TSTP Solution File: RNG045+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG045+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 : n005.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 13:57:31 EDT 2023
% Result : Theorem 7.30s 1.72s
% Output : Proof 10.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG045+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n005.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 01:45:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.20/1.05 Prover 1: Preprocessing ...
% 2.20/1.05 Prover 4: Preprocessing ...
% 2.91/1.09 Prover 6: Preprocessing ...
% 2.91/1.09 Prover 5: Preprocessing ...
% 2.91/1.09 Prover 3: Preprocessing ...
% 2.91/1.09 Prover 0: Preprocessing ...
% 2.91/1.09 Prover 2: Preprocessing ...
% 4.75/1.41 Prover 1: Constructing countermodel ...
% 4.75/1.41 Prover 6: Constructing countermodel ...
% 4.75/1.42 Prover 3: Constructing countermodel ...
% 5.59/1.50 Prover 4: Constructing countermodel ...
% 6.11/1.54 Prover 5: Constructing countermodel ...
% 6.48/1.57 Prover 0: Proving ...
% 6.48/1.63 Prover 2: Proving ...
% 7.30/1.72 Prover 3: proved (1073ms)
% 7.30/1.72
% 7.30/1.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.30/1.72
% 7.30/1.72 Prover 2: stopped
% 7.30/1.72 Prover 0: stopped
% 7.30/1.72 Prover 6: stopped
% 7.30/1.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.30/1.72 Prover 5: stopped
% 7.30/1.72 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.30/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.30/1.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.68/1.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.82/1.76 Prover 7: Preprocessing ...
% 7.82/1.79 Prover 8: Preprocessing ...
% 7.82/1.79 Prover 13: Preprocessing ...
% 7.82/1.79 Prover 11: Preprocessing ...
% 7.82/1.80 Prover 10: Preprocessing ...
% 8.70/1.87 Prover 8: Warning: ignoring some quantifiers
% 8.70/1.87 Prover 8: Constructing countermodel ...
% 8.70/1.88 Prover 10: Constructing countermodel ...
% 8.70/1.90 Prover 13: Constructing countermodel ...
% 8.70/1.91 Prover 7: Constructing countermodel ...
% 8.70/1.95 Prover 11: Constructing countermodel ...
% 8.70/2.02 Prover 10: Found proof (size 32)
% 8.70/2.02 Prover 10: proved (301ms)
% 8.70/2.02 Prover 11: stopped
% 8.70/2.02 Prover 13: stopped
% 8.70/2.03 Prover 7: stopped
% 8.70/2.03 Prover 4: stopped
% 8.70/2.03 Prover 8: stopped
% 9.75/2.03 Prover 1: stopped
% 9.75/2.03
% 9.75/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.75/2.03
% 9.75/2.05 % SZS output start Proof for theBenchmark
% 9.75/2.05 Assumptions after simplification:
% 9.75/2.05 ---------------------------------
% 9.75/2.05
% 9.75/2.05 (mDistr)
