TSTP Solution File: ALG138+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG138+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 : n009.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 16:37:04 EDT 2023
% Result : Unsatisfiable 8.36s 1.88s
% Output : Proof 22.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG138+1 : TPTP v8.1.2. Released v2.7.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n009.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 03:57:20 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.61/0.60 ________ _____
% 0.61/0.60 ___ __ \_________(_)________________________________
% 0.61/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.61/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.61/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.61/0.60
% 0.61/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.61/0.60 (2023-06-19)
% 0.61/0.60
% 0.61/0.60 (c) Philipp Rümmer, 2009-2023
% 0.61/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.61/0.60 Amanda Stjerna.
% 0.61/0.60 Free software under BSD-3-Clause.
% 0.61/0.60
% 0.61/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.61/0.60
% 0.61/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.61/0.62 Running up to 7 provers in parallel.
% 0.61/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.61/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.61/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.61/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.61/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.61/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.61/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.98/1.29 Prover 1: Preprocessing ...
% 3.98/1.29 Prover 4: Preprocessing ...
% 4.61/1.33 Prover 3: Preprocessing ...
% 4.61/1.33 Prover 5: Preprocessing ...
% 4.61/1.33 Prover 0: Preprocessing ...
% 4.61/1.33 Prover 6: Preprocessing ...
% 4.61/1.33 Prover 2: Preprocessing ...
% 7.45/1.72 Prover 2: Constructing countermodel ...
% 7.45/1.72 Prover 3: Constructing countermodel ...
% 7.45/1.72 Prover 0: Constructing countermodel ...
% 7.45/1.73 Prover 6: Constructing countermodel ...
% 7.45/1.75 Prover 1: Constructing countermodel ...
% 7.45/1.75 Prover 4: Constructing countermodel ...
% 8.36/1.88 Prover 0: proved (1255ms)
% 8.36/1.88 Prover 3: proved (1250ms)
% 8.36/1.88 Prover 6: proved (1252ms)
% 8.36/1.88
% 8.36/1.88 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.36/1.88
% 8.36/1.88
% 8.36/1.88 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.36/1.88
% 8.36/1.88
% 8.36/1.88 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.36/1.88
% 8.36/1.88 Prover 2: stopped
% 8.36/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.36/1.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.36/1.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.36/1.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.95/1.97 Prover 5: Constructing countermodel ...
% 8.95/1.99 Prover 5: stopped
% 9.48/2.00 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.16/2.07 Prover 7: Preprocessing ...
% 10.23/2.08 Prover 11: Preprocessing ...
% 10.23/2.10 Prover 8: Preprocessing ...
% 10.42/2.12 Prover 10: Preprocessing ...
% 10.55/2.19 Prover 13: Preprocessing ...
% 11.26/2.28 Prover 8: Constructing countermodel ...
% 11.85/2.31 Prover 7: Constructing countermodel ...
% 11.85/2.37 Prover 11: Constructing countermodel ...
% 12.52/2.42 Prover 13: Constructing countermodel ...
% 12.52/2.42 Prover 10: Constructing countermodel ...
% 19.88/3.38 Prover 1: Found proof (size 552)
% 19.88/3.38 Prover 1: proved (2760ms)
% 19.88/3.39 Prover 7: stopped
% 19.88/3.39 Prover 10: stopped
% 19.88/3.39 Prover 13: stopped
% 19.88/3.39 Prover 11: stopped
% 19.88/3.39 Prover 4: stopped
% 19.88/3.39 Prover 8: stopped
% 19.88/3.39
% 19.88/3.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.88/3.39
% 20.79/3.55 % SZS output start Proof for theBenchmark
% 20.79/3.55 Assumptions after simplification:
% 20.79/3.55 ---------------------------------
% 20.79/3.55
% 20.79/3.55 (ax1)
% 21.29/3.60 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 21.29/3.60 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 21.29/3.60 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 21.29/3.60 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 21.29/3.60 op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 &
% 21.29/3.60 op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 &
% 21.29/3.60 op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 21.29/3.60 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 21.29/3.60 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 21.29/3.60 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 =
% 21.29/3.60 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 |
% 21.29/3.60 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11
% 21.29/3.60 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 |
% 21.29/3.60 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 |
% 21.29/3.60 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 |
% 21.29/3.60 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 21.29/3.60 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3
% 21.29/3.60 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1
% 21.29/3.60 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 21.29/3.60
% 21.29/3.60 (ax10)
% 21.29/3.61 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e2) =
% 21.29/3.61 v1 & op(e1, e2) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e3) | ~ (v0 = e0)))
% 21.29/3.61
% 21.29/3.61 (ax11)
% 21.29/3.61 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e1) =
% 21.29/3.61 v1 & op(e2, e1) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e3) | ~ (v0 = e0)))
% 21.29/3.61
% 21.29/3.61 (ax12)
% 21.29/3.61 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e3) =
% 21.29/3.61 v1 & op(e2, e3) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e0) | ~ (v0 = e1)))
% 21.29/3.61
% 21.29/3.61 (ax13)
% 21.29/3.61 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e2) =
% 21.29/3.61 v1 & op(e3, e2) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e0) | ~ (v0 = e1)))
% 21.29/3.61
% 21.29/3.61 (ax14)
% 21.29/3.61 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e3) =
% 21.29/3.61 v1 & op(e0, e3) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e2) | ~ (v0 = e1)))
% 21.29/3.61
% 21.29/3.61 (ax15)
% 21.29/3.61 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e0) =
% 21.29/3.61 v1 & op(e3, e0) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e2) | ~ (v0 = e1)))
% 21.29/3.61
% 21.29/3.62 (ax16)
% 21.29/3.62 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e2) =
% 21.29/3.62 v1 & op(e0, e2) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e3) | ~ (v0 = e1)))
% 21.29/3.62
% 21.29/3.62 (ax18)
% 21.29/3.62 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e3) =
% 21.29/3.62 v1 & op(e1, e3) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e0) | ~ (v0 = e2)))
% 21.29/3.62
% 21.29/3.62 (ax2)
% 21.47/3.63 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 21.47/3.63 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 21.47/3.63 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 21.47/3.63 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 21.47/3.63 op(e3, e1) = v11 & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 &
% 21.47/3.63 op(e2, e1) = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 &
% 21.47/3.63 op(e1, e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 21.47/3.63 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 21.47/3.63 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 21.47/3.63 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14 = e3 | v11 = e3 | v6 =
% 21.47/3.63 e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 = e3) & (v15 = e2 | v14 = e2 |
% 21.47/3.63 v11 = e2 | v6 = e2) & (v15 = e2 | v13 = e2 | v9 = e2 | v3 = e2) & (v15 =
% 21.47/3.63 e1 | v14 = e1 | v11 = e1 | v6 = e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3
% 21.47/3.63 = e1) & (v15 = e0 | v14 = e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0
% 21.47/3.63 | v9 = e0 | v3 = e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 =
% 21.47/3.63 e2 | v12 = e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 =
% 21.47/3.63 e1) & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 |
% 21.47/3.63 v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) & (v13 =
% 21.47/3.63 e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 | v10 = e0 | v5
% 21.47/3.63 = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) & (v11 = e2 | v10 = e2 |
% 21.47/3.63 v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7 = e1 | v1 = e1) & (v11 = e0
% 21.47/3.63 | v10 = e0 | v7 = e0 | v1 = e0) & (v9 = e3 | v8 = e3 | v7 = e3 | v4 = e3)
% 21.47/3.63 & (v9 = e2 | v8 = e2 | v7 = e2 | v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 |
% 21.47/3.63 v4 = e1) & (v9 = e0 | v8 = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 |
% 21.47/3.63 v4 = e3 | v0 = e3) & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 |
% 21.47/3.63 v5 = e1 | v4 = e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) &
% 21.47/3.63 (v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0
% 21.47/3.63 = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 = e0 |
% 21.47/3.63 v1 = e0))))
% 21.47/3.63
% 21.47/3.63 (ax20)
% 21.47/3.63 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e3) =
% 21.47/3.63 v1 & op(e0, e3) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e1) | ~ (v0 = e2)))
% 21.47/3.63
% 21.47/3.63 (ax23)
% 21.47/3.63 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e0) =
% 21.47/3.63 v1 & op(e1, e0) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e3) | ~ (v0 = e2)))
% 21.47/3.63
% 21.47/3.63 (ax24)
% 21.47/3.64 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e2) =
% 21.47/3.64 v1 & op(e1, e2) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e0) | ~ (v0 = e3)))
% 21.47/3.64
% 21.47/3.64 (ax25)
% 21.47/3.64 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e1) =
% 21.47/3.64 v1 & op(e2, e1) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e0) | ~ (v0 = e3)))
% 21.47/3.64
% 21.47/3.64 (ax26)
% 21.47/3.64 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e2) =
% 21.47/3.64 v1 & op(e0, e2) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e1) | ~ (v0 = e3)))
% 21.47/3.64
% 21.47/3.64 (ax28)
% 21.47/3.64 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e1) =
% 21.47/3.64 v1 & op(e0, e1) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e2) | ~ (v0 = e3)))
% 21.47/3.64
% 21.47/3.64 (ax29)
% 21.47/3.64 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e0) =
% 21.47/3.64 v1 & op(e1, e0) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e2) | ~ (v0 = e3)))
% 21.47/3.64
% 21.47/3.64 (ax3)
% 21.47/3.64 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 21.47/3.64 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 21.47/3.64 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 21.47/3.64 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~
% 21.47/3.64 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 =
% 21.47/3.64 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) &
% 21.47/3.64 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 =
% 21.47/3.64 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~
% 21.47/3.64 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) &
% 21.47/3.64 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) &
% 21.47/3.64 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) &
% 21.47/3.64 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~
% 21.47/3.64 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~
% 21.47/3.64 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) =
% 21.47/3.64 v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) =
% 21.47/3.64 v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9
% 21.47/3.64 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 &
% 21.47/3.64 op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 21.47/3.64 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 21.47/3.64 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 21.47/3.64
% 21.47/3.65 (ax4)
% 21.47/3.65 ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~
% 21.47/3.65 (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 21.47/3.65
% 21.47/3.65 (ax5)
% 21.47/3.65 op(e3, e3) = e3 & op(e2, e2) = e2 & op(e1, e1) = e1 & op(e0, e0) = e0 & $i(e3)
% 21.47/3.65 & $i(e2) & $i(e1) & $i(e0)
% 21.47/3.65
% 21.47/3.65 (ax7)
% 21.47/3.65 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e2) =
% 21.47/3.65 v1 & op(e3, e2) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e1) | ~ (v0 = e0)))
% 21.47/3.65
% 21.47/3.65 (ax9)
% 21.47/3.65 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(v0, e1) =
% 21.47/3.65 v1 & op(e3, e1) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = e2) | ~ (v0 = e0)))
% 21.47/3.65
% 21.47/3.65 (function-axioms)
% 21.47/3.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3,
% 21.47/3.65 v2) = v1) | ~ (op(v3, v2) = v0))
% 21.47/3.65
% 21.47/3.65 Further assumptions not needed in the proof:
% 21.47/3.65 --------------------------------------------
% 21.47/3.65 ax17, ax19, ax21, ax22, ax27, ax6, ax8
% 21.47/3.65
% 21.47/3.65 Those formulas are unsatisfiable:
% 21.47/3.65 ---------------------------------
