TSTP Solution File: RNG047+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG047+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n020.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 13:57:32 EDT 2023
% Result : Theorem 9.75s 2.01s
% Output : Proof 14.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG047+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n020.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 : Sun Aug 27 03:02:14 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.05/1.13 Prover 4: Preprocessing ...
% 3.05/1.13 Prover 1: Preprocessing ...
% 3.05/1.17 Prover 5: Preprocessing ...
% 3.05/1.17 Prover 6: Preprocessing ...
% 3.05/1.17 Prover 2: Preprocessing ...
% 3.05/1.17 Prover 0: Preprocessing ...
% 3.05/1.17 Prover 3: Preprocessing ...
% 7.60/1.73 Prover 1: Constructing countermodel ...
% 7.60/1.74 Prover 3: Constructing countermodel ...
% 7.60/1.77 Prover 6: Proving ...
% 8.20/1.82 Prover 5: Constructing countermodel ...
% 8.84/1.95 Prover 4: Constructing countermodel ...
% 9.61/1.99 Prover 2: Proving ...
% 9.75/2.01 Prover 6: proved (1353ms)
% 9.75/2.01
% 9.75/2.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.75/2.01
% 9.75/2.01 Prover 5: stopped
% 9.75/2.02 Prover 3: stopped
% 9.75/2.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.75/2.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.75/2.02 Prover 2: stopped
% 9.75/2.04 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.75/2.05 Prover 0: Proving ...
% 9.75/2.05 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.75/2.05 Prover 0: stopped
% 9.75/2.05 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.75/2.09 Prover 7: Preprocessing ...
% 10.50/2.11 Prover 8: Preprocessing ...
% 10.50/2.12 Prover 10: Preprocessing ...
% 10.50/2.16 Prover 11: Preprocessing ...
% 10.50/2.17 Prover 13: Preprocessing ...
% 11.22/2.26 Prover 10: Constructing countermodel ...
% 11.22/2.28 Prover 8: Warning: ignoring some quantifiers
% 11.91/2.29 Prover 8: Constructing countermodel ...
% 11.91/2.32 Prover 7: Constructing countermodel ...
% 11.91/2.41 Prover 13: Constructing countermodel ...
% 13.52/2.53 Prover 10: Found proof (size 53)
% 13.52/2.54 Prover 10: proved (501ms)
% 13.52/2.54 Prover 7: stopped
% 13.52/2.54 Prover 13: stopped
% 13.52/2.54 Prover 8: stopped
% 13.52/2.54 Prover 1: stopped
% 13.52/2.54 Prover 4: stopped
% 13.98/2.62 Prover 11: Constructing countermodel ...
% 13.98/2.64 Prover 11: stopped
% 13.98/2.64
% 13.98/2.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.98/2.64
% 13.98/2.65 % SZS output start Proof for theBenchmark
% 13.98/2.66 Assumptions after simplification:
% 13.98/2.66 ---------------------------------
% 13.98/2.66
% 13.98/2.66 (mDefInit)
% 13.98/2.68 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0)
% 13.98/2.68 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 =
% 13.98/2.68 sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0,
% 13.98/2.68 v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ $i(v4) | ~ $i(v1)
% 13.98/2.68 | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, v4) = v5 & $i(v5))) & !
% 13.98/2.68 [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~
% 13.98/2.68 $i(v3) | ~ aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 13.98/2.68 ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 &
% 13.98/2.68 sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 13.98/2.68 aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5 &
% 13.98/2.68 $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~
% 13.98/2.68 $i(v1) | szszuzczcdt0(v3) = v2) & ! [v3: $i] : ( ~
% 13.98/2.68 (aDimensionOf0(v1) = v3) | ~ $i(v1) | aVector0(v1))))))
% 13.98/2.68
% 13.98/2.69 (mDimNat)
% 14.35/2.69 ! [v0: $i] : ! [v1: $i] : ( ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~
% 14.35/2.69 aVector0(v0) | aNaturalNumber0(v1))
% 14.35/2.69
% 14.35/2.69 (mNatExtr)
% 14.35/2.69 $i(sz00) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | ?