% 9.99/2.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 9.99/2.07 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 9.99/2.08 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 9.99/2.08 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6: $i] : ? [v7: $i]
% 9.99/2.08 : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9
% 9.99/2.08 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 &
% 9.99/2.08 sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)))
% 9.99/2.08
% 9.99/2.08 (m__)
% 9.99/2.08 $i(xv) & $i(xu) & $i(xy) & $i(xx) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 9.99/2.08 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 9.99/2.08 $i] : ? [v9: $i] : ( ~ (v9 = v2) & sdtasdt0(v0, v1) = v2 & sdtasdt0(xy, xv)
% 9.99/2.08 = v7 & sdtasdt0(xy, xu) = v6 & sdtasdt0(xx, xv) = v4 & sdtasdt0(xx, xu) = v3
% 9.99/2.08 & sdtpldt0(v6, v7) = v8 & sdtpldt0(v5, v8) = v9 & sdtpldt0(v3, v4) = v5 &
% 9.99/2.08 sdtpldt0(xu, xv) = v1 & sdtpldt0(xx, xy) = v0 & $i(v9) & $i(v8) & $i(v7) &
% 9.99/2.08 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 9.99/2.08
% 9.99/2.08 (m__674)
% 9.99/2.08 $i(xv) & $i(xu) & $i(xy) & $i(xx) & aScalar0(xv) & aScalar0(xu) & aScalar0(xy)
% 9.99/2.08 & aScalar0(xx)
% 9.99/2.08
% 9.99/2.08 (m__733)
% 9.99/2.08 $i(xv) & $i(xu) & $i(xy) & $i(xx) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 9.99/2.08 ? [v3: $i] : ? [v4: $i] : (sdtasdt0(v0, v1) = v2 & sdtasdt0(xy, v1) = v4 &
% 9.99/2.08 sdtasdt0(xx, v1) = v3 & sdtpldt0(v3, v4) = v2 & sdtpldt0(xu, xv) = v1 &
% 9.99/2.08 sdtpldt0(xx, xy) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 9.99/2.08
% 9.99/2.08 (function-axioms)
% 9.99/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.99/2.09 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 9.99/2.09 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 9.99/2.09 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 9.99/2.09 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 9.99/2.09 $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~
% 9.99/2.09 (szszuzczcdt0(v2) = v0))
% 9.99/2.09
% 9.99/2.09 Further assumptions not needed in the proof:
% 9.99/2.09 --------------------------------------------
% 9.99/2.09 mArith, mIH, mIHOrd, mMulSc, mNatExtr, mNatSort, mNegSc, mSZeroSc, mScSort,
% 9.99/2.09 mScZero, mSuccEqu, mSuccNat, mSumSc, mZeroNat
% 9.99/2.09
% 9.99/2.09 Those formulas are unsatisfiable:
% 9.99/2.09 ---------------------------------
% 9.99/2.09
% 9.99/2.09 Begin of proof
% 9.99/2.09 |
% 9.99/2.09 | ALPHA: (m__674) implies:
% 9.99/2.09 | (1) aScalar0(xx)
% 9.99/2.09 | (2) aScalar0(xy)
% 9.99/2.09 | (3) aScalar0(xu)
% 9.99/2.09 | (4) aScalar0(xv)
% 9.99/2.09 |
% 9.99/2.09 | ALPHA: (m__733) implies:
% 9.99/2.09 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 9.99/2.09 | (sdtasdt0(v0, v1) = v2 & sdtasdt0(xy, v1) = v4 & sdtasdt0(xx, v1) = v3
