TSTP Solution File: COM134+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM134+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 : n018.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 18:44:34 EDT 2023
% Result : Theorem 17.91s 3.22s
% Output : Proof 18.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COM134+1 : TPTP v8.1.2. Released v6.4.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 13:01:33 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.59 ________ _____
% 0.18/0.59 ___ __ \_________(_)________________________________
% 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59 (2023-06-19)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2023
% 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59 Amanda Stjerna.
% 0.18/0.59 Free software under BSD-3-Clause.
% 0.18/0.59
% 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.61 Running up to 7 provers in parallel.
% 0.18/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.32/1.35 Prover 4: Preprocessing ...
% 4.32/1.35 Prover 1: Preprocessing ...
% 4.32/1.38 Prover 0: Preprocessing ...
% 4.32/1.38 Prover 6: Preprocessing ...
% 4.32/1.38 Prover 3: Preprocessing ...
% 4.32/1.38 Prover 5: Preprocessing ...
% 4.32/1.38 Prover 2: Preprocessing ...
% 10.27/2.23 Prover 1: Constructing countermodel ...
% 10.27/2.23 Prover 6: Proving ...
% 10.96/2.25 Prover 4: Constructing countermodel ...
% 10.96/2.26 Prover 3: Constructing countermodel ...
% 11.37/2.29 Prover 0: Proving ...
% 11.37/2.35 Prover 5: Proving ...
% 12.52/2.50 Prover 2: Proving ...
% 17.91/3.21 Prover 4: Found proof (size 48)
% 17.91/3.22 Prover 4: proved (2590ms)
% 17.91/3.22 Prover 3: stopped
% 17.91/3.22 Prover 1: stopped
% 17.91/3.22 Prover 0: stopped
% 17.91/3.22 Prover 5: stopped
% 17.91/3.22 Prover 6: stopped
% 17.91/3.22 Prover 2: stopped
% 17.91/3.22
% 17.91/3.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.91/3.22
% 17.91/3.23 % SZS output start Proof for theBenchmark
% 17.91/3.24 Assumptions after simplification:
% 17.91/3.24 ---------------------------------
% 17.91/3.24
% 17.91/3.24 (DIFF-abs-app)
% 17.91/3.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.91/3.26 $i] : ( ~ (vapp(v3, v4) = v5) | ~ (vabs(v0, v1, v2) = v5) | ~ $i(v4) | ~
% 17.91/3.26 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 17.91/3.26
% 17.91/3.26 (DIFF-var-app)
% 17.91/3.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vapp(v1, v2) =
% 17.91/3.26 v3) | ~ (vvar(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 17.91/3.26
% 17.91/3.26 (EQ-app)
% 17.91/3.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1
% 17.91/3.26 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) |
% 17.91/3.27 ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 17.91/3.27 $i] : ! [v4: $i] : (v2 = v0 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) =
% 17.91/3.27 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 17.91/3.27
% 17.91/3.27 (T-app)
% 17.91/3.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.91/3.27 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (varrow(v0, v4) = v5) | ~
% 17.91/3.27 (vtcheck(v1, v6, v4) = v7) | ~ (vtcheck(v1, v2, v5) = 0) | ~ (vapp(v2, v3)
% 17.91/3.27 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 17.91/3.27 [v8: int] : ( ~ (v8 = 0) & vtcheck(v1, v3, v0) = v8)) & ! [v0: $i] : !
% 17.91/3.27 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 17.91/3.27 int] : (v6 = 0 | ~ (vtcheck(v1, v5, v4) = v6) | ~ (vtcheck(v1, v3, v0) =
% 17.91/3.27 0) | ~ (vapp(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 17.91/3.27 $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & varrow(v0,
% 17.91/3.27 v4) = v7 & vtcheck(v1, v2, v7) = v8 & $i(v7))) & ! [v0: $i] : ! [v1:
% 17.91/3.27 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 17.91/3.27 (varrow(v0, v4) = v5) | ~ (vtcheck(v1, v3, v0) = 0) | ~ (vtcheck(v1, v2,
% 17.91/3.27 v5) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.91/3.27 ? [v6: $i] : (vtcheck(v1, v6, v4) = 0 & vapp(v2, v3) = v6 & $i(v6)))
% 17.91/3.27
% 17.91/3.27 (T-inv)
% 17.91/3.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vtcheck(v2, v0, v1) = 0) | ~
% 17.91/3.28 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 17.91/3.28 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ?
% 17.91/3.28 [v11: $i] : ? [v12: int] : ? [v13: int] : ? [v14: $i] : ? [v15: $i] : ?
% 17.91/3.28 [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ?