% 14.35/2.69 [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aNaturalNumber0(v1)))
% 14.35/2.69
% 14.35/2.69 (mSuccEqu)
% 14.35/2.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v1) =
% 14.35/2.69 v2) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 14.35/2.69 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 14.35/2.69
% 14.35/2.69 (m__)
% 14.35/2.69 $i(xt) & $i(xs) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~
% 14.35/2.69 (v3 = v1) & sziznziztdt0(xt) = v2 & sziznziztdt0(xs) = v0 &
% 14.35/2.69 aDimensionOf0(v2) = v3 & aDimensionOf0(v0) = v1 & $i(v3) & $i(v2) & $i(v1) &
% 14.35/2.69 $i(v0))
% 14.35/2.69
% 14.35/2.69 (m__1329)
% 14.35/2.69 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs)
% 14.35/2.69
% 14.35/2.69 (m__1329_01)
% 14.35/2.69 $i(xt) & $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xt)
% 14.35/2.69 = v0 & aDimensionOf0(xs) = v0 & $i(v0))
% 14.35/2.69
% 14.35/2.69 (function-axioms)
% 14.35/2.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.35/2.70 (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : !
% 14.35/2.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) |
% 14.35/2.70 ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 14.35/2.70 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 14.35/2.70 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) =
% 14.35/2.70 v1) | ~ (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 14.35/2.70 $i] : (v1 = v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0))
% 14.35/2.70 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) |
% 14.35/2.70 ~ (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 14.35/2.70 ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 14.35/2.70
% 14.35/2.70 Further assumptions not needed in the proof:
% 14.35/2.70 --------------------------------------------
% 14.35/2.70 mArith, mDistr, mDistr2, mElmSc, mIH, mIHOrd, mLEASm, mLEMon, mLEMonM, mLERef,
% 14.35/2.70 mLETot, mLETrn, mLess, mMDNeg, mMNeg, mMulSc, mNatSort, mNegSc, mPosMon,
% 14.35/2.70 mSZeroSc, mScSort, mScZero, mSqPos, mSqrt, mSuccNat, mSumSc, mVcSort, mZeroNat
% 14.35/2.70
% 14.35/2.70 Those formulas are unsatisfiable:
% 14.35/2.70 ---------------------------------
% 14.35/2.70
% 14.35/2.70 Begin of proof
% 14.35/2.70 |
% 14.35/2.70 | ALPHA: (mNatExtr) implies:
% 14.35/2.70 | (1) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | ? [v1:
% 14.35/2.70 | $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aNaturalNumber0(v1)))
% 14.35/2.70 |
% 14.35/2.70 | ALPHA: (mDefInit) implies:
% 14.35/2.71 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) |
% 14.35/2.71 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2
% 14.35/2.71 | = sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 14.35/2.71 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~
% 14.35/2.71 | $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1,
% 14.35/2.71 | v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 =
% 14.35/2.71 | v1 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~
% 14.35/2.71 | aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 14.35/2.71 | [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7
% 14.35/2.71 | & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 14.35/2.71 | aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4)
