TSTP Solution File: ALG135+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG135+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 : n003.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 16:36:58 EDT 2023
% Result : Unsatisfiable 12.23s 2.48s
% Output : Proof 112.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG135+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 04:26:10 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.62/1.37 Prover 1: Preprocessing ...
% 3.62/1.39 Prover 4: Preprocessing ...
% 3.62/1.44 Prover 5: Preprocessing ...
% 3.62/1.44 Prover 3: Preprocessing ...
% 3.62/1.44 Prover 6: Preprocessing ...
% 3.62/1.44 Prover 0: Preprocessing ...
% 3.62/1.44 Prover 2: Preprocessing ...
% 7.57/1.81 Prover 3: Constructing countermodel ...
% 7.57/1.81 Prover 2: Constructing countermodel ...
% 7.57/1.85 Prover 6: Constructing countermodel ...
% 7.57/1.85 Prover 0: Constructing countermodel ...
% 8.09/1.88 Prover 1: Constructing countermodel ...
% 8.09/1.90 Prover 4: Constructing countermodel ...
% 8.95/2.14 Prover 5: Constructing countermodel ...
% 12.23/2.48 Prover 3: proved (1861ms)
% 12.23/2.48
% 12.23/2.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.23/2.48
% 12.23/2.48 Prover 2: stopped
% 12.23/2.48 Prover 6: stopped
% 12.23/2.48 Prover 0: stopped
% 12.23/2.48 Prover 5: stopped
% 12.23/2.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.23/2.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.23/2.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.23/2.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.23/2.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.71/2.68 Prover 8: Preprocessing ...
% 13.71/2.69 Prover 13: Preprocessing ...
% 13.71/2.70 Prover 10: Preprocessing ...
% 13.71/2.71 Prover 7: Preprocessing ...
% 13.71/2.72 Prover 11: Preprocessing ...
% 15.31/2.89 Prover 8: Constructing countermodel ...
% 16.60/3.04 Prover 13: Constructing countermodel ...
% 16.60/3.06 Prover 7: Constructing countermodel ...
% 16.86/3.08 Prover 10: Constructing countermodel ...
% 16.86/3.11 Prover 11: Constructing countermodel ...
% 59.93/8.88 Prover 13: stopped
% 59.93/8.88 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 62.01/8.97 Prover 16: Preprocessing ...
% 63.45/9.15 Prover 16: Constructing countermodel ...
% 105.85/14.75 Prover 16: Found proof (size 15971)
% 105.85/14.75 Prover 16: proved (5866ms)
% 105.85/14.75 Prover 8: stopped
% 105.85/14.75 Prover 11: stopped
% 105.85/14.76 Prover 7: stopped
% 105.85/14.76 Prover 4: stopped
% 105.85/14.76 Prover 10: stopped
% 105.85/14.76 Prover 1: stopped
% 105.85/14.76
% 106.43/14.76 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 106.43/14.76
% 106.81/14.93 % SZS output start Proof for theBenchmark
% 106.93/14.95 Assumptions after simplification:
% 106.93/14.95 ---------------------------------
% 106.93/14.95
% 106.93/14.95 (ax1)
% 106.96/15.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.96/15.00 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 106.96/15.00 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 106.96/15.00 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v0 & op(e3, e2) = v1 &
% 106.96/15.00 op(e3, e1) = v2 & op(e3, e0) = v3 & op(e2, e3) = v4 & op(e2, e2) = v5 &
% 106.96/15.00 op(e2, e1) = v6 & op(e2, e0) = v7 & op(e1, e3) = v8 & op(e1, e2) = v9 &
% 106.96/15.00 op(e1, e1) = v10 & op(e1, e0) = v11 & op(e0, e3) = v12 & op(e0, e2) = v13 &
% 106.96/15.00 op(e0, e1) = v14 & op(e0, e0) = v15 & $i(v15) & $i(v14) & $i(v13) & $i(v12)
% 106.96/15.00 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 106.96/15.00 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 =
% 106.96/15.00 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 |
% 106.96/15.00 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11
% 106.96/15.00 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 |
% 106.96/15.00 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 |
% 106.96/15.00 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 |
% 106.96/15.00 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 106.96/15.00 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3
% 106.96/15.00 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1
% 106.96/15.00 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 106.96/15.00
% 106.96/15.00 (ax10)
% 106.96/15.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.96/15.00 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e2) = v1 & $i(v1) & ( ~
% 106.96/15.00 (v1 = e0) | ( ~ (v2 = e3) & op(e0, e2) = v2 & $i(v2))))))
% 106.96/15.00
% 106.96/15.00 (ax11)
% 106.96/15.01 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.96/15.01 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e1) = v1 & $i(v1) & ( ~
% 106.96/15.01 (v1 = e0) | ( ~ (v2 = e3) & op(e0, e1) = v2 & $i(v2))))))
% 106.96/15.01
% 106.96/15.01 (ax12)
% 106.96/15.01 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.96/15.01 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e3) = v1 & $i(v1) & ( ~
% 106.96/15.01 (v1 = e1) | ( ~ (v2 = e0) & op(e1, e3) = v2 & $i(v2))))))
% 106.96/15.01
% 106.96/15.01 (ax13)
% 106.96/15.01 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.96/15.01 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e2) = v1 & $i(v1) & ( ~
% 106.96/15.01 (v1 = e1) | ( ~ (v2 = e0) & op(e1, e2) = v2 & $i(v2))))))
% 106.96/15.01
% 106.96/15.01 (ax14)
% 106.96/15.01 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.96/15.01 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e3) = v1 & $i(v1) & ( ~
% 106.96/15.01 (v1 = e1) | ( ~ (v2 = e2) & op(e1, e3) = v2 & $i(v2))))))
% 106.96/15.01
% 106.96/15.01 (ax15)
% 106.96/15.01 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.96/15.01 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e0) = v1 & $i(v1) & ( ~
% 106.96/15.01 (v1 = e1) | ( ~ (v2 = e2) & op(e1, e0) = v2 & $i(v2))))))
% 106.96/15.01
% 106.96/15.01 (ax16)
% 106.96/15.01 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.96/15.01 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e2) = v1 & $i(v1) & ( ~
% 106.96/15.02 (v1 = e1) | ( ~ (v2 = e3) & op(e1, e2) = v2 & $i(v2))))))
% 106.96/15.02
% 106.96/15.02 (ax17)
% 106.96/15.02 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.96/15.02 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e0) = v1 & $i(v1) & ( ~
% 106.96/15.02 (v1 = e1) | ( ~ (v2 = e3) & op(e1, e0) = v2 & $i(v2))))))
% 106.96/15.02
% 106.96/15.02 (ax18)
% 106.96/15.02 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.96/15.02 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e3) = v1 & $i(v1) & ( ~
% 106.96/15.02 (v1 = e2) | ( ~ (v2 = e0) & op(e2, e3) = v2 & $i(v2))))))
% 106.96/15.02
% 106.96/15.02 (ax19)
% 106.96/15.02 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.96/15.02 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e1) = v1 & $i(v1) & ( ~
% 106.96/15.02 (v1 = e2) | ( ~ (v2 = e0) & op(e2, e1) = v2 & $i(v2))))))
% 106.96/15.02
% 106.96/15.02 (ax2)
% 107.26/15.04 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.26/15.04 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 107.26/15.04 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 107.26/15.04 $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18:
% 107.26/15.04 $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23:
% 107.26/15.04 $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28:
% 107.26/15.04 $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? [v33:
% 107.26/15.04 $i] : ? [v34: $i] : ? [v35: $i] : ? [v36: $i] : ? [v37: $i] : ? [v38:
% 107.26/15.04 $i] : ? [v39: $i] : ? [v40: $i] : ? [v41: $i] : ? [v42: $i] : ? [v43:
% 107.26/15.04 $i] : ? [v44: $i] : ? [v45: $i] : ? [v46: $i] : ? [v47: $i] : ? [v48:
% 107.26/15.04 $i] : ? [v49: $i] : ? [v50: $i] : ? [v51: $i] : ? [v52: $i] : ? [v53:
% 107.26/15.04 $i] : ? [v54: $i] : ? [v55: $i] : ? [v56: $i] : ? [v57: $i] : ? [v58:
% 107.26/15.04 $i] : ? [v59: $i] : ? [v60: $i] : ? [v61: $i] : ? [v62: $i] : ? [v63:
% 107.26/15.04 $i] : ? [v64: $i] : ? [v65: $i] : ? [v66: $i] : ? [v67: $i] : ? [v68:
% 107.26/15.04 $i] : ? [v69: $i] : ? [v70: $i] : ? [v71: $i] : ? [v72: $i] : ? [v73:
% 107.26/15.04 $i] : ? [v74: $i] : ? [v75: $i] : ? [v76: $i] : ? [v77: $i] : ? [v78:
% 107.26/15.04 $i] : ? [v79: $i] : ? [v80: $i] : ? [v81: $i] : ? [v82: $i] : ? [v83:
% 107.26/15.04 $i] : ? [v84: $i] : ? [v85: $i] : ? [v86: $i] : ? [v87: $i] : ? [v88:
% 107.26/15.04 $i] : ? [v89: $i] : ? [v90: $i] : ? [v91: $i] : ? [v92: $i] : ? [v93:
% 107.26/15.04 $i] : ? [v94: $i] : ? [v95: $i] : ? [v96: $i] : ? [v97: $i] : ? [v98:
% 107.26/15.04 $i] : ? [v99: $i] : ? [v100: $i] : ? [v101: $i] : ? [v102: $i] : ?
% 107.26/15.04 [v103: $i] : ? [v104: $i] : ? [v105: $i] : ? [v106: $i] : ? [v107: $i] :
% 107.26/15.04 ? [v108: $i] : ? [v109: $i] : ? [v110: $i] : ? [v111: $i] : ? [v112: $i] :
% 107.26/15.04 ? [v113: $i] : ? [v114: $i] : ? [v115: $i] : ? [v116: $i] : ? [v117: $i]
% 107.26/15.04 : ? [v118: $i] : ? [v119: $i] : ? [v120: $i] : ? [v121: $i] : ? [v122:
% 107.26/15.04 $i] : ? [v123: $i] : ? [v124: $i] : ? [v125: $i] : ? [v126: $i] : ?
% 107.26/15.04 [v127: $i] : (((v127 = e0 & op(e0, e3) = e0) | (v126 = e0 & op(e0, e2) = e0) |
% 107.26/15.04 (v125 = e0 & op(e0, e1) = e0) | (v124 = e0 & op(e0, e0) = e0)) & ((v123 =
% 107.26/15.04 e0 & op(e3, e0) = e0) | (v122 = e0 & op(e2, e0) = e0) | (v121 = e0 &
% 107.26/15.04 op(e1, e0) = e0) | (v120 = e0 & op(e0, e0) = e0)) & ((v119 = e1 & op(e0,
% 107.26/15.04 e3) = e1) | (v118 = e1 & op(e0, e2) = e1) | (v117 = e1 & op(e0, e1) =
% 107.26/15.04 e1) | (v116 = e1 & op(e0, e0) = e1)) & ((v115 = e1 & op(e3, e0) = e1) |
% 107.26/15.04 (v114 = e1 & op(e2, e0) = e1) | (v113 = e1 & op(e1, e0) = e1) | (v112 = e1
% 107.26/15.04 & op(e0, e0) = e1)) & ((v111 = e2 & op(e0, e3) = e2) | (v110 = e2 &
% 107.26/15.04 op(e0, e2) = e2) | (v109 = e2 & op(e0, e1) = e2) | (v108 = e2 & op(e0,
% 107.26/15.04 e0) = e2)) & ((v107 = e2 & op(e3, e0) = e2) | (v106 = e2 & op(e2, e0)
% 107.26/15.04 = e2) | (v105 = e2 & op(e1, e0) = e2) | (v104 = e2 & op(e0, e0) = e2)) &
% 107.26/15.04 ((v103 = e3 & op(e0, e3) = e3) | (v102 = e3 & op(e0, e2) = e3) | (v101 = e3
% 107.26/15.04 & op(e0, e1) = e3) | (v100 = e3 & op(e0, e0) = e3)) & ((v99 = e3 &
% 107.26/15.04 op(e3, e0) = e3) | (v98 = e3 & op(e2, e0) = e3) | (v97 = e3 & op(e1, e0)
% 107.26/15.04 = e3) | (v96 = e3 & op(e0, e0) = e3)) & ((v95 = e0 & op(e1, e3) = e0) |
% 107.26/15.04 (v94 = e0 & op(e1, e2) = e0) | (v93 = e0 & op(e1, e1) = e0) | (v92 = e0 &
% 107.26/15.04 op(e1, e0) = e0)) & ((v91 = e0 & op(e3, e1) = e0) | (v90 = e0 & op(e2,
% 107.26/15.04 e1) = e0) | (v89 = e0 & op(e1, e1) = e0) | (v88 = e0 & op(e0, e1) =
% 107.26/15.04 e0)) & ((v87 = e1 & op(e1, e3) = e1) | (v86 = e1 & op(e1, e2) = e1) |
% 107.26/15.04 (v85 = e1 & op(e1, e1) = e1) | (v84 = e1 & op(e1, e0) = e1)) & ((v83 = e1
% 107.26/15.04 & op(e3, e1) = e1) | (v82 = e1 & op(e2, e1) = e1) | (v81 = e1 & op(e1,
% 107.26/15.04 e1) = e1) | (v80 = e1 & op(e0, e1) = e1)) & ((v79 = e2 & op(e1, e3) =
% 107.26/15.04 e2) | (v78 = e2 & op(e1, e2) = e2) | (v77 = e2 & op(e1, e1) = e2) | (v76
% 107.26/15.04 = e2 & op(e1, e0) = e2)) & ((v75 = e2 & op(e3, e1) = e2) | (v74 = e2 &
% 107.26/15.04 op(e2, e1) = e2) | (v73 = e2 & op(e1, e1) = e2) | (v72 = e2 & op(e0, e1)
% 107.26/15.04 = e2)) & ((v71 = e3 & op(e1, e3) = e3) | (v70 = e3 & op(e1, e2) = e3) |
% 107.26/15.04 (v69 = e3 & op(e1, e1) = e3) | (v68 = e3 & op(e1, e0) = e3)) & ((v67 = e3
% 107.26/15.04 & op(e3, e1) = e3) | (v66 = e3 & op(e2, e1) = e3) | (v65 = e3 & op(e1,
% 107.26/15.04 e1) = e3) | (v64 = e3 & op(e0, e1) = e3)) & ((v63 = e0 & op(e2, e3) =
% 107.26/15.04 e0) | (v62 = e0 & op(e2, e2) = e0) | (v61 = e0 & op(e2, e1) = e0) | (v60
% 107.26/15.04 = e0 & op(e2, e0) = e0)) & ((v59 = e0 & op(e3, e2) = e0) | (v58 = e0 &
% 107.26/15.04 op(e2, e2) = e0) | (v57 = e0 & op(e1, e2) = e0) | (v56 = e0 & op(e0, e2)
% 107.26/15.04 = e0)) & ((v55 = e1 & op(e2, e3) = e1) | (v54 = e1 & op(e2, e2) = e1) |
% 107.26/15.04 (v53 = e1 & op(e2, e1) = e1) | (v52 = e1 & op(e2, e0) = e1)) & ((v51 = e1
% 107.26/15.04 & op(e3, e2) = e1) | (v50 = e1 & op(e2, e2) = e1) | (v49 = e1 & op(e1,
% 107.26/15.04 e2) = e1) | (v48 = e1 & op(e0, e2) = e1)) & ((v47 = e2 & op(e2, e3) =
% 107.26/15.04 e2) | (v46 = e2 & op(e2, e2) = e2) | (v45 = e2 & op(e2, e1) = e2) | (v44
% 107.26/15.04 = e2 & op(e2, e0) = e2)) & ((v43 = e2 & op(e3, e2) = e2) | (v42 = e2 &
% 107.26/15.04 op(e2, e2) = e2) | (v41 = e2 & op(e1, e2) = e2) | (v40 = e2 & op(e0, e2)
% 107.26/15.04 = e2)) & ((v39 = e3 & op(e2, e3) = e3) | (v38 = e3 & op(e2, e2) = e3) |
% 107.26/15.04 (v37 = e3 & op(e2, e1) = e3) | (v36 = e3 & op(e2, e0) = e3)) & ((v35 = e3
% 107.26/15.04 & op(e3, e2) = e3) | (v34 = e3 & op(e2, e2) = e3) | (v33 = e3 & op(e1,
% 107.26/15.04 e2) = e3) | (v32 = e3 & op(e0, e2) = e3)) & ((v31 = e0 & op(e3, e3) =
% 107.26/15.04 e0) | (v30 = e0 & op(e3, e2) = e0) | (v29 = e0 & op(e3, e1) = e0) | (v28
% 107.26/15.04 = e0 & op(e3, e0) = e0)) & ((v27 = e0 & op(e3, e3) = e0) | (v26 = e0 &
% 107.26/15.04 op(e2, e3) = e0) | (v25 = e0 & op(e1, e3) = e0) | (v24 = e0 & op(e0, e3)
% 107.26/15.04 = e0)) & ((v23 = e1 & op(e3, e3) = e1) | (v22 = e1 & op(e3, e2) = e1) |
% 107.26/15.04 (v21 = e1 & op(e3, e1) = e1) | (v20 = e1 & op(e3, e0) = e1)) & ((v19 = e1
% 107.26/15.04 & op(e3, e3) = e1) | (v18 = e1 & op(e2, e3) = e1) | (v17 = e1 & op(e1,
% 107.26/15.04 e3) = e1) | (v16 = e1 & op(e0, e3) = e1)) & ((v15 = e2 & op(e3, e3) =
% 107.26/15.04 e2) | (v14 = e2 & op(e3, e2) = e2) | (v13 = e2 & op(e3, e1) = e2) | (v12
% 107.26/15.04 = e2 & op(e3, e0) = e2)) & ((v11 = e2 & op(e3, e3) = e2) | (v10 = e2 &
% 107.26/15.05 op(e2, e3) = e2) | (v9 = e2 & op(e1, e3) = e2) | (v8 = e2 & op(e0, e3) =
% 107.26/15.05 e2)) & ((v7 = e3 & op(e3, e3) = e3) | (v6 = e3 & op(e3, e2) = e3) | (v5
% 107.26/15.05 = e3 & op(e3, e1) = e3) | (v4 = e3 & op(e3, e0) = e3)) & ((v3 = e3 &
% 107.26/15.05 op(e3, e3) = e3) | (v2 = e3 & op(e2, e3) = e3) | (v1 = e3 & op(e1, e3) =
% 107.26/15.05 e3) | (v0 = e3 & op(e0, e3) = e3)))
% 107.26/15.05
% 107.26/15.05 (ax20)
% 107.26/15.05 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.26/15.05 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e3) = v1 & $i(v1) & ( ~
% 107.26/15.05 (v1 = e2) | ( ~ (v2 = e1) & op(e2, e3) = v2 & $i(v2))))))
% 107.26/15.05
% 107.26/15.05 (ax21)
% 107.26/15.05 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.26/15.05 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e0) = v1 & $i(v1) & ( ~
% 107.26/15.05 (v1 = e2) | ( ~ (v2 = e1) & op(e2, e0) = v2 & $i(v2))))))
% 107.26/15.05
% 107.26/15.05 (ax22)
% 107.26/15.05 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.26/15.05 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e1) = v1 & $i(v1) & ( ~
% 107.26/15.05 (v1 = e2) | ( ~ (v2 = e3) & op(e2, e1) = v2 & $i(v2))))))
% 107.26/15.05
% 107.26/15.05 (ax23)
% 107.26/15.05 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.26/15.05 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e0) = v1 & $i(v1) & ( ~
% 107.26/15.05 (v1 = e2) | ( ~ (v2 = e3) & op(e2, e0) = v2 & $i(v2))))))
% 107.26/15.05
% 107.26/15.05 (ax24)
% 107.26/15.05 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.26/15.05 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e2) = v1 & $i(v1) & ( ~
% 107.26/15.05 (v1 = e3) | ( ~ (v2 = e0) & op(e3, e2) = v2 & $i(v2))))))
% 107.26/15.05
% 107.26/15.05 (ax25)
% 107.26/15.05 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.26/15.05 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e1) = v1 & $i(v1) & ( ~
% 107.26/15.05 (v1 = e3) | ( ~ (v2 = e0) & op(e3, e1) = v2 & $i(v2))))))
% 107.26/15.05
% 107.26/15.05 (ax26)
% 107.26/15.05 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.26/15.05 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e2) = v1 & $i(v1) & ( ~
% 107.26/15.05 (v1 = e3) | ( ~ (v2 = e1) & op(e3, e2) = v2 & $i(v2))))))
% 107.26/15.05
% 107.26/15.05 (ax27)
% 107.26/15.06 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.26/15.06 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e0) = v1 & $i(v1) & ( ~
% 107.26/15.06 (v1 = e3) | ( ~ (v2 = e1) & op(e3, e0) = v2 & $i(v2))))))
% 107.26/15.06
% 107.26/15.06 (ax28)
% 107.26/15.06 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.26/15.06 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e1) = v1 & $i(v1) & ( ~
% 107.26/15.06 (v1 = e3) | ( ~ (v2 = e2) & op(e3, e1) = v2 & $i(v2))))))
% 107.26/15.06
% 107.26/15.06 (ax29)
% 107.45/15.06 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.45/15.06 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e0) = v1 & $i(v1) & ( ~
% 107.45/15.06 (v1 = e3) | ( ~ (v2 = e2) & op(e3, e0) = v2 & $i(v2))))))
% 107.45/15.06
% 107.45/15.06 (ax3)
% 107.45/15.06 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.45/15.06 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 107.45/15.06 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 107.45/15.06 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~
% 107.45/15.06 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 =
% 107.45/15.06 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) &
% 107.45/15.06 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 =
% 107.45/15.06 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~
% 107.45/15.06 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) &
% 107.45/15.06 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) &
% 107.45/15.06 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) &
% 107.45/15.06 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~
% 107.45/15.06 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~
% 107.45/15.06 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v1 & op(e3, e2) = v0
% 107.45/15.06 & op(e3, e1) = v2 & op(e3, e0) = v3 & op(e2, e3) = v5 & op(e2, e2) = v4 &
% 107.45/15.06 op(e2, e1) = v6 & op(e2, e0) = v7 & op(e1, e3) = v9 & op(e1, e2) = v8 &
% 107.45/15.06 op(e1, e1) = v10 & op(e1, e0) = v11 & op(e0, e3) = v13 & op(e0, e2) = v12 &
% 107.45/15.06 op(e0, e1) = v14 & op(e0, e0) = v15 & $i(v15) & $i(v14) & $i(v13) & $i(v12)
% 107.45/15.06 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 107.45/15.06 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 107.45/15.06
% 107.45/15.07 (ax4)
% 107.45/15.07 ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~
% 107.45/15.07 (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 107.45/15.07
% 107.45/15.07 (ax5)
% 107.45/15.07 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.45/15.07 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 107.45/15.07 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 107.45/15.07 $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18:
% 107.45/15.07 $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23:
% 107.45/15.07 $i] : (((v22 = e3 & ~ (v23 = e0) & op(e3, e0) = e3 & op(e0, e3) = v23 &
% 107.45/15.07 $i(v23)) | (v20 = e2 & ~ (v21 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 107.45/15.07 v21 & $i(v21)) | (v18 = e1 & ~ (v19 = e0) & op(e1, e0) = e1 & op(e0,
% 107.45/15.07 e1) = v19 & $i(v19))) & ((v16 = e3 & ~ (v17 = e1) & op(e3, e1) = e3 &
% 107.45/15.07 op(e1, e3) = v17 & $i(v17)) | (v14 = e2 & ~ (v15 = e1) & op(e2, e1) =
% 107.45/15.07 e2 & op(e1, e2) = v15 & $i(v15)) | (v12 = e0 & ~ (v13 = e1) & op(e1,
% 107.45/15.07 e0) = v13 & op(e0, e1) = e0 & $i(v13))) & ((v10 = e3 & ~ (v11 = e2) &
% 107.45/15.07 op(e3, e2) = e3 & op(e2, e3) = v11 & $i(v11)) | (v8 = e1 & ~ (v9 = e2)
% 107.45/15.07 & op(e2, e1) = v9 & op(e1, e2) = e1 & $i(v9)) | (v6 = e0 & ~ (v7 = e2)
% 107.45/15.07 & op(e2, e0) = v7 & op(e0, e2) = e0 & $i(v7))) & ((v4 = e2 & ~ (v5 =
% 107.45/15.07 e3) & op(e3, e2) = v5 & op(e2, e3) = e2 & $i(v5)) | (v2 = e1 & ~ (v3
% 107.45/15.07 = e3) & op(e3, e1) = v3 & op(e1, e3) = e1 & $i(v3)) | (v0 = e0 & ~
% 107.45/15.07 (v1 = e3) & op(e3, e0) = v1 & op(e0, e3) = e0 & $i(v1))))
% 107.45/15.07
% 107.45/15.07 (ax6)
% 107.45/15.08 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.45/15.08 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e3) = v1 & $i(v1) & ( ~
% 107.45/15.08 (v1 = e0) | ( ~ (v2 = e1) & op(e0, e3) = v2 & $i(v2))))))
% 107.45/15.08
% 107.45/15.08 (ax7)
% 107.45/15.08 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.45/15.08 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e2) = v1 & $i(v1) & ( ~
% 107.45/15.08 (v1 = e0) | ( ~ (v2 = e1) & op(e0, e2) = v2 & $i(v2))))))
% 107.45/15.08
% 107.45/15.08 (ax8)
% 107.45/15.08 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.45/15.08 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e3) = v1 & $i(v1) & ( ~
% 107.45/15.08 (v1 = e0) | ( ~ (v2 = e2) & op(e0, e3) = v2 & $i(v2))))))
% 107.45/15.08
% 107.45/15.08 (ax9)
% 107.45/15.08 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 107.45/15.08 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e1) = v1 & $i(v1) & ( ~
% 107.45/15.08 (v1 = e0) | ( ~ (v2 = e2) & op(e0, e1) = v2 & $i(v2))))))
% 107.45/15.08
% 107.45/15.08 (function-axioms)
% 107.45/15.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3,
% 107.45/15.08 v2) = v1) | ~ (op(v3, v2) = v0))
% 107.45/15.08
% 107.45/15.08 Those formulas are unsatisfiable:
% 107.45/15.08 ---------------------------------
% 107.45/15.08
% 107.45/15.08 Begin of proof
% 107.45/15.08 |
% 107.45/15.08 | ALPHA: (ax1) implies:
% 107.45/15.09 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 107.45/15.09 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 107.45/15.09 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 107.45/15.09 | ? [v15: $i] : (op(e3, e3) = v0 & op(e3, e2) = v1 & op(e3, e1) = v2 &
% 107.45/15.09 | op(e3, e0) = v3 & op(e2, e3) = v4 & op(e2, e2) = v5 & op(e2, e1) = v6
% 107.45/15.09 | & op(e2, e0) = v7 & op(e1, e3) = v8 & op(e1, e2) = v9 & op(e1, e1) =
% 107.45/15.09 | v10 & op(e1, e0) = v11 & op(e0, e3) = v12 & op(e0, e2) = v13 & op(e0,
% 107.45/15.09 | e1) = v14 & op(e0, e0) = v15 & $i(v15) & $i(v14) & $i(v13) &
% 107.45/15.09 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 107.45/15.09 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15
% 107.45/15.09 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14
% 107.45/15.09 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 |
% 107.45/15.09 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 |
% 107.45/15.09 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3
% 107.45/15.09 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8
% 107.45/15.09 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 =
% 107.45/15.09 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 107.45/15.09 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 =
% 107.45/15.09 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3
% 107.45/15.09 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0
% 107.45/15.09 | = e0))
% 107.45/15.09 |
% 107.45/15.09 | ALPHA: (ax2) implies:
% 107.45/15.10 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 107.45/15.10 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 107.45/15.10 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 107.45/15.10 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19:
% 107.45/15.10 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ?
% 107.45/15.10 | [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i] :
% 107.45/15.10 | ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? [v33:
% 107.45/15.10 | $i] : ? [v34: $i] : ? [v35: $i] : ? [v36: $i] : ? [v37: $i] : ?
% 107.45/15.10 | [v38: $i] : ? [v39: $i] : ? [v40: $i] : ? [v41: $i] : ? [v42: $i] :
% 107.45/15.10 | ? [v43: $i] : ? [v44: $i] : ? [v45: $i] : ? [v46: $i] : ? [v47:
% 107.45/15.10 | $i] : ? [v48: $i] : ? [v49: $i] : ? [v50: $i] : ? [v51: $i] : ?
% 107.45/15.10 | [v52: $i] : ? [v53: $i] : ? [v54: $i] : ? [v55: $i] : ? [v56: $i] :
% 107.45/15.10 | ? [v57: $i] : ? [v58: $i] : ? [v59: $i] : ? [v60: $i] : ? [v61:
% 107.45/15.11 | $i] : ? [v62: $i] : ? [v63: $i] : ? [v64: $i] : ? [v65: $i] : ?
% 107.45/15.11 | [v66: $i] : ? [v67: $i] : ? [v68: $i] : ? [v69: $i] : ? [v70: $i] :
% 107.45/15.11 | ? [v71: $i] : ? [v72: $i] : ? [v73: $i] : ? [v74: $i] : ? [v75:
% 107.45/15.11 | $i] : ? [v76: $i] : ? [v77: $i] : ? [v78: $i] : ? [v79: $i] : ?
% 107.45/15.11 | [v80: $i] : ? [v81: $i] : ? [v82: $i] : ? [v83: $i] : ? [v84: $i] :
% 107.45/15.11 | ? [v85: $i] : ? [v86: $i] : ? [v87: $i] : ? [v88: $i] : ? [v89:
% 107.45/15.11 | $i] : ? [v90: $i] : ? [v91: $i] : ? [v92: $i] : ? [v93: $i] : ?
% 107.45/15.11 | [v94: $i] : ? [v95: $i] : ? [v96: $i] : ? [v97: $i] : ? [v98: $i] :
% 107.45/15.11 | ? [v99: $i] : ? [v100: $i] : ? [v101: $i] : ? [v102: $i] : ?
% 107.45/15.11 | [v103: $i] : ? [v104: $i] : ? [v105: $i] : ? [v106: $i] : ? [v107:
% 107.45/15.11 | $i] : ? [v108: $i] : ? [v109: $i] : ? [v110: $i] : ? [v111: $i] :
% 107.45/15.11 | ? [v112: $i] : ? [v113: $i] : ? [v114: $i] : ? [v115: $i] : ?
% 107.45/15.11 | [v116: $i] : ? [v117: $i] : ? [v118: $i] : ? [v119: $i] : ? [v120:
% 107.45/15.11 | $i] : ? [v121: $i] : ? [v122: $i] : ? [v123: $i] : ? [v124: $i] :
% 107.45/15.11 | ? [v125: $i] : ? [v126: $i] : ? [v127: $i] : (((v127 = e0 & op(e0,
% 107.45/15.11 | e3) = e0) | (v126 = e0 & op(e0, e2) = e0) | (v125 = e0 & op(e0,
% 107.45/15.11 | e1) = e0) | (v124 = e0 & op(e0, e0) = e0)) & ((v123 = e0 &
% 107.45/15.11 | op(e3, e0) = e0) | (v122 = e0 & op(e2, e0) = e0) | (v121 = e0 &
% 107.45/15.11 | op(e1, e0) = e0) | (v120 = e0 & op(e0, e0) = e0)) & ((v119 = e1 &
% 107.45/15.11 | op(e0, e3) = e1) | (v118 = e1 & op(e0, e2) = e1) | (v117 = e1 &
% 107.45/15.11 | op(e0, e1) = e1) | (v116 = e1 & op(e0, e0) = e1)) & ((v115 = e1 &
% 107.45/15.11 | op(e3, e0) = e1) | (v114 = e1 & op(e2, e0) = e1) | (v113 = e1 &
% 107.45/15.11 | op(e1, e0) = e1) | (v112 = e1 & op(e0, e0) = e1)) & ((v111 = e2 &
% 107.45/15.11 | op(e0, e3) = e2) | (v110 = e2 & op(e0, e2) = e2) | (v109 = e2 &
% 107.45/15.11 | op(e0, e1) = e2) | (v108 = e2 & op(e0, e0) = e2)) & ((v107 = e2 &
% 107.45/15.11 | op(e3, e0) = e2) | (v106 = e2 & op(e2, e0) = e2) | (v105 = e2 &
% 107.45/15.11 | op(e1, e0) = e2) | (v104 = e2 & op(e0, e0) = e2)) & ((v103 = e3 &
% 107.45/15.11 | op(e0, e3) = e3) | (v102 = e3 & op(e0, e2) = e3) | (v101 = e3 &
% 107.45/15.11 | op(e0, e1) = e3) | (v100 = e3 & op(e0, e0) = e3)) & ((v99 = e3 &
% 107.45/15.11 | op(e3, e0) = e3) | (v98 = e3 & op(e2, e0) = e3) | (v97 = e3 &
% 107.45/15.11 | op(e1, e0) = e3) | (v96 = e3 & op(e0, e0) = e3)) & ((v95 = e0 &
% 107.45/15.11 | op(e1, e3) = e0) | (v94 = e0 & op(e1, e2) = e0) | (v93 = e0 &
% 107.45/15.11 | op(e1, e1) = e0) | (v92 = e0 & op(e1, e0) = e0)) & ((v91 = e0 &
% 107.45/15.11 | op(e3, e1) = e0) | (v90 = e0 & op(e2, e1) = e0) | (v89 = e0 &
% 107.45/15.11 | op(e1, e1) = e0) | (v88 = e0 & op(e0, e1) = e0)) & ((v87 = e1 &
% 107.45/15.11 | op(e1, e3) = e1) | (v86 = e1 & op(e1, e2) = e1) | (v85 = e1 &
% 107.45/15.11 | op(e1, e1) = e1) | (v84 = e1 & op(e1, e0) = e1)) & ((v83 = e1 &
% 107.45/15.11 | op(e3, e1) = e1) | (v82 = e1 & op(e2, e1) = e1) | (v81 = e1 &
% 107.45/15.11 | op(e1, e1) = e1) | (v80 = e1 & op(e0, e1) = e1)) & ((v79 = e2 &
% 107.45/15.11 | op(e1, e3) = e2) | (v78 = e2 & op(e1, e2) = e2) | (v77 = e2 &
% 107.45/15.11 | op(e1, e1) = e2) | (v76 = e2 & op(e1, e0) = e2)) & ((v75 = e2 &
% 107.45/15.11 | op(e3, e1) = e2) | (v74 = e2 & op(e2, e1) = e2) | (v73 = e2 &
% 107.45/15.11 | op(e1, e1) = e2) | (v72 = e2 & op(e0, e1) = e2)) & ((v71 = e3 &
% 107.45/15.11 | op(e1, e3) = e3) | (v70 = e3 & op(e1, e2) = e3) | (v69 = e3 &
% 107.45/15.11 | op(e1, e1) = e3) | (v68 = e3 & op(e1, e0) = e3)) & ((v67 = e3 &
% 107.45/15.11 | op(e3, e1) = e3) | (v66 = e3 & op(e2, e1) = e3) | (v65 = e3 &
% 107.45/15.11 | op(e1, e1) = e3) | (v64 = e3 & op(e0, e1) = e3)) & ((v63 = e0 &
% 107.45/15.11 | op(e2, e3) = e0) | (v62 = e0 & op(e2, e2) = e0) | (v61 = e0 &
% 107.45/15.11 | op(e2, e1) = e0) | (v60 = e0 & op(e2, e0) = e0)) & ((v59 = e0 &
% 107.45/15.11 | op(e3, e2) = e0) | (v58 = e0 & op(e2, e2) = e0) | (v57 = e0 &
% 107.45/15.11 | op(e1, e2) = e0) | (v56 = e0 & op(e0, e2) = e0)) & ((v55 = e1 &
% 107.45/15.11 | op(e2, e3) = e1) | (v54 = e1 & op(e2, e2) = e1) | (v53 = e1 &
% 107.45/15.11 | op(e2, e1) = e1) | (v52 = e1 & op(e2, e0) = e1)) & ((v51 = e1 &
% 107.45/15.11 | op(e3, e2) = e1) | (v50 = e1 & op(e2, e2) = e1) | (v49 = e1 &
% 107.45/15.11 | op(e1, e2) = e1) | (v48 = e1 & op(e0, e2) = e1)) & ((v47 = e2 &
% 107.45/15.11 | op(e2, e3) = e2) | (v46 = e2 & op(e2, e2) = e2) | (v45 = e2 &
% 107.45/15.11 | op(e2, e1) = e2) | (v44 = e2 & op(e2, e0) = e2)) & ((v43 = e2 &
% 107.45/15.11 | op(e3, e2) = e2) | (v42 = e2 & op(e2, e2) = e2) | (v41 = e2 &
% 107.45/15.11 | op(e1, e2) = e2) | (v40 = e2 & op(e0, e2) = e2)) & ((v39 = e3 &
% 107.45/15.11 | op(e2, e3) = e3) | (v38 = e3 & op(e2, e2) = e3) | (v37 = e3 &
% 107.45/15.11 | op(e2, e1) = e3) | (v36 = e3 & op(e2, e0) = e3)) & ((v35 = e3 &
% 107.45/15.11 | op(e3, e2) = e3) | (v34 = e3 & op(e2, e2) = e3) | (v33 = e3 &
% 107.45/15.11 | op(e1, e2) = e3) | (v32 = e3 & op(e0, e2) = e3)) & ((v31 = e0 &
% 107.45/15.11 | op(e3, e3) = e0) | (v30 = e0 & op(e3, e2) = e0) | (v29 = e0 &
% 107.45/15.11 | op(e3, e1) = e0) | (v28 = e0 & op(e3, e0) = e0)) & ((v27 = e0 &
% 107.45/15.11 | op(e3, e3) = e0) | (v26 = e0 & op(e2, e3) = e0) | (v25 = e0 &
% 107.45/15.11 | op(e1, e3) = e0) | (v24 = e0 & op(e0, e3) = e0)) & ((v23 = e1 &
% 107.45/15.11 | op(e3, e3) = e1) | (v22 = e1 & op(e3, e2) = e1) | (v21 = e1 &
% 107.45/15.11 | op(e3, e1) = e1) | (v20 = e1 & op(e3, e0) = e1)) & ((v19 = e1 &
% 107.45/15.11 | op(e3, e3) = e1) | (v18 = e1 & op(e2, e3) = e1) | (v17 = e1 &
% 107.45/15.11 | op(e1, e3) = e1) | (v16 = e1 & op(e0, e3) = e1)) & ((v15 = e2 &
% 107.45/15.11 | op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v13 = e2 &
% 107.45/15.11 | op(e3, e1) = e2) | (v12 = e2 & op(e3, e0) = e2)) & ((v11 = e2 &
% 107.45/15.11 | op(e3, e3) = e2) | (v10 = e2 & op(e2, e3) = e2) | (v9 = e2 &
% 107.45/15.11 | op(e1, e3) = e2) | (v8 = e2 & op(e0, e3) = e2)) & ((v7 = e3 &
% 107.45/15.11 | op(e3, e3) = e3) | (v6 = e3 & op(e3, e2) = e3) | (v5 = e3 &
% 107.45/15.11 | op(e3, e1) = e3) | (v4 = e3 & op(e3, e0) = e3)) & ((v3 = e3 &
% 107.45/15.11 | op(e3, e3) = e3) | (v2 = e3 & op(e2, e3) = e3) | (v1 = e3 &
% 107.45/15.11 | op(e1, e3) = e3) | (v0 = e3 & op(e0, e3) = e3)))
% 107.45/15.11 |
% 107.45/15.11 | ALPHA: (ax3) implies:
% 107.45/15.11 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 107.45/15.11 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 107.45/15.11 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 107.45/15.11 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~
% 107.45/15.11 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~
% 107.45/15.11 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~
% 107.45/15.11 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12
% 107.45/15.11 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 =
% 107.45/15.11 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9)
% 107.45/15.11 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~
% 107.45/15.11 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6)
% 107.45/15.11 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6
% 107.45/15.11 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) &
% 107.45/15.11 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 =
% 107.45/15.11 | v0) & ~ (v1 = v0) & op(e3, e3) = v1 & op(e3, e2) = v0 & op(e3, e1)
% 107.45/15.11 | = v2 & op(e3, e0) = v3 & op(e2, e3) = v5 & op(e2, e2) = v4 & op(e2,
% 107.45/15.11 | e1) = v6 & op(e2, e0) = v7 & op(e1, e3) = v9 & op(e1, e2) = v8 &
% 107.45/15.11 | op(e1, e1) = v10 & op(e1, e0) = v11 & op(e0, e3) = v13 & op(e0, e2) =
% 107.45/15.11 | v12 & op(e0, e1) = v14 & op(e0, e0) = v15 & $i(v15) & $i(v14) &
% 107.45/15.11 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 107.45/15.11 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 107.45/15.11 |
% 107.45/15.11 | ALPHA: (ax4) implies:
% 107.45/15.11 | (4) ~ (e1 = e0)
% 107.45/15.11 | (5) ~ (e2 = e0)
% 107.45/15.11 | (6) ~ (e3 = e0)
% 107.45/15.11 | (7) ~ (e3 = e1)
% 107.45/15.11 | (8) ~ (e3 = e2)
% 107.45/15.11 |
% 107.45/15.11 | ALPHA: (ax5) implies:
% 107.45/15.12 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 107.45/15.12 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 107.45/15.12 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 107.45/15.12 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19:
% 107.45/15.12 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] :
% 107.45/15.12 | (((v22 = e3 & ~ (v23 = e0) & op(e3, e0) = e3 & op(e0, e3) = v23 &
% 107.45/15.12 | $i(v23)) | (v20 = e2 & ~ (v21 = e0) & op(e2, e0) = e2 & op(e0,
% 107.45/15.12 | e2) = v21 & $i(v21)) | (v18 = e1 & ~ (v19 = e0) & op(e1, e0) =
% 107.45/15.12 | e1 & op(e0, e1) = v19 & $i(v19))) & ((v16 = e3 & ~ (v17 = e1) &
% 107.45/15.12 | op(e3, e1) = e3 & op(e1, e3) = v17 & $i(v17)) | (v14 = e2 & ~
% 107.45/15.12 | (v15 = e1) & op(e2, e1) = e2 & op(e1, e2) = v15 & $i(v15)) | (v12
% 107.45/15.12 | = e0 & ~ (v13 = e1) & op(e1, e0) = v13 & op(e0, e1) = e0 &
% 107.45/15.12 | $i(v13))) & ((v10 = e3 & ~ (v11 = e2) & op(e3, e2) = e3 & op(e2,
% 107.45/15.12 | e3) = v11 & $i(v11)) | (v8 = e1 & ~ (v9 = e2) & op(e2, e1) =
% 107.45/15.12 | v9 & op(e1, e2) = e1 & $i(v9)) | (v6 = e0 & ~ (v7 = e2) & op(e2,
% 107.45/15.12 | e0) = v7 & op(e0, e2) = e0 & $i(v7))) & ((v4 = e2 & ~ (v5 =
% 107.45/15.12 | e3) & op(e3, e2) = v5 & op(e2, e3) = e2 & $i(v5)) | (v2 = e1 &
% 107.45/15.12 | ~ (v3 = e3) & op(e3, e1) = v3 & op(e1, e3) = e1 & $i(v3)) | (v0 =
% 107.45/15.12 | e0 & ~ (v1 = e3) & op(e3, e0) = v1 & op(e0, e3) = e0 & $i(v1))))
% 107.45/15.12 |
% 107.45/15.12 | ALPHA: (ax6) implies:
% 107.45/15.12 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 107.45/15.12 | ( ~ (v0 = e3) | (op(e3, e3) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2
% 107.45/15.12 | = e1) & op(e0, e3) = v2 & $i(v2))))))
% 107.45/15.12 |
% 107.45/15.12 | ALPHA: (ax7) implies:
% 107.45/15.12 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 107.45/15.12 | ( ~ (v0 = e2) | (op(e2, e2) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2
% 107.45/15.12 | = e1) & op(e0, e2) = v2 & $i(v2))))))
% 107.45/15.12 |
% 107.45/15.12 | ALPHA: (ax8) implies:
% 107.45/15.12 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 107.45/15.12 | ( ~ (v0 = e3) | (op(e3, e3) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2
% 107.45/15.12 | = e2) & op(e0, e3) = v2 & $i(v2))))))
% 107.45/15.12 |
% 107.45/15.12 | ALPHA: (ax9) implies:
% 107.45/15.12 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 107.45/15.12 | ( ~ (v0 = e1) | (op(e1, e1) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2
% 107.45/15.12 | = e2) & op(e0, e1) = v2 & $i(v2))))))
% 107.45/15.12 |
% 107.45/15.12 | ALPHA: (ax10) implies:
% 107.45/15.12 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 107.45/15.12 | ( ~ (v0 = e2) | (op(e2, e2) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2
% 107.45/15.12 | = e3) & op(e0, e2) = v2 & $i(v2))))))
% 107.45/15.12 |
% 107.45/15.12 | ALPHA: (ax11) implies:
% 107.45/15.12 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 107.45/15.12 | ( ~ (v0 = e1) | (op(e1, e1) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2
% 107.45/15.12 | = e3) & op(e0, e1) = v2 & $i(v2))))))
% 107.45/15.12 |
% 107.45/15.12 | ALPHA: (ax12) implies:
% 107.45/15.12 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 107.45/15.12 | ( ~ (v0 = e3) | (op(e3, e3) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2
% 107.45/15.12 | = e0) & op(e1, e3) = v2 & $i(v2))))))
% 107.45/15.12 |
% 107.45/15.12 | ALPHA: (ax13) implies:
% 107.45/15.12 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 107.45/15.12 | ( ~ (v0 = e2) | (op(e2, e2) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2
% 107.45/15.12 | = e0) & op(e1, e2) = v2 & $i(v2))))))
% 107.45/15.12 |
% 107.45/15.12 | ALPHA: (ax14) implies:
% 107.45/15.12 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 107.45/15.12 | ( ~ (v0 = e3) | (op(e3, e3) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2
% 107.45/15.12 | = e2) & op(e1, e3) = v2 & $i(v2))))))
% 107.45/15.12 |
% 107.45/15.12 | ALPHA: (ax15) implies:
% 107.45/15.12 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 107.45/15.12 | ( ~ (v0 = e0) | (op(e0, e0) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2
% 107.45/15.12 | = e2) & op(e1, e0) = v2 & $i(v2))))))
% 107.45/15.12 |
% 107.45/15.12 | ALPHA: (ax16) implies:
% 107.45/15.12 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 107.45/15.12 | ( ~ (v0 = e2) | (op(e2, e2) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2
% 107.45/15.12 | = e3) & op(e1, e2) = v2 & $i(v2))))))
% 107.45/15.12 |
% 107.45/15.12 | ALPHA: (ax17) implies:
% 107.45/15.13 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 107.45/15.13 | ( ~ (v0 = e0) | (op(e0, e0) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2
% 107.45/15.13 | = e3) & op(e1, e0) = v2 & $i(v2))))))
% 107.45/15.13 |
% 107.45/15.13 | ALPHA: (ax18) implies:
% 107.45/15.13 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 107.45/15.13 | ( ~ (v0 = e3) | (op(e3, e3) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2
% 107.45/15.13 | = e0) & op(e2, e3) = v2 & $i(v2))))))
% 107.45/15.13 |
% 107.45/15.13 | ALPHA: (ax19) implies:
% 107.45/15.13 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 107.45/15.13 | ( ~ (v0 = e1) | (op(e1, e1) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2
% 107.45/15.13 | = e0) & op(e2, e1) = v2 & $i(v2))))))
% 107.45/15.13 |
% 107.45/15.13 | ALPHA: (ax20) implies:
% 107.45/15.13 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 107.45/15.13 | ( ~ (v0 = e3) | (op(e3, e3) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2
% 107.45/15.13 | = e1) & op(e2, e3) = v2 & $i(v2))))))
% 107.45/15.13 |
% 107.45/15.13 | ALPHA: (ax21) implies:
% 107.45/15.13 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 107.45/15.13 | ( ~ (v0 = e0) | (op(e0, e0) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2
% 107.45/15.13 | = e1) & op(e2, e0) = v2 & $i(v2))))))
% 107.45/15.13 |
% 107.45/15.13 | ALPHA: (ax22) implies:
% 107.45/15.13 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 107.45/15.13 | ( ~ (v0 = e1) | (op(e1, e1) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2
% 107.45/15.13 | = e3) & op(e2, e1) = v2 & $i(v2))))))
% 107.45/15.13 |
% 107.45/15.13 | ALPHA: (ax23) implies:
% 107.45/15.13 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 107.45/15.13 | ( ~ (v0 = e0) | (op(e0, e0) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2
% 107.45/15.13 | = e3) & op(e2, e0) = v2 & $i(v2))))))
% 107.45/15.13 |
% 107.45/15.13 | ALPHA: (ax24) implies:
% 107.45/15.13 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 107.45/15.13 | ( ~ (v0 = e2) | (op(e2, e2) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2
% 107.45/15.13 | = e0) & op(e3, e2) = v2 & $i(v2))))))
% 107.45/15.13 |
% 107.45/15.13 | ALPHA: (ax25) implies:
% 107.45/15.13 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 107.45/15.13 | ( ~ (v0 = e1) | (op(e1, e1) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2
% 107.45/15.13 | = e0) & op(e3, e1) = v2 & $i(v2))))))
% 107.45/15.13 |
% 107.45/15.13 | ALPHA: (ax26) implies:
% 107.45/15.13 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 107.45/15.13 | ( ~ (v0 = e2) | (op(e2, e2) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2
% 107.45/15.13 | = e1) & op(e3, e2) = v2 & $i(v2))))))
% 107.45/15.13 |
% 107.45/15.13 | ALPHA: (ax27) implies:
% 107.45/15.13 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 107.45/15.13 | ( ~ (v0 = e0) | (op(e0, e0) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2
% 107.45/15.13 | = e1) & op(e3, e0) = v2 & $i(v2))))))
% 107.45/15.13 |
% 107.45/15.13 | ALPHA: (ax28) implies:
% 107.45/15.13 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 107.45/15.13 | ( ~ (v0 = e1) | (op(e1, e1) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2
% 107.45/15.13 | = e2) & op(e3, e1) = v2 & $i(v2))))))
% 107.45/15.13 |
% 107.45/15.13 | ALPHA: (ax29) implies:
% 107.45/15.13 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 107.45/15.13 | ( ~ (v0 = e0) | (op(e0, e0) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2
% 107.45/15.13 | = e2) & op(e3, e0) = v2 & $i(v2))))))
% 107.45/15.13 |
% 107.80/15.14 | DELTA: instantiating (19) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 107.80/15.14 | (34) op(e3, e3) = all_4_2 & $i(all_4_2) & ( ~ (all_4_2 = e0) | (op(e0, e0)
% 107.80/15.14 | = all_4_1 & $i(all_4_1) & ( ~ (all_4_1 = e1) | ( ~ (all_4_0 = e2)
% 107.80/15.14 | & op(e1, e0) = all_4_0 & $i(all_4_0)))))
% 107.80/15.14 |
% 107.80/15.14 | ALPHA: (34) implies:
% 107.80/15.14 | (35) op(e3, e3) = all_4_2
% 107.80/15.14 | (36) ~ (all_4_2 = e0) | (op(e0, e0) = all_4_1 & $i(all_4_1) & ( ~ (all_4_1
% 107.80/15.14 | = e1) | ( ~ (all_4_0 = e2) & op(e1, e0) = all_4_0 &
% 107.80/15.14 | $i(all_4_0))))
% 107.80/15.14 |
% 107.80/15.14 | DELTA: instantiating (26) with fresh symbols all_6_0, all_6_1, all_6_2 gives:
% 107.80/15.14 | (37) op(e0, e0) = all_6_2 & $i(all_6_2) & ( ~ (all_6_2 = e1) | (op(e1, e1)
% 107.80/15.14 | = all_6_1 & $i(all_6_1) & ( ~ (all_6_1 = e2) | ( ~ (all_6_0 = e3)
% 107.80/15.14 | & op(e2, e1) = all_6_0 & $i(all_6_0)))))
% 107.80/15.14 |
% 107.80/15.14 | ALPHA: (37) implies:
% 107.80/15.14 | (38) op(e0, e0) = all_6_2
% 107.80/15.14 | (39) ~ (all_6_2 = e1) | (op(e1, e1) = all_6_1 & $i(all_6_1) & ( ~ (all_6_1
% 107.80/15.14 | = e2) | ( ~ (all_6_0 = e3) & op(e2, e1) = all_6_0 &
% 107.80/15.14 | $i(all_6_0))))
% 107.80/15.14 |
% 107.80/15.14 | DELTA: instantiating (20) with fresh symbols all_8_0, all_8_1, all_8_2 gives:
% 107.80/15.14 | (40) op(e0, e0) = all_8_2 & $i(all_8_2) & ( ~ (all_8_2 = e2) | (op(e2, e2)
% 107.80/15.14 | = all_8_1 & $i(all_8_1) & ( ~ (all_8_1 = e1) | ( ~ (all_8_0 = e3)
% 107.80/15.14 | & op(e1, e2) = all_8_0 & $i(all_8_0)))))
% 107.80/15.14 |
% 107.80/15.14 | ALPHA: (40) implies:
% 107.80/15.14 | (41) op(e0, e0) = all_8_2
% 107.80/15.14 | (42) ~ (all_8_2 = e2) | (op(e2, e2) = all_8_1 & $i(all_8_1) & ( ~ (all_8_1
% 107.80/15.14 | = e1) | ( ~ (all_8_0 = e3) & op(e1, e2) = all_8_0 &
% 107.80/15.14 | $i(all_8_0))))
% 107.80/15.14 |
% 107.80/15.14 | DELTA: instantiating (10) with fresh symbols all_10_0, all_10_1, all_10_2
% 107.80/15.14 | gives:
% 107.80/15.14 | (43) op(e2, e2) = all_10_2 & $i(all_10_2) & ( ~ (all_10_2 = e3) | (op(e3,
% 107.80/15.14 | e3) = all_10_1 & $i(all_10_1) & ( ~ (all_10_1 = e0) | ( ~
% 107.80/15.14 | (all_10_0 = e1) & op(e0, e3) = all_10_0 & $i(all_10_0)))))
% 107.80/15.14 |
% 107.80/15.14 | ALPHA: (43) implies:
% 107.80/15.14 | (44) op(e2, e2) = all_10_2
% 107.80/15.14 | (45) ~ (all_10_2 = e3) | (op(e3, e3) = all_10_1 & $i(all_10_1) & ( ~
% 107.80/15.14 | (all_10_1 = e0) | ( ~ (all_10_0 = e1) & op(e0, e3) = all_10_0 &
% 107.80/15.14 | $i(all_10_0))))
% 107.80/15.14 |
% 107.80/15.14 | DELTA: instantiating (21) with fresh symbols all_12_0, all_12_1, all_12_2
% 107.80/15.14 | gives:
% 107.80/15.14 | (46) op(e2, e2) = all_12_2 & $i(all_12_2) & ( ~ (all_12_2 = e0) | (op(e0,
% 107.80/15.14 | e0) = all_12_1 & $i(all_12_1) & ( ~ (all_12_1 = e1) | ( ~
% 107.80/15.14 | (all_12_0 = e3) & op(e1, e0) = all_12_0 & $i(all_12_0)))))
% 107.80/15.14 |
% 107.80/15.14 | ALPHA: (46) implies:
% 107.80/15.14 | (47) op(e2, e2) = all_12_2
% 107.80/15.14 | (48) ~ (all_12_2 = e0) | (op(e0, e0) = all_12_1 & $i(all_12_1) & ( ~
% 107.80/15.14 | (all_12_1 = e1) | ( ~ (all_12_0 = e3) & op(e1, e0) = all_12_0 &
% 107.80/15.14 | $i(all_12_0))))
% 107.80/15.14 |
% 107.80/15.14 | DELTA: instantiating (28) with fresh symbols all_14_0, all_14_1, all_14_2
% 107.80/15.14 | gives:
% 107.80/15.14 | (49) op(e1, e1) = all_14_2 & $i(all_14_2) & ( ~ (all_14_2 = e2) | (op(e2,
% 107.80/15.14 | e2) = all_14_1 & $i(all_14_1) & ( ~ (all_14_1 = e3) | ( ~
% 107.80/15.14 | (all_14_0 = e0) & op(e3, e2) = all_14_0 & $i(all_14_0)))))
% 107.80/15.14 |
% 107.80/15.14 | ALPHA: (49) implies:
% 107.80/15.14 | (50) op(e1, e1) = all_14_2
% 107.80/15.14 | (51) ~ (all_14_2 = e2) | (op(e2, e2) = all_14_1 & $i(all_14_1) & ( ~
% 107.80/15.14 | (all_14_1 = e3) | ( ~ (all_14_0 = e0) & op(e3, e2) = all_14_0 &
% 107.80/15.14 | $i(all_14_0))))
% 107.80/15.14 |
% 107.80/15.14 | DELTA: instantiating (30) with fresh symbols all_16_0, all_16_1, all_16_2
% 107.80/15.14 | gives:
% 107.80/15.14 | (52) op(e0, e0) = all_16_2 & $i(all_16_2) & ( ~ (all_16_2 = e2) | (op(e2,
% 107.80/15.14 | e2) = all_16_1 & $i(all_16_1) & ( ~ (all_16_1 = e3) | ( ~
% 107.80/15.14 | (all_16_0 = e1) & op(e3, e2) = all_16_0 & $i(all_16_0)))))
% 107.80/15.14 |
% 107.80/15.14 | ALPHA: (52) implies:
% 107.80/15.14 | (53) op(e0, e0) = all_16_2
% 107.80/15.14 | (54) ~ (all_16_2 = e2) | (op(e2, e2) = all_16_1 & $i(all_16_1) & ( ~
% 107.80/15.14 | (all_16_1 = e3) | ( ~ (all_16_0 = e1) & op(e3, e2) = all_16_0 &
% 107.80/15.14 | $i(all_16_0))))
% 107.80/15.14 |
% 107.80/15.14 | DELTA: instantiating (22) with fresh symbols all_18_0, all_18_1, all_18_2
% 107.80/15.14 | gives:
% 107.80/15.14 | (55) op(e1, e1) = all_18_2 & $i(all_18_2) & ( ~ (all_18_2 = e3) | (op(e3,
% 107.80/15.14 | e3) = all_18_1 & $i(all_18_1) & ( ~ (all_18_1 = e2) | ( ~
% 107.80/15.14 | (all_18_0 = e0) & op(e2, e3) = all_18_0 & $i(all_18_0)))))
% 107.80/15.14 |
% 107.80/15.14 | ALPHA: (55) implies:
% 107.80/15.15 | (56) op(e1, e1) = all_18_2
% 107.80/15.15 | (57) ~ (all_18_2 = e3) | (op(e3, e3) = all_18_1 & $i(all_18_1) & ( ~
% 107.80/15.15 | (all_18_1 = e2) | ( ~ (all_18_0 = e0) & op(e2, e3) = all_18_0 &
% 107.80/15.15 | $i(all_18_0))))
% 107.80/15.15 |
% 107.80/15.15 | DELTA: instantiating (12) with fresh symbols all_20_0, all_20_1, all_20_2
% 107.80/15.15 | gives:
% 107.80/15.15 | (58) op(e1, e1) = all_20_2 & $i(all_20_2) & ( ~ (all_20_2 = e3) | (op(e3,
% 107.80/15.15 | e3) = all_20_1 & $i(all_20_1) & ( ~ (all_20_1 = e0) | ( ~
% 107.80/15.15 | (all_20_0 = e2) & op(e0, e3) = all_20_0 & $i(all_20_0)))))
% 107.80/15.15 |
% 107.80/15.15 | ALPHA: (58) implies:
% 107.80/15.15 | (59) op(e1, e1) = all_20_2
% 107.80/15.15 | (60) ~ (all_20_2 = e3) | (op(e3, e3) = all_20_1 & $i(all_20_1) & ( ~
% 107.80/15.15 | (all_20_1 = e0) | ( ~ (all_20_0 = e2) & op(e0, e3) = all_20_0 &
% 107.80/15.15 | $i(all_20_0))))
% 107.80/15.15 |
% 107.80/15.15 | DELTA: instantiating (27) with fresh symbols all_22_0, all_22_1, all_22_2
% 107.80/15.15 | gives:
% 107.80/15.15 | (61) op(e1, e1) = all_22_2 & $i(all_22_2) & ( ~ (all_22_2 = e0) | (op(e0,
% 107.80/15.15 | e0) = all_22_1 & $i(all_22_1) & ( ~ (all_22_1 = e2) | ( ~
% 107.80/15.15 | (all_22_0 = e3) & op(e2, e0) = all_22_0 & $i(all_22_0)))))
% 107.80/15.15 |
% 107.80/15.15 | ALPHA: (61) implies:
% 107.80/15.15 | (62) op(e1, e1) = all_22_2
% 107.80/15.15 | (63) ~ (all_22_2 = e0) | (op(e0, e0) = all_22_1 & $i(all_22_1) & ( ~
% 107.80/15.15 | (all_22_1 = e2) | ( ~ (all_22_0 = e3) & op(e2, e0) = all_22_0 &
% 107.80/15.15 | $i(all_22_0))))
% 107.80/15.15 |
% 107.80/15.15 | DELTA: instantiating (29) with fresh symbols all_24_0, all_24_1, all_24_2
% 107.80/15.15 | gives:
% 107.80/15.15 | (64) op(e2, e2) = all_24_2 & $i(all_24_2) & ( ~ (all_24_2 = e1) | (op(e1,
% 107.80/15.15 | e1) = all_24_1 & $i(all_24_1) & ( ~ (all_24_1 = e3) | ( ~
% 107.80/15.15 | (all_24_0 = e0) & op(e3, e1) = all_24_0 & $i(all_24_0)))))