% 17.91/3.28 [v21: int] : ($i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v9) & $i(v8) &
% 17.91/3.28 $i(v7) & $i(v4) & ((v21 = 0 & v19 = v1 & v18 = v0 & varrow(v16, v17) = v1
% 17.91/3.28 & vtcheck(v20, v15, v17) = 0 & vbind(v14, v16, v2) = v20 & vabs(v14,
% 17.91/3.28 v16, v15) = v0 & $i(v20)) | (v13 = 0 & v12 = 0 & v10 = v0 &
% 17.91/3.28 varrow(v9, v1) = v11 & vtcheck(v2, v8, v9) = 0 & vtcheck(v2, v7, v11)
% 17.91/3.28 = 0 & vapp(v7, v8) = v0 & $i(v11)) | (v6 = v3 & v5 = v0 & vlookup(v4,
% 17.91/3.28 v2) = v3 & vsomeType(v1) = v3 & vvar(v4) = v0 & $i(v3)))))
% 17.91/3.28
% 17.91/3.28 (T-subst-IH-app1)
% 17.91/3.28 $i(ve1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 17.91/3.28 : ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (vsubst(v2, v3, ve1)
% 17.91/3.28 = v6) | ~ (vtcheck(v5, ve1, v4) = 0) | ~ (vtcheck(v1, v6, v4) = v7) | ~
% 17.91/3.28 (vbind(v2, v0, v1) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 17.91/3.28 ~ $i(v0) | ? [v8: int] : ( ~ (v8 = 0) & vtcheck(v1, v3, v0) = v8)) & !
% 17.91/3.28 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 17.91/3.28 : ! [v6: int] : (v6 = 0 | ~ (vsubst(v2, v3, ve1) = v5) | ~ (vtcheck(v1, v5,
% 17.91/3.28 v4) = v6) | ~ (vtcheck(v1, v3, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~
% 17.91/3.28 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 17.91/3.28 vtcheck(v7, ve1, v4) = v8 & vbind(v2, v0, v1) = v7 & $i(v7))) & ! [v0:
% 17.91/3.28 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 17.91/3.28 ( ~ (vtcheck(v5, ve1, v4) = 0) | ~ (vtcheck(v1, v3, v0) = 0) | ~ (vbind(v2,
% 17.91/3.28 v0, v1) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 17.91/3.28 $i(v0) | ? [v6: $i] : (vsubst(v2, v3, ve1) = v6 & vtcheck(v1, v6, v4) = 0 &
% 17.91/3.28 $i(v6)))
% 17.91/3.28
% 17.91/3.28 (T-subst-IH-app2)
% 17.91/3.29 $i(ve2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 17.91/3.29 : ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (vsubst(v2, v3, ve2)
% 17.91/3.29 = v6) | ~ (vtcheck(v5, ve2, v4) = 0) | ~ (vtcheck(v1, v6, v4) = v7) | ~
% 17.91/3.29 (vbind(v2, v0, v1) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 17.91/3.29 ~ $i(v0) | ? [v8: int] : ( ~ (v8 = 0) & vtcheck(v1, v3, v0) = v8)) & !
% 17.91/3.29 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 17.91/3.29 : ! [v6: int] : (v6 = 0 | ~ (vsubst(v2, v3, ve2) = v5) | ~ (vtcheck(v1, v5,
% 17.91/3.29 v4) = v6) | ~ (vtcheck(v1, v3, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~
% 17.91/3.29 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 17.91/3.29 vtcheck(v7, ve2, v4) = v8 & vbind(v2, v0, v1) = v7 & $i(v7))) & ! [v0:
% 17.91/3.29 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 17.91/3.29 ( ~ (vtcheck(v5, ve2, v4) = 0) | ~ (vtcheck(v1, v3, v0) = 0) | ~ (vbind(v2,
% 17.91/3.29 v0, v1) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 17.91/3.29 $i(v0) | ? [v6: $i] : (vsubst(v2, v3, ve2) = v6 & vtcheck(v1, v6, v4) = 0 &
% 17.91/3.29 $i(v6)))
% 17.91/3.29
% 17.91/3.29 (T-subst-app)
% 17.91/3.29 $i(ve2) & $i(ve1) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 17.91/3.29 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 =
% 17.91/3.29 0) & vsubst(v3, v4, v0) = v7 & vtcheck(v6, v0, v5) = 0 & vtcheck(v2, v7,
% 17.91/3.29 v5) = v8 & vtcheck(v2, v4, v1) = 0 & vbind(v3, v1, v2) = v6 & vapp(ve1,
% 17.91/3.29 ve2) = v0 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 17.91/3.29 $i(v0))
% 17.91/3.29
% 17.91/3.29 (subst2)
% 17.91/3.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.91/3.29 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v8 = v3 | ~ (vsubst(v0,
% 17.91/3.29 v1, v5) = v7) | ~ (vsubst(v0, v1, v4) = v6) | ~ (vsubst(v0, v1, v2) =
% 17.91/3.29 v3) | ~ (vapp(v6, v7) = v8) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 17.91/3.29 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: $i] : ( ~ (v9 = v2) & vapp(v4, v5)
% 17.91/3.29 = v9 & $i(v9)))
% 17.91/3.29
% 17.91/3.29 (function-axioms)
% 17.91/3.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 17.91/3.29 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0:
% 17.91/3.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.91/3.29 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3,
% 17.91/3.29 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 17.91/3.29 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) =
% 17.91/3.29 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 17.91/3.29 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & !
% 17.91/3.29 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3,
% 17.91/3.29 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.91/3.29 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~
% 17.91/3.29 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.91/3.29 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.91/3.29 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : !
% 17.91/3.29 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~
% 17.91/3.29 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 17.91/3.29 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 17.91/3.29 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0))
% 17.91/3.29 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 17.91/3.29 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] :
% 17.91/3.29 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~
% 17.91/3.29 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 17.91/3.29 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 17.91/3.29 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) =
% 17.91/3.29 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 17.91/3.29 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & !
% 17.91/3.29 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~
% 17.91/3.29 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.91/3.29 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~
% 17.91/3.29 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 17.91/3.29 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0))
% 17.91/3.29
% 17.91/3.29 Further assumptions not needed in the proof:
% 17.91/3.29 --------------------------------------------
% 17.91/3.29 DIFF-empty-bind, DIFF-noExp-someExp, DIFF-noType-someType, DIFF-var-abs, EQ-abs,
% 17.91/3.29 EQ-arrow, EQ-bind, EQ-empty, EQ-noExp, EQ-noType, EQ-someExp, EQ-someType,
% 17.91/3.29 EQ-var, T-Context-Duplicate, T-Context-Swap, T-Strong, T-Weak, T-Weak-FreeVar,
% 17.91/3.29 T-abs, T-var, gensym-is-fresh, getSomeExp0, getSomeType0, isFreeVar0,
% 17.91/3.29 isFreeVar1, isFreeVar2, isSomeExp0, isSomeExp1, isSomeType0, isSomeType1,
% 17.91/3.29 isValue0, isValue1, isValue2, lookup-INV, lookup0, lookup1, lookup2, reduce-INV,
% 17.91/3.29 reduce0, reduce1, reduce2, reduce3, reduce4, reduce5, reduce6, subst-INV,
% 17.91/3.29 subst0, subst1, subst3, subst4, subst5
% 17.91/3.29
% 17.91/3.29 Those formulas are unsatisfiable:
% 17.91/3.29 ---------------------------------
% 17.91/3.29
% 17.91/3.29 Begin of proof
% 17.91/3.30 |
% 17.91/3.30 | ALPHA: (EQ-app) implies:
% 17.91/3.30 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.91/3.30 | (v2 = v0 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4) | ~ $i(v3)
% 17.91/3.30 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 17.91/3.30 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.91/3.30 | (v3 = v1 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4) | ~ $i(v3)
% 17.91/3.30 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 17.91/3.30 |
% 17.91/3.30 | ALPHA: (T-app) implies:
% 18.80/3.30 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 18.80/3.30 | ! [v5: $i] : ( ~ (varrow(v0, v4) = v5) | ~ (vtcheck(v1, v3, v0) = 0) |
% 18.80/3.30 | ~ (vtcheck(v1, v2, v5) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 18.80/3.30 | $i(v1) | ~ $i(v0) | ? [v6: $i] : (vtcheck(v1, v6, v4) = 0 &
% 18.80/3.30 | vapp(v2, v3) = v6 & $i(v6)))
% 18.80/3.30 |
% 18.80/3.30 | ALPHA: (T-subst-IH-app1) implies:
