TSTP Solution File: COM149+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM149+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n010.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 : Wed Aug 30 18:44:37 EDT 2023
% Result : Theorem 12.61s 2.47s
% Output : Proof 16.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM149+1 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 13:26:33 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.25/1.30 Prover 1: Preprocessing ...
% 4.25/1.30 Prover 4: Preprocessing ...
% 4.67/1.34 Prover 5: Preprocessing ...
% 4.67/1.34 Prover 6: Preprocessing ...
% 4.67/1.34 Prover 0: Preprocessing ...
% 4.67/1.34 Prover 2: Preprocessing ...
% 4.67/1.34 Prover 3: Preprocessing ...
% 9.94/2.13 Prover 3: Constructing countermodel ...
% 9.94/2.14 Prover 1: Constructing countermodel ...
% 9.94/2.15 Prover 6: Proving ...
% 9.94/2.20 Prover 4: Constructing countermodel ...
% 10.84/2.25 Prover 0: Proving ...
% 11.68/2.30 Prover 5: Proving ...
% 12.61/2.46 Prover 3: proved (1841ms)
% 12.61/2.47
% 12.61/2.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.61/2.47
% 12.61/2.47 Prover 5: stopped
% 12.61/2.47 Prover 0: stopped
% 12.61/2.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.61/2.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.61/2.47 Prover 6: proved (1846ms)
% 12.61/2.47
% 12.61/2.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.61/2.47
% 12.61/2.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.24/2.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.24/2.51 Prover 2: Proving ...
% 13.24/2.51 Prover 2: stopped
% 13.24/2.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.24/2.54 Prover 1: Found proof (size 24)
% 13.24/2.54 Prover 1: proved (1922ms)
% 13.24/2.54 Prover 4: stopped
% 14.13/2.64 Prover 10: Preprocessing ...
% 14.13/2.65 Prover 13: Preprocessing ...
% 14.13/2.65 Prover 8: Preprocessing ...
% 14.13/2.66 Prover 11: Preprocessing ...
% 14.13/2.66 Prover 7: Preprocessing ...
% 14.13/2.71 Prover 10: stopped
% 14.13/2.77 Prover 11: stopped
% 14.13/2.77 Prover 7: stopped
% 14.13/2.80 Prover 13: stopped
% 15.35/2.88 Prover 8: Warning: ignoring some quantifiers
% 15.35/2.88 Prover 8: Constructing countermodel ...
% 15.35/2.89 Prover 8: stopped
% 15.35/2.89
% 15.35/2.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.35/2.89
% 15.35/2.90 % SZS output start Proof for theBenchmark
% 15.35/2.90 Assumptions after simplification:
% 15.35/2.90 ---------------------------------
% 15.35/2.90
% 15.35/2.90 (DIFF-noType-someType)
% 16.10/2.92 $i(vnoType) & ! [v0: $i] : ( ~ (vsomeType(v0) = vnoType) | ~ $i(v0))
% 16.10/2.92
% 16.10/2.92 (DIFF-var-abs)
% 16.10/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 16.10/2.93 (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 16.10/2.93 $i(v1) | ~ $i(v0))
% 16.10/2.93
% 16.10/2.93 (DIFF-var-app)
% 16.10/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vapp(v1, v2) =
% 16.10/2.93 v3) | ~ (vvar(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 16.10/2.93
% 16.10/2.93 (T-Progress-T-var)
% 16.10/2.93 $i(vempty) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4:
% 16.10/2.93 $i] : ( ~ (v3 = 0) & vreduce(v2) = v4 & vtcheck(vempty, v2, v0) = 0 &
% 16.10/2.93 visValue(v2) = v3 & vvar(v1) = v2 & $i(v4) & $i(v2) & $i(v1) & $i(v0) & !