% 107.80/15.15 |
% 107.80/15.15 | ALPHA: (64) implies:
% 107.80/15.15 | (65) op(e2, e2) = all_24_2
% 107.80/15.15 | (66) ~ (all_24_2 = e1) | (op(e1, e1) = all_24_1 & $i(all_24_1) & ( ~
% 107.80/15.15 | (all_24_1 = e3) | ( ~ (all_24_0 = e0) & op(e3, e1) = all_24_0 &
% 107.80/15.15 | $i(all_24_0))))
% 107.80/15.15 |
% 107.80/15.15 | DELTA: instantiating (11) with fresh symbols all_26_0, all_26_1, all_26_2
% 107.80/15.15 | gives:
% 107.80/15.15 | (67) op(e3, e3) = all_26_2 & $i(all_26_2) & ( ~ (all_26_2 = e2) | (op(e2,
% 107.80/15.15 | e2) = all_26_1 & $i(all_26_1) & ( ~ (all_26_1 = e0) | ( ~
% 107.80/15.15 | (all_26_0 = e1) & op(e0, e2) = all_26_0 & $i(all_26_0)))))
% 107.80/15.15 |
% 107.80/15.15 | ALPHA: (67) implies:
% 107.80/15.15 | (68) op(e3, e3) = all_26_2
% 107.80/15.15 | (69) ~ (all_26_2 = e2) | (op(e2, e2) = all_26_1 & $i(all_26_1) & ( ~
% 107.80/15.15 | (all_26_1 = e0) | ( ~ (all_26_0 = e1) & op(e0, e2) = all_26_0 &
% 107.80/15.15 | $i(all_26_0))))
% 107.80/15.15 |
% 107.80/15.15 | DELTA: instantiating (18) with fresh symbols all_28_0, all_28_1, all_28_2
% 107.80/15.15 | gives:
% 107.80/15.15 | (70) op(e0, e0) = all_28_2 & $i(all_28_2) & ( ~ (all_28_2 = e3) | (op(e3,
% 107.80/15.15 | e3) = all_28_1 & $i(all_28_1) & ( ~ (all_28_1 = e1) | ( ~
% 107.80/15.15 | (all_28_0 = e2) & op(e1, e3) = all_28_0 & $i(all_28_0)))))
% 107.80/15.15 |
% 107.80/15.15 | ALPHA: (70) implies:
% 107.80/15.15 | (71) op(e0, e0) = all_28_2
% 107.80/15.15 | (72) ~ (all_28_2 = e3) | (op(e3, e3) = all_28_1 & $i(all_28_1) & ( ~
% 107.80/15.15 | (all_28_1 = e1) | ( ~ (all_28_0 = e2) & op(e1, e3) = all_28_0 &
% 107.80/15.15 | $i(all_28_0))))
% 107.80/15.15 |
% 107.80/15.15 | DELTA: instantiating (31) with fresh symbols all_30_0, all_30_1, all_30_2
% 107.80/15.15 | gives:
% 107.80/15.15 | (73) op(e2, e2) = all_30_2 & $i(all_30_2) & ( ~ (all_30_2 = e0) | (op(e0,
% 107.80/15.15 | e0) = all_30_1 & $i(all_30_1) & ( ~ (all_30_1 = e3) | ( ~
% 107.80/15.15 | (all_30_0 = e1) & op(e3, e0) = all_30_0 & $i(all_30_0)))))
% 107.80/15.15 |
% 107.80/15.15 | ALPHA: (73) implies:
% 107.80/15.15 | (74) op(e2, e2) = all_30_2
% 107.80/15.15 | (75) ~ (all_30_2 = e0) | (op(e0, e0) = all_30_1 & $i(all_30_1) & ( ~
% 107.80/15.15 | (all_30_1 = e3) | ( ~ (all_30_0 = e1) & op(e3, e0) = all_30_0 &
% 107.80/15.15 | $i(all_30_0))))
% 107.80/15.15 |
% 107.80/15.15 | DELTA: instantiating (33) with fresh symbols all_32_0, all_32_1, all_32_2
% 107.80/15.15 | gives:
% 107.80/15.15 | (76) op(e1, e1) = all_32_2 & $i(all_32_2) & ( ~ (all_32_2 = e0) | (op(e0,
% 107.80/15.15 | e0) = all_32_1 & $i(all_32_1) & ( ~ (all_32_1 = e3) | ( ~
% 107.80/15.15 | (all_32_0 = e2) & op(e3, e0) = all_32_0 & $i(all_32_0)))))
% 107.80/15.15 |
% 107.80/15.15 | ALPHA: (76) implies:
% 107.80/15.15 | (77) op(e1, e1) = all_32_2
% 107.80/15.15 | (78) ~ (all_32_2 = e0) | (op(e0, e0) = all_32_1 & $i(all_32_1) & ( ~
% 107.80/15.15 | (all_32_1 = e3) | ( ~ (all_32_0 = e2) & op(e3, e0) = all_32_0 &
% 107.80/15.15 | $i(all_32_0))))
% 107.80/15.15 |
% 107.80/15.15 | DELTA: instantiating (23) with fresh symbols all_34_0, all_34_1, all_34_2
% 107.80/15.15 | gives:
% 107.80/15.15 | (79) op(e3, e3) = all_34_2 & $i(all_34_2) & ( ~ (all_34_2 = e1) | (op(e1,
% 107.80/15.15 | e1) = all_34_1 & $i(all_34_1) & ( ~ (all_34_1 = e2) | ( ~
% 107.80/15.15 | (all_34_0 = e0) & op(e2, e1) = all_34_0 & $i(all_34_0)))))
% 107.80/15.15 |
% 107.80/15.15 | ALPHA: (79) implies:
% 107.80/15.15 | (80) op(e3, e3) = all_34_2
% 107.80/15.15 | (81) ~ (all_34_2 = e1) | (op(e1, e1) = all_34_1 & $i(all_34_1) & ( ~
% 107.80/15.15 | (all_34_1 = e2) | ( ~ (all_34_0 = e0) & op(e2, e1) = all_34_0 &
% 107.80/15.15 | $i(all_34_0))))
% 107.80/15.15 |
% 107.80/15.15 | DELTA: instantiating (24) with fresh symbols all_36_0, all_36_1, all_36_2
% 107.80/15.15 | gives:
% 107.80/15.16 | (82) op(e0, e0) = all_36_2 & $i(all_36_2) & ( ~ (all_36_2 = e3) | (op(e3,
% 107.80/15.16 | e3) = all_36_1 & $i(all_36_1) & ( ~ (all_36_1 = e2) | ( ~
% 107.80/15.16 | (all_36_0 = e1) & op(e2, e3) = all_36_0 & $i(all_36_0)))))
% 107.80/15.16 |
% 107.80/15.16 | ALPHA: (82) implies:
% 107.80/15.16 | (83) op(e0, e0) = all_36_2
% 107.80/15.16 | (84) ~ (all_36_2 = e3) | (op(e3, e3) = all_36_1 & $i(all_36_1) & ( ~
% 107.80/15.16 | (all_36_1 = e2) | ( ~ (all_36_0 = e1) & op(e2, e3) = all_36_0 &
% 107.80/15.16 | $i(all_36_0))))
% 107.80/15.16 |
% 107.80/15.16 | DELTA: instantiating (32) with fresh symbols all_38_0, all_38_1, all_38_2
% 107.80/15.16 | gives:
% 107.80/15.16 | (85) op(e0, e0) = all_38_2 & $i(all_38_2) & ( ~ (all_38_2 = e1) | (op(e1,
% 107.80/15.16 | e1) = all_38_1 & $i(all_38_1) & ( ~ (all_38_1 = e3) | ( ~
% 107.80/15.16 | (all_38_0 = e2) & op(e3, e1) = all_38_0 & $i(all_38_0)))))
% 107.80/15.16 |
% 107.80/15.16 | ALPHA: (85) implies:
% 107.80/15.16 | (86) op(e0, e0) = all_38_2
% 107.80/15.16 | (87) ~ (all_38_2 = e1) | (op(e1, e1) = all_38_1 & $i(all_38_1) & ( ~
% 107.80/15.16 | (all_38_1 = e3) | ( ~ (all_38_0 = e2) & op(e3, e1) = all_38_0 &
% 107.80/15.16 | $i(all_38_0))))
% 107.80/15.16 |
% 107.80/15.16 | DELTA: instantiating (25) with fresh symbols all_40_0, all_40_1, all_40_2
% 107.80/15.16 | gives:
% 107.80/15.16 | (88) op(e3, e3) = all_40_2 & $i(all_40_2) & ( ~ (all_40_2 = e0) | (op(e0,
% 107.80/15.16 | e0) = all_40_1 & $i(all_40_1) & ( ~ (all_40_1 = e2) | ( ~
% 107.80/15.16 | (all_40_0 = e1) & op(e2, e0) = all_40_0 & $i(all_40_0)))))
% 107.80/15.16 |
% 107.80/15.16 | ALPHA: (88) implies:
% 107.80/15.16 | (89) op(e3, e3) = all_40_2
% 107.80/15.16 | (90) ~ (all_40_2 = e0) | (op(e0, e0) = all_40_1 & $i(all_40_1) & ( ~
% 107.80/15.16 | (all_40_1 = e2) | ( ~ (all_40_0 = e1) & op(e2, e0) = all_40_0 &
% 107.80/15.16 | $i(all_40_0))))
% 107.80/15.16 |
% 107.80/15.16 | DELTA: instantiating (13) with fresh symbols all_42_0, all_42_1, all_42_2
% 107.80/15.16 | gives:
% 107.80/15.16 | (91) op(e3, e3) = all_42_2 & $i(all_42_2) & ( ~ (all_42_2 = e1) | (op(e1,
% 107.80/15.16 | e1) = all_42_1 & $i(all_42_1) & ( ~ (all_42_1 = e0) | ( ~
% 107.80/15.16 | (all_42_0 = e2) & op(e0, e1) = all_42_0 & $i(all_42_0)))))
% 107.80/15.16 |
% 107.80/15.16 | ALPHA: (91) implies:
% 107.80/15.16 | (92) op(e3, e3) = all_42_2
% 107.80/15.16 | (93) ~ (all_42_2 = e1) | (op(e1, e1) = all_42_1 & $i(all_42_1) & ( ~
% 107.80/15.16 | (all_42_1 = e0) | ( ~ (all_42_0 = e2) & op(e0, e1) = all_42_0 &
% 107.80/15.16 | $i(all_42_0))))
% 107.80/15.16 |
% 107.80/15.16 | DELTA: instantiating (14) with fresh symbols all_44_0, all_44_1, all_44_2
% 107.80/15.16 | gives:
% 107.80/15.16 | (94) op(e1, e1) = all_44_2 & $i(all_44_2) & ( ~ (all_44_2 = e2) | (op(e2,
% 107.80/15.16 | e2) = all_44_1 & $i(all_44_1) & ( ~ (all_44_1 = e0) | ( ~
% 107.80/15.16 | (all_44_0 = e3) & op(e0, e2) = all_44_0 & $i(all_44_0)))))
% 107.80/15.16 |
% 107.80/15.16 | ALPHA: (94) implies:
% 107.80/15.16 | (95) op(e1, e1) = all_44_2
% 107.80/15.16 | (96) ~ (all_44_2 = e2) | (op(e2, e2) = all_44_1 & $i(all_44_1) & ( ~
% 107.80/15.16 | (all_44_1 = e0) | ( ~ (all_44_0 = e3) & op(e0, e2) = all_44_0 &
% 107.80/15.16 | $i(all_44_0))))
% 107.80/15.16 |
% 107.80/15.16 | DELTA: instantiating (15) with fresh symbols all_46_0, all_46_1, all_46_2
% 107.80/15.16 | gives:
% 107.80/15.16 | (97) op(e2, e2) = all_46_2 & $i(all_46_2) & ( ~ (all_46_2 = e1) | (op(e1,
% 107.80/15.16 | e1) = all_46_1 & $i(all_46_1) & ( ~ (all_46_1 = e0) | ( ~
% 107.80/15.16 | (all_46_0 = e3) & op(e0, e1) = all_46_0 & $i(all_46_0)))))
% 107.80/15.16 |
% 107.80/15.16 | ALPHA: (97) implies:
% 107.80/15.16 | (98) op(e2, e2) = all_46_2
% 107.80/15.16 | (99) ~ (all_46_2 = e1) | (op(e1, e1) = all_46_1 & $i(all_46_1) & ( ~
% 107.80/15.16 | (all_46_1 = e0) | ( ~ (all_46_0 = e3) & op(e0, e1) = all_46_0 &
% 107.80/15.16 | $i(all_46_0))))
% 107.80/15.16 |
% 107.80/15.16 | DELTA: instantiating (16) with fresh symbols all_48_0, all_48_1, all_48_2
% 107.80/15.16 | gives:
% 107.80/15.16 | (100) op(e2, e2) = all_48_2 & $i(all_48_2) & ( ~ (all_48_2 = e3) | (op(e3,
% 107.80/15.16 | e3) = all_48_1 & $i(all_48_1) & ( ~ (all_48_1 = e1) | ( ~
% 107.80/15.16 | (all_48_0 = e0) & op(e1, e3) = all_48_0 & $i(all_48_0)))))
% 107.80/15.16 |
% 107.80/15.16 | ALPHA: (100) implies:
% 107.80/15.16 | (101) op(e2, e2) = all_48_2
% 107.80/15.16 | (102) ~ (all_48_2 = e3) | (op(e3, e3) = all_48_1 & $i(all_48_1) & ( ~
% 107.80/15.16 | (all_48_1 = e1) | ( ~ (all_48_0 = e0) & op(e1, e3) = all_48_0 &
% 107.80/15.16 | $i(all_48_0))))
% 107.80/15.16 |
% 107.80/15.16 | DELTA: instantiating (17) with fresh symbols all_50_0, all_50_1, all_50_2
% 107.80/15.16 | gives:
% 107.80/15.16 | (103) op(e3, e3) = all_50_2 & $i(all_50_2) & ( ~ (all_50_2 = e2) | (op(e2,
% 107.80/15.16 | e2) = all_50_1 & $i(all_50_1) & ( ~ (all_50_1 = e1) | ( ~
% 107.80/15.16 | (all_50_0 = e0) & op(e1, e2) = all_50_0 & $i(all_50_0)))))
% 107.80/15.16 |
% 107.80/15.16 | ALPHA: (103) implies:
% 107.80/15.16 | (104) op(e3, e3) = all_50_2
% 107.80/15.16 | (105) ~ (all_50_2 = e2) | (op(e2, e2) = all_50_1 & $i(all_50_1) & ( ~
% 107.80/15.16 | (all_50_1 = e1) | ( ~ (all_50_0 = e0) & op(e1, e2) = all_50_0 &
% 107.80/15.16 | $i(all_50_0))))
% 107.80/15.16 |
% 107.80/15.16 | DELTA: instantiating (9) with fresh symbols all_52_0, all_52_1, all_52_2,
% 107.80/15.16 | all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9,
% 107.80/15.16 | all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15,
% 107.80/15.16 | all_52_16, all_52_17, all_52_18, all_52_19, all_52_20, all_52_21,
% 107.80/15.16 | all_52_22, all_52_23 gives:
% 107.80/15.17 | (106) ((all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 107.80/15.17 | all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 107.80/15.17 | op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 107.80/15.17 | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 107.80/15.17 | = all_52_4 & $i(all_52_4))) & ((all_52_7 = e3 & ~ (all_52_6 =
% 107.80/15.17 | e1) & op(e3, e1) = e3 & op(e1, e3) = all_52_6 & $i(all_52_6)) |
% 107.80/15.17 | (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 107.80/15.17 | = all_52_8 & $i(all_52_8)) | (all_52_11 = e0 & ~ (all_52_10 =
% 107.80/15.17 | e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 107.80/15.17 | $i(all_52_10))) & ((all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3,
% 107.80/15.17 | e2) = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)) | (all_52_15
% 107.80/15.17 | = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 & op(e1, e2)
% 107.80/15.17 | = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~ (all_52_16 = e2) &
% 107.80/15.17 | op(e2, e0) = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))) &
% 107.80/15.17 | ((all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 &
% 107.80/15.17 | op(e2, e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~
% 107.80/15.17 | (all_52_20 = e3) & op(e3, e1) = all_52_20 & op(e1, e3) = e1 &
% 107.80/15.17 | $i(all_52_20)) | (all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3,
% 107.80/15.17 | e0) = all_52_22 & op(e0, e3) = e0 & $i(all_52_22)))
% 107.80/15.17 |
% 107.80/15.17 | ALPHA: (106) implies:
% 107.80/15.17 | (107) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 &
% 107.80/15.17 | op(e2, e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20
% 107.80/15.17 | = e3) & op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20))
% 107.80/15.17 | | (all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 &
% 107.80/15.17 | op(e0, e3) = e0 & $i(all_52_22))
% 107.80/15.17 | (108) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3)
% 107.80/15.17 | = all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 =
% 107.80/15.17 | e2) & op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 107.80/15.17 | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 &
% 107.80/15.17 | op(e0, e2) = e0 & $i(all_52_16))
% 107.80/15.17 | (109) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 107.80/15.17 | all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 107.80/15.17 | op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 107.80/15.17 | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 &
% 107.80/15.17 | op(e0, e1) = e0 & $i(all_52_10))
% 107.80/15.17 | (110) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 107.80/15.17 | all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 107.80/15.17 | op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5
% 107.80/15.17 | = e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4
% 107.80/15.17 | & $i(all_52_4))
% 107.80/15.17 |
% 107.80/15.17 | DELTA: instantiating (3) with fresh symbols all_53_0, all_53_1, all_53_2,
% 107.80/15.17 | all_53_3, all_53_4, all_53_5, all_53_6, all_53_7, all_53_8, all_53_9,
% 107.80/15.17 | all_53_10, all_53_11, all_53_12, all_53_13, all_53_14, all_53_15 gives:
% 107.80/15.17 | (111) ~ (all_53_0 = all_53_1) & ~ (all_53_0 = all_53_2) & ~ (all_53_0 =
% 107.80/15.17 | all_53_3) & ~ (all_53_0 = all_53_4) & ~ (all_53_0 = all_53_8) &
% 107.80/15.17 | ~ (all_53_0 = all_53_12) & ~ (all_53_1 = all_53_2) & ~ (all_53_1 =
% 107.80/15.17 | all_53_3) & ~ (all_53_1 = all_53_5) & ~ (all_53_1 = all_53_9) &
% 107.80/15.17 | ~ (all_53_1 = all_53_13) & ~ (all_53_2 = all_53_3) & ~ (all_53_2 =
% 107.80/15.17 | all_53_6) & ~ (all_53_2 = all_53_10) & ~ (all_53_2 = all_53_14) &
% 107.80/15.17 | ~ (all_53_3 = all_53_7) & ~ (all_53_3 = all_53_11) & ~ (all_53_3 =
% 107.80/15.17 | all_53_15) & ~ (all_53_4 = all_53_5) & ~ (all_53_4 = all_53_6) &
% 107.80/15.17 | ~ (all_53_4 = all_53_7) & ~ (all_53_4 = all_53_8) & ~ (all_53_4 =
% 107.80/15.17 | all_53_12) & ~ (all_53_5 = all_53_6) & ~ (all_53_5 = all_53_7) &
% 107.80/15.17 | ~ (all_53_5 = all_53_9) & ~ (all_53_5 = all_53_13) & ~ (all_53_6 =
% 107.80/15.17 | all_53_7) & ~ (all_53_6 = all_53_10) & ~ (all_53_6 = all_53_14) &
% 107.80/15.17 | ~ (all_53_7 = all_53_11) & ~ (all_53_7 = all_53_15) & ~ (all_53_8
% 107.80/15.17 | = all_53_9) & ~ (all_53_8 = all_53_10) & ~ (all_53_8 = all_53_11)
% 107.80/15.17 | & ~ (all_53_8 = all_53_12) & ~ (all_53_9 = all_53_10) & ~
% 107.80/15.17 | (all_53_9 = all_53_11) & ~ (all_53_9 = all_53_13) & ~ (all_53_10 =
% 107.80/15.17 | all_53_11) & ~ (all_53_10 = all_53_14) & ~ (all_53_11 =
% 107.80/15.17 | all_53_15) & ~ (all_53_12 = all_53_13) & ~ (all_53_12 =
% 107.80/15.17 | all_53_14) & ~ (all_53_12 = all_53_15) & ~ (all_53_13 =
% 107.80/15.17 | all_53_14) & ~ (all_53_13 = all_53_15) & ~ (all_53_14 =
% 107.80/15.17 | all_53_15) & op(e3, e3) = all_53_14 & op(e3, e2) = all_53_15 &
% 107.80/15.17 | op(e3, e1) = all_53_13 & op(e3, e0) = all_53_12 & op(e2, e3) =
% 107.80/15.17 | all_53_10 & op(e2, e2) = all_53_11 & op(e2, e1) = all_53_9 & op(e2,
% 107.80/15.17 | e0) = all_53_8 & op(e1, e3) = all_53_6 & op(e1, e2) = all_53_7 &
% 107.80/15.17 | op(e1, e1) = all_53_5 & op(e1, e0) = all_53_4 & op(e0, e3) = all_53_2
% 107.80/15.17 | & op(e0, e2) = all_53_3 & op(e0, e1) = all_53_1 & op(e0, e0) =
% 107.80/15.17 | all_53_0 & $i(all_53_0) & $i(all_53_1) & $i(all_53_2) & $i(all_53_3)
% 107.80/15.17 | & $i(all_53_4) & $i(all_53_5) & $i(all_53_6) & $i(all_53_7) &
% 107.80/15.17 | $i(all_53_8) & $i(all_53_9) & $i(all_53_10) & $i(all_53_11) &
% 107.80/15.17 | $i(all_53_12) & $i(all_53_13) & $i(all_53_14) & $i(all_53_15)
% 107.80/15.17 |
% 107.80/15.17 | ALPHA: (111) implies:
% 107.80/15.17 | (112) ~ (all_53_14 = all_53_15)
% 107.80/15.17 | (113) ~ (all_53_13 = all_53_15)
% 107.80/15.17 | (114) ~ (all_53_13 = all_53_14)
% 107.80/15.17 | (115) ~ (all_53_12 = all_53_15)
% 107.80/15.17 | (116) ~ (all_53_12 = all_53_14)
% 107.80/15.17 | (117) ~ (all_53_12 = all_53_13)
% 107.80/15.17 | (118) ~ (all_53_11 = all_53_15)
% 107.80/15.17 | (119) ~ (all_53_10 = all_53_14)
% 107.80/15.17 | (120) ~ (all_53_10 = all_53_11)
% 107.80/15.17 | (121) ~ (all_53_9 = all_53_13)
% 107.80/15.17 | (122) ~ (all_53_9 = all_53_11)
% 107.80/15.17 | (123) ~ (all_53_9 = all_53_10)
% 107.80/15.17 | (124) ~ (all_53_8 = all_53_12)
% 107.80/15.17 | (125) ~ (all_53_8 = all_53_11)
% 107.80/15.17 | (126) ~ (all_53_8 = all_53_10)
% 107.80/15.17 | (127) ~ (all_53_8 = all_53_9)
% 107.80/15.17 | (128) ~ (all_53_7 = all_53_15)
% 107.97/15.17 | (129) ~ (all_53_7 = all_53_11)
% 107.97/15.17 | (130) ~ (all_53_6 = all_53_14)
% 107.97/15.17 | (131) ~ (all_53_6 = all_53_10)
% 107.97/15.17 | (132) ~ (all_53_6 = all_53_7)
% 107.97/15.17 | (133) ~ (all_53_5 = all_53_13)
% 107.97/15.17 | (134) ~ (all_53_5 = all_53_9)
% 107.97/15.17 | (135) ~ (all_53_5 = all_53_7)
% 107.97/15.17 | (136) ~ (all_53_5 = all_53_6)
% 107.97/15.17 | (137) ~ (all_53_4 = all_53_12)
% 107.97/15.17 | (138) ~ (all_53_4 = all_53_8)
% 107.97/15.17 | (139) ~ (all_53_4 = all_53_7)
% 107.97/15.17 | (140) ~ (all_53_4 = all_53_6)
% 107.97/15.17 | (141) ~ (all_53_4 = all_53_5)
% 107.97/15.17 | (142) ~ (all_53_3 = all_53_15)
% 107.97/15.17 | (143) ~ (all_53_3 = all_53_11)
% 107.97/15.17 | (144) ~ (all_53_3 = all_53_7)
% 107.97/15.17 | (145) ~ (all_53_2 = all_53_14)
% 107.97/15.17 | (146) ~ (all_53_2 = all_53_10)
% 107.97/15.18 | (147) ~ (all_53_2 = all_53_6)
% 107.97/15.18 | (148) ~ (all_53_2 = all_53_3)
% 107.97/15.18 | (149) ~ (all_53_1 = all_53_13)
% 107.97/15.18 | (150) ~ (all_53_1 = all_53_9)
% 107.97/15.18 | (151) ~ (all_53_1 = all_53_5)
% 107.97/15.18 | (152) ~ (all_53_1 = all_53_3)
% 107.97/15.18 | (153) ~ (all_53_1 = all_53_2)
% 107.97/15.18 | (154) ~ (all_53_0 = all_53_12)
% 107.97/15.18 | (155) ~ (all_53_0 = all_53_8)
% 107.97/15.18 | (156) ~ (all_53_0 = all_53_4)
% 107.97/15.18 | (157) ~ (all_53_0 = all_53_3)
% 107.97/15.18 | (158) ~ (all_53_0 = all_53_2)
% 107.97/15.18 | (159) ~ (all_53_0 = all_53_1)
% 107.97/15.18 | (160) op(e0, e0) = all_53_0
% 107.97/15.18 | (161) op(e0, e1) = all_53_1
% 107.97/15.18 | (162) op(e0, e2) = all_53_3
% 107.97/15.18 | (163) op(e0, e3) = all_53_2
% 107.97/15.18 | (164) op(e1, e0) = all_53_4
% 107.97/15.18 | (165) op(e1, e1) = all_53_5
% 107.97/15.18 | (166) op(e1, e2) = all_53_7
% 107.97/15.18 | (167) op(e1, e3) = all_53_6
% 107.97/15.18 | (168) op(e2, e0) = all_53_8
% 107.97/15.18 | (169) op(e2, e1) = all_53_9
% 107.97/15.18 | (170) op(e2, e2) = all_53_11
% 107.97/15.18 | (171) op(e2, e3) = all_53_10
% 107.97/15.18 | (172) op(e3, e0) = all_53_12
% 107.97/15.18 | (173) op(e3, e1) = all_53_13
% 107.97/15.18 | (174) op(e3, e2) = all_53_15
% 107.97/15.18 | (175) op(e3, e3) = all_53_14
% 107.97/15.18 |
% 107.97/15.18 | DELTA: instantiating (1) with fresh symbols all_55_0, all_55_1, all_55_2,
% 107.97/15.18 | all_55_3, all_55_4, all_55_5, all_55_6, all_55_7, all_55_8, all_55_9,
% 107.97/15.18 | all_55_10, all_55_11, all_55_12, all_55_13, all_55_14, all_55_15 gives:
% 107.97/15.18 | (176) op(e3, e3) = all_55_15 & op(e3, e2) = all_55_14 & op(e3, e1) =
% 107.97/15.18 | all_55_13 & op(e3, e0) = all_55_12 & op(e2, e3) = all_55_11 & op(e2,
% 107.97/15.18 | e2) = all_55_10 & op(e2, e1) = all_55_9 & op(e2, e0) = all_55_8 &
% 107.97/15.18 | op(e1, e3) = all_55_7 & op(e1, e2) = all_55_6 & op(e1, e1) = all_55_5
% 107.97/15.18 | & op(e1, e0) = all_55_4 & op(e0, e3) = all_55_3 & op(e0, e2) =
% 107.97/15.18 | all_55_2 & op(e0, e1) = all_55_1 & op(e0, e0) = all_55_0 &
% 107.97/15.18 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3) &
% 107.97/15.18 | $i(all_55_4) & $i(all_55_5) & $i(all_55_6) & $i(all_55_7) &
% 107.97/15.18 | $i(all_55_8) & $i(all_55_9) & $i(all_55_10) & $i(all_55_11) &
% 107.97/15.18 | $i(all_55_12) & $i(all_55_13) & $i(all_55_14) & $i(all_55_15) &
% 107.97/15.18 | (all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0) &
% 107.97/15.18 | (all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0) &
% 107.97/15.18 | (all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0) &
% 107.97/15.18 | (all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0) &
% 107.97/15.18 | (all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0) &
% 107.97/15.18 | (all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0) &
% 107.97/15.18 | (all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0) &
% 107.97/15.18 | (all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0) &
% 107.97/15.18 | (all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0) &
% 107.97/15.18 | (all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0) &
% 107.97/15.18 | (all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0) &
% 107.97/15.18 | (all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0) &
% 107.97/15.18 | (all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0) &
% 107.97/15.18 | (all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0) &
% 107.97/15.18 | (all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0) &
% 107.97/15.18 | (all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0)
% 107.97/15.18 |
% 107.97/15.18 | ALPHA: (176) implies:
% 107.97/15.18 | (177) op(e0, e0) = all_55_0
% 107.97/15.18 | (178) op(e0, e1) = all_55_1
% 107.97/15.18 | (179) op(e0, e2) = all_55_2
% 107.97/15.18 | (180) op(e0, e3) = all_55_3
% 107.97/15.18 | (181) op(e1, e0) = all_55_4
% 107.97/15.18 | (182) op(e1, e1) = all_55_5
% 107.97/15.18 | (183) op(e1, e2) = all_55_6
% 107.97/15.18 | (184) op(e1, e3) = all_55_7
% 107.97/15.18 | (185) op(e2, e0) = all_55_8
% 107.97/15.18 | (186) op(e2, e1) = all_55_9
% 107.97/15.18 | (187) op(e2, e2) = all_55_10
% 107.97/15.18 | (188) op(e2, e3) = all_55_11
% 107.97/15.18 | (189) op(e3, e0) = all_55_12
% 107.97/15.18 | (190) op(e3, e1) = all_55_13
% 107.97/15.18 | (191) op(e3, e2) = all_55_14
% 107.97/15.18 | (192) op(e3, e3) = all_55_15
% 107.97/15.18 | (193) all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 107.97/15.18 | (194) all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 107.97/15.18 | (195) all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 107.97/15.18 | (196) all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 107.97/15.18 | (197) all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 107.97/15.18 | (198) all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 107.97/15.18 | (199) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 107.97/15.18 | (200) all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 107.97/15.18 | (201) all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 107.97/15.18 | (202) all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 107.97/15.18 | (203) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 107.97/15.19 | (204) all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 107.97/15.19 | (205) all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 107.97/15.19 | (206) all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 107.97/15.19 | (207) all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 107.97/15.19 | (208) all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 107.97/15.19 |
% 107.97/15.19 | DELTA: instantiating (2) with fresh symbols all_57_0, all_57_1, all_57_2,
% 107.97/15.19 | all_57_3, all_57_4, all_57_5, all_57_6, all_57_7, all_57_8, all_57_9,
% 107.97/15.19 | all_57_10, all_57_11, all_57_12, all_57_13, all_57_14, all_57_15,
% 107.97/15.19 | all_57_16, all_57_17, all_57_18, all_57_19, all_57_20, all_57_21,
% 107.97/15.19 | all_57_22, all_57_23, all_57_24, all_57_25, all_57_26, all_57_27,
% 107.97/15.19 | all_57_28, all_57_29, all_57_30, all_57_31, all_57_32, all_57_33,
% 107.97/15.19 | all_57_34, all_57_35, all_57_36, all_57_37, all_57_38, all_57_39,
% 107.97/15.19 | all_57_40, all_57_41, all_57_42, all_57_43, all_57_44, all_57_45,
% 107.97/15.19 | all_57_46, all_57_47, all_57_48, all_57_49, all_57_50, all_57_51,
% 107.97/15.19 | all_57_52, all_57_53, all_57_54, all_57_55, all_57_56, all_57_57,
% 107.97/15.19 | all_57_58, all_57_59, all_57_60, all_57_61, all_57_62, all_57_63,
% 107.97/15.19 | all_57_64, all_57_65, all_57_66, all_57_67, all_57_68, all_57_69,
% 107.97/15.19 | all_57_70, all_57_71, all_57_72, all_57_73, all_57_74, all_57_75,
% 107.97/15.19 | all_57_76, all_57_77, all_57_78, all_57_79, all_57_80, all_57_81,
% 107.97/15.19 | all_57_82, all_57_83, all_57_84, all_57_85, all_57_86, all_57_87,
% 107.97/15.19 | all_57_88, all_57_89, all_57_90, all_57_91, all_57_92, all_57_93,
% 107.97/15.19 | all_57_94, all_57_95, all_57_96, all_57_97, all_57_98, all_57_99,
% 107.97/15.19 | all_57_100, all_57_101, all_57_102, all_57_103, all_57_104, all_57_105,
% 107.97/15.19 | all_57_106, all_57_107, all_57_108, all_57_109, all_57_110, all_57_111,
% 107.97/15.19 | all_57_112, all_57_113, all_57_114, all_57_115, all_57_116, all_57_117,
% 107.97/15.19 | all_57_118, all_57_119, all_57_120, all_57_121, all_57_122, all_57_123,
% 107.97/15.19 | all_57_124, all_57_125, all_57_126, all_57_127 gives:
% 107.97/15.19 | (209) ((all_57_0 = e0 & op(e0, e3) = e0) | (all_57_1 = e0 & op(e0, e2) =
% 107.97/15.19 | e0) | (all_57_2 = e0 & op(e0, e1) = e0) | (all_57_3 = e0 & op(e0,
% 107.97/15.19 | e0) = e0)) & ((all_57_4 = e0 & op(e3, e0) = e0) | (all_57_5 =
% 107.97/15.19 | e0 & op(e2, e0) = e0) | (all_57_6 = e0 & op(e1, e0) = e0) |
% 107.97/15.19 | (all_57_7 = e0 & op(e0, e0) = e0)) & ((all_57_8 = e1 & op(e0, e3) =
% 107.97/15.19 | e1) | (all_57_9 = e1 & op(e0, e2) = e1) | (all_57_10 = e1 &
% 107.97/15.19 | op(e0, e1) = e1) | (all_57_11 = e1 & op(e0, e0) = e1)) &
% 107.97/15.19 | ((all_57_12 = e1 & op(e3, e0) = e1) | (all_57_13 = e1 & op(e2, e0) =
% 107.97/15.19 | e1) | (all_57_14 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 107.97/15.19 | op(e0, e0) = e1)) & ((all_57_16 = e2 & op(e0, e3) = e2) |
% 107.97/15.19 | (all_57_17 = e2 & op(e0, e2) = e2) | (all_57_18 = e2 & op(e0, e1) =
% 107.97/15.19 | e2) | (all_57_19 = e2 & op(e0, e0) = e2)) & ((all_57_20 = e2 &
% 107.97/15.19 | op(e3, e0) = e2) | (all_57_21 = e2 & op(e2, e0) = e2) |
% 107.97/15.19 | (all_57_22 = e2 & op(e1, e0) = e2) | (all_57_23 = e2 & op(e0, e0) =
% 107.97/15.19 | e2)) & ((all_57_24 = e3 & op(e0, e3) = e3) | (all_57_25 = e3 &
% 107.97/15.19 | op(e0, e2) = e3) | (all_57_26 = e3 & op(e0, e1) = e3) |
% 107.97/15.19 | (all_57_27 = e3 & op(e0, e0) = e3)) & ((all_57_28 = e3 & op(e3, e0)
% 107.97/15.19 | = e3) | (all_57_29 = e3 & op(e2, e0) = e3) | (all_57_30 = e3 &
% 107.97/15.19 | op(e1, e0) = e3) | (all_57_31 = e3 & op(e0, e0) = e3)) &
% 107.97/15.19 | ((all_57_32 = e0 & op(e1, e3) = e0) | (all_57_33 = e0 & op(e1, e2) =
% 107.97/15.19 | e0) | (all_57_34 = e0 & op(e1, e1) = e0) | (all_57_35 = e0 &
% 107.97/15.19 | op(e1, e0) = e0)) & ((all_57_36 = e0 & op(e3, e1) = e0) |
% 107.97/15.19 | (all_57_37 = e0 & op(e2, e1) = e0) | (all_57_38 = e0 & op(e1, e1) =
% 107.97/15.19 | e0) | (all_57_39 = e0 & op(e0, e1) = e0)) & ((all_57_40 = e1 &
% 107.97/15.19 | op(e1, e3) = e1) | (all_57_41 = e1 & op(e1, e2) = e1) |
% 107.97/15.19 | (all_57_42 = e1 & op(e1, e1) = e1) | (all_57_43 = e1 & op(e1, e0) =
% 107.97/15.19 | e1)) & ((all_57_44 = e1 & op(e3, e1) = e1) | (all_57_45 = e1 &
% 107.97/15.19 | op(e2, e1) = e1) | (all_57_46 = e1 & op(e1, e1) = e1) |
% 107.97/15.19 | (all_57_47 = e1 & op(e0, e1) = e1)) & ((all_57_48 = e2 & op(e1, e3)
% 107.97/15.19 | = e2) | (all_57_49 = e2 & op(e1, e2) = e2) | (all_57_50 = e2 &
% 107.97/15.19 | op(e1, e1) = e2) | (all_57_51 = e2 & op(e1, e0) = e2)) &
% 107.97/15.19 | ((all_57_52 = e2 & op(e3, e1) = e2) | (all_57_53 = e2 & op(e2, e1) =
% 107.97/15.19 | e2) | (all_57_54 = e2 & op(e1, e1) = e2) | (all_57_55 = e2 &
% 107.97/15.19 | op(e0, e1) = e2)) & ((all_57_56 = e3 & op(e1, e3) = e3) |
% 107.97/15.19 | (all_57_57 = e3 & op(e1, e2) = e3) | (all_57_58 = e3 & op(e1, e1) =
% 107.97/15.19 | e3) | (all_57_59 = e3 & op(e1, e0) = e3)) & ((all_57_60 = e3 &
% 107.97/15.19 | op(e3, e1) = e3) | (all_57_61 = e3 & op(e2, e1) = e3) |
% 107.97/15.19 | (all_57_62 = e3 & op(e1, e1) = e3) | (all_57_63 = e3 & op(e0, e1) =
% 107.97/15.19 | e3)) & ((all_57_64 = e0 & op(e2, e3) = e0) | (all_57_65 = e0 &
% 107.97/15.19 | op(e2, e2) = e0) | (all_57_66 = e0 & op(e2, e1) = e0) |
% 107.97/15.19 | (all_57_67 = e0 & op(e2, e0) = e0)) & ((all_57_68 = e0 & op(e3, e2)
% 107.97/15.19 | = e0) | (all_57_69 = e0 & op(e2, e2) = e0) | (all_57_70 = e0 &
% 107.97/15.19 | op(e1, e2) = e0) | (all_57_71 = e0 & op(e0, e2) = e0)) &
% 107.97/15.19 | ((all_57_72 = e1 & op(e2, e3) = e1) | (all_57_73 = e1 & op(e2, e2) =
% 107.97/15.19 | e1) | (all_57_74 = e1 & op(e2, e1) = e1) | (all_57_75 = e1 &
% 107.97/15.19 | op(e2, e0) = e1)) & ((all_57_76 = e1 & op(e3, e2) = e1) |
% 107.97/15.19 | (all_57_77 = e1 & op(e2, e2) = e1) | (all_57_78 = e1 & op(e1, e2) =
% 107.97/15.19 | e1) | (all_57_79 = e1 & op(e0, e2) = e1)) & ((all_57_80 = e2 &
% 107.97/15.19 | op(e2, e3) = e2) | (all_57_81 = e2 & op(e2, e2) = e2) |
% 107.97/15.19 | (all_57_82 = e2 & op(e2, e1) = e2) | (all_57_83 = e2 & op(e2, e0) =
% 107.97/15.19 | e2)) & ((all_57_84 = e2 & op(e3, e2) = e2) | (all_57_85 = e2 &
% 107.97/15.19 | op(e2, e2) = e2) | (all_57_86 = e2 & op(e1, e2) = e2) |
% 107.97/15.19 | (all_57_87 = e2 & op(e0, e2) = e2)) & ((all_57_88 = e3 & op(e2, e3)
% 107.97/15.19 | = e3) | (all_57_89 = e3 & op(e2, e2) = e3) | (all_57_90 = e3 &
% 107.97/15.19 | op(e2, e1) = e3) | (all_57_91 = e3 & op(e2, e0) = e3)) &
% 107.97/15.19 | ((all_57_92 = e3 & op(e3, e2) = e3) | (all_57_93 = e3 & op(e2, e2) =
% 107.97/15.19 | e3) | (all_57_94 = e3 & op(e1, e2) = e3) | (all_57_95 = e3 &
% 107.97/15.19 | op(e0, e2) = e3)) & ((all_57_96 = e0 & op(e3, e3) = e0) |
% 107.97/15.19 | (all_57_97 = e0 & op(e3, e2) = e0) | (all_57_98 = e0 & op(e3, e1) =
% 107.97/15.19 | e0) | (all_57_99 = e0 & op(e3, e0) = e0)) & ((all_57_100 = e0 &
% 107.97/15.19 | op(e3, e3) = e0) | (all_57_101 = e0 & op(e2, e3) = e0) |
% 107.97/15.19 | (all_57_102 = e0 & op(e1, e3) = e0) | (all_57_103 = e0 & op(e0, e3)
% 107.97/15.19 | = e0)) & ((all_57_104 = e1 & op(e3, e3) = e1) | (all_57_105 = e1
% 107.97/15.19 | & op(e3, e2) = e1) | (all_57_106 = e1 & op(e3, e1) = e1) |
% 107.97/15.19 | (all_57_107 = e1 & op(e3, e0) = e1)) & ((all_57_108 = e1 & op(e3,
% 107.97/15.19 | e3) = e1) | (all_57_109 = e1 & op(e2, e3) = e1) | (all_57_110 =
% 107.97/15.19 | e1 & op(e1, e3) = e1) | (all_57_111 = e1 & op(e0, e3) = e1)) &
% 107.97/15.19 | ((all_57_112 = e2 & op(e3, e3) = e2) | (all_57_113 = e2 & op(e3, e2)
% 107.97/15.19 | = e2) | (all_57_114 = e2 & op(e3, e1) = e2) | (all_57_115 = e2 &
% 107.97/15.19 | op(e3, e0) = e2)) & ((all_57_116 = e2 & op(e3, e3) = e2) |
% 107.97/15.19 | (all_57_117 = e2 & op(e2, e3) = e2) | (all_57_118 = e2 & op(e1, e3)
% 107.97/15.19 | = e2) | (all_57_119 = e2 & op(e0, e3) = e2)) & ((all_57_120 = e3
% 107.97/15.19 | & op(e3, e3) = e3) | (all_57_121 = e3 & op(e3, e2) = e3) |
% 107.97/15.19 | (all_57_122 = e3 & op(e3, e1) = e3) | (all_57_123 = e3 & op(e3, e0)
% 107.97/15.19 | = e3)) & ((all_57_124 = e3 & op(e3, e3) = e3) | (all_57_125 = e3
% 107.97/15.19 | & op(e2, e3) = e3) | (all_57_126 = e3 & op(e1, e3) = e3) |
% 107.97/15.19 | (all_57_127 = e3 & op(e0, e3) = e3))
% 107.97/15.19 |
% 107.97/15.19 | ALPHA: (209) implies:
% 107.97/15.20 | (210) (all_57_124 = e3 & op(e3, e3) = e3) | (all_57_125 = e3 & op(e2, e3) =
% 107.97/15.20 | e3) | (all_57_126 = e3 & op(e1, e3) = e3) | (all_57_127 = e3 &
% 107.97/15.20 | op(e0, e3) = e3)
% 107.97/15.20 | (211) (all_57_120 = e3 & op(e3, e3) = e3) | (all_57_121 = e3 & op(e3, e2) =
% 107.97/15.20 | e3) | (all_57_122 = e3 & op(e3, e1) = e3) | (all_57_123 = e3 &
% 107.97/15.20 | op(e3, e0) = e3)
% 107.97/15.20 | (212) (all_57_116 = e2 & op(e3, e3) = e2) | (all_57_117 = e2 & op(e2, e3) =
% 107.97/15.20 | e2) | (all_57_118 = e2 & op(e1, e3) = e2) | (all_57_119 = e2 &
% 107.97/15.20 | op(e0, e3) = e2)
% 107.97/15.20 | (213) (all_57_112 = e2 & op(e3, e3) = e2) | (all_57_113 = e2 & op(e3, e2) =
% 107.97/15.20 | e2) | (all_57_114 = e2 & op(e3, e1) = e2) | (all_57_115 = e2 &
% 107.97/15.20 | op(e3, e0) = e2)
% 107.97/15.20 | (214) (all_57_108 = e1 & op(e3, e3) = e1) | (all_57_109 = e1 & op(e2, e3) =
% 107.97/15.20 | e1) | (all_57_110 = e1 & op(e1, e3) = e1) | (all_57_111 = e1 &
% 107.97/15.20 | op(e0, e3) = e1)
% 107.97/15.20 | (215) (all_57_104 = e1 & op(e3, e3) = e1) | (all_57_105 = e1 & op(e3, e2) =
% 107.97/15.20 | e1) | (all_57_106 = e1 & op(e3, e1) = e1) | (all_57_107 = e1 &
% 107.97/15.20 | op(e3, e0) = e1)
% 107.97/15.20 | (216) (all_57_100 = e0 & op(e3, e3) = e0) | (all_57_101 = e0 & op(e2, e3) =
% 107.97/15.20 | e0) | (all_57_102 = e0 & op(e1, e3) = e0) | (all_57_103 = e0 &
% 107.97/15.20 | op(e0, e3) = e0)
% 107.97/15.20 | (217) (all_57_96 = e0 & op(e3, e3) = e0) | (all_57_97 = e0 & op(e3, e2) =
% 107.97/15.20 | e0) | (all_57_98 = e0 & op(e3, e1) = e0) | (all_57_99 = e0 & op(e3,
% 107.97/15.20 | e0) = e0)
% 107.97/15.20 | (218) (all_57_92 = e3 & op(e3, e2) = e3) | (all_57_93 = e3 & op(e2, e2) =
% 107.97/15.20 | e3) | (all_57_94 = e3 & op(e1, e2) = e3) | (all_57_95 = e3 & op(e0,
% 107.97/15.20 | e2) = e3)
% 107.97/15.20 | (219) (all_57_88 = e3 & op(e2, e3) = e3) | (all_57_89 = e3 & op(e2, e2) =
% 107.97/15.20 | e3) | (all_57_90 = e3 & op(e2, e1) = e3) | (all_57_91 = e3 & op(e2,
% 107.97/15.20 | e0) = e3)
% 107.97/15.20 | (220) (all_57_84 = e2 & op(e3, e2) = e2) | (all_57_85 = e2 & op(e2, e2) =
% 107.97/15.20 | e2) | (all_57_86 = e2 & op(e1, e2) = e2) | (all_57_87 = e2 & op(e0,
% 107.97/15.20 | e2) = e2)
% 107.97/15.20 | (221) (all_57_80 = e2 & op(e2, e3) = e2) | (all_57_81 = e2 & op(e2, e2) =
% 107.97/15.20 | e2) | (all_57_82 = e2 & op(e2, e1) = e2) | (all_57_83 = e2 & op(e2,
% 107.97/15.20 | e0) = e2)
% 107.97/15.20 | (222) (all_57_76 = e1 & op(e3, e2) = e1) | (all_57_77 = e1 & op(e2, e2) =
% 107.97/15.20 | e1) | (all_57_78 = e1 & op(e1, e2) = e1) | (all_57_79 = e1 & op(e0,
% 107.97/15.20 | e2) = e1)
% 107.97/15.20 | (223) (all_57_72 = e1 & op(e2, e3) = e1) | (all_57_73 = e1 & op(e2, e2) =
% 107.97/15.20 | e1) | (all_57_74 = e1 & op(e2, e1) = e1) | (all_57_75 = e1 & op(e2,
% 107.97/15.20 | e0) = e1)
% 107.97/15.20 | (224) (all_57_68 = e0 & op(e3, e2) = e0) | (all_57_69 = e0 & op(e2, e2) =
% 107.97/15.20 | e0) | (all_57_70 = e0 & op(e1, e2) = e0) | (all_57_71 = e0 & op(e0,
% 107.97/15.20 | e2) = e0)
% 107.97/15.20 | (225) (all_57_64 = e0 & op(e2, e3) = e0) | (all_57_65 = e0 & op(e2, e2) =
% 107.97/15.20 | e0) | (all_57_66 = e0 & op(e2, e1) = e0) | (all_57_67 = e0 & op(e2,
% 107.97/15.20 | e0) = e0)
% 107.97/15.20 | (226) (all_57_60 = e3 & op(e3, e1) = e3) | (all_57_61 = e3 & op(e2, e1) =
% 107.97/15.20 | e3) | (all_57_62 = e3 & op(e1, e1) = e3) | (all_57_63 = e3 & op(e0,
% 107.97/15.20 | e1) = e3)
% 107.97/15.20 | (227) (all_57_56 = e3 & op(e1, e3) = e3) | (all_57_57 = e3 & op(e1, e2) =
% 107.97/15.20 | e3) | (all_57_58 = e3 & op(e1, e1) = e3) | (all_57_59 = e3 & op(e1,
% 107.97/15.20 | e0) = e3)
% 107.97/15.20 | (228) (all_57_52 = e2 & op(e3, e1) = e2) | (all_57_53 = e2 & op(e2, e1) =
% 107.97/15.20 | e2) | (all_57_54 = e2 & op(e1, e1) = e2) | (all_57_55 = e2 & op(e0,
% 107.97/15.20 | e1) = e2)
% 107.97/15.20 | (229) (all_57_48 = e2 & op(e1, e3) = e2) | (all_57_49 = e2 & op(e1, e2) =
% 107.97/15.20 | e2) | (all_57_50 = e2 & op(e1, e1) = e2) | (all_57_51 = e2 & op(e1,
% 107.97/15.20 | e0) = e2)
% 107.97/15.20 | (230) (all_57_44 = e1 & op(e3, e1) = e1) | (all_57_45 = e1 & op(e2, e1) =
% 107.97/15.20 | e1) | (all_57_46 = e1 & op(e1, e1) = e1) | (all_57_47 = e1 & op(e0,
% 107.97/15.20 | e1) = e1)
% 107.97/15.20 | (231) (all_57_40 = e1 & op(e1, e3) = e1) | (all_57_41 = e1 & op(e1, e2) =
% 107.97/15.20 | e1) | (all_57_42 = e1 & op(e1, e1) = e1) | (all_57_43 = e1 & op(e1,
% 107.97/15.20 | e0) = e1)
% 107.97/15.20 | (232) (all_57_36 = e0 & op(e3, e1) = e0) | (all_57_37 = e0 & op(e2, e1) =
% 107.97/15.20 | e0) | (all_57_38 = e0 & op(e1, e1) = e0) | (all_57_39 = e0 & op(e0,
% 107.97/15.20 | e1) = e0)
% 107.97/15.20 | (233) (all_57_32 = e0 & op(e1, e3) = e0) | (all_57_33 = e0 & op(e1, e2) =
% 107.97/15.20 | e0) | (all_57_34 = e0 & op(e1, e1) = e0) | (all_57_35 = e0 & op(e1,
% 107.97/15.20 | e0) = e0)
% 107.97/15.21 | (234) (all_57_28 = e3 & op(e3, e0) = e3) | (all_57_29 = e3 & op(e2, e0) =
% 107.97/15.21 | e3) | (all_57_30 = e3 & op(e1, e0) = e3) | (all_57_31 = e3 & op(e0,
% 107.97/15.21 | e0) = e3)
% 107.97/15.21 | (235) (all_57_24 = e3 & op(e0, e3) = e3) | (all_57_25 = e3 & op(e0, e2) =
% 107.97/15.21 | e3) | (all_57_26 = e3 & op(e0, e1) = e3) | (all_57_27 = e3 & op(e0,
% 107.97/15.21 | e0) = e3)
% 107.97/15.21 | (236) (all_57_20 = e2 & op(e3, e0) = e2) | (all_57_21 = e2 & op(e2, e0) =
% 107.97/15.21 | e2) | (all_57_22 = e2 & op(e1, e0) = e2) | (all_57_23 = e2 & op(e0,
% 107.97/15.21 | e0) = e2)
% 107.97/15.21 | (237) (all_57_16 = e2 & op(e0, e3) = e2) | (all_57_17 = e2 & op(e0, e2) =
% 107.97/15.21 | e2) | (all_57_18 = e2 & op(e0, e1) = e2) | (all_57_19 = e2 & op(e0,
% 107.97/15.21 | e0) = e2)
% 107.97/15.21 | (238) (all_57_12 = e1 & op(e3, e0) = e1) | (all_57_13 = e1 & op(e2, e0) =
% 107.97/15.21 | e1) | (all_57_14 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 107.97/15.21 | e0) = e1)
% 107.97/15.21 | (239) (all_57_8 = e1 & op(e0, e3) = e1) | (all_57_9 = e1 & op(e0, e2) = e1)
% 107.97/15.21 | | (all_57_10 = e1 & op(e0, e1) = e1) | (all_57_11 = e1 & op(e0, e0) =
% 107.97/15.21 | e1)
% 107.97/15.21 | (240) (all_57_4 = e0 & op(e3, e0) = e0) | (all_57_5 = e0 & op(e2, e0) = e0)
% 107.97/15.21 | | (all_57_6 = e0 & op(e1, e0) = e0) | (all_57_7 = e0 & op(e0, e0) =
% 107.97/15.21 | e0)
% 107.97/15.21 | (241) (all_57_0 = e0 & op(e0, e3) = e0) | (all_57_1 = e0 & op(e0, e2) = e0)
% 107.97/15.21 | | (all_57_2 = e0 & op(e0, e1) = e0) | (all_57_3 = e0 & op(e0, e0) =
% 107.97/15.21 | e0)
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_8_2, all_28_2, e0, e0,
% 107.97/15.21 | simplifying with (41), (71) gives:
% 107.97/15.21 | (242) all_28_2 = all_8_2
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_36_2, e0, e0,
% 107.97/15.21 | simplifying with (71), (83) gives:
% 107.97/15.21 | (243) all_36_2 = all_28_2
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_16_2, all_36_2, e0, e0,
% 107.97/15.21 | simplifying with (53), (83) gives:
% 107.97/15.21 | (244) all_36_2 = all_16_2
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_53_0, e0, e0,
% 107.97/15.21 | simplifying with (86), (160) gives:
% 107.97/15.21 | (245) all_53_0 = all_38_2
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_53_0, e0, e0,
% 107.97/15.21 | simplifying with (71), (160) gives:
% 107.97/15.21 | (246) all_53_0 = all_28_2
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_53_0, all_55_0, e0, e0,
% 107.97/15.21 | simplifying with (160), (177) gives:
% 107.97/15.21 | (247) all_55_0 = all_53_0
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_6_2, all_55_0, e0, e0,
% 107.97/15.21 | simplifying with (38), (177) gives:
% 107.97/15.21 | (248) all_55_0 = all_6_2
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_53_1, all_55_1, e1, e0,
% 107.97/15.21 | simplifying with (161), (178) gives:
% 107.97/15.21 | (249) all_55_1 = all_53_1
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_53_3, all_55_2, e2, e0,
% 107.97/15.21 | simplifying with (162), (179) gives:
% 107.97/15.21 | (250) all_55_2 = all_53_3
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_53_2, all_55_3, e3, e0,
% 107.97/15.21 | simplifying with (163), (180) gives:
% 107.97/15.21 | (251) all_55_3 = all_53_2
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_53_4, all_55_4, e0, e1,
% 107.97/15.21 | simplifying with (164), (181) gives:
% 107.97/15.21 | (252) all_55_4 = all_53_4
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_14_2, all_20_2, e1, e1,
% 107.97/15.21 | simplifying with (50), (59) gives:
% 107.97/15.21 | (253) all_20_2 = all_14_2
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_32_2, e1, e1,
% 107.97/15.21 | simplifying with (59), (77) gives:
% 107.97/15.21 | (254) all_32_2 = all_20_2
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_18_2, all_32_2, e1, e1,
% 107.97/15.21 | simplifying with (56), (77) gives:
% 107.97/15.21 | (255) all_32_2 = all_18_2
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_32_2, all_53_5, e1, e1,
% 107.97/15.21 | simplifying with (77), (165) gives:
% 107.97/15.21 | (256) all_53_5 = all_32_2
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_53_5, e1, e1,
% 107.97/15.21 | simplifying with (62), (165) gives:
% 107.97/15.21 | (257) all_53_5 = all_22_2
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_53_5, all_55_5, e1, e1,
% 107.97/15.21 | simplifying with (165), (182) gives:
% 107.97/15.21 | (258) all_55_5 = all_53_5
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_44_2, all_55_5, e1, e1,
% 107.97/15.21 | simplifying with (95), (182) gives:
% 107.97/15.21 | (259) all_55_5 = all_44_2
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_53_7, all_55_6, e2, e1,
% 107.97/15.21 | simplifying with (166), (183) gives:
% 107.97/15.21 | (260) all_55_6 = all_53_7
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_53_6, all_55_7, e3, e1,
% 107.97/15.21 | simplifying with (167), (184) gives:
% 107.97/15.21 | (261) all_55_7 = all_53_6
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_53_8, all_55_8, e0, e2,
% 107.97/15.21 | simplifying with (168), (185) gives:
% 107.97/15.21 | (262) all_55_8 = all_53_8
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_53_9, all_55_9, e1, e2,
% 107.97/15.21 | simplifying with (169), (186) gives:
% 107.97/15.21 | (263) all_55_9 = all_53_9
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_30_2, all_46_2, e2, e2,
% 107.97/15.21 | simplifying with (74), (98) gives:
% 107.97/15.21 | (264) all_46_2 = all_30_2
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_10_2, all_46_2, e2, e2,
% 107.97/15.21 | simplifying with (44), (98) gives:
% 107.97/15.21 | (265) all_46_2 = all_10_2
% 107.97/15.21 |
% 107.97/15.21 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_53_11, e2, e2,
% 107.97/15.21 | simplifying with (101), (170) gives:
% 107.97/15.21 | (266) all_53_11 = all_48_2
% 107.97/15.21 |
% 107.97/15.22 | GROUND_INST: instantiating (function-axioms) with all_30_2, all_53_11, e2, e2,
% 107.97/15.22 | simplifying with (74), (170) gives:
% 107.97/15.22 | (267) all_53_11 = all_30_2
% 107.97/15.22 |
% 107.97/15.22 | GROUND_INST: instantiating (function-axioms) with all_12_2, all_53_11, e2, e2,
% 107.97/15.22 | simplifying with (47), (170) gives:
% 107.97/15.22 | (268) all_53_11 = all_12_2
% 107.97/15.22 |
% 107.97/15.22 | GROUND_INST: instantiating (function-axioms) with all_46_2, all_55_10, e2, e2,
% 107.97/15.22 | simplifying with (98), (187) gives:
% 107.97/15.22 | (269) all_55_10 = all_46_2
% 107.97/15.22 |
% 107.97/15.22 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_55_10, e2, e2,
% 107.97/15.22 | simplifying with (65), (187) gives:
% 107.97/15.22 | (270) all_55_10 = all_24_2
% 107.97/15.22 |
% 107.97/15.22 | GROUND_INST: instantiating (function-axioms) with all_53_10, all_55_11, e3,
% 107.97/15.22 | e2, simplifying with (171), (188) gives:
% 107.97/15.22 | (271) all_55_11 = all_53_10
% 107.97/15.22 |
% 107.97/15.22 | GROUND_INST: instantiating (function-axioms) with all_53_12, all_55_12, e0,
% 107.97/15.22 | e3, simplifying with (172), (189) gives:
% 107.97/15.22 | (272) all_55_12 = all_53_12
% 107.97/15.22 |
% 107.97/15.22 | GROUND_INST: instantiating (function-axioms) with all_53_13, all_55_13, e1,
% 107.97/15.22 | e3, simplifying with (173), (190) gives:
% 107.97/15.22 | (273) all_55_13 = all_53_13
% 107.97/15.22 |
% 107.97/15.22 | GROUND_INST: instantiating (function-axioms) with all_53_15, all_55_14, e2,
% 107.97/15.22 | e3, simplifying with (174), (191) gives:
% 107.97/15.22 | (274) all_55_14 = all_53_15
% 107.97/15.22 |
% 107.97/15.22 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_40_2, e3, e3,
% 107.97/15.22 | simplifying with (80), (89) gives:
% 107.97/15.22 | (275) all_40_2 = all_34_2
% 107.97/15.22 |
% 107.97/15.22 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_50_2, e3, e3,
% 107.97/15.22 | simplifying with (89), (104) gives:
% 107.97/15.22 | (276) all_50_2 = all_40_2
% 107.97/15.22 |
% 107.97/15.22 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_50_2, e3, e3,
% 107.97/15.22 | simplifying with (35), (104) gives:
% 107.97/15.22 | (277) all_50_2 = all_4_2
% 107.97/15.22 |
% 107.97/15.22 | GROUND_INST: instantiating (function-axioms) with all_26_2, all_53_14, e3, e3,
% 107.97/15.22 | simplifying with (68), (175) gives:
% 107.97/15.22 | (278) all_53_14 = all_26_2
% 107.97/15.22 |
% 107.97/15.22 | GROUND_INST: instantiating (function-axioms) with all_53_14, all_55_15, e3,
% 107.97/15.22 | e3, simplifying with (175), (192) gives:
% 107.97/15.22 | (279) all_55_15 = all_53_14
% 107.97/15.22 |
% 107.97/15.22 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_55_15, e3, e3,
% 107.97/15.22 | simplifying with (92), (192) gives:
% 107.97/15.22 | (280) all_55_15 = all_42_2
% 107.97/15.22 |
% 107.97/15.22 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_55_15, e3, e3,
% 107.97/15.22 | simplifying with (80), (192) gives:
% 107.97/15.22 | (281) all_55_15 = all_34_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (247), (248) imply:
% 107.97/15.22 | (282) all_53_0 = all_6_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (282) implies:
% 107.97/15.22 | (283) all_53_0 = all_6_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (258), (259) imply:
% 107.97/15.22 | (284) all_53_5 = all_44_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (284) implies:
% 107.97/15.22 | (285) all_53_5 = all_44_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (269), (270) imply:
% 107.97/15.22 | (286) all_46_2 = all_24_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (286) implies:
% 107.97/15.22 | (287) all_46_2 = all_24_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (280), (281) imply:
% 107.97/15.22 | (288) all_42_2 = all_34_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (279), (280) imply:
% 107.97/15.22 | (289) all_53_14 = all_42_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (289) implies:
% 107.97/15.22 | (290) all_53_14 = all_42_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (245), (246) imply:
% 107.97/15.22 | (291) all_38_2 = all_28_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (245), (283) imply:
% 107.97/15.22 | (292) all_38_2 = all_6_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (257), (285) imply:
% 107.97/15.22 | (293) all_44_2 = all_22_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (256), (285) imply:
% 107.97/15.22 | (294) all_44_2 = all_32_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (266), (268) imply:
% 107.97/15.22 | (295) all_48_2 = all_12_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (266), (267) imply:
% 107.97/15.22 | (296) all_48_2 = all_30_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (278), (290) imply:
% 107.97/15.22 | (297) all_42_2 = all_26_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (297) implies:
% 107.97/15.22 | (298) all_42_2 = all_26_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (276), (277) imply:
% 107.97/15.22 | (299) all_40_2 = all_4_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (299) implies:
% 107.97/15.22 | (300) all_40_2 = all_4_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (295), (296) imply:
% 107.97/15.22 | (301) all_30_2 = all_12_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (301) implies:
% 107.97/15.22 | (302) all_30_2 = all_12_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (265), (287) imply:
% 107.97/15.22 | (303) all_24_2 = all_10_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (264), (287) imply:
