TSTP Solution File: NUM450+6 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM450+6 : TPTP v8.1.2. Released v4.0.0.
% 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 : Thu Aug 31 11:47:49 EDT 2023
% Result : Theorem 82.89s 11.69s
% Output : Proof 83.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM450+6 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n010.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 13:24:05 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.63 ________ _____
% 0.22/0.63 ___ __ \_________(_)________________________________
% 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.63
% 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.63 (2023-06-19)
% 0.22/0.63
% 0.22/0.63 (c) Philipp Rümmer, 2009-2023
% 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.63 Amanda Stjerna.
% 0.22/0.63 Free software under BSD-3-Clause.
% 0.22/0.63
% 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.63
% 0.22/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.64 Running up to 7 provers in parallel.
% 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.10/1.38 Prover 1: Preprocessing ...
% 4.10/1.39 Prover 4: Preprocessing ...
% 4.76/1.43 Prover 0: Preprocessing ...
% 4.76/1.43 Prover 3: Preprocessing ...
% 4.76/1.43 Prover 6: Preprocessing ...
% 4.76/1.43 Prover 2: Preprocessing ...
% 4.76/1.43 Prover 5: Preprocessing ...
% 12.60/2.50 Prover 3: Constructing countermodel ...
% 12.60/2.52 Prover 6: Proving ...
% 12.60/2.52 Prover 5: Proving ...
% 13.20/2.55 Prover 1: Constructing countermodel ...
% 13.90/2.70 Prover 2: Proving ...
% 19.76/3.42 Prover 4: Constructing countermodel ...
% 19.76/3.47 Prover 0: Proving ...
% 72.60/10.31 Prover 2: stopped
% 72.74/10.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 73.42/10.44 Prover 7: Preprocessing ...
% 75.04/10.65 Prover 7: Warning: ignoring some quantifiers
% 75.04/10.66 Prover 7: Constructing countermodel ...
% 82.89/11.68 Prover 7: Found proof (size 57)
% 82.89/11.68 Prover 7: proved (1353ms)
% 82.89/11.68 Prover 0: stopped
% 82.89/11.68 Prover 6: stopped
% 82.89/11.68 Prover 3: stopped
% 82.89/11.68 Prover 4: stopped
% 82.89/11.68 Prover 5: stopped
% 82.89/11.68 Prover 1: stopped
% 82.89/11.68
% 82.89/11.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 82.89/11.69
% 82.89/11.69 % SZS output start Proof for theBenchmark
% 82.89/11.70 Assumptions after simplification:
% 82.89/11.70 ---------------------------------
% 82.89/11.70
% 82.89/11.70 (mMulMinOne)
% 82.89/11.72 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 82.89/11.72 $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 82.89/11.72 (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : !
% 82.89/11.72 [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 82.89/11.72 (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : !
% 82.89/11.72 [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 82.89/11.72 (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) = v2 & $i(v2))))
% 82.89/11.72
% 82.89/11.72 (mPrimeDivisor)
% 82.89/11.73 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : (v1 = v0
% 82.89/11.73 | v1 = sz10 | ~ $i(v1) | ~ aInteger0(v1) | ? [v2: $i] : ($i(v2) &
% 82.89/11.73 isPrime0(v2) & aDivisorOf0(v2, v1))) & ! [v1: $i] : ( ~ $i(v1) | ~
% 82.89/11.73 isPrime0(v1) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0)) & ! [v1: $i] :
% 82.89/11.73 ( ~ $i(v1) | ~ isPrime0(v1) | ~ aDivisorOf0(v1, sz10) | ~
% 82.89/11.73 aInteger0(sz10)))
% 83.42/11.73
% 83.42/11.73 (m__)
% 83.42/11.74 $i(xS) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 83.42/11.74 (stldt0(v1) = v2 & sbsmnsldt0(xS) = v1 & smndt0(sz10) = v0 & $i(v2) & $i(v1) &
% 83.42/11.74 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 83.42/11.74 : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ (sdtasdt0(v3,
% 83.42/11.74 v7) = v6) | ~ (sdtpldt0(v5, v0) = v6) | ~ $i(v7) | ~ $i(v5) | ~
% 83.42/11.74 $i(v3) | ~ aInteger0(v7) | ~ aInteger0(v5) | ~ aInteger0(v3) |
% 83.42/11.74 aElementOf0(v5, v4)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 83.42/11.74 $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~
% 83.42/11.74 (sdtpldt0(v5, v0) = v6) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) |
% 83.42/11.74 ~ aInteger0(v3) | sdteqdtlpzmzozddtrp0(v5, sz10, v3)) & ! [v3: $i] : !
% 83.42/11.74 [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~
% 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ (sdtpldt0(v5, v0) = v6) | ~
% 83.42/11.74 $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) | ~ aInteger0(v3) |
% 83.42/11.74 aDivisorOf0(v3, v6)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 83.42/11.74 $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~
% 83.42/11.74 (sdtpldt0(v5, v0) = v6) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) |
% 83.42/11.74 ~ aInteger0(v3) | aInteger0(v5)) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 83.42/11.74 $i] : ! [v6: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) =
% 83.42/11.74 v4) | ~ (sdtpldt0(v5, v0) = v6) | ~ $i(v5) | ~ $i(v3) | ~
% 83.42/11.74 aElementOf0(v5, v4) | ~ aInteger0(v3) | ? [v7: $i] : (sdtasdt0(v3, v7) =
% 83.42/11.74 v6 & $i(v7) & $i(v6) & aInteger0(v7))) & ! [v3: $i] : ! [v4: $i] : !
% 83.42/11.74 [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) =
% 83.42/11.74 v4) | ~ (sdtpldt0(v5, v0) = v6) | ~ $i(v5) | ~ $i(v3) | ~
% 83.42/11.74 sdteqdtlpzmzozddtrp0(v5, sz10, v3) | ~ aInteger0(v5) | ~ aInteger0(v3) |
% 83.42/11.74 aElementOf0(v5, v4)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 83.42/11.74 $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~
% 83.42/11.74 (sdtpldt0(v5, v0) = v6) | ~ $i(v5) | ~ $i(v3) | ~ aDivisorOf0(v3, v6) |
% 83.42/11.74 ~ aInteger0(v5) | ~ aInteger0(v3) | aElementOf0(v5, v4)) & ! [v3: $i] :
% 83.42/11.74 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~
% 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v6) | ~ $i(v5) | ~
% 83.42/11.74 $i(v3) | ~ aElementOf0(v6, xS) | ~ aElementOf0(v5, v6) | ~
% 83.42/11.74 aInteger0(v5) | ~ aInteger0(v3) | aElementOf0(v5, v1)) & ! [v3: $i] : !
% 83.42/11.74 [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) =
% 83.42/11.74 v4) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v2) | ~
% 83.42/11.74 aElementOf0(v5, v1) | ~ aInteger0(v3)) & ! [v3: $i] : ! [v4: $i] : !
% 83.42/11.74 [v5: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~
% 83.42/11.74 $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v2) | ~ aInteger0(v3) |
% 83.42/11.74 aInteger0(v5)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~
% 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~
% 83.42/11.74 aElementOf0(v5, v1) | ~ aInteger0(v3) | aInteger0(v5)) & ! [v3: $i] : !
% 83.42/11.74 [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) =
% 83.42/11.74 v4) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v1) | ~ aInteger0(v3)
% 83.42/11.74 | ? [v6: $i] : ($i(v6) & aElementOf0(v6, xS) & aElementOf0(v5, v6))) & !