% 16.10/2.93 [v5: $i] : ( ~ (vsomeExp(v5) = v4) | ~ $i(v5)))
% 16.10/2.93
% 16.10/2.93 (T-inv)
% 16.10/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vtcheck(v2, v0, v1) = 0) | ~
% 16.10/2.93 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 16.10/2.93 ? [v6: $i] : ? [v7: $i] : (varrow(v5, v6) = v1 & vtcheck(v7, v4, v6) = 0 &
% 16.10/2.93 vbind(v3, v5, v2) = v7 & vabs(v3, v5, v4) = v0 & $i(v7) & $i(v6) & $i(v5)
% 16.10/2.93 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 16.10/2.93 : (varrow(v5, v1) = v6 & vtcheck(v2, v4, v5) = 0 & vtcheck(v2, v3, v6) = 0 &
% 16.10/2.93 vapp(v3, v4) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] :
% 16.10/2.93 (vsomeType(v1) = v3 & $i(v3) & ? [v4: $i] : (vlookup(v4, v2) = v3 &
% 16.10/2.93 vvar(v4) = v0 & $i(v4))))
% 16.10/2.93
% 16.10/2.93 (lookup0)
% 16.10/2.93 $i(vnoType) & $i(vempty) & ! [v0: $i] : ! [v1: $i] : (v1 = vnoType | ~
% 16.10/2.93 (vlookup(v0, vempty) = v1) | ~ $i(v1) | ~ $i(v0))
% 16.10/2.94
% 16.10/2.94 Further assumptions not needed in the proof:
% 16.10/2.94 --------------------------------------------
% 16.10/2.94 DIFF-abs-app, DIFF-empty-bind, DIFF-noExp-someExp, EQ-abs, EQ-app, EQ-arrow,
% 16.10/2.94 EQ-bind, EQ-empty, EQ-noExp, EQ-noType, EQ-someExp, EQ-someType, EQ-var,
% 16.10/2.94 T-Context-Duplicate, T-Context-Swap, T-Strong, T-Weak, T-abs, T-app, T-var,
% 16.10/2.94 gensym-is-fresh, getSomeExp0, getSomeType0, isFreeVar0, isFreeVar1, isFreeVar2,
% 16.10/2.94 isSomeExp0, isSomeExp1, isSomeType0, isSomeType1, isValue0, isValue1, isValue2,
% 16.10/2.94 lookup-INV, lookup1, lookup2, reduce-INV, reduce0, reduce1, reduce2, reduce3,
% 16.10/2.94 reduce4, reduce5, reduce6, subst-INV, subst0, subst1, subst2, subst3, subst4,
% 16.10/2.94 subst5
% 16.10/2.94
% 16.10/2.94 Those formulas are unsatisfiable:
% 16.10/2.94 ---------------------------------
% 16.10/2.94
% 16.10/2.94 Begin of proof
% 16.10/2.94 |
% 16.10/2.94 | ALPHA: (DIFF-noType-someType) implies:
% 16.10/2.94 | (1) ! [v0: $i] : ( ~ (vsomeType(v0) = vnoType) | ~ $i(v0))
% 16.10/2.94 |
% 16.10/2.94 | ALPHA: (lookup0) implies:
% 16.10/2.94 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = vnoType | ~ (vlookup(v0, vempty) =
% 16.10/2.94 | v1) | ~ $i(v1) | ~ $i(v0))
% 16.10/2.94 |
% 16.10/2.94 | ALPHA: (T-Progress-T-var) implies:
% 16.10/2.94 | (3) $i(vempty)
% 16.10/2.94 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: $i] :
% 16.10/2.94 | ( ~ (v3 = 0) & vreduce(v2) = v4 & vtcheck(vempty, v2, v0) = 0 &
% 16.10/2.94 | visValue(v2) = v3 & vvar(v1) = v2 & $i(v4) & $i(v2) & $i(v1) & $i(v0)
% 16.10/2.94 | & ! [v5: $i] : ( ~ (vsomeExp(v5) = v4) | ~ $i(v5)))
% 16.10/2.94 |
% 16.10/2.94 | DELTA: instantiating (4) with fresh symbols all_55_0, all_55_1, all_55_2,
% 16.10/2.94 | all_55_3, all_55_4 gives:
% 16.10/2.94 | (5) ~ (all_55_1 = 0) & vreduce(all_55_2) = all_55_0 & vtcheck(vempty,
% 16.10/2.94 | all_55_2, all_55_4) = 0 & visValue(all_55_2) = all_55_1 &
% 16.10/2.94 | vvar(all_55_3) = all_55_2 & $i(all_55_0) & $i(all_55_2) & $i(all_55_3)
