TSTP Solution File: NUM456+6 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM456+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 : n002.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 11:47:52 EDT 2023
% Result : Theorem 23.05s 3.91s
% Output : Proof 37.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM456+6 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 16:34:17 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.62 ________ _____
% 0.18/0.62 ___ __ \_________(_)________________________________
% 0.18/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.62
% 0.18/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.62 (2023-06-19)
% 0.18/0.62
% 0.18/0.62 (c) Philipp Rümmer, 2009-2023
% 0.18/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.62 Amanda Stjerna.
% 0.18/0.62 Free software under BSD-3-Clause.
% 0.18/0.62
% 0.18/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.62
% 0.18/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.63/0.63 Running up to 7 provers in parallel.
% 0.63/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.63/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.63/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.63/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.63/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.63/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.63/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.82/1.44 Prover 1: Preprocessing ...
% 4.82/1.44 Prover 4: Preprocessing ...
% 5.24/1.48 Prover 5: Preprocessing ...
% 5.24/1.48 Prover 6: Preprocessing ...
% 5.24/1.48 Prover 0: Preprocessing ...
% 5.24/1.48 Prover 3: Preprocessing ...
% 5.24/1.49 Prover 2: Preprocessing ...
% 16.46/3.04 Prover 1: Constructing countermodel ...
% 16.95/3.08 Prover 3: Constructing countermodel ...
% 17.41/3.23 Prover 5: Proving ...
% 17.41/3.24 Prover 6: Proving ...
% 19.80/3.47 Prover 2: Proving ...
% 23.05/3.91 Prover 3: proved (3260ms)
% 23.05/3.91
% 23.05/3.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.05/3.91
% 23.05/3.91 Prover 5: stopped
% 23.05/3.91 Prover 6: stopped
% 23.05/3.91 Prover 2: stopped
% 23.05/3.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 23.05/3.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 23.05/3.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 23.05/3.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 24.22/4.10 Prover 0: Proving ...
% 24.59/4.12 Prover 0: stopped
% 24.59/4.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.91/4.20 Prover 4: Constructing countermodel ...
% 25.65/4.27 Prover 8: Preprocessing ...
% 26.07/4.31 Prover 10: Preprocessing ...
% 26.49/4.37 Prover 11: Preprocessing ...
% 26.49/4.39 Prover 7: Preprocessing ...
% 26.83/4.43 Prover 13: Preprocessing ...
% 27.90/4.73 Prover 10: Warning: ignoring some quantifiers
% 27.90/4.75 Prover 10: Constructing countermodel ...
% 27.90/4.81 Prover 7: Warning: ignoring some quantifiers
% 27.90/4.83 Prover 8: Warning: ignoring some quantifiers
% 27.90/4.84 Prover 8: Constructing countermodel ...
% 27.90/4.84 Prover 7: Constructing countermodel ...
% 30.84/4.94 Prover 13: Warning: ignoring some quantifiers
% 30.84/4.97 Prover 13: Constructing countermodel ...
% 34.12/5.40 Prover 10: Found proof (size 64)
% 34.12/5.40 Prover 10: proved (1492ms)
% 34.12/5.41 Prover 7: stopped
% 34.12/5.41 Prover 8: stopped
% 34.12/5.41 Prover 1: stopped
% 34.12/5.41 Prover 13: stopped
% 34.12/5.41 Prover 4: stopped
% 36.34/5.91 Prover 11: Constructing countermodel ...
% 36.58/5.94 Prover 11: stopped
% 36.58/5.94
% 36.58/5.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.58/5.94
% 36.58/5.97 % SZS output start Proof for theBenchmark
% 36.58/5.97 Assumptions after simplification:
% 36.58/5.97 ---------------------------------
% 36.58/5.97
% 36.58/5.97 (mArSeqClosed)
% 36.58/6.01 $i(cS1395) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 |
% 36.58/6.01 ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 36.58/6.01 aInteger0(v1) | ~ aInteger0(v0) | isClosed0(v2)) & ! [v0: $i] : ! [v1:
% 36.58/6.01 $i] : ! [v2: $i] : (v1 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) |
% 36.58/6.01 ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | aSubsetOf0(v2,
% 36.58/6.01 cS1395))
% 36.58/6.01
% 36.58/6.01 (mIntOne)
% 36.58/6.01 $i(sz10) & aInteger0(sz10)
% 36.58/6.01
% 36.58/6.01 (mMulMinOne)
% 36.93/6.02 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 36.93/6.02 $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 36.93/6.02 (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))))
% 36.93/6.02
% 36.93/6.02 (mPrimeDivisor)
% 36.93/6.02 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : (v1 = v0
% 36.93/6.02 | v1 = sz10 | ~ $i(v1) | ~ aInteger0(v1) | ? [v2: $i] : ($i(v2) &
% 36.93/6.02 isPrime0(v2) & aDivisorOf0(v2, v1))) & ! [v1: $i] : ( ~ $i(v1) | ~
% 36.93/6.02 isPrime0(v1) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0)) & ! [v1: $i] :
% 36.93/6.02 ( ~ $i(v1) | ~ isPrime0(v1) | ~ aDivisorOf0(v1, sz10) | ~
% 36.93/6.02 aInteger0(sz10)))
% 36.93/6.02
% 36.93/6.02 (mSubset)
% 36.93/6.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 36.93/6.03 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 36.93/6.03 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 36.93/6.03 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 36.93/6.03 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 36.93/6.03 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 36.93/6.03
% 36.93/6.03 (m__2079)
% 36.93/6.03 $i(cS2076) & $i(xS) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : (stldt0(v0) =
% 36.93/6.03 cS2076 & sbsmnsldt0(xS) = v0 & smndt0(sz10) = v1 & $i(v1) & $i(v0) &
