TSTP Solution File: ALG036+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG036+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:35:47 EDT 2023
% Result : Theorem 7.53s 1.82s
% Output : Proof 13.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ALG036+1 : TPTP v8.1.2. Released v2.7.0.
% 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 06:02:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.85/1.24 Prover 1: Preprocessing ...
% 3.85/1.24 Prover 4: Preprocessing ...
% 4.15/1.30 Prover 5: Preprocessing ...
% 4.15/1.30 Prover 3: Preprocessing ...
% 4.15/1.30 Prover 2: Preprocessing ...
% 4.15/1.30 Prover 0: Preprocessing ...
% 4.15/1.30 Prover 6: Preprocessing ...
% 6.35/1.64 Prover 2: Constructing countermodel ...
% 6.35/1.64 Prover 6: Constructing countermodel ...
% 6.35/1.64 Prover 4: Constructing countermodel ...
% 6.35/1.64 Prover 1: Constructing countermodel ...
% 6.35/1.64 Prover 3: Constructing countermodel ...
% 6.85/1.65 Prover 0: Constructing countermodel ...
% 7.53/1.82 Prover 6: proved (1179ms)
% 7.53/1.82 Prover 2: proved (1185ms)
% 7.53/1.82
% 7.53/1.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.53/1.82
% 7.53/1.82
% 7.53/1.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.53/1.82
% 7.53/1.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.04/1.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.04/1.83 Prover 0: stopped
% 8.04/1.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.04/1.84 Prover 3: proved (1198ms)
% 8.04/1.84
% 8.04/1.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.04/1.84
% 8.04/1.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.07/1.97 Prover 5: Constructing countermodel ...
% 9.07/1.97 Prover 5: stopped
% 9.07/1.97 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.07/1.98 Prover 8: Preprocessing ...
% 9.07/2.02 Prover 7: Preprocessing ...
% 9.07/2.04 Prover 11: Preprocessing ...
% 9.07/2.05 Prover 10: Preprocessing ...
% 9.07/2.07 Prover 13: Preprocessing ...
% 9.07/2.13 Prover 8: Constructing countermodel ...
% 11.08/2.25 Prover 11: Constructing countermodel ...
% 11.08/2.28 Prover 13: Constructing countermodel ...
% 11.08/2.28 Prover 7: Constructing countermodel ...
% 11.08/2.30 Prover 10: Constructing countermodel ...
% 12.86/2.49 Prover 4: Found proof (size 99)
% 12.86/2.49 Prover 4: proved (1851ms)
% 12.86/2.49 Prover 11: stopped
% 12.86/2.49 Prover 10: stopped
% 12.86/2.49 Prover 13: stopped
% 12.86/2.49 Prover 1: stopped
% 12.86/2.49 Prover 8: stopped
% 12.86/2.49 Prover 7: stopped
% 12.86/2.49
% 12.86/2.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.86/2.50
% 13.08/2.51 % SZS output start Proof for theBenchmark
% 13.08/2.51 Assumptions after simplification:
% 13.08/2.51 ---------------------------------
% 13.08/2.51
% 13.08/2.51 (ax1)
% 13.19/2.55 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 13.19/2.55 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 13.19/2.55 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 13.19/2.55 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 13.19/2.55 op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 &
% 13.19/2.55 op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 &
% 13.19/2.55 op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 13.19/2.55 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 13.19/2.55 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 13.19/2.55 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 =
% 13.19/2.55 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 |
% 13.19/2.55 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11
% 13.19/2.55 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 |
% 13.19/2.55 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 |
% 13.19/2.55 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 |
% 13.19/2.55 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 13.19/2.55 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3
% 13.19/2.55 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1
% 13.19/2.55 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 13.19/2.55
% 13.19/2.55 (ax2)
% 13.19/2.55 op(unit, e3) = e3 & op(unit, e2) = e2 & op(unit, e1) = e1 & op(unit, e0) = e0
% 13.19/2.55 & op(e3, unit) = e3 & op(e2, unit) = e2 & op(e1, unit) = e1 & op(e0, unit) =
% 13.19/2.55 e0 & $i(unit) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & (unit = e3 | unit = e2 |
% 13.19/2.55 unit = e1 | unit = e0)
% 13.19/2.55