% 107.97/15.22 | (304) all_30_2 = all_24_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (304) implies:
% 107.97/15.22 | (305) all_30_2 = all_24_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (293), (294) imply:
% 107.97/15.22 | (306) all_32_2 = all_22_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (306) implies:
% 107.97/15.22 | (307) all_32_2 = all_22_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (288), (298) imply:
% 107.97/15.22 | (308) all_34_2 = all_26_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (308) implies:
% 107.97/15.22 | (309) all_34_2 = all_26_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (275), (300) imply:
% 107.97/15.22 | (310) all_34_2 = all_4_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (310) implies:
% 107.97/15.22 | (311) all_34_2 = all_4_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (291), (292) imply:
% 107.97/15.22 | (312) all_28_2 = all_6_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (312) implies:
% 107.97/15.22 | (313) all_28_2 = all_6_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (243), (244) imply:
% 107.97/15.22 | (314) all_28_2 = all_16_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (314) implies:
% 107.97/15.22 | (315) all_28_2 = all_16_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (309), (311) imply:
% 107.97/15.22 | (316) all_26_2 = all_4_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (254), (307) imply:
% 107.97/15.22 | (317) all_22_2 = all_20_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (255), (307) imply:
% 107.97/15.22 | (318) all_22_2 = all_18_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (302), (305) imply:
% 107.97/15.22 | (319) all_24_2 = all_12_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (319) implies:
% 107.97/15.22 | (320) all_24_2 = all_12_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (242), (315) imply:
% 107.97/15.22 | (321) all_16_2 = all_8_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (313), (315) imply:
% 107.97/15.22 | (322) all_16_2 = all_6_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (303), (320) imply:
% 107.97/15.22 | (323) all_12_2 = all_10_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (317), (318) imply:
% 107.97/15.22 | (324) all_20_2 = all_18_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (324) implies:
% 107.97/15.22 | (325) all_20_2 = all_18_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (253), (325) imply:
% 107.97/15.22 | (326) all_18_2 = all_14_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (321), (322) imply:
% 107.97/15.22 | (327) all_8_2 = all_6_2
% 107.97/15.22 |
% 107.97/15.22 | SIMP: (327) implies:
% 107.97/15.22 | (328) all_8_2 = all_6_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (318), (326) imply:
% 107.97/15.22 | (329) all_22_2 = all_14_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (302), (323) imply:
% 107.97/15.22 | (330) all_30_2 = all_10_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (307), (329) imply:
% 107.97/15.22 | (331) all_32_2 = all_14_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (244), (322) imply:
% 107.97/15.22 | (332) all_36_2 = all_6_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (298), (316) imply:
% 107.97/15.22 | (333) all_42_2 = all_4_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (293), (329) imply:
% 107.97/15.22 | (334) all_44_2 = all_14_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (295), (323) imply:
% 107.97/15.22 | (335) all_48_2 = all_10_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (278), (316) imply:
% 107.97/15.22 | (336) all_53_14 = all_4_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (266), (335) imply:
% 107.97/15.22 | (337) all_53_11 = all_10_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (285), (334) imply:
% 107.97/15.22 | (338) all_53_5 = all_14_2
% 107.97/15.22 |
% 107.97/15.22 | COMBINE_EQS: (280), (333) imply:
% 107.97/15.22 | (339) all_55_15 = all_4_2
% 107.97/15.22 |
% 107.97/15.23 | COMBINE_EQS: (270), (303) imply:
% 107.97/15.23 | (340) all_55_10 = all_10_2
% 107.97/15.23 |
% 107.97/15.23 | COMBINE_EQS: (259), (334) imply:
% 107.97/15.23 | (341) all_55_5 = all_14_2
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (159), (283) imply:
% 107.97/15.23 | (342) ~ (all_53_1 = all_6_2)
% 107.97/15.23 |
% 107.97/15.23 | SIMP: (342) implies:
% 107.97/15.23 | (343) ~ (all_53_1 = all_6_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (158), (283) imply:
% 107.97/15.23 | (344) ~ (all_53_2 = all_6_2)
% 107.97/15.23 |
% 107.97/15.23 | SIMP: (344) implies:
% 107.97/15.23 | (345) ~ (all_53_2 = all_6_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (157), (283) imply:
% 107.97/15.23 | (346) ~ (all_53_3 = all_6_2)
% 107.97/15.23 |
% 107.97/15.23 | SIMP: (346) implies:
% 107.97/15.23 | (347) ~ (all_53_3 = all_6_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (156), (283) imply:
% 107.97/15.23 | (348) ~ (all_53_4 = all_6_2)
% 107.97/15.23 |
% 107.97/15.23 | SIMP: (348) implies:
% 107.97/15.23 | (349) ~ (all_53_4 = all_6_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (155), (283) imply:
% 107.97/15.23 | (350) ~ (all_53_8 = all_6_2)
% 107.97/15.23 |
% 107.97/15.23 | SIMP: (350) implies:
% 107.97/15.23 | (351) ~ (all_53_8 = all_6_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (154), (283) imply:
% 107.97/15.23 | (352) ~ (all_53_12 = all_6_2)
% 107.97/15.23 |
% 107.97/15.23 | SIMP: (352) implies:
% 107.97/15.23 | (353) ~ (all_53_12 = all_6_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (151), (338) imply:
% 107.97/15.23 | (354) ~ (all_53_1 = all_14_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (145), (336) imply:
% 107.97/15.23 | (355) ~ (all_53_2 = all_4_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (143), (337) imply:
% 107.97/15.23 | (356) ~ (all_53_3 = all_10_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (141), (338) imply:
% 107.97/15.23 | (357) ~ (all_53_4 = all_14_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (136), (338) imply:
% 107.97/15.23 | (358) ~ (all_53_6 = all_14_2)
% 107.97/15.23 |
% 107.97/15.23 | SIMP: (358) implies:
% 107.97/15.23 | (359) ~ (all_53_6 = all_14_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (135), (338) imply:
% 107.97/15.23 | (360) ~ (all_53_7 = all_14_2)
% 107.97/15.23 |
% 107.97/15.23 | SIMP: (360) implies:
% 107.97/15.23 | (361) ~ (all_53_7 = all_14_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (134), (338) imply:
% 107.97/15.23 | (362) ~ (all_53_9 = all_14_2)
% 107.97/15.23 |
% 107.97/15.23 | SIMP: (362) implies:
% 107.97/15.23 | (363) ~ (all_53_9 = all_14_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (133), (338) imply:
% 107.97/15.23 | (364) ~ (all_53_13 = all_14_2)
% 107.97/15.23 |
% 107.97/15.23 | SIMP: (364) implies:
% 107.97/15.23 | (365) ~ (all_53_13 = all_14_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (130), (336) imply:
% 107.97/15.23 | (366) ~ (all_53_6 = all_4_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (129), (337) imply:
% 107.97/15.23 | (367) ~ (all_53_7 = all_10_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (125), (337) imply:
% 107.97/15.23 | (368) ~ (all_53_8 = all_10_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (122), (337) imply:
% 107.97/15.23 | (369) ~ (all_53_9 = all_10_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (120), (337) imply:
% 107.97/15.23 | (370) ~ (all_53_10 = all_10_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (119), (336) imply:
% 107.97/15.23 | (371) ~ (all_53_10 = all_4_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (118), (337) imply:
% 107.97/15.23 | (372) ~ (all_53_15 = all_10_2)
% 107.97/15.23 |
% 107.97/15.23 | SIMP: (372) implies:
% 107.97/15.23 | (373) ~ (all_53_15 = all_10_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (116), (336) imply:
% 107.97/15.23 | (374) ~ (all_53_12 = all_4_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (114), (336) imply:
% 107.97/15.23 | (375) ~ (all_53_13 = all_4_2)
% 107.97/15.23 |
% 107.97/15.23 | REDUCE: (112), (336) imply:
% 107.97/15.23 | (376) ~ (all_53_15 = all_4_2)
% 107.97/15.23 |
% 107.97/15.23 | SIMP: (376) implies:
% 107.97/15.23 | (377) ~ (all_53_15 = all_4_2)
% 107.97/15.23 |
% 107.97/15.23 | BETA: splitting (36) gives:
% 107.97/15.23 |
% 107.97/15.23 | Case 1:
% 107.97/15.23 | |
% 107.97/15.23 | | (378) ~ (all_4_2 = e0)
% 107.97/15.23 | |
% 107.97/15.23 | | BETA: splitting (39) gives:
% 107.97/15.23 | |
% 107.97/15.23 | | Case 1:
% 107.97/15.23 | | |
% 107.97/15.23 | | | (379) ~ (all_6_2 = e1)
% 107.97/15.23 | | |
% 107.97/15.23 | | | BETA: splitting (42) gives:
% 107.97/15.23 | | |
% 107.97/15.23 | | | Case 1:
% 107.97/15.23 | | | |
% 107.97/15.23 | | | | (380) ~ (all_8_2 = e2)
% 107.97/15.23 | | | |
% 107.97/15.23 | | | | REDUCE: (328), (380) imply:
% 107.97/15.23 | | | | (381) ~ (all_6_2 = e2)
% 107.97/15.23 | | | |
% 107.97/15.23 | | | | BETA: splitting (45) gives:
% 107.97/15.23 | | | |
% 107.97/15.23 | | | | Case 1:
% 107.97/15.23 | | | | |
% 107.97/15.23 | | | | | (382) ~ (all_10_2 = e3)
% 107.97/15.23 | | | | |
% 107.97/15.23 | | | | | BETA: splitting (48) gives:
% 107.97/15.23 | | | | |
% 107.97/15.23 | | | | | Case 1:
% 107.97/15.23 | | | | | |
% 107.97/15.23 | | | | | | (383) ~ (all_12_2 = e0)
% 107.97/15.23 | | | | | |
% 107.97/15.23 | | | | | | REDUCE: (323), (383) imply:
% 107.97/15.23 | | | | | | (384) ~ (all_10_2 = e0)
% 107.97/15.23 | | | | | |
% 107.97/15.23 | | | | | | BETA: splitting (51) gives:
% 107.97/15.23 | | | | | |
% 107.97/15.23 | | | | | | Case 1:
% 107.97/15.23 | | | | | | |
% 107.97/15.23 | | | | | | | (385) ~ (all_14_2 = e2)
% 107.97/15.23 | | | | | | |
% 107.97/15.23 | | | | | | | BETA: splitting (57) gives:
% 107.97/15.23 | | | | | | |
% 107.97/15.23 | | | | | | | Case 1:
% 107.97/15.23 | | | | | | | |
% 107.97/15.23 | | | | | | | | (386) ~ (all_18_2 = e3)
% 107.97/15.23 | | | | | | | |
% 107.97/15.23 | | | | | | | | REDUCE: (326), (386) imply:
% 107.97/15.23 | | | | | | | | (387) ~ (all_14_2 = e3)
% 107.97/15.23 | | | | | | | |
% 107.97/15.23 | | | | | | | | BETA: splitting (63) gives:
% 107.97/15.23 | | | | | | | |
% 107.97/15.23 | | | | | | | | Case 1:
% 107.97/15.23 | | | | | | | | |
% 107.97/15.23 | | | | | | | | | (388) ~ (all_22_2 = e0)
% 107.97/15.23 | | | | | | | | |
% 107.97/15.23 | | | | | | | | | REDUCE: (329), (388) imply:
% 107.97/15.23 | | | | | | | | | (389) ~ (all_14_2 = e0)
% 107.97/15.23 | | | | | | | | |
% 108.25/15.24 | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (117), (123),
% 108.25/15.24 | | | | | | | | | (126), (127), (148), (152), (153), (161), (162),
% 108.25/15.24 | | | | | | | | | (163), (164), (166), (167), (168), (169), (171),
% 108.25/15.24 | | | | | | | | | (172), (173), (174), (203), (341), (357), (359),
% 108.25/15.24 | | | | | | | | | (361), (385), (387), (389), (function-axioms) are
% 108.25/15.24 | | | | | | | | | inconsistent by sub-proof #216.
% 108.25/15.24 | | | | | | | | |
% 108.25/15.24 | | | | | | | | Case 2:
% 108.25/15.24 | | | | | | | | |
% 108.25/15.24 | | | | | | | | | (390) all_22_2 = e0
% 108.25/15.24 | | | | | | | | |
% 108.25/15.24 | | | | | | | | | COMBINE_EQS: (329), (390) imply:
% 108.25/15.24 | | | | | | | | | (391) all_14_2 = e0
% 108.25/15.24 | | | | | | | | |
% 108.25/15.24 | | | | | | | | | SIMP: (391) implies:
% 108.25/15.24 | | | | | | | | | (392) all_14_2 = e0
% 108.25/15.24 | | | | | | | | |
% 108.25/15.24 | | | | | | | | | COMBINE_EQS: (331), (392) imply:
% 108.25/15.24 | | | | | | | | | (393) all_32_2 = e0
% 108.25/15.24 | | | | | | | | |
% 108.25/15.24 | | | | | | | | | REDUCE: (354), (392) imply:
% 108.25/15.24 | | | | | | | | | (394) ~ (all_53_1 = e0)
% 108.25/15.24 | | | | | | | | |
% 108.25/15.24 | | | | | | | | | REDUCE: (363), (392) imply:
% 108.25/15.24 | | | | | | | | | (395) ~ (all_53_9 = e0)
% 108.25/15.24 | | | | | | | | |
% 108.25/15.24 | | | | | | | | | REDUCE: (365), (392) imply:
% 108.25/15.24 | | | | | | | | | (396) ~ (all_53_13 = e0)
% 108.25/15.24 | | | | | | | | |
% 108.25/15.24 | | | | | | | | | BETA: splitting (78) gives:
% 108.25/15.24 | | | | | | | | |
% 108.25/15.24 | | | | | | | | | Case 1:
% 108.25/15.24 | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | (397) ~ (all_32_2 = e0)
% 108.25/15.24 | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | REDUCE: (393), (397) imply:
% 108.25/15.24 | | | | | | | | | | (398) $false
% 108.25/15.24 | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | CLOSE: (398) is inconsistent.
% 108.25/15.24 | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | Case 2:
% 108.25/15.24 | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | (399) op(e0, e0) = all_32_1 & $i(all_32_1) & ( ~
% 108.25/15.24 | | | | | | | | | | (all_32_1 = e3) | ( ~ (all_32_0 = e2) & op(e3,
% 108.25/15.24 | | | | | | | | | | e0) = all_32_0 & $i(all_32_0)))
% 108.25/15.24 | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | ALPHA: (399) implies:
% 108.25/15.24 | | | | | | | | | | (400) op(e0, e0) = all_32_1
% 108.25/15.24 | | | | | | | | | | (401) ~ (all_32_1 = e3) | ( ~ (all_32_0 = e2) & op(e3,
% 108.25/15.24 | | | | | | | | | | e0) = all_32_0 & $i(all_32_0))
% 108.25/15.24 | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 108.25/15.24 | | | | | | | | | | all_32_1, e0, e0, simplifying with (38), (400)
% 108.25/15.24 | | | | | | | | | | gives:
% 108.25/15.24 | | | | | | | | | | (402) all_32_1 = all_6_2
% 108.25/15.24 | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | BETA: splitting (66) gives:
% 108.25/15.24 | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | Case 1:
% 108.25/15.24 | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | (403) ~ (all_24_2 = e1)
% 108.25/15.24 | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | REDUCE: (303), (403) imply:
% 108.25/15.24 | | | | | | | | | | | (404) ~ (all_10_2 = e1)
% 108.25/15.24 | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (115), (117),
% 108.25/15.24 | | | | | | | | | | | (132), (139), (140), (148), (152), (153), (161),
% 108.25/15.24 | | | | | | | | | | | (162), (163), (164), (166), (167), (168), (169),
% 108.25/15.24 | | | | | | | | | | | (171), (172), (173), (174), (198), (340), (368),
% 108.25/15.24 | | | | | | | | | | | (369), (370), (382), (384), (404),
% 108.25/15.24 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.25/15.24 | | | | | | | | | | | #207.
% 108.25/15.24 | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | Case 2:
% 108.25/15.24 | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | (405) all_24_2 = e1
% 108.25/15.24 | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | COMBINE_EQS: (303), (405) imply:
% 108.25/15.24 | | | | | | | | | | | (406) all_10_2 = e1
% 108.25/15.24 | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | SIMP: (406) implies:
% 108.25/15.24 | | | | | | | | | | | (407) all_10_2 = e1
% 108.25/15.24 | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | REDUCE: (356), (407) imply:
% 108.25/15.24 | | | | | | | | | | | (408) ~ (all_53_3 = e1)
% 108.25/15.24 | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | REDUCE: (367), (407) imply:
% 108.25/15.24 | | | | | | | | | | | (409) ~ (all_53_7 = e1)
% 108.25/15.24 | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | REDUCE: (368), (407) imply:
% 108.25/15.24 | | | | | | | | | | | (410) ~ (all_53_8 = e1)
% 108.25/15.24 | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | REDUCE: (369), (407) imply:
% 108.25/15.24 | | | | | | | | | | | (411) ~ (all_53_9 = e1)
% 108.25/15.24 | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | REDUCE: (373), (407) imply:
% 108.25/15.24 | | | | | | | | | | | (412) ~ (all_53_15 = e1)
% 108.25/15.24 | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | REDUCE: (44), (407) imply:
% 108.25/15.24 | | | | | | | | | | | (413) op(e2, e2) = e1
% 108.25/15.24 | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | BETA: splitting (69) gives:
% 108.25/15.24 | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | Case 1:
% 108.25/15.24 | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | (414) ~ (all_26_2 = e2)
% 108.25/15.24 | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | REDUCE: (316), (414) imply:
% 108.25/15.24 | | | | | | | | | | | | (415) ~ (all_4_2 = e2)
% 108.25/15.24 | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | BETA: splitting (72) gives:
% 108.25/15.24 | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | Case 1:
% 108.25/15.24 | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | (416) ~ (all_28_2 = e3)
% 108.25/15.24 | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | REDUCE: (313), (416) imply:
% 108.25/15.24 | | | | | | | | | | | | | (417) ~ (all_6_2 = e3)
% 108.25/15.24 | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | REF_CLOSE: (35), (108), (142), (162), (166), (172), (173),
% 108.25/15.24 | | | | | | | | | | | | | (174), (208), (217), (222), (248), (353), (378),
% 108.25/15.24 | | | | | | | | | | | | | (379), (381), (396), (408), (409), (412), (417),
% 108.25/15.24 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.25/15.24 | | | | | | | | | | | | | #199.
% 108.25/15.24 | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | Case 2:
% 108.25/15.24 | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | (418) all_28_2 = e3
% 108.25/15.24 | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | COMBINE_EQS: (313), (418) imply:
% 108.25/15.24 | | | | | | | | | | | | | (419) all_6_2 = e3
% 108.25/15.24 | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | COMBINE_EQS: (402), (419) imply:
% 108.25/15.24 | | | | | | | | | | | | | (420) all_32_1 = e3
% 108.25/15.24 | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | REDUCE: (351), (419) imply:
% 108.25/15.24 | | | | | | | | | | | | | (421) ~ (all_53_8 = e3)
% 108.25/15.24 | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | REDUCE: (353), (419) imply:
% 108.25/15.24 | | | | | | | | | | | | | (422) ~ (all_53_12 = e3)
% 108.25/15.24 | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | BETA: splitting (401) gives:
% 108.25/15.24 | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | Case 1:
% 108.25/15.24 | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | (423) ~ (all_32_1 = e3)
% 108.25/15.24 | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | REDUCE: (420), (423) imply:
% 108.25/15.24 | | | | | | | | | | | | | | (424) $false
% 108.25/15.24 | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | CLOSE: (424) is inconsistent.
% 108.25/15.24 | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | Case 2:
% 108.25/15.24 | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | (425) ~ (all_32_0 = e2) & op(e3, e0) = all_32_0 &
% 108.25/15.24 | | | | | | | | | | | | | | $i(all_32_0)
% 108.25/15.24 | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | ALPHA: (425) implies:
% 108.25/15.24 | | | | | | | | | | | | | | (426) ~ (all_32_0 = e2)
% 108.25/15.24 | | | | | | | | | | | | | | (427) op(e3, e0) = all_32_0
% 108.25/15.24 | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 108.25/15.24 | | | | | | | | | | | | | | all_32_0, e0, e3, simplifying with (172), (427)
% 108.25/15.24 | | | | | | | | | | | | | | gives:
% 108.25/15.24 | | | | | | | | | | | | | | (428) all_53_12 = all_32_0
% 108.25/15.24 | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | COMBINE_EQS: (272), (428) imply:
% 108.25/15.24 | | | | | | | | | | | | | | (429) all_55_12 = all_32_0
% 108.25/15.24 | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | REDUCE: (124), (428) imply:
% 108.25/15.24 | | | | | | | | | | | | | | (430) ~ (all_53_8 = all_32_0)
% 108.25/15.24 | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | REDUCE: (374), (428) imply:
% 108.25/15.24 | | | | | | | | | | | | | | (431) ~ (all_32_0 = all_4_2)
% 108.25/15.24 | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | REDUCE: (422), (428) imply:
% 108.25/15.24 | | | | | | | | | | | | | | (432) ~ (all_32_0 = e3)
% 108.25/15.24 | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 108.25/15.24 | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | Case 1:
% 108.25/15.24 | | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | | (433) ~ (all_34_2 = e1)
% 108.25/15.24 | | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | | REDUCE: (311), (433) imply:
% 108.25/15.24 | | | | | | | | | | | | | | | (434) ~ (all_4_2 = e1)
% 108.25/15.24 | | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 108.25/15.24 | | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | | Case 1:
% 108.25/15.24 | | | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | | | (435) all_55_15 = e3
% 108.25/15.24 | | | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (435) imply:
% 108.25/15.24 | | | | | | | | | | | | | | | | (436) all_4_2 = e3
% 108.25/15.24 | | | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | | | SIMP: (436) implies:
% 108.25/15.24 | | | | | | | | | | | | | | | | (437) all_4_2 = e3
% 108.25/15.24 | | | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | | | REDUCE: (371), (437) imply:
% 108.25/15.24 | | | | | | | | | | | | | | | | (438) ~ (all_53_10 = e3)
% 108.25/15.24 | | | | | | | | | | | | | | | |
% 108.25/15.24 | | | | | | | | | | | | | | | | REDUCE: (375), (437) imply:
% 108.25/15.25 | | | | | | | | | | | | | | | | (439) ~ (all_53_13 = e3)
% 108.25/15.25 | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 108.25/15.25 | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.25 | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | (440) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 108.25/15.25 | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 108.25/15.25 | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | ALPHA: (440) implies:
% 108.25/15.25 | | | | | | | | | | | | | | | | | (441) op(e3, e1) = e3
% 108.25/15.25 | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (439), (441), (function-axioms) are
% 108.25/15.25 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #232.
% 108.25/15.25 | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.25 | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | (442) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 108.25/15.25 | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 108.25/15.25 | | | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 108.25/15.25 | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 108.25/15.25 | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | BETA: splitting (442) gives:
% 108.25/15.25 | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.25 | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | (443) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 108.25/15.25 | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)
% 108.25/15.25 | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | ALPHA: (443) implies:
% 108.25/15.25 | | | | | | | | | | | | | | | | | | (444) op(e2, e1) = e2
% 108.25/15.25 | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 108.25/15.25 | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.25 | | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | (445) (all_57_88 = e3 & op(e2, e3) = e3) | (all_57_89 =
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | e3 & op(e2, e2) = e3)
% 108.25/15.25 | | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (171), (413), (438), (445), (function-axioms)
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #196.
% 108.25/15.25 | | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.25 | | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | (446) (all_57_90 = e3 & op(e2, e1) = e3) | (all_57_91 =
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 108.25/15.25 | | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (446) gives:
% 108.25/15.25 | | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | | (447) all_57_90 = e3 & op(e2, e1) = e3
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | | ALPHA: (447) implies:
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | | (448) op(e2, e1) = e3
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (444), (448), (function-axioms) are
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #195.
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | | (449) all_57_91 = e3 & op(e2, e0) = e3
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | | ALPHA: (449) implies:
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | | (450) op(e2, e0) = e3
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (421), (450), (function-axioms) are
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #194.
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.25 | | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.25 | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.25 | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | (451) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 108.25/15.25 | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 108.25/15.25 | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | ALPHA: (451) implies:
% 108.25/15.25 | | | | | | | | | | | | | | | | | | (452) op(e0, e1) = e0
% 108.25/15.25 | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (394), (452), (function-axioms) are
% 108.25/15.25 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #230.
% 108.25/15.25 | | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | | End of split
% 108.25/15.25 | | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | End of split
% 108.25/15.25 | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | Case 2:
% 108.25/15.25 | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | (453) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 108.25/15.25 | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | REF_CLOSE: (339), (378), (415), (434), (453) are inconsistent
% 108.25/15.25 | | | | | | | | | | | | | | | | by sub-proof #191.
% 108.25/15.25 | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | End of split
% 108.25/15.25 | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | Case 2:
% 108.25/15.25 | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | (454) all_34_2 = e1
% 108.25/15.25 | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | COMBINE_EQS: (311), (454) imply:
% 108.25/15.25 | | | | | | | | | | | | | | | (455) all_4_2 = e1
% 108.25/15.25 | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | SIMP: (455) implies:
% 108.25/15.25 | | | | | | | | | | | | | | | (456) all_4_2 = e1
% 108.25/15.25 | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | REDUCE: (431), (456) imply:
% 108.25/15.25 | | | | | | | | | | | | | | | (457) ~ (all_32_0 = e1)
% 108.25/15.25 | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | REF_CLOSE: (109), (121), (127), (161), (168), (169), (173),
% 108.25/15.25 | | | | | | | | | | | | | | | (196), (199), (200), (262), (263), (394), (395),
% 108.25/15.25 | | | | | | | | | | | | | | | (410), (411), (421), (426), (429), (430), (432),
% 108.25/15.25 | | | | | | | | | | | | | | | (457), (function-axioms) are inconsistent by
% 108.25/15.25 | | | | | | | | | | | | | | | sub-proof #181.
% 108.25/15.25 | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | End of split
% 108.25/15.25 | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | End of split
% 108.25/15.25 | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | End of split
% 108.25/15.25 | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | Case 2:
% 108.25/15.25 | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | (458) all_26_2 = e2
% 108.25/15.25 | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | COMBINE_EQS: (316), (458) imply:
% 108.25/15.25 | | | | | | | | | | | | (459) all_4_2 = e2
% 108.25/15.25 | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | SIMP: (459) implies:
% 108.25/15.25 | | | | | | | | | | | | (460) all_4_2 = e2
% 108.25/15.25 | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | REDUCE: (374), (460) imply:
% 108.25/15.25 | | | | | | | | | | | | (461) ~ (all_53_12 = e2)
% 108.25/15.25 | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | BETA: splitting (72) gives:
% 108.25/15.25 | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | Case 1:
% 108.25/15.25 | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | (462) ~ (all_28_2 = e3)
% 108.25/15.25 | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | REDUCE: (313), (462) imply:
% 108.25/15.25 | | | | | | | | | | | | | (463) ~ (all_6_2 = e3)
% 108.25/15.25 | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | REF_CLOSE: (35), (108), (142), (162), (166), (172), (173),
% 108.25/15.25 | | | | | | | | | | | | | (174), (208), (217), (222), (248), (353), (378),
% 108.25/15.25 | | | | | | | | | | | | | (379), (381), (396), (408), (409), (412), (463),
% 108.25/15.25 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.25/15.25 | | | | | | | | | | | | | #199.
% 108.25/15.25 | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | Case 2:
% 108.25/15.25 | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | (464) all_28_2 = e3
% 108.25/15.25 | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | COMBINE_EQS: (313), (464) imply:
% 108.25/15.25 | | | | | | | | | | | | | (465) all_6_2 = e3
% 108.25/15.25 | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | COMBINE_EQS: (402), (465) imply:
% 108.25/15.25 | | | | | | | | | | | | | (466) all_32_1 = e3
% 108.25/15.25 | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | REDUCE: (351), (465) imply:
% 108.25/15.25 | | | | | | | | | | | | | (467) ~ (all_53_8 = e3)
% 108.25/15.25 | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | REDUCE: (353), (465) imply:
% 108.25/15.25 | | | | | | | | | | | | | (468) ~ (all_53_12 = e3)
% 108.25/15.25 | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | BETA: splitting (401) gives:
% 108.25/15.25 | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | Case 1:
% 108.25/15.25 | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | (469) ~ (all_32_1 = e3)
% 108.25/15.25 | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | REDUCE: (466), (469) imply:
% 108.25/15.25 | | | | | | | | | | | | | | (470) $false
% 108.25/15.25 | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | CLOSE: (470) is inconsistent.
% 108.25/15.25 | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | Case 2:
% 108.25/15.25 | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | (471) ~ (all_32_0 = e2) & op(e3, e0) = all_32_0 &
% 108.25/15.25 | | | | | | | | | | | | | | $i(all_32_0)
% 108.25/15.25 | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | ALPHA: (471) implies:
% 108.25/15.25 | | | | | | | | | | | | | | (472) op(e3, e0) = all_32_0
% 108.25/15.25 | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 108.25/15.25 | | | | | | | | | | | | | | all_32_0, e0, e3, simplifying with (172), (472)
% 108.25/15.25 | | | | | | | | | | | | | | gives:
% 108.25/15.25 | | | | | | | | | | | | | | (473) all_53_12 = all_32_0
% 108.25/15.25 | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | COMBINE_EQS: (272), (473) imply:
% 108.25/15.25 | | | | | | | | | | | | | | (474) all_55_12 = all_32_0
% 108.25/15.25 | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | REDUCE: (137), (473) imply:
% 108.25/15.25 | | | | | | | | | | | | | | (475) ~ (all_53_4 = all_32_0)
% 108.25/15.25 | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | REDUCE: (124), (473) imply:
% 108.25/15.25 | | | | | | | | | | | | | | (476) ~ (all_53_8 = all_32_0)
% 108.25/15.25 | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | REDUCE: (468), (473) imply:
% 108.25/15.25 | | | | | | | | | | | | | | (477) ~ (all_32_0 = e3)
% 108.25/15.25 | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | REDUCE: (461), (473) imply:
% 108.25/15.25 | | | | | | | | | | | | | | (478) ~ (all_32_0 = e2)
% 108.25/15.25 | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 108.25/15.25 | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | Case 1:
% 108.25/15.25 | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | (479) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 108.25/15.25 | | | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 108.25/15.25 | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | ALPHA: (479) implies:
% 108.25/15.25 | | | | | | | | | | | | | | | (480) op(e3, e0) = e3
% 108.25/15.25 | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | REF_CLOSE: (172), (468), (480), (function-axioms) are
% 108.25/15.25 | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 108.25/15.25 | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | Case 2:
% 108.25/15.25 | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | (481) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 108.25/15.25 | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 108.25/15.25 | | | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 108.25/15.25 | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 108.25/15.25 | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | BETA: splitting (481) gives:
% 108.25/15.25 | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | Case 1:
% 108.25/15.25 | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | (482) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 108.25/15.25 | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 108.25/15.25 | | | | | | | | | | | | | | | |
% 108.25/15.25 | | | | | | | | | | | | | | | | ALPHA: (482) implies:
% 108.25/15.26 | | | | | | | | | | | | | | | | (483) op(e2, e0) = e2
% 108.25/15.26 | | | | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e2,
% 108.25/15.26 | | | | | | | | | | | | | | | | e0, e2, simplifying with (168), (483) gives:
% 108.25/15.26 | | | | | | | | | | | | | | | | (484) all_53_8 = e2
% 108.25/15.26 | | | | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | | | | | REF_CLOSE: (109), (121), (127), (161), (168), (169), (173),
% 108.25/15.26 | | | | | | | | | | | | | | | | (199), (263), (394), (395), (411), (484),
% 108.25/15.26 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.25/15.26 | | | | | | | | | | | | | | | | #183.
% 108.25/15.26 | | | | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | | | | Case 2:
% 108.25/15.26 | | | | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | | | | | (485) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 108.25/15.26 | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 108.25/15.26 | | | | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | | | | | ALPHA: (485) implies:
% 108.25/15.26 | | | | | | | | | | | | | | | | (486) op(e1, e0) = e1
% 108.25/15.26 | | | | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e1,
% 108.25/15.26 | | | | | | | | | | | | | | | | e0, e1, simplifying with (164), (486) gives:
% 108.25/15.26 | | | | | | | | | | | | | | | | (487) all_53_4 = e1
% 108.25/15.26 | | | | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | | | | | REDUCE: (138), (487) imply:
% 108.25/15.26 | | | | | | | | | | | | | | | | (488) ~ (all_53_8 = e1)
% 108.25/15.26 | | | | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | | | | | REDUCE: (475), (487) imply:
% 108.25/15.26 | | | | | | | | | | | | | | | | (489) ~ (all_32_0 = e1)
% 108.25/15.26 | | | | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | | | | | SIMP: (489) implies:
% 108.25/15.26 | | | | | | | | | | | | | | | | (490) ~ (all_32_0 = e1)
% 108.25/15.26 | | | | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | | | | | REF_CLOSE: (109), (121), (127), (161), (168), (169), (173),
% 108.25/15.26 | | | | | | | | | | | | | | | | (196), (199), (200), (262), (263), (394), (395),
% 108.25/15.26 | | | | | | | | | | | | | | | | (410), (411), (467), (474), (476), (477), (478),
% 108.25/15.26 | | | | | | | | | | | | | | | | (490), (function-axioms) are inconsistent by
% 108.25/15.26 | | | | | | | | | | | | | | | | sub-proof #181.
% 108.25/15.26 | | | | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | | | | End of split
% 108.25/15.26 | | | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | | | End of split
% 108.25/15.26 | | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | | End of split
% 108.25/15.26 | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | End of split
% 108.25/15.26 | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | End of split
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | End of split
% 108.25/15.26 | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | End of split
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | End of split
% 108.25/15.26 | | | | | | | |
% 108.25/15.26 | | | | | | | Case 2:
% 108.25/15.26 | | | | | | | |
% 108.25/15.26 | | | | | | | | (491) all_18_2 = e3
% 108.25/15.26 | | | | | | | |
% 108.25/15.26 | | | | | | | | COMBINE_EQS: (326), (491) imply:
% 108.25/15.26 | | | | | | | | (492) all_14_2 = e3
% 108.25/15.26 | | | | | | | |
% 108.25/15.26 | | | | | | | | SIMP: (492) implies:
% 108.25/15.26 | | | | | | | | (493) all_14_2 = e3
% 108.25/15.26 | | | | | | | |
% 108.25/15.26 | | | | | | | | REDUCE: (361), (493) imply:
% 108.25/15.26 | | | | | | | | (494) ~ (all_53_7 = e3)
% 108.25/15.26 | | | | | | | |
% 108.25/15.26 | | | | | | | | REDUCE: (363), (493) imply:
% 108.25/15.26 | | | | | | | | (495) ~ (all_53_9 = e3)
% 108.25/15.26 | | | | | | | |
% 108.25/15.26 | | | | | | | | REDUCE: (365), (493) imply:
% 108.25/15.26 | | | | | | | | (496) ~ (all_53_13 = e3)
% 108.25/15.26 | | | | | | | |
% 108.25/15.26 | | | | | | | | REDUCE: (50), (493) imply:
% 108.25/15.26 | | | | | | | | (497) op(e1, e1) = e3
% 108.25/15.26 | | | | | | | |
% 108.25/15.26 | | | | | | | | BETA: splitting (66) gives:
% 108.25/15.26 | | | | | | | |
% 108.25/15.26 | | | | | | | | Case 1:
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | | (498) ~ (all_24_2 = e1)
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | | REDUCE: (303), (498) imply:
% 108.25/15.26 | | | | | | | | | (499) ~ (all_10_2 = e1)
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (115), (117),
% 108.25/15.26 | | | | | | | | | (132), (139), (140), (148), (152), (153), (161),
% 108.25/15.26 | | | | | | | | | (162), (163), (164), (166), (167), (168), (169),
% 108.25/15.26 | | | | | | | | | (171), (172), (173), (174), (198), (340), (368),
% 108.25/15.26 | | | | | | | | | (369), (370), (382), (384), (499),
% 108.25/15.26 | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.25/15.26 | | | | | | | | | #207.
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | Case 2:
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | | (500) all_24_2 = e1
% 108.25/15.26 | | | | | | | | | (501) op(e1, e1) = all_24_1 & $i(all_24_1) & ( ~ (all_24_1
% 108.25/15.26 | | | | | | | | | = e3) | ( ~ (all_24_0 = e0) & op(e3, e1) =
% 108.25/15.26 | | | | | | | | | all_24_0 & $i(all_24_0)))
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | | ALPHA: (501) implies:
% 108.25/15.26 | | | | | | | | | (502) op(e1, e1) = all_24_1
% 108.25/15.26 | | | | | | | | | (503) ~ (all_24_1 = e3) | ( ~ (all_24_0 = e0) & op(e3, e1)
% 108.25/15.26 | | | | | | | | | = all_24_0 & $i(all_24_0))
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | | COMBINE_EQS: (303), (500) imply:
% 108.25/15.26 | | | | | | | | | (504) all_10_2 = e1
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | | SIMP: (504) implies:
% 108.25/15.26 | | | | | | | | | (505) all_10_2 = e1
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | | COMBINE_EQS: (265), (505) imply:
% 108.25/15.26 | | | | | | | | | (506) all_46_2 = e1
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | | REDUCE: (356), (505) imply:
% 108.25/15.26 | | | | | | | | | (507) ~ (all_53_3 = e1)
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | | REDUCE: (367), (505) imply:
% 108.25/15.26 | | | | | | | | | (508) ~ (all_53_7 = e1)
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | | REDUCE: (368), (505) imply:
% 108.25/15.26 | | | | | | | | | (509) ~ (all_53_8 = e1)
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | | REDUCE: (369), (505) imply:
% 108.25/15.26 | | | | | | | | | (510) ~ (all_53_9 = e1)
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | | REDUCE: (44), (505) imply:
% 108.25/15.26 | | | | | | | | | (511) op(e2, e2) = e1
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | | BETA: splitting (99) gives:
% 108.25/15.26 | | | | | | | | |
% 108.25/15.26 | | | | | | | | | Case 1:
% 108.25/15.26 | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | (512) ~ (all_46_2 = e1)
% 108.25/15.26 | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | REDUCE: (506), (512) imply:
% 108.25/15.26 | | | | | | | | | | (513) $false
% 108.25/15.26 | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | CLOSE: (513) is inconsistent.
% 108.25/15.26 | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | Case 2:
% 108.25/15.26 | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | (514) op(e1, e1) = all_46_1 & $i(all_46_1) & ( ~
% 108.25/15.26 | | | | | | | | | | (all_46_1 = e0) | ( ~ (all_46_0 = e3) & op(e0,
% 108.25/15.26 | | | | | | | | | | e1) = all_46_0 & $i(all_46_0)))
% 108.25/15.26 | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | ALPHA: (514) implies:
% 108.25/15.26 | | | | | | | | | | (515) op(e1, e1) = all_46_1
% 108.25/15.26 | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_46_1,
% 108.25/15.26 | | | | | | | | | | e1, e1, simplifying with (497), (515) gives:
% 108.25/15.26 | | | | | | | | | | (516) all_46_1 = e3
% 108.25/15.26 | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_24_1,
% 108.25/15.26 | | | | | | | | | | all_46_1, e1, e1, simplifying with (502), (515)
% 108.25/15.26 | | | | | | | | | | gives:
% 108.25/15.26 | | | | | | | | | | (517) all_46_1 = all_24_1
% 108.25/15.26 | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | COMBINE_EQS: (516), (517) imply:
% 108.25/15.26 | | | | | | | | | | (518) all_24_1 = e3
% 108.25/15.26 | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | BETA: splitting (503) gives:
% 108.25/15.26 | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | Case 1:
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | (519) ~ (all_24_1 = e3)
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | REDUCE: (518), (519) imply:
% 108.25/15.26 | | | | | | | | | | | (520) $false
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | CLOSE: (520) is inconsistent.
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | Case 2:
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | (521) ~ (all_24_0 = e0) & op(e3, e1) = all_24_0 &
% 108.25/15.26 | | | | | | | | | | | $i(all_24_0)
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | ALPHA: (521) implies:
% 108.25/15.26 | | | | | | | | | | | (522) ~ (all_24_0 = e0)
% 108.25/15.26 | | | | | | | | | | | (523) op(e3, e1) = all_24_0
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 108.25/15.26 | | | | | | | | | | | all_24_0, e1, e3, simplifying with (173), (523)
% 108.25/15.26 | | | | | | | | | | | gives:
% 108.25/15.26 | | | | | | | | | | | (524) all_53_13 = all_24_0
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | COMBINE_EQS: (273), (524) imply:
% 108.25/15.26 | | | | | | | | | | | (525) all_55_13 = all_24_0
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | REDUCE: (149), (524) imply:
% 108.25/15.26 | | | | | | | | | | | (526) ~ (all_53_1 = all_24_0)
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | REDUCE: (121), (524) imply:
% 108.25/15.26 | | | | | | | | | | | (527) ~ (all_53_9 = all_24_0)
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | REDUCE: (117), (524) imply:
% 108.25/15.26 | | | | | | | | | | | (528) ~ (all_53_12 = all_24_0)
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | REDUCE: (375), (524) imply:
% 108.25/15.26 | | | | | | | | | | | (529) ~ (all_24_0 = all_4_2)
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | REDUCE: (496), (524) imply:
% 108.25/15.26 | | | | | | | | | | | (530) ~ (all_24_0 = e3)
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | BETA: splitting (69) gives:
% 108.25/15.26 | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | Case 1:
% 108.25/15.26 | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | (531) ~ (all_26_2 = e2)
% 108.25/15.26 | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | REDUCE: (316), (531) imply:
% 108.25/15.26 | | | | | | | | | | | | (532) ~ (all_4_2 = e2)
% 108.25/15.26 | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | REF_CLOSE: (81), (108), (109), (150), (161), (162), (166),
% 108.25/15.26 | | | | | | | | | | | | (169), (173), (174), (193), (195), (199), (218),
% 108.25/15.26 | | | | | | | | | | | | (263), (311), (339), (377), (378), (494), (495),
% 108.25/15.26 | | | | | | | | | | | | (508), (510), (511), (522), (523), (525), (527),
% 108.25/15.26 | | | | | | | | | | | | (529), (530), (532), (function-axioms) are
% 108.25/15.26 | | | | | | | | | | | | inconsistent by sub-proof #174.
% 108.25/15.26 | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | Case 2:
% 108.25/15.26 | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | (533) all_26_2 = e2
% 108.25/15.26 | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | COMBINE_EQS: (316), (533) imply:
% 108.25/15.26 | | | | | | | | | | | | (534) all_4_2 = e2
% 108.25/15.26 | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | REDUCE: (371), (534) imply:
% 108.25/15.26 | | | | | | | | | | | | (535) ~ (all_53_10 = e2)
% 108.25/15.26 | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | REDUCE: (529), (534) imply:
% 108.25/15.26 | | | | | | | | | | | | (536) ~ (all_24_0 = e2)
% 108.25/15.26 | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | BETA: splitting (195) gives:
% 108.25/15.26 | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | Case 1:
% 108.25/15.26 | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | | (537) all_55_13 = e3
% 108.25/15.26 | | | | | | | | | | | | |
% 108.25/15.26 | | | | | | | | | | | | | COMBINE_EQS: (525), (537) imply:
% 108.25/15.27 | | | | | | | | | | | | | (538) all_24_0 = e3
% 108.25/15.27 | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | SIMP: (538) implies:
% 108.25/15.27 | | | | | | | | | | | | | (539) all_24_0 = e3
% 108.25/15.27 | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | REDUCE: (530), (539) imply:
% 108.25/15.27 | | | | | | | | | | | | | (540) $false
% 108.25/15.27 | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | CLOSE: (540) is inconsistent.
% 108.25/15.27 | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | Case 2:
% 108.25/15.27 | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | (541) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 108.25/15.27 | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | BETA: splitting (541) gives:
% 108.25/15.27 | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | Case 1:
% 108.25/15.27 | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | (542) all_55_13 = e2
% 108.25/15.27 | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | COMBINE_EQS: (525), (542) imply:
% 108.25/15.27 | | | | | | | | | | | | | | (543) all_24_0 = e2
% 108.25/15.27 | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | SIMP: (543) implies:
% 108.25/15.27 | | | | | | | | | | | | | | (544) all_24_0 = e2
% 108.25/15.27 | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | REDUCE: (536), (544) imply:
% 108.25/15.27 | | | | | | | | | | | | | | (545) $false
% 108.25/15.27 | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | CLOSE: (545) is inconsistent.