% 36.93/6.03 aElementOf0(v1, cS2076) & aElementOf0(sz10, cS2076) & aSet0(v0) &
% 36.93/6.03 aSet0(cS2076) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 36.93/6.03 aElementOf0(v3, xS) | ~ aElementOf0(v2, v3) | ~ aInteger0(v2) |
% 36.93/6.03 aElementOf0(v2, v0)) & ! [v2: $i] : (v2 = v1 | v2 = sz10 | ~ $i(v2) | ~
% 36.93/6.03 aElementOf0(v2, cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2,
% 36.93/6.03 v0) | ~ aElementOf0(v2, cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 36.93/6.03 aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 36.93/6.03 aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3, xS) &
% 36.93/6.03 aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2,
% 36.93/6.03 cS2076) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) | ~ aInteger0(v2) |
% 36.93/6.03 aElementOf0(v2, v0) | aElementOf0(v2, cS2076)))
% 36.93/6.03
% 36.93/6.03 (m__2144)
% 36.93/6.04 $i(xS) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = v1 &
% 36.93/6.04 sbsmnsldt0(xS) = v0 & $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1) &
% 36.93/6.04 aSet0(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (smndt0(v2) = v3) | ~ $i(v2) |
% 36.93/6.05 ~ aElementOf0(v2, v1) | ? [v4: $i] : ? [v5: $i] : ( ~ (v4 = sz00) &
% 36.93/6.05 szAzrzSzezqlpdtcmdtrp0(v2, v4) = v5 & $i(v5) & $i(v4) & aSubsetOf0(v5,
% 36.93/6.05 v1) & aSet0(v5) & aInteger0(v4) & ! [v6: $i] : ! [v7: $i] : ! [v8:
% 36.93/6.05 $i] : ( ~ (sdtasdt0(v4, v8) = v7) | ~ (sdtpldt0(v6, v3) = v7) | ~
% 36.93/6.05 $i(v8) | ~ $i(v6) | ~ aInteger0(v8) | ~ aInteger0(v6) |
% 36.93/6.05 aElementOf0(v6, v5)) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6,
% 36.93/6.05 v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) |
% 36.93/6.05 sdteqdtlpzmzozddtrp0(v6, v2, v4)) & ! [v6: $i] : ! [v7: $i] : ( ~
% 36.93/6.05 (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) |
% 36.93/6.05 aDivisorOf0(v4, v7)) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6,
% 36.93/6.05 v3) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | aInteger0(v6)) &
% 36.93/6.05 ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~
% 36.93/6.05 aElementOf0(v6, v5) | ? [v8: $i] : (sdtasdt0(v4, v8) = v7 & $i(v8) &
% 36.93/6.05 $i(v7) & aInteger0(v8))) & ! [v6: $i] : ! [v7: $i] : ( ~
% 36.93/6.05 (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ sdteqdtlpzmzozddtrp0(v6, v2,
% 36.93/6.05 v4) | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! [v6: $i] : !
% 36.93/6.05 [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aDivisorOf0(v4,
% 36.93/6.05 v7) | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! [v6: $i] : ( ~
% 36.93/6.05 $i(v6) | ~ aElementOf0(v6, v5) | aElementOf0(v6, v1)))) & ! [v2: $i]
% 36.93/6.05 : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xS) | ~
% 36.93/6.05 aElementOf0(v2, v3) | ~ aInteger0(v2) | aElementOf0(v2, v0)) & ! [v2:
% 36.93/6.05 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ~ aElementOf0(v2, v0)) & !
% 36.93/6.05 [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | aInteger0(v2)) & ! [v2:
% 36.93/6.05 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] :
% 36.93/6.05 ( ~ $i(v2) | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) &
% 36.93/6.05 aElementOf0(v3, xS) & aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) |
% 36.93/6.05 ~ aInteger0(v2) | aElementOf0(v2, v1) | aElementOf0(v2, v0)))
% 36.93/6.05
% 36.93/6.05 (m__2171)
% 36.93/6.06 $i(xp) & $i(xS) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 36.93/6.06 $i] : ? [v3: $i] : ( ~ (xp = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v0
% 36.93/6.06 & stldt0(v2) = v3 & sbsmnsldt0(xS) = v2 & smndt0(sz10) = v1 & $i(v3) &
% 36.93/6.06 $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(v0, v3) & aSet0(v2) & aSet0(v0) &
% 36.93/6.06 aInteger0(xp) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtasdt0(xp,
% 36.93/6.06 v6) = v5) | ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v6) | ~ $i(v4) | ~
% 36.93/6.06 aInteger0(v6) | ~ aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: $i] : !
% 36.93/6.06 [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v0)
% 36.93/6.06 | sdteqdtlpzmzozddtrp0(v4, sz10, xp)) & ! [v4: $i] : ! [v5: $i] : ( ~
% 36.93/6.06 (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v0) |
% 36.93/6.06 aDivisorOf0(xp, v5)) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) =
% 36.93/6.06 v5) | ~ $i(v4) | ~ aElementOf0(v4, v0) | aInteger0(v4)) & ! [v4: $i]
% 36.93/6.06 : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4,
% 36.93/6.06 v0) | ? [v6: $i] : (sdtasdt0(xp, v6) = v5 & $i(v6) & $i(v5) &
% 36.93/6.06 aInteger0(v6))) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) =
% 36.93/6.06 v5) | ~ $i(v4) | ~ sdteqdtlpzmzozddtrp0(v4, sz10, xp) | ~
% 36.93/6.06 aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: $i] : ! [v5: $i] : ( ~
% 36.93/6.06 (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aDivisorOf0(xp, v5) | ~
% 36.93/6.06 aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: $i] : ! [v5: $i] : ( ~
% 36.93/6.06 $i(v5) | ~ $i(v4) | ~ aElementOf0(v5, xS) | ~ aElementOf0(v4, v5) | ~
% 36.93/6.06 aInteger0(v4) | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | ~
% 36.93/6.06 aElementOf0(v4, v3) | ~ aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) |
% 36.93/6.06 ~ aElementOf0(v4, v3) | aInteger0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~
% 36.93/6.06 aElementOf0(v4, v2) | aInteger0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~
% 36.93/6.06 aElementOf0(v4, v2) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, xS) &