% 13.19/2.55 (ax3)
% 13.19/2.56 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 13.19/2.56 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 13.19/2.56 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 13.19/2.56 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 13.19/2.56 op(e3, e1) = v11 & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 &
% 13.19/2.56 op(e2, e1) = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 &
% 13.19/2.56 op(e1, e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 13.19/2.56 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 13.19/2.56 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 13.19/2.56 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14 = e3 | v11 = e3 | v6 =
% 13.19/2.56 e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 = e3) & (v15 = e2 | v14 = e2 |
% 13.19/2.56 v11 = e2 | v6 = e2) & (v15 = e2 | v13 = e2 | v9 = e2 | v3 = e2) & (v15 =
% 13.19/2.56 e1 | v14 = e1 | v11 = e1 | v6 = e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3
% 13.19/2.56 = e1) & (v15 = e0 | v14 = e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0
% 13.19/2.56 | v9 = e0 | v3 = e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 =
% 13.19/2.56 e2 | v12 = e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 =
% 13.19/2.56 e1) & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 |
% 13.19/2.56 v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) & (v13 =
% 13.19/2.56 e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 | v10 = e0 | v5
% 13.19/2.56 = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) & (v11 = e2 | v10 = e2 |
% 13.19/2.56 v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7 = e1 | v1 = e1) & (v11 = e0
% 13.19/2.56 | v10 = e0 | v7 = e0 | v1 = e0) & (v9 = e3 | v8 = e3 | v7 = e3 | v4 = e3)
% 13.19/2.56 & (v9 = e2 | v8 = e2 | v7 = e2 | v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 |
% 13.19/2.56 v4 = e1) & (v9 = e0 | v8 = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 |
% 13.19/2.56 v4 = e3 | v0 = e3) & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 |
% 13.19/2.56 v5 = e1 | v4 = e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) &
% 13.19/2.56 (v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0
% 13.19/2.56 = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 = e0 |
% 13.19/2.56 v1 = e0))))
% 13.19/2.56
% 13.19/2.56 (ax4)
% 13.19/2.56 unit = e0 & $i(e0)
% 13.19/2.56
% 13.19/2.56 (ax5)
% 13.19/2.57 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 13.19/2.57 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 13.19/2.57 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 13.19/2.57 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~
% 13.19/2.57 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 =
% 13.19/2.57 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) &
% 13.19/2.57 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 =
% 13.19/2.57 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~
% 13.19/2.57 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) &
% 13.19/2.57 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) &
% 13.19/2.57 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) &
% 13.19/2.57 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~
% 13.19/2.57 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~
% 13.19/2.57 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) =
% 13.19/2.57 v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) =
% 13.19/2.57 v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9
% 13.19/2.57 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 &
% 13.19/2.57 op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 13.19/2.57 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 13.19/2.57 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.19/2.57
% 13.19/2.57 (co1)
% 13.19/2.57 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 13.19/2.57 ? [v3: $i] : (op(e3, e3) = v3 & op(e2, e2) = v2 & op(e1, e1) = v1 & op(e0, e0)
% 13.19/2.57 = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = e3) | ~ (v2 = e3) | ~
% 13.19/2.57 (v1 = e3) | ~ (v0 = e3)) & ( ~ (v3 = e2) | ~ (v2 = e2) | ~ (v1 = e2) |
% 13.19/2.57 ~ (v0 = e2)) & ( ~ (v3 = e1) | ~ (v2 = e1) | ~ (v1 = e1) | ~ (v0 = e1))
% 13.19/2.57 & ( ~ (v3 = e0) | ~ (v2 = e0) | ~ (v1 = e0) | ~ (v0 = e0)) & ((v3 = e3 &
% 13.19/2.57 v2 = e3 & v1 = e3 & v0 = e3) | (v3 = e2 & v2 = e2 & v1 = e2 & v0 = e2) |