% 18.80/3.30 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 18.80/3.30 | ! [v5: $i] : ( ~ (vtcheck(v5, ve1, v4) = 0) | ~ (vtcheck(v1, v3, v0) =
% 18.80/3.30 | 0) | ~ (vbind(v2, v0, v1) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 18.80/3.30 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : (vsubst(v2, v3, ve1) =
% 18.80/3.30 | v6 & vtcheck(v1, v6, v4) = 0 & $i(v6)))
% 18.80/3.30 |
% 18.80/3.30 | ALPHA: (T-subst-IH-app2) implies:
% 18.80/3.30 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 18.80/3.30 | ! [v5: $i] : ( ~ (vtcheck(v5, ve2, v4) = 0) | ~ (vtcheck(v1, v3, v0) =
% 18.80/3.30 | 0) | ~ (vbind(v2, v0, v1) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 18.80/3.30 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : (vsubst(v2, v3, ve2) =
% 18.80/3.30 | v6 & vtcheck(v1, v6, v4) = 0 & $i(v6)))
% 18.80/3.30 |
% 18.80/3.30 | ALPHA: (T-subst-app) implies:
% 18.80/3.30 | (6) $i(ve1)
% 18.80/3.30 | (7) $i(ve2)
% 18.80/3.30 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 18.80/3.30 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 18.80/3.30 | vsubst(v3, v4, v0) = v7 & vtcheck(v6, v0, v5) = 0 & vtcheck(v2, v7,
% 18.80/3.30 | v5) = v8 & vtcheck(v2, v4, v1) = 0 & vbind(v3, v1, v2) = v6 &
% 18.80/3.30 | vapp(ve1, ve2) = v0 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 18.80/3.30 | $i(v2) & $i(v1) & $i(v0))
% 18.80/3.30 |
% 18.80/3.30 | ALPHA: (function-axioms) implies:
% 18.80/3.30 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.80/3.30 | (vapp(v3, v2) = v1) | ~ (vapp(v3, v2) = v0))
% 18.80/3.30 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 18.80/3.30 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1)
% 18.80/3.30 | | ~ (vtcheck(v4, v3, v2) = v0))
% 18.80/3.30 |
% 18.80/3.30 | DELTA: instantiating (8) with fresh symbols all_58_0, all_58_1, all_58_2,
% 18.80/3.31 | all_58_3, all_58_4, all_58_5, all_58_6, all_58_7, all_58_8 gives:
% 18.80/3.31 | (11) ~ (all_58_0 = 0) & vsubst(all_58_5, all_58_4, all_58_8) = all_58_1 &
% 18.80/3.31 | vtcheck(all_58_2, all_58_8, all_58_3) = 0 & vtcheck(all_58_6,
% 18.80/3.31 | all_58_1, all_58_3) = all_58_0 & vtcheck(all_58_6, all_58_4,
% 18.80/3.31 | all_58_7) = 0 & vbind(all_58_5, all_58_7, all_58_6) = all_58_2 &
% 18.80/3.31 | vapp(ve1, ve2) = all_58_8 & $i(all_58_1) & $i(all_58_2) & $i(all_58_3)
% 18.80/3.31 | & $i(all_58_4) & $i(all_58_5) & $i(all_58_6) & $i(all_58_7) &
% 18.80/3.31 | $i(all_58_8)
% 18.80/3.31 |
% 18.80/3.31 | ALPHA: (11) implies:
% 18.80/3.31 | (12) ~ (all_58_0 = 0)
% 18.80/3.31 | (13) $i(all_58_8)
% 18.80/3.31 | (14) $i(all_58_7)
% 18.80/3.31 | (15) $i(all_58_6)
% 18.80/3.31 | (16) $i(all_58_5)
% 18.80/3.31 | (17) $i(all_58_4)
% 18.80/3.31 | (18) $i(all_58_3)
% 18.80/3.31 | (19) $i(all_58_2)
% 18.80/3.31 | (20) $i(all_58_1)
% 18.80/3.31 | (21) vapp(ve1, ve2) = all_58_8
% 18.80/3.31 | (22) vbind(all_58_5, all_58_7, all_58_6) = all_58_2
% 18.80/3.31 | (23) vtcheck(all_58_6, all_58_4, all_58_7) = 0
% 18.80/3.31 | (24) vtcheck(all_58_6, all_58_1, all_58_3) = all_58_0
% 18.80/3.31 | (25) vtcheck(all_58_2, all_58_8, all_58_3) = 0
% 18.80/3.31 | (26) vsubst(all_58_5, all_58_4, all_58_8) = all_58_1
% 18.80/3.31 |
% 18.80/3.31 | GROUND_INST: instantiating (T-inv) with all_58_8, all_58_3, all_58_2,
% 18.80/3.31 | simplifying with (13), (18), (19), (25) gives:
% 18.80/3.31 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: $i] :
% 18.80/3.31 | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int]
% 18.80/3.31 | : ? [v10: int] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ?