% 9.99/2.09 | & sdtpldt0(v3, v4) = v2 & sdtpldt0(xu, xv) = v1 & sdtpldt0(xx, xy) =
% 9.99/2.09 | v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 9.99/2.09 |
% 9.99/2.09 | ALPHA: (m__) implies:
% 9.99/2.09 | (6) $i(xx)
% 9.99/2.09 | (7) $i(xy)
% 9.99/2.09 | (8) $i(xu)
% 9.99/2.09 | (9) $i(xv)
% 9.99/2.09 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 9.99/2.09 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (
% 9.99/2.09 | ~ (v9 = v2) & sdtasdt0(v0, v1) = v2 & sdtasdt0(xy, xv) = v7 &
% 9.99/2.09 | sdtasdt0(xy, xu) = v6 & sdtasdt0(xx, xv) = v4 & sdtasdt0(xx, xu) =
% 9.99/2.09 | v3 & sdtpldt0(v6, v7) = v8 & sdtpldt0(v5, v8) = v9 & sdtpldt0(v3,
% 9.99/2.09 | v4) = v5 & sdtpldt0(xu, xv) = v1 & sdtpldt0(xx, xy) = v0 & $i(v9)
% 9.99/2.09 | & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 9.99/2.09 | $i(v1) & $i(v0))
% 9.99/2.09 |
% 9.99/2.09 | ALPHA: (function-axioms) implies:
% 9.99/2.09 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.99/2.09 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 9.99/2.10 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.99/2.10 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 9.99/2.10 |
% 9.99/2.10 | DELTA: instantiating (5) with fresh symbols all_13_0, all_13_1, all_13_2,
% 9.99/2.10 | all_13_3, all_13_4 gives:
% 9.99/2.10 | (13) sdtasdt0(all_13_4, all_13_3) = all_13_2 & sdtasdt0(xy, all_13_3) =
% 9.99/2.10 | all_13_0 & sdtasdt0(xx, all_13_3) = all_13_1 & sdtpldt0(all_13_1,
% 9.99/2.10 | all_13_0) = all_13_2 & sdtpldt0(xu, xv) = all_13_3 & sdtpldt0(xx,
% 9.99/2.10 | xy) = all_13_4 & $i(all_13_0) & $i(all_13_1) & $i(all_13_2) &
% 9.99/2.10 | $i(all_13_3) & $i(all_13_4)
% 9.99/2.10 |
% 9.99/2.10 | ALPHA: (13) implies:
% 9.99/2.10 | (14) sdtpldt0(xx, xy) = all_13_4
% 9.99/2.10 | (15) sdtpldt0(xu, xv) = all_13_3
% 9.99/2.10 | (16) sdtpldt0(all_13_1, all_13_0) = all_13_2
% 9.99/2.10 | (17) sdtasdt0(xx, all_13_3) = all_13_1
% 9.99/2.10 | (18) sdtasdt0(xy, all_13_3) = all_13_0
% 9.99/2.10 | (19) sdtasdt0(all_13_4, all_13_3) = all_13_2
% 9.99/2.10 |
% 9.99/2.10 | DELTA: instantiating (10) with fresh symbols all_15_0, all_15_1, all_15_2,
% 9.99/2.10 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7, all_15_8, all_15_9
% 9.99/2.10 | gives:
% 9.99/2.10 | (20) ~ (all_15_0 = all_15_7) & sdtasdt0(all_15_9, all_15_8) = all_15_7 &
% 9.99/2.10 | sdtasdt0(xy, xv) = all_15_2 & sdtasdt0(xy, xu) = all_15_3 &
% 9.99/2.10 | sdtasdt0(xx, xv) = all_15_5 & sdtasdt0(xx, xu) = all_15_6 &
% 9.99/2.10 | sdtpldt0(all_15_3, all_15_2) = all_15_1 & sdtpldt0(all_15_4, all_15_1)
% 9.99/2.10 | = all_15_0 & sdtpldt0(all_15_6, all_15_5) = all_15_4 & sdtpldt0(xu,
% 9.99/2.10 | xv) = all_15_8 & sdtpldt0(xx, xy) = all_15_9 & $i(all_15_0) &
% 9.99/2.10 | $i(all_15_1) & $i(all_15_2) & $i(all_15_3) & $i(all_15_4) &