% 13.19/2.57 (v3 = e1 & v2 = e1 & v1 = e1 & v0 = e1) | (v3 = e0 & v2 = e0 & v1 = e0 &
% 13.19/2.57 v0 = e0)))
% 13.19/2.57
% 13.19/2.57 (function-axioms)
% 13.19/2.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3,
% 13.19/2.57 v2) = v1) | ~ (op(v3, v2) = v0))
% 13.19/2.57
% 13.19/2.57 Further assumptions not needed in the proof:
% 13.19/2.57 --------------------------------------------
% 13.19/2.57 ax6
% 13.19/2.57
% 13.19/2.57 Those formulas are unsatisfiable:
% 13.19/2.57 ---------------------------------
% 13.19/2.57
% 13.19/2.57 Begin of proof
% 13.19/2.57 |
% 13.19/2.57 | ALPHA: (ax1) implies:
% 13.19/2.58 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 13.19/2.58 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 13.19/2.58 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 13.19/2.58 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13
% 13.19/2.58 | & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1)
% 13.19/2.58 | = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1,
% 13.19/2.58 | e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 13.19/2.58 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 13.19/2.58 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 13.19/2.58 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15
% 13.19/2.58 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14
% 13.19/2.58 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 |
% 13.19/2.58 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 |
% 13.19/2.58 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3
% 13.19/2.58 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8
% 13.19/2.58 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 =
% 13.19/2.58 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 13.19/2.58 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 =
% 13.19/2.58 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3
% 13.19/2.58 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0
% 13.19/2.58 | = e0))
% 13.19/2.58 |
% 13.19/2.58 | ALPHA: (ax2) implies:
% 13.19/2.58 | (2) op(e0, unit) = e0
% 13.19/2.58 |
% 13.19/2.58 | ALPHA: (ax3) implies:
% 13.19/2.58 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 13.19/2.58 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 13.19/2.58 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 13.19/2.58 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v11
% 13.19/2.58 | & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1)
% 13.19/2.58 | = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 & op(e1,
% 13.19/2.58 | e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 13.19/2.58 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 13.19/2.58 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 13.19/2.58 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14
% 13.19/2.58 | = e3 | v11 = e3 | v6 = e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 =
% 13.19/2.58 | e3) & (v15 = e2 | v14 = e2 | v11 = e2 | v6 = e2) & (v15 = e2 | v13
% 13.19/2.58 | = e2 | v9 = e2 | v3 = e2) & (v15 = e1 | v14 = e1 | v11 = e1 | v6 =
% 13.19/2.58 | e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3 = e1) & (v15 = e0 | v14 =
% 13.19/2.58 | e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0 | v9 = e0 | v3 =
% 13.19/2.58 | e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 = e2 | v12 =
% 13.19/2.58 | e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 = e1)
% 13.19/2.58 | & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 |
% 13.19/2.58 | v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) &
% 13.19/2.58 | (v13 = e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 |
% 13.19/2.58 | v10 = e0 | v5 = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) &
% 13.19/2.58 | (v11 = e2 | v10 = e2 | v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7
% 13.19/2.58 | = e1 | v1 = e1) & (v11 = e0 | v10 = e0 | v7 = e0 | v1 = e0) & (v9 =
% 13.19/2.58 | e3 | v8 = e3 | v7 = e3 | v4 = e3) & (v9 = e2 | v8 = e2 | v7 = e2 |
% 13.19/2.58 | v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 | v4 = e1) & (v9 = e0 | v8
% 13.19/2.58 | = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 | v4 = e3 | v0 = e3)
% 13.19/2.58 | & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 | v5 = e1 | v4 =
% 13.19/2.58 | e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e2
% 13.19/2.58 | | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0
% 13.19/2.58 | = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 =
