: (105) is inconsistent.
% 10.99/2.29 | | |
% 10.99/2.29 | | End of split
% 10.99/2.29 | |
% 10.99/2.29 | End of split
% 10.99/2.29 |
% 10.99/2.29 End of proof
% 10.99/2.29
% 10.99/2.29 Sub-proof #1 shows that the following formulas are inconsistent:
% 10.99/2.29 ----------------------------------------------------------------
% 10.99/2.29 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.99/2.29 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1)
% 10.99/2.29 | ~ (pair_in_list(v4, v3, v2) = v0))
% 10.99/2.29 (2) pair_in_list(all_23_0, all_26_8, all_26_7) = all_95_1 &
% 10.99/2.29 less_than(all_26_6, all_26_7) = all_95_0 & ( ~ (all_95_0 = 0) | ~
% 10.99/2.29 (all_95_1 = 0))
% 10.99/2.29 (3) pair_in_list(all_23_0, all_26_8, all_26_7) = 0
% 10.99/2.29 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.99/2.29 ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3,
% 10.99/2.29 v2) = v0))
% 10.99/2.29 (5) less_than(all_26_6, all_26_7) = 0
% 10.99/2.29
% 10.99/2.29 Begin of proof
% 10.99/2.29 |
% 10.99/2.29 | ALPHA: (2) implies:
% 10.99/2.29 | (6) less_than(all_26_6, all_26_7) = all_95_0
% 10.99/2.29 | (7) pair_in_list(all_23_0, all_26_8, all_26_7) = all_95_1
% 10.99/2.29 | (8) ~ (all_95_0 = 0) | ~ (all_95_1 = 0)
% 10.99/2.29 |
% 10.99/2.29 | GROUND_INST: instantiating (4) with 0, all_95_0, all_26_7, all_26_6,
% 10.99/2.29 | simplifying with (5), (6) gives:
% 10.99/2.29 | (9) all_95_0 = 0
% 10.99/2.29 |
% 10.99/2.29 | GROUND_INST: instantiating (1) with 0, all_95_1, all_26_7, all_26_8, all_23_0,
% 10.99/2.29 | simplifying with (3), (7) gives:
% 10.99/2.29 | (10) all_95_1 = 0
% 10.99/2.29 |
% 10.99/2.29 | BETA: splitting (8) gives:
% 10.99/2.29 |
% 10.99/2.29 | Case 1:
% 10.99/2.29 | |
% 10.99/2.29 | | (11) ~ (all_95_0 = 0)
% 10.99/2.29 | |
% 10.99/2.29 | | REDUCE: (9), (11) imply:
% 10.99/2.29 | | (12) $false
% 10.99/2.29 | |
% 10.99/2.29 | | CLOSE: (12) is inconsistent.
% 10.99/2.29 | |
% 10.99/2.29 | Case 2:
% 10.99/2.29 | |
% 10.99/2.29 | | (13) ~ (all_95_1 = 0)
% 10.99/2.29 | |
% 10.99/2.29 | | REDUCE: (10), (13) imply:
% 10.99/2.29 | | (14) $false
% 10.99/2.29 | |
% 10.99/2.29 | | CLOSE: (14) is inconsistent.
% 10.99/2.29 | |
% 10.99/2.29 | End of split
% 10.99/2.29 |
% 10.99/2.29 End of proof
% 10.99/2.29 % SZS output end Proof for theBenchmark
% 10.99/2.29
% 10.99/2.29 1693ms
%------------------------------------------------------------------------------