% 14.35/2.71 | = v5 & $i(v5))))) & ! [v3: $i] : ( ~
% 14.35/2.71 | (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2)
% 14.35/2.71 | & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) |
% 14.35/2.71 | aVector0(v1))))))
% 14.35/2.71 |
% 14.35/2.71 | ALPHA: (m__1329) implies:
% 14.35/2.71 | (3) aVector0(xs)
% 14.35/2.71 | (4) aVector0(xt)
% 14.35/2.71 |
% 14.35/2.71 | ALPHA: (m__1329_01) implies:
% 14.35/2.71 | (5) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xt) = v0 &
% 14.35/2.71 | aDimensionOf0(xs) = v0 & $i(v0))
% 14.35/2.71 |
% 14.35/2.71 | ALPHA: (m__) implies:
% 14.35/2.71 | (6) $i(xs)
% 14.35/2.71 | (7) $i(xt)
% 14.35/2.71 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v1) &
% 14.35/2.71 | sziznziztdt0(xt) = v2 & sziznziztdt0(xs) = v0 & aDimensionOf0(v2) =
% 14.35/2.71 | v3 & aDimensionOf0(v0) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 14.35/2.71 |
% 14.35/2.71 | ALPHA: (function-axioms) implies:
% 14.35/2.71 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.35/2.71 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0))
% 14.35/2.71 |
% 14.35/2.71 | DELTA: instantiating (5) with fresh symbol all_28_0 gives:
% 14.35/2.71 | (10) ~ (all_28_0 = sz00) & aDimensionOf0(xt) = all_28_0 &
% 14.35/2.71 | aDimensionOf0(xs) = all_28_0 & $i(all_28_0)
% 14.35/2.71 |
% 14.35/2.71 | ALPHA: (10) implies:
% 14.35/2.71 | (11) ~ (all_28_0 = sz00)
% 14.35/2.71 | (12) aDimensionOf0(xs) = all_28_0
% 14.35/2.71 | (13) aDimensionOf0(xt) = all_28_0
% 14.35/2.71 |
% 14.35/2.71 | DELTA: instantiating (8) with fresh symbols all_30_0, all_30_1, all_30_2,
% 14.35/2.71 | all_30_3 gives:
% 14.35/2.71 | (14) ~ (all_30_0 = all_30_2) & sziznziztdt0(xt) = all_30_1 &
% 14.35/2.71 | sziznziztdt0(xs) = all_30_3 & aDimensionOf0(all_30_1) = all_30_0 &
% 14.35/2.71 | aDimensionOf0(all_30_3) = all_30_2 & $i(all_30_0) & $i(all_30_1) &
% 14.35/2.71 | $i(all_30_2) & $i(all_30_3)
% 14.35/2.71 |
% 14.35/2.71 | ALPHA: (14) implies:
% 14.35/2.71 | (15) ~ (all_30_0 = all_30_2)
% 14.35/2.71 | (16) $i(all_30_3)
% 14.35/2.71 | (17) $i(all_30_2)
% 14.35/2.71 | (18) $i(all_30_1)
% 14.35/2.71 | (19) $i(all_30_0)
% 14.35/2.71 | (20) aDimensionOf0(all_30_3) = all_30_2
% 14.35/2.71 | (21) aDimensionOf0(all_30_1) = all_30_0
% 14.35/2.71 | (22) sziznziztdt0(xs) = all_30_3
% 14.35/2.71 | (23) sziznziztdt0(xt) = all_30_1
% 14.35/2.71 |
% 14.35/2.72 | GROUND_INST: instantiating (mDimNat) with xt, all_28_0, simplifying with (4),
% 14.35/2.72 | (7), (13) gives:
% 14.35/2.72 | (24) aNaturalNumber0(all_28_0)
% 14.35/2.72 |
% 14.35/2.72 | GROUND_INST: instantiating (2) with xs, all_30_3, simplifying with (3), (6),
% 14.35/2.72 | (22) gives:
% 14.35/2.72 | (25) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & (v0 = sz00 | ( ! [v1:
% 14.35/2.72 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xs, v2) =
% 14.35/2.72 | v3) | ~ (aDimensionOf0(all_30_3) = v1) | ~ $i(v2) | ~
% 14.35/2.72 | $i(all_30_3) | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(all_30_3,
% 14.35/2.72 | v2) = v3 & $i(v3))) & ! [v1: any] : ! [v2: $i] : (v1 =
% 14.35/2.72 | all_30_3 | ~ (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~
% 14.35/2.72 | aVector0(v1) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 14.35/2.72 | [v6: $i] : ($i(v4) & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5
% 14.35/2.72 | & sdtlbdtrb0(xs, v4) = v6 & $i(v6) & $i(v5) &