% 13.19/2.58 | e0 | v1 = e0))))
% 13.19/2.58 |
% 13.19/2.58 | ALPHA: (ax4) implies:
% 13.19/2.58 | (4) unit = e0
% 13.19/2.58 |
% 13.19/2.58 | ALPHA: (ax5) implies:
% 13.19/2.59 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 13.19/2.59 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 13.19/2.59 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 13.19/2.59 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~
% 13.19/2.59 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~
% 13.19/2.59 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~
% 13.19/2.59 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12
% 13.19/2.59 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 =
% 13.19/2.59 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9)
% 13.19/2.59 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~
% 13.19/2.59 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6)
% 13.19/2.59 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6
% 13.19/2.59 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) &
% 13.19/2.59 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 =
% 13.19/2.59 | v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3,
% 13.19/2.59 | e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 &
% 13.19/2.59 | op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) =
% 13.19/2.59 | v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0,
% 13.19/2.59 | e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) &
% 13.19/2.59 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 13.19/2.59 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.19/2.59 |
% 13.19/2.59 | ALPHA: (co1) implies:
% 13.19/2.59 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (op(e3, e3) =
% 13.19/2.59 | v3 & op(e2, e2) = v2 & op(e1, e1) = v1 & op(e0, e0) = v0 & $i(v3) &
% 13.19/2.59 | $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = e3) | ~ (v2 = e3) | ~ (v1 =
% 13.19/2.59 | e3) | ~ (v0 = e3)) & ( ~ (v3 = e2) | ~ (v2 = e2) | ~ (v1 = e2)
% 13.19/2.59 | | ~ (v0 = e2)) & ( ~ (v3 = e1) | ~ (v2 = e1) | ~ (v1 = e1) | ~
% 13.19/2.59 | (v0 = e1)) & ( ~ (v3 = e0) | ~ (v2 = e0) | ~ (v1 = e0) | ~ (v0 =
% 13.19/2.59 | e0)) & ((v3 = e3 & v2 = e3 & v1 = e3 & v0 = e3) | (v3 = e2 & v2 =
% 13.19/2.59 | e2 & v1 = e2 & v0 = e2) | (v3 = e1 & v2 = e1 & v1 = e1 & v0 = e1)
% 13.19/2.59 | | (v3 = e0 & v2 = e0 & v1 = e0 & v0 = e0)))
% 13.19/2.59 |
% 13.19/2.59 | DELTA: instantiating (6) with fresh symbols all_4_0, all_4_1, all_4_2, all_4_3
% 13.19/2.59 | gives:
% 13.19/2.59 | (7) op(e3, e3) = all_4_0 & op(e2, e2) = all_4_1 & op(e1, e1) = all_4_2 &
% 13.19/2.59 | op(e0, e0) = all_4_3 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) &
% 13.19/2.59 | $i(all_4_3) & ( ~ (all_4_0 = e3) | ~ (all_4_1 = e3) | ~ (all_4_2 =
% 13.19/2.59 | e3) | ~ (all_4_3 = e3)) & ( ~ (all_4_0 = e2) | ~ (all_4_1 = e2) |
% 13.19/2.59 | ~ (all_4_2 = e2) | ~ (all_4_3 = e2)) & ( ~ (all_4_0 = e1) | ~
% 13.19/2.59 | (all_4_1 = e1) | ~ (all_4_2 = e1) | ~ (all_4_3 = e1)) & ( ~
% 13.19/2.59 | (all_4_0 = e0) | ~ (all_4_1 = e0) | ~ (all_4_2 = e0) | ~ (all_4_3
% 13.19/2.59 | = e0)) & ((all_4_0 = e3 & all_4_1 = e3 & all_4_2 = e3 & all_4_3 =
% 13.19/2.59 | e3) | (all_4_0 = e2 & all_4_1 = e2 & all_4_2 = e2 & all_4_3 = e2) |
% 13.19/2.59 | (all_4_0 = e1 & all_4_1 = e1 & all_4_2 = e1 & all_4_3 = e1) |
% 13.19/2.59 | (all_4_0 = e0 & all_4_1 = e0 & all_4_2 = e0 & all_4_3 = e0))
% 13.19/2.59 |
% 13.19/2.59 | ALPHA: (7) implies:
% 13.19/2.59 | (8) op(e0, e0) = all_4_3
% 13.19/2.59 | (9) (all_4_0 = e3 & all_4_1 = e3 & all_4_2 = e3 & all_4_3 = e3) | (all_4_0
% 13.19/2.59 | = e2 & all_4_1 = e2 & all_4_2 = e2 & all_4_3 = e2) | (all_4_0 = e1 &
% 13.19/2.59 | all_4_1 = e1 & all_4_2 = e1 & all_4_3 = e1) | (all_4_0 = e0 & all_4_1
% 13.19/2.60 | = e0 & all_4_2 = e0 & all_4_3 = e0)
% 13.19/2.60 | (10) ~ (all_4_0 = e0) | ~ (all_4_1 = e0) | ~ (all_4_2 = e0) | ~
% 13.19/2.60 | (all_4_3 = e0)
% 13.19/2.60 |
% 13.19/2.60 | DELTA: instantiating (5) with fresh symbols all_6_0, all_6_1, all_6_2,
% 13.19/2.60 | all_6_3, all_6_4, all_6_5, all_6_6, all_6_7, all_6_8, all_6_9,
% 13.19/2.60 | all_6_10, all_6_11, all_6_12, all_6_13, all_6_14, all_6_15 gives:
% 13.19/2.60 | (11) ~ (all_6_0 = all_6_1) & ~ (all_6_0 = all_6_2) & ~ (all_6_0 =
% 13.19/2.60 | all_6_3) & ~ (all_6_0 = all_6_4) & ~ (all_6_0 = all_6_8) & ~
% 13.19/2.60 | (all_6_0 = all_6_12) & ~ (all_6_1 = all_6_2) & ~ (all_6_1 = all_6_3)