% 21.47/3.65
% 21.47/3.65 Begin of proof
% 21.47/3.65 |
% 21.47/3.65 | ALPHA: (ax1) implies:
% 21.47/3.66 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 21.47/3.66 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 21.47/3.66 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 21.47/3.66 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13
% 21.47/3.66 | & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1)
% 21.47/3.66 | = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1,
% 21.47/3.66 | e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 21.47/3.66 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 21.47/3.66 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 21.47/3.66 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15
% 21.47/3.66 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14
% 21.47/3.66 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 |
% 21.47/3.66 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 |
% 21.47/3.66 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3
% 21.47/3.66 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8
% 21.47/3.66 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 =
% 21.47/3.66 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 21.47/3.66 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 =
% 21.47/3.66 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3
% 21.47/3.66 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0
% 21.47/3.66 | = e0))
% 21.47/3.66 |
% 21.47/3.66 | ALPHA: (ax2) implies:
% 21.47/3.67 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 21.47/3.67 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 21.47/3.67 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 21.47/3.67 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v11
% 21.47/3.67 | & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1)
% 21.47/3.67 | = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 & op(e1,
% 21.47/3.67 | e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 21.47/3.67 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 21.47/3.67 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 21.47/3.67 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14
% 21.47/3.67 | = e3 | v11 = e3 | v6 = e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 =
% 21.47/3.67 | e3) & (v15 = e2 | v14 = e2 | v11 = e2 | v6 = e2) & (v15 = e2 | v13
% 21.47/3.67 | = e2 | v9 = e2 | v3 = e2) & (v15 = e1 | v14 = e1 | v11 = e1 | v6 =
% 21.47/3.67 | e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3 = e1) & (v15 = e0 | v14 =
% 21.47/3.67 | e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0 | v9 = e0 | v3 =
% 21.47/3.67 | e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 = e2 | v12 =
% 21.47/3.67 | e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 = e1)
% 21.47/3.67 | & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 |
% 21.47/3.67 | v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) &
% 21.47/3.67 | (v13 = e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 |
% 21.47/3.67 | v10 = e0 | v5 = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) &
% 21.47/3.67 | (v11 = e2 | v10 = e2 | v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7
% 21.47/3.67 | = e1 | v1 = e1) & (v11 = e0 | v10 = e0 | v7 = e0 | v1 = e0) & (v9 =
% 21.47/3.67 | e3 | v8 = e3 | v7 = e3 | v4 = e3) & (v9 = e2 | v8 = e2 | v7 = e2 |
% 21.47/3.67 | v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 | v4 = e1) & (v9 = e0 | v8
% 21.47/3.67 | = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 | v4 = e3 | v0 = e3)
% 21.47/3.67 | & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 | v5 = e1 | v4 =
% 21.47/3.67 | e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e2
% 21.47/3.67 | | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0
% 21.47/3.67 | = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 =
% 21.47/3.67 | e0 | v1 = e0))))
% 21.47/3.67 |
% 21.47/3.67 | ALPHA: (ax3) implies:
% 21.47/3.67 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 21.47/3.67 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 21.47/3.67 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 21.47/3.67 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~
% 21.47/3.67 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~
% 21.47/3.67 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~
% 21.47/3.67 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12
% 21.47/3.67 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 =
% 21.47/3.67 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9)
% 21.47/3.67 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~
% 21.47/3.67 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6)
% 21.47/3.67 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6
% 21.47/3.67 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) &
% 21.47/3.67 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 =
% 21.47/3.67 | v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3,
% 21.47/3.67 | e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 &
% 21.47/3.67 | op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) =
% 21.47/3.67 | v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0,
% 21.47/3.67 | e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) &
% 21.47/3.67 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 21.47/3.67 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 21.47/3.67 |
% 21.47/3.67 | ALPHA: (ax4) implies:
% 21.47/3.67 | (4) ~ (e1 = e0)
% 21.47/3.67 | (5) ~ (e2 = e0)
% 21.47/3.67 | (6) ~ (e2 = e1)
% 21.47/3.67 | (7) ~ (e3 = e1)
% 21.47/3.67 | (8) ~ (e3 = e2)
% 21.47/3.67 |
% 21.47/3.67 | ALPHA: (ax5) implies:
% 21.47/3.67 | (9) op(e0, e0) = e0
% 21.47/3.67 | (10) op(e1, e1) = e1
% 21.47/3.67 | (11) op(e2, e2) = e2
% 21.47/3.67 | (12) op(e3, e3) = e3
% 21.47/3.67 |
% 21.47/3.67 | ALPHA: (ax7) implies:
% 21.47/3.68 | (13) ? [v0: $i] : ? [v1: $i] : (op(v0, e2) = v1 & op(e3, e2) = v0 &
% 21.47/3.68 | $i(v1) & $i(v0) & ( ~ (v1 = e1) | ~ (v0 = e0)))
% 21.47/3.68 |
% 21.47/3.68 | ALPHA: (ax9) implies:
% 21.47/3.68 | (14) ? [v0: $i] : ? [v1: $i] : (op(v0, e1) = v1 & op(e3, e1) = v0 &
% 21.47/3.68 | $i(v1) & $i(v0) & ( ~ (v1 = e2) | ~ (v0 = e0)))
% 21.47/3.68 |
% 21.47/3.68 | ALPHA: (ax10) implies:
% 21.47/3.68 | (15) ? [v0: $i] : ? [v1: $i] : (op(v0, e2) = v1 & op(e1, e2) = v0 &
% 21.47/3.68 | $i(v1) & $i(v0) & ( ~ (v1 = e3) | ~ (v0 = e0)))
% 21.47/3.68 |
% 21.47/3.68 | ALPHA: (ax11) implies:
% 21.47/3.68 | (16) ? [v0: $i] : ? [v1: $i] : (op(v0, e1) = v1 & op(e2, e1) = v0 &
% 21.47/3.68 | $i(v1) & $i(v0) & ( ~ (v1 = e3) | ~ (v0 = e0)))
% 21.47/3.68 |
% 21.47/3.68 | ALPHA: (ax12) implies:
% 21.47/3.68 | (17) ? [v0: $i] : ? [v1: $i] : (op(v0, e3) = v1 & op(e2, e3) = v0 &
% 21.47/3.68 | $i(v1) & $i(v0) & ( ~ (v1 = e0) | ~ (v0 = e1)))
% 21.47/3.68 |
% 21.47/3.68 | ALPHA: (ax13) implies:
% 21.47/3.68 | (18) ? [v0: $i] : ? [v1: $i] : (op(v0, e2) = v1 & op(e3, e2) = v0 &
% 21.47/3.68 | $i(v1) & $i(v0) & ( ~ (v1 = e0) | ~ (v0 = e1)))
% 21.47/3.68 |
% 21.47/3.68 | ALPHA: (ax14) implies:
% 21.47/3.68 | (19) ? [v0: $i] : ? [v1: $i] : (op(v0, e3) = v1 & op(e0, e3) = v0 &
% 21.47/3.68 | $i(v1) & $i(v0) & ( ~ (v1 = e2) | ~ (v0 = e1)))
% 21.47/3.68 |
% 21.47/3.68 | ALPHA: (ax15) implies:
% 21.47/3.68 | (20) ? [v0: $i] : ? [v1: $i] : (op(v0, e0) = v1 & op(e3, e0) = v0 &
% 21.47/3.68 | $i(v1) & $i(v0) & ( ~ (v1 = e2) | ~ (v0 = e1)))
% 21.47/3.68 |
% 21.47/3.68 | ALPHA: (ax16) implies:
% 21.47/3.68 | (21) ? [v0: $i] : ? [v1: $i] : (op(v0, e2) = v1 & op(e0, e2) = v0 &
% 21.47/3.68 | $i(v1) & $i(v0) & ( ~ (v1 = e3) | ~ (v0 = e1)))
% 21.47/3.68 |
% 21.47/3.68 | ALPHA: (ax18) implies:
% 21.47/3.68 | (22) ? [v0: $i] : ? [v1: $i] : (op(v0, e3) = v1 & op(e1, e3) = v0 &
% 21.47/3.68 | $i(v1) & $i(v0) & ( ~ (v1 = e0) | ~ (v0 = e2)))
% 21.47/3.68 |
% 21.47/3.68 | ALPHA: (ax20) implies:
% 21.47/3.68 | (23) ? [v0: $i] : ? [v1: $i] : (op(v0, e3) = v1 & op(e0, e3) = v0 &
% 21.47/3.68 | $i(v1) & $i(v0) & ( ~ (v1 = e1) | ~ (v0 = e2)))
% 21.47/3.68 |
% 21.47/3.68 | ALPHA: (ax23) implies:
% 21.47/3.68 | (24) ? [v0: $i] : ? [v1: $i] : (op(v0, e0) = v1 & op(e1, e0) = v0 &
% 21.47/3.68 | $i(v1) & $i(v0) & ( ~ (v1 = e3) | ~ (v0 = e2)))
% 21.47/3.68 |
% 21.47/3.68 | ALPHA: (ax24) implies:
% 21.47/3.68 | (25) ? [v0: $i] : ? [v1: $i] : (op(v0, e2) = v1 & op(e1, e2) = v0 &
% 21.47/3.68 | $i(v1) & $i(v0) & ( ~ (v1 = e0) | ~ (v0 = e3)))
% 21.47/3.68 |
% 21.47/3.68 | ALPHA: (ax25) implies:
% 21.47/3.68 | (26) ? [v0: $i] : ? [v1: $i] : (op(v0, e1) = v1 & op(e2, e1) = v0 &
% 21.47/3.68 | $i(v1) & $i(v0) & ( ~ (v1 = e0) | ~ (v0 = e3)))
% 21.47/3.68 |
% 21.47/3.68 | ALPHA: (ax26) implies:
% 21.47/3.69 | (27) ? [v0: $i] : ? [v1: $i] : (op(v0, e2) = v1 & op(e0, e2) = v0 &
% 21.47/3.69 | $i(v1) & $i(v0) & ( ~ (v1 = e1) | ~ (v0 = e3)))
% 21.47/3.69 |
% 21.47/3.69 | ALPHA: (ax28) implies:
% 21.47/3.69 | (28) ? [v0: $i] : ? [v1: $i] : (op(v0, e1) = v1 & op(e0, e1) = v0 &
% 21.47/3.69 | $i(v1) & $i(v0) & ( ~ (v1 = e2) | ~ (v0 = e3)))
% 21.47/3.69 |
% 21.47/3.69 | ALPHA: (ax29) implies:
% 21.47/3.69 | (29) ? [v0: $i] : ? [v1: $i] : (op(v0, e0) = v1 & op(e1, e0) = v0 &
% 21.47/3.69 | $i(v1) & $i(v0) & ( ~ (v1 = e2) | ~ (v0 = e3)))
% 21.47/3.69 |
% 21.47/3.69 | DELTA: instantiating (15) with fresh symbols all_4_0, all_4_1 gives:
% 21.47/3.69 | (30) op(all_4_1, e2) = all_4_0 & op(e1, e2) = all_4_1 & $i(all_4_0) &
% 21.47/3.69 | $i(all_4_1) & ( ~ (all_4_0 = e3) | ~ (all_4_1 = e0))
% 21.47/3.69 |
% 21.47/3.69 | ALPHA: (30) implies:
% 21.47/3.69 | (31) op(e1, e2) = all_4_1
% 21.47/3.69 | (32) op(all_4_1, e2) = all_4_0
% 21.47/3.69 | (33) ~ (all_4_0 = e3) | ~ (all_4_1 = e0)
% 21.47/3.69 |
% 21.47/3.69 | DELTA: instantiating (17) with fresh symbols all_6_0, all_6_1 gives:
% 21.47/3.69 | (34) op(all_6_1, e3) = all_6_0 & op(e2, e3) = all_6_1 & $i(all_6_0) &
% 21.47/3.69 | $i(all_6_1) & ( ~ (all_6_0 = e0) | ~ (all_6_1 = e1))
% 21.47/3.69 |
% 21.47/3.69 | ALPHA: (34) implies:
% 21.47/3.69 | (35) op(e2, e3) = all_6_1
% 21.47/3.69 | (36) ~ (all_6_0 = e0) | ~ (all_6_1 = e1)
% 21.47/3.69 |
% 21.47/3.69 | DELTA: instantiating (25) with fresh symbols all_8_0, all_8_1 gives:
% 21.47/3.69 | (37) op(all_8_1, e2) = all_8_0 & op(e1, e2) = all_8_1 & $i(all_8_0) &
% 21.47/3.69 | $i(all_8_1) & ( ~ (all_8_0 = e0) | ~ (all_8_1 = e3))
% 21.47/3.69 |
% 21.47/3.69 | ALPHA: (37) implies:
% 21.47/3.69 | (38) op(e1, e2) = all_8_1
% 21.47/3.69 | (39) op(all_8_1, e2) = all_8_0
% 21.47/3.69 | (40) ~ (all_8_0 = e0) | ~ (all_8_1 = e3)
% 21.47/3.69 |
% 21.47/3.69 | DELTA: instantiating (27) with fresh symbols all_10_0, all_10_1 gives:
% 21.47/3.69 | (41) op(all_10_1, e2) = all_10_0 & op(e0, e2) = all_10_1 & $i(all_10_0) &
% 21.47/3.69 | $i(all_10_1) & ( ~ (all_10_0 = e1) | ~ (all_10_1 = e3))
% 21.47/3.69 |
% 21.47/3.69 | ALPHA: (41) implies:
% 21.47/3.69 | (42) op(e0, e2) = all_10_1
% 21.47/3.69 |
% 21.47/3.69 | DELTA: instantiating (16) with fresh symbols all_12_0, all_12_1 gives:
% 21.47/3.69 | (43) op(all_12_1, e1) = all_12_0 & op(e2, e1) = all_12_1 & $i(all_12_0) &
% 21.47/3.69 | $i(all_12_1) & ( ~ (all_12_0 = e3) | ~ (all_12_1 = e0))
% 21.47/3.69 |
% 21.47/3.69 | ALPHA: (43) implies:
% 21.47/3.69 | (44) op(e2, e1) = all_12_1
% 21.47/3.69 |
% 21.47/3.69 | DELTA: instantiating (22) with fresh symbols all_14_0, all_14_1 gives:
% 21.47/3.69 | (45) op(all_14_1, e3) = all_14_0 & op(e1, e3) = all_14_1 & $i(all_14_0) &
% 21.47/3.69 | $i(all_14_1) & ( ~ (all_14_0 = e0) | ~ (all_14_1 = e2))
% 21.47/3.69 |
% 21.47/3.69 | ALPHA: (45) implies:
% 21.47/3.69 | (46) op(e1, e3) = all_14_1
% 21.47/3.69 |
% 21.47/3.69 | DELTA: instantiating (23) with fresh symbols all_16_0, all_16_1 gives:
% 21.47/3.70 | (47) op(all_16_1, e3) = all_16_0 & op(e0, e3) = all_16_1 & $i(all_16_0) &
% 21.47/3.70 | $i(all_16_1) & ( ~ (all_16_0 = e1) | ~ (all_16_1 = e2))
% 21.47/3.70 |
% 21.47/3.70 | ALPHA: (47) implies:
% 21.47/3.70 | (48) op(e0, e3) = all_16_1
% 21.47/3.70 |
% 21.47/3.70 | DELTA: instantiating (29) with fresh symbols all_20_0, all_20_1 gives:
% 21.47/3.70 | (49) op(all_20_1, e0) = all_20_0 & op(e1, e0) = all_20_1 & $i(all_20_0) &
% 21.47/3.70 | $i(all_20_1) & ( ~ (all_20_0 = e2) | ~ (all_20_1 = e3))
% 21.47/3.70 |
% 21.47/3.70 | ALPHA: (49) implies:
% 21.47/3.70 | (50) op(e1, e0) = all_20_1
% 21.47/3.70 |
% 21.47/3.70 | DELTA: instantiating (20) with fresh symbols all_22_0, all_22_1 gives:
% 21.47/3.70 | (51) op(all_22_1, e0) = all_22_0 & op(e3, e0) = all_22_1 & $i(all_22_0) &
% 21.47/3.70 | $i(all_22_1) & ( ~ (all_22_0 = e2) | ~ (all_22_1 = e1))
% 21.47/3.70 |
% 21.47/3.70 | ALPHA: (51) implies:
% 21.47/3.70 | (52) op(e3, e0) = all_22_1
% 21.47/3.70 |
% 21.47/3.70 | DELTA: instantiating (13) with fresh symbols all_26_0, all_26_1 gives:
% 21.47/3.70 | (53) op(all_26_1, e2) = all_26_0 & op(e3, e2) = all_26_1 & $i(all_26_0) &
% 21.47/3.70 | $i(all_26_1) & ( ~ (all_26_0 = e1) | ~ (all_26_1 = e0))
% 21.47/3.70 |
% 21.47/3.70 | ALPHA: (53) implies:
% 21.47/3.70 | (54) op(e3, e2) = all_26_1
% 21.47/3.70 |
% 21.47/3.70 | DELTA: instantiating (14) with fresh symbols all_28_0, all_28_1 gives:
% 21.47/3.70 | (55) op(all_28_1, e1) = all_28_0 & op(e3, e1) = all_28_1 & $i(all_28_0) &
% 21.47/3.70 | $i(all_28_1) & ( ~ (all_28_0 = e2) | ~ (all_28_1 = e0))
% 21.47/3.70 |
% 21.47/3.70 | ALPHA: (55) implies:
% 21.47/3.70 | (56) op(e3, e1) = all_28_1
% 21.47/3.70 |