% 14.35/2.72 | aNaturalNumber0(v4)) | ( ~ (v3 = v0) & szszuzczcdt0(v2)
% 14.35/2.72 | = v3 & $i(v3))))) & ! [v1: $i] : ( ~
% 14.35/2.72 | (aDimensionOf0(all_30_3) = v1) | ~ $i(all_30_3) |
% 14.35/2.72 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~
% 14.35/2.72 | (aDimensionOf0(all_30_3) = v1) | ~ $i(all_30_3) |
% 14.35/2.72 | aVector0(all_30_3)))))
% 14.35/2.72 |
% 14.35/2.72 | GROUND_INST: instantiating (2) with xt, all_30_1, simplifying with (4), (7),
% 14.35/2.72 | (23) gives:
% 14.35/2.72 | (26) ? [v0: $i] : (aDimensionOf0(xt) = v0 & $i(v0) & (v0 = sz00 | ( ! [v1:
% 14.35/2.72 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xt, v2) =
% 14.35/2.72 | v3) | ~ (aDimensionOf0(all_30_1) = v1) | ~ $i(v2) | ~
% 14.35/2.72 | $i(all_30_1) | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(all_30_1,
% 14.35/2.72 | v2) = v3 & $i(v3))) & ! [v1: any] : ! [v2: $i] : (v1 =
% 14.35/2.72 | all_30_1 | ~ (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~
% 14.35/2.72 | aVector0(v1) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 14.35/2.72 | [v6: $i] : ($i(v4) & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5
% 14.35/2.72 | & sdtlbdtrb0(xt, v4) = v6 & $i(v6) & $i(v5) &
% 14.35/2.72 | aNaturalNumber0(v4)) | ( ~ (v3 = v0) & szszuzczcdt0(v2)
% 14.35/2.72 | = v3 & $i(v3))))) & ! [v1: $i] : ( ~
% 14.35/2.72 | (aDimensionOf0(all_30_1) = v1) | ~ $i(all_30_1) |
% 14.35/2.72 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~
% 14.35/2.72 | (aDimensionOf0(all_30_1) = v1) | ~ $i(all_30_1) |
% 14.35/2.72 | aVector0(all_30_1)))))
% 14.35/2.72 |
% 14.35/2.72 | DELTA: instantiating (26) with fresh symbol all_41_0 gives:
% 14.35/2.73 | (27) aDimensionOf0(xt) = all_41_0 & $i(all_41_0) & (all_41_0 = sz00 | ( !
% 14.35/2.73 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xt, v1) =
% 14.35/2.73 | v2) | ~ (aDimensionOf0(all_30_1) = v0) | ~ $i(v1) | ~
% 14.35/2.73 | $i(all_30_1) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(all_30_1,
% 14.35/2.73 | v1) = v2 & $i(v2))) & ! [v0: any] : ! [v1: $i] : (v0 =
% 14.35/2.73 | all_30_1 | ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~
% 14.35/2.73 | aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ?
% 14.35/2.73 | [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 &
% 14.35/2.73 | sdtlbdtrb0(xt, v3) = v5 & $i(v5) & $i(v4) &
% 14.35/2.73 | aNaturalNumber0(v3)) | ( ~ (v2 = all_41_0) &
% 14.35/2.73 | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : ( ~
% 14.35/2.73 | (aDimensionOf0(all_30_1) = v0) | ~ $i(all_30_1) |
% 14.35/2.73 | szszuzczcdt0(v0) = all_41_0) & ! [v0: $i] : ( ~
% 14.35/2.73 | (aDimensionOf0(all_30_1) = v0) | ~ $i(all_30_1) |
% 14.35/2.73 | aVector0(all_30_1))))
% 14.35/2.73 |
% 14.35/2.73 | ALPHA: (27) implies:
% 14.35/2.73 | (28) $i(all_41_0)
% 14.35/2.73 | (29) aDimensionOf0(xt) = all_41_0
% 14.35/2.73 | (30) all_41_0 = sz00 | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 14.35/2.73 | (sdtlbdtrb0(xt, v1) = v2) | ~ (aDimensionOf0(all_30_1) = v0) | ~
% 14.35/2.73 | $i(v1) | ~ $i(all_30_1) | ~ aNaturalNumber0(v1) |
% 14.35/2.73 | (sdtlbdtrb0(all_30_1, v1) = v2 & $i(v2))) & ! [v0: any] : ! [v1:
% 14.35/2.73 | $i] : (v0 = all_30_1 | ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) |
% 14.35/2.73 | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ?