% 83.42/11.74 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~
% 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~
% 83.42/11.74 aInteger0(v5) | ~ aInteger0(v3) | aElementOf0(v5, v2) | aElementOf0(v5,
% 83.42/11.74 v1)) & ! [v3: $i] : ! [v4: $i] : (v3 = sz00 | ~
% 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3) | ~ aSubsetOf0(v4,
% 83.42/11.74 v2) | ~ aInteger0(v3)) & ! [v3: $i] : ! [v4: $i] : (v3 = sz00 | ~
% 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3) | ~ aInteger0(v3) |
% 83.42/11.74 aSet0(v4)) & ! [v3: $i] : ! [v4: $i] : (v3 = sz00 | ~
% 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3) | ~ aInteger0(v3) |
% 83.42/11.74 aSet0(v1)) & ! [v3: $i] : ! [v4: $i] : (v3 = sz00 | ~
% 83.42/11.74 (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3) | ~ aInteger0(v3) |
% 83.42/11.74 ? [v5: $i] : ($i(v5) & aElementOf0(v5, v4) & ~ aElementOf0(v5, v2))))
% 83.42/11.74
% 83.42/11.74 (m__2079)
% 83.42/11.74 $i(cS2076) & $i(xS) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : (stldt0(v0) =
% 83.42/11.74 cS2076 & sbsmnsldt0(xS) = v0 & smndt0(sz10) = v1 & $i(v1) & $i(v0) &
% 83.42/11.74 aElementOf0(v1, cS2076) & aElementOf0(sz10, cS2076) & aSet0(v0) &
% 83.42/11.74 aSet0(cS2076) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 83.42/11.74 aElementOf0(v3, xS) | ~ aElementOf0(v2, v3) | ~ aInteger0(v2) |
% 83.42/11.74 aElementOf0(v2, v0)) & ! [v2: $i] : (v2 = v1 | v2 = sz10 | ~ $i(v2) | ~
% 83.42/11.74 aElementOf0(v2, cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2,
% 83.42/11.74 v0) | ~ aElementOf0(v2, cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 83.42/11.74 aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 83.42/11.74 aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3, xS) &
% 83.42/11.74 aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2,
% 83.42/11.74 cS2076) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | ~ aInteger0(v2) |
% 83.42/11.74 aElementOf0(v2, v0) | aElementOf0(v2, cS2076)))
% 83.42/11.74
% 83.42/11.74 (m__2144)
% 83.42/11.75 $i(xS) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = v1 &
% 83.42/11.75 sbsmnsldt0(xS) = v0 & $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1) &
% 83.42/11.75 aSet0(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (smndt0(v2) = v3) | ~ $i(v2) |
% 83.42/11.75 ~ aElementOf0(v2, v1) | ? [v4: $i] : ? [v5: $i] : ( ~ (v4 = sz00) &
% 83.42/11.75 szAzrzSzezqlpdtcmdtrp0(v2, v4) = v5 & $i(v5) & $i(v4) & aSubsetOf0(v5,
% 83.42/11.75 v1) & aSet0(v5) & aInteger0(v4) & ! [v6: $i] : ! [v7: $i] : ! [v8:
% 83.42/11.75 $i] : ( ~ (sdtasdt0(v4, v8) = v7) | ~ (sdtpldt0(v6, v3) = v7) | ~
% 83.42/11.75 $i(v8) | ~ $i(v6) | ~ aInteger0(v8) | ~ aInteger0(v6) |
% 83.42/11.75 aElementOf0(v6, v5)) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6,
% 83.42/11.75 v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) |
% 83.42/11.75 sdteqdtlpzmzozddtrp0(v6, v2, v4)) & ! [v6: $i] : ! [v7: $i] : ( ~
% 83.42/11.75 (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) |
% 83.42/11.75 aDivisorOf0(v4, v7)) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6,
% 83.42/11.75 v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | aInteger0(v6)) &
% 83.42/11.75 ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~
% 83.42/11.75 aElementOf0(v6, v5) | ? [v8: $i] : (sdtasdt0(v4, v8) = v7 & $i(v8) &
% 83.42/11.75 $i(v7) & aInteger0(v8))) & ! [v6: $i] : ! [v7: $i] : ( ~
% 83.42/11.75 (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ sdteqdtlpzmzozddtrp0(v6, v2,
% 83.42/11.75 v4) | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! [v6: $i] : !
% 83.42/11.75 [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aDivisorOf0(v4,
% 83.42/11.75 v7) | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! [v6: $i] : ( ~
% 83.42/11.75 $i(v6) | ~ aElementOf0(v6, v5) | aElementOf0(v6, v1)))) & ! [v2: $i]
% 83.42/11.75 : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xS) | ~
% 83.42/11.75 aElementOf0(v2, v3) | ~ aInteger0(v2) | aElementOf0(v2, v0)) & ! [v2:
% 83.42/11.75 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ~ aElementOf0(v2, v0)) & !
% 83.42/11.75 [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | aInteger0(v2)) & ! [v2:
% 83.42/11.75 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] :
% 83.42/11.75 ( ~ $i(v2) | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) &
% 83.42/11.75 aElementOf0(v3, xS) & aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) |
% 83.42/11.75 ~ aInteger0(v2) | aElementOf0(v2, v1) | aElementOf0(v2, v0)))
% 83.42/11.75
% 83.42/11.75 (function-axioms)
% 83.42/11.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 83.42/11.75 (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) | ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) =
% 83.42/11.75 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 83.42/11.75 ~ (sdtslmnbsdt0(v3, v2) = v1) | ~ (sdtslmnbsdt0(v3, v2) = v0)) & ! [v0:
% 83.42/11.75 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 83.42/11.75 (sdtbsmnsldt0(v3, v2) = v1) | ~ (sdtbsmnsldt0(v3, v2) = v0)) & ! [v0: $i]
% 83.42/11.75 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) =
% 83.42/11.75 v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 83.42/11.75 $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3,
% 83.42/11.75 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 83.42/11.75 (stldt0(v2) = v1) | ~ (stldt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 83.42/11.75 [v2: $i] : (v1 = v0 | ~ (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0)) &
% 83.42/11.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~
% 83.42/11.75 (smndt0(v2) = v0))
% 83.42/11.75
% 83.42/11.75 Further assumptions not needed in the proof:
% 83.42/11.75 --------------------------------------------
% 83.42/11.75 mAddAsso, mAddComm, mAddNeg, mAddZero, mArSeq, mArSeqClosed, mClosed,
% 83.42/11.75 mComplement, mDistrib, mDivisor, mElements, mEquMod, mEquModMul, mEquModRef,
% 83.42/11.75 mEquModSym, mEquModTrn, mFinSet, mIntMult, mIntNeg, mIntOne, mIntPlus, mIntZero,
% 83.42/11.75 mIntegers, mInterOpen, mIntersection, mMulAsso, mMulComm, mMulOne, mMulZero,
% 83.42/11.75 mOpen, mPrime, mSets, mSubset, mUnion, mUnionClosed, mUnionOpen, mUnionSClosed,
% 83.42/11.75 mUnionSet, mZeroDiv, m__2046, m__2117
% 83.42/11.75
% 83.42/11.75 Those formulas are unsatisfiable:
% 83.42/11.75 ---------------------------------
% 83.42/11.75
% 83.42/11.75 Begin of proof
% 83.42/11.76 |
% 83.42/11.76 | ALPHA: (mMulMinOne) implies:
% 83.42/11.76 | (1) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 83.42/11.76 | ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 83.42/11.76 | (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] :
% 83.42/11.76 | ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~
% 83.42/11.76 | aInteger0(v1) | (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2)))
% 83.42/11.76 | & ! [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~
% 83.42/11.76 | aInteger0(v1) | (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) = v2 &
% 83.42/11.76 | $i(v2))))
% 83.42/11.76 |
% 83.42/11.76 | ALPHA: (mPrimeDivisor) implies:
% 83.42/11.76 | (2) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : (v1 = v0 | v1
% 83.42/11.76 | = sz10 | ~ $i(v1) | ~ aInteger0(v1) | ? [v2: $i] : ($i(v2) &
% 83.42/11.76 | isPrime0(v2) & aDivisorOf0(v2, v1))) & ! [v1: $i] : ( ~ $i(v1) |
% 83.42/11.76 | ~ isPrime0(v1) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0)) & !