% 21.47/3.70 | DELTA: instantiating (28) with fresh symbols all_30_0, all_30_1 gives:
% 21.47/3.70 | (57) op(all_30_1, e1) = all_30_0 & op(e0, e1) = all_30_1 & $i(all_30_0) &
% 21.47/3.70 | $i(all_30_1) & ( ~ (all_30_0 = e2) | ~ (all_30_1 = e3))
% 21.47/3.70 |
% 21.47/3.70 | ALPHA: (57) implies:
% 21.47/3.70 | (58) op(e0, e1) = all_30_1
% 21.47/3.70 |
% 21.47/3.70 | DELTA: instantiating (24) with fresh symbols all_32_0, all_32_1 gives:
% 21.47/3.70 | (59) op(all_32_1, e0) = all_32_0 & op(e1, e0) = all_32_1 & $i(all_32_0) &
% 21.47/3.70 | $i(all_32_1) & ( ~ (all_32_0 = e3) | ~ (all_32_1 = e2))
% 21.47/3.70 |
% 21.47/3.70 | ALPHA: (59) implies:
% 21.47/3.70 | (60) op(e1, e0) = all_32_1
% 21.47/3.70 |
% 21.47/3.70 | DELTA: instantiating (19) with fresh symbols all_34_0, all_34_1 gives:
% 21.47/3.70 | (61) op(all_34_1, e3) = all_34_0 & op(e0, e3) = all_34_1 & $i(all_34_0) &
% 21.47/3.70 | $i(all_34_1) & ( ~ (all_34_0 = e2) | ~ (all_34_1 = e1))
% 21.47/3.70 |
% 21.47/3.70 | ALPHA: (61) implies:
% 21.47/3.70 | (62) op(e0, e3) = all_34_1
% 21.47/3.70 |
% 21.47/3.70 | DELTA: instantiating (26) with fresh symbols all_36_0, all_36_1 gives:
% 21.47/3.70 | (63) op(all_36_1, e1) = all_36_0 & op(e2, e1) = all_36_1 & $i(all_36_0) &
% 21.47/3.70 | $i(all_36_1) & ( ~ (all_36_0 = e0) | ~ (all_36_1 = e3))
% 21.47/3.70 |
% 21.47/3.70 | ALPHA: (63) implies:
% 21.47/3.70 | (64) op(e2, e1) = all_36_1
% 21.47/3.70 |
% 21.47/3.70 | DELTA: instantiating (21) with fresh symbols all_38_0, all_38_1 gives:
% 21.47/3.70 | (65) op(all_38_1, e2) = all_38_0 & op(e0, e2) = all_38_1 & $i(all_38_0) &
% 21.47/3.70 | $i(all_38_1) & ( ~ (all_38_0 = e3) | ~ (all_38_1 = e1))
% 21.47/3.70 |
% 21.47/3.70 | ALPHA: (65) implies:
% 21.47/3.70 | (66) op(e0, e2) = all_38_1
% 21.47/3.70 |
% 21.47/3.70 | DELTA: instantiating (18) with fresh symbols all_46_0, all_46_1 gives:
% 21.47/3.70 | (67) op(all_46_1, e2) = all_46_0 & op(e3, e2) = all_46_1 & $i(all_46_0) &
% 21.47/3.70 | $i(all_46_1) & ( ~ (all_46_0 = e0) | ~ (all_46_1 = e1))
% 21.47/3.70 |
% 21.47/3.70 | ALPHA: (67) implies:
% 21.47/3.70 | (68) op(e3, e2) = all_46_1
% 21.47/3.70 |
% 21.47/3.70 | DELTA: instantiating (3) with fresh symbols all_52_0, all_52_1, all_52_2,
% 21.47/3.70 | all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9,
% 21.47/3.70 | all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15 gives:
% 21.47/3.71 | (69) ~ (all_52_0 = all_52_1) & ~ (all_52_0 = all_52_2) & ~ (all_52_0 =
% 21.47/3.71 | all_52_3) & ~ (all_52_0 = all_52_4) & ~ (all_52_0 = all_52_8) & ~
% 21.47/3.71 | (all_52_0 = all_52_12) & ~ (all_52_1 = all_52_2) & ~ (all_52_1 =
% 21.47/3.71 | all_52_3) & ~ (all_52_1 = all_52_5) & ~ (all_52_1 = all_52_9) & ~
% 21.47/3.71 | (all_52_1 = all_52_13) & ~ (all_52_2 = all_52_3) & ~ (all_52_2 =
% 21.47/3.71 | all_52_6) & ~ (all_52_2 = all_52_10) & ~ (all_52_2 = all_52_14) &
% 21.47/3.71 | ~ (all_52_3 = all_52_7) & ~ (all_52_3 = all_52_11) & ~ (all_52_3 =
% 21.47/3.71 | all_52_15) & ~ (all_52_4 = all_52_5) & ~ (all_52_4 = all_52_6) &
% 21.47/3.71 | ~ (all_52_4 = all_52_7) & ~ (all_52_4 = all_52_8) & ~ (all_52_4 =
% 21.84/3.71 | all_52_12) & ~ (all_52_5 = all_52_6) & ~ (all_52_5 = all_52_7) &
% 21.84/3.71 | ~ (all_52_5 = all_52_9) & ~ (all_52_5 = all_52_13) & ~ (all_52_6 =
% 21.84/3.71 | all_52_7) & ~ (all_52_6 = all_52_10) & ~ (all_52_6 = all_52_14) &
% 21.84/3.71 | ~ (all_52_7 = all_52_11) & ~ (all_52_7 = all_52_15) & ~ (all_52_8 =
% 21.84/3.71 | all_52_9) & ~ (all_52_8 = all_52_10) & ~ (all_52_8 = all_52_11) &
% 21.84/3.71 | ~ (all_52_8 = all_52_12) & ~ (all_52_9 = all_52_10) & ~ (all_52_9 =
% 21.84/3.71 | all_52_11) & ~ (all_52_9 = all_52_13) & ~ (all_52_10 = all_52_11)
% 21.84/3.71 | & ~ (all_52_10 = all_52_14) & ~ (all_52_11 = all_52_15) & ~
% 21.84/3.71 | (all_52_12 = all_52_13) & ~ (all_52_12 = all_52_14) & ~ (all_52_12 =
% 21.84/3.71 | all_52_15) & ~ (all_52_13 = all_52_14) & ~ (all_52_13 = all_52_15)
% 21.84/3.71 | & ~ (all_52_14 = all_52_15) & op(e3, e3) = all_52_0 & op(e3, e2) =
% 21.84/3.71 | all_52_4 & op(e3, e1) = all_52_8 & op(e3, e0) = all_52_12 & op(e2, e3)
% 21.84/3.71 | = all_52_1 & op(e2, e2) = all_52_5 & op(e2, e1) = all_52_9 & op(e2,
% 21.84/3.71 | e0) = all_52_13 & op(e1, e3) = all_52_2 & op(e1, e2) = all_52_6 &
% 21.84/3.71 | op(e1, e1) = all_52_10 & op(e1, e0) = all_52_14 & op(e0, e3) =
% 21.84/3.71 | all_52_3 & op(e0, e2) = all_52_7 & op(e0, e1) = all_52_11 & op(e0, e0)
% 21.84/3.71 | = all_52_15 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) &
% 21.84/3.71 | $i(all_52_3) & $i(all_52_4) & $i(all_52_5) & $i(all_52_6) &
% 21.84/3.71 | $i(all_52_7) & $i(all_52_8) & $i(all_52_9) & $i(all_52_10) &
% 21.84/3.71 | $i(all_52_11) & $i(all_52_12) & $i(all_52_13) & $i(all_52_14) &
% 21.84/3.71 | $i(all_52_15)
% 21.84/3.71 |
% 21.84/3.71 | ALPHA: (69) implies:
% 21.84/3.71 | (70) ~ (all_52_14 = all_52_15)
% 21.84/3.71 | (71) ~ (all_52_12 = all_52_15)
% 21.84/3.71 | (72) ~ (all_52_12 = all_52_14)
% 21.84/3.71 | (73) ~ (all_52_10 = all_52_11)
% 21.84/3.71 | (74) ~ (all_52_9 = all_52_11)
% 21.84/3.71 | (75) ~ (all_52_7 = all_52_11)
% 21.84/3.71 | (76) ~ (all_52_6 = all_52_10)
% 21.84/3.71 | (77) ~ (all_52_5 = all_52_6)
% 21.84/3.71 | (78) ~ (all_52_4 = all_52_12)
% 21.84/3.71 | (79) ~ (all_52_4 = all_52_7)
% 21.84/3.71 | (80) ~ (all_52_4 = all_52_6)
% 21.84/3.71 | (81) ~ (all_52_4 = all_52_5)
% 21.84/3.71 | (82) ~ (all_52_3 = all_52_7)
% 21.84/3.71 | (83) ~ (all_52_2 = all_52_10)
% 21.84/3.71 | (84) ~ (all_52_1 = all_52_9)
% 21.84/3.71 | (85) ~ (all_52_1 = all_52_5)
% 21.84/3.71 | (86) ~ (all_52_1 = all_52_3)
% 21.84/3.71 | (87) ~ (all_52_1 = all_52_2)
% 21.84/3.71 | (88) ~ (all_52_0 = all_52_12)
% 21.84/3.71 | (89) ~ (all_52_0 = all_52_8)
% 21.84/3.71 | (90) ~ (all_52_0 = all_52_4)
% 21.84/3.71 | (91) ~ (all_52_0 = all_52_3)
% 21.84/3.71 | (92) ~ (all_52_0 = all_52_1)
% 21.84/3.71 | (93) op(e0, e0) = all_52_15
% 21.84/3.71 | (94) op(e0, e1) = all_52_11
% 21.84/3.71 | (95) op(e0, e2) = all_52_7
% 21.84/3.71 | (96) op(e0, e3) = all_52_3
% 21.84/3.71 | (97) op(e1, e0) = all_52_14
% 21.84/3.71 | (98) op(e1, e1) = all_52_10
% 21.84/3.71 | (99) op(e1, e2) = all_52_6
% 21.84/3.71 | (100) op(e1, e3) = all_52_2
% 21.84/3.71 | (101) op(e2, e1) = all_52_9
% 21.84/3.71 | (102) op(e2, e2) = all_52_5
% 21.84/3.71 | (103) op(e2, e3) = all_52_1
% 21.84/3.71 | (104) op(e3, e0) = all_52_12
% 21.84/3.71 | (105) op(e3, e1) = all_52_8
% 21.84/3.71 | (106) op(e3, e2) = all_52_4
% 21.84/3.71 | (107) op(e3, e3) = all_52_0
% 21.84/3.71 |
% 21.84/3.71 | DELTA: instantiating (1) with fresh symbols all_54_0, all_54_1, all_54_2,
% 21.84/3.71 | all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9,
% 21.84/3.71 | all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives:
% 21.84/3.72 | (108) op(e3, e3) = all_54_0 & op(e3, e2) = all_54_1 & op(e3, e1) = all_54_2
% 21.84/3.72 | & op(e3, e0) = all_54_3 & op(e2, e3) = all_54_4 & op(e2, e2) =
% 21.84/3.72 | all_54_5 & op(e2, e1) = all_54_6 & op(e2, e0) = all_54_7 & op(e1, e3)
% 21.84/3.72 | = all_54_8 & op(e1, e2) = all_54_9 & op(e1, e1) = all_54_10 & op(e1,
% 21.84/3.72 | e0) = all_54_11 & op(e0, e3) = all_54_12 & op(e0, e2) = all_54_13 &
% 21.84/3.72 | op(e0, e1) = all_54_14 & op(e0, e0) = all_54_15 & $i(all_54_0) &
% 21.84/3.72 | $i(all_54_1) & $i(all_54_2) & $i(all_54_3) & $i(all_54_4) &
% 21.84/3.72 | $i(all_54_5) & $i(all_54_6) & $i(all_54_7) & $i(all_54_8) &
% 21.84/3.72 | $i(all_54_9) & $i(all_54_10) & $i(all_54_11) & $i(all_54_12) &
% 21.84/3.72 | $i(all_54_13) & $i(all_54_14) & $i(all_54_15) & (all_54_0 = e3 |
% 21.84/3.72 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0) & (all_54_1 = e3 |
% 21.84/3.72 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0) & (all_54_2 = e3 |
% 21.84/3.72 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0) & (all_54_3 = e3 |
% 21.84/3.72 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0) & (all_54_4 = e3 |
% 21.84/3.72 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0) & (all_54_5 = e3 |
% 21.84/3.72 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0) & (all_54_6 = e3 |
% 21.84/3.72 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0) & (all_54_7 = e3 |
% 21.84/3.72 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0) & (all_54_8 = e3 |
% 21.84/3.72 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0) & (all_54_9 = e3 |
% 21.84/3.72 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0) & (all_54_10 = e3 |
% 21.84/3.72 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0) & (all_54_11 = e3
% 21.84/3.72 | | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0) & (all_54_12 =
% 21.84/3.72 | e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0) & (all_54_13
% 21.84/3.72 | = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0) &
% 21.84/3.72 | (all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0) &
% 21.84/3.72 | (all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0)
% 21.84/3.72 |
% 21.84/3.72 | ALPHA: (108) implies:
% 21.84/3.72 | (109) op(e0, e0) = all_54_15
% 21.84/3.72 | (110) op(e0, e1) = all_54_14
% 21.84/3.72 | (111) op(e0, e2) = all_54_13
% 21.84/3.72 | (112) op(e0, e3) = all_54_12
% 21.84/3.72 | (113) op(e1, e0) = all_54_11
% 21.84/3.72 | (114) op(e1, e1) = all_54_10
% 21.84/3.72 | (115) op(e1, e2) = all_54_9
% 21.84/3.72 | (116) op(e1, e3) = all_54_8
% 21.84/3.72 | (117) op(e2, e1) = all_54_6
% 21.84/3.72 | (118) op(e2, e2) = all_54_5
% 21.84/3.72 | (119) op(e2, e3) = all_54_4
% 21.84/3.72 | (120) op(e3, e0) = all_54_3
% 21.84/3.72 | (121) op(e3, e1) = all_54_2
% 21.84/3.72 | (122) op(e3, e2) = all_54_1
% 21.84/3.72 | (123) op(e3, e3) = all_54_0
% 21.84/3.72 | (124) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 21.84/3.72 | (125) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 21.84/3.72 | (126) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 21.84/3.72 | (127) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 21.84/3.72 | (128) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 21.84/3.72 | (129) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 21.84/3.72 |
% 21.84/3.72 | DELTA: instantiating (2) with fresh symbols all_56_0, all_56_1, all_56_2,
% 21.84/3.72 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9,
% 21.84/3.72 | all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15 gives:
% 21.84/3.72 | (130) op(e3, e3) = all_56_0 & op(e3, e2) = all_56_1 & op(e3, e1) = all_56_4
% 21.84/3.72 | & op(e3, e0) = all_56_9 & op(e2, e3) = all_56_2 & op(e2, e2) =
% 21.84/3.72 | all_56_3 & op(e2, e1) = all_56_5 & op(e2, e0) = all_56_10 & op(e1,
% 21.84/3.72 | e3) = all_56_6 & op(e1, e2) = all_56_7 & op(e1, e1) = all_56_8 &
% 21.84/3.72 | op(e1, e0) = all_56_11 & op(e0, e3) = all_56_12 & op(e0, e2) =
% 21.84/3.72 | all_56_13 & op(e0, e1) = all_56_14 & op(e0, e0) = all_56_15 &
% 21.84/3.72 | $i(all_56_0) & $i(all_56_1) & $i(all_56_2) & $i(all_56_3) &
% 21.84/3.72 | $i(all_56_4) & $i(all_56_5) & $i(all_56_6) & $i(all_56_7) &
% 21.84/3.72 | $i(all_56_8) & $i(all_56_9) & $i(all_56_10) & $i(all_56_11) &
% 21.84/3.72 | $i(all_56_12) & $i(all_56_13) & $i(all_56_14) & $i(all_56_15) &
% 21.84/3.72 | (all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3) &
% 21.84/3.72 | (all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3) &
% 21.84/3.72 | (all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2) &
% 21.84/3.72 | (all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2) &
% 21.84/3.72 | (all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1) &
% 21.84/3.72 | (all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1) &
% 21.84/3.72 | (all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0) &
% 21.84/3.72 | (all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0) &
% 21.84/3.72 | (all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3) &
% 21.84/3.72 | (all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2) &
% 21.84/3.72 | (all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1) &
% 21.84/3.72 | (all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0) &
% 21.84/3.72 | (all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3) &
% 21.84/3.72 | (all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2) &
% 21.84/3.72 | (all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1) &
% 21.84/3.72 | (all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0) &
% 21.84/3.72 | (all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3) &
% 21.84/3.72 | (all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2) &
% 21.84/3.72 | (all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1) &
% 21.84/3.73 | (all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0) &
% 21.84/3.73 | (all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3) &
% 21.84/3.73 | (all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2) &
% 21.84/3.73 | (all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1) &
% 21.84/3.73 | (all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0) &
% 21.84/3.73 | (all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3) &
% 21.84/3.73 | (all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2) &
% 21.84/3.73 | (all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1) &
% 21.84/3.73 | (all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3) &
% 21.84/3.73 | (all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2) &
% 21.84/3.73 | (all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1) &