% 18.80/3.31 | [v14: $i] : ? [v15: int] : ? [v16: int] : ? [v17: $i] : ? [v18:
% 18.80/3.31 | int] : ($i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v6) & $i(v5) &
% 18.80/3.31 | $i(v4) & $i(v1) & ((v18 = 0 & v16 = all_58_3 & v15 = all_58_8 &
% 18.80/3.31 | varrow(v13, v14) = all_58_3 & vtcheck(v17, v12, v14) = 0 &
% 18.80/3.31 | vbind(v11, v13, all_58_2) = v17 & vabs(v11, v13, v12) = all_58_8
% 18.80/3.31 | & $i(v17)) | (v10 = 0 & v9 = 0 & v7 = all_58_8 & varrow(v6,
% 18.80/3.31 | all_58_3) = v8 & vtcheck(all_58_2, v5, v6) = 0 &
% 18.80/3.31 | vtcheck(all_58_2, v4, v8) = 0 & vapp(v4, v5) = all_58_8 &
% 18.80/3.31 | $i(v8)) | (v3 = v0 & v2 = all_58_8 & vlookup(v1, all_58_2) = v0
% 18.80/3.31 | & vsomeType(all_58_3) = v0 & vvar(v1) = all_58_8 & $i(v0))))
% 18.80/3.31 |
% 18.80/3.31 | DELTA: instantiating (27) with fresh symbols all_71_0, all_71_1, all_71_2,
% 18.80/3.31 | all_71_3, all_71_4, all_71_5, all_71_6, all_71_7, all_71_8, all_71_9,
% 18.80/3.31 | all_71_10, all_71_11, all_71_12, all_71_13, all_71_14, all_71_15,
% 18.80/3.31 | all_71_16, all_71_17, all_71_18 gives:
% 18.80/3.31 | (28) $i(all_71_4) & $i(all_71_5) & $i(all_71_6) & $i(all_71_7) &
% 18.80/3.31 | $i(all_71_12) & $i(all_71_13) & $i(all_71_14) & $i(all_71_17) &
% 18.80/3.31 | ((all_71_0 = 0 & all_71_2 = all_58_3 & all_71_3 = all_58_8 &
% 18.80/3.31 | varrow(all_71_5, all_71_4) = all_58_3 & vtcheck(all_71_1,
% 18.80/3.31 | all_71_6, all_71_4) = 0 & vbind(all_71_7, all_71_5, all_58_2) =
% 18.80/3.31 | all_71_1 & vabs(all_71_7, all_71_5, all_71_6) = all_58_8 &
% 18.80/3.31 | $i(all_71_1)) | (all_71_8 = 0 & all_71_9 = 0 & all_71_11 =
% 18.80/3.31 | all_58_8 & varrow(all_71_12, all_58_3) = all_71_10 &
% 18.80/3.31 | vtcheck(all_58_2, all_71_13, all_71_12) = 0 & vtcheck(all_58_2,
% 18.80/3.31 | all_71_14, all_71_10) = 0 & vapp(all_71_14, all_71_13) =
% 18.80/3.31 | all_58_8 & $i(all_71_10)) | (all_71_15 = all_71_18 & all_71_16 =
% 18.80/3.31 | all_58_8 & vlookup(all_71_17, all_58_2) = all_71_18 &
% 18.80/3.31 | vsomeType(all_58_3) = all_71_18 & vvar(all_71_17) = all_58_8 &
% 18.80/3.31 | $i(all_71_18)))
% 18.80/3.31 |
% 18.80/3.31 | ALPHA: (28) implies:
% 18.80/3.31 | (29) $i(all_71_17)
% 18.80/3.31 | (30) $i(all_71_14)
% 18.80/3.31 | (31) $i(all_71_13)
% 18.80/3.31 | (32) $i(all_71_12)
% 18.80/3.31 | (33) $i(all_71_7)
% 18.80/3.31 | (34) $i(all_71_6)
% 18.80/3.31 | (35) $i(all_71_5)
% 18.80/3.32 | (36) (all_71_0 = 0 & all_71_2 = all_58_3 & all_71_3 = all_58_8 &
% 18.80/3.32 | varrow(all_71_5, all_71_4) = all_58_3 & vtcheck(all_71_1, all_71_6,
% 18.80/3.32 | all_71_4) = 0 & vbind(all_71_7, all_71_5, all_58_2) = all_71_1 &
% 18.80/3.32 | vabs(all_71_7, all_71_5, all_71_6) = all_58_8 & $i(all_71_1)) |
% 18.80/3.32 | (all_71_8 = 0 & all_71_9 = 0 & all_71_11 = all_58_8 &
% 18.80/3.32 | varrow(all_71_12, all_58_3) = all_71_10 & vtcheck(all_58_2,
% 18.80/3.32 | all_71_13, all_71_12) = 0 & vtcheck(all_58_2, all_71_14,
% 18.80/3.32 | all_71_10) = 0 & vapp(all_71_14, all_71_13) = all_58_8 &