% 83.42/11.76 | [v1: $i] : ( ~ $i(v1) | ~ isPrime0(v1) | ~ aDivisorOf0(v1, sz10) |
% 83.42/11.76 | ~ aInteger0(sz10)))
% 83.42/11.76 |
% 83.42/11.76 | ALPHA: (m__2079) implies:
% 83.42/11.76 | (3) ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = cS2076 & sbsmnsldt0(xS) = v0
% 83.42/11.76 | & smndt0(sz10) = v1 & $i(v1) & $i(v0) & aElementOf0(v1, cS2076) &
% 83.42/11.76 | aElementOf0(sz10, cS2076) & aSet0(v0) & aSet0(cS2076) & ! [v2: $i] :
% 83.42/11.76 | ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xS) | ~
% 83.42/11.76 | aElementOf0(v2, v3) | ~ aInteger0(v2) | aElementOf0(v2, v0)) & !
% 83.42/11.76 | [v2: $i] : (v2 = v1 | v2 = sz10 | ~ $i(v2) | ~ aElementOf0(v2,
% 83.42/11.76 | cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | ~
% 83.42/11.76 | aElementOf0(v2, cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 83.42/11.76 | aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) |
% 83.42/11.76 | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3, xS)
% 83.42/11.76 | & aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | ~
% 83.42/11.76 | aElementOf0(v2, cS2076) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2)
% 83.42/11.76 | | ~ aInteger0(v2) | aElementOf0(v2, v0) | aElementOf0(v2,
% 83.42/11.76 | cS2076)))
% 83.42/11.76 |
% 83.42/11.76 | ALPHA: (m__2144) implies:
% 83.42/11.77 | (4) ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = v1 & sbsmnsldt0(xS) = v0 &
% 83.42/11.77 | $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1) & aSet0(v0) & ! [v2:
% 83.42/11.77 | $i] : ! [v3: $i] : ( ~ (smndt0(v2) = v3) | ~ $i(v2) | ~
% 83.42/11.77 | aElementOf0(v2, v1) | ? [v4: $i] : ? [v5: $i] : ( ~ (v4 = sz00) &
% 83.42/11.77 | szAzrzSzezqlpdtcmdtrp0(v2, v4) = v5 & $i(v5) & $i(v4) &
% 83.42/11.77 | aSubsetOf0(v5, v1) & aSet0(v5) & aInteger0(v4) & ! [v6: $i] : !
% 83.42/11.77 | [v7: $i] : ! [v8: $i] : ( ~ (sdtasdt0(v4, v8) = v7) | ~
% 83.42/11.77 | (sdtpldt0(v6, v3) = v7) | ~ $i(v8) | ~ $i(v6) | ~
% 83.42/11.77 | aInteger0(v8) | ~ aInteger0(v6) | aElementOf0(v6, v5)) & !
% 83.42/11.77 | [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6)
% 83.42/11.77 | | ~ aElementOf0(v6, v5) | sdteqdtlpzmzozddtrp0(v6, v2, v4)) &
% 83.42/11.77 | ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~
% 83.42/11.77 | $i(v6) | ~ aElementOf0(v6, v5) | aDivisorOf0(v4, v7)) & !
% 83.42/11.77 | [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6)
% 83.42/11.77 | | ~ aElementOf0(v6, v5) | aInteger0(v6)) & ! [v6: $i] : !
% 83.42/11.77 | [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~
% 83.42/11.77 | aElementOf0(v6, v5) | ? [v8: $i] : (sdtasdt0(v4, v8) = v7 &
% 83.42/11.77 | $i(v8) & $i(v7) & aInteger0(v8))) & ! [v6: $i] : ! [v7: $i]
% 83.42/11.77 | : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~
% 83.42/11.77 | sdteqdtlpzmzozddtrp0(v6, v2, v4) | ~ aInteger0(v6) |
% 83.42/11.77 | aElementOf0(v6, v5)) & ! [v6: $i] : ! [v7: $i] : ( ~
% 83.42/11.77 | (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aDivisorOf0(v4, v7) |
% 83.42/11.77 | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! [v6: $i] : ( ~
% 83.42/11.77 | $i(v6) | ~ aElementOf0(v6, v5) | aElementOf0(v6, v1)))) & !
% 83.42/11.77 | [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3,
% 83.42/11.77 | xS) | ~ aElementOf0(v2, v3) | ~ aInteger0(v2) | aElementOf0(v2,
% 83.42/11.77 | v0)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ~
% 83.42/11.77 | aElementOf0(v2, v0)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 83.42/11.77 | aElementOf0(v2, v1) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) |
% 83.42/11.77 | ~ aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) |
% 83.42/11.77 | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3,
% 83.42/11.77 | xS) & aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | ~
% 83.42/11.77 | aInteger0(v2) | aElementOf0(v2, v1) | aElementOf0(v2, v0)))
% 83.42/11.77 |
% 83.42/11.77 | ALPHA: (m__) implies:
% 83.42/11.77 | (5) $i(sz10)
% 83.42/11.78 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (stldt0(v1) = v2 &
% 83.42/11.78 | sbsmnsldt0(xS) = v1 & smndt0(sz10) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 83.42/11.78 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 83.42/11.78 | (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~
% 83.42/11.78 | (sdtasdt0(v3, v7) = v6) | ~ (sdtpldt0(v5, v0) = v6) | ~ $i(v7) |
% 83.42/11.78 | ~ $i(v5) | ~ $i(v3) | ~ aInteger0(v7) | ~ aInteger0(v5) | ~
% 83.42/11.78 | aInteger0(v3) | aElementOf0(v5, v4)) & ! [v3: $i] : ! [v4: $i] :
% 83.42/11.78 | ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~
% 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ (sdtpldt0(v5, v0) =
% 83.42/11.78 | v6) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) | ~
% 83.42/11.78 | aInteger0(v3) | sdteqdtlpzmzozddtrp0(v5, sz10, v3)) & ! [v3: $i] :
% 83.42/11.78 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~
% 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ (sdtpldt0(v5, v0) =
% 83.42/11.78 | v6) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) | ~
% 83.42/11.78 | aInteger0(v3) | aDivisorOf0(v3, v6)) & ! [v3: $i] : ! [v4: $i] :
% 83.42/11.78 | ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~
% 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ (sdtpldt0(v5, v0) =
% 83.42/11.78 | v6) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) | ~
% 83.42/11.78 | aInteger0(v3) | aInteger0(v5)) & ! [v3: $i] : ! [v4: $i] : !