% 21.84/3.73 | (all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0)
% 21.84/3.73 | & (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)))
% 21.84/3.73 |
% 21.84/3.73 | ALPHA: (130) implies:
% 21.84/3.73 | (131) op(e0, e0) = all_56_15
% 21.84/3.73 | (132) op(e0, e1) = all_56_14
% 21.84/3.73 | (133) op(e0, e2) = all_56_13
% 21.84/3.73 | (134) op(e0, e3) = all_56_12
% 21.84/3.73 | (135) op(e1, e0) = all_56_11
% 21.84/3.73 | (136) op(e1, e1) = all_56_8
% 21.84/3.73 | (137) op(e1, e2) = all_56_7
% 21.84/3.73 | (138) op(e1, e3) = all_56_6
% 21.84/3.73 | (139) op(e2, e1) = all_56_5
% 21.84/3.73 | (140) op(e2, e2) = all_56_3
% 21.84/3.73 | (141) op(e2, e3) = all_56_2
% 21.84/3.73 | (142) op(e3, e0) = all_56_9
% 21.84/3.73 | (143) op(e3, e1) = all_56_4
% 21.84/3.73 | (144) op(e3, e2) = all_56_1
% 21.84/3.73 | (145) op(e3, e3) = all_56_0
% 21.84/3.73 | (146) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1
% 21.84/3.73 | (147) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3
% 21.84/3.73 | (148) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0
% 21.84/3.73 | (149) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2
% 21.84/3.73 | (150) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3
% 21.84/3.73 | (151) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0
% 21.84/3.73 | (152) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3
% 21.84/3.73 | (153) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1
% 21.84/3.73 |
% 21.84/3.73 | GROUND_INST: instantiating (function-axioms) with all_52_15, all_54_15, e0,
% 21.84/3.73 | e0, simplifying with (93), (109) gives:
% 21.84/3.73 | (154) all_54_15 = all_52_15
% 21.84/3.73 |
% 21.84/3.73 | GROUND_INST: instantiating (function-axioms) with all_54_15, all_56_15, e0,
% 21.84/3.73 | e0, simplifying with (109), (131) gives:
% 21.84/3.73 | (155) all_56_15 = all_54_15
% 21.84/3.73 |
% 21.84/3.73 | GROUND_INST: instantiating (function-axioms) with e0, all_56_15, e0, e0,
% 21.84/3.73 | simplifying with (9), (131) gives:
% 21.84/3.73 | (156) all_56_15 = e0
% 21.84/3.73 |
% 21.84/3.73 | GROUND_INST: instantiating (function-axioms) with all_52_11, all_54_14, e1,
% 21.84/3.73 | e0, simplifying with (94), (110) gives:
% 21.84/3.73 | (157) all_54_14 = all_52_11
% 21.84/3.73 |
% 21.84/3.73 | GROUND_INST: instantiating (function-axioms) with all_54_14, all_56_14, e1,
% 21.84/3.73 | e0, simplifying with (110), (132) gives:
% 21.84/3.73 | (158) all_56_14 = all_54_14
% 21.84/3.73 |
% 21.84/3.73 | GROUND_INST: instantiating (function-axioms) with all_30_1, all_56_14, e1, e0,
% 21.84/3.73 | simplifying with (58), (132) gives:
% 21.84/3.73 | (159) all_56_14 = all_30_1
% 21.84/3.73 |
% 21.84/3.73 | GROUND_INST: instantiating (function-axioms) with all_38_1, all_54_13, e2, e0,
% 21.84/3.73 | simplifying with (66), (111) gives:
% 21.84/3.73 | (160) all_54_13 = all_38_1
% 21.84/3.73 |
% 21.84/3.73 | GROUND_INST: instantiating (function-axioms) with all_54_13, all_56_13, e2,
% 21.84/3.73 | e0, simplifying with (111), (133) gives:
% 21.84/3.73 | (161) all_56_13 = all_54_13
% 21.84/3.73 |
% 21.84/3.73 | GROUND_INST: instantiating (function-axioms) with all_52_7, all_56_13, e2, e0,
% 21.84/3.73 | simplifying with (95), (133) gives:
% 21.84/3.73 | (162) all_56_13 = all_52_7
% 21.84/3.73 |
% 21.84/3.73 | GROUND_INST: instantiating (function-axioms) with all_10_1, all_56_13, e2, e0,
% 21.84/3.73 | simplifying with (42), (133) gives:
% 21.84/3.73 | (163) all_56_13 = all_10_1
% 21.84/3.73 |
% 21.84/3.73 | GROUND_INST: instantiating (function-axioms) with all_16_1, all_54_12, e3, e0,
% 21.84/3.73 | simplifying with (48), (112) gives:
% 21.84/3.73 | (164) all_54_12 = all_16_1
% 21.84/3.73 |
% 21.84/3.73 | GROUND_INST: instantiating (function-axioms) with all_54_12, all_56_12, e3,
% 21.84/3.73 | e0, simplifying with (112), (134) gives:
% 21.84/3.73 | (165) all_56_12 = all_54_12
% 21.84/3.73 |
% 21.84/3.73 | GROUND_INST: instantiating (function-axioms) with all_52_3, all_56_12, e3, e0,
% 21.84/3.73 | simplifying with (96), (134) gives:
% 21.84/3.73 | (166) all_56_12 = all_52_3
% 21.84/3.73 |
% 21.84/3.73 | GROUND_INST: instantiating (function-axioms) with all_34_1, all_56_12, e3, e0,
% 21.84/3.73 | simplifying with (62), (134) gives:
% 21.84/3.73 | (167) all_56_12 = all_34_1
% 21.84/3.73 |
% 21.84/3.73 | GROUND_INST: instantiating (function-axioms) with all_32_1, all_54_11, e0, e1,
% 21.84/3.73 | simplifying with (60), (113) gives:
% 21.84/3.73 | (168) all_54_11 = all_32_1
% 21.84/3.73 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_20_1, all_54_11, e0, e1,
% 21.84/3.74 | simplifying with (50), (113) gives:
% 21.84/3.74 | (169) all_54_11 = all_20_1
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_54_11, all_56_11, e0,
% 21.84/3.74 | e1, simplifying with (113), (135) gives:
% 21.84/3.74 | (170) all_56_11 = all_54_11
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_52_14, all_56_11, e0,
% 21.84/3.74 | e1, simplifying with (97), (135) gives:
% 21.84/3.74 | (171) all_56_11 = all_52_14
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_54_10, all_56_8, e1, e1,
% 21.84/3.74 | simplifying with (114), (136) gives:
% 21.84/3.74 | (172) all_56_8 = all_54_10
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_52_10, all_56_8, e1, e1,
% 21.84/3.74 | simplifying with (98), (136) gives:
% 21.84/3.74 | (173) all_56_8 = all_52_10
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with e1, all_56_8, e1, e1,
% 21.84/3.74 | simplifying with (10), (136) gives:
% 21.84/3.74 | (174) all_56_8 = e1
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_52_6, all_54_9, e2, e1,
% 21.84/3.74 | simplifying with (99), (115) gives:
% 21.84/3.74 | (175) all_54_9 = all_52_6
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_8_1, all_54_9, e2, e1,
% 21.84/3.74 | simplifying with (38), (115) gives:
% 21.84/3.74 | (176) all_54_9 = all_8_1
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_54_9, all_56_7, e2, e1,
% 21.84/3.74 | simplifying with (115), (137) gives:
% 21.84/3.74 | (177) all_56_7 = all_54_9
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_4_1, all_56_7, e2, e1,
% 21.84/3.74 | simplifying with (31), (137) gives:
% 21.84/3.74 | (178) all_56_7 = all_4_1
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_52_2, all_54_8, e3, e1,
% 21.84/3.74 | simplifying with (100), (116) gives:
% 21.84/3.74 | (179) all_54_8 = all_52_2
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_54_8, all_56_6, e3, e1,
% 21.84/3.74 | simplifying with (116), (138) gives:
% 21.84/3.74 | (180) all_56_6 = all_54_8
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_14_1, all_56_6, e3, e1,
% 21.84/3.74 | simplifying with (46), (138) gives:
% 21.84/3.74 | (181) all_56_6 = all_14_1
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_36_1, all_52_9, e1, e2,
% 21.84/3.74 | simplifying with (64), (101) gives:
% 21.84/3.74 | (182) all_52_9 = all_36_1
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_52_9, all_54_6, e1, e2,
% 21.84/3.74 | simplifying with (101), (117) gives:
% 21.84/3.74 | (183) all_54_6 = all_52_9
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_54_6, all_56_5, e1, e2,
% 21.84/3.74 | simplifying with (117), (139) gives:
% 21.84/3.74 | (184) all_56_5 = all_54_6
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_12_1, all_56_5, e1, e2,
% 21.84/3.74 | simplifying with (44), (139) gives:
% 21.84/3.74 | (185) all_56_5 = all_12_1
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_54_5, all_56_3, e2, e2,
% 21.84/3.74 | simplifying with (118), (140) gives:
% 21.84/3.74 | (186) all_56_3 = all_54_5
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_52_5, all_56_3, e2, e2,
% 21.84/3.74 | simplifying with (102), (140) gives:
% 21.84/3.74 | (187) all_56_3 = all_52_5
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with e2, all_56_3, e2, e2,
% 21.84/3.74 | simplifying with (11), (140) gives:
% 21.84/3.74 | (188) all_56_3 = e2
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_6_1, all_54_4, e3, e2,
% 21.84/3.74 | simplifying with (35), (119) gives:
% 21.84/3.74 | (189) all_54_4 = all_6_1
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_54_4, all_56_2, e3, e2,
% 21.84/3.74 | simplifying with (119), (141) gives:
% 21.84/3.74 | (190) all_56_2 = all_54_4
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_52_1, all_56_2, e3, e2,
% 21.84/3.74 | simplifying with (103), (141) gives:
% 21.84/3.74 | (191) all_56_2 = all_52_1
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_22_1, all_54_3, e0, e3,
% 21.84/3.74 | simplifying with (52), (120) gives:
% 21.84/3.74 | (192) all_54_3 = all_22_1
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_54_3, all_56_9, e0, e3,
% 21.84/3.74 | simplifying with (120), (142) gives:
% 21.84/3.74 | (193) all_56_9 = all_54_3
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_52_12, all_56_9, e0, e3,
% 21.84/3.74 | simplifying with (104), (142) gives:
% 21.84/3.74 | (194) all_56_9 = all_52_12
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_28_1, all_54_2, e1, e3,
% 21.84/3.74 | simplifying with (56), (121) gives:
% 21.84/3.74 | (195) all_54_2 = all_28_1
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_54_2, all_56_4, e1, e3,
% 21.84/3.74 | simplifying with (121), (143) gives:
% 21.84/3.74 | (196) all_56_4 = all_54_2
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_52_8, all_56_4, e1, e3,
% 21.84/3.74 | simplifying with (105), (143) gives:
% 21.84/3.74 | (197) all_56_4 = all_52_8
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_46_1, all_54_1, e2, e3,
% 21.84/3.74 | simplifying with (68), (122) gives:
% 21.84/3.74 | (198) all_54_1 = all_46_1
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_26_1, all_54_1, e2, e3,
% 21.84/3.74 | simplifying with (54), (122) gives:
% 21.84/3.74 | (199) all_54_1 = all_26_1
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_54_1, all_56_1, e2, e3,
% 21.84/3.74 | simplifying with (122), (144) gives:
% 21.84/3.74 | (200) all_56_1 = all_54_1
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_52_4, all_56_1, e2, e3,
% 21.84/3.74 | simplifying with (106), (144) gives:
% 21.84/3.74 | (201) all_56_1 = all_52_4
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_52_0, all_54_0, e3, e3,
% 21.84/3.74 | simplifying with (107), (123) gives:
% 21.84/3.74 | (202) all_54_0 = all_52_0
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with all_54_0, all_56_0, e3, e3,
% 21.84/3.74 | simplifying with (123), (145) gives:
% 21.84/3.74 | (203) all_56_0 = all_54_0
% 21.84/3.74 |
% 21.84/3.74 | GROUND_INST: instantiating (function-axioms) with e3, all_56_0, e3, e3,
% 21.84/3.74 | simplifying with (12), (145) gives:
% 21.84/3.74 | (204) all_56_0 = e3
% 21.84/3.74 |
% 21.84/3.74 | COMBINE_EQS: (203), (204) imply:
% 21.84/3.74 | (205) all_54_0 = e3
% 21.84/3.74 |
% 21.84/3.74 | SIMP: (205) implies:
% 21.84/3.74 | (206) all_54_0 = e3
% 21.84/3.74 |
% 21.84/3.74 | COMBINE_EQS: (200), (201) imply:
% 21.84/3.74 | (207) all_54_1 = all_52_4
% 21.84/3.74 |
% 21.84/3.74 | SIMP: (207) implies:
% 21.84/3.74 | (208) all_54_1 = all_52_4
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (190), (191) imply:
% 21.84/3.75 | (209) all_54_4 = all_52_1
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (209) implies:
% 21.84/3.75 | (210) all_54_4 = all_52_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (186), (188) imply:
% 21.84/3.75 | (211) all_54_5 = e2
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (186), (187) imply:
% 21.84/3.75 | (212) all_54_5 = all_52_5
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (196), (197) imply:
% 21.84/3.75 | (213) all_54_2 = all_52_8
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (213) implies:
% 21.84/3.75 | (214) all_54_2 = all_52_8
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (184), (185) imply:
% 21.84/3.75 | (215) all_54_6 = all_12_1
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (215) implies:
% 21.84/3.75 | (216) all_54_6 = all_12_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (180), (181) imply:
% 21.84/3.75 | (217) all_54_8 = all_14_1
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (217) implies:
% 21.84/3.75 | (218) all_54_8 = all_14_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (177), (178) imply:
% 21.84/3.75 | (219) all_54_9 = all_4_1
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (219) implies:
% 21.84/3.75 | (220) all_54_9 = all_4_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (172), (174) imply:
% 21.84/3.75 | (221) all_54_10 = e1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (172), (173) imply:
% 21.84/3.75 | (222) all_54_10 = all_52_10
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (193), (194) imply:
% 21.84/3.75 | (223) all_54_3 = all_52_12
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (223) implies:
% 21.84/3.75 | (224) all_54_3 = all_52_12
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (170), (171) imply:
% 21.84/3.75 | (225) all_54_11 = all_52_14
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (225) implies:
% 21.84/3.75 | (226) all_54_11 = all_52_14
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (165), (166) imply:
% 21.84/3.75 | (227) all_54_12 = all_52_3
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (227) implies:
% 21.84/3.75 | (228) all_54_12 = all_52_3
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (166), (167) imply:
% 21.84/3.75 | (229) all_52_3 = all_34_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (161), (162) imply:
% 21.84/3.75 | (230) all_54_13 = all_52_7
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (230) implies:
% 21.84/3.75 | (231) all_54_13 = all_52_7
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (162), (163) imply:
% 21.84/3.75 | (232) all_52_7 = all_10_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (158), (159) imply:
% 21.84/3.75 | (233) all_54_14 = all_30_1
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (233) implies:
% 21.84/3.75 | (234) all_54_14 = all_30_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (155), (156) imply:
% 21.84/3.75 | (235) all_54_15 = e0
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (235) implies:
% 21.84/3.75 | (236) all_54_15 = e0
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (202), (206) imply:
% 21.84/3.75 | (237) all_52_0 = e3
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (199), (208) imply:
% 21.84/3.75 | (238) all_52_4 = all_26_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (198), (208) imply:
% 21.84/3.75 | (239) all_52_4 = all_46_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (195), (214) imply:
% 21.84/3.75 | (240) all_52_8 = all_28_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (192), (224) imply:
% 21.84/3.75 | (241) all_52_12 = all_22_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (189), (210) imply:
% 21.84/3.75 | (242) all_52_1 = all_6_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (211), (212) imply:
% 21.84/3.75 | (243) all_52_5 = e2
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (243) implies:
% 21.84/3.75 | (244) all_52_5 = e2
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (183), (216) imply:
% 21.84/3.75 | (245) all_52_9 = all_12_1
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (245) implies:
% 21.84/3.75 | (246) all_52_9 = all_12_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (179), (218) imply:
% 21.84/3.75 | (247) all_52_2 = all_14_1
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (247) implies:
% 21.84/3.75 | (248) all_52_2 = all_14_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (175), (176) imply:
% 21.84/3.75 | (249) all_52_6 = all_8_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (175), (220) imply:
% 21.84/3.75 | (250) all_52_6 = all_4_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (221), (222) imply:
% 21.84/3.75 | (251) all_52_10 = e1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (169), (226) imply:
% 21.84/3.75 | (252) all_52_14 = all_20_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (168), (226) imply:
% 21.84/3.75 | (253) all_52_14 = all_32_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (164), (228) imply:
% 21.84/3.75 | (254) all_52_3 = all_16_1
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (254) implies:
% 21.84/3.75 | (255) all_52_3 = all_16_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (160), (231) imply:
% 21.84/3.75 | (256) all_52_7 = all_38_1
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (256) implies:
% 21.84/3.75 | (257) all_52_7 = all_38_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (157), (234) imply:
% 21.84/3.75 | (258) all_52_11 = all_30_1
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (258) implies:
% 21.84/3.75 | (259) all_52_11 = all_30_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (154), (236) imply:
% 21.84/3.75 | (260) all_52_15 = e0
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (260) implies:
% 21.84/3.75 | (261) all_52_15 = e0
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (229), (255) imply:
% 21.84/3.75 | (262) all_34_1 = all_16_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (238), (239) imply:
% 21.84/3.75 | (263) all_46_1 = all_26_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (249), (250) imply:
% 21.84/3.75 | (264) all_8_1 = all_4_1
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (264) implies:
% 21.84/3.75 | (265) all_8_1 = all_4_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (232), (257) imply:
% 21.84/3.75 | (266) all_38_1 = all_10_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (182), (246) imply:
% 21.84/3.75 | (267) all_36_1 = all_12_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (252), (253) imply:
% 21.84/3.75 | (268) all_32_1 = all_20_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (160), (266) imply:
% 21.84/3.75 | (269) all_54_13 = all_10_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (166), (255) imply:
% 21.84/3.75 | (270) all_56_12 = all_16_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (171), (252) imply:
% 21.84/3.75 | (271) all_56_11 = all_20_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (197), (240) imply:
% 21.84/3.75 | (272) all_56_4 = all_28_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (191), (242) imply:
% 21.84/3.75 | (273) all_56_2 = all_6_1
% 21.84/3.75 |
% 21.84/3.75 | COMBINE_EQS: (201), (238) imply:
% 21.84/3.75 | (274) all_56_1 = all_26_1
% 21.84/3.75 |
% 21.84/3.75 | REDUCE: (92), (237), (242) imply:
% 21.84/3.75 | (275) ~ (all_6_1 = e3)
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (275) implies:
% 21.84/3.75 | (276) ~ (all_6_1 = e3)
% 21.84/3.75 |
% 21.84/3.75 | REDUCE: (91), (237), (255) imply:
% 21.84/3.75 | (277) ~ (all_16_1 = e3)
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (277) implies:
% 21.84/3.75 | (278) ~ (all_16_1 = e3)
% 21.84/3.75 |
% 21.84/3.75 | REDUCE: (90), (237), (238) imply:
% 21.84/3.75 | (279) ~ (all_26_1 = e3)
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (279) implies:
% 21.84/3.75 | (280) ~ (all_26_1 = e3)
% 21.84/3.75 |
% 21.84/3.75 | REDUCE: (89), (237), (240) imply:
% 21.84/3.75 | (281) ~ (all_28_1 = e3)
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (281) implies:
% 21.84/3.75 | (282) ~ (all_28_1 = e3)
% 21.84/3.75 |
% 21.84/3.75 | REDUCE: (88), (237), (241) imply:
% 21.84/3.75 | (283) ~ (all_22_1 = e3)
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (283) implies:
% 21.84/3.75 | (284) ~ (all_22_1 = e3)
% 21.84/3.75 |
% 21.84/3.75 | REDUCE: (87), (242), (248) imply:
% 21.84/3.75 | (285) ~ (all_14_1 = all_6_1)
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (285) implies:
% 21.84/3.75 | (286) ~ (all_14_1 = all_6_1)
% 21.84/3.75 |
% 21.84/3.75 | REDUCE: (86), (242), (255) imply:
% 21.84/3.75 | (287) ~ (all_16_1 = all_6_1)
% 21.84/3.75 |
% 21.84/3.75 | SIMP: (287) implies:
% 21.84/3.75 | (288) ~ (all_16_1 = all_6_1)
% 21.84/3.75 |
% 21.84/3.75 | REDUCE: (85), (242), (244) imply:
% 21.84/3.75 | (289) ~ (all_6_1 = e2)
% 21.84/3.75 |
% 21.84/3.76 | REDUCE: (84), (242), (246) imply:
% 21.84/3.76 | (290) ~ (all_12_1 = all_6_1)
% 21.84/3.76 |
% 21.84/3.76 | SIMP: (290) implies:
% 21.84/3.76 | (291) ~ (all_12_1 = all_6_1)
% 21.84/3.76 |
% 21.84/3.76 | REDUCE: (83), (248), (251) imply:
% 21.84/3.76 | (292) ~ (all_14_1 = e1)
% 21.84/3.76 |
% 21.84/3.76 | REDUCE: (82), (232), (255) imply:
% 21.84/3.76 | (293) ~ (all_16_1 = all_10_1)
% 21.84/3.76 |
% 21.84/3.76 | REDUCE: (81), (238), (244) imply:
% 21.84/3.76 | (294) ~ (all_26_1 = e2)
% 21.84/3.76 |
% 21.84/3.76 | REDUCE: (80), (238), (250) imply:
% 21.84/3.76 | (295) ~ (all_26_1 = all_4_1)
% 21.84/3.76 |
% 21.84/3.76 | REDUCE: (79), (232), (238) imply:
% 21.84/3.76 | (296) ~ (all_26_1 = all_10_1)
% 21.84/3.76 |
% 21.84/3.76 | REDUCE: (78), (238), (241) imply:
% 21.84/3.76 | (297) ~ (all_26_1 = all_22_1)
% 21.84/3.76 |
% 21.84/3.76 | REDUCE: (77), (244), (250) imply:
% 21.84/3.76 | (298) ~ (all_4_1 = e2)
% 21.84/3.76 |
% 21.84/3.76 | SIMP: (298) implies:
% 21.84/3.76 | (299) ~ (all_4_1 = e2)
% 21.84/3.76 |
% 21.84/3.76 | REDUCE: (76), (250), (251) imply:
% 21.84/3.76 | (300) ~ (all_4_1 = e1)
% 21.84/3.76 |
% 21.84/3.76 | REDUCE: (75), (232), (259) imply:
% 21.84/3.76 | (301) ~ (all_30_1 = all_10_1)
% 21.84/3.76 |
% 21.84/3.76 | SIMP: (301) implies:
% 21.84/3.76 | (302) ~ (all_30_1 = all_10_1)
% 21.84/3.76 |
% 21.84/3.76 | REDUCE: (74), (246), (259) imply:
% 21.84/3.76 | (303) ~ (all_30_1 = all_12_1)
% 21.84/3.76 |
% 21.84/3.76 | SIMP: (303) implies:
% 21.84/3.76 | (304) ~ (all_30_1 = all_12_1)
% 21.84/3.76 |
% 21.84/3.76 | REDUCE: (73), (251), (259) imply:
% 21.84/3.76 | (305) ~ (all_30_1 = e1)
% 21.84/3.76 |
% 21.84/3.76 | SIMP: (305) implies:
% 21.84/3.76 | (306) ~ (all_30_1 = e1)
% 21.84/3.76 |
% 21.84/3.76 | REDUCE: (72), (241), (252) imply:
% 21.84/3.76 | (307) ~ (all_22_1 = all_20_1)
% 21.84/3.76 |
% 21.84/3.76 | REDUCE: (71), (241), (261) imply:
% 21.84/3.76 | (308) ~ (all_22_1 = e0)
% 21.84/3.76 |
% 21.84/3.76 | REDUCE: (70), (252), (261) imply:
% 21.84/3.76 | (309) ~ (all_20_1 = e0)
% 21.84/3.76 |
% 21.84/3.76 | REDUCE: (39), (265) imply:
% 21.84/3.76 | (310) op(all_4_1, e2) = all_8_0
% 21.84/3.76 |
% 21.84/3.76 | GROUND_INST: instantiating (function-axioms) with all_4_0, all_8_0, e2,
% 21.84/3.76 | all_4_1, simplifying with (32), (310) gives:
% 21.84/3.76 | (311) all_8_0 = all_4_0
% 21.84/3.76 |
% 21.84/3.76 | BETA: splitting (33) gives:
% 21.84/3.76 |
% 21.84/3.76 | Case 1:
% 21.84/3.76 | |
% 21.84/3.76 | | (312) ~ (all_4_0 = e3)
% 21.84/3.76 | |
% 21.84/3.76 | | BETA: splitting (36) gives:
% 21.84/3.76 | |
% 21.84/3.76 | | Case 1:
% 21.84/3.76 | | |
% 21.84/3.76 | | | (313) ~ (all_6_1 = e1)
% 21.84/3.76 | | |
% 21.84/3.76 | | | BETA: splitting (127) gives:
% 21.84/3.76 | | |
% 21.84/3.76 | | | Case 1:
% 21.84/3.76 | | | |
% 21.84/3.76 | | | | (314) all_54_4 = e3
% 21.84/3.76 | | | |
% 21.84/3.76 | | | | COMBINE_EQS: (189), (314) imply:
% 21.84/3.76 | | | | (315) all_6_1 = e3
% 21.84/3.76 | | | |
% 21.84/3.76 | | | | REDUCE: (276), (315) imply:
% 21.84/3.76 | | | | (316) $false
% 21.84/3.76 | | | |
% 21.84/3.76 | | | | CLOSE: (316) is inconsistent.
% 21.84/3.76 | | | |
% 21.84/3.76 | | | Case 2:
% 21.84/3.76 | | | |
% 21.84/3.76 | | | | (317) ~ (all_54_4 = e3)
% 21.84/3.76 | | | | (318) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 21.84/3.76 | | | |
% 21.84/3.76 | | | | BETA: splitting (318) gives:
% 21.84/3.76 | | | |
% 21.84/3.76 | | | | Case 1:
% 21.84/3.76 | | | | |
% 21.84/3.76 | | | | | (319) all_54_4 = e2
% 21.84/3.76 | | | | |
% 21.84/3.76 | | | | | COMBINE_EQS: (189), (319) imply:
% 21.84/3.76 | | | | | (320) all_6_1 = e2
% 21.84/3.76 | | | | |
% 21.84/3.76 | | | | | REDUCE: (289), (320) imply:
% 21.84/3.76 | | | | | (321) $false
% 21.84/3.76 | | | | |
% 21.84/3.76 | | | | | CLOSE: (321) is inconsistent.
% 21.84/3.76 | | | | |
% 21.84/3.76 | | | | Case 2:
% 21.84/3.76 | | | | |
% 21.84/3.76 | | | | | (322) all_54_4 = e1 | all_54_4 = e0
% 21.84/3.76 | | | | |
% 21.84/3.76 | | | | | BETA: splitting (322) gives:
% 21.84/3.76 | | | | |
% 21.84/3.76 | | | | | Case 1:
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | | (323) all_54_4 = e1
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | | COMBINE_EQS: (189), (323) imply:
% 21.84/3.76 | | | | | | (324) all_6_1 = e1
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | | REDUCE: (313), (324) imply:
% 21.84/3.76 | | | | | | (325) $false
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | | CLOSE: (325) is inconsistent.
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | Case 2:
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | | (326) all_54_4 = e0
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | | COMBINE_EQS: (189), (326) imply:
% 21.84/3.76 | | | | | | (327) all_6_1 = e0
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | | COMBINE_EQS: (273), (327) imply:
% 21.84/3.76 | | | | | | (328) all_56_2 = e0
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | | REDUCE: (288), (327) imply:
% 21.84/3.76 | | | | | | (329) ~ (all_16_1 = e0)
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | | REDUCE: (286), (327) imply:
% 21.84/3.76 | | | | | | (330) ~ (all_14_1 = e0)
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | | REDUCE: (291), (327) imply:
% 21.84/3.76 | | | | | | (331) ~ (all_12_1 = e0)
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | | REDUCE: (276), (327) imply:
% 21.84/3.76 | | | | | | (332) ~ (e3 = e0)
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | | SIMP: (332) implies:
% 21.84/3.76 | | | | | | (333) ~ (e3 = e0)
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | | REDUCE: (313), (327) imply:
% 21.84/3.76 | | | | | | (334) ~ (e1 = e0)
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | | BETA: splitting (126) gives:
% 21.84/3.76 | | | | | |
% 21.84/3.76 | | | | | | Case 1:
% 21.84/3.76 | | | | | | |
% 21.84/3.76 | | | | | | | (335) all_54_6 = e3
% 21.84/3.76 | | | | | | |
% 21.84/3.76 | | | | | | | COMBINE_EQS: (216), (335) imply:
% 21.84/3.76 | | | | | | | (336) all_12_1 = e3
% 21.84/3.76 | | | | | | |
% 21.84/3.76 | | | | | | | REDUCE: (304), (336) imply:
% 21.84/3.76 | | | | | | | (337) ~ (all_30_1 = e3)
% 21.84/3.76 | | | | | | |
% 21.84/3.76 | | | | | | | BETA: splitting (147) gives:
% 21.84/3.76 | | | | | | |
% 21.84/3.76 | | | | | | | Case 1:
% 21.84/3.76 | | | | | | | |
% 21.84/3.76 | | | | | | | | (338) all_56_12 = e3
% 21.84/3.76 | | | | | | | |
% 21.84/3.76 | | | | | | | | COMBINE_EQS: (270), (338) imply:
% 21.84/3.76 | | | | | | | | (339) all_16_1 = e3
% 21.84/3.76 | | | | | | | |
% 21.84/3.76 | | | | | | | | REDUCE: (278), (339) imply:
% 21.84/3.76 | | | | | | | | (340) $false
% 21.84/3.76 | | | | | | | |
% 21.84/3.76 | | | | | | | | CLOSE: (340) is inconsistent.