% 13.19/2.60 | & ~ (all_6_1 = all_6_5) & ~ (all_6_1 = all_6_9) & ~ (all_6_1 =
% 13.19/2.60 | all_6_13) & ~ (all_6_2 = all_6_3) & ~ (all_6_2 = all_6_6) & ~
% 13.19/2.60 | (all_6_2 = all_6_10) & ~ (all_6_2 = all_6_14) & ~ (all_6_3 =
% 13.19/2.60 | all_6_7) & ~ (all_6_3 = all_6_11) & ~ (all_6_3 = all_6_15) & ~
% 13.19/2.60 | (all_6_4 = all_6_5) & ~ (all_6_4 = all_6_6) & ~ (all_6_4 = all_6_7)
% 13.19/2.60 | & ~ (all_6_4 = all_6_8) & ~ (all_6_4 = all_6_12) & ~ (all_6_5 =
% 13.19/2.60 | all_6_6) & ~ (all_6_5 = all_6_7) & ~ (all_6_5 = all_6_9) & ~
% 13.19/2.60 | (all_6_5 = all_6_13) & ~ (all_6_6 = all_6_7) & ~ (all_6_6 =
% 13.19/2.60 | all_6_10) & ~ (all_6_6 = all_6_14) & ~ (all_6_7 = all_6_11) & ~
% 13.19/2.60 | (all_6_7 = all_6_15) & ~ (all_6_8 = all_6_9) & ~ (all_6_8 =
% 13.19/2.60 | all_6_10) & ~ (all_6_8 = all_6_11) & ~ (all_6_8 = all_6_12) & ~
% 13.19/2.60 | (all_6_9 = all_6_10) & ~ (all_6_9 = all_6_11) & ~ (all_6_9 =
% 13.19/2.60 | all_6_13) & ~ (all_6_10 = all_6_11) & ~ (all_6_10 = all_6_14) & ~
% 13.19/2.60 | (all_6_11 = all_6_15) & ~ (all_6_12 = all_6_13) & ~ (all_6_12 =
% 13.19/2.60 | all_6_14) & ~ (all_6_12 = all_6_15) & ~ (all_6_13 = all_6_14) & ~
% 13.19/2.60 | (all_6_13 = all_6_15) & ~ (all_6_14 = all_6_15) & op(e3, e3) =
% 13.19/2.60 | all_6_0 & op(e3, e2) = all_6_4 & op(e3, e1) = all_6_8 & op(e3, e0) =
% 13.19/2.60 | all_6_12 & op(e2, e3) = all_6_1 & op(e2, e2) = all_6_5 & op(e2, e1) =
% 13.19/2.60 | all_6_9 & op(e2, e0) = all_6_13 & op(e1, e3) = all_6_2 & op(e1, e2) =
% 13.19/2.60 | all_6_6 & op(e1, e1) = all_6_10 & op(e1, e0) = all_6_14 & op(e0, e3) =
% 13.19/2.60 | all_6_3 & op(e0, e2) = all_6_7 & op(e0, e1) = all_6_11 & op(e0, e0) =
% 13.19/2.60 | all_6_15 & $i(all_6_0) & $i(all_6_1) & $i(all_6_2) & $i(all_6_3) &
% 13.19/2.60 | $i(all_6_4) & $i(all_6_5) & $i(all_6_6) & $i(all_6_7) & $i(all_6_8) &
% 13.19/2.60 | $i(all_6_9) & $i(all_6_10) & $i(all_6_11) & $i(all_6_12) &
% 13.19/2.60 | $i(all_6_13) & $i(all_6_14) & $i(all_6_15)
% 13.19/2.60 |
% 13.19/2.60 | ALPHA: (11) implies:
% 13.19/2.60 | (12) op(e0, e0) = all_6_15
% 13.19/2.60 |
% 13.19/2.60 | DELTA: instantiating (1) with fresh symbols all_8_0, all_8_1, all_8_2,
% 13.19/2.60 | all_8_3, all_8_4, all_8_5, all_8_6, all_8_7, all_8_8, all_8_9,
% 13.19/2.60 | all_8_10, all_8_11, all_8_12, all_8_13, all_8_14, all_8_15 gives:
% 13.19/2.60 | (13) op(e3, e3) = all_8_0 & op(e3, e2) = all_8_1 & op(e3, e1) = all_8_2 &
% 13.19/2.60 | op(e3, e0) = all_8_3 & op(e2, e3) = all_8_4 & op(e2, e2) = all_8_5 &
% 13.19/2.60 | op(e2, e1) = all_8_6 & op(e2, e0) = all_8_7 & op(e1, e3) = all_8_8 &
% 13.19/2.60 | op(e1, e2) = all_8_9 & op(e1, e1) = all_8_10 & op(e1, e0) = all_8_11 &
% 13.19/2.60 | op(e0, e3) = all_8_12 & op(e0, e2) = all_8_13 & op(e0, e1) = all_8_14
% 13.19/2.60 | & op(e0, e0) = all_8_15 & $i(all_8_0) & $i(all_8_1) & $i(all_8_2) &
% 13.19/2.60 | $i(all_8_3) & $i(all_8_4) & $i(all_8_5) & $i(all_8_6) & $i(all_8_7) &
% 13.19/2.60 | $i(all_8_8) & $i(all_8_9) & $i(all_8_10) & $i(all_8_11) & $i(all_8_12)
% 13.19/2.60 | & $i(all_8_13) & $i(all_8_14) & $i(all_8_15) & (all_8_0 = e3 | all_8_0
% 13.19/2.60 | = e2 | all_8_0 = e1 | all_8_0 = e0) & (all_8_1 = e3 | all_8_1 = e2 |
% 13.19/2.60 | all_8_1 = e1 | all_8_1 = e0) & (all_8_2 = e3 | all_8_2 = e2 |
% 13.19/2.60 | all_8_2 = e1 | all_8_2 = e0) & (all_8_3 = e3 | all_8_3 = e2 |
% 13.19/2.60 | all_8_3 = e1 | all_8_3 = e0) & (all_8_4 = e3 | all_8_4 = e2 |
% 13.19/2.60 | all_8_4 = e1 | all_8_4 = e0) & (all_8_5 = e3 | all_8_5 = e2 |
% 13.19/2.60 | all_8_5 = e1 | all_8_5 = e0) & (all_8_6 = e3 | all_8_6 = e2 |
% 13.19/2.60 | all_8_6 = e1 | all_8_6 = e0) & (all_8_7 = e3 | all_8_7 = e2 |
% 13.19/2.60 | all_8_7 = e1 | all_8_7 = e0) & (all_8_8 = e3 | all_8_8 = e2 |
% 13.19/2.60 | all_8_8 = e1 | all_8_8 = e0) & (all_8_9 = e3 | all_8_9 = e2 |
% 13.19/2.60 | all_8_9 = e1 | all_8_9 = e0) & (all_8_10 = e3 | all_8_10 = e2 |
% 13.19/2.60 | all_8_10 = e1 | all_8_10 = e0) & (all_8_11 = e3 | all_8_11 = e2 |
% 13.19/2.60 | all_8_11 = e1 | all_8_11 = e0) & (all_8_12 = e3 | all_8_12 = e2 |
% 13.19/2.60 | all_8_12 = e1 | all_8_12 = e0) & (all_8_13 = e3 | all_8_13 = e2 |
% 13.19/2.60 | all_8_13 = e1 | all_8_13 = e0) & (all_8_14 = e3 | all_8_14 = e2 |
% 13.19/2.60 | all_8_14 = e1 | all_8_14 = e0) & (all_8_15 = e3 | all_8_15 = e2 |
% 13.19/2.60 | all_8_15 = e1 | all_8_15 = e0)
% 13.19/2.60 |
% 13.19/2.60 | ALPHA: (13) implies:
% 13.19/2.60 | (14) op(e0, e0) = all_8_15
% 13.19/2.60 |