% 9.99/2.10 | $i(all_15_5) & $i(all_15_6) & $i(all_15_7) & $i(all_15_8) &
% 9.99/2.10 | $i(all_15_9)
% 9.99/2.10 |
% 9.99/2.10 | ALPHA: (20) implies:
% 9.99/2.10 | (21) ~ (all_15_0 = all_15_7)
% 9.99/2.10 | (22) sdtpldt0(xx, xy) = all_15_9
% 9.99/2.10 | (23) sdtpldt0(xu, xv) = all_15_8
% 9.99/2.10 | (24) sdtpldt0(all_15_6, all_15_5) = all_15_4
% 9.99/2.10 | (25) sdtpldt0(all_15_4, all_15_1) = all_15_0
% 9.99/2.10 | (26) sdtpldt0(all_15_3, all_15_2) = all_15_1
% 9.99/2.10 | (27) sdtasdt0(xx, xu) = all_15_6
% 9.99/2.10 | (28) sdtasdt0(xx, xv) = all_15_5
% 9.99/2.10 | (29) sdtasdt0(xy, xu) = all_15_3
% 9.99/2.10 | (30) sdtasdt0(xy, xv) = all_15_2
% 9.99/2.10 | (31) sdtasdt0(all_15_9, all_15_8) = all_15_7
% 9.99/2.10 |
% 9.99/2.10 | GROUND_INST: instantiating (11) with all_13_4, all_15_9, xy, xx, simplifying
% 9.99/2.10 | with (14), (22) gives:
% 9.99/2.10 | (32) all_15_9 = all_13_4
% 9.99/2.10 |
% 9.99/2.10 | GROUND_INST: instantiating (11) with all_13_3, all_15_8, xv, xu, simplifying
% 9.99/2.10 | with (15), (23) gives:
% 9.99/2.10 | (33) all_15_8 = all_13_3
% 9.99/2.10 |
% 9.99/2.10 | REDUCE: (31), (32), (33) imply:
% 9.99/2.10 | (34) sdtasdt0(all_13_4, all_13_3) = all_15_7
% 9.99/2.10 |
% 9.99/2.10 | GROUND_INST: instantiating (12) with all_13_2, all_15_7, all_13_3, all_13_4,
% 9.99/2.10 | simplifying with (19), (34) gives:
% 9.99/2.10 | (35) all_15_7 = all_13_2
% 9.99/2.10 |
% 9.99/2.10 | REDUCE: (21), (35) imply:
% 9.99/2.10 | (36) ~ (all_15_0 = all_13_2)
% 9.99/2.10 |
% 9.99/2.10 | GROUND_INST: instantiating (mDistr) with xx, xu, xv, all_15_6, all_15_5,
% 9.99/2.10 | all_15_4, simplifying with (1), (3), (4), (6), (8), (9), (24),
% 9.99/2.10 | (27), (28) gives:
% 9.99/2.11 | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1,
% 9.99/2.11 | xv) = v2 & sdtasdt0(xu, xv) = v3 & sdtasdt0(xx, v0) = all_15_4 &
% 9.99/2.11 | sdtpldt0(all_15_5, v3) = v2 & sdtpldt0(xu, xv) = v0 & sdtpldt0(xx,
% 9.99/2.11 | xu) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_15_4))
% 9.99/2.11 |
% 9.99/2.11 | GROUND_INST: instantiating (mDistr) with xy, xu, xv, all_15_3, all_15_2,
% 9.99/2.11 | all_15_1, simplifying with (2), (3), (4), (7), (8), (9), (26),
% 9.99/2.11 | (29), (30) gives:
% 9.99/2.11 | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1,
% 9.99/2.11 | xv) = v2 & sdtasdt0(xu, xv) = v3 & sdtasdt0(xy, v0) = all_15_1 &
% 9.99/2.11 | sdtpldt0(all_15_2, v3) = v2 & sdtpldt0(xu, xv) = v0 & sdtpldt0(xy,
% 9.99/2.11 | xu) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_15_1))
% 9.99/2.11 |
% 9.99/2.11 | DELTA: instantiating (38) with fresh symbols all_34_0, all_34_1, all_34_2,
% 9.99/2.11 | all_34_3 gives:
% 9.99/2.11 | (39) sdtasdt0(all_34_2, xv) = all_34_1 & sdtasdt0(xu, xv) = all_34_0 &
% 9.99/2.11 | sdtasdt0(xy, all_34_3) = all_15_1 & sdtpldt0(all_15_2, all_34_0) =