% 83.42/11.78 | [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~
% 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ (sdtpldt0(v5, v0) =
% 83.42/11.78 | v6) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) | ~
% 83.42/11.78 | aInteger0(v3) | ? [v7: $i] : (sdtasdt0(v3, v7) = v6 & $i(v7) &
% 83.42/11.78 | $i(v6) & aInteger0(v7))) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 83.42/11.78 | $i] : ! [v6: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10,
% 83.42/11.78 | v3) = v4) | ~ (sdtpldt0(v5, v0) = v6) | ~ $i(v5) | ~ $i(v3)
% 83.42/11.78 | | ~ sdteqdtlpzmzozddtrp0(v5, sz10, v3) | ~ aInteger0(v5) | ~
% 83.42/11.78 | aInteger0(v3) | aElementOf0(v5, v4)) & ! [v3: $i] : ! [v4: $i] :
% 83.42/11.78 | ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~
% 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ (sdtpldt0(v5, v0) =
% 83.42/11.78 | v6) | ~ $i(v5) | ~ $i(v3) | ~ aDivisorOf0(v3, v6) | ~
% 83.42/11.78 | aInteger0(v5) | ~ aInteger0(v3) | aElementOf0(v5, v4)) & ! [v3:
% 83.42/11.78 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~
% 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v6) | ~ $i(v5) |
% 83.42/11.78 | ~ $i(v3) | ~ aElementOf0(v6, xS) | ~ aElementOf0(v5, v6) | ~
% 83.42/11.78 | aInteger0(v5) | ~ aInteger0(v3) | aElementOf0(v5, v1)) & ! [v3:
% 83.42/11.78 | $i] : ! [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~
% 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v5) | ~ $i(v3) |
% 83.42/11.78 | ~ aElementOf0(v5, v2) | ~ aElementOf0(v5, v1) | ~ aInteger0(v3))
% 83.42/11.78 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~
% 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v5) | ~ $i(v3) |
% 83.42/11.78 | ~ aElementOf0(v5, v2) | ~ aInteger0(v3) | aInteger0(v5)) & ! [v3:
% 83.42/11.78 | $i] : ! [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~
% 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v5) | ~ $i(v3) |
% 83.42/11.78 | ~ aElementOf0(v5, v1) | ~ aInteger0(v3) | aInteger0(v5)) & ! [v3:
% 83.42/11.78 | $i] : ! [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~
% 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v5) | ~ $i(v3) |
% 83.42/11.78 | ~ aElementOf0(v5, v1) | ~ aInteger0(v3) | ? [v6: $i] : ($i(v6) &
% 83.42/11.78 | aElementOf0(v6, xS) & aElementOf0(v5, v6))) & ! [v3: $i] : !
% 83.42/11.78 | [v4: $i] : ! [v5: $i] : (v3 = sz00 | ~
% 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v5) | ~ $i(v3) |
% 83.42/11.78 | ~ aInteger0(v5) | ~ aInteger0(v3) | aElementOf0(v5, v2) |
% 83.42/11.78 | aElementOf0(v5, v1)) & ! [v3: $i] : ! [v4: $i] : (v3 = sz00 | ~
% 83.42/11.78 | (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3) | ~
% 83.42/11.78 | aSubsetOf0(v4, v2) | ~ aInteger0(v3)) & ! [v3: $i] : ! [v4: $i]
% 83.69/11.78 | : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3)
% 83.69/11.78 | | ~ aInteger0(v3) | aSet0(v4)) & ! [v3: $i] : ! [v4: $i] : (v3 =
% 83.69/11.78 | sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3) | ~
% 83.69/11.78 | aInteger0(v3) | aSet0(v1)) & ! [v3: $i] : ! [v4: $i] : (v3 = sz00
% 83.69/11.78 | | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v3) = v4) | ~ $i(v3) | ~
% 83.69/11.78 | aInteger0(v3) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v4) & ~
% 83.69/11.78 | aElementOf0(v5, v2))))
% 83.69/11.78 |
% 83.69/11.78 | ALPHA: (function-axioms) implies:
% 83.69/11.78 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) =
% 83.69/11.78 | v1) | ~ (smndt0(v2) = v0))
% 83.69/11.78 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbsmnsldt0(v2)
% 83.69/11.78 | = v1) | ~ (sbsmnsldt0(v2) = v0))
% 83.69/11.78 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (stldt0(v2) =
% 83.69/11.78 | v1) | ~ (stldt0(v2) = v0))
% 83.69/11.78 |
% 83.69/11.79 | DELTA: instantiating (2) with fresh symbol all_36_0 gives:
% 83.69/11.79 | (10) smndt0(sz10) = all_36_0 & $i(all_36_0) & ! [v0: any] : (v0 = all_36_0
% 83.69/11.79 | | v0 = sz10 | ~ $i(v0) | ~ aInteger0(v0) | ? [v1: $i] : ($i(v1) &
% 83.69/11.79 | isPrime0(v1) & aDivisorOf0(v1, v0))) & ! [v0: $i] : ( ~ $i(v0) |
% 83.69/11.79 | ~ isPrime0(v0) | ~ aDivisorOf0(v0, all_36_0) | ~
% 83.69/11.79 | aInteger0(all_36_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ isPrime0(v0) |
% 83.69/11.79 | ~ aDivisorOf0(v0, sz10) | ~ aInteger0(sz10))
% 83.69/11.79 |
% 83.69/11.79 | ALPHA: (10) implies:
% 83.69/11.79 | (11) smndt0(sz10) = all_36_0
% 83.69/11.79 |
% 83.69/11.79 | DELTA: instantiating (1) with fresh symbol all_39_0 gives:
% 83.69/11.79 | (12) smndt0(sz10) = all_39_0 & $i(all_39_0) & ! [v0: $i] : ! [v1: $i] : (
% 83.69/11.79 | ~ (sdtasdt0(v0, all_39_0) = v1) | ~ $i(v0) | ~ aInteger0(v0) |
% 83.69/11.79 | (sdtasdt0(all_39_0, v0) = v1 & smndt0(v0) = v1 & $i(v1))) & ! [v0:
% 83.69/11.79 | $i] : ! [v1: $i] : ( ~ (sdtasdt0(all_39_0, v0) = v1) | ~ $i(v0) |
% 83.69/11.79 | ~ aInteger0(v0) | (sdtasdt0(v0, all_39_0) = v1 & smndt0(v0) = v1 &
% 83.69/11.79 | $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~
% 83.69/11.79 | $i(v0) | ~ aInteger0(v0) | (sdtasdt0(v0, all_39_0) = v1 &
% 83.69/11.79 | sdtasdt0(all_39_0, v0) = v1 & $i(v1)))
% 83.69/11.79 |
% 83.69/11.79 | ALPHA: (12) implies:
% 83.69/11.79 | (13) smndt0(sz10) = all_39_0
% 83.69/11.79 |
% 83.69/11.79 | DELTA: instantiating (3) with fresh symbols all_42_0, all_42_1 gives:
% 83.69/11.79 | (14) stldt0(all_42_1) = cS2076 & sbsmnsldt0(xS) = all_42_1 & smndt0(sz10) =
% 83.69/11.79 | all_42_0 & $i(all_42_0) & $i(all_42_1) & aElementOf0(all_42_0, cS2076)
% 83.69/11.79 | & aElementOf0(sz10, cS2076) & aSet0(all_42_1) & aSet0(cS2076) & !