% 13.19/2.60 | DELTA: instantiating (3) with fresh symbols all_10_0, all_10_1, all_10_2,
% 13.19/2.60 | all_10_3, all_10_4, all_10_5, all_10_6, all_10_7, all_10_8, all_10_9,
% 13.19/2.60 | all_10_10, all_10_11, all_10_12, all_10_13, all_10_14, all_10_15 gives:
% 13.19/2.61 | (15) op(e3, e3) = all_10_0 & op(e3, e2) = all_10_1 & op(e3, e1) = all_10_4
% 13.19/2.61 | & op(e3, e0) = all_10_9 & op(e2, e3) = all_10_2 & op(e2, e2) =
% 13.19/2.61 | all_10_3 & op(e2, e1) = all_10_5 & op(e2, e0) = all_10_10 & op(e1, e3)
% 13.19/2.61 | = all_10_6 & op(e1, e2) = all_10_7 & op(e1, e1) = all_10_8 & op(e1,
% 13.19/2.61 | e0) = all_10_11 & op(e0, e3) = all_10_12 & op(e0, e2) = all_10_13 &
% 13.19/2.61 | op(e0, e1) = all_10_14 & op(e0, e0) = all_10_15 & $i(all_10_0) &
% 13.19/2.61 | $i(all_10_1) & $i(all_10_2) & $i(all_10_3) & $i(all_10_4) &
% 13.19/2.61 | $i(all_10_5) & $i(all_10_6) & $i(all_10_7) & $i(all_10_8) &
% 13.19/2.61 | $i(all_10_9) & $i(all_10_10) & $i(all_10_11) & $i(all_10_12) &
% 13.19/2.61 | $i(all_10_13) & $i(all_10_14) & $i(all_10_15) & (all_10_0 = e3 |
% 13.19/2.61 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3) & (all_10_0 = e3 |
% 13.19/2.61 | all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3) & (all_10_0 = e2 |
% 13.19/2.61 | all_10_1 = e2 | all_10_4 = e2 | all_10_9 = e2) & (all_10_0 = e2 |
% 13.19/2.61 | all_10_2 = e2 | all_10_6 = e2 | all_10_12 = e2) & (all_10_0 = e1 |
% 13.19/2.61 | all_10_1 = e1 | all_10_4 = e1 | all_10_9 = e1) & (all_10_0 = e1 |
% 13.19/2.61 | all_10_2 = e1 | all_10_6 = e1 | all_10_12 = e1) & (all_10_0 = e0 |
% 13.19/2.61 | all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0) & (all_10_0 = e0 |
% 13.19/2.61 | all_10_2 = e0 | all_10_6 = e0 | all_10_12 = e0) & (all_10_1 = e3 |
% 13.19/2.61 | all_10_3 = e3 | all_10_7 = e3 | all_10_13 = e3) & (all_10_1 = e2 |
% 13.19/2.61 | all_10_3 = e2 | all_10_7 = e2 | all_10_13 = e2) & (all_10_1 = e1 |
% 13.19/2.61 | all_10_3 = e1 | all_10_7 = e1 | all_10_13 = e1) & (all_10_1 = e0 |
% 13.19/2.61 | all_10_3 = e0 | all_10_7 = e0 | all_10_13 = e0) & (all_10_2 = e3 |
% 13.19/2.61 | all_10_3 = e3 | all_10_5 = e3 | all_10_10 = e3) & (all_10_2 = e2 |
% 13.19/2.61 | all_10_3 = e2 | all_10_5 = e2 | all_10_10 = e2) & (all_10_2 = e1 |
% 13.19/2.61 | all_10_3 = e1 | all_10_5 = e1 | all_10_10 = e1) & (all_10_2 = e0 |
% 13.19/2.61 | all_10_3 = e0 | all_10_5 = e0 | all_10_10 = e0) & (all_10_4 = e3 |
% 13.19/2.61 | all_10_5 = e3 | all_10_8 = e3 | all_10_14 = e3) & (all_10_4 = e2 |
% 13.19/2.61 | all_10_5 = e2 | all_10_8 = e2 | all_10_14 = e2) & (all_10_4 = e1 |
% 13.19/2.61 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1) & (all_10_4 = e0 |
% 13.19/2.61 | all_10_5 = e0 | all_10_8 = e0 | all_10_14 = e0) & (all_10_6 = e3 |
% 13.19/2.61 | all_10_7 = e3 | all_10_8 = e3 | all_10_11 = e3) & (all_10_6 = e2 |
% 13.19/2.61 | all_10_7 = e2 | all_10_8 = e2 | all_10_11 = e2) & (all_10_6 = e1 |
% 13.19/2.61 | all_10_7 = e1 | all_10_8 = e1 | all_10_11 = e1) & (all_10_6 = e0 |
% 13.19/2.61 | all_10_7 = e0 | all_10_8 = e0 | all_10_11 = e0) & (all_10_9 = e3 |
% 13.19/2.61 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3) & (all_10_9 = e2 |
% 13.19/2.61 | all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2) & (all_10_9 = e1 |
% 13.19/2.61 | all_10_10 = e1 | all_10_11 = e1 | all_10_15 = e1) & (all_10_12 = e3
% 13.19/2.61 | | all_10_13 = e3 | all_10_14 = e3 | all_10_15 = e3) & (all_10_12 =
% 13.19/2.61 | e2 | all_10_13 = e2 | all_10_14 = e2 | all_10_15 = e2) & (all_10_12
% 13.19/2.61 | = e1 | all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1) &
% 13.19/2.61 | (all_10_15 = e0 | ((all_10_9 = e0 | all_10_10 = e0 | all_10_11 = e0) &
% 13.19/2.61 | (all_10_12 = e0 | all_10_13 = e0 | all_10_14 = e0)))
% 13.19/2.61 |
% 13.19/2.61 | ALPHA: (15) implies:
% 13.19/2.61 | (16) op(e0, e0) = all_10_15
% 13.19/2.61 |
% 13.19/2.61 | REDUCE: (2), (4) imply:
% 13.19/2.61 | (17) op(e0, e0) = e0
% 13.19/2.61 |
% 13.19/2.61 | GROUND_INST: instantiating (function-axioms) with all_8_15, all_10_15, e0, e0,
% 13.19/2.61 | simplifying with (14), (16) gives:
% 13.19/2.61 | (18) all_10_15 = all_8_15
% 13.19/2.61 |
% 13.19/2.61 | GROUND_INST: instantiating (function-axioms) with all_6_15, all_10_15, e0, e0,
% 13.19/2.61 | simplifying with (12), (16) gives:
% 13.19/2.61 | (19) all_10_15 = all_6_15
% 13.19/2.61 |
% 13.19/2.61 | GROUND_INST: instantiating (function-axioms) with all_4_3, all_10_15, e0, e0,