% 36.93/6.06 aElementOf0(v4, v5))) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4,
% 36.93/6.06 v0) | aElementOf0(v4, v3)) & ! [v4: $i] : ( ~ $i(v4) | ~ aInteger0(v4)
% 36.93/6.06 | aElementOf0(v4, v3) | aElementOf0(v4, v2)))
% 36.93/6.06
% 36.93/6.06 (m__2203)
% 36.93/6.06 $i(cS2200) & $i(xp) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 36.93/6.06 [v3: $i] : ? [v4: $i] : ( ~ (v2 = v0) & ~ (v2 = sz10) &
% 36.93/6.06 szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v1 & sdtasdt0(xp, v4) = v3 & sdtpldt0(v2,
% 36.93/6.06 v0) = v3 & smndt0(sz10) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)
% 36.93/6.06 & aElementOf0(v2, v1) & sdteqdtlpzmzozddtrp0(v2, sz10, xp) & aDivisorOf0(xp,
% 36.93/6.06 v3) & aInteger0(v4) & aInteger0(v2) & ~ aElementOf0(v2, cS2200))
% 36.93/6.06
% 36.93/6.06 (function-axioms)
% 36.93/6.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 36.93/6.07 (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) | ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) =
% 36.93/6.07 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 36.93/6.07 ~ (sdtslmnbsdt0(v3, v2) = v1) | ~ (sdtslmnbsdt0(v3, v2) = v0)) & ! [v0:
% 36.93/6.07 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 36.93/6.07 (sdtbsmnsldt0(v3, v2) = v1) | ~ (sdtbsmnsldt0(v3, v2) = v0)) & ! [v0: $i]
% 36.93/6.07 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) =
% 36.93/6.07 v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 36.93/6.07 $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3,
% 36.93/6.07 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 36.93/6.07 (stldt0(v2) = v1) | ~ (stldt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 36.93/6.07 [v2: $i] : (v1 = v0 | ~ (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0)) &
% 36.93/6.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~
% 36.93/6.07 (smndt0(v2) = v0))
% 36.93/6.07
% 36.93/6.07 Further assumptions not needed in the proof:
% 36.93/6.07 --------------------------------------------
% 36.93/6.07 mAddAsso, mAddComm, mAddNeg, mAddZero, mArSeq, mClosed, mComplement, mDistrib,
% 36.93/6.07 mDivisor, mElements, mEquMod, mEquModMul, mEquModRef, mEquModSym, mEquModTrn,
% 36.93/6.07 mFinSet, mIntMult, mIntNeg, mIntPlus, mIntZero, mIntegers, mInterOpen,
% 36.93/6.07 mIntersection, mMulAsso, mMulComm, mMulOne, mMulZero, mOpen, mPrime, mSets,
% 36.93/6.07 mUnion, mUnionClosed, mUnionOpen, mUnionSClosed, mUnionSet, mZeroDiv, m__,
% 36.93/6.07 m__2046, m__2117
% 36.93/6.07
% 36.93/6.07 Those formulas are unsatisfiable:
% 36.93/6.07 ---------------------------------
% 36.93/6.07
% 36.93/6.07 Begin of proof
% 36.93/6.07 |
% 36.93/6.07 | ALPHA: (mIntOne) implies:
% 36.93/6.07 | (1) aInteger0(sz10)
% 36.93/6.07 |
% 36.93/6.07 | ALPHA: (mMulMinOne) implies:
% 36.93/6.07 | (2) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 36.93/6.07 | ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 36.93/6.07 | (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))))
% 36.93/6.07 |
% 36.93/6.07 | ALPHA: (mPrimeDivisor) implies:
% 36.93/6.08 | (3) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : (v1 = v0 | v1
% 36.93/6.08 | = sz10 | ~ $i(v1) | ~ aInteger0(v1) | ? [v2: $i] : ($i(v2) &
% 36.93/6.08 | isPrime0(v2) & aDivisorOf0(v2, v1))) & ! [v1: $i] : ( ~ $i(v1) |
% 36.93/6.08 | ~ isPrime0(v1) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0)) & !
% 36.93/6.08 | [v1: $i] : ( ~ $i(v1) | ~ isPrime0(v1) | ~ aDivisorOf0(v1, sz10) |
% 36.93/6.08 | ~ aInteger0(sz10)))
% 36.93/6.08 |
% 36.93/6.08 | ALPHA: (mSubset) implies:
% 36.93/6.08 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 36.93/6.08 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~
% 36.93/6.08 | aSet0(v0) | aElementOf0(v2, v0))
% 36.93/6.08 |
% 36.93/6.08 | ALPHA: (mArSeqClosed) implies:
% 36.93/6.08 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~
% 36.93/6.08 | (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 36.93/6.08 | aInteger0(v1) | ~ aInteger0(v0) | isClosed0(v2))
% 36.93/6.08 |
% 36.93/6.08 | ALPHA: (m__2079) implies:
% 36.93/6.09 | (6) ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = cS2076 & sbsmnsldt0(xS) = v0
% 36.93/6.09 | & smndt0(sz10) = v1 & $i(v1) & $i(v0) & aElementOf0(v1, cS2076) &
% 36.93/6.09 | aElementOf0(sz10, cS2076) & aSet0(v0) & aSet0(cS2076) & ! [v2: $i] :
% 36.93/6.09 | ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xS) | ~
% 36.93/6.09 | aElementOf0(v2, v3) | ~ aInteger0(v2) | aElementOf0(v2, v0)) & !
% 36.93/6.09 | [v2: $i] : (v2 = v1 | v2 = sz10 | ~ $i(v2) | ~ aElementOf0(v2,
% 36.93/6.09 | cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | ~
% 36.93/6.09 | aElementOf0(v2, cS2076)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 36.93/6.09 | aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) |
% 36.93/6.09 | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3, xS)
% 36.93/6.09 | & aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | ~
% 36.93/6.09 | aElementOf0(v2, cS2076) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2)
% 36.93/6.09 | | ~ aInteger0(v2) | aElementOf0(v2, v0) | aElementOf0(v2,
% 36.93/6.09 | cS2076)))
% 36.93/6.09 |
% 36.93/6.09 | ALPHA: (m__2144) implies:
% 36.93/6.10 | (7) ? [v0: $i] : ? [v1: $i] : (stldt0(v0) = v1 & sbsmnsldt0(xS) = v0 &
% 36.93/6.10 | $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1) & aSet0(v0) & ! [v2:
% 36.93/6.10 | $i] : ! [v3: $i] : ( ~ (smndt0(v2) = v3) | ~ $i(v2) | ~
% 36.93/6.10 | aElementOf0(v2, v1) | ? [v4: $i] : ? [v5: $i] : ( ~ (v4 = sz00) &
% 36.93/6.10 | szAzrzSzezqlpdtcmdtrp0(v2, v4) = v5 & $i(v5) & $i(v4) &
% 36.93/6.10 | aSubsetOf0(v5, v1) & aSet0(v5) & aInteger0(v4) & ! [v6: $i] : !