% 14.35/2.73 | [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 &
% 14.35/2.73 | sdtlbdtrb0(xt, v3) = v5 & $i(v5) & $i(v4) &
% 14.35/2.73 | aNaturalNumber0(v3)) | ( ~ (v2 = all_41_0) &
% 14.35/2.73 | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : ( ~
% 14.35/2.73 | (aDimensionOf0(all_30_1) = v0) | ~ $i(all_30_1) |
% 14.35/2.73 | szszuzczcdt0(v0) = all_41_0) & ! [v0: $i] : ( ~
% 14.35/2.73 | (aDimensionOf0(all_30_1) = v0) | ~ $i(all_30_1) |
% 14.35/2.73 | aVector0(all_30_1)))
% 14.35/2.73 |
% 14.35/2.73 | DELTA: instantiating (25) with fresh symbol all_43_0 gives:
% 14.35/2.73 | (31) aDimensionOf0(xs) = all_43_0 & $i(all_43_0) & (all_43_0 = sz00 | ( !
% 14.35/2.73 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xs, v1) =
% 14.35/2.73 | v2) | ~ (aDimensionOf0(all_30_3) = v0) | ~ $i(v1) | ~
% 14.35/2.73 | $i(all_30_3) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(all_30_3,
% 14.35/2.73 | v1) = v2 & $i(v2))) & ! [v0: any] : ! [v1: $i] : (v0 =
% 14.35/2.73 | all_30_3 | ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~
% 14.35/2.73 | aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ?
% 14.35/2.73 | [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 &
% 14.35/2.73 | sdtlbdtrb0(xs, v3) = v5 & $i(v5) & $i(v4) &
% 14.35/2.73 | aNaturalNumber0(v3)) | ( ~ (v2 = all_43_0) &
% 14.35/2.73 | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : ( ~
% 14.35/2.73 | (aDimensionOf0(all_30_3) = v0) | ~ $i(all_30_3) |
% 14.35/2.73 | szszuzczcdt0(v0) = all_43_0) & ! [v0: $i] : ( ~
% 14.35/2.73 | (aDimensionOf0(all_30_3) = v0) | ~ $i(all_30_3) |
% 14.35/2.73 | aVector0(all_30_3))))
% 14.35/2.73 |
% 14.35/2.73 | ALPHA: (31) implies:
% 14.35/2.73 | (32) aDimensionOf0(xs) = all_43_0
% 14.35/2.74 | (33) all_43_0 = sz00 | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 14.35/2.74 | (sdtlbdtrb0(xs, v1) = v2) | ~ (aDimensionOf0(all_30_3) = v0) | ~
% 14.35/2.74 | $i(v1) | ~ $i(all_30_3) | ~ aNaturalNumber0(v1) |
% 14.35/2.74 | (sdtlbdtrb0(all_30_3, v1) = v2 & $i(v2))) & ! [v0: any] : ! [v1:
% 14.35/2.74 | $i] : (v0 = all_30_3 | ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) |
% 14.35/2.74 | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ?