% 18.80/3.32 | $i(all_71_10)) | (all_71_15 = all_71_18 & all_71_16 = all_58_8 &
% 18.80/3.32 | vlookup(all_71_17, all_58_2) = all_71_18 & vsomeType(all_58_3) =
% 18.80/3.32 | all_71_18 & vvar(all_71_17) = all_58_8 & $i(all_71_18))
% 18.80/3.32 |
% 18.80/3.32 | BETA: splitting (36) gives:
% 18.80/3.32 |
% 18.80/3.32 | Case 1:
% 18.80/3.32 | |
% 18.80/3.32 | | (37) all_71_0 = 0 & all_71_2 = all_58_3 & all_71_3 = all_58_8 &
% 18.80/3.32 | | varrow(all_71_5, all_71_4) = all_58_3 & vtcheck(all_71_1, all_71_6,
% 18.80/3.32 | | all_71_4) = 0 & vbind(all_71_7, all_71_5, all_58_2) = all_71_1 &
% 18.80/3.32 | | vabs(all_71_7, all_71_5, all_71_6) = all_58_8 & $i(all_71_1)
% 18.80/3.32 | |
% 18.80/3.32 | | ALPHA: (37) implies:
% 18.80/3.32 | | (38) vabs(all_71_7, all_71_5, all_71_6) = all_58_8
% 18.80/3.32 | |
% 18.80/3.32 | | GROUND_INST: instantiating (DIFF-abs-app) with all_71_7, all_71_5, all_71_6,
% 18.80/3.32 | | ve1, ve2, all_58_8, simplifying with (6), (7), (21), (33),
% 18.80/3.32 | | (34), (35), (38) gives:
% 18.80/3.32 | | (39) $false
% 18.80/3.32 | |
% 18.80/3.32 | | CLOSE: (39) is inconsistent.
% 18.80/3.32 | |
% 18.80/3.32 | Case 2:
% 18.80/3.32 | |
% 18.80/3.32 | | (40) (all_71_8 = 0 & all_71_9 = 0 & all_71_11 = all_58_8 &
% 18.80/3.32 | | varrow(all_71_12, all_58_3) = all_71_10 & vtcheck(all_58_2,
% 18.80/3.32 | | all_71_13, all_71_12) = 0 & vtcheck(all_58_2, all_71_14,
% 18.80/3.32 | | all_71_10) = 0 & vapp(all_71_14, all_71_13) = all_58_8 &
% 18.80/3.32 | | $i(all_71_10)) | (all_71_15 = all_71_18 & all_71_16 = all_58_8 &
% 18.80/3.32 | | vlookup(all_71_17, all_58_2) = all_71_18 & vsomeType(all_58_3) =
% 18.80/3.32 | | all_71_18 & vvar(all_71_17) = all_58_8 & $i(all_71_18))
% 18.80/3.32 | |
% 18.80/3.32 | | BETA: splitting (40) gives:
% 18.80/3.32 | |
% 18.80/3.32 | | Case 1:
% 18.80/3.32 | | |
% 18.80/3.32 | | | (41) all_71_8 = 0 & all_71_9 = 0 & all_71_11 = all_58_8 &
% 18.80/3.32 | | | varrow(all_71_12, all_58_3) = all_71_10 & vtcheck(all_58_2,
% 18.80/3.32 | | | all_71_13, all_71_12) = 0 & vtcheck(all_58_2, all_71_14,
% 18.80/3.32 | | | all_71_10) = 0 & vapp(all_71_14, all_71_13) = all_58_8 &
% 18.80/3.32 | | | $i(all_71_10)
% 18.80/3.32 | | |
% 18.80/3.32 | | | ALPHA: (41) implies:
% 18.80/3.32 | | | (42) $i(all_71_10)
% 18.80/3.32 | | | (43) vapp(all_71_14, all_71_13) = all_58_8
% 18.80/3.32 | | | (44) vtcheck(all_58_2, all_71_14, all_71_10) = 0
% 18.80/3.32 | | | (45) vtcheck(all_58_2, all_71_13, all_71_12) = 0
% 18.80/3.32 | | | (46) varrow(all_71_12, all_58_3) = all_71_10
% 18.80/3.32 | | |
% 18.80/3.32 | | | GROUND_INST: instantiating (2) with ve1, ve2, all_71_14, all_71_13,
% 18.80/3.32 | | | all_58_8, simplifying with (6), (7), (21), (30), (31), (43)
% 18.80/3.32 | | | gives:
% 18.80/3.32 | | | (47) all_71_13 = ve2
% 18.80/3.32 | | |
% 18.80/3.32 | | | GROUND_INST: instantiating (1) with ve1, ve2, all_71_14, all_71_13,
% 18.80/3.32 | | | all_58_8, simplifying with (6), (7), (21), (30), (31), (43)