% 9.99/2.11 | all_34_1 & sdtpldt0(xu, xv) = all_34_3 & sdtpldt0(xy, xu) = all_34_2 &
% 9.99/2.11 | $i(all_34_0) & $i(all_34_1) & $i(all_34_2) & $i(all_34_3) &
% 9.99/2.11 | $i(all_15_1)
% 9.99/2.11 |
% 9.99/2.11 | ALPHA: (39) implies:
% 9.99/2.11 | (40) sdtpldt0(xu, xv) = all_34_3
% 9.99/2.11 | (41) sdtasdt0(xy, all_34_3) = all_15_1
% 9.99/2.11 |
% 9.99/2.11 | DELTA: instantiating (37) with fresh symbols all_36_0, all_36_1, all_36_2,
% 9.99/2.11 | all_36_3 gives:
% 10.25/2.11 | (42) sdtasdt0(all_36_2, xv) = all_36_1 & sdtasdt0(xu, xv) = all_36_0 &
% 10.25/2.11 | sdtasdt0(xx, all_36_3) = all_15_4 & sdtpldt0(all_15_5, all_36_0) =
% 10.25/2.11 | all_36_1 & sdtpldt0(xu, xv) = all_36_3 & sdtpldt0(xx, xu) = all_36_2 &
% 10.25/2.11 | $i(all_36_0) & $i(all_36_1) & $i(all_36_2) & $i(all_36_3) &
% 10.25/2.11 | $i(all_15_4)
% 10.25/2.11 |
% 10.25/2.11 | ALPHA: (42) implies:
% 10.25/2.11 | (43) sdtpldt0(xu, xv) = all_36_3
% 10.25/2.11 | (44) sdtasdt0(xx, all_36_3) = all_15_4
% 10.25/2.11 |
% 10.25/2.11 | GROUND_INST: instantiating (11) with all_13_3, all_36_3, xv, xu, simplifying
% 10.25/2.11 | with (15), (43) gives:
% 10.25/2.11 | (45) all_36_3 = all_13_3
% 10.25/2.11 |
% 10.25/2.11 | GROUND_INST: instantiating (11) with all_34_3, all_36_3, xv, xu, simplifying
% 10.25/2.11 | with (40), (43) gives:
% 10.25/2.11 | (46) all_36_3 = all_34_3
% 10.25/2.11 |
% 10.25/2.11 | COMBINE_EQS: (45), (46) imply:
% 10.25/2.11 | (47) all_34_3 = all_13_3
% 10.25/2.11 |
% 10.25/2.11 | SIMP: (47) implies:
% 10.25/2.11 | (48) all_34_3 = all_13_3
% 10.25/2.11 |
% 10.25/2.11 | REDUCE: (41), (48) imply:
% 10.25/2.11 | (49) sdtasdt0(xy, all_13_3) = all_15_1
% 10.25/2.11 |
% 10.25/2.11 | REDUCE: (44), (45) imply:
% 10.25/2.11 | (50) sdtasdt0(xx, all_13_3) = all_15_4
% 10.25/2.11 |
% 10.25/2.11 | GROUND_INST: instantiating (12) with all_13_1, all_15_4, all_13_3, xx,
% 10.25/2.11 | simplifying with (17), (50) gives:
% 10.25/2.11 | (51) all_15_4 = all_13_1
% 10.25/2.11 |
% 10.25/2.11 | GROUND_INST: instantiating (12) with all_13_0, all_15_1, all_13_3, xy,
% 10.25/2.11 | simplifying with (18), (49) gives:
% 10.25/2.11 | (52) all_15_1 = all_13_0
% 10.25/2.11 |
% 10.25/2.11 | REDUCE: (25), (51), (52) imply:
% 10.25/2.11 | (53) sdtpldt0(all_13_1, all_13_0) = all_15_0
% 10.25/2.11 |
% 10.25/2.11 | GROUND_INST: instantiating (11) with all_13_2, all_15_0, all_13_0, all_13_1,
% 10.25/2.11 | simplifying with (16), (53) gives:
% 10.25/2.11 | (54) all_15_0 = all_13_2
% 10.25/2.11 |
% 10.25/2.11 | REDUCE: (36), (54) imply:
% 10.25/2.11 | (55) $false
% 10.25/2.11 |
% 10.25/2.11 | CLOSE: (55) is inconsistent.
% 10.25/2.11 |
% 10.25/2.11 End of proof
% 10.25/2.11 % SZS output end Proof for theBenchmark
% 10.25/2.12
% 10.25/2.12 1494ms
%------------------------------------------------------------------------------