% 14.35/2.74 | [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 &
% 14.35/2.74 | sdtlbdtrb0(xs, v3) = v5 & $i(v5) & $i(v4) &
% 14.35/2.74 | aNaturalNumber0(v3)) | ( ~ (v2 = all_43_0) &
% 14.35/2.74 | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : ( ~
% 14.35/2.74 | (aDimensionOf0(all_30_3) = v0) | ~ $i(all_30_3) |
% 14.35/2.74 | szszuzczcdt0(v0) = all_43_0) & ! [v0: $i] : ( ~
% 14.35/2.74 | (aDimensionOf0(all_30_3) = v0) | ~ $i(all_30_3) |
% 14.35/2.74 | aVector0(all_30_3)))
% 14.35/2.74 |
% 14.35/2.74 | GROUND_INST: instantiating (9) with all_28_0, all_43_0, xs, simplifying with
% 14.35/2.74 | (12), (32) gives:
% 14.35/2.74 | (34) all_43_0 = all_28_0
% 14.35/2.74 |
% 14.35/2.74 | GROUND_INST: instantiating (9) with all_28_0, all_41_0, xt, simplifying with
% 14.35/2.74 | (13), (29) gives:
% 14.35/2.74 | (35) all_41_0 = all_28_0
% 14.35/2.74 |
% 14.35/2.74 | REDUCE: (28), (35) imply:
% 14.35/2.74 | (36) $i(all_28_0)
% 14.35/2.74 |
% 14.35/2.74 | BETA: splitting (30) gives:
% 14.35/2.74 |
% 14.35/2.74 | Case 1:
% 14.35/2.74 | |
% 14.35/2.74 | | (37) all_41_0 = sz00
% 14.35/2.74 | |
% 14.35/2.74 | | COMBINE_EQS: (35), (37) imply:
% 14.35/2.74 | | (38) all_28_0 = sz00
% 14.35/2.74 | |
% 14.35/2.74 | | SIMP: (38) implies:
% 14.35/2.74 | | (39) all_28_0 = sz00
% 14.35/2.74 | |
% 14.35/2.74 | | REDUCE: (11), (39) imply:
% 14.35/2.74 | | (40) $false
% 14.35/2.74 | |
% 14.35/2.74 | | CLOSE: (40) is inconsistent.
% 14.35/2.74 | |
% 14.35/2.74 | Case 2:
% 14.35/2.74 | |
% 14.35/2.74 | | (41) ~ (all_41_0 = sz00)
% 14.35/2.74 | | (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xt, v1) =
% 14.35/2.74 | | v2) | ~ (aDimensionOf0(all_30_1) = v0) | ~ $i(v1) | ~
% 14.35/2.74 | | $i(all_30_1) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(all_30_1, v1)
% 14.35/2.74 | | = v2 & $i(v2))) & ! [v0: any] : ! [v1: $i] : (v0 = all_30_1 |
% 14.35/2.74 | | ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | ? [v2:
% 14.35/2.74 | | any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~
% 14.35/2.74 | | (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) =
% 14.35/2.74 | | v5 & $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 14.35/2.74 | | all_41_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0:
% 14.35/2.74 | | $i] : ( ~ (aDimensionOf0(all_30_1) = v0) | ~ $i(all_30_1) |
% 14.35/2.74 | | szszuzczcdt0(v0) = all_41_0) & ! [v0: $i] : ( ~
% 14.35/2.74 | | (aDimensionOf0(all_30_1) = v0) | ~ $i(all_30_1) |
% 14.35/2.74 | | aVector0(all_30_1))
% 14.35/2.74 | |
% 14.35/2.74 | | ALPHA: (42) implies:
% 14.35/2.75 | | (43) ! [v0: $i] : ( ~ (aDimensionOf0(all_30_1) = v0) | ~ $i(all_30_1) |
% 14.35/2.75 | | aVector0(all_30_1))
% 14.35/2.75 | | (44) ! [v0: $i] : ( ~ (aDimensionOf0(all_30_1) = v0) | ~ $i(all_30_1) |
% 14.35/2.75 | | szszuzczcdt0(v0) = all_41_0)
% 14.35/2.75 | |
% 14.35/2.75 | | GROUND_INST: instantiating (44) with all_30_0, simplifying with (18), (21)
% 14.35/2.75 | | gives:
% 14.35/2.75 | | (45) szszuzczcdt0(all_30_0) = all_41_0
% 14.35/2.75 | |
% 14.35/2.75 | | GROUND_INST: instantiating (43) with all_30_0, simplifying with (18), (21)
% 14.35/2.75 | | gives:
% 14.35/2.75 | | (46) aVector0(all_30_1)
% 14.35/2.75 | |
% 14.35/2.75 | | REDUCE: (35), (45) imply:
% 14.35/2.75 | | (47) szszuzczcdt0(all_30_0) = all_28_0
% 14.35/2.75 | |
% 14.35/2.75 | | BETA: splitting (33) gives:
% 14.35/2.75 | |
% 14.35/2.75 | | Case 1:
% 14.35/2.75 | | |
% 14.35/2.75 | | | (48) all_43_0 = sz00
% 14.35/2.75 | | |
% 14.35/2.75 | | | COMBINE_EQS: (34), (48) imply:
% 14.35/2.75 | | | (49) all_28_0 = sz00
% 14.35/2.75 | | |
% 14.35/2.75 | | | REDUCE: (11), (49) imply:
% 14.35/2.75 | | | (50) $false
% 14.35/2.75 | | |
% 14.35/2.75 | | | CLOSE: (50) is inconsistent.