% 108.25/15.27 | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | Case 2:
% 108.25/15.27 | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | (546) all_55_13 = e1 | all_55_13 = e0
% 108.25/15.27 | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | BETA: splitting (546) gives:
% 108.25/15.27 | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | Case 1:
% 108.25/15.27 | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | (547) all_55_13 = e1
% 108.25/15.27 | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | COMBINE_EQS: (525), (547) imply:
% 108.25/15.27 | | | | | | | | | | | | | | | (548) all_24_0 = e1
% 108.25/15.27 | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | SIMP: (548) implies:
% 108.25/15.27 | | | | | | | | | | | | | | | (549) all_24_0 = e1
% 108.25/15.27 | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | REDUCE: (526), (549) imply:
% 108.25/15.27 | | | | | | | | | | | | | | | (550) ~ (all_53_1 = e1)
% 108.25/15.27 | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | REDUCE: (528), (549) imply:
% 108.25/15.27 | | | | | | | | | | | | | | | (551) ~ (all_53_12 = e1)
% 108.25/15.27 | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 108.25/15.27 | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | Case 1:
% 108.25/15.27 | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | (552) (all_57_8 = e1 & op(e0, e3) = e1) | (all_57_9 = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | & op(e0, e2) = e1)
% 108.25/15.27 | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | BETA: splitting (552) gives:
% 108.25/15.27 | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | (553) all_57_8 = e1 & op(e0, e3) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | ALPHA: (553) implies:
% 108.25/15.27 | | | | | | | | | | | | | | | | | (554) op(e0, e3) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.27 | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | (555) (all_57_12 = e1 & op(e3, e0) = e1) | (all_57_13 =
% 108.25/15.27 | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 108.25/15.27 | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | BETA: splitting (555) gives:
% 108.25/15.27 | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | (556) all_57_12 = e1 & op(e3, e0) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | ALPHA: (556) implies:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | (557) op(e3, e0) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | e1, e0, e3, simplifying with (172), (557) gives:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | (558) all_53_12 = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | REDUCE: (551), (558) imply:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | (559) $false
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | CLOSE: (559) is inconsistent.
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | (560) all_57_13 = e1 & op(e2, e0) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | ALPHA: (560) implies:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | (561) op(e2, e0) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (509), (561), (function-axioms) are
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #173.
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.27 | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.27 | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | (562) (all_57_14 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 108.25/15.27 | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 108.25/15.27 | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | BETA: splitting (562) gives:
% 108.25/15.27 | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | (563) all_57_14 = e1 & op(e1, e0) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | ALPHA: (563) implies:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | (564) op(e1, e0) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e1,
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (163), (554) gives:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | (565) all_53_2 = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e1,
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | e0, e1, simplifying with (164), (564) gives:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | (566) all_53_4 = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | REDUCE: (140), (566) imply:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | (567) ~ (all_53_6 = e1)
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | SIMP: (567) implies:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | (568) ~ (all_53_6 = e1)
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | | (569) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2)
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | | = all_52_18 & op(e2, e3) = e2 & $i(all_52_18)
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (535), (569), (function-axioms) are
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #215.
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | | (570) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | | (all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22))
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (554), (568), (570), (function-axioms)
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #172.
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | (571) all_57_15 = e1 & op(e0, e0) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | ALPHA: (571) implies:
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | (572) op(e0, e0) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (379), (572), (function-axioms) are
% 108.25/15.27 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #171.
% 108.25/15.27 | | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.27 | | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | End of split
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | (573) all_57_9 = e1 & op(e0, e2) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | ALPHA: (573) implies:
% 108.25/15.27 | | | | | | | | | | | | | | | | | (574) op(e0, e2) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (507), (574), (function-axioms) are
% 108.25/15.27 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #204.
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | End of split
% 108.25/15.27 | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | Case 2:
% 108.25/15.27 | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | (575) (all_57_10 = e1 & op(e0, e1) = e1) | (all_57_11 =
% 108.25/15.27 | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 108.25/15.27 | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | BETA: splitting (575) gives:
% 108.25/15.27 | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | (576) all_57_10 = e1 & op(e0, e1) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | ALPHA: (576) implies:
% 108.25/15.27 | | | | | | | | | | | | | | | | | (577) op(e0, e1) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (550), (577), (function-axioms) are
% 108.25/15.27 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #170.
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | (578) all_57_11 = e1 & op(e0, e0) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | ALPHA: (578) implies:
% 108.25/15.27 | | | | | | | | | | | | | | | | | (579) op(e0, e0) = e1
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (379), (579), (function-axioms) are
% 108.25/15.27 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #171.
% 108.25/15.27 | | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | | End of split
% 108.25/15.27 | | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | End of split
% 108.25/15.27 | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | Case 2:
% 108.25/15.27 | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | (580) all_55_13 = e0
% 108.25/15.27 | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | COMBINE_EQS: (525), (580) imply:
% 108.25/15.27 | | | | | | | | | | | | | | | (581) all_24_0 = e0
% 108.25/15.27 | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | SIMP: (581) implies:
% 108.25/15.27 | | | | | | | | | | | | | | | (582) all_24_0 = e0
% 108.25/15.27 | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | REDUCE: (522), (582) imply:
% 108.25/15.27 | | | | | | | | | | | | | | | (583) $false
% 108.25/15.27 | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | | CLOSE: (583) is inconsistent.
% 108.25/15.27 | | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | | End of split
% 108.25/15.27 | | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | | End of split
% 108.25/15.27 | | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | | End of split
% 108.25/15.27 | | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | | End of split
% 108.25/15.27 | | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | | End of split
% 108.25/15.27 | | | | | | | | | |
% 108.25/15.27 | | | | | | | | | End of split
% 108.25/15.27 | | | | | | | | |
% 108.25/15.27 | | | | | | | | End of split
% 108.25/15.27 | | | | | | | |
% 108.25/15.27 | | | | | | | End of split
% 108.25/15.27 | | | | | | |
% 108.25/15.27 | | | | | | Case 2:
% 108.25/15.27 | | | | | | |
% 108.25/15.27 | | | | | | | (584) all_14_2 = e2
% 108.25/15.28 | | | | | | | (585) op(e2, e2) = all_14_1 & $i(all_14_1) & ( ~ (all_14_1 =
% 108.25/15.28 | | | | | | | e3) | ( ~ (all_14_0 = e0) & op(e3, e2) = all_14_0 &
% 108.25/15.28 | | | | | | | $i(all_14_0)))
% 108.25/15.28 | | | | | | |
% 108.25/15.28 | | | | | | | ALPHA: (585) implies:
% 108.25/15.28 | | | | | | | (586) op(e2, e2) = all_14_1
% 108.25/15.28 | | | | | | |
% 108.25/15.28 | | | | | | | COMBINE_EQS: (334), (584) imply:
% 108.25/15.28 | | | | | | | (587) all_44_2 = e2
% 108.25/15.28 | | | | | | |
% 108.25/15.28 | | | | | | | REDUCE: (354), (584) imply:
% 108.25/15.28 | | | | | | | (588) ~ (all_53_1 = e2)
% 108.25/15.28 | | | | | | |
% 108.25/15.28 | | | | | | | REDUCE: (363), (584) imply:
% 108.25/15.28 | | | | | | | (589) ~ (all_53_9 = e2)
% 108.25/15.28 | | | | | | |
% 108.25/15.28 | | | | | | | REDUCE: (50), (584) imply:
% 108.25/15.28 | | | | | | | (590) op(e1, e1) = e2
% 108.25/15.28 | | | | | | |
% 108.25/15.28 | | | | | | | BETA: splitting (96) gives:
% 108.25/15.28 | | | | | | |
% 108.25/15.28 | | | | | | | Case 1:
% 108.25/15.28 | | | | | | | |
% 108.25/15.28 | | | | | | | | (591) ~ (all_44_2 = e2)
% 108.25/15.28 | | | | | | | |
% 108.25/15.28 | | | | | | | | REDUCE: (587), (591) imply:
% 108.25/15.28 | | | | | | | | (592) $false
% 108.25/15.28 | | | | | | | |
% 108.25/15.28 | | | | | | | | CLOSE: (592) is inconsistent.
% 108.25/15.28 | | | | | | | |
% 108.25/15.28 | | | | | | | Case 2:
% 108.25/15.28 | | | | | | | |
% 108.25/15.28 | | | | | | | | (593) op(e2, e2) = all_44_1 & $i(all_44_1) & ( ~ (all_44_1 =
% 108.25/15.28 | | | | | | | | e0) | ( ~ (all_44_0 = e3) & op(e0, e2) = all_44_0 &
% 108.25/15.28 | | | | | | | | $i(all_44_0)))
% 108.25/15.28 | | | | | | | |
% 108.25/15.28 | | | | | | | | ALPHA: (593) implies:
% 108.25/15.28 | | | | | | | | (594) op(e2, e2) = all_44_1
% 108.25/15.28 | | | | | | | |
% 108.25/15.28 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 108.25/15.28 | | | | | | | | all_44_1, e2, e2, simplifying with (44), (594)
% 108.25/15.28 | | | | | | | | gives:
% 108.25/15.28 | | | | | | | | (595) all_44_1 = all_10_2
% 108.25/15.28 | | | | | | | |
% 108.25/15.28 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 108.25/15.28 | | | | | | | | all_44_1, e2, e2, simplifying with (586), (594)
% 108.25/15.28 | | | | | | | | gives:
% 108.25/15.28 | | | | | | | | (596) all_44_1 = all_14_1
% 108.25/15.28 | | | | | | | |
% 108.25/15.28 | | | | | | | | COMBINE_EQS: (595), (596) imply:
% 108.25/15.28 | | | | | | | | (597) all_14_1 = all_10_2
% 108.25/15.28 | | | | | | | |
% 108.25/15.28 | | | | | | | | BETA: splitting (66) gives:
% 108.25/15.28 | | | | | | | |
% 108.25/15.28 | | | | | | | | Case 1:
% 108.25/15.28 | | | | | | | | |
% 108.25/15.28 | | | | | | | | | (598) ~ (all_24_2 = e1)
% 108.25/15.28 | | | | | | | | |
% 108.25/15.28 | | | | | | | | | REDUCE: (303), (598) imply:
% 108.25/15.28 | | | | | | | | | (599) ~ (all_10_2 = e1)
% 108.25/15.28 | | | | | | | | |
% 108.25/15.28 | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (115), (117),
% 108.25/15.28 | | | | | | | | | (132), (139), (140), (148), (152), (153), (161),
% 108.25/15.28 | | | | | | | | | (162), (163), (164), (166), (167), (168), (169),
% 108.25/15.28 | | | | | | | | | (171), (172), (173), (174), (198), (340), (368),
% 108.25/15.28 | | | | | | | | | (369), (370), (382), (384), (599),
% 108.25/15.28 | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.25/15.28 | | | | | | | | | #207.
% 108.25/15.28 | | | | | | | | |
% 108.25/15.28 | | | | | | | | Case 2:
% 108.25/15.28 | | | | | | | | |
% 108.25/15.28 | | | | | | | | | (600) all_24_2 = e1
% 108.25/15.28 | | | | | | | | | (601) op(e1, e1) = all_24_1 & $i(all_24_1) & ( ~ (all_24_1
% 108.25/15.28 | | | | | | | | | = e3) | ( ~ (all_24_0 = e0) & op(e3, e1) =
% 108.25/15.28 | | | | | | | | | all_24_0 & $i(all_24_0)))
% 108.25/15.28 | | | | | | | | |
% 108.25/15.28 | | | | | | | | | ALPHA: (601) implies:
% 108.25/15.28 | | | | | | | | | (602) op(e1, e1) = all_24_1
% 108.25/15.28 | | | | | | | | |
% 108.25/15.28 | | | | | | | | | COMBINE_EQS: (303), (600) imply:
% 108.25/15.28 | | | | | | | | | (603) all_10_2 = e1
% 108.25/15.28 | | | | | | | | |
% 108.25/15.28 | | | | | | | | | COMBINE_EQS: (265), (603) imply:
% 108.25/15.28 | | | | | | | | | (604) all_46_2 = e1
% 108.25/15.28 | | | | | | | | |
% 108.25/15.28 | | | | | | | | | REDUCE: (356), (603) imply:
% 108.25/15.28 | | | | | | | | | (605) ~ (all_53_3 = e1)
% 108.25/15.28 | | | | | | | | |
% 108.25/15.28 | | | | | | | | | REDUCE: (367), (603) imply:
% 108.25/15.28 | | | | | | | | | (606) ~ (all_53_7 = e1)
% 108.25/15.28 | | | | | | | | |
% 108.25/15.28 | | | | | | | | | REDUCE: (44), (603) imply:
% 108.25/15.28 | | | | | | | | | (607) op(e2, e2) = e1
% 108.25/15.28 | | | | | | | | |
% 108.25/15.28 | | | | | | | | | BETA: splitting (99) gives:
% 108.25/15.28 | | | | | | | | |
% 108.25/15.28 | | | | | | | | | Case 1:
% 108.25/15.28 | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | (608) ~ (all_46_2 = e1)
% 108.25/15.28 | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | REDUCE: (604), (608) imply:
% 108.25/15.28 | | | | | | | | | | (609) $false
% 108.25/15.28 | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | CLOSE: (609) is inconsistent.
% 108.25/15.28 | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | Case 2:
% 108.25/15.28 | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | (610) op(e1, e1) = all_46_1 & $i(all_46_1) & ( ~
% 108.25/15.28 | | | | | | | | | | (all_46_1 = e0) | ( ~ (all_46_0 = e3) & op(e0,
% 108.25/15.28 | | | | | | | | | | e1) = all_46_0 & $i(all_46_0)))
% 108.25/15.28 | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | ALPHA: (610) implies:
% 108.25/15.28 | | | | | | | | | | (611) op(e1, e1) = all_46_1
% 108.25/15.28 | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_46_1,
% 108.25/15.28 | | | | | | | | | | e1, e1, simplifying with (590), (611) gives:
% 108.25/15.28 | | | | | | | | | | (612) all_46_1 = e2
% 108.25/15.28 | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_24_1,
% 108.25/15.28 | | | | | | | | | | all_46_1, e1, e1, simplifying with (602), (611)
% 108.25/15.28 | | | | | | | | | | gives:
% 108.25/15.28 | | | | | | | | | | (613) all_46_1 = all_24_1
% 108.25/15.28 | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | COMBINE_EQS: (612), (613) imply:
% 108.25/15.28 | | | | | | | | | | (614) all_24_1 = e2
% 108.25/15.28 | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | BETA: splitting (69) gives:
% 108.25/15.28 | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | Case 1:
% 108.25/15.28 | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | (615) ~ (all_26_2 = e2)
% 108.25/15.28 | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | REDUCE: (316), (615) imply:
% 108.25/15.28 | | | | | | | | | | | (616) ~ (all_4_2 = e2)
% 108.25/15.28 | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | BETA: splitting (72) gives:
% 108.25/15.28 | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | Case 1:
% 108.25/15.28 | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | (617) ~ (all_28_2 = e3)
% 108.25/15.28 | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | REDUCE: (313), (617) imply:
% 108.25/15.28 | | | | | | | | | | | | (618) ~ (all_6_2 = e3)
% 108.25/15.28 | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | BETA: splitting (208) gives:
% 108.25/15.28 | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | Case 1:
% 108.25/15.28 | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | (619) all_55_0 = e3
% 108.25/15.28 | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | COMBINE_EQS: (248), (619) imply:
% 108.25/15.28 | | | | | | | | | | | | | (620) all_6_2 = e3
% 108.25/15.28 | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | REDUCE: (618), (620) imply:
% 108.25/15.28 | | | | | | | | | | | | | (621) $false
% 108.25/15.28 | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | CLOSE: (621) is inconsistent.
% 108.25/15.28 | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | Case 2:
% 108.25/15.28 | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | (622) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 108.25/15.28 | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | BETA: splitting (622) gives:
% 108.25/15.28 | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | Case 1:
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | (623) all_55_0 = e2
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | COMBINE_EQS: (248), (623) imply:
% 108.25/15.28 | | | | | | | | | | | | | | (624) all_6_2 = e2
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | REDUCE: (381), (624) imply:
% 108.25/15.28 | | | | | | | | | | | | | | (625) $false
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | CLOSE: (625) is inconsistent.
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | Case 2:
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | (626) all_55_0 = e1 | all_55_0 = e0
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | BETA: splitting (626) gives:
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | Case 1:
% 108.25/15.28 | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | (627) all_55_0 = e1
% 108.25/15.28 | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | COMBINE_EQS: (248), (627) imply:
% 108.25/15.28 | | | | | | | | | | | | | | | (628) all_6_2 = e1
% 108.25/15.28 | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | REDUCE: (379), (628) imply:
% 108.25/15.28 | | | | | | | | | | | | | | | (629) $false
% 108.25/15.28 | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | CLOSE: (629) is inconsistent.
% 108.25/15.28 | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | Case 2:
% 108.25/15.28 | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | (630) all_55_0 = e0
% 108.25/15.28 | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | COMBINE_EQS: (248), (630) imply:
% 108.25/15.28 | | | | | | | | | | | | | | | (631) all_6_2 = e0
% 108.25/15.28 | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | REDUCE: (343), (631) imply:
% 108.25/15.28 | | | | | | | | | | | | | | | (632) ~ (all_53_1 = e0)
% 108.25/15.28 | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | REDUCE: (347), (631) imply:
% 108.25/15.28 | | | | | | | | | | | | | | | (633) ~ (all_53_3 = e0)
% 108.25/15.28 | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 108.25/15.28 | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | Case 1:
% 108.25/15.28 | | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | | (634) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 108.25/15.28 | | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 108.25/15.28 | | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | | REF_CLOSE: (108), (113), (162), (166), (173), (174), (606),
% 108.25/15.28 | | | | | | | | | | | | | | | | (633), (634), (function-axioms) are inconsistent
% 108.25/15.28 | | | | | | | | | | | | | | | | by sub-proof #168.
% 108.25/15.28 | | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | Case 2:
% 108.25/15.28 | | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | | (635) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 108.25/15.28 | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 108.25/15.28 | | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 108.25/15.28 | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 108.25/15.28 | | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | | REF_CLOSE: (161), (169), (589), (632), (635),
% 108.25/15.28 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.25/15.28 | | | | | | | | | | | | | | | | #229.
% 108.25/15.28 | | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | End of split
% 108.25/15.28 | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | End of split
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | End of split
% 108.25/15.28 | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | End of split
% 108.25/15.28 | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | Case 2:
% 108.25/15.28 | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | (636) all_28_2 = e3
% 108.25/15.28 | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | COMBINE_EQS: (313), (636) imply:
% 108.25/15.28 | | | | | | | | | | | | (637) all_6_2 = e3
% 108.25/15.28 | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | REDUCE: (351), (637) imply:
% 108.25/15.28 | | | | | | | | | | | | (638) ~ (all_53_8 = e3)
% 108.25/15.28 | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | REDUCE: (38), (637) imply:
% 108.25/15.28 | | | | | | | | | | | | (639) op(e0, e0) = e3
% 108.25/15.28 | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | BETA: splitting (81) gives:
% 108.25/15.28 | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | Case 1:
% 108.25/15.28 | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | (640) ~ (all_34_2 = e1)
% 108.25/15.28 | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | REDUCE: (311), (640) imply:
% 108.25/15.28 | | | | | | | | | | | | | (641) ~ (all_4_2 = e1)
% 108.25/15.28 | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | BETA: splitting (193) gives:
% 108.25/15.28 | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | Case 1:
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | (642) all_55_15 = e3
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | COMBINE_EQS: (339), (642) imply:
% 108.25/15.28 | | | | | | | | | | | | | | (643) all_4_2 = e3
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | SIMP: (643) implies:
% 108.25/15.28 | | | | | | | | | | | | | | (644) all_4_2 = e3
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | REDUCE: (371), (644) imply:
% 108.25/15.28 | | | | | | | | | | | | | | (645) ~ (all_53_10 = e3)
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | REDUCE: (375), (644) imply:
% 108.25/15.28 | | | | | | | | | | | | | | (646) ~ (all_53_13 = e3)
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | REDUCE: (377), (644) imply:
% 108.25/15.28 | | | | | | | | | | | | | | (647) ~ (all_53_15 = e3)
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 108.25/15.28 | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | Case 1:
% 108.25/15.28 | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | (648) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 108.25/15.28 | | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 108.25/15.28 | | | | | | | | | | | | | | |
% 108.25/15.28 | | | | | | | | | | | | | | | ALPHA: (648) implies:
% 108.25/15.29 | | | | | | | | | | | | | | | (649) op(e3, e2) = e3
% 108.25/15.29 | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | REF_CLOSE: (174), (647), (649), (function-axioms) are
% 108.25/15.29 | | | | | | | | | | | | | | | inconsistent by sub-proof #214.
% 108.25/15.29 | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | Case 2:
% 108.25/15.29 | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | (650) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 108.25/15.29 | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 108.25/15.29 | | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 108.25/15.29 | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 108.25/15.29 | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | BETA: splitting (650) gives:
% 108.25/15.29 | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | Case 1:
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | (651) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 108.25/15.29 | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | ALPHA: (651) implies:
% 108.25/15.29 | | | | | | | | | | | | | | | | (652) op(e1, e2) = e1
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | REF_CLOSE: (166), (606), (652), (function-axioms) are
% 108.25/15.29 | | | | | | | | | | | | | | | | inconsistent by sub-proof #233.
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | Case 2:
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | (653) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 108.25/15.29 | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | ALPHA: (653) implies:
% 108.25/15.29 | | | | | | | | | | | | | | | | (654) op(e0, e2) = e0
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.29 | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | (655) (all_57_88 = e3 & op(e2, e3) = e3) | (all_57_89 =
% 108.25/15.29 | | | | | | | | | | | | | | | | | e3 & op(e2, e2) = e3)
% 108.25/15.29 | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (171), (607), (645), (655), (function-axioms)
% 108.25/15.29 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #196.
% 108.25/15.29 | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.29 | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | (656) (all_57_90 = e3 & op(e2, e1) = e3) | (all_57_91 =
% 108.25/15.29 | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 108.25/15.29 | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | BETA: splitting (656) gives:
% 108.25/15.29 | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.29 | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | (657) all_57_90 = e3 & op(e2, e1) = e3
% 108.25/15.29 | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | ALPHA: (657) implies:
% 108.25/15.29 | | | | | | | | | | | | | | | | | | (658) op(e2, e1) = e3
% 108.25/15.29 | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 108.25/15.29 | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.29 | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | (659) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 108.25/15.29 | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | ALPHA: (659) implies:
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | (660) op(e3, e1) = e3
% 108.25/15.29 | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (646), (660), (function-axioms) are
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #232.
% 108.25/15.29 | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.29 | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | (661) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 108.25/15.29 | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | BETA: splitting (661) gives:
% 108.25/15.29 | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | | (662) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | | ALPHA: (662) implies:
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | | (663) op(e2, e1) = e2
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (658), (663), (function-axioms) are
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #195.
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | | (664) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | | ALPHA: (664) implies:
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | | (665) op(e0, e1) = e0
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (152), (161), (162), (654), (665),
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | | #167.
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.29 | | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.29 | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.29 | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | (666) all_57_91 = e3 & op(e2, e0) = e3
% 108.25/15.29 | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | ALPHA: (666) implies:
% 108.25/15.29 | | | | | | | | | | | | | | | | | | (667) op(e2, e0) = e3
% 108.25/15.29 | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (638), (667), (function-axioms) are
% 108.25/15.29 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #194.
% 108.25/15.29 | | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | End of split
% 108.25/15.29 | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | End of split
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | End of split
% 108.25/15.29 | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | End of split
% 108.25/15.29 | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | Case 2:
% 108.25/15.29 | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | (668) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 108.25/15.29 | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | REF_CLOSE: (339), (378), (616), (641), (668) are inconsistent
% 108.25/15.29 | | | | | | | | | | | | | | by sub-proof #191.
% 108.25/15.29 | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | End of split
% 108.25/15.29 | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | Case 2:
% 108.25/15.29 | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | (669) all_34_2 = e1
% 108.25/15.29 | | | | | | | | | | | | | (670) op(e1, e1) = all_34_1 & $i(all_34_1) & ( ~
% 108.25/15.29 | | | | | | | | | | | | | (all_34_1 = e2) | ( ~ (all_34_0 = e0) & op(e2,
% 108.25/15.29 | | | | | | | | | | | | | e1) = all_34_0 & $i(all_34_0)))
% 108.25/15.29 | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | ALPHA: (670) implies:
% 108.25/15.29 | | | | | | | | | | | | | (671) op(e1, e1) = all_34_1
% 108.25/15.29 | | | | | | | | | | | | | (672) ~ (all_34_1 = e2) | ( ~ (all_34_0 = e0) & op(e2,
% 108.25/15.29 | | | | | | | | | | | | | e1) = all_34_0 & $i(all_34_0))
% 108.25/15.29 | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | COMBINE_EQS: (311), (669) imply:
% 108.25/15.29 | | | | | | | | | | | | | (673) all_4_2 = e1
% 108.25/15.29 | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | SIMP: (673) implies:
% 108.25/15.29 | | | | | | | | | | | | | (674) all_4_2 = e1
% 108.25/15.29 | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | COMBINE_EQS: (333), (674) imply:
% 108.25/15.29 | | | | | | | | | | | | | (675) all_42_2 = e1
% 108.25/15.29 | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | REDUCE: (355), (674) imply:
% 108.25/15.29 | | | | | | | | | | | | | (676) ~ (all_53_2 = e1)
% 108.25/15.29 | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | BETA: splitting (93) gives:
% 108.25/15.29 | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | Case 1:
% 108.25/15.29 | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | (677) ~ (all_42_2 = e1)
% 108.25/15.29 | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | REDUCE: (675), (677) imply:
% 108.25/15.29 | | | | | | | | | | | | | | (678) $false
% 108.25/15.29 | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | CLOSE: (678) is inconsistent.
% 108.25/15.29 | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | Case 2:
% 108.25/15.29 | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | (679) op(e1, e1) = all_42_1 & $i(all_42_1) & ( ~
% 108.25/15.29 | | | | | | | | | | | | | | (all_42_1 = e0) | ( ~ (all_42_0 = e2) & op(e0,
% 108.25/15.29 | | | | | | | | | | | | | | e1) = all_42_0 & $i(all_42_0)))
% 108.25/15.29 | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | ALPHA: (679) implies:
% 108.25/15.29 | | | | | | | | | | | | | | (680) op(e1, e1) = all_42_1
% 108.25/15.29 | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 108.25/15.29 | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | Case 1:
% 108.25/15.29 | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | (681) (all_57_8 = e1 & op(e0, e3) = e1) | (all_57_9 = e1
% 108.25/15.29 | | | | | | | | | | | | | | | & op(e0, e2) = e1)
% 108.25/15.29 | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | BETA: splitting (681) gives:
% 108.25/15.29 | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | Case 1:
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | (682) all_57_8 = e1 & op(e0, e3) = e1
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | ALPHA: (682) implies:
% 108.25/15.29 | | | | | | | | | | | | | | | | (683) op(e0, e3) = e1
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | REF_CLOSE: (163), (676), (683), (function-axioms) are
% 108.25/15.29 | | | | | | | | | | | | | | | | inconsistent by sub-proof #166.
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | Case 2:
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | (684) all_57_9 = e1 & op(e0, e2) = e1
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | ALPHA: (684) implies:
% 108.25/15.29 | | | | | | | | | | | | | | | | (685) op(e0, e2) = e1
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | REF_CLOSE: (162), (605), (685), (function-axioms) are
% 108.25/15.29 | | | | | | | | | | | | | | | | inconsistent by sub-proof #204.
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | End of split
% 108.25/15.29 | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | Case 2:
% 108.25/15.29 | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | (686) (all_57_10 = e1 & op(e0, e1) = e1) | (all_57_11 =
% 108.25/15.29 | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 108.25/15.29 | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | BETA: splitting (686) gives:
% 108.25/15.29 | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | Case 1:
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | (687) all_57_10 = e1 & op(e0, e1) = e1
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | ALPHA: (687) implies:
% 108.25/15.29 | | | | | | | | | | | | | | | | (688) op(e0, e1) = e1
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e1,
% 108.25/15.29 | | | | | | | | | | | | | | | | e1, e0, simplifying with (161), (688) gives:
% 108.25/15.29 | | | | | | | | | | | | | | | | (689) all_53_1 = e1
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_42_1,
% 108.25/15.29 | | | | | | | | | | | | | | | | e1, e1, simplifying with (590), (680) gives:
% 108.25/15.29 | | | | | | | | | | | | | | | | (690) all_42_1 = e2
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_34_1,
% 108.25/15.29 | | | | | | | | | | | | | | | | all_42_1, e1, e1, simplifying with (671), (680)
% 108.25/15.29 | | | | | | | | | | | | | | | | gives:
% 108.25/15.29 | | | | | | | | | | | | | | | | (691) all_42_1 = all_34_1
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | COMBINE_EQS: (690), (691) imply:
% 108.25/15.29 | | | | | | | | | | | | | | | | (692) all_34_1 = e2
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | REDUCE: (150), (689) imply:
% 108.25/15.29 | | | | | | | | | | | | | | | | (693) ~ (all_53_9 = e1)
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | SIMP: (693) implies:
% 108.25/15.29 | | | | | | | | | | | | | | | | (694) ~ (all_53_9 = e1)
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 108.25/15.29 | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.29 | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | (695) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 108.25/15.29 | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 108.25/15.29 | | | | | | | | | | | | | | | | |
% 108.25/15.29 | | | | | | | | | | | | | | | | | ALPHA: (695) implies:
% 108.25/15.29 | | | | | | | | | | | | | | | | | (696) op(e3, e1) = e3
% 108.25/15.30 | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | BETA: splitting (672) gives:
% 108.25/15.30 | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (697) ~ (all_34_1 = e2)
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | REDUCE: (692), (697) imply:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (698) $false
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | CLOSE: (698) is inconsistent.
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (699) ~ (all_34_0 = e0) & op(e2, e1) = all_34_0 &
% 108.25/15.30 | | | | | | | | | | | | | | | | | | $i(all_34_0)
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | ALPHA: (699) implies:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (700) ~ (all_34_0 = e0)
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (701) op(e2, e1) = all_34_0
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 108.25/15.30 | | | | | | | | | | | | | | | | | | all_34_0, e1, e2, simplifying with (169), (701)
% 108.25/15.30 | | | | | | | | | | | | | | | | | | gives:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (702) all_53_9 = all_34_0
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 108.25/15.30 | | | | | | | | | | | | | | | | | | e3, e1, e3, simplifying with (173), (696) gives:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (703) all_53_13 = e3
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (702) imply:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (704) all_55_9 = all_34_0
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | REDUCE: (121), (702), (703) imply:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (705) ~ (all_34_0 = e3)
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | REDUCE: (589), (702) imply:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (706) ~ (all_34_0 = e2)
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | REDUCE: (694), (702) imply:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (707) ~ (all_34_0 = e1)
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | (708) all_55_9 = e3
% 108.25/15.30 | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (704), (708) imply:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | (709) all_34_0 = e3
% 108.25/15.30 | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | REDUCE: (705), (709) imply:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | (710) $false
% 108.25/15.30 | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | CLOSE: (710) is inconsistent.
% 108.25/15.30 | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | (711) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 108.25/15.30 | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (711) gives:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | (712) all_55_9 = e2
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (704), (712) imply:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | (713) all_34_0 = e2
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | REDUCE: (706), (713) imply:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | (714) $false
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | CLOSE: (714) is inconsistent.
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | (715) all_55_9 = e1 | all_55_9 = e0
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | BETA: splitting (715) gives:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | | (716) all_55_9 = e1
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (704), (716) imply:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | | (717) all_34_0 = e1
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | | REDUCE: (707), (717) imply:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | | (718) $false
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | | CLOSE: (718) is inconsistent.
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | | (719) all_55_9 = e0
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (704), (719) imply:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | | (720) all_34_0 = e0
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | | REDUCE: (700), (720) imply:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | | (721) $false
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | | CLOSE: (721) is inconsistent.
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.30 | | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | End of split
% 108.25/15.30 | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.30 | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | (722) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 108.25/15.30 | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 108.25/15.30 | | | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 108.25/15.30 | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 108.25/15.30 | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | BETA: splitting (722) gives:
% 108.25/15.30 | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (723) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 108.25/15.30 | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | ALPHA: (723) implies:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (724) op(e2, e1) = e2
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (589), (724), (function-axioms) are
% 108.25/15.30 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #231.
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (725) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 108.25/15.30 | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | ALPHA: (725) implies:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (726) op(e0, e1) = e0
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e0, e1,
% 108.25/15.30 | | | | | | | | | | | | | | | | | | e0, simplifying with (688), (726) gives:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (727) e1 = e0
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | REDUCE: (4), (727) imply:
% 108.25/15.30 | | | | | | | | | | | | | | | | | | (728) $false
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | | CLOSE: (728) is inconsistent.
% 108.25/15.30 | | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | | End of split
% 108.25/15.30 | | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | End of split
% 108.25/15.30 | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | Case 2:
% 108.25/15.30 | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | (729) all_57_11 = e1 & op(e0, e0) = e1
% 108.25/15.30 | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | ALPHA: (729) implies:
% 108.25/15.30 | | | | | | | | | | | | | | | | (730) op(e0, e0) = e1
% 108.25/15.30 | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (639), (730), (function-axioms) are
% 108.25/15.30 | | | | | | | | | | | | | | | | inconsistent by sub-proof #165.
% 108.25/15.30 | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | End of split
% 108.25/15.30 | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | End of split
% 108.25/15.30 | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | End of split
% 108.25/15.30 | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | End of split
% 108.25/15.30 | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | End of split
% 108.25/15.30 | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | Case 2:
% 108.25/15.30 | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | (731) all_26_2 = e2
% 108.25/15.30 | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | COMBINE_EQS: (316), (731) imply:
% 108.25/15.30 | | | | | | | | | | | (732) all_4_2 = e2
% 108.25/15.30 | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | SIMP: (732) implies:
% 108.25/15.30 | | | | | | | | | | | (733) all_4_2 = e2
% 108.25/15.30 | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | COMBINE_EQS: (277), (733) imply:
% 108.25/15.30 | | | | | | | | | | | (734) all_50_2 = e2
% 108.25/15.30 | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | REDUCE: (355), (733) imply:
% 108.25/15.30 | | | | | | | | | | | (735) ~ (all_53_2 = e2)
% 108.25/15.30 | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | BETA: splitting (105) gives:
% 108.25/15.30 | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | Case 1:
% 108.25/15.30 | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | (736) ~ (all_50_2 = e2)
% 108.25/15.30 | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | REDUCE: (734), (736) imply:
% 108.25/15.30 | | | | | | | | | | | | (737) $false
% 108.25/15.30 | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | CLOSE: (737) is inconsistent.
% 108.25/15.30 | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | Case 2:
% 108.25/15.30 | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | (738) op(e2, e2) = all_50_1 & $i(all_50_1) & ( ~
% 108.25/15.30 | | | | | | | | | | | | (all_50_1 = e1) | ( ~ (all_50_0 = e0) & op(e1,
% 108.25/15.30 | | | | | | | | | | | | e2) = all_50_0 & $i(all_50_0)))
% 108.25/15.30 | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | ALPHA: (738) implies:
% 108.25/15.30 | | | | | | | | | | | | (739) op(e2, e2) = all_50_1
% 108.25/15.30 | | | | | | | | | | | | (740) ~ (all_50_1 = e1) | ( ~ (all_50_0 = e0) & op(e1,
% 108.25/15.30 | | | | | | | | | | | | e2) = all_50_0 & $i(all_50_0))
% 108.25/15.30 | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | BETA: splitting (237) gives:
% 108.25/15.30 | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | Case 1:
% 108.25/15.30 | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | (741) (all_57_16 = e2 & op(e0, e3) = e2) | (all_57_17 =
% 108.25/15.30 | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 108.25/15.30 | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | BETA: splitting (741) gives:
% 108.25/15.30 | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | Case 1:
% 108.25/15.30 | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | (742) all_57_16 = e2 & op(e0, e3) = e2
% 108.25/15.30 | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | ALPHA: (742) implies:
% 108.25/15.30 | | | | | | | | | | | | | | (743) op(e0, e3) = e2
% 108.25/15.30 | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | REF_CLOSE: (163), (735), (743), (function-axioms) are
% 108.25/15.30 | | | | | | | | | | | | | | inconsistent by sub-proof #164.
% 108.25/15.30 | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | Case 2:
% 108.25/15.30 | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | (744) all_57_17 = e2 & op(e0, e2) = e2
% 108.25/15.30 | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | ALPHA: (744) implies:
% 108.25/15.30 | | | | | | | | | | | | | | (745) op(e0, e2) = e2
% 108.25/15.30 | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e2,
% 108.25/15.30 | | | | | | | | | | | | | | e2, e0, simplifying with (162), (745) gives:
% 108.25/15.30 | | | | | | | | | | | | | | (746) all_53_3 = e2
% 108.25/15.30 | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_50_1,
% 108.25/15.30 | | | | | | | | | | | | | | e2, e2, simplifying with (607), (739) gives:
% 108.25/15.30 | | | | | | | | | | | | | | (747) all_50_1 = e1
% 108.25/15.30 | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | REDUCE: (144), (746) imply:
% 108.25/15.30 | | | | | | | | | | | | | | (748) ~ (all_53_7 = e2)
% 108.25/15.30 | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | SIMP: (748) implies:
% 108.25/15.30 | | | | | | | | | | | | | | (749) ~ (all_53_7 = e2)
% 108.25/15.30 | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 108.25/15.30 | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | Case 1:
% 108.25/15.30 | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | (750) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 108.25/15.30 | | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 108.25/15.30 | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | ALPHA: (750) implies:
% 108.25/15.30 | | | | | | | | | | | | | | | (751) op(e3, e2) = e3
% 108.25/15.30 | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | BETA: splitting (740) gives:
% 108.25/15.30 | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | Case 1:
% 108.25/15.30 | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | (752) ~ (all_50_1 = e1)
% 108.25/15.30 | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | REDUCE: (747), (752) imply:
% 108.25/15.30 | | | | | | | | | | | | | | | | (753) $false
% 108.25/15.30 | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | CLOSE: (753) is inconsistent.
% 108.25/15.30 | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | Case 2:
% 108.25/15.30 | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | (754) ~ (all_50_0 = e0) & op(e1, e2) = all_50_0 &
% 108.25/15.30 | | | | | | | | | | | | | | | | $i(all_50_0)
% 108.25/15.30 | | | | | | | | | | | | | | | |
% 108.25/15.30 | | | | | | | | | | | | | | | | ALPHA: (754) implies:
% 108.25/15.31 | | | | | | | | | | | | | | | | (755) ~ (all_50_0 = e0)
% 108.25/15.31 | | | | | | | | | | | | | | | | (756) op(e1, e2) = all_50_0
% 108.25/15.31 | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7,
% 108.25/15.31 | | | | | | | | | | | | | | | | all_50_0, e2, e1, simplifying with (166), (756)
% 108.25/15.31 | | | | | | | | | | | | | | | | gives:
% 108.25/15.31 | | | | | | | | | | | | | | | | (757) all_53_7 = all_50_0
% 108.25/15.31 | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 108.25/15.31 | | | | | | | | | | | | | | | | e3, e2, e3, simplifying with (174), (751) gives:
% 108.25/15.31 | | | | | | | | | | | | | | | | (758) all_53_15 = e3
% 108.25/15.31 | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (757) imply:
% 108.25/15.31 | | | | | | | | | | | | | | | | (759) all_55_6 = all_50_0
% 108.25/15.31 | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | REDUCE: (128), (757), (758) imply:
% 108.25/15.31 | | | | | | | | | | | | | | | | (760) ~ (all_50_0 = e3)
% 108.25/15.31 | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | REDUCE: (749), (757) imply:
% 108.25/15.31 | | | | | | | | | | | | | | | | (761) ~ (all_50_0 = e2)
% 108.25/15.31 | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | REDUCE: (606), (757) imply:
% 108.25/15.31 | | | | | | | | | | | | | | | | (762) ~ (all_50_0 = e1)
% 108.25/15.31 | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 108.25/15.31 | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.31 | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | (763) all_55_6 = e3
% 108.25/15.31 | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | COMBINE_EQS: (759), (763) imply:
% 108.25/15.31 | | | | | | | | | | | | | | | | | (764) all_50_0 = e3
% 108.25/15.31 | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | SIMP: (764) implies:
% 108.25/15.31 | | | | | | | | | | | | | | | | | (765) all_50_0 = e3
% 108.25/15.31 | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | REDUCE: (760), (765) imply:
% 108.25/15.31 | | | | | | | | | | | | | | | | | (766) $false
% 108.25/15.31 | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | CLOSE: (766) is inconsistent.
% 108.25/15.31 | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.31 | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | (767) all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 108.25/15.31 | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | BETA: splitting (767) gives:
% 108.25/15.31 | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.31 | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | (768) all_55_6 = e2
% 108.25/15.31 | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (759), (768) imply:
% 108.25/15.31 | | | | | | | | | | | | | | | | | | (769) all_50_0 = e2
% 108.25/15.31 | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | SIMP: (769) implies:
% 108.25/15.31 | | | | | | | | | | | | | | | | | | (770) all_50_0 = e2
% 108.25/15.31 | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | REDUCE: (761), (770) imply:
% 108.25/15.31 | | | | | | | | | | | | | | | | | | (771) $false
% 108.25/15.31 | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | CLOSE: (771) is inconsistent.
% 108.25/15.31 | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.31 | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | (772) all_55_6 = e1 | all_55_6 = e0
% 108.25/15.31 | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | BETA: splitting (772) gives:
% 108.25/15.31 | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.31 | | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | (773) all_55_6 = e1
% 108.25/15.31 | | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (759), (773) imply:
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | (774) all_50_0 = e1
% 108.25/15.31 | | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | SIMP: (774) implies:
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | (775) all_50_0 = e1
% 108.25/15.31 | | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | REDUCE: (762), (775) imply:
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | (776) $false
% 108.25/15.31 | | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | CLOSE: (776) is inconsistent.
% 108.25/15.31 | | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.31 | | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | (777) all_55_6 = e0
% 108.25/15.31 | | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (759), (777) imply:
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | (778) all_50_0 = e0
% 108.25/15.31 | | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | SIMP: (778) implies:
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | (779) all_50_0 = e0
% 108.25/15.31 | | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | REDUCE: (755), (779) imply:
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | (780) $false
% 108.25/15.31 | | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | | CLOSE: (780) is inconsistent.
% 108.25/15.31 | | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.31 | | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | | End of split
% 108.25/15.31 | | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | | End of split
% 108.25/15.31 | | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | End of split
% 108.25/15.31 | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | Case 2:
% 108.25/15.31 | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | (781) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 108.25/15.31 | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 108.25/15.31 | | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 108.25/15.31 | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 108.25/15.31 | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | | REF_CLOSE: (5), (166), (606), (745), (781), (function-axioms)
% 108.25/15.31 | | | | | | | | | | | | | | | are inconsistent by sub-proof #162.
% 108.25/15.31 | | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | | End of split
% 108.25/15.31 | | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | End of split
% 108.25/15.31 | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | Case 2:
% 108.25/15.31 | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | (782) (all_57_18 = e2 & op(e0, e1) = e2) | (all_57_19 =
% 108.25/15.31 | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 108.25/15.31 | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | | REF_CLOSE: (38), (161), (381), (588), (782),
% 108.25/15.31 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.25/15.31 | | | | | | | | | | | | | #159.
% 108.25/15.31 | | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | | End of split
% 108.25/15.31 | | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | | End of split
% 108.25/15.31 | | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | End of split
% 108.25/15.31 | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | End of split
% 108.25/15.31 | | | | | | | | |
% 108.25/15.31 | | | | | | | | End of split
% 108.25/15.31 | | | | | | | |
% 108.25/15.31 | | | | | | | End of split
% 108.25/15.31 | | | | | | |
% 108.25/15.31 | | | | | | End of split
% 108.25/15.31 | | | | | |
% 108.25/15.31 | | | | | Case 2:
% 108.25/15.31 | | | | | |
% 108.25/15.31 | | | | | | (783) all_12_2 = e0
% 108.25/15.31 | | | | | | (784) op(e0, e0) = all_12_1 & $i(all_12_1) & ( ~ (all_12_1 = e1)
% 108.25/15.31 | | | | | | | ( ~ (all_12_0 = e3) & op(e1, e0) = all_12_0 &
% 108.25/15.31 | | | | | | $i(all_12_0)))
% 108.25/15.31 | | | | | |
% 108.25/15.31 | | | | | | ALPHA: (784) implies:
% 108.25/15.31 | | | | | | (785) op(e0, e0) = all_12_1
% 108.25/15.31 | | | | | |
% 108.25/15.31 | | | | | | COMBINE_EQS: (323), (783) imply:
% 108.25/15.31 | | | | | | (786) all_10_2 = e0
% 108.25/15.31 | | | | | |
% 108.25/15.31 | | | | | | SIMP: (786) implies:
% 108.25/15.31 | | | | | | (787) all_10_2 = e0
% 108.25/15.31 | | | | | |
% 108.25/15.31 | | | | | | COMBINE_EQS: (330), (787) imply:
% 108.25/15.31 | | | | | | (788) all_30_2 = e0
% 108.25/15.31 | | | | | |
% 108.25/15.31 | | | | | | REDUCE: (356), (787) imply:
% 108.25/15.31 | | | | | | (789) ~ (all_53_3 = e0)
% 108.25/15.31 | | | | | |
% 108.25/15.31 | | | | | | REDUCE: (367), (787) imply:
% 108.25/15.31 | | | | | | (790) ~ (all_53_7 = e0)
% 108.25/15.31 | | | | | |
% 108.25/15.31 | | | | | | REDUCE: (369), (787) imply:
% 108.25/15.31 | | | | | | (791) ~ (all_53_9 = e0)
% 108.25/15.31 | | | | | |
% 108.25/15.31 | | | | | | REDUCE: (370), (787) imply:
% 108.25/15.31 | | | | | | (792) ~ (all_53_10 = e0)
% 108.25/15.31 | | | | | |
% 108.25/15.31 | | | | | | REDUCE: (373), (787) imply:
% 108.25/15.31 | | | | | | (793) ~ (all_53_15 = e0)
% 108.25/15.31 | | | | | |
% 108.25/15.31 | | | | | | REDUCE: (382), (787) imply:
% 108.25/15.31 | | | | | | (794) ~ (e3 = e0)
% 108.25/15.31 | | | | | |
% 108.25/15.31 | | | | | | REDUCE: (44), (787) imply:
% 108.25/15.31 | | | | | | (795) op(e2, e2) = e0
% 108.25/15.31 | | | | | |
% 108.25/15.31 | | | | | | BETA: splitting (75) gives:
% 108.25/15.31 | | | | | |
% 108.25/15.31 | | | | | | Case 1:
% 108.25/15.31 | | | | | | |
% 108.25/15.31 | | | | | | | (796) ~ (all_30_2 = e0)
% 108.25/15.31 | | | | | | |
% 108.25/15.31 | | | | | | | REDUCE: (788), (796) imply:
% 108.25/15.31 | | | | | | | (797) $false
% 108.25/15.31 | | | | | | |
% 108.25/15.31 | | | | | | | CLOSE: (797) is inconsistent.
% 108.25/15.31 | | | | | | |
% 108.25/15.31 | | | | | | Case 2:
% 108.25/15.31 | | | | | | |
% 108.25/15.31 | | | | | | | (798) op(e0, e0) = all_30_1 & $i(all_30_1) & ( ~ (all_30_1 =
% 108.25/15.31 | | | | | | | e3) | ( ~ (all_30_0 = e1) & op(e3, e0) = all_30_0 &
% 108.25/15.31 | | | | | | | $i(all_30_0)))
% 108.25/15.31 | | | | | | |
% 108.25/15.31 | | | | | | | ALPHA: (798) implies:
% 108.25/15.31 | | | | | | | (799) op(e0, e0) = all_30_1
% 108.25/15.31 | | | | | | | (800) ~ (all_30_1 = e3) | ( ~ (all_30_0 = e1) & op(e3, e0) =
% 108.25/15.31 | | | | | | | all_30_0 & $i(all_30_0))
% 108.25/15.31 | | | | | | |
% 108.25/15.31 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 108.25/15.31 | | | | | | | all_30_1, e0, e0, simplifying with (38), (799) gives:
% 108.25/15.31 | | | | | | | (801) all_30_1 = all_6_2
% 108.25/15.31 | | | | | | |
% 108.25/15.31 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_1,
% 108.25/15.31 | | | | | | | all_30_1, e0, e0, simplifying with (785), (799)
% 108.25/15.31 | | | | | | | gives:
% 108.25/15.31 | | | | | | | (802) all_30_1 = all_12_1
% 108.25/15.31 | | | | | | |
% 108.25/15.31 | | | | | | | COMBINE_EQS: (801), (802) imply:
% 108.25/15.31 | | | | | | | (803) all_12_1 = all_6_2
% 108.25/15.31 | | | | | | |
% 108.25/15.31 | | | | | | | BETA: splitting (51) gives:
% 108.25/15.31 | | | | | | |
% 108.25/15.31 | | | | | | | Case 1:
% 108.25/15.31 | | | | | | | |
% 108.25/15.31 | | | | | | | | (804) ~ (all_14_2 = e2)
% 108.25/15.31 | | | | | | | |
% 108.25/15.31 | | | | | | | | BETA: splitting (57) gives:
% 108.25/15.31 | | | | | | | |
% 108.25/15.31 | | | | | | | | Case 1:
% 108.25/15.31 | | | | | | | | |
% 108.25/15.31 | | | | | | | | | (805) ~ (all_18_2 = e3)
% 108.25/15.31 | | | | | | | | |
% 108.25/15.31 | | | | | | | | | REDUCE: (326), (805) imply:
% 108.25/15.31 | | | | | | | | | (806) ~ (all_14_2 = e3)
% 108.25/15.31 | | | | | | | | |
% 108.25/15.31 | | | | | | | | | BETA: splitting (63) gives:
% 108.25/15.31 | | | | | | | | |
% 108.25/15.31 | | | | | | | | | Case 1:
% 108.25/15.31 | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | (807) ~ (all_22_2 = e0)
% 108.25/15.31 | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | REDUCE: (329), (807) imply:
% 108.25/15.31 | | | | | | | | | | (808) ~ (all_14_2 = e0)
% 108.25/15.31 | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (117), (123),
% 108.25/15.31 | | | | | | | | | | (126), (127), (148), (152), (153), (161), (162),
% 108.25/15.31 | | | | | | | | | | (163), (164), (166), (167), (168), (169), (171),
% 108.25/15.31 | | | | | | | | | | (172), (173), (174), (203), (341), (357), (359),
% 108.25/15.31 | | | | | | | | | | (361), (804), (806), (808), (function-axioms) are
% 108.25/15.31 | | | | | | | | | | inconsistent by sub-proof #216.
% 108.25/15.31 | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | Case 2:
% 108.25/15.31 | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | (809) all_22_2 = e0
% 108.25/15.31 | | | | | | | | | | (810) op(e0, e0) = all_22_1 & $i(all_22_1) & ( ~
% 108.25/15.31 | | | | | | | | | | (all_22_1 = e2) | ( ~ (all_22_0 = e3) & op(e2,
% 108.25/15.31 | | | | | | | | | | e0) = all_22_0 & $i(all_22_0)))
% 108.25/15.31 | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | ALPHA: (810) implies:
% 108.25/15.31 | | | | | | | | | | (811) op(e0, e0) = all_22_1
% 108.25/15.31 | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | COMBINE_EQS: (329), (809) imply:
% 108.25/15.31 | | | | | | | | | | (812) all_14_2 = e0
% 108.25/15.31 | | | | | | | | | |
% 108.25/15.31 | | | | | | | | | | SIMP: (812) implies:
% 108.25/15.31 | | | | | | | | | | (813) all_14_2 = e0
% 108.25/15.31 | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | COMBINE_EQS: (331), (813) imply:
% 108.25/15.32 | | | | | | | | | | (814) all_32_2 = e0
% 108.25/15.32 | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | REDUCE: (359), (813) imply:
% 108.25/15.32 | | | | | | | | | | (815) ~ (all_53_6 = e0)
% 108.25/15.32 | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | REDUCE: (365), (813) imply:
% 108.25/15.32 | | | | | | | | | | (816) ~ (all_53_13 = e0)
% 108.25/15.32 | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | BETA: splitting (216) gives:
% 108.25/15.32 | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | Case 1:
% 108.25/15.32 | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | (817) (all_57_100 = e0 & op(e3, e3) = e0) | (all_57_101
% 108.25/15.32 | | | | | | | | | | | = e0 & op(e2, e3) = e0)
% 108.25/15.32 | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | BETA: splitting (817) gives:
% 108.25/15.32 | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | Case 1:
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | (818) all_57_100 = e0 & op(e3, e3) = e0
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | ALPHA: (818) implies:
% 108.25/15.32 | | | | | | | | | | | | (819) op(e3, e3) = e0
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | REF_CLOSE: (35), (378), (819), (function-axioms) are
% 108.25/15.32 | | | | | | | | | | | | inconsistent by sub-proof #206.
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | Case 2:
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | (820) all_57_101 = e0 & op(e2, e3) = e0
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | ALPHA: (820) implies:
% 108.25/15.32 | | | | | | | | | | | | (821) op(e2, e3) = e0
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | REF_CLOSE: (171), (792), (821), (function-axioms) are
% 108.25/15.32 | | | | | | | | | | | | inconsistent by sub-proof #158.
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | End of split
% 108.25/15.32 | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | Case 2:
% 108.25/15.32 | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | (822) (all_57_102 = e0 & op(e1, e3) = e0) | (all_57_103
% 108.25/15.32 | | | | | | | | | | | = e0 & op(e0, e3) = e0)
% 108.25/15.32 | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | BETA: splitting (822) gives:
% 108.25/15.32 | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | Case 1:
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | (823) all_57_102 = e0 & op(e1, e3) = e0
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | ALPHA: (823) implies:
% 108.25/15.32 | | | | | | | | | | | | (824) op(e1, e3) = e0
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | REF_CLOSE: (167), (815), (824), (function-axioms) are
% 108.25/15.32 | | | | | | | | | | | | inconsistent by sub-proof #157.
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | Case 2:
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | (825) all_57_103 = e0 & op(e0, e3) = e0
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | ALPHA: (825) implies:
% 108.25/15.32 | | | | | | | | | | | | (826) op(e0, e3) = e0
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | BETA: splitting (78) gives:
% 108.25/15.32 | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | Case 1:
% 108.25/15.32 | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | (827) ~ (all_32_2 = e0)
% 108.25/15.32 | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | REDUCE: (814), (827) imply:
% 108.25/15.32 | | | | | | | | | | | | | (828) $false
% 108.25/15.32 | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | CLOSE: (828) is inconsistent.
% 108.25/15.32 | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | Case 2:
% 108.25/15.32 | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | (829) op(e0, e0) = all_32_1 & $i(all_32_1) & ( ~
% 108.25/15.32 | | | | | | | | | | | | | (all_32_1 = e3) | ( ~ (all_32_0 = e2) & op(e3,
% 108.25/15.32 | | | | | | | | | | | | | e0) = all_32_0 & $i(all_32_0)))
% 108.25/15.32 | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | ALPHA: (829) implies:
% 108.25/15.32 | | | | | | | | | | | | | (830) op(e0, e0) = all_32_1
% 108.25/15.32 | | | | | | | | | | | | | (831) ~ (all_32_1 = e3) | ( ~ (all_32_0 = e2) & op(e3,
% 108.25/15.32 | | | | | | | | | | | | | e0) = all_32_0 & $i(all_32_0))
% 108.25/15.32 | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | BETA: splitting (217) gives:
% 108.25/15.32 | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | Case 1:
% 108.25/15.32 | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | (832) (all_57_96 = e0 & op(e3, e3) = e0) | (all_57_97 =
% 108.25/15.32 | | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 108.25/15.32 | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | REF_CLOSE: (35), (174), (378), (793), (832),
% 108.25/15.32 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.25/15.32 | | | | | | | | | | | | | | #155.
% 108.25/15.32 | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | Case 2:
% 108.25/15.32 | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | (833) (all_57_98 = e0 & op(e3, e1) = e0) | (all_57_99 =
% 108.25/15.32 | | | | | | | | | | | | | | e0 & op(e3, e0) = e0)
% 108.25/15.32 | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | BETA: splitting (833) gives:
% 108.25/15.32 | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | Case 1:
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | (834) all_57_98 = e0 & op(e3, e1) = e0
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | ALPHA: (834) implies:
% 108.25/15.32 | | | | | | | | | | | | | | | (835) op(e3, e1) = e0
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | REF_CLOSE: (173), (816), (835), (function-axioms) are
% 108.25/15.32 | | | | | | | | | | | | | | | inconsistent by sub-proof #202.