% 83.69/11.79 | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1,
% 83.69/11.79 | xS) | ~ aElementOf0(v0, v1) | ~ aInteger0(v0) | aElementOf0(v0,
% 83.69/11.79 | all_42_1)) & ! [v0: any] : (v0 = all_42_0 | v0 = sz10 | ~ $i(v0)
% 83.69/11.79 | | ~ aElementOf0(v0, cS2076)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 83.69/11.79 | aElementOf0(v0, all_42_1) | ~ aElementOf0(v0, cS2076)) & ! [v0:
% 83.69/11.79 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_42_1) | aInteger0(v0)) &
% 83.69/11.79 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_42_1) | ? [v1: $i] :
% 83.69/11.79 | ($i(v1) & aElementOf0(v1, xS) & aElementOf0(v0, v1))) & ! [v0: $i]
% 83.69/11.79 | : ( ~ $i(v0) | ~ aElementOf0(v0, cS2076) | aInteger0(v0)) & ! [v0:
% 83.69/11.79 | $i] : ( ~ $i(v0) | ~ aInteger0(v0) | aElementOf0(v0, all_42_1) |
% 83.69/11.79 | aElementOf0(v0, cS2076))
% 83.69/11.79 |
% 83.69/11.79 | ALPHA: (14) implies:
% 83.69/11.79 | (15) aElementOf0(sz10, cS2076)
% 83.69/11.79 | (16) smndt0(sz10) = all_42_0
% 83.69/11.79 | (17) sbsmnsldt0(xS) = all_42_1
% 83.69/11.79 | (18) stldt0(all_42_1) = cS2076
% 83.69/11.79 |
% 83.69/11.79 | DELTA: instantiating (4) with fresh symbols all_45_0, all_45_1 gives:
% 83.69/11.80 | (19) stldt0(all_45_1) = all_45_0 & sbsmnsldt0(xS) = all_45_1 & $i(all_45_0)
% 83.69/11.80 | & $i(all_45_1) & isClosed0(all_45_1) & isOpen0(all_45_0) &
% 83.69/11.80 | aSet0(all_45_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) |
% 83.69/11.80 | ~ $i(v0) | ~ aElementOf0(v0, all_45_0) | ? [v2: $i] : ? [v3: $i]
% 83.69/11.80 | : ( ~ (v2 = sz00) & szAzrzSzezqlpdtcmdtrp0(v0, v2) = v3 & $i(v3) &
% 83.69/11.80 | $i(v2) & aSubsetOf0(v3, all_45_0) & aSet0(v3) & aInteger0(v2) & !
% 83.69/11.80 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtasdt0(v2, v6) = v5)
% 83.69/11.80 | | ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v6) | ~ $i(v4) | ~
% 83.69/11.80 | aInteger0(v6) | ~ aInteger0(v4) | aElementOf0(v4, v3)) & !
% 83.69/11.80 | [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) |
% 83.69/11.80 | ~ aElementOf0(v4, v3) | sdteqdtlpzmzozddtrp0(v4, v0, v2)) & !
% 83.69/11.80 | [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) |
% 83.69/11.80 | ~ aElementOf0(v4, v3) | aDivisorOf0(v2, v5)) & ! [v4: $i] : !
% 83.69/11.80 | [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~
% 83.69/11.80 | aElementOf0(v4, v3) | aInteger0(v4)) & ! [v4: $i] : ! [v5: $i]
% 83.69/11.80 | : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v3)
% 83.69/11.80 | | ? [v6: $i] : (sdtasdt0(v2, v6) = v5 & $i(v6) & $i(v5) &
% 83.69/11.80 | aInteger0(v6))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 83.69/11.80 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~
% 83.69/11.80 | sdteqdtlpzmzozddtrp0(v4, v0, v2) | ~ aInteger0(v4) |
% 83.69/11.80 | aElementOf0(v4, v3)) & ! [v4: $i] : ! [v5: $i] : ( ~
% 83.69/11.80 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aDivisorOf0(v2, v5) |
% 83.69/11.80 | ~ aInteger0(v4) | aElementOf0(v4, v3)) & ! [v4: $i] : ( ~
% 83.69/11.80 | $i(v4) | ~ aElementOf0(v4, v3) | aElementOf0(v4, all_45_0)))) &
% 83.69/11.80 | ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 83.69/11.80 | aElementOf0(v1, xS) | ~ aElementOf0(v0, v1) | ~ aInteger0(v0) |
% 83.69/11.80 | aElementOf0(v0, all_45_1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 83.69/11.80 | aElementOf0(v0, all_45_0) | ~ aElementOf0(v0, all_45_1)) & ! [v0:
% 83.69/11.80 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_45_0) | aInteger0(v0)) &
% 83.69/11.80 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_45_1) |
% 83.69/11.80 | aInteger0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 83.69/11.80 | all_45_1) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, xS) &
% 83.69/11.80 | aElementOf0(v0, v1))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 83.69/11.80 | aInteger0(v0) | aElementOf0(v0, all_45_0) | aElementOf0(v0,
% 83.69/11.80 | all_45_1))
% 83.69/11.80 |
% 83.69/11.80 | ALPHA: (19) implies:
% 83.69/11.80 | (20) sbsmnsldt0(xS) = all_45_1
% 83.69/11.80 | (21) stldt0(all_45_1) = all_45_0
% 83.69/11.80 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~
% 83.69/11.80 | aElementOf0(v0, all_45_0) | ? [v2: $i] : ? [v3: $i] : ( ~ (v2 =
% 83.69/11.80 | sz00) & szAzrzSzezqlpdtcmdtrp0(v0, v2) = v3 & $i(v3) & $i(v2) &
% 83.69/11.80 | aSubsetOf0(v3, all_45_0) & aSet0(v3) & aInteger0(v2) & ! [v4: $i]
% 83.69/11.80 | : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtasdt0(v2, v6) = v5) | ~
% 83.69/11.80 | (sdtpldt0(v4, v1) = v5) | ~ $i(v6) | ~ $i(v4) | ~
% 83.69/11.80 | aInteger0(v6) | ~ aInteger0(v4) | aElementOf0(v4, v3)) & !
% 83.69/11.80 | [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) |
% 83.69/11.80 | ~ aElementOf0(v4, v3) | sdteqdtlpzmzozddtrp0(v4, v0, v2)) & !
% 83.69/11.80 | [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) |
% 83.69/11.80 | ~ aElementOf0(v4, v3) | aDivisorOf0(v2, v5)) & ! [v4: $i] : !