% 36.93/6.10 | [v7: $i] : ! [v8: $i] : ( ~ (sdtasdt0(v4, v8) = v7) | ~
% 36.93/6.10 | (sdtpldt0(v6, v3) = v7) | ~ $i(v8) | ~ $i(v6) | ~
% 36.93/6.10 | aInteger0(v8) | ~ aInteger0(v6) | aElementOf0(v6, v5)) & !
% 36.93/6.10 | [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6)
% 36.93/6.10 | | ~ aElementOf0(v6, v5) | sdteqdtlpzmzozddtrp0(v6, v2, v4)) &
% 36.93/6.10 | ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~
% 36.93/6.10 | $i(v6) | ~ aElementOf0(v6, v5) | aDivisorOf0(v4, v7)) & !
% 36.93/6.10 | [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6)
% 36.93/6.10 | | ~ aElementOf0(v6, v5) | aInteger0(v6)) & ! [v6: $i] : !
% 36.93/6.10 | [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~
% 36.93/6.10 | aElementOf0(v6, v5) | ? [v8: $i] : (sdtasdt0(v4, v8) = v7 &
% 36.93/6.10 | $i(v8) & $i(v7) & aInteger0(v8))) & ! [v6: $i] : ! [v7: $i]
% 36.93/6.10 | : ( ~ (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~
% 36.93/6.10 | sdteqdtlpzmzozddtrp0(v6, v2, v4) | ~ aInteger0(v6) |
% 36.93/6.10 | aElementOf0(v6, v5)) & ! [v6: $i] : ! [v7: $i] : ( ~
% 36.93/6.10 | (sdtpldt0(v6, v3) = v7) | ~ $i(v6) | ~ aDivisorOf0(v4, v7) |
% 36.93/6.10 | ~ aInteger0(v6) | aElementOf0(v6, v5)) & ! [v6: $i] : ( ~
% 36.93/6.10 | $i(v6) | ~ aElementOf0(v6, v5) | aElementOf0(v6, v1)))) & !
% 36.93/6.10 | [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3,
% 36.93/6.10 | xS) | ~ aElementOf0(v2, v3) | ~ aInteger0(v2) | aElementOf0(v2,
% 36.93/6.10 | v0)) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ~
% 36.93/6.10 | aElementOf0(v2, v0)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 36.93/6.10 | aElementOf0(v2, v1) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) |
% 36.93/6.10 | ~ aElementOf0(v2, v0) | aInteger0(v2)) & ! [v2: $i] : ( ~ $i(v2) |
% 36.93/6.10 | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & aElementOf0(v3,
% 36.93/6.10 | xS) & aElementOf0(v2, v3))) & ! [v2: $i] : ( ~ $i(v2) | ~
% 36.93/6.10 | aInteger0(v2) | aElementOf0(v2, v1) | aElementOf0(v2, v0)))
% 36.93/6.10 |
% 36.93/6.10 | ALPHA: (m__2171) implies:
% 36.93/6.11 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (xp = sz00)
% 36.93/6.11 | & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v0 & stldt0(v2) = v3 &
% 36.93/6.11 | sbsmnsldt0(xS) = v2 & smndt0(sz10) = v1 & $i(v3) & $i(v2) & $i(v1) &
% 36.93/6.11 | $i(v0) & aSubsetOf0(v0, v3) & aSet0(v2) & aSet0(v0) & aInteger0(xp) &
% 36.93/6.11 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtasdt0(xp, v6) = v5)
% 36.93/6.11 | | ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v6) | ~ $i(v4) | ~
% 36.93/6.11 | aInteger0(v6) | ~ aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4:
% 36.93/6.11 | $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~
% 36.93/6.11 | aElementOf0(v4, v0) | sdteqdtlpzmzozddtrp0(v4, sz10, xp)) & ! [v4:
% 36.93/6.11 | $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~
% 36.93/6.11 | aElementOf0(v4, v0) | aDivisorOf0(xp, v5)) & ! [v4: $i] : ! [v5:
% 36.93/6.11 | $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4,
% 36.93/6.11 | v0) | aInteger0(v4)) & ! [v4: $i] : ! [v5: $i] : ( ~
% 36.93/6.11 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v0) | ?
% 36.93/6.11 | [v6: $i] : (sdtasdt0(xp, v6) = v5 & $i(v6) & $i(v5) &
% 36.93/6.11 | aInteger0(v6))) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4,
% 36.93/6.11 | v1) = v5) | ~ $i(v4) | ~ sdteqdtlpzmzozddtrp0(v4, sz10, xp) |
% 36.93/6.11 | ~ aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: $i] : ! [v5: $i]
% 36.93/6.11 | : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aDivisorOf0(xp, v5) |
% 36.93/6.11 | ~ aInteger0(v4) | aElementOf0(v4, v0)) & ! [v4: $i] : ! [v5: $i]
% 36.93/6.11 | : ( ~ $i(v5) | ~ $i(v4) | ~ aElementOf0(v5, xS) | ~
% 36.93/6.11 | aElementOf0(v4, v5) | ~ aInteger0(v4) | aElementOf0(v4, v2)) & !