% 16.10/2.94 | & $i(all_55_4) & ! [v0: $i] : ( ~ (vsomeExp(v0) = all_55_0) | ~
% 16.10/2.94 | $i(v0))
% 16.10/2.94 |
% 16.10/2.94 | ALPHA: (5) implies:
% 16.10/2.94 | (6) $i(all_55_4)
% 16.10/2.94 | (7) $i(all_55_3)
% 16.10/2.94 | (8) $i(all_55_2)
% 16.10/2.94 | (9) vvar(all_55_3) = all_55_2
% 16.10/2.94 | (10) vtcheck(vempty, all_55_2, all_55_4) = 0
% 16.10/2.94 |
% 16.10/2.94 | GROUND_INST: instantiating (T-inv) with all_55_2, all_55_4, vempty,
% 16.10/2.94 | simplifying with (3), (6), (8), (10) gives:
% 16.10/2.95 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 16.10/2.95 | (varrow(v2, v3) = all_55_4 & vtcheck(v4, v1, v3) = 0 & vbind(v0, v2,
% 16.10/2.95 | vempty) = v4 & vabs(v0, v2, v1) = all_55_2 & $i(v4) & $i(v3) &
% 16.10/2.95 | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 16.10/2.95 | : ? [v3: $i] : (varrow(v2, all_55_4) = v3 & vtcheck(vempty, v1, v2) =
% 16.10/2.95 | 0 & vtcheck(vempty, v0, v3) = 0 & vapp(v0, v1) = all_55_2 & $i(v3) &
% 16.10/2.95 | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : (vsomeType(all_55_4) = v0
% 16.10/2.95 | & $i(v0) & ? [v1: $i] : (vlookup(v1, vempty) = v0 & vvar(v1) =
% 16.10/2.95 | all_55_2 & $i(v1)))
% 16.10/2.95 |
% 16.10/2.95 | BETA: splitting (11) gives:
% 16.10/2.95 |
% 16.10/2.95 | Case 1:
% 16.10/2.95 | |
% 16.10/2.95 | | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 16.10/2.95 | | : (varrow(v2, v3) = all_55_4 & vtcheck(v4, v1, v3) = 0 & vbind(v0,
% 16.10/2.95 | | v2, vempty) = v4 & vabs(v0, v2, v1) = all_55_2 & $i(v4) & $i(v3)
% 16.10/2.95 | | & $i(v2) & $i(v1) & $i(v0))
% 16.10/2.95 | |
% 16.10/2.95 | | DELTA: instantiating (12) with fresh symbols all_70_0, all_70_1, all_70_2,
% 16.10/2.95 | | all_70_3, all_70_4 gives:
% 16.10/2.95 | | (13) varrow(all_70_2, all_70_1) = all_55_4 & vtcheck(all_70_0, all_70_3,
% 16.10/2.95 | | all_70_1) = 0 & vbind(all_70_4, all_70_2, vempty) = all_70_0 &
% 16.10/2.95 | | vabs(all_70_4, all_70_2, all_70_3) = all_55_2 & $i(all_70_0) &
% 16.10/2.95 | | $i(all_70_1) & $i(all_70_2) & $i(all_70_3) & $i(all_70_4)
% 16.10/2.95 | |
% 16.10/2.95 | | ALPHA: (13) implies:
% 16.10/2.95 | | (14) $i(all_70_4)
% 16.10/2.95 | | (15) $i(all_70_3)
% 16.10/2.95 | | (16) $i(all_70_2)
% 16.10/2.95 | | (17) vabs(all_70_4, all_70_2, all_70_3) = all_55_2
% 16.10/2.95 | |
% 16.10/2.95 | | GROUND_INST: instantiating (DIFF-var-abs) with all_55_3, all_70_4, all_70_2,
% 16.10/2.95 | | all_70_3, all_55_2, simplifying with (7), (9), (14), (15),
% 16.10/2.95 | | (16), (17) gives:
% 16.10/2.95 | | (18) $false
% 16.10/2.95 | |
% 16.10/2.95 | | CLOSE: (18) is inconsistent.
% 16.10/2.95 | |
% 16.10/2.95 | Case 2:
% 16.10/2.95 | |
% 16.10/2.95 | | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (varrow(v2,
% 16.10/2.95 | | all_55_4) = v3 & vtcheck(vempty, v1, v2) = 0 & vtcheck(vempty,
% 16.10/2.95 | | v0, v3) = 0 & vapp(v0, v1) = all_55_2 & $i(v3) & $i(v2) & $i(v1)
% 16.10/2.95 | | & $i(v0)) | ? [v0: $i] : (vsomeType(all_55_4) = v0 & $i(v0) & ?