% 83.69/11.80 | [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~
% 83.69/11.80 | aElementOf0(v4, v3) | aInteger0(v4)) & ! [v4: $i] : ! [v5: $i]
% 83.69/11.80 | : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v3)
% 83.69/11.80 | | ? [v6: $i] : (sdtasdt0(v2, v6) = v5 & $i(v6) & $i(v5) &
% 83.69/11.80 | aInteger0(v6))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 83.69/11.80 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~
% 83.69/11.80 | sdteqdtlpzmzozddtrp0(v4, v0, v2) | ~ aInteger0(v4) |
% 83.69/11.80 | aElementOf0(v4, v3)) & ! [v4: $i] : ! [v5: $i] : ( ~
% 83.69/11.80 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aDivisorOf0(v2, v5) |
% 83.69/11.80 | ~ aInteger0(v4) | aElementOf0(v4, v3)) & ! [v4: $i] : ( ~
% 83.69/11.80 | $i(v4) | ~ aElementOf0(v4, v3) | aElementOf0(v4, all_45_0))))
% 83.69/11.80 |
% 83.69/11.80 | DELTA: instantiating (6) with fresh symbols all_48_0, all_48_1, all_48_2
% 83.69/11.80 | gives:
% 83.69/11.81 | (23) stldt0(all_48_1) = all_48_0 & sbsmnsldt0(xS) = all_48_1 & smndt0(sz10)
% 83.69/11.81 | = all_48_2 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) & ! [v0: $i]
% 83.69/11.81 | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v0 = sz00 |
% 83.69/11.81 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ (sdtasdt0(v0, v4) =
% 83.69/11.81 | v3) | ~ (sdtpldt0(v2, all_48_2) = v3) | ~ $i(v4) | ~ $i(v2) |
% 83.69/11.81 | ~ $i(v0) | ~ aInteger0(v4) | ~ aInteger0(v2) | ~ aInteger0(v0) |
% 83.69/11.81 | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 83.69/11.81 | [v3: $i] : (v0 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) |
% 83.69/11.81 | ~ (sdtpldt0(v2, all_48_2) = v3) | ~ $i(v2) | ~ $i(v0) | ~
% 83.69/11.81 | aElementOf0(v2, v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v2,
% 83.69/11.81 | sz10, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 83.69/11.81 | : (v0 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~
% 83.69/11.81 | (sdtpldt0(v2, all_48_2) = v3) | ~ $i(v2) | ~ $i(v0) | ~
% 83.69/11.81 | aElementOf0(v2, v1) | ~ aInteger0(v0) | aDivisorOf0(v0, v3)) & !
% 83.69/11.81 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = sz00 | ~
% 83.69/11.81 | (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ (sdtpldt0(v2, all_48_2)
% 83.69/11.81 | = v3) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 83.69/11.81 | aInteger0(v0) | aInteger0(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 83.69/11.81 | $i] : ! [v3: $i] : (v0 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10,
% 83.69/11.81 | v0) = v1) | ~ (sdtpldt0(v2, all_48_2) = v3) | ~ $i(v2) | ~
% 83.69/11.81 | $i(v0) | ~ aElementOf0(v2, v1) | ~ aInteger0(v0) | ? [v4: $i] :
% 83.69/11.81 | (sdtasdt0(v0, v4) = v3 & $i(v4) & $i(v3) & aInteger0(v4))) & ! [v0:
% 83.69/11.81 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = sz00 | ~
% 83.69/11.81 | (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ (sdtpldt0(v2, all_48_2)
% 83.69/11.81 | = v3) | ~ $i(v2) | ~ $i(v0) | ~ sdteqdtlpzmzozddtrp0(v2, sz10,
% 83.69/11.81 | v0) | ~ aInteger0(v2) | ~ aInteger0(v0) | aElementOf0(v2, v1)) &
% 83.69/11.81 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = sz00 |
% 83.69/11.81 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ (sdtpldt0(v2,
% 83.69/11.81 | all_48_2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ aDivisorOf0(v0, v3)
% 83.69/11.81 | | ~ aInteger0(v2) | ~ aInteger0(v0) | aElementOf0(v2, v1)) & !
% 83.69/11.81 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = sz00 | ~
% 83.69/11.81 | (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~
% 83.69/11.81 | $i(v0) | ~ aElementOf0(v3, xS) | ~ aElementOf0(v2, v3) | ~
% 83.69/11.81 | aInteger0(v2) | ~ aInteger0(v0) | aElementOf0(v2, all_48_1)) & !
% 83.69/11.81 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~
% 83.69/11.81 | (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 83.69/11.81 | aElementOf0(v2, all_48_0) | ~ aElementOf0(v2, all_48_1) | ~
% 83.69/11.81 | aInteger0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 =
% 83.69/11.81 | sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v2) | ~
% 83.69/11.81 | $i(v0) | ~ aElementOf0(v2, all_48_0) | ~ aInteger0(v0) |
% 83.69/11.81 | aInteger0(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 =
% 83.69/11.81 | sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v2) | ~
% 83.69/11.81 | $i(v0) | ~ aElementOf0(v2, all_48_1) | ~ aInteger0(v0) |
% 83.69/11.81 | aInteger0(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 =
% 83.69/11.81 | sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v2) | ~
% 83.69/11.81 | $i(v0) | ~ aElementOf0(v2, all_48_1) | ~ aInteger0(v0) | ? [v3:
% 83.69/11.81 | $i] : ($i(v3) & aElementOf0(v3, xS) & aElementOf0(v2, v3))) & !
% 83.69/11.81 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~
% 83.69/11.81 | (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 83.69/11.81 | aInteger0(v2) | ~ aInteger0(v0) | aElementOf0(v2, all_48_0) |
% 83.69/11.81 | aElementOf0(v2, all_48_1)) & ! [v0: $i] : ! [v1: $i] : (v0 = sz00
% 83.69/11.81 | | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v0) | ~
% 83.69/11.81 | aSubsetOf0(v1, all_48_0) | ~ aInteger0(v0)) & ! [v0: $i] : ! [v1:
% 83.69/11.81 | $i] : (v0 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~
% 83.69/11.81 | $i(v0) | ~ aInteger0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] :
% 83.69/11.81 | (v0 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v0) |
% 83.69/11.81 | ~ aInteger0(v0) | aSet0(all_48_1)) & ! [v0: $i] : ! [v1: $i] : (v0
% 83.69/11.81 | = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v0) | ~
% 83.69/11.81 | aInteger0(v0) | ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~
% 83.69/11.81 | aElementOf0(v2, all_48_0)))
% 83.69/11.81 |
% 83.69/11.81 | ALPHA: (23) implies:
% 83.69/11.81 | (24) smndt0(sz10) = all_48_2
% 83.69/11.81 | (25) sbsmnsldt0(xS) = all_48_1
% 83.69/11.81 | (26) stldt0(all_48_1) = all_48_0
% 83.69/11.81 | (27) ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~
% 83.69/11.81 | (szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1) | ~ $i(v0) | ~
% 83.69/11.81 | aSubsetOf0(v1, all_48_0) | ~ aInteger0(v0))
% 83.69/11.81 |
% 83.69/11.81 | GROUND_INST: instantiating (7) with all_36_0, all_42_0, sz10, simplifying with
% 83.69/11.81 | (11), (16) gives:
% 83.69/11.81 | (28) all_42_0 = all_36_0
% 83.69/11.81 |
% 83.69/11.81 | GROUND_INST: instantiating (7) with all_42_0, all_48_2, sz10, simplifying with
% 83.69/11.81 | (16), (24) gives:
% 83.69/11.81 | (29) all_48_2 = all_42_0
% 83.69/11.81 |
% 83.69/11.81 | GROUND_INST: instantiating (7) with all_39_0, all_48_2, sz10, simplifying with
% 83.69/11.81 | (13), (24) gives:
% 83.69/11.81 | (30) all_48_2 = all_39_0
% 83.69/11.81 |
% 83.69/11.81 | GROUND_INST: instantiating (8) with all_45_1, all_48_1, xS, simplifying with
% 83.69/11.81 | (20), (25) gives:
% 83.69/11.81 | (31) all_48_1 = all_45_1
% 83.69/11.81 |
% 83.69/11.81 | GROUND_INST: instantiating (8) with all_42_1, all_48_1, xS, simplifying with
% 83.69/11.81 | (17), (25) gives:
% 83.69/11.81 | (32) all_48_1 = all_42_1
% 83.69/11.81 |
% 83.69/11.81 | GROUND_INST: instantiating (9) with all_45_0, all_48_0, all_45_1, simplifying
% 83.69/11.81 | with (21) gives:
% 83.69/11.81 | (33) all_48_0 = all_45_0 | ~ (stldt0(all_45_1) = all_48_0)
% 83.69/11.81 |
% 83.69/11.81 | GROUND_INST: instantiating (9) with cS2076, all_48_0, all_42_1, simplifying
% 83.69/11.81 | with (18) gives:
% 83.69/11.81 | (34) all_48_0 = cS2076 | ~ (stldt0(all_42_1) = all_48_0)
% 83.69/11.81 |
% 83.69/11.81 | COMBINE_EQS: (31), (32) imply:
% 83.69/11.81 | (35) all_45_1 = all_42_1
% 83.69/11.81 |
% 83.69/11.81 | SIMP: (35) implies:
% 83.69/11.81 | (36) all_45_1 = all_42_1
% 83.69/11.81 |
% 83.69/11.81 | COMBINE_EQS: (29), (30) imply:
% 83.69/11.81 | (37) all_42_0 = all_39_0
% 83.69/11.81 |
% 83.69/11.81 | SIMP: (37) implies:
% 83.69/11.81 | (38) all_42_0 = all_39_0
% 83.69/11.81 |
% 83.69/11.81 | COMBINE_EQS: (28), (38) imply:
% 83.69/11.81 | (39) all_39_0 = all_36_0
% 83.69/11.81 |
% 83.69/11.81 | SIMP: (39) implies:
% 83.69/11.81 | (40) all_39_0 = all_36_0
% 83.69/11.81 |
% 83.69/11.81 | REDUCE: (26), (32) imply:
% 83.69/11.81 | (41) stldt0(all_42_1) = all_48_0
% 83.69/11.81 |
% 83.69/11.81 | BETA: splitting (33) gives:
% 83.69/11.81 |
% 83.69/11.81 | Case 1:
% 83.69/11.81 | |
% 83.69/11.81 | | (42) ~ (stldt0(all_45_1) = all_48_0)
% 83.69/11.81 | |
% 83.69/11.81 | | REDUCE: (36), (42) imply:
% 83.69/11.81 | | (43) ~ (stldt0(all_42_1) = all_48_0)
% 83.69/11.81 | |
% 83.69/11.81 | | PRED_UNIFY: (41), (43) imply:
% 83.69/11.81 | | (44) $false
% 83.69/11.81 | |
% 83.69/11.81 | | CLOSE: (44) is inconsistent.