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | Case 2:
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | (836) all_57_99 = e0 & op(e3, e0) = e0
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | ALPHA: (836) implies:
% 108.25/15.32 | | | | | | | | | | | | | | | (837) op(e3, e0) = e0
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 108.25/15.32 | | | | | | | | | | | | | | | all_32_1, e0, e0, simplifying with (38), (830)
% 108.25/15.32 | | | | | | | | | | | | | | | gives:
% 108.25/15.32 | | | | | | | | | | | | | | | (838) all_32_1 = all_6_2
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 108.25/15.32 | | | | | | | | | | | | | | | all_32_1, e0, e0, simplifying with (811), (830)
% 108.25/15.32 | | | | | | | | | | | | | | | gives:
% 108.25/15.32 | | | | | | | | | | | | | | | (839) all_32_1 = all_22_1
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e0,
% 108.25/15.32 | | | | | | | | | | | | | | | e3, e0, simplifying with (163), (826) gives:
% 108.25/15.32 | | | | | | | | | | | | | | | (840) all_53_2 = e0
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 108.25/15.32 | | | | | | | | | | | | | | | e0, e0, e3, simplifying with (172), (837) gives:
% 108.25/15.32 | | | | | | | | | | | | | | | (841) all_53_12 = e0
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | COMBINE_EQS: (838), (839) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | (842) all_22_1 = all_6_2
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | REDUCE: (153), (840) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | (843) ~ (all_53_1 = e0)
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | REDUCE: (148), (840) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | (844) ~ (all_53_3 = e0)
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | REDUCE: (147), (840) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | (845) ~ (all_53_6 = e0)
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | REDUCE: (146), (840) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | (846) ~ (all_53_10 = e0)
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | REDUCE: (137), (841) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | (847) ~ (all_53_4 = e0)
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | REDUCE: (353), (841) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | (848) ~ (all_6_2 = e0)
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | SIMP: (848) implies:
% 108.25/15.32 | | | | | | | | | | | | | | | (849) ~ (all_6_2 = e0)
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | REDUCE: (374), (841) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | (850) ~ (all_4_2 = e0)
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 108.25/15.32 | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | Case 1:
% 108.25/15.32 | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | (851) all_55_0 = e3
% 108.25/15.32 | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (851) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | | (852) all_6_2 = e3
% 108.25/15.32 | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | SIMP: (852) implies:
% 108.25/15.32 | | | | | | | | | | | | | | | | (853) all_6_2 = e3
% 108.25/15.32 | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | COMBINE_EQS: (313), (853) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | | (854) all_28_2 = e3
% 108.25/15.32 | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | COMBINE_EQS: (801), (853) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | | (855) all_30_1 = e3
% 108.25/15.32 | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | COMBINE_EQS: (838), (853) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | | (856) all_32_1 = e3
% 108.25/15.32 | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (853) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | | (857) all_36_2 = e3
% 108.25/15.32 | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | REDUCE: (343), (853) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | | (858) ~ (all_53_1 = e3)
% 108.25/15.32 | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 108.25/15.32 | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.32 | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | (859) ~ (all_28_2 = e3)
% 108.25/15.32 | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | REDUCE: (854), (859) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | | | (860) $false
% 108.25/15.32 | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | CLOSE: (860) is inconsistent.
% 108.25/15.32 | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.32 | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | (861) op(e3, e3) = all_28_1 & $i(all_28_1) & ( ~
% 108.25/15.32 | | | | | | | | | | | | | | | | | (all_28_1 = e1) | ( ~ (all_28_0 = e2) & op(e1,
% 108.25/15.32 | | | | | | | | | | | | | | | | | e3) = all_28_0 & $i(all_28_0)))
% 108.25/15.32 | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | ALPHA: (861) implies:
% 108.25/15.32 | | | | | | | | | | | | | | | | | (862) op(e3, e3) = all_28_1
% 108.25/15.32 | | | | | | | | | | | | | | | | | (863) ~ (all_28_1 = e1) | ( ~ (all_28_0 = e2) & op(e1,
% 108.25/15.32 | | | | | | | | | | | | | | | | | e3) = all_28_0 & $i(all_28_0))
% 108.25/15.32 | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 108.25/15.32 | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.32 | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | (864) ~ (all_36_2 = e3)
% 108.25/15.32 | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | REDUCE: (857), (864) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | | | | (865) $false
% 108.25/15.32 | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | CLOSE: (865) is inconsistent.
% 108.25/15.32 | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.32 | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | (866) op(e3, e3) = all_36_1 & $i(all_36_1) & ( ~
% 108.25/15.32 | | | | | | | | | | | | | | | | | | (all_36_1 = e2) | ( ~ (all_36_0 = e1) & op(e2,
% 108.25/15.32 | | | | | | | | | | | | | | | | | | e3) = all_36_0 & $i(all_36_0)))
% 108.25/15.32 | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | ALPHA: (866) implies:
% 108.25/15.32 | | | | | | | | | | | | | | | | | | (867) op(e3, e3) = all_36_1
% 108.25/15.32 | | | | | | | | | | | | | | | | | | (868) ~ (all_36_1 = e2) | ( ~ (all_36_0 = e1) & op(e2,
% 108.25/15.32 | | | | | | | | | | | | | | | | | | e3) = all_36_0 & $i(all_36_0))
% 108.25/15.32 | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | BETA: splitting (800) gives:
% 108.25/15.32 | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.32 | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | (869) ~ (all_30_1 = e3)
% 108.25/15.32 | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | REDUCE: (855), (869) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | (870) $false
% 108.25/15.32 | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | CLOSE: (870) is inconsistent.
% 108.25/15.32 | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.32 | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | (871) ~ (all_30_0 = e1) & op(e3, e0) = all_30_0 &
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | $i(all_30_0)
% 108.25/15.32 | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | ALPHA: (871) implies:
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | (872) ~ (all_30_0 = e1)
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | (873) op(e3, e0) = all_30_0
% 108.25/15.32 | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (831) gives:
% 108.25/15.32 | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | (874) ~ (all_32_1 = e3)
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (856), (874) imply:
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | (875) $false
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | CLOSE: (875) is inconsistent.
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | (876) ~ (all_32_0 = e2) & op(e3, e0) = all_32_0 &
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | $i(all_32_0)
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | ALPHA: (876) implies:
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | (877) op(e3, e0) = all_32_0
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_32_0,
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (837), (877) gives:
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | (878) all_32_0 = e0
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_0,
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | all_32_0, e0, e3, simplifying with (873), (877)
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | gives:
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | (879) all_32_0 = all_30_0
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | all_36_1, e3, e3, simplifying with (35), (867)
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | gives:
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | (880) all_36_1 = all_4_2
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_1,
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | all_36_1, e3, e3, simplifying with (862), (867)
% 108.25/15.32 | | | | | | | | | | | | | | | | | | | | gives:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | (881) all_36_1 = all_28_1
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (880), (881) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | (882) all_28_1 = all_4_2
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (878), (879) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | (883) all_30_0 = e0
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | REDUCE: (872), (883) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | (884) ~ (e1 = e0)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | (885) ~ (all_26_2 = e2)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | REDUCE: (316), (885) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | (886) ~ (all_4_2 = e2)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | (887) ~ (all_34_2 = e1)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (311), (887) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | (888) ~ (all_4_2 = e1)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (889) all_55_15 = e3
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (889) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (890) all_4_2 = e3
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (890) implies:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (891) all_4_2 = e3
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (891) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (892) ~ (all_53_13 = e3)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | (893) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (893) implies:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | (894) op(e3, e1) = e3
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (892), (894), (function-axioms) are
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #232.
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | (895) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (895) gives:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | (896) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (896) implies:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | (897) op(e2, e1) = e2
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (898) (all_57_60 = e3 & op(e3, e1) = e3) | (all_57_61 =
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e1) = e3)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (898) gives:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (899) all_57_60 = e3 & op(e3, e1) = e3
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (899) implies:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (900) op(e3, e1) = e3
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (892), (900), (function-axioms) are
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #232.
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (901) all_57_61 = e3 & op(e2, e1) = e3
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (901) implies:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (902) op(e2, e1) = e3
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (897), (902), (function-axioms) are
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #195.
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (903) (all_57_62 = e3 & op(e1, e1) = e3) | (all_57_63 =
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (903) gives:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (904) all_57_62 = e3 & op(e1, e1) = e3
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (904) implies:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (905) op(e1, e1) = e3
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (107), (109), (123), (140), (147),
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (163), (164), (166), (167), (169), (171),
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (173), (232), (233), (790), (791), (843), (847),
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (892), (905), (function-axioms) are inconsistent
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #146.
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (906) all_57_63 = e3 & op(e0, e1) = e3
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (906) implies:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (907) op(e0, e1) = e3
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (858), (907), (function-axioms) are
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #145.
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | (908) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (908) implies:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | (909) op(e0, e1) = e0
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (843), (909), (function-axioms) are
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #230.
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (910) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (339), (378), (886), (888), (910) are inconsistent
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #191.
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | (911) all_34_2 = e1
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (311), (911) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | (912) all_4_2 = e1
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | SIMP: (912) implies:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | (913) all_4_2 = e1
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (882), (913) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | (914) all_28_1 = e1
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (913) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | (915) ~ (all_53_6 = e1)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (913) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | (916) ~ (all_53_10 = e1)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (863) gives:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (917) ~ (all_28_1 = e1)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (914), (917) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (918) $false
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (918) is inconsistent.
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (919) ~ (all_28_0 = e2) & op(e1, e3) = all_28_0 &
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | $i(all_28_0)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (919) implies:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (920) ~ (all_28_0 = e2)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (921) op(e1, e3) = all_28_0
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | all_28_0, e3, e1, simplifying with (167), (921)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | gives:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (922) all_53_6 = all_28_0
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (922) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (923) all_55_7 = all_28_0
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (922) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (924) ~ (all_53_10 = all_28_0)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (924) implies:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (925) ~ (all_53_10 = all_28_0)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (915), (922) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (926) ~ (all_28_0 = e1)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (815), (922) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | (927) ~ (all_28_0 = e0)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | (928) all_55_7 = e3
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (923), (928) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | (929) all_28_0 = e3
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (925), (929) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | (930) ~ (all_53_10 = e3)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | (931) all_55_11 = e3
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (930), (931) are inconsistent by sub-proof
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | #144.
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | (932) all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (932) gives:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (933) all_55_11 = e2
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (933) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (934) all_53_10 = e2
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (934) implies:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (935) all_53_10 = e2
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (935) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (936) ~ (all_53_8 = e2)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (935) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (937) ~ (all_53_9 = e2)
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (109), (110), (113), (117), (139), (148),
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (153), (161), (162), (163), (164), (166), (168),
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (172), (173), (174), (826), (936), (937),
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | #210.
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (938) all_55_11 = e1 | all_55_11 = e0
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (938) gives:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (939) all_55_11 = e1
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (939) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (940) all_53_10 = e1
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (940) implies:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (941) all_53_10 = e1
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (916), (941) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (942) $false
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (942) is inconsistent.
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (943) all_55_11 = e0
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (792), (943) are inconsistent by sub-proof
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | #143.
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | (944) all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (920), (923), (926), (927), (944) are inconsistent
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #142.
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | (945) all_26_2 = e2
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (945) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | (946) all_4_2 = e2
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (880), (946) imply:
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | (947) all_36_1 = e2
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.33 | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (946) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | (948) ~ (all_53_6 = e2)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (946) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | (949) ~ (all_53_10 = e2)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (868) gives:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | (950) ~ (all_36_1 = e2)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (947), (950) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | (951) $false
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (951) is inconsistent.
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | (952) ~ (all_36_0 = e1) & op(e2, e3) = all_36_0 &
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_36_0)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (952) implies:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | (953) ~ (all_36_0 = e1)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | (954) op(e2, e3) = all_36_0
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_10,
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | all_36_0, e3, e2, simplifying with (171), (954)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | gives:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | (955) all_53_10 = all_36_0
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (955) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | (956) all_55_11 = all_36_0
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (955) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | (957) ~ (all_53_6 = all_36_0)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (949), (955) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | (958) ~ (all_36_0 = e2)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (792), (955) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | (959) ~ (all_36_0 = e0)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | (960) all_55_11 = e3
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (956), (960) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | (961) all_36_0 = e3
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (957), (961) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | (962) ~ (all_53_6 = e3)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | (963) all_55_7 = e3
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (963) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | (964) all_53_6 = e3
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (962), (964) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | (965) $false
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (965) is inconsistent.
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | (966) all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (966) gives:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | (967) all_55_7 = e2
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (967) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | (968) all_53_6 = e2
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (948), (968) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | (969) $false
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (969) is inconsistent.
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | (970) all_55_7 = e1 | all_55_7 = e0
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (970) gives:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (971) all_55_7 = e1
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (971) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (972) all_53_6 = e1
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (972) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (973) ~ (all_53_4 = e1)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (972) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (974) ~ (all_53_7 = e1)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (974) implies:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (975) ~ (all_53_7 = e1)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (976) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (976) implies:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (977) op(e3, e2) = e3
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (978) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (837), (978), (function-axioms) are
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #141.
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (979) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (113), (127), (161), (164), (168), (169),
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173), (174), (843), (973), (977), (979),
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #220.
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (980) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (166), (789), (975), (980),
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | #218.
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (981) all_55_7 = e0
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (981) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (982) all_53_6 = e0
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (815), (982) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (983) $false
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (983) is inconsistent.
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | (984) all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (984) gives:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | (985) all_55_11 = e2
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (956), (985) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | (986) all_36_0 = e2
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (958), (986) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | (987) $false
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (987) is inconsistent.
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | (988) all_55_11 = e1 | all_55_11 = e0
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (988) gives:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | (989) all_55_11 = e1
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (956), (989) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | (990) all_36_0 = e1
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (953), (990) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | (991) $false
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (991) is inconsistent.
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | (992) all_55_11 = e0
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (956), (992) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | (993) all_36_0 = e0
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (959), (993) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | (994) $false
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (994) is inconsistent.
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | Case 2:
% 108.25/15.34 | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | (995) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 108.25/15.34 | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | BETA: splitting (995) gives:
% 108.25/15.34 | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.34 | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | (996) all_55_0 = e2
% 108.25/15.34 | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (996) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | (997) all_6_2 = e2
% 108.25/15.34 | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | SIMP: (997) implies:
% 108.25/15.34 | | | | | | | | | | | | | | | | | (998) all_6_2 = e2
% 108.25/15.34 | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | REDUCE: (381), (998) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | (999) $false
% 108.25/15.34 | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | CLOSE: (999) is inconsistent.
% 108.25/15.34 | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.34 | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | (1000) all_55_0 = e1 | all_55_0 = e0
% 108.25/15.34 | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | BETA: splitting (1000) gives:
% 108.25/15.34 | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.34 | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | (1001) all_55_0 = e1
% 108.25/15.34 | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (1001) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | (1002) all_6_2 = e1
% 108.25/15.34 | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | SIMP: (1002) implies:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | (1003) all_6_2 = e1
% 108.25/15.34 | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | REDUCE: (379), (1003) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | (1004) $false
% 108.25/15.34 | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | CLOSE: (1004) is inconsistent.
% 108.25/15.34 | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.34 | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | (1005) all_55_0 = e0
% 108.25/15.34 | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (1005) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | (1006) all_6_2 = e0
% 108.25/15.34 | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | SIMP: (1006) implies:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | (1007) all_6_2 = e0
% 108.25/15.34 | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | REDUCE: (849), (1007) imply:
% 108.25/15.34 | | | | | | | | | | | | | | | | | | (1008) $false
% 108.25/15.34 | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | | CLOSE: (1008) is inconsistent.
% 108.25/15.34 | | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | End of split
% 108.25/15.34 | | | | | | | | |
% 108.25/15.34 | | | | | | | | Case 2:
% 108.25/15.34 | | | | | | | | |
% 108.25/15.34 | | | | | | | | | (1009) all_18_2 = e3
% 108.25/15.34 | | | | | | | | | (1010) op(e3, e3) = all_18_1 & $i(all_18_1) & ( ~ (all_18_1
% 108.25/15.34 | | | | | | | | | = e2) | ( ~ (all_18_0 = e0) & op(e2, e3) =
% 108.25/15.34 | | | | | | | | | all_18_0 & $i(all_18_0)))
% 108.25/15.34 | | | | | | | | |
% 108.25/15.34 | | | | | | | | | ALPHA: (1010) implies:
% 108.25/15.34 | | | | | | | | | (1011) op(e3, e3) = all_18_1
% 108.25/15.34 | | | | | | | | |
% 108.25/15.34 | | | | | | | | | COMBINE_EQS: (326), (1009) imply:
% 108.25/15.34 | | | | | | | | | (1012) all_14_2 = e3
% 108.25/15.34 | | | | | | | | |
% 108.25/15.34 | | | | | | | | | SIMP: (1012) implies:
% 108.25/15.34 | | | | | | | | | (1013) all_14_2 = e3
% 108.25/15.34 | | | | | | | | |
% 108.25/15.34 | | | | | | | | | COMBINE_EQS: (253), (1013) imply:
% 108.25/15.34 | | | | | | | | | (1014) all_20_2 = e3
% 108.25/15.34 | | | | | | | | |
% 108.25/15.34 | | | | | | | | | REDUCE: (361), (1013) imply:
% 108.25/15.34 | | | | | | | | | (1015) ~ (all_53_7 = e3)
% 108.25/15.34 | | | | | | | | |
% 108.25/15.34 | | | | | | | | | REDUCE: (363), (1013) imply:
% 108.25/15.34 | | | | | | | | | (1016) ~ (all_53_9 = e3)
% 108.25/15.34 | | | | | | | | |
% 108.25/15.34 | | | | | | | | | REDUCE: (365), (1013) imply:
% 108.25/15.34 | | | | | | | | | (1017) ~ (all_53_13 = e3)
% 108.25/15.34 | | | | | | | | |
% 108.25/15.34 | | | | | | | | | REDUCE: (50), (1013) imply:
% 108.25/15.34 | | | | | | | | | (1018) op(e1, e1) = e3
% 108.25/15.34 | | | | | | | | |
% 108.25/15.34 | | | | | | | | | BETA: splitting (60) gives:
% 108.25/15.34 | | | | | | | | |
% 108.25/15.34 | | | | | | | | | Case 1:
% 108.25/15.34 | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | (1019) ~ (all_20_2 = e3)
% 108.25/15.34 | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | REDUCE: (1014), (1019) imply:
% 108.25/15.34 | | | | | | | | | | (1020) $false
% 108.25/15.34 | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | CLOSE: (1020) is inconsistent.
% 108.25/15.34 | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | Case 2:
% 108.25/15.34 | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | (1021) op(e3, e3) = all_20_1 & $i(all_20_1) & ( ~
% 108.25/15.34 | | | | | | | | | | (all_20_1 = e0) | ( ~ (all_20_0 = e2) & op(e0,
% 108.25/15.34 | | | | | | | | | | e3) = all_20_0 & $i(all_20_0)))
% 108.25/15.34 | | | | | | | | | |
% 108.25/15.34 | | | | | | | | | | ALPHA: (1021) implies:
% 108.25/15.35 | | | | | | | | | | (1022) op(e3, e3) = all_20_1
% 108.25/15.35 | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 108.25/15.35 | | | | | | | | | | all_20_1, e3, e3, simplifying with (35), (1022)
% 108.25/15.35 | | | | | | | | | | gives:
% 108.25/15.35 | | | | | | | | | | (1023) all_20_1 = all_4_2
% 108.25/15.35 | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 108.25/15.35 | | | | | | | | | | all_20_1, e3, e3, simplifying with (1011), (1022)
% 108.25/15.35 | | | | | | | | | | gives:
% 108.25/15.35 | | | | | | | | | | (1024) all_20_1 = all_18_1
% 108.25/15.35 | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | COMBINE_EQS: (1023), (1024) imply:
% 108.25/15.35 | | | | | | | | | | (1025) all_18_1 = all_4_2
% 108.25/15.35 | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | SIMP: (1025) implies:
% 108.25/15.35 | | | | | | | | | | (1026) all_18_1 = all_4_2
% 108.25/15.35 | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | BETA: splitting (69) gives:
% 108.25/15.35 | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | Case 1:
% 108.25/15.35 | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | (1027) ~ (all_26_2 = e2)
% 108.25/15.35 | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | REDUCE: (316), (1027) imply:
% 108.25/15.35 | | | | | | | | | | | (1028) ~ (all_4_2 = e2)
% 108.25/15.35 | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | BETA: splitting (72) gives:
% 108.25/15.35 | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | Case 1:
% 108.25/15.35 | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | (1029) ~ (all_28_2 = e3)
% 108.25/15.35 | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | REDUCE: (313), (1029) imply:
% 108.25/15.35 | | | | | | | | | | | | (1030) ~ (all_6_2 = e3)
% 108.25/15.35 | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | BETA: splitting (208) gives:
% 108.25/15.35 | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | Case 1:
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | (1031) all_55_0 = e3
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | COMBINE_EQS: (248), (1031) imply:
% 108.25/15.35 | | | | | | | | | | | | | (1032) all_6_2 = e3
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | REDUCE: (1030), (1032) imply:
% 108.25/15.35 | | | | | | | | | | | | | (1033) $false
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | CLOSE: (1033) is inconsistent.
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | Case 2:
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | (1034) ~ (all_55_0 = e3)
% 108.25/15.35 | | | | | | | | | | | | | (1035) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | BETA: splitting (1035) gives:
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | Case 1:
% 108.25/15.35 | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | (1036) all_55_0 = e2
% 108.25/15.35 | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | COMBINE_EQS: (248), (1036) imply:
% 108.25/15.35 | | | | | | | | | | | | | | (1037) all_6_2 = e2
% 108.25/15.35 | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | REDUCE: (381), (1037) imply:
% 108.25/15.35 | | | | | | | | | | | | | | (1038) $false
% 108.25/15.35 | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | CLOSE: (1038) is inconsistent.
% 108.25/15.35 | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | Case 2:
% 108.25/15.35 | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | (1039) all_55_0 = e1 | all_55_0 = e0
% 108.25/15.35 | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | BETA: splitting (1039) gives:
% 108.25/15.35 | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | Case 1:
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | (1040) all_55_0 = e1
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | COMBINE_EQS: (248), (1040) imply:
% 108.25/15.35 | | | | | | | | | | | | | | | (1041) all_6_2 = e1
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | REDUCE: (379), (1041) imply:
% 108.25/15.35 | | | | | | | | | | | | | | | (1042) $false
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | CLOSE: (1042) is inconsistent.
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | Case 2:
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | (1043) all_55_0 = e0
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | COMBINE_EQS: (248), (1043) imply:
% 108.25/15.35 | | | | | | | | | | | | | | | (1044) all_6_2 = e0
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | REDUCE: (343), (1044) imply:
% 108.25/15.35 | | | | | | | | | | | | | | | (1045) ~ (all_53_1 = e0)
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | REDUCE: (349), (1044) imply:
% 108.25/15.35 | | | | | | | | | | | | | | | (1046) ~ (all_53_4 = e0)
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | REDUCE: (379), (1044) imply:
% 108.25/15.35 | | | | | | | | | | | | | | | (1047) ~ (e1 = e0)
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (107), (109), (123), (140), (147),
% 108.25/15.35 | | | | | | | | | | | | | | | (161), (163), (164), (166), (167), (169), (171),
% 108.25/15.35 | | | | | | | | | | | | | | | (173), (232), (233), (790), (791), (1017), (1018),
% 108.25/15.35 | | | | | | | | | | | | | | | (1045), (1046), (function-axioms) are inconsistent
% 108.25/15.35 | | | | | | | | | | | | | | | by sub-proof #146.
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | End of split
% 108.25/15.35 | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | End of split
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | End of split
% 108.25/15.35 | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | Case 2:
% 108.25/15.35 | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | (1048) all_28_2 = e3
% 108.25/15.35 | | | | | | | | | | | | (1049) op(e3, e3) = all_28_1 & $i(all_28_1) & ( ~
% 108.25/15.35 | | | | | | | | | | | | (all_28_1 = e1) | ( ~ (all_28_0 = e2) & op(e1,
% 108.25/15.35 | | | | | | | | | | | | e3) = all_28_0 & $i(all_28_0)))
% 108.25/15.35 | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | ALPHA: (1049) implies:
% 108.25/15.35 | | | | | | | | | | | | (1050) op(e3, e3) = all_28_1
% 108.25/15.35 | | | | | | | | | | | | (1051) ~ (all_28_1 = e1) | ( ~ (all_28_0 = e2) & op(e1,
% 108.25/15.35 | | | | | | | | | | | | e3) = all_28_0 & $i(all_28_0))
% 108.25/15.35 | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | COMBINE_EQS: (313), (1048) imply:
% 108.25/15.35 | | | | | | | | | | | | (1052) all_6_2 = e3
% 108.25/15.35 | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | COMBINE_EQS: (332), (1052) imply:
% 108.25/15.35 | | | | | | | | | | | | (1053) all_36_2 = e3
% 108.25/15.35 | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | REDUCE: (347), (1052) imply:
% 108.25/15.35 | | | | | | | | | | | | (1054) ~ (all_53_3 = e3)
% 108.25/15.35 | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | REDUCE: (351), (1052) imply:
% 108.25/15.35 | | | | | | | | | | | | (1055) ~ (all_53_8 = e3)
% 108.25/15.35 | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | BETA: splitting (84) gives:
% 108.25/15.35 | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | Case 1:
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | (1056) ~ (all_36_2 = e3)
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | REDUCE: (1053), (1056) imply:
% 108.25/15.35 | | | | | | | | | | | | | (1057) $false
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | CLOSE: (1057) is inconsistent.
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | Case 2:
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | (1058) op(e3, e3) = all_36_1 & $i(all_36_1) & ( ~
% 108.25/15.35 | | | | | | | | | | | | | (all_36_1 = e2) | ( ~ (all_36_0 = e1) & op(e2,
% 108.25/15.35 | | | | | | | | | | | | | e3) = all_36_0 & $i(all_36_0)))
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | ALPHA: (1058) implies:
% 108.25/15.35 | | | | | | | | | | | | | (1059) op(e3, e3) = all_36_1
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | BETA: splitting (218) gives:
% 108.25/15.35 | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | Case 1:
% 108.25/15.35 | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | (1060) (all_57_92 = e3 & op(e3, e2) = e3) | (all_57_93 =
% 108.25/15.35 | | | | | | | | | | | | | | e3 & op(e2, e2) = e3)
% 108.25/15.35 | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | BETA: splitting (1060) gives:
% 108.25/15.35 | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | Case 1:
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | (1061) all_57_92 = e3 & op(e3, e2) = e3
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | ALPHA: (1061) implies:
% 108.25/15.35 | | | | | | | | | | | | | | | (1062) op(e3, e2) = e3
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 108.25/15.35 | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | Case 1:
% 108.25/15.35 | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | (1063) (all_57_88 = e3 & op(e2, e3) = e3) | (all_57_89 =
% 108.25/15.35 | | | | | | | | | | | | | | | | e3 & op(e2, e2) = e3)
% 108.25/15.35 | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | BETA: splitting (1063) gives:
% 108.25/15.35 | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.35 | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | (1064) all_57_88 = e3 & op(e2, e3) = e3
% 108.25/15.35 | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | ALPHA: (1064) implies:
% 108.25/15.35 | | | | | | | | | | | | | | | | | (1065) op(e2, e3) = e3
% 108.25/15.35 | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_10,
% 108.25/15.35 | | | | | | | | | | | | | | | | | e3, e3, e2, simplifying with (171), (1065) gives:
% 108.25/15.35 | | | | | | | | | | | | | | | | | (1066) all_53_10 = e3
% 108.25/15.35 | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 108.25/15.35 | | | | | | | | | | | | | | | | | e3, e2, e3, simplifying with (174), (1062) gives:
% 108.25/15.35 | | | | | | | | | | | | | | | | | (1067) all_53_15 = e3
% 108.25/15.35 | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 108.25/15.35 | | | | | | | | | | | | | | | | | all_36_1, e3, e3, simplifying with (35), (1059)
% 108.25/15.35 | | | | | | | | | | | | | | | | | gives:
% 108.25/15.35 | | | | | | | | | | | | | | | | | (1068) all_36_1 = all_4_2
% 108.25/15.35 | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_1,
% 108.25/15.35 | | | | | | | | | | | | | | | | | all_36_1, e3, e3, simplifying with (1050), (1059)
% 108.25/15.35 | | | | | | | | | | | | | | | | | gives:
% 108.25/15.35 | | | | | | | | | | | | | | | | | (1069) all_36_1 = all_28_1
% 108.25/15.35 | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | COMBINE_EQS: (1068), (1069) imply:
% 108.25/15.35 | | | | | | | | | | | | | | | | | (1070) all_28_1 = all_4_2
% 108.25/15.35 | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | REDUCE: (131), (1066) imply:
% 108.25/15.35 | | | | | | | | | | | | | | | | | (1071) ~ (all_53_6 = e3)
% 108.25/15.35 | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | REDUCE: (377), (1067) imply:
% 108.25/15.35 | | | | | | | | | | | | | | | | | (1072) ~ (all_4_2 = e3)
% 108.25/15.35 | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | SIMP: (1072) implies:
% 108.25/15.35 | | | | | | | | | | | | | | | | | (1073) ~ (all_4_2 = e3)
% 108.25/15.35 | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 108.25/15.35 | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.35 | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | (1074) all_55_15 = e3
% 108.25/15.35 | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (339), (1073), (1074) are inconsistent by
% 108.25/15.35 | | | | | | | | | | | | | | | | | | sub-proof #140.
% 108.25/15.35 | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.35 | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | (1075) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 108.25/15.35 | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | BETA: splitting (1075) gives:
% 108.25/15.35 | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | (1076) all_55_15 = e2
% 108.25/15.35 | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (339), (1028), (1076) are inconsistent by
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | sub-proof #193.
% 108.25/15.35 | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | (1077) all_55_15 = e1 | all_55_15 = e0
% 108.25/15.35 | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (1077) gives:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | (1078) all_55_15 = e1
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (1078) imply:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | (1079) all_4_2 = e1
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | SIMP: (1079) implies:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | (1080) all_4_2 = e1
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1070), (1080) imply:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | (1081) all_28_1 = e1
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (1080) imply:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | (1082) ~ (all_53_6 = e1)
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | (1083) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2)
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | = all_52_18 & op(e2, e3) = e2 & $i(all_52_18)
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1083) implies:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | (1084) ~ (all_52_18 = e3)
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | (1085) op(e3, e2) = all_52_18
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1062), (1084), (1085), (function-axioms) are
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #234.
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | (1086) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | (all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22))
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1086) gives:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | | (1087) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1087) implies:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | | (1088) op(e1, e3) = e1
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1082), (1088), (function-axioms) are
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #223.
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.35 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | (1089) all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22)
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1089) implies:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | (1090) op(e0, e3) = e0
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1051) gives:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | (1091) ~ (all_28_1 = e1)
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1081), (1091) imply:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | (1092) $false
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1092) is inconsistent.
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | (1093) ~ (all_28_0 = e2) & op(e1, e3) = all_28_0 &
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | $i(all_28_0)
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1093) implies:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | (1094) ~ (all_28_0 = e2)
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | (1095) op(e1, e3) = all_28_0
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e0,
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (163), (1090) gives:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | (1096) all_53_2 = e0
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | all_28_0, e3, e1, simplifying with (167), (1095)
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | gives:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | (1097) all_53_6 = all_28_0
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (1097) imply:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | (1098) all_55_7 = all_28_0
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (1096), (1097) imply:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | (1099) ~ (all_28_0 = e0)
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1099) implies:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | (1100) ~ (all_28_0 = e0)
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1071), (1097) imply:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | (1101) ~ (all_28_0 = e3)
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1082), (1097) imply:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | (1102) ~ (all_28_0 = e1)
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | | (1103) all_55_7 = e3
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1098), (1103) imply:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | | (1104) all_28_0 = e3
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1101), (1104) imply:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | | (1105) $false
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1105) is inconsistent.
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | | (1106) all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1094), (1098), (1100), (1102), (1106) are
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #142.
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | (1107) all_55_15 = e0
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (339), (378), (1107) are inconsistent by sub-proof
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | | #192.
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.36 | | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.36 | | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | End of split
% 108.25/15.36 | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.36 | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | (1108) all_57_89 = e3 & op(e2, e2) = e3
% 108.25/15.36 | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | ALPHA: (1108) implies:
% 108.25/15.36 | | | | | | | | | | | | | | | | | (1109) op(e2, e2) = e3
% 108.25/15.36 | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (795), (1109), (function-axioms) are
% 108.25/15.36 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #139.
% 108.25/15.36 | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | End of split
% 108.25/15.36 | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | Case 2:
% 108.25/15.36 | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | (1110) (all_57_90 = e3 & op(e2, e1) = e3) | (all_57_91 =
% 108.25/15.36 | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 108.25/15.36 | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | BETA: splitting (1110) gives:
% 108.25/15.36 | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.36 | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | (1111) all_57_90 = e3 & op(e2, e1) = e3
% 108.25/15.36 | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | ALPHA: (1111) implies:
% 108.25/15.36 | | | | | | | | | | | | | | | | | (1112) op(e2, e1) = e3
% 108.25/15.36 | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1016), (1112), (function-axioms) are
% 108.25/15.36 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #138.
% 108.25/15.36 | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.36 | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | (1113) all_57_91 = e3 & op(e2, e0) = e3
% 108.25/15.36 | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | ALPHA: (1113) implies:
% 108.25/15.36 | | | | | | | | | | | | | | | | | (1114) op(e2, e0) = e3
% 108.25/15.36 | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1055), (1114), (function-axioms) are
% 108.25/15.36 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #194.
% 108.25/15.36 | | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | | End of split
% 108.25/15.36 | | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | End of split
% 108.25/15.36 | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | Case 2:
% 108.25/15.36 | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | (1115) all_57_93 = e3 & op(e2, e2) = e3
% 108.25/15.36 | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | ALPHA: (1115) implies:
% 108.25/15.36 | | | | | | | | | | | | | | | (1116) op(e2, e2) = e3
% 108.25/15.36 | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | REF_CLOSE: (6), (795), (1116), (function-axioms) are
% 108.25/15.36 | | | | | | | | | | | | | | | inconsistent by sub-proof #139.
% 108.25/15.36 | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | End of split
% 108.25/15.36 | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | Case 2:
% 108.25/15.36 | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | (1117) (all_57_94 = e3 & op(e1, e2) = e3) | (all_57_95 =
% 108.25/15.36 | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 108.25/15.36 | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | BETA: splitting (1117) gives:
% 108.25/15.36 | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | Case 1:
% 108.25/15.36 | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | (1118) all_57_94 = e3 & op(e1, e2) = e3
% 108.25/15.36 | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | ALPHA: (1118) implies:
% 108.25/15.36 | | | | | | | | | | | | | | | (1119) op(e1, e2) = e3
% 108.25/15.36 | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | REF_CLOSE: (166), (1015), (1119), (function-axioms) are
% 108.25/15.36 | | | | | | | | | | | | | | | inconsistent by sub-proof #179.
% 108.25/15.36 | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | Case 2:
% 108.25/15.36 | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | (1120) all_57_95 = e3 & op(e0, e2) = e3
% 108.25/15.36 | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | ALPHA: (1120) implies:
% 108.25/15.36 | | | | | | | | | | | | | | | (1121) op(e0, e2) = e3
% 108.25/15.36 | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | | REF_CLOSE: (162), (1054), (1121), (function-axioms) are
% 108.25/15.36 | | | | | | | | | | | | | | | inconsistent by sub-proof #137.
% 108.25/15.36 | | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | | End of split
% 108.25/15.36 | | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | End of split
% 108.25/15.36 | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | End of split
% 108.25/15.36 | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | End of split
% 108.25/15.36 | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | Case 2:
% 108.25/15.36 | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | (1122) all_26_2 = e2
% 108.25/15.36 | | | | | | | | | | | (1123) op(e2, e2) = all_26_1 & $i(all_26_1) & ( ~
% 108.25/15.36 | | | | | | | | | | | (all_26_1 = e0) | ( ~ (all_26_0 = e1) & op(e0,
% 108.25/15.36 | | | | | | | | | | | e2) = all_26_0 & $i(all_26_0)))
% 108.25/15.36 | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | ALPHA: (1123) implies:
% 108.25/15.36 | | | | | | | | | | | (1124) op(e2, e2) = all_26_1
% 108.25/15.36 | | | | | | | | | | | (1125) ~ (all_26_1 = e0) | ( ~ (all_26_0 = e1) & op(e0,
% 108.25/15.36 | | | | | | | | | | | e2) = all_26_0 & $i(all_26_0))
% 108.25/15.36 | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | COMBINE_EQS: (316), (1122) imply:
% 108.25/15.36 | | | | | | | | | | | (1126) all_4_2 = e2
% 108.25/15.36 | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | COMBINE_EQS: (277), (1126) imply:
% 108.25/15.36 | | | | | | | | | | | (1127) all_50_2 = e2
% 108.25/15.36 | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | REDUCE: (371), (1126) imply:
% 108.25/15.36 | | | | | | | | | | | (1128) ~ (all_53_10 = e2)
% 108.25/15.36 | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | REDUCE: (375), (1126) imply:
% 108.25/15.36 | | | | | | | | | | | (1129) ~ (all_53_13 = e2)
% 108.25/15.36 | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | BETA: splitting (105) gives:
% 108.25/15.36 | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | Case 1:
% 108.25/15.36 | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | (1130) ~ (all_50_2 = e2)
% 108.25/15.36 | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | REDUCE: (1127), (1130) imply:
% 108.25/15.36 | | | | | | | | | | | | (1131) $false
% 108.25/15.36 | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | CLOSE: (1131) is inconsistent.
% 108.25/15.36 | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | Case 2:
% 108.25/15.36 | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | (1132) op(e2, e2) = all_50_1 & $i(all_50_1) & ( ~
% 108.25/15.36 | | | | | | | | | | | | (all_50_1 = e1) | ( ~ (all_50_0 = e0) & op(e1,
% 108.25/15.36 | | | | | | | | | | | | e2) = all_50_0 & $i(all_50_0)))
% 108.25/15.36 | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | ALPHA: (1132) implies:
% 108.25/15.36 | | | | | | | | | | | | (1133) op(e2, e2) = all_50_1
% 108.25/15.36 | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_50_1,
% 108.25/15.36 | | | | | | | | | | | | e2, e2, simplifying with (795), (1133) gives:
% 108.25/15.36 | | | | | | | | | | | | (1134) all_50_1 = e0
% 108.25/15.36 | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_1,
% 108.25/15.36 | | | | | | | | | | | | all_50_1, e2, e2, simplifying with (1124), (1133)
% 108.25/15.36 | | | | | | | | | | | | gives:
% 108.25/15.36 | | | | | | | | | | | | (1135) all_50_1 = all_26_1
% 108.25/15.36 | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | COMBINE_EQS: (1134), (1135) imply:
% 108.25/15.36 | | | | | | | | | | | | (1136) all_26_1 = e0
% 108.25/15.36 | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | BETA: splitting (1125) gives:
% 108.25/15.36 | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | Case 1:
% 108.25/15.36 | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | (1137) ~ (all_26_1 = e0)
% 108.25/15.36 | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | REDUCE: (1136), (1137) imply:
% 108.25/15.36 | | | | | | | | | | | | | (1138) $false
% 108.25/15.36 | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | CLOSE: (1138) is inconsistent.
% 108.25/15.36 | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | Case 2:
% 108.25/15.36 | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | (1139) ~ (all_26_0 = e1) & op(e0, e2) = all_26_0 &
% 108.25/15.36 | | | | | | | | | | | | | $i(all_26_0)
% 108.25/15.36 | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | ALPHA: (1139) implies:
% 108.25/15.36 | | | | | | | | | | | | | (1140) ~ (all_26_0 = e1)
% 108.25/15.36 | | | | | | | | | | | | | (1141) op(e0, e2) = all_26_0
% 108.25/15.36 | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 108.25/15.36 | | | | | | | | | | | | | all_26_0, e2, e0, simplifying with (162), (1141)
% 108.25/15.36 | | | | | | | | | | | | | gives:
% 108.25/15.36 | | | | | | | | | | | | | (1142) all_53_3 = all_26_0
% 108.25/15.36 | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | COMBINE_EQS: (250), (1142) imply:
% 108.25/15.36 | | | | | | | | | | | | | (1143) all_55_2 = all_26_0
% 108.25/15.36 | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | REDUCE: (152), (1142) imply:
% 108.25/15.36 | | | | | | | | | | | | | (1144) ~ (all_53_1 = all_26_0)
% 108.25/15.36 | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | REDUCE: (144), (1142) imply:
% 108.25/15.36 | | | | | | | | | | | | | (1145) ~ (all_53_7 = all_26_0)
% 108.25/15.36 | | | | | | | | | | | | |
% 108.25/15.36 | | | | | | | | | | | | | SIMP: (1145) implies:
% 108.25/15.36 | | | | | | | | | | | | | (1146) ~ (all_53_7 = all_26_0)
% 108.25/15.36 | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | REDUCE: (347), (1142) imply:
% 108.25/15.37 | | | | | | | | | | | | | (1147) ~ (all_26_0 = all_6_2)
% 108.25/15.37 | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | REDUCE: (789), (1142) imply:
% 108.25/15.37 | | | | | | | | | | | | | (1148) ~ (all_26_0 = e0)
% 108.25/15.37 | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | BETA: splitting (72) gives:
% 108.25/15.37 | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | Case 1:
% 108.25/15.37 | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | (1149) ~ (all_28_2 = e3)
% 108.25/15.37 | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | REDUCE: (313), (1149) imply:
% 108.25/15.37 | | | | | | | | | | | | | | (1150) ~ (all_6_2 = e3)
% 108.25/15.37 | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 108.25/15.37 | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | Case 1:
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | (1151) all_55_0 = e3
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | COMBINE_EQS: (248), (1151) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | (1152) all_6_2 = e3
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | REDUCE: (1150), (1152) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | (1153) $false
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | CLOSE: (1153) is inconsistent.
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | Case 2:
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | (1154) ~ (all_55_0 = e3)
% 108.25/15.37 | | | | | | | | | | | | | | | (1155) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | BETA: splitting (1155) gives:
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | Case 1:
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | (1156) all_55_0 = e2
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (1156) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | | (1157) all_6_2 = e2
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | REDUCE: (381), (1157) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | | (1158) $false
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | CLOSE: (1158) is inconsistent.
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | Case 2:
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | (1159) all_55_0 = e1 | all_55_0 = e0
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | BETA: splitting (1159) gives:
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | (1160) all_55_0 = e1
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (1160) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | | | (1161) all_6_2 = e1
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | REDUCE: (379), (1161) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | | | (1162) $false
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | CLOSE: (1162) is inconsistent.
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | (1163) all_55_0 = e0
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (1163) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | | | (1164) all_6_2 = e0
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | REDUCE: (345), (1164) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | | | (1165) ~ (all_53_2 = e0)
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | REDUCE: (349), (1164) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | | | (1166) ~ (all_53_4 = e0)
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | REDUCE: (379), (1164) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | | | (1167) ~ (e1 = e0)
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (107), (163), (164), (166), (167),
% 108.25/15.37 | | | | | | | | | | | | | | | | | (171), (233), (790), (1018), (1128), (1165),
% 108.25/15.37 | | | | | | | | | | | | | | | | | (1166), (function-axioms) are inconsistent by
% 108.25/15.37 | | | | | | | | | | | | | | | | | sub-proof #148.
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | Case 2:
% 108.25/15.37 | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | (1168) all_28_2 = e3
% 108.25/15.37 | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | COMBINE_EQS: (313), (1168) imply:
% 108.25/15.37 | | | | | | | | | | | | | | (1169) all_6_2 = e3
% 108.25/15.37 | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | REDUCE: (353), (1169) imply:
% 108.25/15.37 | | | | | | | | | | | | | | (1170) ~ (all_53_12 = e3)
% 108.25/15.37 | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | REDUCE: (1147), (1169) imply:
% 108.25/15.37 | | | | | | | | | | | | | | (1171) ~ (all_26_0 = e3)
% 108.25/15.37 | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 108.25/15.37 | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | Case 1:
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | (1172) all_55_2 = e3
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | COMBINE_EQS: (1143), (1172) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | (1173) all_26_0 = e3
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | REDUCE: (1171), (1173) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | (1174) $false
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | CLOSE: (1174) is inconsistent.
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | Case 2:
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | (1175) ~ (all_55_2 = e3)
% 108.25/15.37 | | | | | | | | | | | | | | | (1176) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | BETA: splitting (1176) gives:
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | Case 1:
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | (1177) all_55_2 = e2
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | COMBINE_EQS: (1143), (1177) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | | (1178) all_26_0 = e2
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | SIMP: (1178) implies:
% 108.25/15.37 | | | | | | | | | | | | | | | | (1179) all_26_0 = e2
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | REDUCE: (1144), (1179) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | | (1180) ~ (all_53_1 = e2)
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | REDUCE: (1146), (1179) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | | (1181) ~ (all_53_7 = e2)
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | REDUCE: (1171), (1179) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | | (1182) ~ (e3 = e2)
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | (1183) (all_57_52 = e2 & op(e3, e1) = e2) | (all_57_53 =
% 108.25/15.37 | | | | | | | | | | | | | | | | | e2 & op(e2, e1) = e2)
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | BETA: splitting (1183) gives:
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | (1184) all_57_52 = e2 & op(e3, e1) = e2
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | ALPHA: (1184) implies:
% 108.25/15.37 | | | | | | | | | | | | | | | | | | (1185) op(e3, e1) = e2
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (1129), (1185), (function-axioms) are
% 108.25/15.37 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #136.
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | (1186) all_57_53 = e2 & op(e2, e1) = e2
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | ALPHA: (1186) implies:
% 108.25/15.37 | | | | | | | | | | | | | | | | | | (1187) op(e2, e1) = e2
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.37 | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | (1188) all_55_6 = e3
% 108.25/15.37 | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (1015), (1188) are inconsistent by
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | sub-proof #135.
% 108.25/15.37 | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.37 | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | (1189) all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 108.25/15.37 | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | BETA: splitting (1189) gives:
% 108.25/15.37 | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | (1190) all_55_6 = e2
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (1181), (1190) are inconsistent by
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | sub-proof #134.
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | (1191) all_55_6 = e1 | all_55_6 = e0
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1191) gives:
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | | (1192) all_55_6 = e1
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (1192) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | | (1193) all_53_7 = e1
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | | SIMP: (1193) implies:
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | | (1194) all_53_7 = e1
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (1194) imply:
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | | (1195) ~ (all_53_4 = e1)
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (127), (164), (168), (169), (172), (1170),
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | | (1187), (1195), (function-axioms) are inconsistent
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | | by sub-proof #133.
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | | (1196) all_55_6 = e0
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (790), (1196) are inconsistent by sub-proof
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | | #132.
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | (1197) (all_57_54 = e2 & op(e1, e1) = e2) | (all_57_55 =
% 108.25/15.37 | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | BETA: splitting (1197) gives:
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | (1198) all_57_54 = e2 & op(e1, e1) = e2
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | ALPHA: (1198) implies:
% 108.25/15.37 | | | | | | | | | | | | | | | | | | (1199) op(e1, e1) = e2
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1018), (1199), (function-axioms) are
% 108.25/15.37 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #131.
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | (1200) all_57_55 = e2 & op(e0, e1) = e2
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | ALPHA: (1200) implies:
% 108.25/15.37 | | | | | | | | | | | | | | | | | | (1201) op(e0, e1) = e2
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (1180), (1201), (function-axioms) are
% 108.25/15.37 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #161.
% 108.25/15.37 | | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | Case 2:
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | (1202) all_55_2 = e1 | all_55_2 = e0
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | | REF_CLOSE: (1140), (1143), (1148), (1202) are inconsistent by
% 108.25/15.37 | | | | | | | | | | | | | | | | sub-proof #130.
% 108.25/15.37 | | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | | |
% 108.25/15.37 | | | | | | | | | End of split
% 108.25/15.37 | | | | | | | | |
% 108.25/15.37 | | | | | | | | End of split
% 108.25/15.37 | | | | | | | |
% 108.25/15.37 | | | | | | | Case 2:
% 108.25/15.37 | | | | | | | |
% 108.25/15.37 | | | | | | | | (1203) all_14_2 = e2
% 108.25/15.37 | | | | | | | | (1204) op(e2, e2) = all_14_1 & $i(all_14_1) & ( ~ (all_14_1 =
% 108.25/15.37 | | | | | | | | e3) | ( ~ (all_14_0 = e0) & op(e3, e2) = all_14_0
% 108.25/15.37 | | | | | | | | & $i(all_14_0)))
% 108.25/15.37 | | | | | | | |
% 108.25/15.37 | | | | | | | | ALPHA: (1204) implies:
% 108.25/15.37 | | | | | | | | (1205) op(e2, e2) = all_14_1
% 108.25/15.37 | | | | | | | |
% 108.25/15.37 | | | | | | | | COMBINE_EQS: (334), (1203) imply:
% 108.25/15.37 | | | | | | | | (1206) all_44_2 = e2
% 108.25/15.37 | | | | | | | |
% 108.25/15.37 | | | | | | | | REDUCE: (354), (1203) imply:
% 108.25/15.37 | | | | | | | | (1207) ~ (all_53_1 = e2)
% 108.25/15.37 | | | | | | | |
% 108.25/15.37 | | | | | | | | REDUCE: (357), (1203) imply:
% 108.25/15.37 | | | | | | | | (1208) ~ (all_53_4 = e2)
% 108.25/15.37 | | | | | | | |
% 108.25/15.37 | | | | | | | | REDUCE: (359), (1203) imply:
% 108.25/15.37 | | | | | | | | (1209) ~ (all_53_6 = e2)
% 108.25/15.37 | | | | | | | |
% 108.25/15.37 | | | | | | | | REDUCE: (363), (1203) imply:
% 108.25/15.37 | | | | | | | | (1210) ~ (all_53_9 = e2)
% 108.25/15.37 | | | | | | | |
% 108.25/15.37 | | | | | | | | REDUCE: (365), (1203) imply:
% 108.25/15.37 | | | | | | | | (1211) ~ (all_53_13 = e2)
% 108.25/15.37 | | | | | | | |
% 108.25/15.37 | | | | | | | | REDUCE: (50), (1203) imply:
% 108.25/15.37 | | | | | | | | (1212) op(e1, e1) = e2
% 108.25/15.37 | | | | | | | |
% 108.25/15.37 | | | | | | | | BETA: splitting (96) gives:
% 108.25/15.37 | | | | | | | |
% 108.25/15.37 | | | | | | | | Case 1:
% 108.25/15.37 | | | | | | | | |
% 108.25/15.37 | | | | | | | | | (1213) ~ (all_44_2 = e2)
% 108.25/15.37 | | | | | | | | |
% 108.25/15.37 | | | | | | | | | REDUCE: (1206), (1213) imply:
% 108.25/15.37 | | | | | | | | | (1214) $false
% 108.25/15.37 | | | | | | | | |
% 108.25/15.37 | | | | | | | | | CLOSE: (1214) is inconsistent.
% 108.25/15.37 | | | | | | | | |
% 108.25/15.37 | | | | | | | | Case 2:
% 108.25/15.37 | | | | | | | | |
% 108.25/15.37 | | | | | | | | | (1215) op(e2, e2) = all_44_1 & $i(all_44_1) & ( ~ (all_44_1
% 108.25/15.37 | | | | | | | | | = e0) | ( ~ (all_44_0 = e3) & op(e0, e2) =
% 108.25/15.37 | | | | | | | | | all_44_0 & $i(all_44_0)))
% 108.25/15.37 | | | | | | | | |
% 108.25/15.37 | | | | | | | | | ALPHA: (1215) implies:
% 108.25/15.37 | | | | | | | | | (1216) op(e2, e2) = all_44_1
% 108.25/15.37 | | | | | | | | | (1217) ~ (all_44_1 = e0) | ( ~ (all_44_0 = e3) & op(e0,
% 108.25/15.37 | | | | | | | | | e2) = all_44_0 & $i(all_44_0))
% 108.25/15.37 | | | | | | | | |
% 108.25/15.37 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_44_1,
% 108.25/15.37 | | | | | | | | | e2, e2, simplifying with (795), (1216) gives:
% 108.25/15.38 | | | | | | | | | (1218) all_44_1 = e0
% 108.25/15.38 | | | | | | | | |
% 108.25/15.38 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 108.25/15.38 | | | | | | | | | all_44_1, e2, e2, simplifying with (1205), (1216)
% 108.25/15.38 | | | | | | | | | gives:
% 108.25/15.38 | | | | | | | | | (1219) all_44_1 = all_14_1
% 108.25/15.38 | | | | | | | | |
% 108.25/15.38 | | | | | | | | | COMBINE_EQS: (1218), (1219) imply:
% 108.25/15.38 | | | | | | | | | (1220) all_14_1 = e0
% 108.25/15.38 | | | | | | | | |
% 108.25/15.38 | | | | | | | | | SIMP: (1220) implies:
% 108.25/15.38 | | | | | | | | | (1221) all_14_1 = e0
% 108.25/15.38 | | | | | | | | |
% 108.25/15.38 | | | | | | | | | BETA: splitting (1217) gives:
% 108.25/15.38 | | | | | | | | |
% 108.25/15.38 | | | | | | | | | Case 1:
% 108.25/15.38 | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | (1222) ~ (all_44_1 = e0)
% 108.25/15.38 | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | REDUCE: (1218), (1222) imply:
% 108.25/15.38 | | | | | | | | | | (1223) $false
% 108.25/15.38 | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | CLOSE: (1223) is inconsistent.
% 108.25/15.38 | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | Case 2:
% 108.25/15.38 | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | (1224) ~ (all_44_0 = e3) & op(e0, e2) = all_44_0 &
% 108.25/15.38 | | | | | | | | | | $i(all_44_0)
% 108.25/15.38 | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | ALPHA: (1224) implies:
% 108.25/15.38 | | | | | | | | | | (1225) op(e0, e2) = all_44_0
% 108.25/15.38 | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 108.25/15.38 | | | | | | | | | | all_44_0, e2, e0, simplifying with (162), (1225)
% 108.25/15.38 | | | | | | | | | | gives:
% 108.25/15.38 | | | | | | | | | | (1226) all_53_3 = all_44_0
% 108.25/15.38 | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | COMBINE_EQS: (250), (1226) imply:
% 108.25/15.38 | | | | | | | | | | (1227) all_55_2 = all_44_0
% 108.25/15.38 | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | REDUCE: (148), (1226) imply:
% 108.25/15.38 | | | | | | | | | | (1228) ~ (all_53_2 = all_44_0)
% 108.25/15.38 | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | REDUCE: (144), (1226) imply:
% 108.25/15.38 | | | | | | | | | | (1229) ~ (all_53_7 = all_44_0)
% 108.25/15.38 | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | SIMP: (1229) implies:
% 108.25/15.38 | | | | | | | | | | (1230) ~ (all_53_7 = all_44_0)
% 108.25/15.38 | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | REDUCE: (347), (1226) imply:
% 108.25/15.38 | | | | | | | | | | (1231) ~ (all_44_0 = all_6_2)
% 108.25/15.38 | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | BETA: splitting (69) gives:
% 108.25/15.38 | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | Case 1:
% 108.25/15.38 | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | (1232) ~ (all_26_2 = e2)
% 108.25/15.38 | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | REDUCE: (316), (1232) imply:
% 108.25/15.38 | | | | | | | | | | | (1233) ~ (all_4_2 = e2)
% 108.25/15.38 | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | BETA: splitting (72) gives:
% 108.25/15.38 | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | Case 1:
% 108.25/15.38 | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | (1234) ~ (all_28_2 = e3)
% 108.25/15.38 | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | REDUCE: (313), (1234) imply:
% 108.25/15.38 | | | | | | | | | | | | (1235) ~ (all_6_2 = e3)
% 108.25/15.38 | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | REF_CLOSE: (35), (109), (161), (169), (172), (173), (174),
% 108.25/15.38 | | | | | | | | | | | | (208), (217), (248), (343), (353), (378), (379),
% 108.25/15.38 | | | | | | | | | | | | (381), (793), (1210), (1235), (function-axioms)
% 108.25/15.38 | | | | | | | | | | | | are inconsistent by sub-proof #128.
% 108.25/15.38 | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | Case 2:
% 108.25/15.38 | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | (1236) all_28_2 = e3
% 108.25/15.38 | | | | | | | | | | | | (1237) op(e3, e3) = all_28_1 & $i(all_28_1) & ( ~
% 108.25/15.38 | | | | | | | | | | | | (all_28_1 = e1) | ( ~ (all_28_0 = e2) & op(e1,
% 108.25/15.38 | | | | | | | | | | | | e3) = all_28_0 & $i(all_28_0)))
% 108.25/15.38 | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | ALPHA: (1237) implies:
% 108.25/15.38 | | | | | | | | | | | | (1238) op(e3, e3) = all_28_1
% 108.25/15.38 | | | | | | | | | | | | (1239) ~ (all_28_1 = e1) | ( ~ (all_28_0 = e2) & op(e1,
% 108.25/15.38 | | | | | | | | | | | | e3) = all_28_0 & $i(all_28_0))
% 108.25/15.38 | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | COMBINE_EQS: (313), (1236) imply:
% 108.25/15.38 | | | | | | | | | | | | (1240) all_6_2 = e3
% 108.25/15.38 | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | COMBINE_EQS: (801), (1240) imply:
% 108.25/15.38 | | | | | | | | | | | | (1241) all_30_1 = e3
% 108.25/15.38 | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | COMBINE_EQS: (332), (1240) imply:
% 108.25/15.38 | | | | | | | | | | | | (1242) all_36_2 = e3
% 108.25/15.38 | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | REDUCE: (349), (1240) imply:
% 108.25/15.38 | | | | | | | | | | | | (1243) ~ (all_53_4 = e3)
% 108.25/15.38 | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | REDUCE: (353), (1240) imply:
% 108.25/15.38 | | | | | | | | | | | | (1244) ~ (all_53_12 = e3)
% 108.25/15.38 | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | REDUCE: (1231), (1240) imply:
% 108.25/15.38 | | | | | | | | | | | | (1245) ~ (all_44_0 = e3)
% 108.25/15.38 | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | BETA: splitting (84) gives:
% 108.25/15.38 | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | Case 1:
% 108.25/15.38 | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | (1246) ~ (all_36_2 = e3)
% 108.25/15.38 | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | REDUCE: (1242), (1246) imply:
% 108.25/15.38 | | | | | | | | | | | | | (1247) $false
% 108.25/15.38 | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | CLOSE: (1247) is inconsistent.