% 21.84/3.76 | | | | | | | |
% 21.84/3.76 | | | | | | | Case 2:
% 21.84/3.76 | | | | | | | |
% 21.84/3.76 | | | | | | | | (341) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3
% 21.84/3.76 | | | | | | | |
% 21.84/3.76 | | | | | | | | BETA: splitting (148) gives:
% 21.84/3.76 | | | | | | | |
% 21.84/3.76 | | | | | | | | Case 1:
% 21.84/3.76 | | | | | | | | |
% 21.84/3.76 | | | | | | | | | (342) all_56_6 = e0
% 21.84/3.76 | | | | | | | | |
% 21.84/3.76 | | | | | | | | | REF_CLOSE: (181), (330), (342) are inconsistent by sub-proof
% 21.84/3.76 | | | | | | | | | #5.
% 21.84/3.76 | | | | | | | | |
% 21.84/3.76 | | | | | | | | Case 2:
% 21.84/3.76 | | | | | | | | |
% 21.84/3.76 | | | | | | | | | (343) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0
% 21.84/3.76 | | | | | | | | |
% 21.84/3.76 | | | | | | | | | BETA: splitting (341) gives:
% 21.84/3.76 | | | | | | | | |
% 21.84/3.76 | | | | | | | | | Case 1:
% 21.84/3.76 | | | | | | | | | |
% 21.84/3.76 | | | | | | | | | | (344) all_56_13 = e3
% 21.84/3.76 | | | | | | | | | |
% 21.84/3.76 | | | | | | | | | | COMBINE_EQS: (163), (344) imply:
% 21.84/3.76 | | | | | | | | | | (345) all_10_1 = e3
% 21.84/3.76 | | | | | | | | | |
% 21.84/3.76 | | | | | | | | | | SIMP: (345) implies:
% 21.84/3.76 | | | | | | | | | | (346) all_10_1 = e3
% 21.84/3.76 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | REDUCE: (42), (346) imply:
% 21.84/3.77 | | | | | | | | | | (347) op(e0, e2) = e3
% 21.84/3.77 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | BETA: splitting (343) gives:
% 21.84/3.77 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | Case 1:
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | (348) all_56_7 = e0
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | COMBINE_EQS: (178), (348) imply:
% 21.84/3.77 | | | | | | | | | | | (349) all_4_1 = e0
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | REDUCE: (32), (349) imply:
% 21.84/3.77 | | | | | | | | | | | (350) op(e0, e2) = all_4_0
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_0,
% 21.84/3.77 | | | | | | | | | | | e2, e0, simplifying with (347), (350) gives:
% 21.84/3.77 | | | | | | | | | | | (351) all_4_0 = e3
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | REDUCE: (312), (351) imply:
% 21.84/3.77 | | | | | | | | | | | (352) $false
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | CLOSE: (352) is inconsistent.
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | Case 2:
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | (353) all_56_8 = e0 | all_56_11 = e0
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | REF_CLOSE: (4), (174), (271), (309), (353) are inconsistent
% 21.84/3.77 | | | | | | | | | | | by sub-proof #4.
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | End of split
% 21.84/3.77 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | Case 2:
% 21.84/3.77 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | (354) all_56_14 = e3 | all_56_15 = e3
% 21.84/3.77 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | BETA: splitting (354) gives:
% 21.84/3.77 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | Case 1:
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | (355) all_56_14 = e3
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | REF_CLOSE: (159), (337), (355) are inconsistent by sub-proof
% 21.84/3.77 | | | | | | | | | | | #3.
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | Case 2:
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | (356) all_56_15 = e3
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | COMBINE_EQS: (156), (356) imply:
% 21.84/3.77 | | | | | | | | | | | (357) e3 = e0
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | SIMP: (357) implies:
% 21.84/3.77 | | | | | | | | | | | (358) e3 = e0
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | REDUCE: (333), (358) imply:
% 21.84/3.77 | | | | | | | | | | | (359) $false
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | CLOSE: (359) is inconsistent.
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | End of split
% 21.84/3.77 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | End of split
% 21.84/3.77 | | | | | | | | |
% 21.84/3.77 | | | | | | | | End of split
% 21.84/3.77 | | | | | | | |
% 21.84/3.77 | | | | | | | End of split
% 21.84/3.77 | | | | | | |
% 21.84/3.77 | | | | | | Case 2:
% 21.84/3.77 | | | | | | |
% 21.84/3.77 | | | | | | | (360) ~ (all_54_6 = e3)
% 21.84/3.77 | | | | | | |
% 21.84/3.77 | | | | | | | REDUCE: (216), (360) imply:
% 21.84/3.77 | | | | | | | (361) ~ (all_12_1 = e3)
% 21.84/3.77 | | | | | | |
% 21.84/3.77 | | | | | | | BETA: splitting (148) gives:
% 21.84/3.77 | | | | | | |
% 21.84/3.77 | | | | | | | Case 1:
% 21.84/3.77 | | | | | | | |
% 21.84/3.77 | | | | | | | | (362) all_56_6 = e0
% 21.84/3.77 | | | | | | | |
% 21.84/3.77 | | | | | | | | REF_CLOSE: (181), (330), (362) are inconsistent by sub-proof #5.
% 21.84/3.77 | | | | | | | |
% 21.84/3.77 | | | | | | | Case 2:
% 21.84/3.77 | | | | | | | |
% 21.84/3.77 | | | | | | | | (363) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0
% 21.84/3.77 | | | | | | | |
% 21.84/3.77 | | | | | | | | BETA: splitting (153) gives:
% 21.84/3.77 | | | | | | | |
% 21.84/3.77 | | | | | | | | Case 1:
% 21.84/3.77 | | | | | | | | |
% 21.84/3.77 | | | | | | | | | (364) all_56_0 = e1
% 21.84/3.77 | | | | | | | | |
% 21.84/3.77 | | | | | | | | | COMBINE_EQS: (204), (364) imply:
% 21.84/3.77 | | | | | | | | | (365) e3 = e1
% 21.84/3.77 | | | | | | | | |
% 21.84/3.77 | | | | | | | | | REDUCE: (7), (365) imply:
% 21.84/3.77 | | | | | | | | | (366) $false
% 21.84/3.77 | | | | | | | | |
% 21.84/3.77 | | | | | | | | | CLOSE: (366) is inconsistent.
% 21.84/3.77 | | | | | | | | |
% 21.84/3.77 | | | | | | | | Case 2:
% 21.84/3.77 | | | | | | | | |
% 21.84/3.77 | | | | | | | | | (367) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1
% 21.84/3.77 | | | | | | | | |
% 21.84/3.77 | | | | | | | | | BETA: splitting (152) gives:
% 21.84/3.77 | | | | | | | | |
% 21.84/3.77 | | | | | | | | | Case 1:
% 21.84/3.77 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | (368) all_56_1 = e3
% 21.84/3.77 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | COMBINE_EQS: (274), (368) imply:
% 21.84/3.77 | | | | | | | | | | (369) all_26_1 = e3
% 21.84/3.77 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | REDUCE: (280), (369) imply:
% 21.84/3.77 | | | | | | | | | | (370) $false
% 21.84/3.77 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | CLOSE: (370) is inconsistent.
% 21.84/3.77 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | Case 2:
% 21.84/3.77 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | (371) all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3
% 21.84/3.77 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | BETA: splitting (150) gives:
% 21.84/3.77 | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | Case 1:
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | (372) all_56_4 = e3
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | COMBINE_EQS: (272), (372) imply:
% 21.84/3.77 | | | | | | | | | | | (373) all_28_1 = e3
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | REDUCE: (282), (373) imply:
% 21.84/3.77 | | | | | | | | | | | (374) $false
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | CLOSE: (374) is inconsistent.
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | Case 2:
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | (375) all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | BETA: splitting (371) gives:
% 21.84/3.77 | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | Case 1:
% 21.84/3.77 | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | (376) all_56_3 = e3
% 21.84/3.77 | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | REF_CLOSE: (8), (188), (376) are inconsistent by sub-proof
% 21.84/3.77 | | | | | | | | | | | | #2.
% 21.84/3.77 | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | Case 2:
% 21.84/3.77 | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | (377) all_56_7 = e3 | all_56_13 = e3
% 21.84/3.77 | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | BETA: splitting (367) gives:
% 21.84/3.77 | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | Case 1:
% 21.84/3.77 | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | (378) all_56_2 = e1
% 21.84/3.77 | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | COMBINE_EQS: (328), (378) imply:
% 21.84/3.77 | | | | | | | | | | | | | (379) e1 = e0
% 21.84/3.77 | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | SIMP: (379) implies:
% 21.84/3.77 | | | | | | | | | | | | | (380) e1 = e0
% 21.84/3.77 | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | REDUCE: (4), (380) imply:
% 21.84/3.77 | | | | | | | | | | | | | (381) $false
% 21.84/3.77 | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | CLOSE: (381) is inconsistent.
% 21.84/3.77 | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | Case 2:
% 21.84/3.77 | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | (382) all_56_6 = e1 | all_56_12 = e1
% 21.84/3.77 | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | BETA: splitting (382) gives:
% 21.84/3.77 | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | Case 1:
% 21.84/3.77 | | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | | (383) all_56_6 = e1
% 21.84/3.77 | | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | | COMBINE_EQS: (181), (383) imply:
% 21.84/3.77 | | | | | | | | | | | | | | (384) all_14_1 = e1
% 21.84/3.77 | | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | | REDUCE: (292), (384) imply:
% 21.84/3.77 | | | | | | | | | | | | | | (385) $false
% 21.84/3.77 | | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | | CLOSE: (385) is inconsistent.
% 21.84/3.77 | | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | Case 2:
% 21.84/3.77 | | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | | (386) all_56_12 = e1
% 21.84/3.77 | | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | | COMBINE_EQS: (270), (386) imply:
% 21.84/3.77 | | | | | | | | | | | | | | (387) all_16_1 = e1
% 21.84/3.77 | | | | | | | | | | | | | |
% 21.84/3.77 | | | | | | | | | | | | | | REDUCE: (293), (387) imply:
% 22.16/3.77 | | | | | | | | | | | | | | (388) ~ (all_10_1 = e1)
% 22.16/3.77 | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | SIMP: (388) implies:
% 22.16/3.77 | | | | | | | | | | | | | | (389) ~ (all_10_1 = e1)
% 22.16/3.77 | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 22.16/3.77 | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | Case 1:
% 22.16/3.77 | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | (390) all_54_13 = e3
% 22.16/3.77 | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | COMBINE_EQS: (269), (390) imply:
% 22.16/3.77 | | | | | | | | | | | | | | | (391) all_10_1 = e3
% 22.16/3.77 | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | REDUCE: (302), (391) imply:
% 22.16/3.77 | | | | | | | | | | | | | | | (392) ~ (all_30_1 = e3)
% 22.16/3.77 | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | BETA: splitting (375) gives:
% 22.16/3.77 | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | Case 1:
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | (393) all_56_5 = e3
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (393) imply:
% 22.16/3.77 | | | | | | | | | | | | | | | | (394) all_12_1 = e3
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | REDUCE: (361), (394) imply:
% 22.16/3.77 | | | | | | | | | | | | | | | | (395) $false
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | CLOSE: (395) is inconsistent.
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | Case 2:
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | (396) all_56_8 = e3 | all_56_14 = e3
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | BETA: splitting (396) gives:
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | Case 1:
% 22.16/3.77 | | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | | (397) all_56_8 = e3
% 22.16/3.77 | | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (397) imply:
% 22.16/3.77 | | | | | | | | | | | | | | | | | (398) e3 = e1
% 22.16/3.77 | | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | | SIMP: (398) implies:
% 22.16/3.77 | | | | | | | | | | | | | | | | | (399) e3 = e1
% 22.16/3.77 | | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | | REDUCE: (7), (399) imply:
% 22.16/3.77 | | | | | | | | | | | | | | | | | (400) $false
% 22.16/3.77 | | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | | CLOSE: (400) is inconsistent.
% 22.16/3.77 | | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | Case 2:
% 22.16/3.77 | | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | | (401) all_56_14 = e3
% 22.16/3.77 | | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (392), (401) are inconsistent by sub-proof
% 22.16/3.77 | | | | | | | | | | | | | | | | | #3.
% 22.16/3.77 | | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | End of split
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | End of split
% 22.16/3.77 | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | Case 2:
% 22.16/3.77 | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | (402) ~ (all_54_13 = e3)
% 22.16/3.77 | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | REDUCE: (269), (402) imply:
% 22.16/3.77 | | | | | | | | | | | | | | | (403) ~ (all_10_1 = e3)
% 22.16/3.77 | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | BETA: splitting (377) gives:
% 22.16/3.77 | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | Case 1:
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | (404) all_56_7 = e3
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (174), (271), (309), (333), (363), (404) are
% 22.16/3.77 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1.
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | Case 2:
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | (405) all_56_13 = e3
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (405) imply:
% 22.16/3.77 | | | | | | | | | | | | | | | | (406) all_10_1 = e3
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | REDUCE: (403), (406) imply:
% 22.16/3.77 | | | | | | | | | | | | | | | | (407) $false
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | | CLOSE: (407) is inconsistent.
% 22.16/3.77 | | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | | End of split
% 22.16/3.77 | | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | | End of split
% 22.16/3.77 | | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | | End of split
% 22.16/3.77 | | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | | End of split
% 22.16/3.77 | | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | | End of split
% 22.16/3.77 | | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | | End of split
% 22.16/3.77 | | | | | | | | | |
% 22.16/3.77 | | | | | | | | | End of split
% 22.16/3.77 | | | | | | | | |
% 22.16/3.77 | | | | | | | | End of split
% 22.16/3.77 | | | | | | | |
% 22.16/3.77 | | | | | | | End of split
% 22.16/3.77 | | | | | | |
% 22.16/3.77 | | | | | | End of split
% 22.16/3.77 | | | | | |
% 22.16/3.77 | | | | | End of split
% 22.16/3.77 | | | | |
% 22.16/3.77 | | | | End of split
% 22.16/3.77 | | | |
% 22.16/3.77 | | | End of split
% 22.16/3.77 | | |
% 22.16/3.77 | | Case 2:
% 22.16/3.77 | | |
% 22.16/3.77 | | | (408) all_6_1 = e1
% 22.16/3.77 | | |
% 22.16/3.77 | | | REDUCE: (288), (408) imply:
% 22.16/3.78 | | | (409) ~ (all_16_1 = e1)
% 22.16/3.78 | | |
% 22.16/3.78 | | | REDUCE: (276), (408) imply:
% 22.16/3.78 | | | (410) ~ (e3 = e1)
% 22.16/3.78 | | |
% 22.16/3.78 | | | BETA: splitting (146) gives:
% 22.16/3.78 | | |
% 22.16/3.78 | | | Case 1:
% 22.16/3.78 | | | |
% 22.16/3.78 | | | | (411) all_56_12 = e1
% 22.16/3.78 | | | |
% 22.16/3.78 | | | | COMBINE_EQS: (270), (411) imply:
% 22.16/3.78 | | | | (412) all_16_1 = e1
% 22.16/3.78 | | | |
% 22.16/3.78 | | | | REDUCE: (409), (412) imply:
% 22.16/3.78 | | | | (413) $false
% 22.16/3.78 | | | |
% 22.16/3.78 | | | | CLOSE: (413) is inconsistent.