% 83.69/11.81 | |
% 83.69/11.81 | Case 2:
% 83.69/11.81 | |
% 83.69/11.81 | | (45) all_48_0 = all_45_0
% 83.69/11.81 | |
% 83.69/11.81 | | BETA: splitting (34) gives:
% 83.69/11.81 | |
% 83.69/11.81 | | Case 1:
% 83.69/11.81 | | |
% 83.69/11.81 | | | (46) ~ (stldt0(all_42_1) = all_48_0)
% 83.69/11.81 | | |
% 83.69/11.81 | | | PRED_UNIFY: (41), (46) imply:
% 83.69/11.82 | | | (47) $false
% 83.69/11.82 | | |
% 83.69/11.82 | | | CLOSE: (47) is inconsistent.
% 83.69/11.82 | | |
% 83.69/11.82 | | Case 2:
% 83.69/11.82 | | |
% 83.69/11.82 | | | (48) all_48_0 = cS2076
% 83.69/11.82 | | |
% 83.69/11.82 | | | COMBINE_EQS: (45), (48) imply:
% 83.69/11.82 | | | (49) all_45_0 = cS2076
% 83.69/11.82 | | |
% 83.69/11.82 | | | GROUND_INST: instantiating (22) with sz10, all_36_0, simplifying with (5),
% 83.69/11.82 | | | (11) gives:
% 83.69/11.82 | | | (50) ~ aElementOf0(sz10, all_45_0) | ? [v0: $i] : ? [v1: $i] : ( ~
% 83.69/11.82 | | | (v0 = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1 & $i(v1) &
% 83.69/11.82 | | | $i(v0) & aSubsetOf0(v1, all_45_0) & aSet0(v1) & aInteger0(v0) &
% 83.69/11.82 | | | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v0, v4) =
% 83.69/11.82 | | | v3) | ~ (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v4) | ~
% 83.69/11.82 | | | $i(v2) | ~ aInteger0(v4) | ~ aInteger0(v2) | aElementOf0(v2,
% 83.69/11.82 | | | v1)) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v2,
% 83.69/11.82 | | | all_36_0) = v3) | ~ $i(v2) | ~ aElementOf0(v2, v1) |
% 83.69/11.82 | | | sdteqdtlpzmzozddtrp0(v2, sz10, v0)) & ! [v2: $i] : ! [v3:
% 83.69/11.82 | | | $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v2) | ~
% 83.69/11.82 | | | aElementOf0(v2, v1) | aDivisorOf0(v0, v3)) & ! [v2: $i] : !
% 83.69/11.82 | | | [v3: $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v2) | ~
% 83.69/11.82 | | | aElementOf0(v2, v1) | aInteger0(v2)) & ! [v2: $i] : ! [v3:
% 83.69/11.82 | | | $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v2) | ~
% 83.69/11.82 | | | aElementOf0(v2, v1) | ? [v4: $i] : (sdtasdt0(v0, v4) = v3 &
% 83.69/11.82 | | | $i(v4) & $i(v3) & aInteger0(v4))) & ! [v2: $i] : ! [v3:
% 83.69/11.82 | | | $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v2) | ~
% 83.69/11.82 | | | sdteqdtlpzmzozddtrp0(v2, sz10, v0) | ~ aInteger0(v2) |
% 83.69/11.82 | | | aElementOf0(v2, v1)) & ! [v2: $i] : ! [v3: $i] : ( ~
% 83.69/11.82 | | | (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v2) | ~ aDivisorOf0(v0,
% 83.69/11.82 | | | v3) | ~ aInteger0(v2) | aElementOf0(v2, v1)) & ! [v2: $i]
% 83.69/11.82 | | | : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2,
% 83.69/11.82 | | | all_45_0)))
% 83.69/11.82 | | |
% 83.69/11.82 | | | BETA: splitting (50) gives:
% 83.69/11.82 | | |
% 83.69/11.82 | | | Case 1:
% 83.69/11.82 | | | |
% 83.69/11.82 | | | | (51) ~ aElementOf0(sz10, all_45_0)
% 83.69/11.82 | | | |
% 83.69/11.82 | | | | REDUCE: (49), (51) imply:
% 83.69/11.82 | | | | (52) ~ aElementOf0(sz10, cS2076)
% 83.69/11.82 | | | |
% 83.69/11.82 | | | | PRED_UNIFY: (15), (52) imply:
% 83.69/11.82 | | | | (53) $false
% 83.69/11.82 | | | |
% 83.69/11.82 | | | | CLOSE: (53) is inconsistent.
% 83.69/11.82 | | | |
% 83.69/11.82 | | | Case 2:
% 83.69/11.82 | | | |
% 83.69/11.82 | | | | (54) ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = sz00) &
% 83.69/11.82 | | | | szAzrzSzezqlpdtcmdtrp0(sz10, v0) = v1 & $i(v1) & $i(v0) &
% 83.69/11.82 | | | | aSubsetOf0(v1, all_45_0) & aSet0(v1) & aInteger0(v0) & ! [v2:
% 83.69/11.82 | | | | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v0, v4) =
% 83.69/11.82 | | | | v3) | ~ (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v4) | ~
% 83.69/11.82 | | | | $i(v2) | ~ aInteger0(v4) | ~ aInteger0(v2) |
% 83.69/11.82 | | | | aElementOf0(v2, v1)) & ! [v2: $i] : ! [v3: $i] : ( ~
% 83.69/11.82 | | | | (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v2) | ~
% 83.69/11.82 | | | | aElementOf0(v2, v1) | sdteqdtlpzmzozddtrp0(v2, sz10, v0)) &
% 83.69/11.82 | | | | ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) |
% 83.69/11.82 | | | | ~ $i(v2) | ~ aElementOf0(v2, v1) | aDivisorOf0(v0, v3)) &
% 83.69/11.82 | | | | ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) |
% 83.69/11.82 | | | | ~ $i(v2) | ~ aElementOf0(v2, v1) | aInteger0(v2)) & !