% 36.93/6.11 | [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4,
% 36.93/6.11 | v2)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v3) |
% 36.93/6.11 | aInteger0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2)
% 36.93/6.11 | | aInteger0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4,
% 36.93/6.11 | v2) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, xS) &
% 36.93/6.12 | aElementOf0(v4, v5))) & ! [v4: $i] : ( ~ $i(v4) | ~
% 36.93/6.12 | aElementOf0(v4, v0) | aElementOf0(v4, v3)) & ! [v4: $i] : ( ~
% 36.93/6.12 | $i(v4) | ~ aInteger0(v4) | aElementOf0(v4, v3) | aElementOf0(v4,
% 36.93/6.12 | v2)))
% 36.93/6.12 |
% 36.93/6.12 | ALPHA: (m__2203) implies:
% 36.93/6.12 | (9) $i(sz10)
% 36.93/6.12 | (10) $i(xp)
% 36.93/6.12 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 36.93/6.12 | ( ~ (v2 = v0) & ~ (v2 = sz10) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v1
% 36.93/6.12 | & sdtasdt0(xp, v4) = v3 & sdtpldt0(v2, v0) = v3 & smndt0(sz10) = v0
% 36.93/6.12 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v2, v1) &
% 36.93/6.12 | sdteqdtlpzmzozddtrp0(v2, sz10, xp) & aDivisorOf0(xp, v3) &
% 36.93/6.12 | aInteger0(v4) & aInteger0(v2) & ~ aElementOf0(v2, cS2200))
% 36.93/6.12 |
% 36.93/6.12 | ALPHA: (function-axioms) implies:
% 36.93/6.12 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) =
% 36.93/6.12 | v1) | ~ (smndt0(v2) = v0))
% 36.93/6.12 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 36.93/6.12 | (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0))
% 36.93/6.12 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (stldt0(v2) =
% 36.93/6.12 | v1) | ~ (stldt0(v2) = v0))
% 36.93/6.12 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 36.93/6.12 | (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) | ~
% 36.93/6.12 | (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v0))
% 36.93/6.12 |
% 36.93/6.13 | DELTA: instantiating (2) with fresh symbol all_36_0 gives:
% 36.93/6.13 | (16) smndt0(sz10) = all_36_0 & $i(all_36_0) & ! [v0: $i] : ! [v1: $i] : (
% 36.93/6.13 | ~ (sdtasdt0(all_36_0, v0) = v1) | ~ $i(v0) | ~ aInteger0(v0) |
% 36.93/6.13 | (sdtasdt0(v0, all_36_0) = v1 & smndt0(v0) = v1 & $i(v1)))
% 36.93/6.13 |
% 36.93/6.13 | ALPHA: (16) implies:
% 36.93/6.13 | (17) smndt0(sz10) = all_36_0
% 36.93/6.13 |
% 36.93/6.13 | DELTA: instantiating (11) with fresh symbols all_39_0, all_39_1, all_39_2,
% 36.93/6.13 | all_39_3, all_39_4 gives:
% 36.93/6.13 | (18) ~ (all_39_2 = all_39_4) & ~ (all_39_2 = sz10) &
% 36.93/6.13 | szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_39_3 & sdtasdt0(xp, all_39_0) =
% 36.93/6.13 | all_39_1 & sdtpldt0(all_39_2, all_39_4) = all_39_1 & smndt0(sz10) =
% 36.93/6.13 | all_39_4 & $i(all_39_0) & $i(all_39_1) & $i(all_39_2) & $i(all_39_3) &
% 36.93/6.13 | $i(all_39_4) & aElementOf0(all_39_2, all_39_3) &
% 36.93/6.13 | sdteqdtlpzmzozddtrp0(all_39_2, sz10, xp) & aDivisorOf0(xp, all_39_1) &
% 36.93/6.13 | aInteger0(all_39_0) & aInteger0(all_39_2) & ~ aElementOf0(all_39_2,
% 36.93/6.13 | cS2200)
% 36.93/6.13 |
% 36.93/6.13 | ALPHA: (18) implies:
% 36.93/6.13 | (19) ~ (all_39_2 = sz10)
% 36.93/6.13 | (20) ~ (all_39_2 = all_39_4)
% 36.93/6.13 | (21) aElementOf0(all_39_2, all_39_3)
% 36.93/6.13 | (22) $i(all_39_2)
% 36.93/6.13 | (23) smndt0(sz10) = all_39_4
% 36.93/6.13 | (24) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_39_3
% 36.93/6.13 |
% 36.93/6.13 | DELTA: instantiating (3) with fresh symbol all_41_0 gives:
% 36.93/6.13 | (25) smndt0(sz10) = all_41_0 & $i(all_41_0) & ! [v0: any] : (v0 = all_41_0
% 36.93/6.13 | | v0 = sz10 | ~ $i(v0) | ~ aInteger0(v0) | ? [v1: $i] : ($i(v1) &
% 36.93/6.13 | isPrime0(v1) & aDivisorOf0(v1, v0))) & ! [v0: $i] : ( ~ $i(v0) |
% 36.93/6.13 | ~ isPrime0(v0) | ~ aDivisorOf0(v0, all_41_0) | ~
% 36.93/6.13 | aInteger0(all_41_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ isPrime0(v0) |
% 36.93/6.14 | ~ aDivisorOf0(v0, sz10) | ~ aInteger0(sz10))
% 36.93/6.14 |
% 36.93/6.14 | ALPHA: (25) implies:
% 36.93/6.14 | (26) smndt0(sz10) = all_41_0
% 36.93/6.14 |
% 36.93/6.14 | DELTA: instantiating (6) with fresh symbols all_44_0, all_44_1 gives:
% 36.93/6.14 | (27) stldt0(all_44_1) = cS2076 & sbsmnsldt0(xS) = all_44_1 & smndt0(sz10) =
% 36.93/6.14 | all_44_0 & $i(all_44_0) & $i(all_44_1) & aElementOf0(all_44_0, cS2076)
% 36.93/6.14 | & aElementOf0(sz10, cS2076) & aSet0(all_44_1) & aSet0(cS2076) & !