% 13.19/2.61 | simplifying with (8), (16) gives:
% 13.19/2.61 | (20) all_10_15 = all_4_3
% 13.19/2.61 |
% 13.19/2.61 | GROUND_INST: instantiating (function-axioms) with e0, all_10_15, e0, e0,
% 13.19/2.61 | simplifying with (16), (17) gives:
% 13.19/2.61 | (21) all_10_15 = e0
% 13.19/2.61 |
% 13.19/2.61 | COMBINE_EQS: (18), (21) imply:
% 13.19/2.61 | (22) all_8_15 = e0
% 13.19/2.61 |
% 13.19/2.61 | COMBINE_EQS: (18), (20) imply:
% 13.19/2.61 | (23) all_8_15 = all_4_3
% 13.19/2.61 |
% 13.19/2.61 | COMBINE_EQS: (18), (19) imply:
% 13.19/2.61 | (24) all_8_15 = all_6_15
% 13.19/2.61 |
% 13.19/2.61 | COMBINE_EQS: (22), (24) imply:
% 13.19/2.61 | (25) all_6_15 = e0
% 13.19/2.61 |
% 13.19/2.61 | COMBINE_EQS: (23), (24) imply:
% 13.19/2.61 | (26) all_6_15 = all_4_3
% 13.19/2.61 |
% 13.19/2.61 | COMBINE_EQS: (25), (26) imply:
% 13.19/2.61 | (27) all_4_3 = e0
% 13.19/2.61 |
% 13.19/2.61 | BETA: splitting (9) gives:
% 13.19/2.61 |
% 13.19/2.61 | Case 1:
% 13.19/2.61 | |
% 13.19/2.61 | | (28) (all_4_0 = e3 & all_4_1 = e3 & all_4_2 = e3 & all_4_3 = e3) |
% 13.19/2.61 | | (all_4_0 = e2 & all_4_1 = e2 & all_4_2 = e2 & all_4_3 = e2)
% 13.19/2.61 | |
% 13.19/2.61 | | BETA: splitting (28) gives:
% 13.19/2.61 | |
% 13.19/2.61 | | Case 1:
% 13.19/2.61 | | |
% 13.19/2.61 | | | (29) all_4_0 = e3 & all_4_1 = e3 & all_4_2 = e3 & all_4_3 = e3
% 13.19/2.61 | | |
% 13.19/2.61 | | | ALPHA: (29) implies:
% 13.19/2.61 | | | (30) all_4_3 = e3
% 13.19/2.61 | | | (31) all_4_2 = e3
% 13.19/2.61 | | | (32) all_4_1 = e3
% 13.19/2.61 | | | (33) all_4_0 = e3
% 13.19/2.61 | | |
% 13.19/2.61 | | | COMBINE_EQS: (27), (30) imply:
% 13.19/2.61 | | | (34) e3 = e0
% 13.19/2.61 | | |
% 13.19/2.61 | | | SIMP: (34) implies:
% 13.19/2.61 | | | (35) e3 = e0
% 13.19/2.61 | | |
% 13.19/2.61 | | | COMBINE_EQS: (31), (35) imply:
% 13.19/2.61 | | | (36) all_4_2 = e0
% 13.19/2.61 | | |
% 13.19/2.61 | | | COMBINE_EQS: (32), (35) imply:
% 13.19/2.61 | | | (37) all_4_1 = e0
% 13.19/2.61 | | |
% 13.19/2.61 | | | COMBINE_EQS: (33), (35) imply:
% 13.19/2.61 | | | (38) all_4_0 = e0
% 13.19/2.62 | | |
% 13.19/2.62 | | | REF_CLOSE: (10), (27), (36), (37), (38) are inconsistent by sub-proof #1.
% 13.19/2.62 | | |
% 13.19/2.62 | | Case 2:
% 13.19/2.62 | | |
% 13.19/2.62 | | | (39) all_4_0 = e2 & all_4_1 = e2 & all_4_2 = e2 & all_4_3 = e2
% 13.19/2.62 | | |
% 13.19/2.62 | | | ALPHA: (39) implies:
% 13.19/2.62 | | | (40) all_4_3 = e2
% 13.19/2.62 | | | (41) all_4_2 = e2
% 13.19/2.62 | | | (42) all_4_1 = e2
% 13.19/2.62 | | | (43) all_4_0 = e2
% 13.19/2.62 | | |
% 13.19/2.62 | | | COMBINE_EQS: (27), (40) imply:
% 13.19/2.62 | | | (44) e2 = e0
% 13.19/2.62 | | |
% 13.19/2.62 | | | SIMP: (44) implies:
% 13.19/2.62 | | | (45) e2 = e0
% 13.19/2.62 | | |
% 13.19/2.62 | | | COMBINE_EQS: (41), (45) imply:
% 13.19/2.62 | | | (46) all_4_2 = e0
% 13.19/2.62 | | |
% 13.19/2.62 | | | COMBINE_EQS: (42), (45) imply:
% 13.19/2.62 | | | (47) all_4_1 = e0
% 13.19/2.62 | | |
% 13.19/2.62 | | | COMBINE_EQS: (43), (45) imply:
% 13.19/2.62 | | | (48) all_4_0 = e0
% 13.19/2.62 | | |
% 13.19/2.62 | | | REF_CLOSE: (10), (27), (46), (47), (48) are inconsistent by sub-proof #1.
% 13.19/2.62 | | |
% 13.19/2.62 | | End of split
% 13.19/2.62 | |
% 13.19/2.62 | Case 2:
% 13.19/2.62 | |
% 13.19/2.62 | | (49) (all_4_0 = e1 & all_4_1 = e1 & all_4_2 = e1 & all_4_3 = e1) |
% 13.19/2.62 | | (all_4_0 = e0 & all_4_1 = e0 & all_4_2 = e0 & all_4_3 = e0)
% 13.19/2.62 | |
% 13.19/2.62 | | BETA: splitting (49) gives:
% 13.19/2.62 | |
% 13.19/2.62 | | Case 1:
% 13.19/2.62 | | |
% 13.19/2.62 | | | (50) all_4_0 = e1 & all_4_1 = e1 & all_4_2 = e1 & all_4_3 = e1
% 13.19/2.62 | | |
% 13.19/2.62 | | | ALPHA: (50) implies:
% 13.19/2.62 | | | (51) all_4_3 = e1
% 13.19/2.62 | | | (52) all_4_2 = e1
% 13.19/2.62 | | | (53) all_4_1 = e1
% 13.19/2.62 | | | (54) all_4_0 = e1
% 13.19/2.62 | | |
% 13.19/2.62 | | | COMBINE_EQS: (27), (51) imply:
% 13.19/2.62 | | | (55) e1 = e0
% 13.19/2.62 | | |
% 13.19/2.62 | | | SIMP: (55) implies:
% 13.19/2.62 | | | (56) e1 = e0
% 13.19/2.62 | | |
% 13.19/2.62 | | | COMBINE_EQS: (52), (56) imply:
% 13.62/2.62 | | | (57) all_4_2 = e0
% 13.62/2.62 | | |
% 13.62/2.62 | | | COMBINE_EQS: (53), (56) imply:
% 13.62/2.62 | | | (58) all_4_1 = e0
% 13.62/2.62 | | |
% 13.62/2.62 | | | COMBINE_EQS: (54), (56) imply:
% 13.62/2.62 | | | (59) all_4_0 = e0
% 13.62/2.62 | | |
% 13.62/2.62 | | | REF_CLOSE: (10), (27), (57), (58), (59) are inconsistent by sub-proof #1.