% 108.25/15.38 | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | Case 2:
% 108.25/15.38 | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | (1248) op(e3, e3) = all_36_1 & $i(all_36_1) & ( ~
% 108.25/15.38 | | | | | | | | | | | | | (all_36_1 = e2) | ( ~ (all_36_0 = e1) & op(e2,
% 108.25/15.38 | | | | | | | | | | | | | e3) = all_36_0 & $i(all_36_0)))
% 108.25/15.38 | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | ALPHA: (1248) implies:
% 108.25/15.38 | | | | | | | | | | | | | (1249) op(e3, e3) = all_36_1
% 108.25/15.38 | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | BETA: splitting (800) gives:
% 108.25/15.38 | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | Case 1:
% 108.25/15.38 | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | (1250) ~ (all_30_1 = e3)
% 108.25/15.38 | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | REDUCE: (1241), (1250) imply:
% 108.25/15.38 | | | | | | | | | | | | | | (1251) $false
% 108.25/15.38 | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | CLOSE: (1251) is inconsistent.
% 108.25/15.38 | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | Case 2:
% 108.25/15.38 | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | (1252) ~ (all_30_0 = e1) & op(e3, e0) = all_30_0 &
% 108.25/15.38 | | | | | | | | | | | | | | $i(all_30_0)
% 108.25/15.38 | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | ALPHA: (1252) implies:
% 108.25/15.38 | | | | | | | | | | | | | | (1253) op(e3, e0) = all_30_0
% 108.25/15.38 | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 108.25/15.38 | | | | | | | | | | | | | | all_30_0, e0, e3, simplifying with (172), (1253)
% 108.25/15.38 | | | | | | | | | | | | | | gives:
% 108.25/15.38 | | | | | | | | | | | | | | (1254) all_53_12 = all_30_0
% 108.25/15.38 | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 108.25/15.38 | | | | | | | | | | | | | | all_36_1, e3, e3, simplifying with (35), (1249)
% 108.25/15.38 | | | | | | | | | | | | | | gives:
% 108.25/15.38 | | | | | | | | | | | | | | (1255) all_36_1 = all_4_2
% 108.25/15.38 | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_1,
% 108.25/15.38 | | | | | | | | | | | | | | all_36_1, e3, e3, simplifying with (1238), (1249)
% 108.25/15.38 | | | | | | | | | | | | | | gives:
% 108.25/15.38 | | | | | | | | | | | | | | (1256) all_36_1 = all_28_1
% 108.25/15.38 | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | COMBINE_EQS: (1255), (1256) imply:
% 108.25/15.38 | | | | | | | | | | | | | | (1257) all_28_1 = all_4_2
% 108.25/15.38 | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | REDUCE: (374), (1254) imply:
% 108.25/15.38 | | | | | | | | | | | | | | (1258) ~ (all_30_0 = all_4_2)
% 108.25/15.38 | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 108.25/15.38 | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | Case 1:
% 108.25/15.38 | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | (1259) ~ (all_34_2 = e1)
% 108.25/15.38 | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | REDUCE: (311), (1259) imply:
% 108.25/15.38 | | | | | | | | | | | | | | | (1260) ~ (all_4_2 = e1)
% 108.25/15.38 | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 108.25/15.38 | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | Case 1:
% 108.25/15.38 | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | (1261) all_55_15 = e3
% 108.25/15.38 | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (1261) imply:
% 108.25/15.38 | | | | | | | | | | | | | | | | (1262) all_4_2 = e3
% 108.25/15.38 | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | SIMP: (1262) implies:
% 108.25/15.38 | | | | | | | | | | | | | | | | (1263) all_4_2 = e3
% 108.25/15.38 | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | REDUCE: (366), (1263) imply:
% 108.25/15.38 | | | | | | | | | | | | | | | | (1264) ~ (all_53_6 = e3)
% 108.25/15.38 | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | REDUCE: (377), (1263) imply:
% 108.25/15.38 | | | | | | | | | | | | | | | | (1265) ~ (all_53_15 = e3)
% 108.25/15.38 | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 108.25/15.38 | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.38 | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | (1266) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 108.25/15.38 | | | | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 108.25/15.38 | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | ALPHA: (1266) implies:
% 108.25/15.38 | | | | | | | | | | | | | | | | | (1267) op(e3, e2) = e3
% 108.25/15.38 | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (1265), (1267), (function-axioms) are
% 108.25/15.38 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #214.
% 108.25/15.38 | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.38 | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | (1268) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 108.25/15.38 | | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 108.25/15.38 | | | | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 108.25/15.38 | | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 108.25/15.38 | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | BETA: splitting (1268) gives:
% 108.25/15.38 | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.38 | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | (1269) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 108.25/15.38 | | | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 108.25/15.38 | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | ALPHA: (1269) implies:
% 108.25/15.38 | | | | | | | | | | | | | | | | | | (1270) op(e1, e2) = e1
% 108.25/15.38 | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 108.25/15.38 | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.38 | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | (1271) (all_57_56 = e3 & op(e1, e3) = e3) | (all_57_57 =
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3)
% 108.25/15.38 | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | BETA: splitting (1271) gives:
% 108.25/15.38 | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | (1272) all_57_56 = e3 & op(e1, e3) = e3
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1264), (1272), (function-axioms) are
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #127.
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | (1273) all_57_57 = e3 & op(e1, e2) = e3
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | ALPHA: (1273) implies:
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | (1274) op(e1, e2) = e3
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e1,
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (166), (1270) gives:
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | (1275) all_53_7 = e1
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e3,
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (166), (1274) gives:
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | (1276) all_53_7 = e3
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1275), (1276) imply:
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | (1277) e3 = e1
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | SIMP: (1277) implies:
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | (1278) e3 = e1
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1278) imply:
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | (1279) $false
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | | CLOSE: (1279) is inconsistent.
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.38 | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.38 | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | (1280) (all_57_58 = e3 & op(e1, e1) = e3) | (all_57_59 =
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 108.25/15.38 | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (1212), (1243), (1280),
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.25/15.38 | | | | | | | | | | | | | | | | | | | #125.
% 108.25/15.38 | | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.38 | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.38 | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | (1281) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 108.25/15.38 | | | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 108.25/15.38 | | | | | | | | | | | | | | | | | |
% 108.25/15.38 | | | | | | | | | | | | | | | | | | ALPHA: (1281) implies:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | (1282) op(e0, e2) = e0
% 108.25/15.39 | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (789), (1282), (function-axioms) are
% 108.25/15.39 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 108.25/15.39 | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | End of split
% 108.25/15.39 | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | End of split
% 108.25/15.39 | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | Case 2:
% 108.25/15.39 | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | (1283) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 108.25/15.39 | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | REF_CLOSE: (339), (378), (1233), (1260), (1283) are
% 108.25/15.39 | | | | | | | | | | | | | | | | inconsistent by sub-proof #191.
% 108.25/15.39 | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | End of split
% 108.25/15.39 | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | Case 2:
% 108.25/15.39 | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | (1284) all_34_2 = e1
% 108.25/15.39 | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | COMBINE_EQS: (311), (1284) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | (1285) all_4_2 = e1
% 108.25/15.39 | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | SIMP: (1285) implies:
% 108.25/15.39 | | | | | | | | | | | | | | | (1286) all_4_2 = e1
% 108.25/15.39 | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | COMBINE_EQS: (1257), (1286) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | (1287) all_28_1 = e1
% 108.25/15.39 | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | REDUCE: (355), (1286) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | (1288) ~ (all_53_2 = e1)
% 108.25/15.39 | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | REDUCE: (366), (1286) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | (1289) ~ (all_53_6 = e1)
% 108.25/15.39 | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | REDUCE: (371), (1286) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | (1290) ~ (all_53_10 = e1)
% 108.25/15.39 | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | REDUCE: (375), (1286) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | (1291) ~ (all_53_13 = e1)
% 108.25/15.39 | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | REDUCE: (377), (1286) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | (1292) ~ (all_53_15 = e1)
% 108.25/15.39 | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | REDUCE: (1258), (1286) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | (1293) ~ (all_30_0 = e1)
% 108.25/15.39 | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | BETA: splitting (1239) gives:
% 108.25/15.39 | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | Case 1:
% 108.25/15.39 | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | (1294) ~ (all_28_1 = e1)
% 108.25/15.39 | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | REDUCE: (1287), (1294) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | | (1295) $false
% 108.25/15.39 | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | CLOSE: (1295) is inconsistent.
% 108.25/15.39 | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | Case 2:
% 108.25/15.39 | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | (1296) ~ (all_28_0 = e2) & op(e1, e3) = all_28_0 &
% 108.25/15.39 | | | | | | | | | | | | | | | | $i(all_28_0)
% 108.25/15.39 | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | ALPHA: (1296) implies:
% 108.25/15.39 | | | | | | | | | | | | | | | | (1297) op(e1, e3) = all_28_0
% 108.25/15.39 | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 108.25/15.39 | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.39 | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | (1298) (all_57_104 = e1 & op(e3, e3) = e1) | (all_57_105
% 108.25/15.39 | | | | | | | | | | | | | | | | | = e1 & op(e3, e2) = e1)
% 108.25/15.39 | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | BETA: splitting (1298) gives:
% 108.25/15.39 | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.39 | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 108.25/15.39 | | | | | | | | | | | | | | | | | | all_28_0, e3, e1, simplifying with (167), (1297)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | gives:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | (1299) all_53_6 = all_28_0
% 108.25/15.39 | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (1299) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | (1300) all_55_7 = all_28_0
% 108.25/15.39 | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | REDUCE: (140), (1299) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | (1301) ~ (all_53_4 = all_28_0)
% 108.25/15.39 | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | REDUCE: (132), (1299) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | (1302) ~ (all_53_7 = all_28_0)
% 108.25/15.39 | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | SIMP: (1302) implies:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | (1303) ~ (all_53_7 = all_28_0)
% 108.25/15.39 | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | REDUCE: (131), (1299) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | (1304) ~ (all_53_10 = all_28_0)
% 108.25/15.39 | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | SIMP: (1304) implies:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | (1305) ~ (all_53_10 = all_28_0)
% 108.25/15.39 | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | REDUCE: (1209), (1299) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | (1306) ~ (all_28_0 = e2)
% 108.25/15.39 | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 108.25/15.39 | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | (1307) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | ALPHA: (1307) implies:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | (1308) op(e3, e2) = e3
% 108.25/15.39 | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | e3, e2, e3, simplifying with (174), (1308) gives:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | (1309) all_53_15 = e3
% 108.25/15.39 | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | REDUCE: (113), (1309) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | (1310) ~ (all_53_13 = e3)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | (1311) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | ALPHA: (1311) implies:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | (1312) op(e3, e1) = e3
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (1310), (1312), (function-axioms) are
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #232.
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | (1313) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1313) gives:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | (1314) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1314) implies:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | (1315) op(e2, e1) = e2
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1210), (1315), (function-axioms) are
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #231.
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | (1316) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1316) implies:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | (1317) op(e0, e1) = e0
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | (1318) all_55_13 = e3
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (1318) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | (1319) all_53_13 = e3
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1319) implies:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | (1320) all_53_13 = e3
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1310), (1320) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | (1321) $false
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1321) is inconsistent.
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | (1322) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (161), (273), (1211), (1291), (1317),
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | (1322), (function-axioms) are inconsistent by
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | sub-proof #124.
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.39 | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | (1323) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 108.25/15.39 | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | BETA: splitting (1323) gives:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | (1324) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | ALPHA: (1324) implies:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | (1325) op(e1, e2) = e1
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e1,
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (166), (1325) gives:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | (1326) all_53_7 = e1
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (1326) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | (1327) ~ (all_53_4 = e1)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | REDUCE: (1303), (1326) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | (1328) ~ (all_28_0 = e1)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | SIMP: (1328) implies:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | (1329) ~ (all_28_0 = e1)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | (1330) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1330) implies:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | (1331) op(e3, e0) = e3
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (1244), (1331), (function-axioms) are
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | (1332) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1332) gives:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | (1333) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1333) implies:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | (1334) op(e2, e0) = e2
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | (1335) all_55_2 = e3
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1227), (1335) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | (1336) all_44_0 = e3
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1336) implies:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | (1337) all_44_0 = e3
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1245), (1337) imply:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | (1338) $false
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1338) is inconsistent.
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | (1339) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | | (1340) all_55_4 = e3
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (252), (1243), (1340) are inconsistent by
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #123.
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.39 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | (1341) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1341) gives:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | (1342) all_55_4 = e2
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (1342) imply:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | (1343) all_53_4 = e2
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1208), (1343) imply:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | (1344) $false
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1344) is inconsistent.
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | (1345) all_55_4 = e1 | all_55_4 = e0
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1345) gives:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (1346) all_55_4 = e1
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (1346) imply:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (1347) all_53_4 = e1
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1327), (1347) imply:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (1348) $false
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1348) is inconsistent.
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (1349) all_55_4 = e0
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (1349) imply:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (1350) all_53_4 = e0
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1301), (1350) imply:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (1351) ~ (all_28_0 = e0)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1351) implies:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (1352) ~ (all_28_0 = e0)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1353) all_55_7 = e3
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1300), (1353) imply:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1354) all_28_0 = e3
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1354) implies:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1355) all_28_0 = e3
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1305), (1355) imply:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1356) ~ (all_53_10 = e3)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1357) all_55_11 = e3
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (1356), (1357) are inconsistent by
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #144.
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1358) all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1358) gives:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1359) all_55_11 = e2
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (1359) imply:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1360) all_53_10 = e2
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1360) implies:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1361) all_53_10 = e2
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (1361) imply:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1362) ~ (all_53_8 = e2)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1334), (1362), (function-axioms) are
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #227.
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1363) ~ (all_55_11 = e2)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1364) all_55_11 = e1 | all_55_11 = e0
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (271), (1363) imply:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1365) ~ (all_53_10 = e2)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1366) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_18 & op(e2, e3) = e2 & $i(all_52_18)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (1365), (1366), (function-axioms) are
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #215.
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1367) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22))
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1367) gives:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1368) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1368) implies:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1369) op(e1, e3) = e1
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1289), (1369), (function-axioms) are
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #223.
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1370) all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1370) implies:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1371) op(e0, e3) = e0
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1339) gives:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1372) all_55_2 = e2
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1227), (1372) imply:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1373) all_44_0 = e2
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1228), (1373) imply:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1374) ~ (all_53_2 = e2)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (163), (205), (251), (271), (1288), (1290),
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1364), (1371), (1374), (function-axioms) are
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #120.
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1375) all_55_2 = e1 | all_55_2 = e0
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (166), (250), (789), (1325), (1375),
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #119.
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1376) all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1300), (1306), (1329), (1352), (1376) are
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #142.
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | (1377) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1377) implies:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | (1378) op(e1, e0) = e1
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1327), (1378), (function-axioms) are
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #226.
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | (1379) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | ALPHA: (1379) implies:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | (1380) op(e0, e2) = e0
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (789), (1380), (function-axioms) are
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | (1381) all_57_105 = e1 & op(e3, e2) = e1
% 108.25/15.40 | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | ALPHA: (1381) implies:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | (1382) op(e3, e2) = e1
% 108.25/15.40 | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (1292), (1382), (function-axioms) are
% 108.25/15.40 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #205.
% 108.25/15.40 | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | (1383) (all_57_106 = e1 & op(e3, e1) = e1) | (all_57_107
% 108.25/15.40 | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1)
% 108.25/15.40 | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | BETA: splitting (1383) gives:
% 108.25/15.40 | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.40 | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | (1384) all_57_106 = e1 & op(e3, e1) = e1
% 108.25/15.40 | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | ALPHA: (1384) implies:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | (1385) op(e3, e1) = e1
% 108.25/15.40 | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (1291), (1385), (function-axioms) are
% 108.25/15.40 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #118.
% 108.25/15.40 | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | (1386) all_57_107 = e1 & op(e3, e0) = e1
% 108.25/15.40 | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | ALPHA: (1386) implies:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | (1387) op(e3, e0) = e1
% 108.25/15.40 | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_0, e1,
% 108.25/15.40 | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (1253), (1387) gives:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | (1388) all_30_0 = e1
% 108.25/15.40 | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | REDUCE: (1293), (1388) imply:
% 108.25/15.40 | | | | | | | | | | | | | | | | | | (1389) $false
% 108.25/15.40 | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | | CLOSE: (1389) is inconsistent.
% 108.25/15.40 | | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | End of split
% 108.25/15.40 | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | (1390) all_26_2 = e2
% 108.25/15.40 | | | | | | | | | | | (1391) op(e2, e2) = all_26_1 & $i(all_26_1) & ( ~
% 108.25/15.40 | | | | | | | | | | | (all_26_1 = e0) | ( ~ (all_26_0 = e1) & op(e0,
% 108.25/15.40 | | | | | | | | | | | e2) = all_26_0 & $i(all_26_0)))
% 108.25/15.40 | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | ALPHA: (1391) implies:
% 108.25/15.40 | | | | | | | | | | | (1392) op(e2, e2) = all_26_1
% 108.25/15.40 | | | | | | | | | | | (1393) ~ (all_26_1 = e0) | ( ~ (all_26_0 = e1) & op(e0,
% 108.25/15.40 | | | | | | | | | | | e2) = all_26_0 & $i(all_26_0))
% 108.25/15.40 | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | COMBINE_EQS: (316), (1390) imply:
% 108.25/15.40 | | | | | | | | | | | (1394) all_4_2 = e2
% 108.25/15.40 | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | SIMP: (1394) implies:
% 108.25/15.40 | | | | | | | | | | | (1395) all_4_2 = e2
% 108.25/15.40 | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | COMBINE_EQS: (277), (1395) imply:
% 108.25/15.40 | | | | | | | | | | | (1396) all_50_2 = e2
% 108.25/15.40 | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | REDUCE: (355), (1395) imply:
% 108.25/15.40 | | | | | | | | | | | (1397) ~ (all_53_2 = e2)
% 108.25/15.40 | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | REDUCE: (374), (1395) imply:
% 108.25/15.40 | | | | | | | | | | | (1398) ~ (all_53_12 = e2)
% 108.25/15.40 | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | BETA: splitting (105) gives:
% 108.25/15.40 | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | Case 1:
% 108.25/15.40 | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | (1399) ~ (all_50_2 = e2)
% 108.25/15.40 | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | REDUCE: (1396), (1399) imply:
% 108.25/15.40 | | | | | | | | | | | | (1400) $false
% 108.25/15.40 | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | | CLOSE: (1400) is inconsistent.
% 108.25/15.40 | | | | | | | | | | | |
% 108.25/15.40 | | | | | | | | | | | Case 2:
% 108.25/15.40 | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | (1401) op(e2, e2) = all_50_1 & $i(all_50_1) & ( ~
% 108.25/15.41 | | | | | | | | | | | | (all_50_1 = e1) | ( ~ (all_50_0 = e0) & op(e1,
% 108.25/15.41 | | | | | | | | | | | | e2) = all_50_0 & $i(all_50_0)))
% 108.25/15.41 | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | ALPHA: (1401) implies:
% 108.25/15.41 | | | | | | | | | | | | (1402) op(e2, e2) = all_50_1
% 108.25/15.41 | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | BETA: splitting (236) gives:
% 108.25/15.41 | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | Case 1:
% 108.25/15.41 | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | (1403) (all_57_20 = e2 & op(e3, e0) = e2) | (all_57_21 =
% 108.25/15.41 | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 108.25/15.41 | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | BETA: splitting (1403) gives:
% 108.25/15.41 | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | Case 1:
% 108.25/15.41 | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | (1404) all_57_20 = e2 & op(e3, e0) = e2
% 108.25/15.41 | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | ALPHA: (1404) implies:
% 108.25/15.41 | | | | | | | | | | | | | | (1405) op(e3, e0) = e2
% 108.25/15.41 | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | REF_CLOSE: (172), (1398), (1405), (function-axioms) are
% 108.25/15.41 | | | | | | | | | | | | | | inconsistent by sub-proof #117.
% 108.25/15.41 | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | Case 2:
% 108.25/15.41 | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | (1406) all_57_21 = e2 & op(e2, e0) = e2
% 108.25/15.41 | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | ALPHA: (1406) implies:
% 108.25/15.41 | | | | | | | | | | | | | | (1407) op(e2, e0) = e2
% 108.25/15.41 | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 108.25/15.41 | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | Case 1:
% 108.25/15.41 | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | (1408) (all_57_16 = e2 & op(e0, e3) = e2) | (all_57_17 =
% 108.25/15.41 | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 108.25/15.41 | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | BETA: splitting (1408) gives:
% 108.25/15.41 | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | Case 1:
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | (1409) all_57_16 = e2 & op(e0, e3) = e2
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | ALPHA: (1409) implies:
% 108.25/15.41 | | | | | | | | | | | | | | | | (1410) op(e0, e3) = e2
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1397), (1410), (function-axioms) are
% 108.25/15.41 | | | | | | | | | | | | | | | | inconsistent by sub-proof #164.
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | Case 2:
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | (1411) all_57_17 = e2 & op(e0, e2) = e2
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | ALPHA: (1411) implies:
% 108.25/15.41 | | | | | | | | | | | | | | | | (1412) op(e0, e2) = e2
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_44_0, e2,
% 108.25/15.41 | | | | | | | | | | | | | | | | e2, e0, simplifying with (1225), (1412) gives:
% 108.25/15.41 | | | | | | | | | | | | | | | | (1413) all_44_0 = e2
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e2,
% 108.25/15.41 | | | | | | | | | | | | | | | | e0, e2, simplifying with (168), (1407) gives:
% 108.25/15.41 | | | | | | | | | | | | | | | | (1414) all_53_8 = e2
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_50_1,
% 108.25/15.41 | | | | | | | | | | | | | | | | e2, e2, simplifying with (795), (1402) gives:
% 108.25/15.41 | | | | | | | | | | | | | | | | (1415) all_50_1 = e0
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_1,
% 108.25/15.41 | | | | | | | | | | | | | | | | all_50_1, e2, e2, simplifying with (1392), (1402)
% 108.25/15.41 | | | | | | | | | | | | | | | | gives:
% 108.25/15.41 | | | | | | | | | | | | | | | | (1416) all_50_1 = all_26_1
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | COMBINE_EQS: (1415), (1416) imply:
% 108.25/15.41 | | | | | | | | | | | | | | | | (1417) all_26_1 = e0
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | SIMP: (1417) implies:
% 108.25/15.41 | | | | | | | | | | | | | | | | (1418) all_26_1 = e0
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | REDUCE: (1230), (1413) imply:
% 108.25/15.41 | | | | | | | | | | | | | | | | (1419) ~ (all_53_7 = e2)
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | REDUCE: (127), (1414) imply:
% 108.25/15.41 | | | | | | | | | | | | | | | | (1420) ~ (all_53_9 = e2)
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | REDUCE: (124), (1414) imply:
% 108.25/15.41 | | | | | | | | | | | | | | | | (1421) ~ (all_53_12 = e2)
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | REDUCE: (1231), (1413) imply:
% 108.25/15.41 | | | | | | | | | | | | | | | | (1422) ~ (all_6_2 = e2)
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | BETA: splitting (1393) gives:
% 108.25/15.41 | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.41 | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | (1423) ~ (all_26_1 = e0)
% 108.25/15.41 | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | REDUCE: (1418), (1423) imply:
% 108.25/15.41 | | | | | | | | | | | | | | | | | (1424) $false
% 108.25/15.41 | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | CLOSE: (1424) is inconsistent.
% 108.25/15.41 | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.41 | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | (1425) ~ (all_26_0 = e1) & op(e0, e2) = all_26_0 &
% 108.25/15.41 | | | | | | | | | | | | | | | | | $i(all_26_0)
% 108.25/15.41 | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | ALPHA: (1425) implies:
% 108.25/15.41 | | | | | | | | | | | | | | | | | (1426) op(e0, e2) = all_26_0
% 108.25/15.41 | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_26_0,
% 108.25/15.41 | | | | | | | | | | | | | | | | | e2, e0, simplifying with (1412), (1426) gives:
% 108.25/15.41 | | | | | | | | | | | | | | | | | (1427) all_26_0 = e2
% 108.25/15.41 | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 108.25/15.41 | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.41 | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | (1428) ~ (all_28_2 = e3)
% 108.25/15.41 | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | REDUCE: (313), (1428) imply:
% 108.25/15.41 | | | | | | | | | | | | | | | | | | (1429) ~ (all_6_2 = e3)
% 108.25/15.41 | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (109), (161), (169), (172), (173), (174),
% 108.25/15.41 | | | | | | | | | | | | | | | | | | (208), (217), (248), (343), (353), (378), (379),
% 108.25/15.41 | | | | | | | | | | | | | | | | | | (381), (793), (1210), (1429), (function-axioms)
% 108.25/15.41 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #128.
% 108.25/15.41 | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.41 | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | (1430) all_28_2 = e3
% 108.25/15.41 | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (313), (1430) imply:
% 108.25/15.41 | | | | | | | | | | | | | | | | | | (1431) all_6_2 = e3
% 108.25/15.41 | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | SIMP: (1431) implies:
% 108.25/15.41 | | | | | | | | | | | | | | | | | | (1432) all_6_2 = e3
% 108.25/15.41 | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (801), (1432) imply:
% 108.25/15.41 | | | | | | | | | | | | | | | | | | (1433) all_30_1 = e3
% 108.25/15.41 | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | REDUCE: (349), (1432) imply:
% 108.25/15.41 | | | | | | | | | | | | | | | | | | (1434) ~ (all_53_4 = e3)
% 108.25/15.41 | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | REDUCE: (353), (1432) imply:
% 108.25/15.41 | | | | | | | | | | | | | | | | | | (1435) ~ (all_53_12 = e3)
% 108.25/15.41 | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | BETA: splitting (800) gives:
% 108.25/15.41 | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | Case 1:
% 108.25/15.41 | | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | (1436) ~ (all_30_1 = e3)
% 108.25/15.41 | | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | REDUCE: (1433), (1436) imply:
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | (1437) $false
% 108.25/15.41 | | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | CLOSE: (1437) is inconsistent.
% 108.25/15.41 | | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | Case 2:
% 108.25/15.41 | | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | (1438) ~ (all_30_0 = e1) & op(e3, e0) = all_30_0 &
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | $i(all_30_0)
% 108.25/15.41 | | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | ALPHA: (1438) implies:
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | (1439) ~ (all_30_0 = e1)
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | (1440) op(e3, e0) = all_30_0
% 108.25/15.41 | | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | all_30_0, e0, e3, simplifying with (172), (1440)
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | gives:
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | (1441) all_53_12 = all_30_0
% 108.25/15.41 | | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (1441) imply:
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | (1442) all_55_12 = all_30_0
% 108.25/15.41 | | | | | | | | | | | | | | | | | | |
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | REDUCE: (137), (1441) imply:
% 108.25/15.41 | | | | | | | | | | | | | | | | | | | (1443) ~ (all_53_4 = all_30_0)
% 108.25/15.41 | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | REDUCE: (1435), (1441) imply:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | (1444) ~ (all_30_0 = e3)
% 108.69/15.41 | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | REDUCE: (1398), (1441) imply:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | (1445) ~ (all_30_0 = e2)
% 108.69/15.41 | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | (1446) all_55_12 = e3
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1442), (1446) imply:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | (1447) all_30_0 = e3
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | SIMP: (1447) implies:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | (1448) all_30_0 = e3
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (1444), (1448) imply:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | (1449) $false
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | CLOSE: (1449) is inconsistent.
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | (1450) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1450) gives:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | (1451) all_55_12 = e2
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1442), (1451) imply:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | (1452) all_30_0 = e2
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | SIMP: (1452) implies:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | (1453) all_30_0 = e2
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1445), (1453) imply:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | (1454) $false
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1454) is inconsistent.
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | (1455) ~ (all_55_12 = e2)
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | (1456) all_55_12 = e1 | all_55_12 = e0
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1456) gives:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | (1457) all_55_12 = e1
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1442), (1457) imply:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | (1458) all_30_0 = e1
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1458) implies:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | (1459) all_30_0 = e1
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1439), (1459) imply:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | (1460) $false
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1460) is inconsistent.
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | (1461) all_55_12 = e0
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1442), (1461) imply:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | (1462) all_30_0 = e0
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1462) implies:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | (1463) all_30_0 = e0
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1443), (1463) imply:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | (1464) ~ (all_53_4 = e0)
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1445), (1463) imply:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | (1465) ~ (e2 = e0)
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | (1466) all_55_4 = e3
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (252), (1434), (1466) are inconsistent by
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #123.
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | (1467) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1467) gives:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | (1468) all_55_4 = e2
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (252), (1208), (1468) are inconsistent by
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #116.
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | (1469) all_55_4 = e1 | all_55_4 = e0
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1469) gives:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | | (1470) all_55_4 = e1
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (1470) imply:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | | (1471) all_53_4 = e1
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1471) implies:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | | (1472) all_53_4 = e1
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (1472) imply:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | | (1473) ~ (all_53_7 = e1)
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1473) implies:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | | (1474) ~ (all_53_7 = e1)
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (1475) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1475) implies:
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (1476) op(e3, e2) = e3
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1477) all_55_6 = e3
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (1477) imply:
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1478) all_53_7 = e3
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (1478) imply:
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1479) ~ (all_53_15 = e3)
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1479) implies:
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1480) ~ (all_53_15 = e3)
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (1476), (1480), (function-axioms) are
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #214.
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1481) all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (790), (1419), (1474), (1481) are
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #114.
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (1482) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (166), (1412), (1474), (1482),
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | | #162.
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | (1483) all_55_4 = e0
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (252), (1464), (1483) are inconsistent by
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #113.
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | Case 2:
% 108.69/15.42 | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | (1484) (all_57_18 = e2 & op(e0, e1) = e2) | (all_57_19 =
% 108.69/15.42 | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 108.69/15.42 | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | | REF_CLOSE: (38), (161), (381), (1207), (1484),
% 108.69/15.42 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.69/15.42 | | | | | | | | | | | | | | | #159.
% 108.69/15.42 | | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | Case 2:
% 108.69/15.42 | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | (1485) (all_57_22 = e2 & op(e1, e0) = e2) | (all_57_23 =
% 108.69/15.42 | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 108.69/15.42 | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | BETA: splitting (1485) gives:
% 108.69/15.42 | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | Case 1:
% 108.69/15.42 | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | (1486) all_57_22 = e2 & op(e1, e0) = e2
% 108.69/15.42 | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | ALPHA: (1486) implies:
% 108.69/15.42 | | | | | | | | | | | | | | (1487) op(e1, e0) = e2
% 108.69/15.42 | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | REF_CLOSE: (164), (1208), (1487), (function-axioms) are
% 108.69/15.42 | | | | | | | | | | | | | | inconsistent by sub-proof #112.
% 108.69/15.42 | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | Case 2:
% 108.69/15.42 | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | (1488) all_57_23 = e2 & op(e0, e0) = e2
% 108.69/15.42 | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | ALPHA: (1488) implies:
% 108.69/15.42 | | | | | | | | | | | | | | (1489) op(e0, e0) = e2
% 108.69/15.42 | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | | REF_CLOSE: (38), (381), (1489), (function-axioms) are
% 108.69/15.42 | | | | | | | | | | | | | | inconsistent by sub-proof #160.
% 108.69/15.42 | | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | End of split
% 108.69/15.42 | | | | | | | | |
% 108.69/15.42 | | | | | | | | End of split
% 108.69/15.42 | | | | | | | |
% 108.69/15.42 | | | | | | | End of split
% 108.69/15.42 | | | | | | |
% 108.69/15.42 | | | | | | End of split
% 108.69/15.42 | | | | | |
% 108.69/15.42 | | | | | End of split
% 108.69/15.42 | | | | |
% 108.69/15.42 | | | | Case 2:
% 108.69/15.42 | | | | |
% 108.69/15.42 | | | | | (1490) all_10_2 = e3
% 108.69/15.42 | | | | | (1491) op(e3, e3) = all_10_1 & $i(all_10_1) & ( ~ (all_10_1 = e0) |
% 108.69/15.42 | | | | | ( ~ (all_10_0 = e1) & op(e0, e3) = all_10_0 &
% 108.69/15.42 | | | | | $i(all_10_0)))
% 108.69/15.42 | | | | |
% 108.69/15.42 | | | | | ALPHA: (1491) implies:
% 108.69/15.42 | | | | | (1492) op(e3, e3) = all_10_1
% 108.69/15.42 | | | | |
% 108.69/15.42 | | | | | COMBINE_EQS: (335), (1490) imply:
% 108.69/15.42 | | | | | (1493) all_48_2 = e3
% 108.69/15.42 | | | | |
% 108.69/15.42 | | | | | REDUCE: (356), (1490) imply:
% 108.69/15.42 | | | | | (1494) ~ (all_53_3 = e3)
% 108.69/15.42 | | | | |
% 108.69/15.42 | | | | | REDUCE: (367), (1490) imply:
% 108.69/15.42 | | | | | (1495) ~ (all_53_7 = e3)
% 108.69/15.42 | | | | |
% 108.69/15.42 | | | | | REDUCE: (369), (1490) imply:
% 108.69/15.42 | | | | | (1496) ~ (all_53_9 = e3)
% 108.69/15.42 | | | | |
% 108.69/15.42 | | | | | REDUCE: (370), (1490) imply:
% 108.69/15.42 | | | | | (1497) ~ (all_53_10 = e3)
% 108.69/15.42 | | | | |
% 108.69/15.42 | | | | | REDUCE: (373), (1490) imply:
% 108.69/15.42 | | | | | (1498) ~ (all_53_15 = e3)
% 108.69/15.42 | | | | |
% 108.69/15.42 | | | | | REDUCE: (44), (1490) imply:
% 108.69/15.42 | | | | | (1499) op(e2, e2) = e3
% 108.69/15.42 | | | | |
% 108.69/15.42 | | | | | BETA: splitting (102) gives:
% 108.69/15.42 | | | | |
% 108.69/15.42 | | | | | Case 1:
% 108.69/15.42 | | | | | |
% 108.69/15.42 | | | | | | (1500) ~ (all_48_2 = e3)
% 108.69/15.42 | | | | | |
% 108.69/15.42 | | | | | | REDUCE: (1493), (1500) imply:
% 108.69/15.42 | | | | | | (1501) $false
% 108.69/15.42 | | | | | |
% 108.69/15.42 | | | | | | CLOSE: (1501) is inconsistent.
% 108.69/15.42 | | | | | |
% 108.69/15.42 | | | | | Case 2:
% 108.69/15.42 | | | | | |
% 108.69/15.42 | | | | | | (1502) op(e3, e3) = all_48_1 & $i(all_48_1) & ( ~ (all_48_1 = e1)
% 108.69/15.42 | | | | | | | ( ~ (all_48_0 = e0) & op(e1, e3) = all_48_0 &
% 108.69/15.42 | | | | | | $i(all_48_0)))
% 108.69/15.42 | | | | | |
% 108.69/15.42 | | | | | | ALPHA: (1502) implies:
% 108.69/15.42 | | | | | | (1503) op(e3, e3) = all_48_1
% 108.69/15.42 | | | | | |
% 108.69/15.42 | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, all_48_1,
% 108.69/15.42 | | | | | | e3, e3, simplifying with (35), (1503) gives:
% 108.69/15.42 | | | | | | (1504) all_48_1 = all_4_2
% 108.69/15.42 | | | | | |
% 108.69/15.42 | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 108.69/15.42 | | | | | | all_48_1, e3, e3, simplifying with (1492), (1503)
% 108.69/15.42 | | | | | | gives:
% 108.69/15.42 | | | | | | (1505) all_48_1 = all_10_1
% 108.69/15.42 | | | | | |
% 108.69/15.42 | | | | | | COMBINE_EQS: (1504), (1505) imply:
% 108.69/15.42 | | | | | | (1506) all_10_1 = all_4_2
% 108.69/15.42 | | | | | |
% 108.69/15.42 | | | | | | BETA: splitting (51) gives:
% 108.69/15.42 | | | | | |
% 108.69/15.42 | | | | | | Case 1:
% 108.69/15.42 | | | | | | |
% 108.69/15.42 | | | | | | | (1507) ~ (all_14_2 = e2)
% 108.69/15.42 | | | | | | |
% 108.69/15.42 | | | | | | | BETA: splitting (57) gives:
% 108.69/15.42 | | | | | | |
% 108.69/15.42 | | | | | | | Case 1:
% 108.69/15.42 | | | | | | | |
% 108.69/15.42 | | | | | | | | (1508) ~ (all_18_2 = e3)
% 108.69/15.42 | | | | | | | |
% 108.69/15.42 | | | | | | | | REDUCE: (326), (1508) imply:
% 108.69/15.42 | | | | | | | | (1509) ~ (all_14_2 = e3)
% 108.69/15.42 | | | | | | | |
% 108.69/15.42 | | | | | | | | BETA: splitting (63) gives:
% 108.69/15.42 | | | | | | | |
% 108.69/15.42 | | | | | | | | Case 1:
% 108.69/15.42 | | | | | | | | |
% 108.69/15.42 | | | | | | | | | (1510) ~ (all_22_2 = e0)
% 108.69/15.42 | | | | | | | | |
% 108.69/15.42 | | | | | | | | | REDUCE: (329), (1510) imply:
% 108.69/15.42 | | | | | | | | | (1511) ~ (all_14_2 = e0)
% 108.69/15.42 | | | | | | | | |
% 108.69/15.42 | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (117), (123),
% 108.69/15.42 | | | | | | | | | (126), (127), (148), (152), (153), (161), (162),
% 108.69/15.42 | | | | | | | | | (163), (164), (166), (167), (168), (169), (171),
% 108.69/15.42 | | | | | | | | | (172), (173), (174), (203), (341), (357), (359),
% 108.69/15.42 | | | | | | | | | (361), (1507), (1509), (1511), (function-axioms)
% 108.69/15.42 | | | | | | | | | are inconsistent by sub-proof #216.
% 108.69/15.42 | | | | | | | | |
% 108.69/15.42 | | | | | | | | Case 2:
% 108.69/15.42 | | | | | | | | |
% 108.69/15.42 | | | | | | | | | (1512) all_22_2 = e0
% 108.69/15.42 | | | | | | | | | (1513) op(e0, e0) = all_22_1 & $i(all_22_1) & ( ~ (all_22_1
% 108.69/15.42 | | | | | | | | | = e2) | ( ~ (all_22_0 = e3) & op(e2, e0) =
% 108.69/15.42 | | | | | | | | | all_22_0 & $i(all_22_0)))
% 108.69/15.42 | | | | | | | | |
% 108.69/15.42 | | | | | | | | | ALPHA: (1513) implies:
% 108.69/15.42 | | | | | | | | | (1514) op(e0, e0) = all_22_1
% 108.69/15.42 | | | | | | | | |
% 108.69/15.42 | | | | | | | | | COMBINE_EQS: (329), (1512) imply:
% 108.69/15.42 | | | | | | | | | (1515) all_14_2 = e0
% 108.69/15.42 | | | | | | | | |
% 108.69/15.42 | | | | | | | | | SIMP: (1515) implies:
% 108.69/15.42 | | | | | | | | | (1516) all_14_2 = e0
% 108.69/15.42 | | | | | | | | |
% 108.69/15.42 | | | | | | | | | COMBINE_EQS: (331), (1516) imply:
% 108.69/15.42 | | | | | | | | | (1517) all_32_2 = e0
% 108.69/15.42 | | | | | | | | |
% 108.69/15.42 | | | | | | | | | REDUCE: (361), (1516) imply:
% 108.69/15.42 | | | | | | | | | (1518) ~ (all_53_7 = e0)
% 108.69/15.42 | | | | | | | | |
% 108.69/15.42 | | | | | | | | | REDUCE: (1509), (1516) imply:
% 108.69/15.42 | | | | | | | | | (1519) ~ (e3 = e0)
% 108.69/15.42 | | | | | | | | |
% 108.69/15.42 | | | | | | | | | REDUCE: (50), (1516) imply:
% 108.69/15.42 | | | | | | | | | (1520) op(e1, e1) = e0
% 108.69/15.42 | | | | | | | | |
% 108.69/15.42 | | | | | | | | | BETA: splitting (78) gives:
% 108.69/15.42 | | | | | | | | |
% 108.69/15.42 | | | | | | | | | Case 1:
% 108.69/15.42 | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | (1521) ~ (all_32_2 = e0)
% 108.69/15.42 | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | REDUCE: (1517), (1521) imply:
% 108.69/15.42 | | | | | | | | | | (1522) $false
% 108.69/15.42 | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | CLOSE: (1522) is inconsistent.
% 108.69/15.42 | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | Case 2:
% 108.69/15.42 | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | (1523) op(e0, e0) = all_32_1 & $i(all_32_1) & ( ~
% 108.69/15.42 | | | | | | | | | | (all_32_1 = e3) | ( ~ (all_32_0 = e2) & op(e3,
% 108.69/15.42 | | | | | | | | | | e0) = all_32_0 & $i(all_32_0)))
% 108.69/15.42 | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | ALPHA: (1523) implies:
% 108.69/15.42 | | | | | | | | | | (1524) op(e0, e0) = all_32_1
% 108.69/15.42 | | | | | | | | | | (1525) ~ (all_32_1 = e3) | ( ~ (all_32_0 = e2) & op(e3,
% 108.69/15.42 | | | | | | | | | | e0) = all_32_0 & $i(all_32_0))
% 108.69/15.42 | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 108.69/15.42 | | | | | | | | | | all_32_1, e0, e0, simplifying with (38), (1524)
% 108.69/15.42 | | | | | | | | | | gives:
% 108.69/15.42 | | | | | | | | | | (1526) all_32_1 = all_6_2
% 108.69/15.42 | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 108.69/15.42 | | | | | | | | | | all_32_1, e0, e0, simplifying with (1514), (1524)
% 108.69/15.42 | | | | | | | | | | gives:
% 108.69/15.42 | | | | | | | | | | (1527) all_32_1 = all_22_1
% 108.69/15.42 | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | COMBINE_EQS: (1526), (1527) imply:
% 108.69/15.42 | | | | | | | | | | (1528) all_22_1 = all_6_2
% 108.69/15.42 | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | BETA: splitting (69) gives:
% 108.69/15.42 | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | Case 1:
% 108.69/15.42 | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | (1529) ~ (all_26_2 = e2)
% 108.69/15.42 | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | REDUCE: (316), (1529) imply:
% 108.69/15.42 | | | | | | | | | | | (1530) ~ (all_4_2 = e2)
% 108.69/15.42 | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | BETA: splitting (72) gives:
% 108.69/15.42 | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | Case 1:
% 108.69/15.42 | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | (1531) ~ (all_28_2 = e3)
% 108.69/15.42 | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | REDUCE: (313), (1531) imply:
% 108.69/15.42 | | | | | | | | | | | | (1532) ~ (all_6_2 = e3)
% 108.69/15.42 | | | | | | | | | | | |
% 108.69/15.42 | | | | | | | | | | | | REF_CLOSE: (108), (109), (142), (144), (152), (161), (162),
% 108.69/15.42 | | | | | | | | | | | | (166), (169), (173), (174), (206), (208), (224),
% 108.69/15.42 | | | | | | | | | | | | (228), (248), (250), (343), (347), (379), (381),
% 108.69/15.42 | | | | | | | | | | | | (1494), (1498), (1499), (1518), (1520), (1532),
% 108.69/15.43 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.69/15.43 | | | | | | | | | | | | #105.
% 108.69/15.43 | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | Case 2:
% 108.69/15.43 | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | (1533) all_28_2 = e3
% 108.69/15.43 | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | COMBINE_EQS: (313), (1533) imply:
% 108.69/15.43 | | | | | | | | | | | | (1534) all_6_2 = e3
% 108.69/15.43 | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | SIMP: (1534) implies:
% 108.69/15.43 | | | | | | | | | | | | (1535) all_6_2 = e3
% 108.69/15.43 | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | COMBINE_EQS: (1526), (1535) imply:
% 108.69/15.43 | | | | | | | | | | | | (1536) all_32_1 = e3
% 108.69/15.43 | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | REDUCE: (343), (1535) imply:
% 108.69/15.43 | | | | | | | | | | | | (1537) ~ (all_53_1 = e3)
% 108.69/15.43 | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | REDUCE: (349), (1535) imply:
% 108.69/15.43 | | | | | | | | | | | | (1538) ~ (all_53_4 = e3)
% 108.69/15.43 | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | REDUCE: (353), (1535) imply:
% 108.69/15.43 | | | | | | | | | | | | (1539) ~ (all_53_12 = e3)
% 108.69/15.43 | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | BETA: splitting (226) gives:
% 108.69/15.43 | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | (1540) (all_57_60 = e3 & op(e3, e1) = e3) | (all_57_61 =
% 108.69/15.43 | | | | | | | | | | | | | e3 & op(e2, e1) = e3)
% 108.69/15.43 | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | BETA: splitting (1540) gives:
% 108.69/15.43 | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | (1541) all_57_60 = e3 & op(e3, e1) = e3
% 108.69/15.43 | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | ALPHA: (1541) implies:
% 108.69/15.43 | | | | | | | | | | | | | | (1542) op(e3, e1) = e3
% 108.69/15.43 | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 108.69/15.43 | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | (1543) (all_57_56 = e3 & op(e1, e3) = e3) | (all_57_57 =
% 108.69/15.43 | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3)
% 108.69/15.43 | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | BETA: splitting (1543) gives:
% 108.69/15.43 | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | (1544) all_57_56 = e3 & op(e1, e3) = e3
% 108.69/15.43 | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | ALPHA: (1544) implies:
% 108.69/15.43 | | | | | | | | | | | | | | | | (1545) op(e1, e3) = e3
% 108.69/15.43 | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | BETA: splitting (1525) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1546) ~ (all_32_1 = e3)
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | REDUCE: (1536), (1546) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1547) $false
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | CLOSE: (1547) is inconsistent.
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1548) ~ (all_32_0 = e2) & op(e3, e0) = all_32_0 &
% 108.69/15.43 | | | | | | | | | | | | | | | | | $i(all_32_0)
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | ALPHA: (1548) implies:
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1549) ~ (all_32_0 = e2)
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1550) op(e3, e0) = all_32_0
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e3,
% 108.69/15.43 | | | | | | | | | | | | | | | | | e3, e1, simplifying with (167), (1545) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1551) all_53_6 = e3
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 108.69/15.43 | | | | | | | | | | | | | | | | | all_32_0, e0, e3, simplifying with (172), (1550)
% 108.69/15.43 | | | | | | | | | | | | | | | | | gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1552) all_53_12 = all_32_0
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 108.69/15.43 | | | | | | | | | | | | | | | | | e3, e1, e3, simplifying with (173), (1542) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1553) all_53_13 = e3
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (1552) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1554) all_55_12 = all_32_0
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | REDUCE: (137), (1552) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1555) ~ (all_53_4 = all_32_0)
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | REDUCE: (132), (1551) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1556) ~ (all_53_7 = e3)
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | REDUCE: (115), (1552) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1557) ~ (all_53_15 = all_32_0)
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | SIMP: (1557) implies:
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1558) ~ (all_53_15 = all_32_0)
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | REDUCE: (374), (1552) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1559) ~ (all_32_0 = all_4_2)
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | REDUCE: (1539), (1552) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1560) ~ (all_32_0 = e3)
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | REDUCE: (113), (1553) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1561) ~ (all_53_15 = e3)
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | REDUCE: (375), (1553) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1562) ~ (all_4_2 = e3)
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | SIMP: (1562) implies:
% 108.69/15.43 | | | | | | | | | | | | | | | | | (1563) ~ (all_4_2 = e3)
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | (1564) all_55_15 = e3
% 108.69/15.43 | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | REF_CLOSE: (339), (1563), (1564) are inconsistent by
% 108.69/15.43 | | | | | | | | | | | | | | | | | | sub-proof #140.
% 108.69/15.43 | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.43 | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | (1565) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 108.69/15.43 | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | BETA: splitting (1565) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | (1566) all_55_15 = e2
% 108.69/15.43 | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (339), (1530), (1566) are inconsistent by
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | sub-proof #193.
% 108.69/15.43 | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | (1567) all_55_15 = e1 | all_55_15 = e0
% 108.69/15.43 | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | BETA: splitting (1567) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | (1568) all_55_15 = e1
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (1568) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | (1569) all_4_2 = e1
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | SIMP: (1569) implies:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | (1570) all_4_2 = e1
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | REDUCE: (377), (1570) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | (1571) ~ (all_53_15 = e1)
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | REDUCE: (1559), (1570) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | (1572) ~ (all_32_0 = e1)
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | (1573) all_55_12 = e3
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1554), (1560), (1573) are inconsistent by
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | sub-proof #190.
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | (1574) ~ (all_55_12 = e3)
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | (1575) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1575) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | (1576) all_55_12 = e2
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1549), (1554), (1576) are inconsistent by
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | sub-proof #189.
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | (1577) all_55_12 = e1 | all_55_12 = e0
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1577) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | (1578) all_55_12 = e1
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1554), (1572), (1578) are inconsistent by
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #188.
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | (1579) all_55_12 = e0
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1554), (1579) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | (1580) all_32_0 = e0
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1580) implies:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | (1581) all_32_0 = e0
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1555), (1581) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | (1582) ~ (all_53_4 = e0)
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1558), (1581) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | (1583) ~ (all_53_15 = e0)
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1550), (1581) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | (1584) op(e3, e0) = e0
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | (1585) all_55_14 = e3
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (1585) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | (1586) all_53_15 = e3
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1586) implies:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | (1587) all_53_15 = e3
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1498), (1587) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | (1588) $false
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1588) is inconsistent.
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | (1589) all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1589) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | (1590) all_55_14 = e2
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (1590) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | (1591) all_53_15 = e2
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1591) implies:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | (1592) all_53_15 = e2
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (1592) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | (1593) ~ (all_53_7 = e2)
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (1594) all_55_6 = e3
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (1594) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (1595) all_53_7 = e3
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1495), (1595) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (1596) $false
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1596) is inconsistent.
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (1597) all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1597) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1598) all_55_6 = e2
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (1598) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1599) all_53_7 = e2
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1593), (1599) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1600) $false
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1600) is inconsistent.
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1601) all_55_6 = e1 | all_55_6 = e0
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1601) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1602) all_55_6 = e1
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (1602) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1603) all_53_7 = e1
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (1603) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1604) ~ (all_53_4 = e1)
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1605) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1584), (1605), (function-axioms) are
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #141.
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1606) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1606) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1607) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1607) implies:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1608) op(e2, e0) = e2
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1609) all_55_4 = e3
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (1609) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1610) all_53_4 = e3
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1538), (1610) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1611) $false
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1611) is inconsistent.
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1612) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1612) gives:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1613) all_55_4 = e2
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (1613) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1614) all_53_4 = e2
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (1614) imply:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1615) ~ (all_53_8 = e2)
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1615) implies:
% 108.69/15.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1616) ~ (all_53_8 = e2)
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1608), (1616), (function-axioms) are
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #227.
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1617) all_55_4 = e1 | all_55_4 = e0
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (252), (1582), (1604), (1617) are inconsistent by
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #104.
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1618) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1618) implies:
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1619) op(e1, e0) = e1
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1604), (1619), (function-axioms) are
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #226.
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1620) all_55_6 = e0
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (1620) imply:
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1621) all_53_7 = e0
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1518), (1621) imply:
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1622) $false
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1622) is inconsistent.
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | (1623) all_55_14 = e1 | all_55_14 = e0
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (274), (1571), (1583), (1623) are inconsistent by
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #103.
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | (1624) all_55_15 = e0
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (339), (378), (1624) are inconsistent by sub-proof
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | | #192.
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | (1625) all_57_57 = e3 & op(e1, e2) = e3
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | ALPHA: (1625) implies:
% 108.69/15.44 | | | | | | | | | | | | | | | | (1626) op(e1, e2) = e3
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | REF_CLOSE: (166), (1495), (1626), (function-axioms) are
% 108.69/15.44 | | | | | | | | | | | | | | | | inconsistent by sub-proof #179.
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | (1627) (all_57_58 = e3 & op(e1, e1) = e3) | (all_57_59 =
% 108.69/15.44 | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 108.69/15.44 | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | BETA: splitting (1627) gives:
% 108.69/15.44 | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | Case 1:
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | (1628) all_57_58 = e3 & op(e1, e1) = e3
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | ALPHA: (1628) implies:
% 108.69/15.44 | | | | | | | | | | | | | | | | (1629) op(e1, e1) = e3
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1520), (1629), (function-axioms) are
% 108.69/15.44 | | | | | | | | | | | | | | | | inconsistent by sub-proof #152.
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | (1630) all_57_59 = e3 & op(e1, e0) = e3
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | ALPHA: (1630) implies:
% 108.69/15.44 | | | | | | | | | | | | | | | | (1631) op(e1, e0) = e3
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1538), (1631), (function-axioms) are
% 108.69/15.44 | | | | | | | | | | | | | | | | inconsistent by sub-proof #126.
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | (1632) all_57_61 = e3 & op(e2, e1) = e3
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | ALPHA: (1632) implies:
% 108.69/15.44 | | | | | | | | | | | | | | (1633) op(e2, e1) = e3
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | REF_CLOSE: (169), (1496), (1633), (function-axioms) are
% 108.69/15.44 | | | | | | | | | | | | | | inconsistent by sub-proof #138.
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | (1634) (all_57_62 = e3 & op(e1, e1) = e3) | (all_57_63 =
% 108.69/15.44 | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | BETA: splitting (1634) gives:
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | Case 1:
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | (1635) all_57_62 = e3 & op(e1, e1) = e3
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | ALPHA: (1635) implies:
% 108.69/15.44 | | | | | | | | | | | | | | (1636) op(e1, e1) = e3
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | REF_CLOSE: (6), (1520), (1636), (function-axioms) are
% 108.69/15.44 | | | | | | | | | | | | | | inconsistent by sub-proof #152.
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | (1637) all_57_63 = e3 & op(e0, e1) = e3
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | ALPHA: (1637) implies:
% 108.69/15.44 | | | | | | | | | | | | | | (1638) op(e0, e1) = e3
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | REF_CLOSE: (161), (1537), (1638), (function-axioms) are
% 108.69/15.44 | | | | | | | | | | | | | | inconsistent by sub-proof #145.
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | (1639) all_26_2 = e2
% 108.69/15.44 | | | | | | | | | | | (1640) op(e2, e2) = all_26_1 & $i(all_26_1) & ( ~
% 108.69/15.44 | | | | | | | | | | | (all_26_1 = e0) | ( ~ (all_26_0 = e1) & op(e0,
% 108.69/15.44 | | | | | | | | | | | e2) = all_26_0 & $i(all_26_0)))
% 108.69/15.44 | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | ALPHA: (1640) implies:
% 108.69/15.44 | | | | | | | | | | | (1641) op(e2, e2) = all_26_1
% 108.69/15.44 | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | COMBINE_EQS: (316), (1639) imply:
% 108.69/15.44 | | | | | | | | | | | (1642) all_4_2 = e2
% 108.69/15.44 | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | SIMP: (1642) implies:
% 108.69/15.44 | | | | | | | | | | | (1643) all_4_2 = e2
% 108.69/15.44 | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | COMBINE_EQS: (277), (1643) imply:
% 108.69/15.44 | | | | | | | | | | | (1644) all_50_2 = e2
% 108.69/15.44 | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | REDUCE: (371), (1643) imply:
% 108.69/15.44 | | | | | | | | | | | (1645) ~ (all_53_10 = e2)
% 108.69/15.44 | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | BETA: splitting (105) gives:
% 108.69/15.44 | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | Case 1:
% 108.69/15.44 | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | (1646) ~ (all_50_2 = e2)
% 108.69/15.44 | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | REDUCE: (1644), (1646) imply:
% 108.69/15.44 | | | | | | | | | | | | (1647) $false
% 108.69/15.44 | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | CLOSE: (1647) is inconsistent.