% 36.93/6.14 | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1,
% 36.93/6.14 | xS) | ~ aElementOf0(v0, v1) | ~ aInteger0(v0) | aElementOf0(v0,
% 36.93/6.14 | all_44_1)) & ! [v0: any] : (v0 = all_44_0 | v0 = sz10 | ~ $i(v0)
% 36.93/6.14 | | ~ aElementOf0(v0, cS2076)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 36.93/6.14 | aElementOf0(v0, all_44_1) | ~ aElementOf0(v0, cS2076)) & ! [v0:
% 36.93/6.14 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_44_1) | aInteger0(v0)) &
% 36.93/6.14 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_44_1) | ? [v1: $i] :
% 36.93/6.14 | ($i(v1) & aElementOf0(v1, xS) & aElementOf0(v0, v1))) & ! [v0: $i]
% 36.93/6.14 | : ( ~ $i(v0) | ~ aElementOf0(v0, cS2076) | aInteger0(v0)) & ! [v0:
% 36.93/6.14 | $i] : ( ~ $i(v0) | ~ aInteger0(v0) | aElementOf0(v0, all_44_1) |
% 36.93/6.14 | aElementOf0(v0, cS2076))
% 36.93/6.14 |
% 36.93/6.14 | ALPHA: (27) implies:
% 36.93/6.14 | (28) aSet0(cS2076)
% 36.93/6.14 | (29) smndt0(sz10) = all_44_0
% 36.93/6.14 | (30) sbsmnsldt0(xS) = all_44_1
% 36.93/6.14 | (31) stldt0(all_44_1) = cS2076
% 36.93/6.14 | (32) ! [v0: any] : (v0 = all_44_0 | v0 = sz10 | ~ $i(v0) | ~
% 36.93/6.14 | aElementOf0(v0, cS2076))
% 36.93/6.14 |
% 36.93/6.14 | DELTA: instantiating (8) with fresh symbols all_47_0, all_47_1, all_47_2,
% 36.93/6.14 | all_47_3 gives:
% 36.93/6.15 | (33) ~ (xp = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_47_3 &
% 36.93/6.15 | stldt0(all_47_1) = all_47_0 & sbsmnsldt0(xS) = all_47_1 & smndt0(sz10)
% 36.93/6.15 | = all_47_2 & $i(all_47_0) & $i(all_47_1) & $i(all_47_2) & $i(all_47_3)
% 36.93/6.15 | & aSubsetOf0(all_47_3, all_47_0) & aSet0(all_47_1) & aSet0(all_47_3) &
% 36.93/6.15 | aInteger0(xp) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 36.93/6.15 | (sdtasdt0(xp, v2) = v1) | ~ (sdtpldt0(v0, all_47_2) = v1) | ~
% 36.93/6.15 | $i(v2) | ~ $i(v0) | ~ aInteger0(v2) | ~ aInteger0(v0) |
% 36.93/6.15 | aElementOf0(v0, all_47_3)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 36.93/6.15 | (sdtpldt0(v0, all_47_2) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 36.93/6.15 | all_47_3) | sdteqdtlpzmzozddtrp0(v0, sz10, xp)) & ! [v0: $i] : !
% 36.93/6.15 | [v1: $i] : ( ~ (sdtpldt0(v0, all_47_2) = v1) | ~ $i(v0) | ~
% 36.93/6.15 | aElementOf0(v0, all_47_3) | aDivisorOf0(xp, v1)) & ! [v0: $i] : !
% 36.93/6.15 | [v1: $i] : ( ~ (sdtpldt0(v0, all_47_2) = v1) | ~ $i(v0) | ~
% 36.93/6.15 | aElementOf0(v0, all_47_3) | aInteger0(v0)) & ! [v0: $i] : ! [v1:
% 36.93/6.15 | $i] : ( ~ (sdtpldt0(v0, all_47_2) = v1) | ~ $i(v0) | ~
% 36.93/6.15 | aElementOf0(v0, all_47_3) | ? [v2: $i] : (sdtasdt0(xp, v2) = v1 &
% 36.93/6.15 | $i(v2) & $i(v1) & aInteger0(v2))) & ! [v0: $i] : ! [v1: $i] : (
% 36.93/6.15 | ~ (sdtpldt0(v0, all_47_2) = v1) | ~ $i(v0) | ~
% 36.93/6.15 | sdteqdtlpzmzozddtrp0(v0, sz10, xp) | ~ aInteger0(v0) |
% 36.93/6.15 | aElementOf0(v0, all_47_3)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 36.93/6.15 | (sdtpldt0(v0, all_47_2) = v1) | ~ $i(v0) | ~ aDivisorOf0(xp, v1) |
% 36.93/6.15 | ~ aInteger0(v0) | aElementOf0(v0, all_47_3)) & ! [v0: $i] : !
% 36.93/6.15 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xS) | ~
% 36.93/6.15 | aElementOf0(v0, v1) | ~ aInteger0(v0) | aElementOf0(v0, all_47_1))
% 36.93/6.15 | & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_47_0) | ~
% 36.93/6.15 | aElementOf0(v0, all_47_1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 36.93/6.15 | aElementOf0(v0, all_47_0) | aInteger0(v0)) & ! [v0: $i] : ( ~
% 36.93/6.15 | $i(v0) | ~ aElementOf0(v0, all_47_1) | aInteger0(v0)) & ! [v0: $i]
% 36.93/6.15 | : ( ~ $i(v0) | ~ aElementOf0(v0, all_47_1) | ? [v1: $i] : ($i(v1) &
% 36.93/6.15 | aElementOf0(v1, xS) & aElementOf0(v0, v1))) & ! [v0: $i] : ( ~
% 36.93/6.15 | $i(v0) | ~ aElementOf0(v0, all_47_3) | aElementOf0(v0, all_47_0)) &
% 36.93/6.15 | ! [v0: $i] : ( ~ $i(v0) | ~ aInteger0(v0) | aElementOf0(v0,
% 36.93/6.15 | all_47_0) | aElementOf0(v0, all_47_1))
% 36.93/6.15 |
% 36.93/6.15 | ALPHA: (33) implies:
% 36.93/6.15 | (34) ~ (xp = sz00)
% 36.93/6.15 | (35) aInteger0(xp)
% 36.93/6.15 | (36) aSubsetOf0(all_47_3, all_47_0)
% 36.93/6.15 | (37) $i(all_47_3)
% 36.93/6.15 | (38) $i(all_47_0)
% 36.93/6.15 | (39) smndt0(sz10) = all_47_2
% 36.93/6.15 | (40) sbsmnsldt0(xS) = all_47_1
% 36.93/6.15 | (41) stldt0(all_47_1) = all_47_0
% 36.93/6.15 | (42) szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_47_3
% 36.93/6.15 |
% 36.93/6.15 | DELTA: instantiating (7) with fresh symbols all_50_0, all_50_1 gives:
% 36.93/6.16 | (43) stldt0(all_50_1) = all_50_0 & sbsmnsldt0(xS) = all_50_1 & $i(all_50_0)
% 36.93/6.16 | & $i(all_50_1) & isClosed0(all_50_1) & isOpen0(all_50_0) &
% 36.93/6.16 | aSet0(all_50_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) |
% 36.93/6.16 | ~ $i(v0) | ~ aElementOf0(v0, all_50_0) | ? [v2: $i] : ? [v3: $i]
% 36.93/6.16 | : ( ~ (v2 = sz00) & szAzrzSzezqlpdtcmdtrp0(v0, v2) = v3 & $i(v3) &
% 36.93/6.16 | $i(v2) & aSubsetOf0(v3, all_50_0) & aSet0(v3) & aInteger0(v2) & !