% 16.10/2.95 | | [v1: $i] : (vlookup(v1, vempty) = v0 & vvar(v1) = all_55_2 &
% 16.10/2.95 | | $i(v1)))
% 16.10/2.95 | |
% 16.10/2.95 | | BETA: splitting (19) gives:
% 16.10/2.95 | |
% 16.10/2.95 | | Case 1:
% 16.10/2.95 | | |
% 16.10/2.95 | | | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 16.10/2.95 | | | (varrow(v2, all_55_4) = v3 & vtcheck(vempty, v1, v2) = 0 &
% 16.10/2.95 | | | vtcheck(vempty, v0, v3) = 0 & vapp(v0, v1) = all_55_2 & $i(v3) &
% 16.10/2.95 | | | $i(v2) & $i(v1) & $i(v0))
% 16.10/2.95 | | |
% 16.10/2.95 | | | DELTA: instantiating (20) with fresh symbols all_70_0, all_70_1, all_70_2,
% 16.10/2.95 | | | all_70_3 gives:
% 16.10/2.95 | | | (21) varrow(all_70_1, all_55_4) = all_70_0 & vtcheck(vempty, all_70_2,
% 16.10/2.95 | | | all_70_1) = 0 & vtcheck(vempty, all_70_3, all_70_0) = 0 &
% 16.10/2.95 | | | vapp(all_70_3, all_70_2) = all_55_2 & $i(all_70_0) & $i(all_70_1)
% 16.10/2.95 | | | & $i(all_70_2) & $i(all_70_3)
% 16.10/2.96 | | |
% 16.10/2.96 | | | ALPHA: (21) implies:
% 16.10/2.96 | | | (22) $i(all_70_3)
% 16.10/2.96 | | | (23) $i(all_70_2)
% 16.10/2.96 | | | (24) vapp(all_70_3, all_70_2) = all_55_2
% 16.10/2.96 | | |
% 16.10/2.96 | | | GROUND_INST: instantiating (DIFF-var-app) with all_55_3, all_70_3,
% 16.10/2.96 | | | all_70_2, all_55_2, simplifying with (7), (9), (22), (23),
% 16.10/2.96 | | | (24) gives:
% 16.10/2.96 | | | (25) $false
% 16.10/2.96 | | |
% 16.10/2.96 | | | CLOSE: (25) is inconsistent.
% 16.10/2.96 | | |
% 16.10/2.96 | | Case 2:
% 16.10/2.96 | | |
% 16.10/2.96 | | | (26) ? [v0: $i] : (vsomeType(all_55_4) = v0 & $i(v0) & ? [v1: $i] :
% 16.10/2.96 | | | (vlookup(v1, vempty) = v0 & vvar(v1) = all_55_2 & $i(v1)))
% 16.10/2.96 | | |
% 16.10/2.96 | | | DELTA: instantiating (26) with fresh symbol all_70_0 gives:
% 16.10/2.96 | | | (27) vsomeType(all_55_4) = all_70_0 & $i(all_70_0) & ? [v0: $i] :
% 16.10/2.96 | | | (vlookup(v0, vempty) = all_70_0 & vvar(v0) = all_55_2 & $i(v0))
% 16.10/2.96 | | |
% 16.10/2.96 | | | ALPHA: (27) implies:
% 16.10/2.96 | | | (28) $i(all_70_0)
% 16.10/2.96 | | | (29) vsomeType(all_55_4) = all_70_0
% 16.10/2.96 | | | (30) ? [v0: $i] : (vlookup(v0, vempty) = all_70_0 & vvar(v0) =
% 16.10/2.96 | | | all_55_2 & $i(v0))
% 16.10/2.96 | | |
% 16.10/2.96 | | | DELTA: instantiating (30) with fresh symbol all_72_0 gives:
% 16.10/2.96 | | | (31) vlookup(all_72_0, vempty) = all_70_0 & vvar(all_72_0) = all_55_2 &
% 16.10/2.96 | | | $i(all_72_0)
% 16.10/2.96 | | |
% 16.10/2.96 | | | ALPHA: (31) implies:
% 16.10/2.96 | | | (32) $i(all_72_0)
% 16.10/2.96 | | | (33) vlookup(all_72_0, vempty) = all_70_0
% 16.10/2.96 | | |
% 16.10/2.96 | | | GROUND_INST: instantiating (2) with all_72_0, all_70_0, simplifying with
% 16.10/2.96 | | | (28), (32), (33) gives:
% 16.10/2.96 | | | (34) all_70_0 = vnoType
% 16.10/2.96 | | |
% 16.10/2.96 | | | REDUCE: (29), (34) imply:
% 16.10/2.96 | | | (35) vsomeType(all_55_4) = vnoType
% 16.10/2.96 | | |
% 16.10/2.96 | | | GROUND_INST: instantiating (1) with all_55_4, simplifying with (6), (35)
% 16.10/2.96 | | | gives:
% 16.10/2.96 | | | (36) $false
% 16.10/2.96 | | |
% 16.10/2.96 | | | CLOSE: (36) is inconsistent.
% 16.10/2.96 | | |
% 16.10/2.96 | | End of split
% 16.10/2.96 | |
% 16.10/2.96 | End of split
% 16.10/2.96 |
% 16.10/2.96 End of proof
% 16.10/2.96 % SZS output end Proof for theBenchmark
% 16.10/2.96
% 16.10/2.96 2360ms
%------------------------------------------------------------------------------