% 83.69/11.82 | | | | [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) |
% 83.69/11.82 | | | | ~ $i(v2) | ~ aElementOf0(v2, v1) | ? [v4: $i] :
% 83.69/11.82 | | | | (sdtasdt0(v0, v4) = v3 & $i(v4) & $i(v3) & aInteger0(v4))) &
% 83.69/11.82 | | | | ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3)
% 83.69/11.82 | | | | | ~ $i(v2) | ~ sdteqdtlpzmzozddtrp0(v2, sz10, v0) | ~
% 83.69/11.82 | | | | aInteger0(v2) | aElementOf0(v2, v1)) & ! [v2: $i] : ! [v3:
% 83.69/11.82 | | | | $i] : ( ~ (sdtpldt0(v2, all_36_0) = v3) | ~ $i(v2) | ~
% 83.69/11.82 | | | | aDivisorOf0(v0, v3) | ~ aInteger0(v2) | aElementOf0(v2,
% 83.69/11.82 | | | | v1)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) |
% 83.69/11.82 | | | | aElementOf0(v2, all_45_0)))
% 83.69/11.82 | | | |
% 83.69/11.82 | | | | DELTA: instantiating (54) with fresh symbols all_92_0, all_92_1 gives:
% 83.69/11.82 | | | | (55) ~ (all_92_1 = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, all_92_1) =
% 83.69/11.82 | | | | all_92_0 & $i(all_92_0) & $i(all_92_1) & aSubsetOf0(all_92_0,
% 83.69/11.82 | | | | all_45_0) & aSet0(all_92_0) & aInteger0(all_92_1) & ! [v0:
% 83.69/11.82 | | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(all_92_1, v2)
% 83.69/11.82 | | | | = v1) | ~ (sdtpldt0(v0, all_36_0) = v1) | ~ $i(v2) | ~
% 83.69/11.82 | | | | $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v0) | aElementOf0(v0,
% 83.69/11.82 | | | | all_92_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0,
% 83.69/11.82 | | | | all_36_0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_92_0)
% 83.69/11.82 | | | | | sdteqdtlpzmzozddtrp0(v0, sz10, all_92_1)) & ! [v0: $i] : !
% 83.69/11.82 | | | | [v1: $i] : ( ~ (sdtpldt0(v0, all_36_0) = v1) | ~ $i(v0) | ~
% 83.69/11.82 | | | | aElementOf0(v0, all_92_0) | aDivisorOf0(all_92_1, v1)) & !
% 83.69/11.82 | | | | [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, all_36_0) = v1) | ~
% 83.69/11.82 | | | | $i(v0) | ~ aElementOf0(v0, all_92_0) | aInteger0(v0)) & !
% 83.69/11.82 | | | | [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, all_36_0) = v1) | ~
% 83.69/11.82 | | | | $i(v0) | ~ aElementOf0(v0, all_92_0) | ? [v2: $i] :
% 83.69/11.82 | | | | (sdtasdt0(all_92_1, v2) = v1 & $i(v2) & $i(v1) &
% 83.69/11.82 | | | | aInteger0(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 83.69/11.82 | | | | (sdtpldt0(v0, all_36_0) = v1) | ~ $i(v0) | ~
% 83.69/11.82 | | | | sdteqdtlpzmzozddtrp0(v0, sz10, all_92_1) | ~ aInteger0(v0) |
% 83.69/11.82 | | | | aElementOf0(v0, all_92_0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 83.69/11.82 | | | | (sdtpldt0(v0, all_36_0) = v1) | ~ $i(v0) | ~
% 83.69/11.82 | | | | aDivisorOf0(all_92_1, v1) | ~ aInteger0(v0) | aElementOf0(v0,
% 83.69/11.82 | | | | all_92_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 83.69/11.82 | | | | all_92_0) | aElementOf0(v0, all_45_0))
% 83.69/11.82 | | | |
% 83.69/11.82 | | | | ALPHA: (55) implies:
% 83.69/11.82 | | | | (56) ~ (all_92_1 = sz00)
% 83.69/11.82 | | | | (57) aInteger0(all_92_1)
% 83.69/11.82 | | | | (58) aSubsetOf0(all_92_0, all_45_0)
% 83.69/11.82 | | | | (59) $i(all_92_1)
% 83.69/11.83 | | | | (60) szAzrzSzezqlpdtcmdtrp0(sz10, all_92_1) = all_92_0
% 83.69/11.83 | | | |
% 83.69/11.83 | | | | REDUCE: (49), (58) imply:
% 83.69/11.83 | | | | (61) aSubsetOf0(all_92_0, cS2076)
% 83.69/11.83 | | | |
% 83.69/11.83 | | | | GROUND_INST: instantiating (27) with all_92_1, all_92_0, simplifying
% 83.69/11.83 | | | | with (57), (59), (60) gives:
% 83.69/11.83 | | | | (62) all_92_1 = sz00 | ~ aSubsetOf0(all_92_0, all_48_0)
% 83.69/11.83 | | | |
% 83.69/11.83 | | | | BETA: splitting (62) gives:
% 83.69/11.83 | | | |
% 83.69/11.83 | | | | Case 1:
% 83.69/11.83 | | | | |
% 83.69/11.83 | | | | | (63) ~ aSubsetOf0(all_92_0, all_48_0)
% 83.69/11.83 | | | | |
% 83.69/11.83 | | | | | REDUCE: (48), (63) imply:
% 83.69/11.83 | | | | | (64) ~ aSubsetOf0(all_92_0, cS2076)
% 83.69/11.83 | | | | |
% 83.69/11.83 | | | | | PRED_UNIFY: (61), (64) imply:
% 83.69/11.83 | | | | | (65) $false
% 83.69/11.83 | | | | |
% 83.69/11.83 | | | | | CLOSE: (65) is inconsistent.
% 83.69/11.83 | | | | |
% 83.69/11.83 | | | | Case 2:
% 83.69/11.83 | | | | |
% 83.69/11.83 | | | | | (66) all_92_1 = sz00
% 83.69/11.83 | | | | |
% 83.69/11.83 | | | | | REDUCE: (56), (66) imply:
% 83.69/11.83 | | | | | (67) $false
% 83.69/11.83 | | | | |
% 83.69/11.83 | | | | | CLOSE: (67) is inconsistent.
% 83.69/11.83 | | | | |
% 83.69/11.83 | | | | End of split
% 83.69/11.83 | | | |
% 83.69/11.83 | | | End of split
% 83.69/11.83 | | |
% 83.69/11.83 | | End of split
% 83.69/11.83 | |
% 83.69/11.83 | End of split
% 83.69/11.83 |
% 83.69/11.83 End of proof
% 83.69/11.83 % SZS output end Proof for theBenchmark
% 83.69/11.83
% 83.69/11.83 11199ms
%------------------------------------------------------------------------------