% 18.80/3.32 | | | gives:
% 18.80/3.32 | | | (48) all_71_14 = ve1
% 18.80/3.32 | | |
% 18.80/3.32 | | | REDUCE: (45), (47) imply:
% 18.80/3.33 | | | (49) vtcheck(all_58_2, ve2, all_71_12) = 0
% 18.80/3.33 | | |
% 18.80/3.33 | | | REDUCE: (44), (48) imply:
% 18.80/3.33 | | | (50) vtcheck(all_58_2, ve1, all_71_10) = 0
% 18.80/3.33 | | |
% 18.80/3.33 | | | GROUND_INST: instantiating (4) with all_58_7, all_58_6, all_58_5,
% 18.80/3.33 | | | all_58_4, all_71_10, all_58_2, simplifying with (14), (15),
% 18.80/3.33 | | | (16), (17), (22), (23), (42), (50) gives:
% 18.80/3.33 | | | (51) ? [v0: $i] : (vsubst(all_58_5, all_58_4, ve1) = v0 &
% 18.80/3.33 | | | vtcheck(all_58_6, v0, all_71_10) = 0 & $i(v0))
% 18.80/3.33 | | |
% 18.80/3.33 | | | GROUND_INST: instantiating (5) with all_58_7, all_58_6, all_58_5,
% 18.80/3.33 | | | all_58_4, all_71_12, all_58_2, simplifying with (14), (15),
% 18.80/3.33 | | | (16), (17), (22), (23), (32), (49) gives:
% 18.80/3.33 | | | (52) ? [v0: $i] : (vsubst(all_58_5, all_58_4, ve2) = v0 &
% 18.80/3.33 | | | vtcheck(all_58_6, v0, all_71_12) = 0 & $i(v0))
% 18.80/3.33 | | |
% 18.80/3.33 | | | DELTA: instantiating (52) with fresh symbol all_153_0 gives:
% 18.80/3.33 | | | (53) vsubst(all_58_5, all_58_4, ve2) = all_153_0 & vtcheck(all_58_6,
% 18.80/3.33 | | | all_153_0, all_71_12) = 0 & $i(all_153_0)
% 18.80/3.33 | | |
% 18.80/3.33 | | | ALPHA: (53) implies:
% 18.80/3.33 | | | (54) $i(all_153_0)
% 18.80/3.33 | | | (55) vtcheck(all_58_6, all_153_0, all_71_12) = 0
% 18.80/3.33 | | | (56) vsubst(all_58_5, all_58_4, ve2) = all_153_0
% 18.80/3.33 | | |
% 18.80/3.33 | | | DELTA: instantiating (51) with fresh symbol all_155_0 gives:
% 18.80/3.33 | | | (57) vsubst(all_58_5, all_58_4, ve1) = all_155_0 & vtcheck(all_58_6,
% 18.80/3.33 | | | all_155_0, all_71_10) = 0 & $i(all_155_0)
% 18.80/3.33 | | |
% 18.80/3.33 | | | ALPHA: (57) implies:
% 18.80/3.33 | | | (58) $i(all_155_0)
% 18.80/3.33 | | | (59) vtcheck(all_58_6, all_155_0, all_71_10) = 0
% 18.80/3.33 | | | (60) vsubst(all_58_5, all_58_4, ve1) = all_155_0
% 18.80/3.33 | | |
% 18.80/3.33 | | | GROUND_INST: instantiating (3) with all_71_12, all_58_6, all_155_0,
% 18.80/3.33 | | | all_153_0, all_58_3, all_71_10, simplifying with (15), (18),
% 18.80/3.33 | | | (32), (46), (54), (55), (58), (59) gives:
% 18.80/3.33 | | | (61) ? [v0: $i] : (vtcheck(all_58_6, v0, all_58_3) = 0 &
% 18.80/3.33 | | | vapp(all_155_0, all_153_0) = v0 & $i(v0))
% 18.80/3.33 | | |
% 18.80/3.33 | | | DELTA: instantiating (61) with fresh symbol all_178_0 gives:
% 18.80/3.33 | | | (62) vtcheck(all_58_6, all_178_0, all_58_3) = 0 & vapp(all_155_0,
% 18.80/3.33 | | | all_153_0) = all_178_0 & $i(all_178_0)
% 18.80/3.33 | | |
% 18.80/3.33 | | | ALPHA: (62) implies:
% 18.80/3.33 | | | (63) vapp(all_155_0, all_153_0) = all_178_0
% 18.80/3.33 | | | (64) vtcheck(all_58_6, all_178_0, all_58_3) = 0
% 18.80/3.33 | | |
% 18.80/3.33 | | | GROUND_INST: instantiating (subst2) with all_58_5, all_58_4, all_58_8,