% 108.69/15.44 | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | (1648) op(e2, e2) = all_50_1 & $i(all_50_1) & ( ~
% 108.69/15.44 | | | | | | | | | | | | (all_50_1 = e1) | ( ~ (all_50_0 = e0) & op(e1,
% 108.69/15.44 | | | | | | | | | | | | e2) = all_50_0 & $i(all_50_0)))
% 108.69/15.44 | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | ALPHA: (1648) implies:
% 108.69/15.44 | | | | | | | | | | | | (1649) op(e2, e2) = all_50_1
% 108.69/15.44 | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_50_1,
% 108.69/15.44 | | | | | | | | | | | | e2, e2, simplifying with (1499), (1649) gives:
% 108.69/15.44 | | | | | | | | | | | | (1650) all_50_1 = e3
% 108.69/15.44 | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_1,
% 108.69/15.44 | | | | | | | | | | | | all_50_1, e2, e2, simplifying with (1641), (1649)
% 108.69/15.44 | | | | | | | | | | | | gives:
% 108.69/15.44 | | | | | | | | | | | | (1651) all_50_1 = all_26_1
% 108.69/15.44 | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | COMBINE_EQS: (1650), (1651) imply:
% 108.69/15.44 | | | | | | | | | | | | (1652) all_26_1 = e3
% 108.69/15.44 | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | BETA: splitting (72) gives:
% 108.69/15.44 | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | Case 1:
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | (1653) ~ (all_28_2 = e3)
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | REDUCE: (313), (1653) imply:
% 108.69/15.44 | | | | | | | | | | | | | (1654) ~ (all_6_2 = e3)
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | REF_CLOSE: (108), (109), (142), (144), (152), (161), (162),
% 108.69/15.44 | | | | | | | | | | | | | (166), (169), (173), (174), (206), (208), (224),
% 108.69/15.44 | | | | | | | | | | | | | (228), (248), (250), (343), (347), (379), (381),
% 108.69/15.44 | | | | | | | | | | | | | (1494), (1498), (1499), (1518), (1520), (1654),
% 108.69/15.44 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.69/15.44 | | | | | | | | | | | | | #105.
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | (1655) all_28_2 = e3
% 108.69/15.44 | | | | | | | | | | | | | (1656) op(e3, e3) = all_28_1 & $i(all_28_1) & ( ~
% 108.69/15.44 | | | | | | | | | | | | | (all_28_1 = e1) | ( ~ (all_28_0 = e2) & op(e1,
% 108.69/15.44 | | | | | | | | | | | | | e3) = all_28_0 & $i(all_28_0)))
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | ALPHA: (1656) implies:
% 108.69/15.44 | | | | | | | | | | | | | (1657) op(e3, e3) = all_28_1
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | COMBINE_EQS: (313), (1655) imply:
% 108.69/15.44 | | | | | | | | | | | | | (1658) all_6_2 = e3
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | COMBINE_EQS: (332), (1658) imply:
% 108.69/15.44 | | | | | | | | | | | | | (1659) all_36_2 = e3
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | REDUCE: (345), (1658) imply:
% 108.69/15.44 | | | | | | | | | | | | | (1660) ~ (all_53_2 = e3)
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | BETA: splitting (84) gives:
% 108.69/15.44 | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | Case 1:
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | (1661) ~ (all_36_2 = e3)
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | REDUCE: (1659), (1661) imply:
% 108.69/15.44 | | | | | | | | | | | | | | (1662) $false
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | CLOSE: (1662) is inconsistent.
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | (1663) op(e3, e3) = all_36_1 & $i(all_36_1) & ( ~
% 108.69/15.44 | | | | | | | | | | | | | | (all_36_1 = e2) | ( ~ (all_36_0 = e1) & op(e2,
% 108.69/15.44 | | | | | | | | | | | | | | e3) = all_36_0 & $i(all_36_0)))
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | ALPHA: (1663) implies:
% 108.69/15.44 | | | | | | | | | | | | | | (1664) op(e3, e3) = all_36_1
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 108.69/15.44 | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | Case 1:
% 108.69/15.44 | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | (1665) (all_57_124 = e3 & op(e3, e3) = e3) | (all_57_125
% 108.69/15.44 | | | | | | | | | | | | | | | = e3 & op(e2, e3) = e3)
% 108.69/15.44 | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | BETA: splitting (1665) gives:
% 108.69/15.44 | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | Case 1:
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | (1666) all_57_124 = e3 & op(e3, e3) = e3
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | ALPHA: (1666) implies:
% 108.69/15.44 | | | | | | | | | | | | | | | | (1667) op(e3, e3) = e3
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | REF_CLOSE: (35), (107), (108), (109), (110), (123), (126),
% 108.69/15.44 | | | | | | | | | | | | | | | | (127), (132), (139), (140), (148), (152), (153),
% 108.69/15.44 | | | | | | | | | | | | | | | | (161), (162), (163), (164), (166), (167), (168),
% 108.69/15.44 | | | | | | | | | | | | | | | | (169), (171), (172), (173), (174), (374), (375),
% 108.69/15.44 | | | | | | | | | | | | | | | | (377), (1657), (1664), (1667), (function-axioms)
% 108.69/15.44 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #97.
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | (1668) all_57_125 = e3 & op(e2, e3) = e3
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | ALPHA: (1668) implies:
% 108.69/15.44 | | | | | | | | | | | | | | | | (1669) op(e2, e3) = e3
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | REF_CLOSE: (171), (1497), (1669), (function-axioms) are
% 108.69/15.44 | | | | | | | | | | | | | | | | inconsistent by sub-proof #198.
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | End of split
% 108.69/15.44 | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | Case 2:
% 108.69/15.44 | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | (1670) (all_57_126 = e3 & op(e1, e3) = e3) | (all_57_127
% 108.69/15.44 | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3)
% 108.69/15.44 | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | BETA: splitting (1670) gives:
% 108.69/15.44 | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | Case 1:
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | (1671) all_57_126 = e3 & op(e1, e3) = e3
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | ALPHA: (1671) implies:
% 108.69/15.44 | | | | | | | | | | | | | | | | (1672) op(e1, e3) = e3
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 108.69/15.44 | | | | | | | | | | | | | | | |
% 108.69/15.44 | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.44 | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | (1673) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2)
% 108.69/15.45 | | | | | | | | | | | | | | | | | = all_52_18 & op(e2, e3) = e2 & $i(all_52_18)
% 108.69/15.45 | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (1645), (1673), (function-axioms) are
% 108.69/15.45 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #215.
% 108.69/15.45 | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.45 | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | (1674) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 108.69/15.45 | | | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) |
% 108.69/15.45 | | | | | | | | | | | | | | | | | (all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 108.69/15.45 | | | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22))
% 108.69/15.45 | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | BETA: splitting (1674) gives:
% 108.69/15.45 | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.45 | | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | | (1675) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 108.69/15.45 | | | | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)
% 108.69/15.45 | | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | | ALPHA: (1675) implies:
% 108.69/15.45 | | | | | | | | | | | | | | | | | | (1676) op(e1, e3) = e1
% 108.69/15.45 | | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e1, e3,
% 108.69/15.45 | | | | | | | | | | | | | | | | | | e1, simplifying with (1672), (1676) gives:
% 108.69/15.45 | | | | | | | | | | | | | | | | | | (1677) e3 = e1
% 108.69/15.45 | | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | | REDUCE: (7), (1677) imply:
% 108.69/15.45 | | | | | | | | | | | | | | | | | | (1678) $false
% 108.69/15.45 | | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | | CLOSE: (1678) is inconsistent.
% 108.69/15.45 | | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.45 | | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | | (1679) all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 108.69/15.45 | | | | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22)
% 108.69/15.45 | | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | | ALPHA: (1679) implies:
% 108.69/15.45 | | | | | | | | | | | | | | | | | | (1680) op(e0, e3) = e0
% 108.69/15.45 | | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e0,
% 108.69/15.45 | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (163), (1680) gives:
% 108.69/15.45 | | | | | | | | | | | | | | | | | | (1681) all_53_2 = e0
% 108.69/15.45 | | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | | REDUCE: (153), (1681) imply:
% 108.69/15.45 | | | | | | | | | | | | | | | | | | (1682) ~ (all_53_1 = e0)
% 108.69/15.45 | | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | | REDUCE: (148), (1681) imply:
% 108.69/15.45 | | | | | | | | | | | | | | | | | | (1683) ~ (all_53_3 = e0)
% 108.69/15.45 | | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | | SIMP: (1683) implies:
% 108.69/15.45 | | | | | | | | | | | | | | | | | | (1684) ~ (all_53_3 = e0)
% 108.69/15.45 | | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (108), (109), (142), (144), (152), (161),
% 108.69/15.45 | | | | | | | | | | | | | | | | | | (162), (166), (169), (173), (174), (206), (224),
% 108.69/15.45 | | | | | | | | | | | | | | | | | | (228), (250), (1494), (1498), (1499), (1518),
% 108.69/15.45 | | | | | | | | | | | | | | | | | | (1520), (1682), (1684), (function-axioms) are
% 108.69/15.45 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106.
% 108.69/15.45 | | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | Case 2:
% 108.69/15.45 | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | (1685) all_57_127 = e3 & op(e0, e3) = e3
% 108.69/15.45 | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | ALPHA: (1685) implies:
% 108.69/15.45 | | | | | | | | | | | | | | | | (1686) op(e0, e3) = e3
% 108.69/15.45 | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e3,
% 108.69/15.45 | | | | | | | | | | | | | | | | e3, e0, simplifying with (163), (1686) gives:
% 108.69/15.45 | | | | | | | | | | | | | | | | (1687) all_53_2 = e3
% 108.69/15.45 | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | REDUCE: (1660), (1687) imply:
% 108.69/15.45 | | | | | | | | | | | | | | | | (1688) $false
% 108.69/15.45 | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | | CLOSE: (1688) is inconsistent.
% 108.69/15.45 | | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | |
% 108.69/15.45 | | | | | | | | End of split
% 108.69/15.45 | | | | | | | |
% 108.69/15.45 | | | | | | | Case 2:
% 108.69/15.45 | | | | | | | |
% 108.69/15.45 | | | | | | | | (1689) all_18_2 = e3
% 108.69/15.45 | | | | | | | |
% 108.69/15.45 | | | | | | | | COMBINE_EQS: (326), (1689) imply:
% 108.69/15.45 | | | | | | | | (1690) all_14_2 = e3
% 108.69/15.45 | | | | | | | |
% 108.69/15.45 | | | | | | | | SIMP: (1690) implies:
% 108.69/15.45 | | | | | | | | (1691) all_14_2 = e3
% 108.69/15.45 | | | | | | | |
% 108.69/15.45 | | | | | | | | REDUCE: (365), (1691) imply:
% 108.69/15.45 | | | | | | | | (1692) ~ (all_53_13 = e3)
% 108.69/15.45 | | | | | | | |
% 108.69/15.45 | | | | | | | | BETA: splitting (72) gives:
% 108.69/15.45 | | | | | | | |
% 108.69/15.45 | | | | | | | | Case 1:
% 108.69/15.45 | | | | | | | | |
% 108.69/15.45 | | | | | | | | | (1693) ~ (all_28_2 = e3)
% 108.69/15.45 | | | | | | | | |
% 108.69/15.45 | | | | | | | | | REDUCE: (313), (1693) imply:
% 108.69/15.45 | | | | | | | | | (1694) ~ (all_6_2 = e3)
% 108.69/15.45 | | | | | | | | |
% 108.69/15.45 | | | | | | | | | BETA: splitting (208) gives:
% 108.69/15.45 | | | | | | | | |
% 108.69/15.45 | | | | | | | | | Case 1:
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | (1695) all_55_0 = e3
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | COMBINE_EQS: (248), (1695) imply:
% 108.69/15.45 | | | | | | | | | | (1696) all_6_2 = e3
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | REDUCE: (1694), (1696) imply:
% 108.69/15.45 | | | | | | | | | | (1697) $false
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | CLOSE: (1697) is inconsistent.
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | Case 2:
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | (1698) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | BETA: splitting (1698) gives:
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | Case 1:
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | (1699) all_55_0 = e2
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | COMBINE_EQS: (248), (1699) imply:
% 108.69/15.45 | | | | | | | | | | | (1700) all_6_2 = e2
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | REDUCE: (381), (1700) imply:
% 108.69/15.45 | | | | | | | | | | | (1701) $false
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | CLOSE: (1701) is inconsistent.
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | Case 2:
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | (1702) all_55_0 = e1 | all_55_0 = e0
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | BETA: splitting (1702) gives:
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | Case 1:
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | (1703) all_55_0 = e1
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | COMBINE_EQS: (248), (1703) imply:
% 108.69/15.45 | | | | | | | | | | | | (1704) all_6_2 = e1
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | REDUCE: (379), (1704) imply:
% 108.69/15.45 | | | | | | | | | | | | (1705) $false
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | CLOSE: (1705) is inconsistent.
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | Case 2:
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | (1706) all_55_0 = e0
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | COMBINE_EQS: (248), (1706) imply:
% 108.69/15.45 | | | | | | | | | | | | (1707) all_6_2 = e0
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | REDUCE: (343), (1707) imply:
% 108.69/15.45 | | | | | | | | | | | | (1708) ~ (all_53_1 = e0)
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | REDUCE: (347), (1707) imply:
% 108.69/15.45 | | | | | | | | | | | | (1709) ~ (all_53_3 = e0)
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | BETA: splitting (108) gives:
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | Case 1:
% 108.69/15.45 | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | (1710) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 108.69/15.45 | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 108.69/15.45 | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | ALPHA: (1710) implies:
% 108.69/15.45 | | | | | | | | | | | | | (1711) op(e3, e2) = e3
% 108.69/15.45 | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | REF_CLOSE: (174), (1498), (1711), (function-axioms) are
% 108.69/15.45 | | | | | | | | | | | | | inconsistent by sub-proof #214.
% 108.69/15.45 | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | Case 2:
% 108.69/15.45 | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | (1712) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 108.69/15.45 | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 108.69/15.45 | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 108.69/15.45 | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 108.69/15.45 | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | BETA: splitting (1712) gives:
% 108.69/15.45 | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | Case 1:
% 108.69/15.45 | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | (1713) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 108.69/15.45 | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 108.69/15.45 | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | ALPHA: (1713) implies:
% 108.69/15.45 | | | | | | | | | | | | | | (1714) ~ (all_52_14 = e2)
% 108.69/15.45 | | | | | | | | | | | | | | (1715) op(e2, e1) = all_52_14
% 108.69/15.45 | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 108.69/15.45 | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | Case 1:
% 108.69/15.45 | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | (1716) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 108.69/15.45 | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 108.69/15.45 | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | ALPHA: (1716) implies:
% 108.69/15.45 | | | | | | | | | | | | | | | (1717) op(e3, e1) = e3
% 108.69/15.45 | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | REF_CLOSE: (173), (1692), (1717), (function-axioms) are
% 108.69/15.45 | | | | | | | | | | | | | | | inconsistent by sub-proof #232.
% 108.69/15.45 | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | Case 2:
% 108.69/15.45 | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | (1718) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 108.69/15.45 | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 108.69/15.45 | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 108.69/15.45 | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 108.69/15.45 | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | | REF_CLOSE: (161), (169), (1708), (1714), (1715), (1718),
% 108.69/15.45 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.69/15.45 | | | | | | | | | | | | | | | #107.
% 108.69/15.45 | | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | Case 2:
% 108.69/15.45 | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | (1719) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 108.69/15.45 | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 108.69/15.45 | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | ALPHA: (1719) implies:
% 108.69/15.45 | | | | | | | | | | | | | | (1720) op(e0, e2) = e0
% 108.69/15.45 | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | | REF_CLOSE: (162), (1709), (1720), (function-axioms) are
% 108.69/15.45 | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 108.69/15.45 | | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | |
% 108.69/15.45 | | | | | | | | Case 2:
% 108.69/15.45 | | | | | | | | |
% 108.69/15.45 | | | | | | | | | (1721) all_28_2 = e3
% 108.69/15.45 | | | | | | | | | (1722) op(e3, e3) = all_28_1 & $i(all_28_1) & ( ~ (all_28_1
% 108.69/15.45 | | | | | | | | | = e1) | ( ~ (all_28_0 = e2) & op(e1, e3) =
% 108.69/15.45 | | | | | | | | | all_28_0 & $i(all_28_0)))
% 108.69/15.45 | | | | | | | | |
% 108.69/15.45 | | | | | | | | | ALPHA: (1722) implies:
% 108.69/15.45 | | | | | | | | | (1723) op(e3, e3) = all_28_1
% 108.69/15.45 | | | | | | | | |
% 108.69/15.45 | | | | | | | | | COMBINE_EQS: (313), (1721) imply:
% 108.69/15.45 | | | | | | | | | (1724) all_6_2 = e3
% 108.69/15.45 | | | | | | | | |
% 108.69/15.45 | | | | | | | | | COMBINE_EQS: (332), (1724) imply:
% 108.69/15.45 | | | | | | | | | (1725) all_36_2 = e3
% 108.69/15.45 | | | | | | | | |
% 108.69/15.45 | | | | | | | | | REDUCE: (353), (1724) imply:
% 108.69/15.45 | | | | | | | | | (1726) ~ (all_53_12 = e3)
% 108.69/15.45 | | | | | | | | |
% 108.69/15.45 | | | | | | | | | BETA: splitting (211) gives:
% 108.69/15.45 | | | | | | | | |
% 108.69/15.45 | | | | | | | | | Case 1:
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | (1727) (all_57_120 = e3 & op(e3, e3) = e3) | (all_57_121
% 108.69/15.45 | | | | | | | | | | = e3 & op(e3, e2) = e3)
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | BETA: splitting (1727) gives:
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | Case 1:
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | (1728) all_57_120 = e3 & op(e3, e3) = e3
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | ALPHA: (1728) implies:
% 108.69/15.45 | | | | | | | | | | | (1729) op(e3, e3) = e3
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | BETA: splitting (84) gives:
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | Case 1:
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | (1730) ~ (all_36_2 = e3)
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | REDUCE: (1725), (1730) imply:
% 108.69/15.45 | | | | | | | | | | | | (1731) $false
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | CLOSE: (1731) is inconsistent.
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | Case 2:
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | (1732) op(e3, e3) = all_36_1 & $i(all_36_1) & ( ~
% 108.69/15.45 | | | | | | | | | | | | (all_36_1 = e2) | ( ~ (all_36_0 = e1) & op(e2,
% 108.69/15.45 | | | | | | | | | | | | e3) = all_36_0 & $i(all_36_0)))
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | ALPHA: (1732) implies:
% 108.69/15.45 | | | | | | | | | | | | (1733) op(e3, e3) = all_36_1
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | | REF_CLOSE: (35), (107), (108), (109), (110), (123), (126),
% 108.69/15.45 | | | | | | | | | | | | (127), (132), (139), (140), (148), (152), (153),
% 108.69/15.45 | | | | | | | | | | | | (161), (162), (163), (164), (166), (167), (168),
% 108.69/15.45 | | | | | | | | | | | | (169), (171), (172), (173), (174), (374), (375),
% 108.69/15.45 | | | | | | | | | | | | (377), (1723), (1729), (1733), (function-axioms)
% 108.69/15.45 | | | | | | | | | | | | are inconsistent by sub-proof #97.
% 108.69/15.45 | | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | Case 2:
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | (1734) all_57_121 = e3 & op(e3, e2) = e3
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | ALPHA: (1734) implies:
% 108.69/15.45 | | | | | | | | | | | (1735) op(e3, e2) = e3
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | | REF_CLOSE: (174), (1498), (1735), (function-axioms) are
% 108.69/15.45 | | | | | | | | | | | inconsistent by sub-proof #214.
% 108.69/15.45 | | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | Case 2:
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | (1736) (all_57_122 = e3 & op(e3, e1) = e3) | (all_57_123
% 108.69/15.45 | | | | | | | | | | = e3 & op(e3, e0) = e3)
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | | REF_CLOSE: (172), (173), (1692), (1726), (1736),
% 108.69/15.45 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.69/15.45 | | | | | | | | | | #96.
% 108.69/15.45 | | | | | | | | | |
% 108.69/15.45 | | | | | | | | | End of split
% 108.69/15.45 | | | | | | | | |
% 108.69/15.45 | | | | | | | | End of split
% 108.69/15.45 | | | | | | | |
% 108.69/15.45 | | | | | | | End of split
% 108.69/15.45 | | | | | | |
% 108.69/15.45 | | | | | | Case 2:
% 108.69/15.45 | | | | | | |
% 108.69/15.46 | | | | | | | (1737) all_14_2 = e2
% 108.69/15.46 | | | | | | | (1738) op(e2, e2) = all_14_1 & $i(all_14_1) & ( ~ (all_14_1 =
% 108.69/15.46 | | | | | | | e3) | ( ~ (all_14_0 = e0) & op(e3, e2) = all_14_0 &
% 108.69/15.46 | | | | | | | $i(all_14_0)))
% 108.69/15.46 | | | | | | |
% 108.69/15.46 | | | | | | | ALPHA: (1738) implies:
% 108.69/15.46 | | | | | | | (1739) op(e2, e2) = all_14_1
% 108.69/15.46 | | | | | | | (1740) ~ (all_14_1 = e3) | ( ~ (all_14_0 = e0) & op(e3, e2) =
% 108.69/15.46 | | | | | | | all_14_0 & $i(all_14_0))
% 108.69/15.46 | | | | | | |
% 108.69/15.46 | | | | | | | COMBINE_EQS: (334), (1737) imply:
% 108.69/15.46 | | | | | | | (1741) all_44_2 = e2
% 108.69/15.46 | | | | | | |
% 108.69/15.46 | | | | | | | REDUCE: (354), (1737) imply:
% 108.69/15.46 | | | | | | | (1742) ~ (all_53_1 = e2)
% 108.69/15.46 | | | | | | |
% 108.69/15.46 | | | | | | | REDUCE: (357), (1737) imply:
% 108.69/15.46 | | | | | | | (1743) ~ (all_53_4 = e2)
% 108.69/15.46 | | | | | | |
% 108.69/15.46 | | | | | | | REDUCE: (363), (1737) imply:
% 108.69/15.46 | | | | | | | (1744) ~ (all_53_9 = e2)
% 108.69/15.46 | | | | | | |
% 108.69/15.46 | | | | | | | REDUCE: (50), (1737) imply:
% 108.69/15.46 | | | | | | | (1745) op(e1, e1) = e2
% 108.69/15.46 | | | | | | |
% 108.69/15.46 | | | | | | | BETA: splitting (96) gives:
% 108.69/15.46 | | | | | | |
% 108.69/15.46 | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | |
% 108.69/15.46 | | | | | | | | (1746) ~ (all_44_2 = e2)
% 108.69/15.46 | | | | | | | |
% 108.69/15.46 | | | | | | | | REDUCE: (1741), (1746) imply:
% 108.69/15.46 | | | | | | | | (1747) $false
% 108.69/15.46 | | | | | | | |
% 108.69/15.46 | | | | | | | | CLOSE: (1747) is inconsistent.
% 108.69/15.46 | | | | | | | |
% 108.69/15.46 | | | | | | | Case 2:
% 108.69/15.46 | | | | | | | |
% 108.69/15.46 | | | | | | | | (1748) op(e2, e2) = all_44_1 & $i(all_44_1) & ( ~ (all_44_1 =
% 108.69/15.46 | | | | | | | | e0) | ( ~ (all_44_0 = e3) & op(e0, e2) = all_44_0
% 108.69/15.46 | | | | | | | | & $i(all_44_0)))
% 108.69/15.46 | | | | | | | |
% 108.69/15.46 | | | | | | | | ALPHA: (1748) implies:
% 108.69/15.46 | | | | | | | | (1749) op(e2, e2) = all_44_1
% 108.69/15.46 | | | | | | | |
% 108.69/15.46 | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_44_1,
% 108.69/15.46 | | | | | | | | e2, e2, simplifying with (1499), (1749) gives:
% 108.69/15.46 | | | | | | | | (1750) all_44_1 = e3
% 108.69/15.46 | | | | | | | |
% 108.69/15.46 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 108.69/15.46 | | | | | | | | all_44_1, e2, e2, simplifying with (1739), (1749)
% 108.69/15.46 | | | | | | | | gives:
% 108.69/15.46 | | | | | | | | (1751) all_44_1 = all_14_1
% 108.69/15.46 | | | | | | | |
% 108.69/15.46 | | | | | | | | COMBINE_EQS: (1750), (1751) imply:
% 108.69/15.46 | | | | | | | | (1752) all_14_1 = e3
% 108.69/15.46 | | | | | | | |
% 108.69/15.46 | | | | | | | | SIMP: (1752) implies:
% 108.69/15.46 | | | | | | | | (1753) all_14_1 = e3
% 108.69/15.46 | | | | | | | |
% 108.69/15.46 | | | | | | | | BETA: splitting (1740) gives:
% 108.69/15.46 | | | | | | | |
% 108.69/15.46 | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | |
% 108.69/15.46 | | | | | | | | | (1754) ~ (all_14_1 = e3)
% 108.69/15.46 | | | | | | | | |
% 108.69/15.46 | | | | | | | | | REDUCE: (1753), (1754) imply:
% 108.69/15.46 | | | | | | | | | (1755) $false
% 108.69/15.46 | | | | | | | | |
% 108.69/15.46 | | | | | | | | | CLOSE: (1755) is inconsistent.
% 108.69/15.46 | | | | | | | | |
% 108.69/15.46 | | | | | | | | Case 2:
% 108.69/15.46 | | | | | | | | |
% 108.69/15.46 | | | | | | | | | (1756) ~ (all_14_0 = e0) & op(e3, e2) = all_14_0 &
% 108.69/15.46 | | | | | | | | | $i(all_14_0)
% 108.69/15.46 | | | | | | | | |
% 108.69/15.46 | | | | | | | | | ALPHA: (1756) implies:
% 108.69/15.46 | | | | | | | | | (1757) ~ (all_14_0 = e0)
% 108.69/15.46 | | | | | | | | | (1758) op(e3, e2) = all_14_0
% 108.69/15.46 | | | | | | | | |
% 108.69/15.46 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 108.69/15.46 | | | | | | | | | all_14_0, e2, e3, simplifying with (174), (1758)
% 108.69/15.46 | | | | | | | | | gives:
% 108.69/15.46 | | | | | | | | | (1759) all_53_15 = all_14_0
% 108.69/15.46 | | | | | | | | |
% 108.69/15.46 | | | | | | | | | COMBINE_EQS: (274), (1759) imply:
% 108.69/15.46 | | | | | | | | | (1760) all_55_14 = all_14_0
% 108.69/15.46 | | | | | | | | |
% 108.69/15.46 | | | | | | | | | REDUCE: (128), (1759) imply:
% 108.69/15.46 | | | | | | | | | (1761) ~ (all_53_7 = all_14_0)
% 108.69/15.46 | | | | | | | | |
% 108.69/15.46 | | | | | | | | | REDUCE: (115), (1759) imply:
% 108.69/15.46 | | | | | | | | | (1762) ~ (all_53_12 = all_14_0)
% 108.69/15.46 | | | | | | | | |
% 108.69/15.46 | | | | | | | | | REDUCE: (113), (1759) imply:
% 108.69/15.46 | | | | | | | | | (1763) ~ (all_53_13 = all_14_0)
% 108.69/15.46 | | | | | | | | |
% 108.69/15.46 | | | | | | | | | REDUCE: (377), (1759) imply:
% 108.69/15.46 | | | | | | | | | (1764) ~ (all_14_0 = all_4_2)
% 108.69/15.46 | | | | | | | | |
% 108.69/15.46 | | | | | | | | | REDUCE: (1498), (1759) imply:
% 108.69/15.46 | | | | | | | | | (1765) ~ (all_14_0 = e3)
% 108.69/15.46 | | | | | | | | |
% 108.69/15.46 | | | | | | | | | BETA: splitting (69) gives:
% 108.69/15.46 | | | | | | | | |
% 108.69/15.46 | | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | (1766) ~ (all_26_2 = e2)
% 108.69/15.46 | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | REDUCE: (316), (1766) imply:
% 108.69/15.46 | | | | | | | | | | (1767) ~ (all_4_2 = e2)
% 108.69/15.46 | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | BETA: splitting (72) gives:
% 108.69/15.46 | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | (1768) ~ (all_28_2 = e3)
% 108.69/15.46 | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | REDUCE: (313), (1768) imply:
% 108.69/15.46 | | | | | | | | | | | (1769) ~ (all_6_2 = e3)
% 108.69/15.46 | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | BETA: splitting (208) gives:
% 108.69/15.46 | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | (1770) all_55_0 = e3
% 108.69/15.46 | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | COMBINE_EQS: (248), (1770) imply:
% 108.69/15.46 | | | | | | | | | | | | (1771) all_6_2 = e3
% 108.69/15.46 | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | REDUCE: (1769), (1771) imply:
% 108.69/15.46 | | | | | | | | | | | | (1772) $false
% 108.69/15.46 | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | CLOSE: (1772) is inconsistent.
% 108.69/15.46 | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | Case 2:
% 108.69/15.46 | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | (1773) ~ (all_55_0 = e3)
% 108.69/15.46 | | | | | | | | | | | | (1774) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 108.69/15.46 | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | BETA: splitting (1774) gives:
% 108.69/15.46 | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | (1775) all_55_0 = e2
% 108.69/15.46 | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | COMBINE_EQS: (248), (1775) imply:
% 108.69/15.46 | | | | | | | | | | | | | (1776) all_6_2 = e2
% 108.69/15.46 | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | REDUCE: (381), (1776) imply:
% 108.69/15.46 | | | | | | | | | | | | | (1777) $false
% 108.69/15.46 | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | CLOSE: (1777) is inconsistent.
% 108.69/15.46 | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | Case 2:
% 108.69/15.46 | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | (1778) all_55_0 = e1 | all_55_0 = e0
% 108.69/15.46 | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | BETA: splitting (1778) gives:
% 108.69/15.46 | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | (1779) all_55_0 = e1
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | COMBINE_EQS: (248), (1779) imply:
% 108.69/15.46 | | | | | | | | | | | | | | (1780) all_6_2 = e1
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | REDUCE: (379), (1780) imply:
% 108.69/15.46 | | | | | | | | | | | | | | (1781) $false
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | CLOSE: (1781) is inconsistent.
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | Case 2:
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | (1782) all_55_0 = e0
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | COMBINE_EQS: (248), (1782) imply:
% 108.69/15.46 | | | | | | | | | | | | | | (1783) all_6_2 = e0
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | REDUCE: (343), (1783) imply:
% 108.69/15.46 | | | | | | | | | | | | | | (1784) ~ (all_53_1 = e0)
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | REDUCE: (353), (1783) imply:
% 108.69/15.46 | | | | | | | | | | | | | | (1785) ~ (all_53_12 = e0)
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | REDUCE: (1769), (1783) imply:
% 108.69/15.46 | | | | | | | | | | | | | | (1786) ~ (e3 = e0)
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | (1787) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 108.69/15.46 | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | ALPHA: (1787) implies:
% 108.69/15.46 | | | | | | | | | | | | | | | (1788) op(e3, e1) = e3
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | (1789) (all_57_96 = e0 & op(e3, e3) = e0) | (all_57_97 =
% 108.69/15.46 | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 108.69/15.46 | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | BETA: splitting (1789) gives:
% 108.69/15.46 | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | (1790) all_57_96 = e0 & op(e3, e3) = e0
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | ALPHA: (1790) implies:
% 108.69/15.46 | | | | | | | | | | | | | | | | | (1791) op(e3, e3) = e0
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (378), (1791), (function-axioms) are
% 108.69/15.46 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #206.
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | (1792) all_57_97 = e0 & op(e3, e2) = e0
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | ALPHA: (1792) implies:
% 108.69/15.46 | | | | | | | | | | | | | | | | | (1793) op(e3, e2) = e0
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_0, e0,
% 108.69/15.46 | | | | | | | | | | | | | | | | | e2, e3, simplifying with (1758), (1793) gives:
% 108.69/15.46 | | | | | | | | | | | | | | | | | (1794) all_14_0 = e0
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | REDUCE: (1757), (1794) imply:
% 108.69/15.46 | | | | | | | | | | | | | | | | | (1795) $false
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | CLOSE: (1795) is inconsistent.
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | End of split
% 108.69/15.46 | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | Case 2:
% 108.69/15.46 | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | (1796) (all_57_98 = e0 & op(e3, e1) = e0) | (all_57_99 =
% 108.69/15.46 | | | | | | | | | | | | | | | | e0 & op(e3, e0) = e0)
% 108.69/15.46 | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (172), (173), (1785), (1788), (1796),
% 108.69/15.46 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.69/15.46 | | | | | | | | | | | | | | | | #129.
% 108.69/15.46 | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | End of split
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | Case 2:
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | (1797) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 108.69/15.46 | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 108.69/15.46 | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 108.69/15.46 | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | REF_CLOSE: (161), (169), (1744), (1784), (1797),
% 108.69/15.46 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.69/15.46 | | | | | | | | | | | | | | | #229.
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | End of split
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | End of split
% 108.69/15.46 | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | End of split
% 108.69/15.46 | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | End of split
% 108.69/15.46 | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | Case 2:
% 108.69/15.46 | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | (1798) all_28_2 = e3
% 108.69/15.46 | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | COMBINE_EQS: (313), (1798) imply:
% 108.69/15.46 | | | | | | | | | | | (1799) all_6_2 = e3
% 108.69/15.46 | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | REDUCE: (343), (1799) imply:
% 108.69/15.46 | | | | | | | | | | | (1800) ~ (all_53_1 = e3)
% 108.69/15.46 | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | REDUCE: (349), (1799) imply:
% 108.69/15.46 | | | | | | | | | | | (1801) ~ (all_53_4 = e3)
% 108.69/15.46 | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | BETA: splitting (226) gives:
% 108.69/15.46 | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | (1802) (all_57_60 = e3 & op(e3, e1) = e3) | (all_57_61 =
% 108.69/15.46 | | | | | | | | | | | | e3 & op(e2, e1) = e3)
% 108.69/15.46 | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | BETA: splitting (1802) gives:
% 108.69/15.46 | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | (1803) all_57_60 = e3 & op(e3, e1) = e3
% 108.69/15.46 | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | ALPHA: (1803) implies:
% 108.69/15.46 | | | | | | | | | | | | | (1804) op(e3, e1) = e3
% 108.69/15.46 | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | BETA: splitting (227) gives:
% 108.69/15.46 | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | (1805) (all_57_56 = e3 & op(e1, e3) = e3) | (all_57_57 =
% 108.69/15.46 | | | | | | | | | | | | | | e3 & op(e1, e2) = e3)
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | BETA: splitting (1805) gives:
% 108.69/15.46 | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | (1806) all_57_56 = e3 & op(e1, e3) = e3
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | ALPHA: (1806) implies:
% 108.69/15.46 | | | | | | | | | | | | | | | (1807) op(e1, e3) = e3
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e3,
% 108.69/15.46 | | | | | | | | | | | | | | | e3, e1, simplifying with (167), (1807) gives:
% 108.69/15.46 | | | | | | | | | | | | | | | (1808) all_53_6 = e3
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 108.69/15.46 | | | | | | | | | | | | | | | e3, e1, e3, simplifying with (173), (1804) gives:
% 108.69/15.46 | | | | | | | | | | | | | | | (1809) all_53_13 = e3
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | REDUCE: (132), (1808) imply:
% 108.69/15.46 | | | | | | | | | | | | | | | (1810) ~ (all_53_7 = e3)
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | REDUCE: (117), (1809) imply:
% 108.69/15.46 | | | | | | | | | | | | | | | (1811) ~ (all_53_12 = e3)
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | REDUCE: (1763), (1809) imply:
% 108.69/15.46 | | | | | | | | | | | | | | | (1812) ~ (all_14_0 = e3)
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | REDUCE: (375), (1809) imply:
% 108.69/15.46 | | | | | | | | | | | | | | | (1813) ~ (all_4_2 = e3)
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | SIMP: (1813) implies:
% 108.69/15.46 | | | | | | | | | | | | | | | (1814) ~ (all_4_2 = e3)
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 108.69/15.46 | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | (1815) all_55_15 = e3
% 108.69/15.46 | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | REF_CLOSE: (339), (1814), (1815) are inconsistent by
% 108.69/15.46 | | | | | | | | | | | | | | | | sub-proof #140.
% 108.69/15.46 | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | Case 2:
% 108.69/15.46 | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | (1816) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 108.69/15.46 | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | BETA: splitting (1816) gives:
% 108.69/15.46 | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | (1817) all_55_15 = e2
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | REF_CLOSE: (339), (1767), (1817) are inconsistent by
% 108.69/15.46 | | | | | | | | | | | | | | | | | sub-proof #193.
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | (1818) all_55_15 = e1 | all_55_15 = e0
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | BETA: splitting (1818) gives:
% 108.69/15.46 | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.46 | | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | | (1819) all_55_15 = e1
% 108.69/15.46 | | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (1819) imply:
% 108.69/15.46 | | | | | | | | | | | | | | | | | | (1820) all_4_2 = e1
% 108.69/15.46 | | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | | SIMP: (1820) implies:
% 108.69/15.46 | | | | | | | | | | | | | | | | | | (1821) all_4_2 = e1
% 108.69/15.46 | | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | | REDUCE: (374), (1821) imply:
% 108.69/15.46 | | | | | | | | | | | | | | | | | | (1822) ~ (all_53_12 = e1)
% 108.69/15.46 | | | | | | | | | | | | | | | | | |
% 108.69/15.46 | | | | | | | | | | | | | | | | | | REDUCE: (1764), (1821) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | (1823) ~ (all_14_0 = e1)
% 108.69/15.47 | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 108.69/15.47 | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | (1824) all_55_14 = e3
% 108.69/15.47 | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1760), (1765), (1824) are inconsistent by
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | sub-proof #95.
% 108.69/15.47 | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | (1825) ~ (all_55_14 = e3)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | (1826) all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | BETA: splitting (1826) gives:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | (1827) all_55_14 = e2
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1760), (1827) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | (1828) all_14_0 = e2
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | SIMP: (1828) implies:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | (1829) all_14_0 = e2
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (1761), (1829) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | (1830) ~ (all_53_7 = e2)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (1762), (1829) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | (1831) ~ (all_53_12 = e2)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (1765), (1829) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | (1832) ~ (e3 = e2)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (1758), (1829) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | (1833) op(e3, e2) = e2
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | (1834) all_55_12 = e3
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (1811), (1834) are inconsistent by
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | sub-proof #94.
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | (1835) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1835) gives:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | (1836) all_55_12 = e2
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (1831), (1836) are inconsistent by
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | sub-proof #93.
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | (1837) all_55_12 = e1 | all_55_12 = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1837) gives:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | (1838) all_55_12 = e1
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (1822), (1838) are inconsistent by
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #92.
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | (1839) all_55_12 = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (1839) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | (1840) all_53_12 = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1840) implies:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | (1841) all_53_12 = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (1841) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | (1842) ~ (all_53_4 = e0)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | (1843) all_55_4 = e3
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (252), (1801), (1843) are inconsistent by
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #123.
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | (1844) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1844) gives:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | (1845) all_55_4 = e2
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (252), (1743), (1845) are inconsistent by
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #116.
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | (1846) all_55_4 = e1 | all_55_4 = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1846) gives:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (1847) all_55_4 = e1
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (1847) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (1848) all_53_4 = e1
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1848) implies:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (1849) all_53_4 = e1
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (1849) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (1850) ~ (all_53_7 = e1)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1850) implies:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (1851) ~ (all_53_7 = e1)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1852) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1833), (1852), (function-axioms) are
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #91.
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1853) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1853) gives:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1854) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1854) implies:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1855) op(e1, e2) = e1
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (1851), (1855), (function-axioms) are
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #233.
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1856) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1856) implies:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1857) op(e0, e2) = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1858) all_55_6 = e3
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (1858) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1859) all_53_7 = e3
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1495), (1859) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1860) $false
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1860) is inconsistent.
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1861) all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1861) gives:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1862) all_55_6 = e2
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (1862) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1863) all_53_7 = e2
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1830), (1863) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1864) $false
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1864) is inconsistent.
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1865) all_55_6 = e1 | all_55_6 = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1865) gives:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1866) all_55_6 = e1
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (1866) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1867) all_53_7 = e1
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1851), (1867) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1868) $false
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1868) is inconsistent.
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1869) all_55_6 = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (1869) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1870) all_53_7 = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (1870) imply:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1871) ~ (all_53_3 = e0)
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (1857), (1871), (function-axioms) are
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (1872) all_55_4 = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (252), (1842), (1872) are inconsistent by
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #113.
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | (1873) all_55_14 = e1 | all_55_14 = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1757), (1760), (1823), (1873) are inconsistent by
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | | sub-proof #90.
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | (1874) all_55_15 = e0
% 108.69/15.47 | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | | REF_CLOSE: (339), (378), (1874) are inconsistent by sub-proof
% 108.69/15.47 | | | | | | | | | | | | | | | | | | #192.
% 108.69/15.47 | | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | (1875) all_57_57 = e3 & op(e1, e2) = e3
% 108.69/15.47 | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | ALPHA: (1875) implies:
% 108.69/15.47 | | | | | | | | | | | | | | | (1876) op(e1, e2) = e3
% 108.69/15.47 | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | | REF_CLOSE: (166), (1495), (1876), (function-axioms) are
% 108.69/15.47 | | | | | | | | | | | | | | | inconsistent by sub-proof #179.
% 108.69/15.47 | | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | (1877) (all_57_58 = e3 & op(e1, e1) = e3) | (all_57_59 =
% 108.69/15.47 | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 108.69/15.47 | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (1745), (1801), (1877),
% 108.69/15.47 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.69/15.47 | | | | | | | | | | | | | | #125.
% 108.69/15.47 | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | (1878) all_57_61 = e3 & op(e2, e1) = e3
% 108.69/15.47 | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | ALPHA: (1878) implies:
% 108.69/15.47 | | | | | | | | | | | | | (1879) op(e2, e1) = e3
% 108.69/15.47 | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | REF_CLOSE: (169), (1496), (1879), (function-axioms) are
% 108.69/15.47 | | | | | | | | | | | | | inconsistent by sub-proof #138.
% 108.69/15.47 | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | (1880) (all_57_62 = e3 & op(e1, e1) = e3) | (all_57_63 =
% 108.69/15.47 | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 108.69/15.47 | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | REF_CLOSE: (8), (161), (1745), (1800), (1880),
% 108.69/15.47 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.69/15.47 | | | | | | | | | | | | #89.
% 108.69/15.47 | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | End of split
% 108.69/15.47 | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | (1881) all_26_2 = e2
% 108.69/15.47 | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | COMBINE_EQS: (316), (1881) imply:
% 108.69/15.47 | | | | | | | | | | (1882) all_4_2 = e2
% 108.69/15.47 | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | SIMP: (1882) implies:
% 108.69/15.47 | | | | | | | | | | (1883) all_4_2 = e2
% 108.69/15.47 | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | REDUCE: (355), (1883) imply:
% 108.69/15.47 | | | | | | | | | | (1884) ~ (all_53_2 = e2)
% 108.69/15.47 | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | REDUCE: (1764), (1883) imply:
% 108.69/15.47 | | | | | | | | | | (1885) ~ (all_14_0 = e2)
% 108.69/15.47 | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | BETA: splitting (194) gives:
% 108.69/15.47 | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | (1886) all_55_14 = e3
% 108.69/15.47 | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | REF_CLOSE: (1760), (1765), (1886) are inconsistent by
% 108.69/15.47 | | | | | | | | | | | sub-proof #95.
% 108.69/15.47 | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | (1887) ~ (all_55_14 = e3)
% 108.69/15.47 | | | | | | | | | | | (1888) all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 108.69/15.47 | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | BETA: splitting (1888) gives:
% 108.69/15.47 | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | (1889) all_55_14 = e2
% 108.69/15.47 | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | REF_CLOSE: (1760), (1885), (1889) are inconsistent by
% 108.69/15.47 | | | | | | | | | | | | sub-proof #88.
% 108.69/15.47 | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | Case 2:
% 108.69/15.47 | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | (1890) all_55_14 = e1 | all_55_14 = e0
% 108.69/15.47 | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | BETA: splitting (237) gives:
% 108.69/15.47 | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | (1891) (all_57_16 = e2 & op(e0, e3) = e2) | (all_57_17 =
% 108.69/15.47 | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 108.69/15.47 | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | BETA: splitting (1891) gives:
% 108.69/15.47 | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | Case 1:
% 108.69/15.47 | | | | | | | | | | | | | |
% 108.69/15.47 | | | | | | | | | | | | | | (1892) all_57_16 = e2 & op(e0, e3) = e2
% 109.31/15.47 | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | ALPHA: (1892) implies:
% 109.31/15.47 | | | | | | | | | | | | | | (1893) op(e0, e3) = e2
% 109.31/15.47 | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | REF_CLOSE: (163), (1884), (1893), (function-axioms) are
% 109.31/15.47 | | | | | | | | | | | | | | inconsistent by sub-proof #164.
% 109.31/15.47 | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | Case 2:
% 109.31/15.47 | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | (1894) all_57_17 = e2 & op(e0, e2) = e2
% 109.31/15.47 | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | ALPHA: (1894) implies:
% 109.31/15.47 | | | | | | | | | | | | | | (1895) op(e0, e2) = e2
% 109.31/15.47 | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | BETA: splitting (1890) gives:
% 109.31/15.47 | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | Case 1:
% 109.31/15.47 | | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | | (1896) all_55_14 = e1
% 109.31/15.47 | | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | | COMBINE_EQS: (1760), (1896) imply:
% 109.31/15.47 | | | | | | | | | | | | | | | (1897) all_14_0 = e1
% 109.31/15.47 | | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | | SIMP: (1897) implies:
% 109.31/15.47 | | | | | | | | | | | | | | | (1898) all_14_0 = e1
% 109.31/15.47 | | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | | REDUCE: (1761), (1898) imply:
% 109.31/15.47 | | | | | | | | | | | | | | | (1899) ~ (all_53_7 = e1)
% 109.31/15.47 | | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | | REDUCE: (1765), (1898) imply:
% 109.31/15.47 | | | | | | | | | | | | | | | (1900) ~ (e3 = e1)
% 109.31/15.47 | | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | | REDUCE: (1758), (1898) imply:
% 109.31/15.47 | | | | | | | | | | | | | | | (1901) op(e3, e2) = e1
% 109.31/15.47 | | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 109.31/15.47 | | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | | Case 1:
% 109.31/15.47 | | | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | | | (1902) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 109.31/15.47 | | | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 109.31/15.47 | | | | | | | | | | | | | | | |
% 109.31/15.47 | | | | | | | | | | | | | | | | ALPHA: (1902) implies:
% 109.31/15.48 | | | | | | | | | | | | | | | | (1903) op(e3, e2) = e3
% 109.31/15.48 | | | | | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (174), (1901), (1903), (function-axioms) are
% 109.31/15.48 | | | | | | | | | | | | | | | | inconsistent by sub-proof #87.
% 109.31/15.48 | | | | | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | | | | Case 2:
% 109.31/15.48 | | | | | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | | | | | (1904) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 109.31/15.48 | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 109.31/15.48 | | | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 109.31/15.48 | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 109.31/15.48 | | | | | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (166), (1895), (1899), (1904),
% 109.31/15.48 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.31/15.48 | | | | | | | | | | | | | | | | #162.
% 109.31/15.48 | | | | | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | | | | End of split
% 109.31/15.48 | | | | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | | | Case 2:
% 109.31/15.48 | | | | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | | | | (1905) all_55_14 = e0
% 109.31/15.48 | | | | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | | | | REF_CLOSE: (1757), (1760), (1905) are inconsistent by
% 109.31/15.48 | | | | | | | | | | | | | | | sub-proof #86.
% 109.31/15.48 | | | | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | | | End of split
% 109.31/15.48 | | | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | | End of split
% 109.31/15.48 | | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | Case 2:
% 109.31/15.48 | | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | | (1906) (all_57_18 = e2 & op(e0, e1) = e2) | (all_57_19 =
% 109.31/15.48 | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 109.31/15.48 | | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | | REF_CLOSE: (38), (161), (381), (1742), (1906),
% 109.31/15.48 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.31/15.48 | | | | | | | | | | | | | #159.
% 109.31/15.48 | | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | End of split
% 109.31/15.48 | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | End of split
% 109.31/15.48 | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | End of split
% 109.31/15.48 | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | End of split
% 109.31/15.48 | | | | | | | | |
% 109.31/15.48 | | | | | | | | End of split
% 109.31/15.48 | | | | | | | |
% 109.31/15.48 | | | | | | | End of split
% 109.31/15.48 | | | | | | |
% 109.31/15.48 | | | | | | End of split
% 109.31/15.48 | | | | | |
% 109.31/15.48 | | | | | End of split
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | End of split
% 109.31/15.48 | | | |
% 109.31/15.48 | | | Case 2:
% 109.31/15.48 | | | |
% 109.31/15.48 | | | | (1907) all_8_2 = e2
% 109.31/15.48 | | | | (1908) op(e2, e2) = all_8_1 & $i(all_8_1) & ( ~ (all_8_1 = e1) | ( ~
% 109.31/15.48 | | | | (all_8_0 = e3) & op(e1, e2) = all_8_0 & $i(all_8_0)))
% 109.31/15.48 | | | |
% 109.31/15.48 | | | | ALPHA: (1908) implies:
% 109.31/15.48 | | | | (1909) op(e2, e2) = all_8_1
% 109.31/15.48 | | | | (1910) ~ (all_8_1 = e1) | ( ~ (all_8_0 = e3) & op(e1, e2) = all_8_0
% 109.31/15.48 | | | | & $i(all_8_0))
% 109.31/15.48 | | | |
% 109.31/15.48 | | | | COMBINE_EQS: (328), (1907) imply:
% 109.31/15.48 | | | | (1911) all_6_2 = e2
% 109.31/15.48 | | | |
% 109.31/15.48 | | | | SIMP: (1911) implies:
% 109.31/15.48 | | | | (1912) all_6_2 = e2
% 109.31/15.48 | | | |
% 109.31/15.48 | | | | COMBINE_EQS: (322), (1912) imply:
% 109.31/15.48 | | | | (1913) all_16_2 = e2
% 109.31/15.48 | | | |
% 109.31/15.48 | | | | REDUCE: (343), (1912) imply:
% 109.31/15.48 | | | | (1914) ~ (all_53_1 = e2)
% 109.31/15.48 | | | |
% 109.31/15.48 | | | | REDUCE: (345), (1912) imply:
% 109.31/15.48 | | | | (1915) ~ (all_53_2 = e2)
% 109.31/15.48 | | | |
% 109.31/15.48 | | | | REDUCE: (347), (1912) imply:
% 109.31/15.48 | | | | (1916) ~ (all_53_3 = e2)
% 109.31/15.48 | | | |
% 109.31/15.48 | | | | REDUCE: (349), (1912) imply:
% 109.31/15.48 | | | | (1917) ~ (all_53_4 = e2)
% 109.31/15.48 | | | |
% 109.31/15.48 | | | | REDUCE: (351), (1912) imply:
% 109.31/15.48 | | | | (1918) ~ (all_53_8 = e2)
% 109.31/15.48 | | | |
% 109.31/15.48 | | | | REDUCE: (379), (1912) imply:
% 109.31/15.48 | | | | (1919) ~ (e2 = e1)
% 109.31/15.48 | | | |
% 109.31/15.48 | | | | REDUCE: (38), (1912) imply:
% 109.31/15.48 | | | | (1920) op(e0, e0) = e2
% 109.31/15.48 | | | |
% 109.31/15.48 | | | | BETA: splitting (54) gives:
% 109.31/15.48 | | | |
% 109.31/15.48 | | | | Case 1:
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | (1921) ~ (all_16_2 = e2)
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | REDUCE: (1913), (1921) imply:
% 109.31/15.48 | | | | | (1922) $false
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | CLOSE: (1922) is inconsistent.
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | Case 2:
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | (1923) op(e2, e2) = all_16_1 & $i(all_16_1) & ( ~ (all_16_1 = e3) |
% 109.31/15.48 | | | | | ( ~ (all_16_0 = e1) & op(e3, e2) = all_16_0 &
% 109.31/15.48 | | | | | $i(all_16_0)))
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | ALPHA: (1923) implies:
% 109.31/15.48 | | | | | (1924) op(e2, e2) = all_16_1
% 109.31/15.48 | | | | | (1925) ~ (all_16_1 = e3) | ( ~ (all_16_0 = e1) & op(e3, e2) =
% 109.31/15.48 | | | | | all_16_0 & $i(all_16_0))
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, all_16_1,
% 109.31/15.48 | | | | | e2, e2, simplifying with (44), (1924) gives:
% 109.31/15.48 | | | | | (1926) all_16_1 = all_10_2
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, all_16_1,
% 109.31/15.48 | | | | | e2, e2, simplifying with (1909), (1924) gives:
% 109.31/15.48 | | | | | (1927) all_16_1 = all_8_1
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | COMBINE_EQS: (1926), (1927) imply:
% 109.31/15.48 | | | | | (1928) all_10_2 = all_8_1
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | COMBINE_EQS: (323), (1928) imply:
% 109.31/15.48 | | | | | (1929) all_12_2 = all_8_1
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | COMBINE_EQS: (303), (1928) imply:
% 109.31/15.48 | | | | | (1930) all_24_2 = all_8_1
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | COMBINE_EQS: (330), (1928) imply:
% 109.31/15.48 | | | | | (1931) all_30_2 = all_8_1
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | COMBINE_EQS: (265), (1928) imply:
% 109.31/15.48 | | | | | (1932) all_46_2 = all_8_1
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | COMBINE_EQS: (335), (1928) imply:
% 109.31/15.48 | | | | | (1933) all_48_2 = all_8_1
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | COMBINE_EQS: (340), (1928) imply:
% 109.31/15.48 | | | | | (1934) all_55_10 = all_8_1
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | REDUCE: (356), (1928) imply:
% 109.31/15.48 | | | | | (1935) ~ (all_53_3 = all_8_1)
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | REDUCE: (367), (1928) imply:
% 109.31/15.48 | | | | | (1936) ~ (all_53_7 = all_8_1)
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | REDUCE: (368), (1928) imply:
% 109.31/15.48 | | | | | (1937) ~ (all_53_8 = all_8_1)
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | REDUCE: (369), (1928) imply:
% 109.31/15.48 | | | | | (1938) ~ (all_53_9 = all_8_1)
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | REDUCE: (370), (1928) imply:
% 109.31/15.48 | | | | | (1939) ~ (all_53_10 = all_8_1)
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | REDUCE: (373), (1928) imply:
% 109.31/15.48 | | | | | (1940) ~ (all_53_15 = all_8_1)
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | BETA: splitting (45) gives:
% 109.31/15.48 | | | | |
% 109.31/15.48 | | | | | Case 1:
% 109.31/15.48 | | | | | |
% 109.31/15.48 | | | | | | (1941) ~ (all_10_2 = e3)
% 109.31/15.48 | | | | | |
% 109.31/15.48 | | | | | | REDUCE: (1928), (1941) imply:
% 109.31/15.48 | | | | | | (1942) ~ (all_8_1 = e3)
% 109.31/15.48 | | | | | |
% 109.31/15.48 | | | | | | BETA: splitting (48) gives:
% 109.31/15.48 | | | | | |
% 109.31/15.48 | | | | | | Case 1:
% 109.31/15.48 | | | | | | |
% 109.31/15.48 | | | | | | | (1943) ~ (all_12_2 = e0)
% 109.31/15.48 | | | | | | |
% 109.31/15.48 | | | | | | | REDUCE: (1929), (1943) imply:
% 109.31/15.48 | | | | | | | (1944) ~ (all_8_1 = e0)
% 109.31/15.48 | | | | | | |
% 109.31/15.48 | | | | | | | BETA: splitting (51) gives:
% 109.31/15.48 | | | | | | |
% 109.31/15.48 | | | | | | | Case 1:
% 109.31/15.48 | | | | | | | |
% 109.31/15.48 | | | | | | | | (1945) ~ (all_14_2 = e2)
% 109.31/15.48 | | | | | | | |
% 109.31/15.48 | | | | | | | | BETA: splitting (57) gives:
% 109.31/15.48 | | | | | | | |
% 109.31/15.48 | | | | | | | | Case 1:
% 109.31/15.48 | | | | | | | | |
% 109.31/15.48 | | | | | | | | | (1946) ~ (all_18_2 = e3)
% 109.31/15.48 | | | | | | | | |
% 109.31/15.48 | | | | | | | | | REDUCE: (326), (1946) imply:
% 109.31/15.48 | | | | | | | | | (1947) ~ (all_14_2 = e3)
% 109.31/15.48 | | | | | | | | |
% 109.31/15.48 | | | | | | | | | BETA: splitting (63) gives:
% 109.31/15.48 | | | | | | | | |
% 109.31/15.48 | | | | | | | | | Case 1:
% 109.31/15.48 | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | (1948) ~ (all_22_2 = e0)
% 109.31/15.48 | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | REDUCE: (329), (1948) imply:
% 109.31/15.48 | | | | | | | | | | (1949) ~ (all_14_2 = e0)
% 109.31/15.48 | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (117), (123),
% 109.31/15.48 | | | | | | | | | | (126), (127), (148), (152), (153), (161), (162),
% 109.31/15.48 | | | | | | | | | | (163), (164), (166), (167), (168), (169), (171),
% 109.31/15.48 | | | | | | | | | | (172), (173), (174), (203), (341), (357), (359),
% 109.31/15.48 | | | | | | | | | | (361), (1945), (1947), (1949), (function-axioms)
% 109.31/15.48 | | | | | | | | | | are inconsistent by sub-proof #216.