% 14.35/2.75 | | |
% 14.35/2.75 | | Case 2:
% 14.35/2.75 | | |
% 14.35/2.75 | | | (51) ~ (all_43_0 = sz00)
% 14.35/2.75 | | | (52) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xs, v1)
% 14.35/2.75 | | | = v2) | ~ (aDimensionOf0(all_30_3) = v0) | ~ $i(v1) | ~
% 14.35/2.75 | | | $i(all_30_3) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(all_30_3,
% 14.35/2.75 | | | v1) = v2 & $i(v2))) & ! [v0: any] : ! [v1: $i] : (v0 =
% 14.35/2.75 | | | all_30_3 | ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~
% 14.35/2.75 | | | aVector0(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ?
% 14.35/2.75 | | | [v5: $i] : ($i(v3) & (( ~ (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 &
% 14.35/2.75 | | | sdtlbdtrb0(xs, v3) = v5 & $i(v5) & $i(v4) &
% 14.35/2.75 | | | aNaturalNumber0(v3)) | ( ~ (v2 = all_43_0) &
% 14.35/2.75 | | | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : ( ~
% 14.35/2.75 | | | (aDimensionOf0(all_30_3) = v0) | ~ $i(all_30_3) |
% 14.35/2.75 | | | szszuzczcdt0(v0) = all_43_0) & ! [v0: $i] : ( ~
% 14.35/2.75 | | | (aDimensionOf0(all_30_3) = v0) | ~ $i(all_30_3) |
% 14.35/2.75 | | | aVector0(all_30_3))
% 14.35/2.75 | | |
% 14.35/2.75 | | | ALPHA: (52) implies:
% 14.35/2.75 | | | (53) ! [v0: $i] : ( ~ (aDimensionOf0(all_30_3) = v0) | ~ $i(all_30_3)
% 14.35/2.75 | | | | aVector0(all_30_3))
% 14.35/2.75 | | | (54) ! [v0: $i] : ( ~ (aDimensionOf0(all_30_3) = v0) | ~ $i(all_30_3)
% 14.35/2.75 | | | | szszuzczcdt0(v0) = all_43_0)
% 14.35/2.75 | | |
% 14.35/2.75 | | | GROUND_INST: instantiating (54) with all_30_2, simplifying with (16), (20)
% 14.35/2.75 | | | gives:
% 14.35/2.75 | | | (55) szszuzczcdt0(all_30_2) = all_43_0
% 14.35/2.75 | | |
% 14.35/2.75 | | | GROUND_INST: instantiating (53) with all_30_2, simplifying with (16), (20)
% 14.35/2.75 | | | gives:
% 14.35/2.75 | | | (56) aVector0(all_30_3)
% 14.35/2.75 | | |
% 14.35/2.75 | | | REDUCE: (34), (55) imply:
% 14.35/2.75 | | | (57) szszuzczcdt0(all_30_2) = all_28_0
% 14.35/2.75 | | |
% 14.35/2.75 | | | GROUND_INST: instantiating (1) with all_28_0, simplifying with (24), (36)
% 14.35/2.75 | | | gives:
% 14.35/2.75 | | | (58) all_28_0 = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = all_28_0 &
% 14.35/2.75 | | | $i(v0) & aNaturalNumber0(v0))
% 14.35/2.75 | | |
% 14.35/2.75 | | | GROUND_INST: instantiating (mDimNat) with all_30_3, all_30_2, simplifying
% 14.35/2.75 | | | with (16), (20), (56) gives:
% 14.35/2.75 | | | (59) aNaturalNumber0(all_30_2)
% 14.35/2.75 | | |
% 14.35/2.75 | | | GROUND_INST: instantiating (mDimNat) with all_30_1, all_30_0, simplifying
% 14.35/2.75 | | | with (18), (21), (46) gives:
% 14.35/2.75 | | | (60) aNaturalNumber0(all_30_0)
% 14.35/2.75 | | |
% 14.35/2.75 | | | BETA: splitting (58) gives:
% 14.35/2.75 | | |
% 14.35/2.75 | | | Case 1:
% 14.35/2.75 | | | |
% 14.35/2.75 | | | | (61) all_28_0 = sz00
% 14.35/2.75 | | | |
% 14.35/2.75 | | | | REDUCE: (11), (61) imply:
% 14.35/2.75 | | | | (62) $false
% 14.35/2.75 | | | |
% 14.35/2.75 | | | | CLOSE: (62) is inconsistent.