% 18.80/3.33 | | | all_58_1, ve1, ve2, all_155_0, all_153_0, all_178_0,
% 18.80/3.33 | | | simplifying with (6), (7), (13), (16), (17), (20), (26),
% 18.80/3.33 | | | (56), (60), (63) gives:
% 18.80/3.33 | | | (65) all_178_0 = all_58_1 | ? [v0: any] : ( ~ (v0 = all_58_8) &
% 18.80/3.33 | | | vapp(ve1, ve2) = v0 & $i(v0))
% 18.80/3.33 | | |
% 18.80/3.33 | | | BETA: splitting (65) gives:
% 18.80/3.33 | | |
% 18.80/3.33 | | | Case 1:
% 18.80/3.33 | | | |
% 18.80/3.33 | | | | (66) all_178_0 = all_58_1
% 18.80/3.33 | | | |
% 18.80/3.33 | | | | REDUCE: (64), (66) imply:
% 18.80/3.33 | | | | (67) vtcheck(all_58_6, all_58_1, all_58_3) = 0
% 18.80/3.33 | | | |
% 18.80/3.33 | | | | GROUND_INST: instantiating (10) with all_58_0, 0, all_58_3, all_58_1,
% 18.80/3.33 | | | | all_58_6, simplifying with (24), (67) gives:
% 18.80/3.33 | | | | (68) all_58_0 = 0
% 18.80/3.33 | | | |
% 18.80/3.33 | | | | REDUCE: (12), (68) imply:
% 18.80/3.33 | | | | (69) $false
% 18.80/3.33 | | | |
% 18.80/3.33 | | | | CLOSE: (69) is inconsistent.
% 18.80/3.33 | | | |
% 18.80/3.33 | | | Case 2:
% 18.80/3.33 | | | |
% 18.80/3.34 | | | | (70) ? [v0: any] : ( ~ (v0 = all_58_8) & vapp(ve1, ve2) = v0 &
% 18.80/3.34 | | | | $i(v0))
% 18.80/3.34 | | | |
% 18.80/3.34 | | | | DELTA: instantiating (70) with fresh symbol all_213_0 gives:
% 18.80/3.34 | | | | (71) ~ (all_213_0 = all_58_8) & vapp(ve1, ve2) = all_213_0 &
% 18.80/3.34 | | | | $i(all_213_0)
% 18.80/3.34 | | | |
% 18.80/3.34 | | | | ALPHA: (71) implies:
% 18.80/3.34 | | | | (72) ~ (all_213_0 = all_58_8)
% 18.80/3.34 | | | | (73) vapp(ve1, ve2) = all_213_0
% 18.80/3.34 | | | |
% 18.80/3.34 | | | | GROUND_INST: instantiating (9) with all_58_8, all_213_0, ve2, ve1,
% 18.80/3.34 | | | | simplifying with (21), (73) gives:
% 18.80/3.34 | | | | (74) all_213_0 = all_58_8
% 18.80/3.34 | | | |
% 18.80/3.34 | | | | REDUCE: (72), (74) imply:
% 18.80/3.34 | | | | (75) $false
% 18.80/3.34 | | | |
% 18.80/3.34 | | | | CLOSE: (75) is inconsistent.
% 18.80/3.34 | | | |
% 18.80/3.34 | | | End of split
% 18.80/3.34 | | |
% 18.80/3.34 | | Case 2:
% 18.80/3.34 | | |
% 18.80/3.34 | | | (76) all_71_15 = all_71_18 & all_71_16 = all_58_8 & vlookup(all_71_17,
% 18.80/3.34 | | | all_58_2) = all_71_18 & vsomeType(all_58_3) = all_71_18 &
% 18.80/3.34 | | | vvar(all_71_17) = all_58_8 & $i(all_71_18)
% 18.80/3.34 | | |
% 18.80/3.34 | | | ALPHA: (76) implies:
% 18.80/3.34 | | | (77) vvar(all_71_17) = all_58_8
% 18.80/3.34 | | |
% 18.80/3.34 | | | GROUND_INST: instantiating (DIFF-var-app) with all_71_17, ve1, ve2,
% 18.80/3.34 | | | all_58_8, simplifying with (6), (7), (21), (29), (77) gives:
% 18.80/3.34 | | | (78) $false
% 18.80/3.34 | | |
% 18.80/3.34 | | | CLOSE: (78) is inconsistent.
% 18.80/3.34 | | |
% 18.80/3.34 | | End of split
% 18.80/3.34 | |
% 18.80/3.34 | End of split
% 18.80/3.34 |
% 18.80/3.34 End of proof
% 18.80/3.34 % SZS output end Proof for theBenchmark
% 18.80/3.34
% 18.80/3.34 2744ms
%------------------------------------------------------------------------------