% 13.62/2.62 | | |
% 13.62/2.62 | | Case 2:
% 13.62/2.62 | | |
% 13.62/2.62 | | | (60) all_4_0 = e0 & all_4_1 = e0 & all_4_2 = e0 & all_4_3 = e0
% 13.62/2.62 | | |
% 13.62/2.62 | | | ALPHA: (60) implies:
% 13.62/2.62 | | | (61) all_4_2 = e0
% 13.62/2.62 | | | (62) all_4_1 = e0
% 13.62/2.62 | | | (63) all_4_0 = e0
% 13.62/2.62 | | |
% 13.62/2.62 | | | REF_CLOSE: (10), (27), (61), (62), (63) are inconsistent by sub-proof #1.
% 13.62/2.62 | | |
% 13.62/2.62 | | End of split
% 13.62/2.62 | |
% 13.62/2.62 | End of split
% 13.62/2.62 |
% 13.62/2.62 End of proof
% 13.62/2.62
% 13.62/2.62 Sub-proof #1 shows that the following formulas are inconsistent:
% 13.62/2.62 ----------------------------------------------------------------
% 13.62/2.62 (1) all_4_3 = e0
% 13.62/2.62 (2) all_4_2 = e0
% 13.62/2.62 (3) all_4_0 = e0
% 13.62/2.62 (4) all_4_1 = e0
% 13.62/2.62 (5) ~ (all_4_0 = e0) | ~ (all_4_1 = e0) | ~ (all_4_2 = e0) | ~ (all_4_3 =
% 13.62/2.62 e0)
% 13.62/2.62
% 13.62/2.62 Begin of proof
% 13.62/2.62 |
% 13.62/2.62 | BETA: splitting (5) gives:
% 13.62/2.62 |
% 13.62/2.62 | Case 1:
% 13.62/2.62 | |
% 13.62/2.62 | | (6) ~ (all_4_0 = e0)
% 13.62/2.62 | |
% 13.62/2.62 | | REDUCE: (3), (6) imply:
% 13.62/2.62 | | (7) $false
% 13.62/2.62 | |
% 13.62/2.62 | | CLOSE: (7) is inconsistent.
% 13.62/2.62 | |
% 13.62/2.62 | Case 2:
% 13.62/2.62 | |
% 13.62/2.62 | | (8) ~ (all_4_1 = e0) | ~ (all_4_2 = e0) | ~ (all_4_3 = e0)
% 13.62/2.62 | |
% 13.62/2.62 | | BETA: splitting (8) gives:
% 13.62/2.62 | |
% 13.62/2.62 | | Case 1:
% 13.62/2.62 | | |
% 13.62/2.62 | | | (9) ~ (all_4_1 = e0)
% 13.62/2.62 | | |
% 13.62/2.62 | | | REDUCE: (4), (9) imply:
% 13.62/2.62 | | | (10) $false
% 13.62/2.62 | | |
% 13.62/2.62 | | | CLOSE: (10) is inconsistent.
% 13.62/2.62 | | |
% 13.62/2.62 | | Case 2:
% 13.62/2.62 | | |
% 13.62/2.62 | | | (11) ~ (all_4_2 = e0) | ~ (all_4_3 = e0)
% 13.62/2.62 | | |
% 13.62/2.62 | | | BETA: splitting (11) gives:
% 13.62/2.62 | | |
% 13.62/2.62 | | | Case 1:
% 13.62/2.62 | | | |
% 13.62/2.62 | | | | (12) ~ (all_4_2 = e0)
% 13.62/2.62 | | | |
% 13.62/2.62 | | | | REDUCE: (2), (12) imply:
% 13.62/2.62 | | | | (13) $false
% 13.62/2.62 | | | |
% 13.62/2.62 | | | | CLOSE: (13) is inconsistent.
% 13.62/2.62 | | | |
% 13.62/2.62 | | | Case 2:
% 13.62/2.62 | | | |
% 13.62/2.62 | | | | (14) ~ (all_4_3 = e0)
% 13.62/2.62 | | | |
% 13.62/2.62 | | | | REDUCE: (1), (14) imply:
% 13.62/2.62 | | | | (15) $false
% 13.62/2.62 | | | |
% 13.62/2.62 | | | | CLOSE: (15) is inconsistent.
% 13.62/2.62 | | | |
% 13.62/2.62 | | | End of split
% 13.62/2.62 | | |
% 13.62/2.62 | | End of split
% 13.62/2.62 | |
% 13.62/2.62 | End of split
% 13.62/2.62 |
% 13.62/2.62 End of proof
% 13.62/2.62 % SZS output end Proof for theBenchmark
% 13.62/2.63
% 13.62/2.63 2009ms
%------------------------------------------------------------------------------