% 36.93/6.16 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtasdt0(v2, v6) = v5)
% 36.93/6.16 | | ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v6) | ~ $i(v4) | ~
% 36.93/6.16 | aInteger0(v6) | ~ aInteger0(v4) | aElementOf0(v4, v3)) & !
% 36.93/6.16 | [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) |
% 36.93/6.16 | ~ aElementOf0(v4, v3) | sdteqdtlpzmzozddtrp0(v4, v0, v2)) & !
% 36.93/6.16 | [v4: $i] : ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) |
% 36.93/6.16 | ~ aElementOf0(v4, v3) | aDivisorOf0(v2, v5)) & ! [v4: $i] : !
% 36.93/6.16 | [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~
% 36.93/6.16 | aElementOf0(v4, v3) | aInteger0(v4)) & ! [v4: $i] : ! [v5: $i]
% 36.93/6.16 | : ( ~ (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aElementOf0(v4, v3)
% 36.93/6.16 | | ? [v6: $i] : (sdtasdt0(v2, v6) = v5 & $i(v6) & $i(v5) &
% 36.93/6.16 | aInteger0(v6))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 36.93/6.16 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~
% 36.93/6.16 | sdteqdtlpzmzozddtrp0(v4, v0, v2) | ~ aInteger0(v4) |
% 36.93/6.16 | aElementOf0(v4, v3)) & ! [v4: $i] : ! [v5: $i] : ( ~
% 36.93/6.16 | (sdtpldt0(v4, v1) = v5) | ~ $i(v4) | ~ aDivisorOf0(v2, v5) |
% 36.93/6.16 | ~ aInteger0(v4) | aElementOf0(v4, v3)) & ! [v4: $i] : ( ~
% 36.93/6.16 | $i(v4) | ~ aElementOf0(v4, v3) | aElementOf0(v4, all_50_0)))) &
% 36.93/6.16 | ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 36.93/6.16 | aElementOf0(v1, xS) | ~ aElementOf0(v0, v1) | ~ aInteger0(v0) |
% 36.93/6.16 | aElementOf0(v0, all_50_1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 36.93/6.16 | aElementOf0(v0, all_50_0) | ~ aElementOf0(v0, all_50_1)) & ! [v0:
% 36.93/6.16 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_50_0) | aInteger0(v0)) &
% 36.93/6.16 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_50_1) |
% 36.93/6.16 | aInteger0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 36.93/6.16 | all_50_1) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, xS) &
% 36.93/6.16 | aElementOf0(v0, v1))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 36.93/6.16 | aInteger0(v0) | aElementOf0(v0, all_50_0) | aElementOf0(v0,
% 36.93/6.16 | all_50_1))
% 36.93/6.16 |
% 36.93/6.16 | ALPHA: (43) implies:
% 36.93/6.16 | (44) sbsmnsldt0(xS) = all_50_1
% 36.93/6.16 | (45) stldt0(all_50_1) = all_50_0
% 36.93/6.16 |
% 36.93/6.17 | GROUND_INST: instantiating (12) with all_44_0, all_47_2, sz10, simplifying
% 36.93/6.17 | with (29), (39) gives:
% 36.93/6.17 | (46) all_47_2 = all_44_0
% 36.93/6.17 |
% 36.93/6.17 | GROUND_INST: instantiating (12) with all_41_0, all_47_2, sz10, simplifying
% 36.93/6.17 | with (26), (39) gives:
% 36.93/6.17 | (47) all_47_2 = all_41_0
% 36.93/6.17 |
% 36.93/6.17 | GROUND_INST: instantiating (12) with all_39_4, all_47_2, sz10, simplifying
% 36.93/6.17 | with (23), (39) gives:
% 36.93/6.17 | (48) all_47_2 = all_39_4
% 36.93/6.17 |
% 36.93/6.17 | GROUND_INST: instantiating (12) with all_36_0, all_47_2, sz10, simplifying
% 36.93/6.17 | with (17), (39) gives:
% 36.93/6.17 | (49) all_47_2 = all_36_0
% 36.93/6.17 |
% 36.93/6.17 | GROUND_INST: instantiating (13) with all_47_1, all_50_1, xS, simplifying with
% 36.93/6.17 | (40), (44) gives:
% 36.93/6.17 | (50) all_50_1 = all_47_1
% 36.93/6.17 |
% 36.93/6.17 | GROUND_INST: instantiating (13) with all_44_1, all_50_1, xS, simplifying with
% 36.93/6.17 | (30), (44) gives:
% 36.93/6.17 | (51) all_50_1 = all_44_1
% 36.93/6.17 |
% 36.93/6.17 | GROUND_INST: instantiating (15) with all_39_3, all_47_3, xp, sz10, simplifying
% 36.93/6.17 | with (24), (42) gives:
% 36.93/6.17 | (52) all_47_3 = all_39_3
% 36.93/6.17 |
% 36.93/6.17 | COMBINE_EQS: (50), (51) imply:
% 36.93/6.17 | (53) all_47_1 = all_44_1
% 36.93/6.17 |
% 36.93/6.17 | SIMP: (53) implies:
% 36.93/6.17 | (54) all_47_1 = all_44_1