% 22.16/3.78 | | | |
% 22.16/3.78 | | | Case 2:
% 22.16/3.78 | | | |
% 22.16/3.78 | | | | (414) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1
% 22.16/3.78 | | | |
% 22.16/3.78 | | | | BETA: splitting (414) gives:
% 22.16/3.78 | | | |
% 22.16/3.78 | | | | Case 1:
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | (415) all_56_13 = e1
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | COMBINE_EQS: (163), (415) imply:
% 22.16/3.78 | | | | | (416) all_10_1 = e1
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | SIMP: (416) implies:
% 22.16/3.78 | | | | | (417) all_10_1 = e1
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | REDUCE: (296), (417) imply:
% 22.16/3.78 | | | | | (418) ~ (all_26_1 = e1)
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | BETA: splitting (152) gives:
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | Case 1:
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | (419) all_56_1 = e3
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | COMBINE_EQS: (274), (419) imply:
% 22.16/3.78 | | | | | | (420) all_26_1 = e3
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | REDUCE: (280), (420) imply:
% 22.16/3.78 | | | | | | (421) $false
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | CLOSE: (421) is inconsistent.
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | Case 2:
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | (422) all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | BETA: splitting (422) gives:
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | Case 1:
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | | (423) all_56_3 = e3
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | | REF_CLOSE: (8), (188), (423) are inconsistent by sub-proof #2.
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | Case 2:
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | | (424) all_56_7 = e3 | all_56_13 = e3
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | | BETA: splitting (424) gives:
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | | Case 1:
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | (425) all_56_7 = e3
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | COMBINE_EQS: (178), (425) imply:
% 22.16/3.78 | | | | | | | | (426) all_4_1 = e3
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | COMBINE_EQS: (265), (426) imply:
% 22.16/3.78 | | | | | | | | (427) all_8_1 = e3
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | REDUCE: (32), (426) imply:
% 22.16/3.78 | | | | | | | | (428) op(e3, e2) = all_4_0
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | BETA: splitting (40) gives:
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | Case 1:
% 22.16/3.78 | | | | | | | | |
% 22.16/3.78 | | | | | | | | | (429) ~ (all_8_1 = e3)
% 22.16/3.78 | | | | | | | | |
% 22.16/3.78 | | | | | | | | | REDUCE: (427), (429) imply:
% 22.16/3.78 | | | | | | | | | (430) $false
% 22.16/3.78 | | | | | | | | |
% 22.16/3.78 | | | | | | | | | CLOSE: (430) is inconsistent.
% 22.16/3.78 | | | | | | | | |
% 22.16/3.78 | | | | | | | | Case 2:
% 22.16/3.78 | | | | | | | | |
% 22.16/3.78 | | | | | | | | | (431) ~ (all_8_0 = e0)
% 22.16/3.78 | | | | | | | | |
% 22.16/3.78 | | | | | | | | | REDUCE: (311), (431) imply:
% 22.16/3.78 | | | | | | | | | (432) ~ (all_4_0 = e0)
% 22.16/3.78 | | | | | | | | |
% 22.16/3.78 | | | | | | | | | BETA: splitting (129) gives:
% 22.16/3.78 | | | | | | | | |
% 22.16/3.78 | | | | | | | | | Case 1:
% 22.16/3.78 | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | (433) all_54_1 = e3
% 22.16/3.78 | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | COMBINE_EQS: (199), (433) imply:
% 22.16/3.78 | | | | | | | | | | (434) all_26_1 = e3
% 22.16/3.78 | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | REDUCE: (280), (434) imply:
% 22.16/3.78 | | | | | | | | | | (435) $false
% 22.16/3.78 | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | CLOSE: (435) is inconsistent.
% 22.16/3.78 | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | Case 2:
% 22.16/3.78 | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | (436) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 22.16/3.78 | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | BETA: splitting (436) gives:
% 22.16/3.78 | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | Case 1:
% 22.16/3.78 | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | (437) all_54_1 = e2
% 22.16/3.78 | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | COMBINE_EQS: (199), (437) imply:
% 22.16/3.78 | | | | | | | | | | | (438) all_26_1 = e2
% 22.16/3.78 | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | REDUCE: (294), (438) imply:
% 22.16/3.78 | | | | | | | | | | | (439) $false
% 22.16/3.78 | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | CLOSE: (439) is inconsistent.
% 22.16/3.78 | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | Case 2:
% 22.16/3.78 | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | (440) all_54_1 = e1 | all_54_1 = e0
% 22.16/3.78 | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | BETA: splitting (440) gives:
% 22.16/3.78 | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | Case 1:
% 22.16/3.78 | | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | | (441) all_54_1 = e1
% 22.16/3.78 | | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | | COMBINE_EQS: (199), (441) imply:
% 22.16/3.78 | | | | | | | | | | | | (442) all_26_1 = e1
% 22.16/3.78 | | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | | REDUCE: (418), (442) imply:
% 22.16/3.78 | | | | | | | | | | | | (443) $false
% 22.16/3.78 | | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | | CLOSE: (443) is inconsistent.
% 22.16/3.78 | | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | Case 2:
% 22.16/3.78 | | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | | (444) all_54_1 = e0
% 22.16/3.78 | | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | | COMBINE_EQS: (199), (444) imply:
% 22.16/3.78 | | | | | | | | | | | | (445) all_26_1 = e0
% 22.16/3.78 | | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | | REDUCE: (54), (445) imply:
% 22.16/3.78 | | | | | | | | | | | | (446) op(e3, e2) = e0
% 22.16/3.78 | | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0,
% 22.16/3.78 | | | | | | | | | | | | e2, e3, simplifying with (428), (446) gives:
% 22.16/3.78 | | | | | | | | | | | | (447) all_4_0 = e0
% 22.16/3.78 | | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | | REDUCE: (432), (447) imply:
% 22.16/3.78 | | | | | | | | | | | | (448) $false
% 22.16/3.78 | | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | | CLOSE: (448) is inconsistent.
% 22.16/3.78 | | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | | End of split
% 22.16/3.78 | | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | | End of split
% 22.16/3.78 | | | | | | | | | |
% 22.16/3.78 | | | | | | | | | End of split
% 22.16/3.78 | | | | | | | | |
% 22.16/3.78 | | | | | | | | End of split
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | Case 2:
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | (449) all_56_13 = e3
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | COMBINE_EQS: (415), (449) imply:
% 22.16/3.78 | | | | | | | | (450) e3 = e1
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | SIMP: (450) implies:
% 22.16/3.78 | | | | | | | | (451) e3 = e1
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | REDUCE: (7), (451) imply:
% 22.16/3.78 | | | | | | | | (452) $false
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | CLOSE: (452) is inconsistent.
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | End of split
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | End of split
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | End of split
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | Case 2:
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | (453) all_56_14 = e1 | all_56_15 = e1
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | BETA: splitting (453) gives:
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | Case 1:
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | (454) all_56_14 = e1
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | COMBINE_EQS: (159), (454) imply:
% 22.16/3.78 | | | | | | (455) all_30_1 = e1
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | SIMP: (455) implies:
% 22.16/3.78 | | | | | | (456) all_30_1 = e1
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | REDUCE: (306), (456) imply:
% 22.16/3.78 | | | | | | (457) $false
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | CLOSE: (457) is inconsistent.
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | Case 2:
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | (458) all_56_15 = e1
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | COMBINE_EQS: (156), (458) imply:
% 22.16/3.78 | | | | | | (459) e1 = e0
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | SIMP: (459) implies:
% 22.16/3.78 | | | | | | (460) e1 = e0
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | REDUCE: (4), (460) imply:
% 22.16/3.78 | | | | | | (461) $false
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | CLOSE: (461) is inconsistent.
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | End of split
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | End of split
% 22.16/3.78 | | | |
% 22.16/3.78 | | | End of split
% 22.16/3.78 | | |
% 22.16/3.78 | | End of split
% 22.16/3.78 | |
% 22.16/3.78 | Case 2:
% 22.16/3.78 | |
% 22.16/3.78 | | (462) all_4_0 = e3
% 22.16/3.78 | | (463) ~ (all_4_1 = e0)
% 22.16/3.78 | |
% 22.16/3.78 | | REDUCE: (32), (462) imply:
% 22.16/3.78 | | (464) op(all_4_1, e2) = e3
% 22.16/3.78 | |
% 22.16/3.78 | | BETA: splitting (125) gives:
% 22.16/3.78 | |
% 22.16/3.78 | | Case 1:
% 22.16/3.78 | | |
% 22.16/3.78 | | | (465) all_54_9 = e3
% 22.16/3.78 | | |
% 22.16/3.78 | | | COMBINE_EQS: (220), (465) imply:
% 22.16/3.78 | | | (466) all_4_1 = e3
% 22.16/3.78 | | |
% 22.16/3.78 | | | COMBINE_EQS: (178), (466) imply:
% 22.16/3.78 | | | (467) all_56_7 = e3
% 22.16/3.78 | | |
% 22.16/3.78 | | | REDUCE: (463), (466) imply:
% 22.16/3.78 | | | (468) ~ (e3 = e0)
% 22.16/3.78 | | |
% 22.16/3.78 | | | REDUCE: (464), (466) imply:
% 22.16/3.78 | | | (469) op(e3, e2) = e3
% 22.16/3.78 | | |
% 22.16/3.78 | | | BETA: splitting (148) gives:
% 22.16/3.78 | | |
% 22.16/3.78 | | | Case 1:
% 22.16/3.78 | | | |
% 22.16/3.78 | | | | (470) all_56_6 = e0
% 22.16/3.78 | | | |
% 22.16/3.78 | | | | BETA: splitting (149) gives:
% 22.16/3.78 | | | |
% 22.16/3.78 | | | | Case 1:
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | (471) all_56_6 = e2
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | COMBINE_EQS: (470), (471) imply:
% 22.16/3.78 | | | | | (472) e2 = e0
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | SIMP: (472) implies:
% 22.16/3.78 | | | | | (473) e2 = e0
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | REDUCE: (5), (473) imply:
% 22.16/3.78 | | | | | (474) $false
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | CLOSE: (474) is inconsistent.
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | Case 2:
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | (475) all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | BETA: splitting (475) gives:
% 22.16/3.78 | | | | |
% 22.16/3.78 | | | | | Case 1:
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | (476) all_56_7 = e2
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | COMBINE_EQS: (467), (476) imply:
% 22.16/3.78 | | | | | | (477) e3 = e2
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | REDUCE: (8), (477) imply:
% 22.16/3.78 | | | | | | (478) $false
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | CLOSE: (478) is inconsistent.
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | Case 2:
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | (479) all_56_8 = e2 | all_56_11 = e2
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | BETA: splitting (479) gives:
% 22.16/3.78 | | | | | |
% 22.16/3.78 | | | | | | Case 1:
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | | (480) all_56_8 = e2
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | | COMBINE_EQS: (174), (480) imply:
% 22.16/3.78 | | | | | | | (481) e2 = e1
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | | SIMP: (481) implies:
% 22.16/3.78 | | | | | | | (482) e2 = e1
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | | REDUCE: (6), (482) imply:
% 22.16/3.78 | | | | | | | (483) $false
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | | CLOSE: (483) is inconsistent.
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | Case 2:
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | | (484) all_56_11 = e2
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | | COMBINE_EQS: (271), (484) imply:
% 22.16/3.78 | | | | | | | (485) all_20_1 = e2
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | | REDUCE: (307), (485) imply:
% 22.16/3.78 | | | | | | | (486) ~ (all_22_1 = e2)
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | | BETA: splitting (128) gives:
% 22.16/3.78 | | | | | | |
% 22.16/3.78 | | | | | | | Case 1:
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | (487) all_54_3 = e3
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | COMBINE_EQS: (192), (487) imply:
% 22.16/3.78 | | | | | | | | (488) all_22_1 = e3
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | REDUCE: (284), (488) imply:
% 22.16/3.78 | | | | | | | | (489) $false
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | CLOSE: (489) is inconsistent.
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | Case 2:
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | (490) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | BETA: splitting (490) gives:
% 22.16/3.78 | | | | | | | |
% 22.16/3.78 | | | | | | | | Case 1:
% 22.16/3.78 | | | | | | | | |
% 22.16/3.78 | | | | | | | | | (491) all_54_3 = e2
% 22.16/3.78 | | | | | | | | |
% 22.16/3.78 | | | | | | | | | COMBINE_EQS: (192), (491) imply:
% 22.16/3.78 | | | | | | | | | (492) all_22_1 = e2
% 22.16/3.78 | | | | | | | | |
% 22.16/3.78 | | | | | | | | | REDUCE: (486), (492) imply:
% 22.16/3.78 | | | | | | | | | (493) $false
% 22.16/3.78 | | | | | | | | |
% 22.16/3.78 | | | | | | | | | CLOSE: (493) is inconsistent.
% 22.16/3.78 | | | | | | | | |
% 22.16/3.79 | | | | | | | | Case 2:
% 22.16/3.79 | | | | | | | | |
% 22.16/3.79 | | | | | | | | | (494) all_54_3 = e1 | all_54_3 = e0
% 22.16/3.79 | | | | | | | | |
% 22.16/3.79 | | | | | | | | | BETA: splitting (494) gives:
% 22.16/3.79 | | | | | | | | |
% 22.16/3.79 | | | | | | | | | Case 1:
% 22.16/3.79 | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | (495) all_54_3 = e1
% 22.16/3.79 | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | COMBINE_EQS: (192), (495) imply:
% 22.16/3.79 | | | | | | | | | | (496) all_22_1 = e1
% 22.16/3.79 | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | REDUCE: (297), (496) imply:
% 22.16/3.79 | | | | | | | | | | (497) ~ (all_26_1 = e1)
% 22.16/3.79 | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | BETA: splitting (129) gives:
% 22.16/3.79 | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | Case 1:
% 22.16/3.79 | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | (498) all_54_1 = e3
% 22.16/3.79 | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | COMBINE_EQS: (199), (498) imply:
% 22.16/3.79 | | | | | | | | | | | (499) all_26_1 = e3
% 22.16/3.79 | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | REDUCE: (280), (499) imply:
% 22.16/3.79 | | | | | | | | | | | (500) $false
% 22.16/3.79 | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | CLOSE: (500) is inconsistent.