% 14.35/2.75 | | | |
% 14.35/2.75 | | | Case 2:
% 14.35/2.75 | | | |
% 14.35/2.75 | | | | (63) ? [v0: $i] : (szszuzczcdt0(v0) = all_28_0 & $i(v0) &
% 14.35/2.75 | | | | aNaturalNumber0(v0))
% 14.35/2.76 | | | |
% 14.35/2.76 | | | | DELTA: instantiating (63) with fresh symbol all_71_0 gives:
% 14.35/2.76 | | | | (64) szszuzczcdt0(all_71_0) = all_28_0 & $i(all_71_0) &
% 14.35/2.76 | | | | aNaturalNumber0(all_71_0)
% 14.35/2.76 | | | |
% 14.35/2.76 | | | | ALPHA: (64) implies:
% 14.35/2.76 | | | | (65) aNaturalNumber0(all_71_0)
% 14.35/2.76 | | | | (66) $i(all_71_0)
% 14.35/2.76 | | | | (67) szszuzczcdt0(all_71_0) = all_28_0
% 14.35/2.76 | | | |
% 14.35/2.76 | | | | GROUND_INST: instantiating (mSuccEqu) with all_30_0, all_71_0, all_28_0,
% 14.35/2.76 | | | | simplifying with (19), (47), (60), (65), (66), (67) gives:
% 14.35/2.76 | | | | (68) all_71_0 = all_30_0
% 14.35/2.76 | | | |
% 14.35/2.76 | | | | GROUND_INST: instantiating (mSuccEqu) with all_30_2, all_71_0, all_28_0,
% 14.35/2.76 | | | | simplifying with (17), (57), (59), (65), (66), (67) gives:
% 14.35/2.76 | | | | (69) all_71_0 = all_30_2
% 14.35/2.76 | | | |
% 14.35/2.76 | | | | COMBINE_EQS: (68), (69) imply:
% 14.35/2.76 | | | | (70) all_30_0 = all_30_2
% 14.35/2.76 | | | |
% 14.35/2.76 | | | | SIMP: (70) implies:
% 14.35/2.76 | | | | (71) all_30_0 = all_30_2
% 14.35/2.76 | | | |
% 14.35/2.76 | | | | REDUCE: (15), (71) imply:
% 14.35/2.76 | | | | (72) $false
% 14.35/2.76 | | | |
% 14.35/2.76 | | | | CLOSE: (72) is inconsistent.
% 14.35/2.76 | | | |
% 14.35/2.76 | | | End of split
% 14.35/2.76 | | |
% 14.35/2.76 | | End of split
% 14.35/2.76 | |
% 14.35/2.76 | End of split
% 14.35/2.76 |
% 14.35/2.76 End of proof
% 14.35/2.76 % SZS output end Proof for theBenchmark
% 14.35/2.76
% 14.35/2.76 2127ms
%------------------------------------------------------------------------------