% 36.93/6.17 |
% 36.93/6.17 | COMBINE_EQS: (46), (49) imply:
% 36.93/6.17 | (55) all_44_0 = all_36_0
% 36.93/6.17 |
% 36.93/6.17 | COMBINE_EQS: (46), (48) imply:
% 36.93/6.17 | (56) all_44_0 = all_39_4
% 36.93/6.17 |
% 36.93/6.17 | COMBINE_EQS: (46), (47) imply:
% 36.93/6.17 | (57) all_44_0 = all_41_0
% 36.93/6.17 |
% 36.93/6.17 | COMBINE_EQS: (55), (57) imply:
% 36.93/6.17 | (58) all_41_0 = all_36_0
% 36.93/6.17 |
% 36.93/6.17 | COMBINE_EQS: (56), (57) imply:
% 36.93/6.17 | (59) all_41_0 = all_39_4
% 36.93/6.17 |
% 36.93/6.17 | COMBINE_EQS: (58), (59) imply:
% 36.93/6.17 | (60) all_39_4 = all_36_0
% 36.93/6.17 |
% 36.93/6.17 | SIMP: (60) implies:
% 37.67/6.17 | (61) all_39_4 = all_36_0
% 37.67/6.17 |
% 37.67/6.17 | REDUCE: (20), (61) imply:
% 37.67/6.17 | (62) ~ (all_39_2 = all_36_0)
% 37.67/6.17 |
% 37.67/6.17 | REDUCE: (45), (51) imply:
% 37.67/6.18 | (63) stldt0(all_44_1) = all_50_0
% 37.67/6.18 |
% 37.67/6.18 | REDUCE: (41), (54) imply:
% 37.67/6.18 | (64) stldt0(all_44_1) = all_47_0
% 37.67/6.18 |
% 37.67/6.18 | REDUCE: (37), (52) imply:
% 37.67/6.18 | (65) $i(all_39_3)
% 37.67/6.18 |
% 37.67/6.18 | REDUCE: (36), (52) imply:
% 37.67/6.18 | (66) aSubsetOf0(all_39_3, all_47_0)
% 37.67/6.18 |
% 37.67/6.18 | GROUND_INST: instantiating (14) with cS2076, all_50_0, all_44_1, simplifying
% 37.67/6.18 | with (31), (63) gives:
% 37.67/6.18 | (67) all_50_0 = cS2076
% 37.67/6.18 |
% 37.67/6.18 | GROUND_INST: instantiating (14) with all_47_0, all_50_0, all_44_1, simplifying
% 37.67/6.18 | with (63), (64) gives:
% 37.67/6.18 | (68) all_50_0 = all_47_0
% 37.67/6.18 |
% 37.67/6.18 | COMBINE_EQS: (67), (68) imply:
% 37.67/6.18 | (69) all_47_0 = cS2076
% 37.67/6.18 |
% 37.67/6.18 | REDUCE: (38), (69) imply:
% 37.67/6.18 | (70) $i(cS2076)
% 37.67/6.18 |
% 37.67/6.18 | REDUCE: (66), (69) imply:
% 37.67/6.18 | (71) aSubsetOf0(all_39_3, cS2076)
% 37.67/6.18 |
% 37.67/6.18 | GROUND_INST: instantiating (4) with cS2076, all_39_3, all_39_2, simplifying
% 37.67/6.18 | with (21), (22), (28), (65), (70), (71) gives:
% 37.67/6.18 | (72) aElementOf0(all_39_2, cS2076)
% 37.67/6.18 |
% 37.67/6.18 | GROUND_INST: instantiating (5) with sz10, xp, all_39_3, simplifying with (1),
% 37.67/6.18 | (9), (10), (24), (35) gives:
% 37.67/6.18 | (73) xp = sz00 | isClosed0(all_39_3)
% 37.67/6.18 |
% 37.67/6.18 | BETA: splitting (73) gives:
% 37.67/6.18 |
% 37.67/6.18 | Case 1:
% 37.67/6.18 | |
% 37.67/6.18 | |
% 37.67/6.18 | | GROUND_INST: instantiating (32) with all_39_2, simplifying with (22), (72)
% 37.67/6.18 | | gives:
% 37.67/6.18 | | (74) all_44_0 = all_39_2 | all_39_2 = sz10
% 37.67/6.18 | |
% 37.67/6.18 | | BETA: splitting (74) gives:
% 37.67/6.18 | |
% 37.67/6.18 | | Case 1:
% 37.67/6.18 | | |
% 37.67/6.18 | | | (75) all_44_0 = all_39_2
% 37.67/6.18 | | |
% 37.67/6.18 | | | COMBINE_EQS: (55), (75) imply:
% 37.67/6.18 | | | (76) all_39_2 = all_36_0
% 37.67/6.18 | | |
% 37.67/6.18 | | | REDUCE: (62), (76) imply:
% 37.67/6.18 | | | (77) $false
% 37.67/6.18 | | |
% 37.67/6.18 | | | CLOSE: (77) is inconsistent.
% 37.67/6.18 | | |
% 37.67/6.18 | | Case 2:
% 37.67/6.18 | | |
% 37.67/6.19 | | | (78) all_39_2 = sz10
% 37.67/6.19 | | |
% 37.67/6.19 | | | REDUCE: (19), (78) imply:
% 37.67/6.19 | | | (79) $false
% 37.67/6.19 | | |
% 37.67/6.19 | | | CLOSE: (79) is inconsistent.
% 37.67/6.19 | | |
% 37.67/6.19 | | End of split
% 37.67/6.19 | |
% 37.67/6.19 | Case 2:
% 37.67/6.19 | |
% 37.67/6.19 | | (80) xp = sz00
% 37.67/6.19 | |
% 37.67/6.19 | | REDUCE: (34), (80) imply:
% 37.67/6.19 | | (81) $false
% 37.67/6.19 | |
% 37.67/6.19 | | CLOSE: (81) is inconsistent.
% 37.67/6.19 | |
% 37.67/6.19 | End of split
% 37.67/6.19 |
% 37.67/6.19 End of proof
% 37.67/6.19 % SZS output end Proof for theBenchmark
% 37.67/6.19
% 37.67/6.19 5569ms
%------------------------------------------------------------------------------