% 22.16/3.79 | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | Case 2:
% 22.16/3.79 | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | (501) ~ (all_54_1 = e3)
% 22.16/3.79 | | | | | | | | | | | (502) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 22.16/3.79 | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | BETA: splitting (502) gives:
% 22.16/3.79 | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | Case 1:
% 22.16/3.79 | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | (503) all_54_1 = e2
% 22.16/3.79 | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | COMBINE_EQS: (199), (503) imply:
% 22.16/3.79 | | | | | | | | | | | | (504) all_26_1 = e2
% 22.16/3.79 | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | SIMP: (504) implies:
% 22.16/3.79 | | | | | | | | | | | | (505) all_26_1 = e2
% 22.16/3.79 | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | REDUCE: (294), (505) imply:
% 22.16/3.79 | | | | | | | | | | | | (506) $false
% 22.16/3.79 | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | CLOSE: (506) is inconsistent.
% 22.16/3.79 | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | Case 2:
% 22.16/3.79 | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | (507) all_54_1 = e1 | all_54_1 = e0
% 22.16/3.79 | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | BETA: splitting (151) gives:
% 22.16/3.79 | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | Case 1:
% 22.16/3.79 | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | (508) all_56_1 = e0
% 22.16/3.79 | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | COMBINE_EQS: (274), (508) imply:
% 22.16/3.79 | | | | | | | | | | | | | (509) all_26_1 = e0
% 22.16/3.79 | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | REDUCE: (280), (509) imply:
% 22.16/3.79 | | | | | | | | | | | | | (510) ~ (e3 = e0)
% 22.16/3.79 | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | REDUCE: (54), (509) imply:
% 22.16/3.79 | | | | | | | | | | | | | (511) op(e3, e2) = e0
% 22.16/3.79 | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e2,
% 22.16/3.79 | | | | | | | | | | | | | e3, simplifying with (469), (511) gives:
% 22.16/3.79 | | | | | | | | | | | | | (512) e3 = e0
% 22.16/3.79 | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | REDUCE: (468), (512) imply:
% 22.16/3.79 | | | | | | | | | | | | | (513) $false
% 22.16/3.79 | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | CLOSE: (513) is inconsistent.
% 22.16/3.79 | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | Case 2:
% 22.16/3.79 | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | (514) ~ (all_56_1 = e0)
% 22.16/3.79 | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | REDUCE: (274), (514) imply:
% 22.16/3.79 | | | | | | | | | | | | | (515) ~ (all_26_1 = e0)
% 22.16/3.79 | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | BETA: splitting (507) gives:
% 22.16/3.79 | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | Case 1:
% 22.16/3.79 | | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | | (516) all_54_1 = e1
% 22.16/3.79 | | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | | COMBINE_EQS: (199), (516) imply:
% 22.16/3.79 | | | | | | | | | | | | | | (517) all_26_1 = e1
% 22.16/3.79 | | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | | SIMP: (517) implies:
% 22.16/3.79 | | | | | | | | | | | | | | (518) all_26_1 = e1
% 22.16/3.79 | | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | | REDUCE: (497), (518) imply:
% 22.16/3.79 | | | | | | | | | | | | | | (519) $false
% 22.16/3.79 | | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | | CLOSE: (519) is inconsistent.
% 22.16/3.79 | | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | Case 2:
% 22.16/3.79 | | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | | (520) all_54_1 = e0
% 22.16/3.79 | | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | | COMBINE_EQS: (199), (520) imply:
% 22.16/3.79 | | | | | | | | | | | | | | (521) all_26_1 = e0
% 22.16/3.79 | | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | | SIMP: (521) implies:
% 22.16/3.79 | | | | | | | | | | | | | | (522) all_26_1 = e0
% 22.16/3.79 | | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | | REDUCE: (515), (522) imply:
% 22.16/3.79 | | | | | | | | | | | | | | (523) $false
% 22.16/3.79 | | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | | CLOSE: (523) is inconsistent.
% 22.16/3.79 | | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | | End of split
% 22.16/3.79 | | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | | End of split
% 22.16/3.79 | | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | | End of split
% 22.16/3.79 | | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | End of split
% 22.16/3.79 | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | Case 2:
% 22.16/3.79 | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | (524) all_54_3 = e0
% 22.16/3.79 | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | COMBINE_EQS: (192), (524) imply:
% 22.16/3.79 | | | | | | | | | | (525) all_22_1 = e0
% 22.16/3.79 | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | REDUCE: (308), (525) imply:
% 22.16/3.79 | | | | | | | | | | (526) $false
% 22.16/3.79 | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | | CLOSE: (526) is inconsistent.
% 22.16/3.79 | | | | | | | | | |
% 22.16/3.79 | | | | | | | | | End of split
% 22.16/3.79 | | | | | | | | |
% 22.16/3.79 | | | | | | | | End of split
% 22.16/3.79 | | | | | | | |
% 22.16/3.79 | | | | | | | End of split
% 22.16/3.79 | | | | | | |
% 22.16/3.79 | | | | | | End of split
% 22.16/3.79 | | | | | |
% 22.16/3.79 | | | | | End of split
% 22.16/3.79 | | | | |
% 22.16/3.79 | | | | End of split
% 22.16/3.79 | | | |
% 22.16/3.79 | | | Case 2:
% 22.16/3.79 | | | |
% 22.16/3.79 | | | | (527) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0
% 22.16/3.79 | | | |
% 22.16/3.79 | | | | REF_CLOSE: (4), (174), (271), (309), (467), (468), (527) are
% 22.16/3.79 | | | | inconsistent by sub-proof #1.
% 22.16/3.79 | | | |
% 22.16/3.79 | | | End of split
% 22.16/3.79 | | |
% 22.16/3.79 | | Case 2:
% 22.16/3.79 | | |
% 22.16/3.79 | | | (528) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 22.16/3.79 | | |
% 22.16/3.79 | | | BETA: splitting (528) gives:
% 22.16/3.79 | | |
% 22.16/3.79 | | | Case 1:
% 22.16/3.79 | | | |
% 22.16/3.79 | | | | (529) all_54_9 = e2
% 22.16/3.79 | | | |
% 22.16/3.79 | | | | COMBINE_EQS: (220), (529) imply:
% 22.16/3.79 | | | | (530) all_4_1 = e2
% 22.16/3.79 | | | |
% 22.16/3.79 | | | | REDUCE: (299), (530) imply:
% 22.16/3.79 | | | | (531) $false
% 22.16/3.79 | | | |
% 22.16/3.79 | | | | CLOSE: (531) is inconsistent.
% 22.16/3.79 | | | |
% 22.16/3.79 | | | Case 2:
% 22.16/3.79 | | | |
% 22.16/3.79 | | | | (532) all_54_9 = e1 | all_54_9 = e0
% 22.16/3.79 | | | |
% 22.16/3.79 | | | | BETA: splitting (532) gives:
% 22.16/3.79 | | | |
% 22.16/3.79 | | | | Case 1:
% 22.16/3.79 | | | | |
% 22.16/3.79 | | | | | (533) all_54_9 = e1
% 22.16/3.79 | | | | |
% 22.16/3.79 | | | | | COMBINE_EQS: (220), (533) imply:
% 22.16/3.79 | | | | | (534) all_4_1 = e1
% 22.16/3.79 | | | | |
% 22.16/3.79 | | | | | REDUCE: (300), (534) imply:
% 22.16/3.79 | | | | | (535) $false
% 22.16/3.79 | | | | |
% 22.16/3.79 | | | | | CLOSE: (535) is inconsistent.
% 22.16/3.79 | | | | |
% 22.16/3.79 | | | | Case 2:
% 22.16/3.79 | | | | |
% 22.16/3.79 | | | | | (536) all_54_9 = e0
% 22.16/3.79 | | | | |
% 22.16/3.79 | | | | | COMBINE_EQS: (220), (536) imply:
% 22.16/3.79 | | | | | (537) all_4_1 = e0
% 22.16/3.79 | | | | |
% 22.16/3.79 | | | | | REDUCE: (463), (537) imply:
% 22.16/3.79 | | | | | (538) $false
% 22.16/3.79 | | | | |
% 22.16/3.79 | | | | | CLOSE: (538) is inconsistent.
% 22.16/3.79 | | | | |
% 22.16/3.79 | | | | End of split
% 22.16/3.79 | | | |
% 22.16/3.79 | | | End of split
% 22.16/3.79 | | |
% 22.16/3.79 | | End of split
% 22.16/3.79 | |
% 22.16/3.79 | End of split
% 22.16/3.79 |
% 22.16/3.79 End of proof
% 22.16/3.79
% 22.16/3.79 Sub-proof #1 shows that the following formulas are inconsistent:
% 22.16/3.79 ----------------------------------------------------------------
% 22.16/3.79 (1) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0
% 22.16/3.79 (2) ~ (e3 = e0)
% 22.16/3.79 (3) ~ (all_20_1 = e0)
% 22.16/3.79 (4) all_56_8 = e1
% 22.16/3.79 (5) all_56_11 = all_20_1
% 22.16/3.79 (6) ~ (e1 = e0)
% 22.16/3.79 (7) all_56_7 = e3
% 22.16/3.79
% 22.16/3.79 Begin of proof
% 22.16/3.79 |
% 22.16/3.79 | BETA: splitting (1) gives:
% 22.16/3.79 |
% 22.16/3.79 | Case 1:
% 22.16/3.79 | |
% 22.16/3.79 | | (8) all_56_7 = e0
% 22.16/3.79 | |
% 22.16/3.79 | | COMBINE_EQS: (7), (8) imply:
% 22.16/3.79 | | (9) e3 = e0
% 22.16/3.79 | |
% 22.16/3.79 | | REDUCE: (2), (9) imply:
% 22.16/3.79 | | (10) $false
% 22.16/3.79 | |
% 22.16/3.79 | | CLOSE: (10) is inconsistent.
% 22.16/3.79 | |
% 22.16/3.79 | Case 2:
% 22.16/3.79 | |
% 22.16/3.79 | | (11) all_56_8 = e0 | all_56_11 = e0
% 22.16/3.79 | |
% 22.16/3.79 | | REF_CLOSE: (3), (4), (5), (6), (11) are inconsistent by sub-proof #4.
% 22.16/3.79 | |
% 22.16/3.79 | End of split
% 22.16/3.79 |
% 22.16/3.79 End of proof
% 22.16/3.79
% 22.16/3.79 Sub-proof #2 shows that the following formulas are inconsistent:
% 22.16/3.79 ----------------------------------------------------------------
% 22.16/3.79 (1) all_56_3 = e3
% 22.16/3.79 (2) all_56_3 = e2
% 22.16/3.79 (3) ~ (e3 = e2)
% 22.16/3.79
% 22.16/3.79 Begin of proof
% 22.16/3.79 |
% 22.16/3.79 | COMBINE_EQS: (1), (2) imply:
% 22.16/3.79 | (4) e3 = e2
% 22.16/3.79 |
% 22.16/3.79 | SIMP: (4) implies:
% 22.16/3.79 | (5) e3 = e2
% 22.16/3.79 |
% 22.16/3.79 | REDUCE: (3), (5) imply:
% 22.16/3.79 | (6) $false
% 22.16/3.79 |
% 22.16/3.79 | CLOSE: (6) is inconsistent.
% 22.16/3.79 |
% 22.16/3.79 End of proof
% 22.16/3.79
% 22.16/3.79 Sub-proof #3 shows that the following formulas are inconsistent:
% 22.16/3.79 ----------------------------------------------------------------
% 22.16/3.79 (1) all_56_14 = all_30_1
% 22.16/3.79 (2) all_56_14 = e3
% 22.16/3.79 (3) ~ (all_30_1 = e3)
% 22.16/3.79
% 22.16/3.79 Begin of proof
% 22.16/3.79 |
% 22.16/3.79 | COMBINE_EQS: (1), (2) imply:
% 22.16/3.79 | (4) all_30_1 = e3
% 22.16/3.79 |
% 22.16/3.79 | SIMP: (4) implies:
% 22.16/3.79 | (5) all_30_1 = e3
% 22.16/3.79 |
% 22.16/3.79 | REDUCE: (3), (5) imply:
% 22.16/3.79 | (6) $false
% 22.16/3.79 |
% 22.16/3.79 | CLOSE: (6) is inconsistent.
% 22.16/3.79 |
% 22.16/3.79 End of proof
% 22.16/3.79
% 22.16/3.79 Sub-proof #4 shows that the following formulas are inconsistent:
% 22.16/3.79 ----------------------------------------------------------------
% 22.16/3.79 (1) ~ (all_20_1 = e0)
% 22.16/3.79 (2) all_56_8 = e1
% 22.16/3.79 (3) all_56_11 = all_20_1
% 22.16/3.79 (4) ~ (e1 = e0)
% 22.16/3.79 (5) all_56_8 = e0 | all_56_11 = e0
% 22.16/3.79
% 22.16/3.79 Begin of proof
% 22.16/3.79 |
% 22.16/3.79 | BETA: splitting (5) gives:
% 22.16/3.79 |
% 22.16/3.79 | Case 1:
% 22.16/3.79 | |
% 22.16/3.79 | | (6) all_56_8 = e0
% 22.16/3.79 | |
% 22.16/3.79 | | COMBINE_EQS: (2), (6) imply:
% 22.16/3.79 | | (7) e1 = e0
% 22.16/3.79 | |
% 22.16/3.79 | | REDUCE: (4), (7) imply:
% 22.16/3.79 | | (8) $false
% 22.16/3.79 | |
% 22.16/3.79 | | CLOSE: (8) is inconsistent.
% 22.16/3.79 | |
% 22.16/3.79 | Case 2:
% 22.16/3.79 | |
% 22.16/3.79 | | (9) all_56_11 = e0
% 22.16/3.79 | |
% 22.16/3.79 | | COMBINE_EQS: (3), (9) imply:
% 22.16/3.79 | | (10) all_20_1 = e0
% 22.16/3.79 | |
% 22.16/3.79 | | REDUCE: (1), (10) imply:
% 22.16/3.79 | | (11) $false
% 22.16/3.79 | |
% 22.16/3.79 | | CLOSE: (11) is inconsistent.
% 22.16/3.79 | |
% 22.16/3.79 | End of split
% 22.16/3.79 |
% 22.16/3.79 End of proof
% 22.16/3.79
% 22.16/3.79 Sub-proof #5 shows that the following formulas are inconsistent:
% 22.16/3.79 ----------------------------------------------------------------
% 22.16/3.79 (1) all_56_6 = all_14_1
% 22.16/3.79 (2) all_56_6 = e0
% 22.16/3.79 (3) ~ (all_14_1 = e0)
% 22.16/3.79
% 22.16/3.79 Begin of proof
% 22.16/3.79 |
% 22.16/3.79 | COMBINE_EQS: (1), (2) imply:
% 22.16/3.79 | (4) all_14_1 = e0
% 22.16/3.79 |
% 22.16/3.79 | SIMP: (4) implies:
% 22.16/3.79 | (5) all_14_1 = e0
% 22.16/3.79 |
% 22.16/3.79 | REDUCE: (3), (5) imply:
% 22.16/3.79 | (6) $false
% 22.16/3.79 |
% 22.16/3.79 | CLOSE: (6) is inconsistent.
% 22.16/3.79 |
% 22.16/3.79 End of proof
% 22.16/3.79 % SZS output end Proof for theBenchmark
% 22.16/3.79
% 22.16/3.79 3188ms
%------------------------------------------------------------------------------