% 109.31/15.48 | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | Case 2:
% 109.31/15.48 | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | (1950) all_22_2 = e0
% 109.31/15.48 | | | | | | | | | | (1951) op(e0, e0) = all_22_1 & $i(all_22_1) & ( ~
% 109.31/15.48 | | | | | | | | | | (all_22_1 = e2) | ( ~ (all_22_0 = e3) & op(e2,
% 109.31/15.48 | | | | | | | | | | e0) = all_22_0 & $i(all_22_0)))
% 109.31/15.48 | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | ALPHA: (1951) implies:
% 109.31/15.48 | | | | | | | | | | (1952) op(e0, e0) = all_22_1
% 109.31/15.48 | | | | | | | | | | (1953) ~ (all_22_1 = e2) | ( ~ (all_22_0 = e3) & op(e2,
% 109.31/15.48 | | | | | | | | | | e0) = all_22_0 & $i(all_22_0))
% 109.31/15.48 | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | COMBINE_EQS: (329), (1950) imply:
% 109.31/15.48 | | | | | | | | | | (1954) all_14_2 = e0
% 109.31/15.48 | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | COMBINE_EQS: (331), (1954) imply:
% 109.31/15.48 | | | | | | | | | | (1955) all_32_2 = e0
% 109.31/15.48 | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | REDUCE: (354), (1954) imply:
% 109.31/15.48 | | | | | | | | | | (1956) ~ (all_53_1 = e0)
% 109.31/15.48 | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | REDUCE: (365), (1954) imply:
% 109.31/15.48 | | | | | | | | | | (1957) ~ (all_53_13 = e0)
% 109.31/15.48 | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | REDUCE: (50), (1954) imply:
% 109.31/15.48 | | | | | | | | | | (1958) op(e1, e1) = e0
% 109.31/15.48 | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | BETA: splitting (78) gives:
% 109.31/15.48 | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | Case 1:
% 109.31/15.48 | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | (1959) ~ (all_32_2 = e0)
% 109.31/15.48 | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | REDUCE: (1955), (1959) imply:
% 109.31/15.48 | | | | | | | | | | | (1960) $false
% 109.31/15.48 | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | CLOSE: (1960) is inconsistent.
% 109.31/15.48 | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | Case 2:
% 109.31/15.48 | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | (1961) op(e0, e0) = all_32_1 & $i(all_32_1) & ( ~
% 109.31/15.48 | | | | | | | | | | | (all_32_1 = e3) | ( ~ (all_32_0 = e2) & op(e3,
% 109.31/15.48 | | | | | | | | | | | e0) = all_32_0 & $i(all_32_0)))
% 109.31/15.48 | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | ALPHA: (1961) implies:
% 109.31/15.48 | | | | | | | | | | | (1962) op(e0, e0) = all_32_1
% 109.31/15.48 | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_32_1,
% 109.31/15.48 | | | | | | | | | | | e0, e0, simplifying with (1920), (1962) gives:
% 109.31/15.48 | | | | | | | | | | | (1963) all_32_1 = e2
% 109.31/15.48 | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 109.31/15.48 | | | | | | | | | | | all_32_1, e0, e0, simplifying with (1952), (1962)
% 109.31/15.48 | | | | | | | | | | | gives:
% 109.31/15.48 | | | | | | | | | | | (1964) all_32_1 = all_22_1
% 109.31/15.48 | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | COMBINE_EQS: (1963), (1964) imply:
% 109.31/15.48 | | | | | | | | | | | (1965) all_22_1 = e2
% 109.31/15.48 | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | BETA: splitting (1953) gives:
% 109.31/15.48 | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | Case 1:
% 109.31/15.48 | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | (1966) ~ (all_22_1 = e2)
% 109.31/15.48 | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | REDUCE: (1965), (1966) imply:
% 109.31/15.48 | | | | | | | | | | | | (1967) $false
% 109.31/15.48 | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | CLOSE: (1967) is inconsistent.
% 109.31/15.48 | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | Case 2:
% 109.31/15.48 | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | (1968) ~ (all_22_0 = e3) & op(e2, e0) = all_22_0 &
% 109.31/15.48 | | | | | | | | | | | | $i(all_22_0)
% 109.31/15.48 | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | ALPHA: (1968) implies:
% 109.31/15.48 | | | | | | | | | | | | (1969) ~ (all_22_0 = e3)
% 109.31/15.48 | | | | | | | | | | | | (1970) op(e2, e0) = all_22_0
% 109.31/15.48 | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 109.31/15.48 | | | | | | | | | | | | all_22_0, e0, e2, simplifying with (168), (1970)
% 109.31/15.48 | | | | | | | | | | | | gives:
% 109.31/15.48 | | | | | | | | | | | | (1971) all_53_8 = all_22_0
% 109.31/15.48 | | | | | | | | | | | |
% 109.31/15.48 | | | | | | | | | | | | COMBINE_EQS: (262), (1971) imply:
% 109.31/15.49 | | | | | | | | | | | | (1972) all_55_8 = all_22_0
% 109.31/15.49 | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | REDUCE: (124), (1971) imply:
% 109.31/15.49 | | | | | | | | | | | | (1973) ~ (all_53_12 = all_22_0)
% 109.31/15.49 | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | SIMP: (1973) implies:
% 109.31/15.49 | | | | | | | | | | | | (1974) ~ (all_53_12 = all_22_0)
% 109.31/15.49 | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | REDUCE: (1937), (1971) imply:
% 109.31/15.49 | | | | | | | | | | | | (1975) ~ (all_22_0 = all_8_1)
% 109.31/15.49 | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | REDUCE: (1918), (1971) imply:
% 109.31/15.49 | | | | | | | | | | | | (1976) ~ (all_22_0 = e2)
% 109.31/15.49 | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | BETA: splitting (66) gives:
% 109.31/15.49 | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | Case 1:
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | (1977) ~ (all_24_2 = e1)
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | REDUCE: (1930), (1977) imply:
% 109.31/15.49 | | | | | | | | | | | | | (1978) ~ (all_8_1 = e1)
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | REF_CLOSE: (109), (161), (169), (173), (198), (228), (1914),
% 109.31/15.49 | | | | | | | | | | | | | (1934), (1938), (1942), (1944), (1956), (1958),
% 109.31/15.49 | | | | | | | | | | | | | (1978), (function-axioms) are inconsistent by
% 109.31/15.49 | | | | | | | | | | | | | sub-proof #83.
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | Case 2:
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | (1979) all_24_2 = e1
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | COMBINE_EQS: (1930), (1979) imply:
% 109.31/15.49 | | | | | | | | | | | | | (1980) all_8_1 = e1
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | SIMP: (1980) implies:
% 109.31/15.49 | | | | | | | | | | | | | (1981) all_8_1 = e1
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | REDUCE: (1935), (1981) imply:
% 109.31/15.49 | | | | | | | | | | | | | (1982) ~ (all_53_3 = e1)
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | REDUCE: (1936), (1981) imply:
% 109.31/15.49 | | | | | | | | | | | | | (1983) ~ (all_53_7 = e1)
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | REDUCE: (1940), (1981) imply:
% 109.31/15.49 | | | | | | | | | | | | | (1984) ~ (all_53_15 = e1)
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | REDUCE: (1975), (1981) imply:
% 109.31/15.49 | | | | | | | | | | | | | (1985) ~ (all_22_0 = e1)
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | BETA: splitting (200) gives:
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | Case 1:
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | (1986) all_55_8 = e3
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | COMBINE_EQS: (1972), (1986) imply:
% 109.31/15.49 | | | | | | | | | | | | | | (1987) all_22_0 = e3
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | REDUCE: (1969), (1987) imply:
% 109.31/15.49 | | | | | | | | | | | | | | (1988) $false
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | CLOSE: (1988) is inconsistent.
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | Case 2:
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | (1989) ~ (all_55_8 = e3)
% 109.31/15.49 | | | | | | | | | | | | | | (1990) all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | BETA: splitting (1990) gives:
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | Case 1:
% 109.31/15.49 | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | (1991) all_55_8 = e2
% 109.31/15.49 | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | COMBINE_EQS: (1972), (1991) imply:
% 109.31/15.49 | | | | | | | | | | | | | | | (1992) all_22_0 = e2
% 109.31/15.49 | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | REDUCE: (1976), (1992) imply:
% 109.31/15.49 | | | | | | | | | | | | | | | (1993) $false
% 109.31/15.49 | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | CLOSE: (1993) is inconsistent.
% 109.31/15.49 | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | Case 2:
% 109.31/15.49 | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | (1994) all_55_8 = e1 | all_55_8 = e0
% 109.31/15.49 | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | BETA: splitting (1994) gives:
% 109.31/15.49 | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | Case 1:
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | (1995) all_55_8 = e1
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | COMBINE_EQS: (1972), (1995) imply:
% 109.31/15.49 | | | | | | | | | | | | | | | | (1996) all_22_0 = e1
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | REDUCE: (1985), (1996) imply:
% 109.31/15.49 | | | | | | | | | | | | | | | | (1997) $false
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | CLOSE: (1997) is inconsistent.
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | Case 2:
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | (1998) all_55_8 = e0
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | COMBINE_EQS: (1972), (1998) imply:
% 109.31/15.49 | | | | | | | | | | | | | | | | (1999) all_22_0 = e0
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | REDUCE: (1974), (1999) imply:
% 109.31/15.49 | | | | | | | | | | | | | | | | (2000) ~ (all_53_12 = e0)
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | REDUCE: (1969), (1999) imply:
% 109.31/15.49 | | | | | | | | | | | | | | | | (2001) ~ (e3 = e0)
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | REF_CLOSE: (35), (108), (142), (162), (166), (172), (173),
% 109.31/15.49 | | | | | | | | | | | | | | | | (174), (217), (222), (378), (1957), (1982),
% 109.31/15.49 | | | | | | | | | | | | | | | | (1983), (1984), (2000), (2001), (function-axioms)
% 109.31/15.49 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #200.
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | End of split
% 109.31/15.49 | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | End of split
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | End of split
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | End of split
% 109.31/15.49 | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | End of split
% 109.31/15.49 | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | End of split
% 109.31/15.49 | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | End of split
% 109.31/15.49 | | | | | | | | |
% 109.31/15.49 | | | | | | | | Case 2:
% 109.31/15.49 | | | | | | | | |
% 109.31/15.49 | | | | | | | | | (2002) all_18_2 = e3
% 109.31/15.49 | | | | | | | | |
% 109.31/15.49 | | | | | | | | | COMBINE_EQS: (326), (2002) imply:
% 109.31/15.49 | | | | | | | | | (2003) all_14_2 = e3
% 109.31/15.49 | | | | | | | | |
% 109.31/15.49 | | | | | | | | | REDUCE: (354), (2003) imply:
% 109.31/15.49 | | | | | | | | | (2004) ~ (all_53_1 = e3)
% 109.31/15.49 | | | | | | | | |
% 109.31/15.49 | | | | | | | | | REDUCE: (357), (2003) imply:
% 109.31/15.49 | | | | | | | | | (2005) ~ (all_53_4 = e3)
% 109.31/15.49 | | | | | | | | |
% 109.31/15.49 | | | | | | | | | REDUCE: (361), (2003) imply:
% 109.31/15.49 | | | | | | | | | (2006) ~ (all_53_7 = e3)
% 109.31/15.49 | | | | | | | | |
% 109.31/15.49 | | | | | | | | | REDUCE: (363), (2003) imply:
% 109.31/15.49 | | | | | | | | | (2007) ~ (all_53_9 = e3)
% 109.31/15.49 | | | | | | | | |
% 109.31/15.49 | | | | | | | | | REDUCE: (365), (2003) imply:
% 109.31/15.49 | | | | | | | | | (2008) ~ (all_53_13 = e3)
% 109.31/15.49 | | | | | | | | |
% 109.31/15.49 | | | | | | | | | REDUCE: (50), (2003) imply:
% 109.31/15.49 | | | | | | | | | (2009) op(e1, e1) = e3
% 109.31/15.49 | | | | | | | | |
% 109.31/15.49 | | | | | | | | | BETA: splitting (66) gives:
% 109.31/15.49 | | | | | | | | |
% 109.31/15.49 | | | | | | | | | Case 1:
% 109.31/15.49 | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | (2010) ~ (all_24_2 = e1)
% 109.31/15.49 | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | REDUCE: (1930), (2010) imply:
% 109.31/15.49 | | | | | | | | | | (2011) ~ (all_8_1 = e1)
% 109.31/15.49 | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | BETA: splitting (198) gives:
% 109.31/15.49 | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | Case 1:
% 109.31/15.49 | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | (2012) all_55_10 = e3
% 109.31/15.49 | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | COMBINE_EQS: (1934), (2012) imply:
% 109.31/15.49 | | | | | | | | | | | (2013) all_8_1 = e3
% 109.31/15.49 | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | REDUCE: (1942), (2013) imply:
% 109.31/15.49 | | | | | | | | | | | (2014) $false
% 109.31/15.49 | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | CLOSE: (2014) is inconsistent.
% 109.31/15.49 | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | Case 2:
% 109.31/15.49 | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | (2015) ~ (all_55_10 = e3)
% 109.31/15.49 | | | | | | | | | | | (2016) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 109.31/15.49 | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | BETA: splitting (2016) gives:
% 109.31/15.49 | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | Case 1:
% 109.31/15.49 | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | (2017) all_55_10 = e2
% 109.31/15.49 | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | COMBINE_EQS: (1934), (2017) imply:
% 109.31/15.49 | | | | | | | | | | | | (2018) all_8_1 = e2
% 109.31/15.49 | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | REDUCE: (1936), (2018) imply:
% 109.31/15.49 | | | | | | | | | | | | (2019) ~ (all_53_7 = e2)
% 109.31/15.49 | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | REDUCE: (1938), (2018) imply:
% 109.31/15.49 | | | | | | | | | | | | (2020) ~ (all_53_9 = e2)
% 109.31/15.49 | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | REDUCE: (1942), (2018) imply:
% 109.31/15.49 | | | | | | | | | | | | (2021) ~ (e3 = e2)
% 109.31/15.49 | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | BETA: splitting (109) gives:
% 109.31/15.49 | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | Case 1:
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | (2022) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 109.31/15.49 | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | ALPHA: (2022) implies:
% 109.31/15.49 | | | | | | | | | | | | | (2023) op(e3, e1) = e3
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | REF_CLOSE: (173), (2008), (2023), (function-axioms) are
% 109.31/15.49 | | | | | | | | | | | | | inconsistent by sub-proof #232.
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | Case 2:
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | (2024) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.31/15.49 | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 109.31/15.49 | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.31/15.49 | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | BETA: splitting (2024) gives:
% 109.31/15.49 | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | Case 1:
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | (2025) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.31/15.49 | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | ALPHA: (2025) implies:
% 109.31/15.49 | | | | | | | | | | | | | | (2026) op(e2, e1) = e2
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | REF_CLOSE: (169), (2020), (2026), (function-axioms) are
% 109.31/15.49 | | | | | | | | | | | | | | inconsistent by sub-proof #231.
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | Case 2:
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | (2027) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.31/15.49 | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | ALPHA: (2027) implies:
% 109.31/15.49 | | | | | | | | | | | | | | (2028) ~ (all_52_10 = e1)
% 109.31/15.49 | | | | | | | | | | | | | | (2029) op(e0, e1) = e0
% 109.31/15.49 | | | | | | | | | | | | | | (2030) op(e1, e0) = all_52_10
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 109.31/15.49 | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | Case 1:
% 109.31/15.49 | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | (2031) (all_57_48 = e2 & op(e1, e3) = e2) | (all_57_49 =
% 109.31/15.49 | | | | | | | | | | | | | | | e2 & op(e1, e2) = e2)
% 109.31/15.49 | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | BETA: splitting (2031) gives:
% 109.31/15.49 | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | Case 1:
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | (2032) all_57_48 = e2 & op(e1, e3) = e2
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | ALPHA: (2032) implies:
% 109.31/15.49 | | | | | | | | | | | | | | | | (2033) op(e1, e3) = e2
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4,
% 109.31/15.49 | | | | | | | | | | | | | | | | all_52_10, e0, e1, simplifying with (164), (2030)
% 109.31/15.49 | | | | | | | | | | | | | | | | gives:
% 109.31/15.49 | | | | | | | | | | | | | | | | (2034) all_53_4 = all_52_10
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e2,
% 109.31/15.49 | | | | | | | | | | | | | | | | e3, e1, simplifying with (167), (2033) gives:
% 109.31/15.49 | | | | | | | | | | | | | | | | (2035) all_53_6 = e2
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (2034) imply:
% 109.31/15.49 | | | | | | | | | | | | | | | | (2036) all_55_4 = all_52_10
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | REDUCE: (2005), (2034) imply:
% 109.31/15.49 | | | | | | | | | | | | | | | | (2037) ~ (all_52_10 = e3)
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | REDUCE: (1917), (2034) imply:
% 109.31/15.49 | | | | | | | | | | | | | | | | (2038) ~ (all_52_10 = e2)
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | REDUCE: (131), (2035) imply:
% 109.31/15.49 | | | | | | | | | | | | | | | | (2039) ~ (all_53_10 = e2)
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | SIMP: (2039) implies:
% 109.31/15.49 | | | | | | | | | | | | | | | | (2040) ~ (all_53_10 = e2)
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 109.31/15.49 | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | Case 1:
% 109.31/15.49 | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | (2041) all_55_4 = e3
% 109.31/15.49 | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2036), (2041) imply:
% 109.31/15.49 | | | | | | | | | | | | | | | | | (2042) all_52_10 = e3
% 109.31/15.49 | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | SIMP: (2042) implies:
% 109.31/15.49 | | | | | | | | | | | | | | | | | (2043) all_52_10 = e3
% 109.31/15.49 | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | REDUCE: (2037), (2043) imply:
% 109.31/15.49 | | | | | | | | | | | | | | | | | (2044) $false
% 109.31/15.49 | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | CLOSE: (2044) is inconsistent.
% 109.31/15.49 | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | Case 2:
% 109.31/15.49 | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | (2045) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 109.31/15.49 | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 109.31/15.49 | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | Case 1:
% 109.31/15.49 | | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | (2046) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 109.31/15.49 | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 109.31/15.49 | | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | ALPHA: (2046) implies:
% 109.31/15.49 | | | | | | | | | | | | | | | | | | (2047) op(e3, e0) = e3
% 109.31/15.49 | | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 109.31/15.49 | | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | Case 1:
% 109.31/15.49 | | | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | (2048) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2)
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | = all_52_18 & op(e2, e3) = e2 & $i(all_52_18)
% 109.31/15.49 | | | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (2040), (2048), (function-axioms) are
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #215.
% 109.31/15.49 | | | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | Case 2:
% 109.31/15.49 | | | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | (2049) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | (all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22))
% 109.31/15.49 | | | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | BETA: splitting (2049) gives:
% 109.31/15.49 | | | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | Case 1:
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | | (2050) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1919), (2033), (2050), (function-axioms) are
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #82.
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | Case 2:
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | | (2051) all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22)
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.49 | | | | | | | | | | | | | | | | | | | | ALPHA: (2051) implies:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | (2052) ~ (all_52_22 = e3)
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | (2053) op(e3, e0) = all_52_22
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (2047), (2052), (2053), (function-axioms)
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #222.
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | End of split
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | End of split
% 109.31/15.50 | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | (2054) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 109.31/15.50 | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 109.31/15.50 | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 109.31/15.50 | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | BETA: splitting (2054) gives:
% 109.31/15.50 | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | Case 1:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | (2055) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | ALPHA: (2055) implies:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | (2056) op(e2, e0) = e2
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1918), (2056), (function-axioms) are
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #227.
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | (2057) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | ALPHA: (2057) implies:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | (2058) op(e1, e0) = e1
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | BETA: splitting (2045) gives:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | Case 1:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | (2059) all_55_4 = e2
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2036), (2059) imply:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | (2060) all_52_10 = e2
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | SIMP: (2060) implies:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | (2061) all_52_10 = e2
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (2038), (2061) imply:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | (2062) $false
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | CLOSE: (2062) is inconsistent.
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | (2063) all_55_4 = e1 | all_55_4 = e0
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2063) gives:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | (2064) all_55_4 = e1
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2036), (2064) imply:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | (2065) all_52_10 = e1
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | SIMP: (2065) implies:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | (2066) all_52_10 = e1
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2028), (2066) imply:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | (2067) $false
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | CLOSE: (2067) is inconsistent.
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | (2068) all_55_4 = e0
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2036), (2068) imply:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | (2069) all_52_10 = e0
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | SIMP: (2069) implies:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | (2070) all_52_10 = e0
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2028), (2070) imply:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | (2071) ~ (e1 = e0)
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2030), (2070) imply:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | (2072) op(e1, e0) = e0
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2058), (2072), (function-axioms) are
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #81.
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | | End of split
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | End of split
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | End of split
% 109.31/15.50 | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | End of split
% 109.31/15.50 | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | End of split
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | (2073) all_57_49 = e2 & op(e1, e2) = e2
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | ALPHA: (2073) implies:
% 109.31/15.50 | | | | | | | | | | | | | | | | (2074) op(e1, e2) = e2
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2019), (2074), (function-axioms) are
% 109.31/15.50 | | | | | | | | | | | | | | | | inconsistent by sub-proof #80.
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | End of split
% 109.31/15.50 | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | (2075) (all_57_50 = e2 & op(e1, e1) = e2) | (all_57_51 =
% 109.31/15.50 | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 109.31/15.50 | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | BETA: splitting (2075) gives:
% 109.31/15.50 | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | Case 1:
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | (2076) all_57_50 = e2 & op(e1, e1) = e2
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | ALPHA: (2076) implies:
% 109.31/15.50 | | | | | | | | | | | | | | | | (2077) op(e1, e1) = e2
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (161), (169), (173), (226), (2007),
% 109.31/15.50 | | | | | | | | | | | | | | | | (2008), (2029), (2077), (function-axioms) are
% 109.31/15.50 | | | | | | | | | | | | | | | | inconsistent by sub-proof #79.
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | (2078) all_57_51 = e2 & op(e1, e0) = e2
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | ALPHA: (2078) implies:
% 109.31/15.50 | | | | | | | | | | | | | | | | (2079) op(e1, e0) = e2
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1917), (2079), (function-axioms) are
% 109.31/15.50 | | | | | | | | | | | | | | | | inconsistent by sub-proof #112.
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | End of split
% 109.31/15.50 | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | End of split
% 109.31/15.50 | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | End of split
% 109.31/15.50 | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | End of split
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | (2080) all_55_10 = e1 | all_55_10 = e0
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | REF_CLOSE: (1934), (1944), (2011), (2080) are inconsistent by
% 109.31/15.50 | | | | | | | | | | | | sub-proof #84.
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | End of split
% 109.31/15.50 | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | End of split
% 109.31/15.50 | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | (2081) all_24_2 = e1
% 109.31/15.50 | | | | | | | | | | (2082) op(e1, e1) = all_24_1 & $i(all_24_1) & ( ~
% 109.31/15.50 | | | | | | | | | | (all_24_1 = e3) | ( ~ (all_24_0 = e0) & op(e3,
% 109.31/15.50 | | | | | | | | | | e1) = all_24_0 & $i(all_24_0)))
% 109.31/15.50 | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | ALPHA: (2082) implies:
% 109.31/15.50 | | | | | | | | | | (2083) op(e1, e1) = all_24_1
% 109.31/15.50 | | | | | | | | | | (2084) ~ (all_24_1 = e3) | ( ~ (all_24_0 = e0) & op(e3,
% 109.31/15.50 | | | | | | | | | | e1) = all_24_0 & $i(all_24_0))
% 109.31/15.50 | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | COMBINE_EQS: (1930), (2081) imply:
% 109.31/15.50 | | | | | | | | | | (2085) all_8_1 = e1
% 109.31/15.50 | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | COMBINE_EQS: (1932), (2085) imply:
% 109.31/15.50 | | | | | | | | | | (2086) all_46_2 = e1
% 109.31/15.50 | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | REDUCE: (1935), (2085) imply:
% 109.31/15.50 | | | | | | | | | | (2087) ~ (all_53_3 = e1)
% 109.31/15.50 | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | REDUCE: (1936), (2085) imply:
% 109.31/15.50 | | | | | | | | | | (2088) ~ (all_53_7 = e1)
% 109.31/15.50 | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | REDUCE: (1938), (2085) imply:
% 109.31/15.50 | | | | | | | | | | (2089) ~ (all_53_9 = e1)
% 109.31/15.50 | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | REDUCE: (1909), (2085) imply:
% 109.31/15.50 | | | | | | | | | | (2090) op(e2, e2) = e1
% 109.31/15.50 | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | BETA: splitting (99) gives:
% 109.31/15.50 | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | Case 1:
% 109.31/15.50 | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | (2091) ~ (all_46_2 = e1)
% 109.31/15.50 | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | REDUCE: (2086), (2091) imply:
% 109.31/15.50 | | | | | | | | | | | (2092) $false
% 109.31/15.50 | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | CLOSE: (2092) is inconsistent.
% 109.31/15.50 | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | (2093) op(e1, e1) = all_46_1 & $i(all_46_1) & ( ~
% 109.31/15.50 | | | | | | | | | | | (all_46_1 = e0) | ( ~ (all_46_0 = e3) & op(e0,
% 109.31/15.50 | | | | | | | | | | | e1) = all_46_0 & $i(all_46_0)))
% 109.31/15.50 | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | ALPHA: (2093) implies:
% 109.31/15.50 | | | | | | | | | | | (2094) op(e1, e1) = all_46_1
% 109.31/15.50 | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_46_1,
% 109.31/15.50 | | | | | | | | | | | e1, e1, simplifying with (2009), (2094) gives:
% 109.31/15.50 | | | | | | | | | | | (2095) all_46_1 = e3
% 109.31/15.50 | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_24_1,
% 109.31/15.50 | | | | | | | | | | | all_46_1, e1, e1, simplifying with (2083), (2094)
% 109.31/15.50 | | | | | | | | | | | gives:
% 109.31/15.50 | | | | | | | | | | | (2096) all_46_1 = all_24_1
% 109.31/15.50 | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | COMBINE_EQS: (2095), (2096) imply:
% 109.31/15.50 | | | | | | | | | | | (2097) all_24_1 = e3
% 109.31/15.50 | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | SIMP: (2097) implies:
% 109.31/15.50 | | | | | | | | | | | (2098) all_24_1 = e3
% 109.31/15.50 | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | BETA: splitting (2084) gives:
% 109.31/15.50 | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | Case 1:
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | (2099) ~ (all_24_1 = e3)
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | REDUCE: (2098), (2099) imply:
% 109.31/15.50 | | | | | | | | | | | | (2100) $false
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | CLOSE: (2100) is inconsistent.
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | (2101) ~ (all_24_0 = e0) & op(e3, e1) = all_24_0 &
% 109.31/15.50 | | | | | | | | | | | | $i(all_24_0)
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | ALPHA: (2101) implies:
% 109.31/15.50 | | | | | | | | | | | | (2102) ~ (all_24_0 = e0)
% 109.31/15.50 | | | | | | | | | | | | (2103) op(e3, e1) = all_24_0
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 109.31/15.50 | | | | | | | | | | | | all_24_0, e1, e3, simplifying with (173), (2103)
% 109.31/15.50 | | | | | | | | | | | | gives:
% 109.31/15.50 | | | | | | | | | | | | (2104) all_53_13 = all_24_0
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | COMBINE_EQS: (273), (2104) imply:
% 109.31/15.50 | | | | | | | | | | | | (2105) all_55_13 = all_24_0
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | REDUCE: (149), (2104) imply:
% 109.31/15.50 | | | | | | | | | | | | (2106) ~ (all_53_1 = all_24_0)
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | REDUCE: (121), (2104) imply:
% 109.31/15.50 | | | | | | | | | | | | (2107) ~ (all_53_9 = all_24_0)
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | REDUCE: (375), (2104) imply:
% 109.31/15.50 | | | | | | | | | | | | (2108) ~ (all_24_0 = all_4_2)
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | REDUCE: (2008), (2104) imply:
% 109.31/15.50 | | | | | | | | | | | | (2109) ~ (all_24_0 = e3)
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | BETA: splitting (69) gives:
% 109.31/15.50 | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | Case 1:
% 109.31/15.50 | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | (2110) ~ (all_26_2 = e2)
% 109.31/15.50 | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | REDUCE: (316), (2110) imply:
% 109.31/15.50 | | | | | | | | | | | | | (2111) ~ (all_4_2 = e2)
% 109.31/15.50 | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | REF_CLOSE: (81), (108), (109), (150), (161), (162), (166),
% 109.31/15.50 | | | | | | | | | | | | | (169), (173), (174), (193), (195), (199), (218),
% 109.31/15.50 | | | | | | | | | | | | | (263), (311), (339), (377), (378), (2006), (2007),
% 109.31/15.50 | | | | | | | | | | | | | (2088), (2089), (2090), (2102), (2103), (2105),
% 109.31/15.50 | | | | | | | | | | | | | (2107), (2108), (2109), (2111), (function-axioms)
% 109.31/15.50 | | | | | | | | | | | | | are inconsistent by sub-proof #174.
% 109.31/15.50 | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | (2112) all_26_2 = e2
% 109.31/15.50 | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | COMBINE_EQS: (316), (2112) imply:
% 109.31/15.50 | | | | | | | | | | | | | (2113) all_4_2 = e2
% 109.31/15.50 | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | REDUCE: (2108), (2113) imply:
% 109.31/15.50 | | | | | | | | | | | | | (2114) ~ (all_24_0 = e2)
% 109.31/15.50 | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | BETA: splitting (195) gives:
% 109.31/15.50 | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | Case 1:
% 109.31/15.50 | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | (2115) all_55_13 = e3
% 109.31/15.50 | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | COMBINE_EQS: (2105), (2115) imply:
% 109.31/15.50 | | | | | | | | | | | | | | (2116) all_24_0 = e3
% 109.31/15.50 | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | REDUCE: (2109), (2116) imply:
% 109.31/15.50 | | | | | | | | | | | | | | (2117) $false
% 109.31/15.50 | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | CLOSE: (2117) is inconsistent.
% 109.31/15.50 | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | (2118) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 109.31/15.50 | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | BETA: splitting (2118) gives:
% 109.31/15.50 | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | Case 1:
% 109.31/15.50 | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | (2119) all_55_13 = e2
% 109.31/15.50 | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | COMBINE_EQS: (2105), (2119) imply:
% 109.31/15.50 | | | | | | | | | | | | | | | (2120) all_24_0 = e2
% 109.31/15.50 | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | REDUCE: (2114), (2120) imply:
% 109.31/15.50 | | | | | | | | | | | | | | | (2121) $false
% 109.31/15.50 | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | CLOSE: (2121) is inconsistent.
% 109.31/15.50 | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | (2122) all_55_13 = e1 | all_55_13 = e0
% 109.31/15.50 | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | BETA: splitting (2122) gives:
% 109.31/15.50 | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | Case 1:
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | (2123) all_55_13 = e1
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | COMBINE_EQS: (2105), (2123) imply:
% 109.31/15.50 | | | | | | | | | | | | | | | | (2124) all_24_0 = e1
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | REDUCE: (2106), (2124) imply:
% 109.31/15.50 | | | | | | | | | | | | | | | | (2125) ~ (all_53_1 = e1)
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 109.31/15.50 | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | Case 1:
% 109.31/15.50 | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | (2126) all_55_1 = e3
% 109.31/15.50 | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (2004), (2126) are inconsistent by
% 109.31/15.50 | | | | | | | | | | | | | | | | | sub-proof #78.
% 109.31/15.50 | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | (2127) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 109.31/15.50 | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | BETA: splitting (2127) gives:
% 109.31/15.50 | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | Case 1:
% 109.31/15.50 | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | (2128) all_55_1 = e2
% 109.31/15.50 | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (1914), (2128) are inconsistent by
% 109.31/15.50 | | | | | | | | | | | | | | | | | | sub-proof #77.
% 109.31/15.50 | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | (2129) all_55_1 = e1 | all_55_1 = e0
% 109.31/15.50 | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | BETA: splitting (2129) gives:
% 109.31/15.50 | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | Case 1:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | (2130) all_55_1 = e1
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (2130) imply:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | (2131) all_53_1 = e1
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | REDUCE: (2125), (2131) imply:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | (2132) $false
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | CLOSE: (2132) is inconsistent.
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | Case 2:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | (2133) all_55_1 = e0
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (2133) imply:
% 109.31/15.50 | | | | | | | | | | | | | | | | | | | (2134) all_53_1 = e0
% 109.31/15.50 | | | | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | REDUCE: (152), (2134) imply:
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | (2135) ~ (all_53_3 = e0)
% 109.31/15.51 | | | | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | SIMP: (2135) implies:
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | (2136) ~ (all_53_3 = e0)
% 109.31/15.51 | | | | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 109.31/15.51 | | | | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | Case 1:
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | | (2137) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | | ALPHA: (2137) implies:
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | | (2138) op(e3, e2) = e3
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (142), (174), (206), (250), (1916), (2087),
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | | (2136), (2138), (function-axioms) are inconsistent
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | | by sub-proof #76.
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | Case 2:
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | | (2139) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (166), (2088), (2136), (2139),
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | | #218.
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | | | | End of split
% 109.31/15.51 | | | | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | | | End of split
% 109.31/15.51 | | | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | | End of split
% 109.31/15.51 | | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | End of split
% 109.31/15.51 | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | Case 2:
% 109.31/15.51 | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | (2140) all_55_13 = e0
% 109.31/15.51 | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | COMBINE_EQS: (2105), (2140) imply:
% 109.31/15.51 | | | | | | | | | | | | | | | | (2141) all_24_0 = e0
% 109.31/15.51 | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | REDUCE: (2102), (2141) imply:
% 109.31/15.51 | | | | | | | | | | | | | | | | (2142) $false
% 109.31/15.51 | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | | CLOSE: (2142) is inconsistent.
% 109.31/15.51 | | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | | End of split
% 109.31/15.51 | | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | | End of split
% 109.31/15.51 | | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | End of split
% 109.31/15.51 | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | End of split
% 109.31/15.51 | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | End of split
% 109.31/15.51 | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | End of split
% 109.31/15.51 | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | End of split
% 109.31/15.51 | | | | | | | | |
% 109.31/15.51 | | | | | | | | End of split
% 109.31/15.51 | | | | | | | |
% 109.31/15.51 | | | | | | | Case 2:
% 109.31/15.51 | | | | | | | |
% 109.31/15.51 | | | | | | | | (2143) all_14_2 = e2
% 109.31/15.51 | | | | | | | | (2144) op(e2, e2) = all_14_1 & $i(all_14_1) & ( ~ (all_14_1 =
% 109.31/15.51 | | | | | | | | e3) | ( ~ (all_14_0 = e0) & op(e3, e2) = all_14_0
% 109.31/15.51 | | | | | | | | & $i(all_14_0)))
% 109.31/15.51 | | | | | | | |
% 109.31/15.51 | | | | | | | | ALPHA: (2144) implies:
% 109.31/15.51 | | | | | | | | (2145) op(e2, e2) = all_14_1
% 109.31/15.51 | | | | | | | |
% 109.31/15.51 | | | | | | | | COMBINE_EQS: (334), (2143) imply:
% 109.31/15.51 | | | | | | | | (2146) all_44_2 = e2
% 109.31/15.51 | | | | | | | |
% 109.31/15.51 | | | | | | | | REDUCE: (361), (2143) imply:
% 109.31/15.51 | | | | | | | | (2147) ~ (all_53_7 = e2)
% 109.31/15.51 | | | | | | | |
% 109.31/15.51 | | | | | | | | BETA: splitting (96) gives:
% 109.31/15.51 | | | | | | | |
% 109.31/15.51 | | | | | | | | Case 1:
% 109.31/15.51 | | | | | | | | |
% 109.31/15.51 | | | | | | | | | (2148) ~ (all_44_2 = e2)
% 109.31/15.51 | | | | | | | | |
% 109.31/15.51 | | | | | | | | | REDUCE: (2146), (2148) imply:
% 109.31/15.51 | | | | | | | | | (2149) $false
% 109.31/15.51 | | | | | | | | |
% 109.31/15.51 | | | | | | | | | CLOSE: (2149) is inconsistent.
% 109.31/15.51 | | | | | | | | |
% 109.31/15.51 | | | | | | | | Case 2:
% 109.31/15.51 | | | | | | | | |
% 109.31/15.51 | | | | | | | | | (2150) op(e2, e2) = all_44_1 & $i(all_44_1) & ( ~ (all_44_1
% 109.31/15.51 | | | | | | | | | = e0) | ( ~ (all_44_0 = e3) & op(e0, e2) =
% 109.31/15.51 | | | | | | | | | all_44_0 & $i(all_44_0)))
% 109.31/15.51 | | | | | | | | |
% 109.31/15.51 | | | | | | | | | ALPHA: (2150) implies:
% 109.31/15.51 | | | | | | | | | (2151) op(e2, e2) = all_44_1
% 109.31/15.51 | | | | | | | | |
% 109.31/15.51 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1,
% 109.31/15.51 | | | | | | | | | all_44_1, e2, e2, simplifying with (1909), (2151)
% 109.31/15.51 | | | | | | | | | gives:
% 109.31/15.51 | | | | | | | | | (2152) all_44_1 = all_8_1
% 109.31/15.51 | | | | | | | | |
% 109.31/15.51 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 109.31/15.51 | | | | | | | | | all_44_1, e2, e2, simplifying with (2145), (2151)
% 109.31/15.51 | | | | | | | | | gives:
% 109.31/15.51 | | | | | | | | | (2153) all_44_1 = all_14_1
% 109.31/15.51 | | | | | | | | |
% 109.31/15.51 | | | | | | | | | COMBINE_EQS: (2152), (2153) imply:
% 109.31/15.51 | | | | | | | | | (2154) all_14_1 = all_8_1
% 109.31/15.51 | | | | | | | | |
% 109.31/15.51 | | | | | | | | | BETA: splitting (66) gives:
% 109.31/15.51 | | | | | | | | |
% 109.31/15.51 | | | | | | | | | Case 1:
% 109.31/15.51 | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | (2155) ~ (all_24_2 = e1)
% 109.31/15.51 | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | REDUCE: (1930), (2155) imply:
% 109.31/15.51 | | | | | | | | | | (2156) ~ (all_8_1 = e1)
% 109.31/15.51 | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (115), (117),
% 109.31/15.51 | | | | | | | | | | (132), (139), (140), (148), (152), (153), (161),
% 109.31/15.51 | | | | | | | | | | (162), (163), (164), (166), (167), (168), (169),
% 109.31/15.51 | | | | | | | | | | (171), (172), (173), (174), (198), (1934), (1937),
% 109.31/15.51 | | | | | | | | | | (1938), (1939), (1942), (1944), (2156),
% 109.31/15.51 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.31/15.51 | | | | | | | | | | #75.
% 109.31/15.51 | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | Case 2:
% 109.31/15.51 | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | (2157) all_24_2 = e1
% 109.31/15.51 | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | COMBINE_EQS: (1930), (2157) imply:
% 109.31/15.51 | | | | | | | | | | (2158) all_8_1 = e1
% 109.31/15.51 | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | SIMP: (2158) implies:
% 109.31/15.51 | | | | | | | | | | (2159) all_8_1 = e1
% 109.31/15.51 | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | REDUCE: (1935), (2159) imply:
% 109.31/15.51 | | | | | | | | | | (2160) ~ (all_53_3 = e1)
% 109.31/15.51 | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | REDUCE: (1936), (2159) imply:
% 109.31/15.51 | | | | | | | | | | (2161) ~ (all_53_7 = e1)
% 109.31/15.51 | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | REDUCE: (1909), (2159) imply:
% 109.31/15.51 | | | | | | | | | | (2162) op(e2, e2) = e1
% 109.31/15.51 | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | BETA: splitting (220) gives:
% 109.31/15.51 | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | Case 1:
% 109.31/15.51 | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | (2163) (all_57_84 = e2 & op(e3, e2) = e2) | (all_57_85 =
% 109.31/15.51 | | | | | | | | | | | e2 & op(e2, e2) = e2)
% 109.31/15.51 | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | BETA: splitting (2163) gives:
% 109.31/15.51 | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | Case 1:
% 109.31/15.51 | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | (2164) all_57_84 = e2 & op(e3, e2) = e2
% 109.31/15.51 | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | ALPHA: (2164) implies:
% 109.31/15.51 | | | | | | | | | | | | (2165) op(e3, e2) = e2
% 109.31/15.51 | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | BETA: splitting (1910) gives:
% 109.31/15.51 | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | Case 1:
% 109.31/15.51 | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | (2166) ~ (all_8_1 = e1)
% 109.31/15.51 | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (115), (117),
% 109.31/15.51 | | | | | | | | | | | | | (132), (139), (140), (148), (152), (153), (161),
% 109.31/15.51 | | | | | | | | | | | | | (162), (163), (164), (166), (167), (168), (169),
% 109.31/15.51 | | | | | | | | | | | | | (171), (172), (173), (174), (198), (1934), (1937),
% 109.31/15.51 | | | | | | | | | | | | | (1938), (1939), (1942), (1944), (2166),
% 109.31/15.51 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.31/15.51 | | | | | | | | | | | | | #75.
% 109.31/15.51 | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | Case 2:
% 109.31/15.51 | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | (2167) ~ (all_8_0 = e3) & op(e1, e2) = all_8_0 &
% 109.31/15.51 | | | | | | | | | | | | | $i(all_8_0)
% 109.31/15.51 | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | ALPHA: (2167) implies:
% 109.31/15.51 | | | | | | | | | | | | | (2168) ~ (all_8_0 = e3)
% 109.31/15.51 | | | | | | | | | | | | | (2169) op(e1, e2) = all_8_0
% 109.31/15.51 | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7,
% 109.31/15.51 | | | | | | | | | | | | | all_8_0, e2, e1, simplifying with (166), (2169)
% 109.31/15.51 | | | | | | | | | | | | | gives:
% 109.31/15.51 | | | | | | | | | | | | | (2170) all_53_7 = all_8_0
% 109.31/15.51 | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 109.31/15.51 | | | | | | | | | | | | | e2, e2, e3, simplifying with (174), (2165) gives:
% 109.31/15.51 | | | | | | | | | | | | | (2171) all_53_15 = e2
% 109.31/15.51 | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | COMBINE_EQS: (260), (2170) imply:
% 109.31/15.51 | | | | | | | | | | | | | (2172) all_55_6 = all_8_0
% 109.31/15.51 | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | REDUCE: (144), (2170) imply:
% 109.31/15.51 | | | | | | | | | | | | | (2173) ~ (all_53_3 = all_8_0)
% 109.31/15.51 | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | REDUCE: (2147), (2170) imply:
% 109.31/15.51 | | | | | | | | | | | | | (2174) ~ (all_8_0 = e2)
% 109.31/15.51 | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | REDUCE: (2161), (2170) imply:
% 109.31/15.51 | | | | | | | | | | | | | (2175) ~ (all_8_0 = e1)
% 109.31/15.51 | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | BETA: splitting (108) gives:
% 109.31/15.51 | | | | | | | | | | | | |
% 109.31/15.51 | | | | | | | | | | | | | Case 1:
% 109.31/15.51 | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | (2176) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 109.48/15.51 | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 109.48/15.51 | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | ALPHA: (2176) implies:
% 109.48/15.51 | | | | | | | | | | | | | | (2177) op(e3, e2) = e3
% 109.48/15.51 | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 109.48/15.51 | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | Case 1:
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | (2178) all_55_6 = e3
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | REF_CLOSE: (2168), (2172), (2178) are inconsistent by
% 109.48/15.51 | | | | | | | | | | | | | | | sub-proof #74.
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | Case 2:
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | (2179) all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | BETA: splitting (2179) gives:
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | Case 1:
% 109.48/15.51 | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | (2180) all_55_6 = e2
% 109.48/15.51 | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | REF_CLOSE: (2172), (2174), (2180) are inconsistent by
% 109.48/15.51 | | | | | | | | | | | | | | | | sub-proof #73.
% 109.48/15.51 | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | Case 2:
% 109.48/15.51 | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | (2181) all_55_6 = e1 | all_55_6 = e0
% 109.48/15.51 | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | BETA: splitting (2181) gives:
% 109.48/15.51 | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | Case 1:
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | (2182) all_55_6 = e1
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | REF_CLOSE: (2172), (2175), (2182) are inconsistent by
% 109.48/15.51 | | | | | | | | | | | | | | | | | sub-proof #72.
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | Case 2:
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | (2183) all_55_6 = e0
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2172), (2183) imply:
% 109.48/15.51 | | | | | | | | | | | | | | | | | (2184) all_8_0 = e0
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | SIMP: (2184) implies:
% 109.48/15.51 | | | | | | | | | | | | | | | | | (2185) all_8_0 = e0
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | REDUCE: (2173), (2185) imply:
% 109.48/15.51 | | | | | | | | | | | | | | | | | (2186) ~ (all_53_3 = e0)
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | REF_CLOSE: (142), (174), (206), (250), (1916), (2160),
% 109.48/15.51 | | | | | | | | | | | | | | | | | (2177), (2186), (function-axioms) are inconsistent
% 109.48/15.51 | | | | | | | | | | | | | | | | | by sub-proof #76.
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | End of split
% 109.48/15.51 | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | End of split
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | End of split
% 109.48/15.51 | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | Case 2:
% 109.48/15.51 | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | (2187) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 109.48/15.51 | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 109.48/15.51 | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 109.48/15.51 | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 109.48/15.51 | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | BETA: splitting (2187) gives:
% 109.48/15.51 | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | Case 1:
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | (2188) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 109.48/15.51 | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | ALPHA: (2188) implies:
% 109.48/15.51 | | | | | | | | | | | | | | | (2189) op(e1, e2) = e1
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | REF_CLOSE: (166), (2161), (2189), (function-axioms) are
% 109.48/15.51 | | | | | | | | | | | | | | | inconsistent by sub-proof #233.
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | Case 2:
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | (2190) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 109.48/15.51 | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | ALPHA: (2190) implies:
% 109.48/15.51 | | | | | | | | | | | | | | | (2191) op(e0, e2) = e0
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | Case 1:
% 109.48/15.51 | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | (2192) all_55_6 = e3
% 109.48/15.51 | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | REF_CLOSE: (2168), (2172), (2192) are inconsistent by
% 109.48/15.51 | | | | | | | | | | | | | | | | sub-proof #74.
% 109.48/15.51 | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | Case 2:
% 109.48/15.51 | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | (2193) all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 109.48/15.51 | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | BETA: splitting (2193) gives:
% 109.48/15.51 | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | Case 1:
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | (2194) all_55_6 = e2
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | REF_CLOSE: (2172), (2174), (2194) are inconsistent by
% 109.48/15.51 | | | | | | | | | | | | | | | | | sub-proof #73.
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | Case 2:
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | (2195) all_55_6 = e1 | all_55_6 = e0
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | BETA: splitting (2195) gives:
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | Case 1:
% 109.48/15.51 | | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | | (2196) all_55_6 = e1
% 109.48/15.51 | | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2172), (2175), (2196) are inconsistent by
% 109.48/15.51 | | | | | | | | | | | | | | | | | | sub-proof #72.
% 109.48/15.51 | | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | Case 2:
% 109.48/15.51 | | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | | (2197) all_55_6 = e0
% 109.48/15.51 | | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2172), (2197) imply:
% 109.48/15.51 | | | | | | | | | | | | | | | | | | (2198) all_8_0 = e0
% 109.48/15.51 | | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | | SIMP: (2198) implies:
% 109.48/15.51 | | | | | | | | | | | | | | | | | | (2199) all_8_0 = e0
% 109.48/15.51 | | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | | REDUCE: (2173), (2199) imply:
% 109.48/15.51 | | | | | | | | | | | | | | | | | | (2200) ~ (all_53_3 = e0)
% 109.48/15.51 | | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2191), (2200), (function-axioms) are
% 109.48/15.51 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 109.48/15.51 | | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | | End of split
% 109.48/15.51 | | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | | End of split
% 109.48/15.51 | | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | | End of split
% 109.48/15.51 | | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | | End of split
% 109.48/15.51 | | | | | | | | | | | | | |
% 109.48/15.51 | | | | | | | | | | | | | End of split
% 109.48/15.51 | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | End of split
% 109.48/15.52 | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | Case 2:
% 109.48/15.52 | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | (2201) all_57_85 = e2 & op(e2, e2) = e2
% 109.48/15.52 | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | ALPHA: (2201) implies:
% 109.48/15.52 | | | | | | | | | | | | (2202) op(e2, e2) = e2
% 109.48/15.52 | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e2, e2,
% 109.48/15.52 | | | | | | | | | | | | e2, simplifying with (2162), (2202) gives:
% 109.48/15.52 | | | | | | | | | | | | (2203) e2 = e1
% 109.48/15.52 | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | REDUCE: (1919), (2203) imply:
% 109.48/15.52 | | | | | | | | | | | | (2204) $false
% 109.48/15.52 | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | CLOSE: (2204) is inconsistent.
% 109.48/15.52 | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | End of split
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | Case 2:
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | (2205) (all_57_86 = e2 & op(e1, e2) = e2) | (all_57_87 =
% 109.48/15.52 | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | REF_CLOSE: (162), (166), (1916), (2147), (2205),
% 109.48/15.52 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.48/15.52 | | | | | | | | | | | #70.
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | End of split
% 109.48/15.52 | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | End of split
% 109.48/15.52 | | | | | | | | |
% 109.48/15.52 | | | | | | | | End of split
% 109.48/15.52 | | | | | | | |
% 109.48/15.52 | | | | | | | End of split
% 109.48/15.52 | | | | | | |
% 109.48/15.52 | | | | | | Case 2:
% 109.48/15.52 | | | | | | |
% 109.48/15.52 | | | | | | | (2206) all_12_2 = e0
% 109.48/15.52 | | | | | | | (2207) op(e0, e0) = all_12_1 & $i(all_12_1) & ( ~ (all_12_1 =
% 109.48/15.52 | | | | | | | e1) | ( ~ (all_12_0 = e3) & op(e1, e0) = all_12_0 &
% 109.48/15.52 | | | | | | | $i(all_12_0)))
% 109.48/15.52 | | | | | | |
% 109.48/15.52 | | | | | | | ALPHA: (2207) implies:
% 109.48/15.52 | | | | | | | (2208) op(e0, e0) = all_12_1
% 109.48/15.52 | | | | | | |
% 109.48/15.52 | | | | | | | COMBINE_EQS: (1929), (2206) imply:
% 109.48/15.52 | | | | | | | (2209) all_8_1 = e0
% 109.48/15.52 | | | | | | |
% 109.48/15.52 | | | | | | | SIMP: (2209) implies:
% 109.48/15.52 | | | | | | | (2210) all_8_1 = e0
% 109.48/15.52 | | | | | | |
% 109.48/15.52 | | | | | | | COMBINE_EQS: (1931), (2210) imply:
% 109.48/15.52 | | | | | | | (2211) all_30_2 = e0
% 109.48/15.52 | | | | | | |
% 109.48/15.52 | | | | | | | REDUCE: (1935), (2210) imply:
% 109.48/15.52 | | | | | | | (2212) ~ (all_53_3 = e0)
% 109.48/15.52 | | | | | | |
% 109.48/15.52 | | | | | | | REDUCE: (1937), (2210) imply:
% 109.48/15.52 | | | | | | | (2213) ~ (all_53_8 = e0)
% 109.48/15.52 | | | | | | |
% 109.48/15.52 | | | | | | | REDUCE: (1940), (2210) imply:
% 109.48/15.52 | | | | | | | (2214) ~ (all_53_15 = e0)
% 109.48/15.52 | | | | | | |
% 109.48/15.52 | | | | | | | REDUCE: (1909), (2210) imply:
% 109.48/15.52 | | | | | | | (2215) op(e2, e2) = e0
% 109.48/15.52 | | | | | | |
% 109.48/15.52 | | | | | | | BETA: splitting (75) gives:
% 109.48/15.52 | | | | | | |
% 109.48/15.52 | | | | | | | Case 1:
% 109.48/15.52 | | | | | | | |
% 109.48/15.52 | | | | | | | | (2216) ~ (all_30_2 = e0)
% 109.48/15.52 | | | | | | | |
% 109.48/15.52 | | | | | | | | REDUCE: (2211), (2216) imply:
% 109.48/15.52 | | | | | | | | (2217) $false
% 109.48/15.52 | | | | | | | |
% 109.48/15.52 | | | | | | | | CLOSE: (2217) is inconsistent.
% 109.48/15.52 | | | | | | | |
% 109.48/15.52 | | | | | | | Case 2:
% 109.48/15.52 | | | | | | | |
% 109.48/15.52 | | | | | | | | (2218) op(e0, e0) = all_30_1 & $i(all_30_1) & ( ~ (all_30_1 =
% 109.48/15.52 | | | | | | | | e3) | ( ~ (all_30_0 = e1) & op(e3, e0) = all_30_0
% 109.48/15.52 | | | | | | | | & $i(all_30_0)))
% 109.48/15.52 | | | | | | | |
% 109.48/15.52 | | | | | | | | ALPHA: (2218) implies:
% 109.48/15.52 | | | | | | | | (2219) op(e0, e0) = all_30_1
% 109.48/15.52 | | | | | | | |
% 109.48/15.52 | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_30_1,
% 109.48/15.52 | | | | | | | | e0, e0, simplifying with (1920), (2219) gives:
% 109.48/15.52 | | | | | | | | (2220) all_30_1 = e2
% 109.48/15.52 | | | | | | | |
% 109.48/15.52 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_1,
% 109.48/15.52 | | | | | | | | all_30_1, e0, e0, simplifying with (2208), (2219)
% 109.48/15.52 | | | | | | | | gives:
% 109.48/15.52 | | | | | | | | (2221) all_30_1 = all_12_1
% 109.48/15.52 | | | | | | | |
% 109.48/15.52 | | | | | | | | COMBINE_EQS: (2220), (2221) imply:
% 109.48/15.52 | | | | | | | | (2222) all_12_1 = e2
% 109.48/15.52 | | | | | | | |
% 109.48/15.52 | | | | | | | | BETA: splitting (51) gives:
% 109.48/15.52 | | | | | | | |
% 109.48/15.52 | | | | | | | | Case 1:
% 109.48/15.52 | | | | | | | | |
% 109.48/15.52 | | | | | | | | | (2223) ~ (all_14_2 = e2)
% 109.48/15.52 | | | | | | | | |
% 109.48/15.52 | | | | | | | | | BETA: splitting (57) gives:
% 109.48/15.52 | | | | | | | | |
% 109.48/15.52 | | | | | | | | | Case 1:
% 109.48/15.52 | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | (2224) ~ (all_18_2 = e3)
% 109.48/15.52 | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | REDUCE: (326), (2224) imply:
% 109.48/15.52 | | | | | | | | | | (2225) ~ (all_14_2 = e3)
% 109.48/15.52 | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | BETA: splitting (63) gives:
% 109.48/15.52 | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | Case 1:
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | (2226) ~ (all_22_2 = e0)
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | REDUCE: (329), (2226) imply:
% 109.48/15.52 | | | | | | | | | | | (2227) ~ (all_14_2 = e0)
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (117), (123),
% 109.48/15.52 | | | | | | | | | | | (126), (127), (148), (152), (153), (161), (162),
% 109.48/15.52 | | | | | | | | | | | (163), (164), (166), (167), (168), (169), (171),
% 109.48/15.52 | | | | | | | | | | | (172), (173), (174), (203), (341), (357), (359),
% 109.48/15.52 | | | | | | | | | | | (361), (2223), (2225), (2227), (function-axioms)
% 109.48/15.52 | | | | | | | | | | | are inconsistent by sub-proof #216.
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | Case 2:
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | (2228) all_22_2 = e0
% 109.48/15.52 | | | | | | | | | | | (2229) op(e0, e0) = all_22_1 & $i(all_22_1) & ( ~
% 109.48/15.52 | | | | | | | | | | | (all_22_1 = e2) | ( ~ (all_22_0 = e3) & op(e2,
% 109.48/15.52 | | | | | | | | | | | e0) = all_22_0 & $i(all_22_0)))
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | ALPHA: (2229) implies:
% 109.48/15.52 | | | | | | | | | | | (2230) op(e0, e0) = all_22_1
% 109.48/15.52 | | | | | | | | | | | (2231) ~ (all_22_1 = e2) | ( ~ (all_22_0 = e3) & op(e2,
% 109.48/15.52 | | | | | | | | | | | e0) = all_22_0 & $i(all_22_0))
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | COMBINE_EQS: (329), (2228) imply:
% 109.48/15.52 | | | | | | | | | | | (2232) all_14_2 = e0
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | SIMP: (2232) implies:
% 109.48/15.52 | | | | | | | | | | | (2233) all_14_2 = e0
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | COMBINE_EQS: (331), (2233) imply:
% 109.48/15.52 | | | | | | | | | | | (2234) all_32_2 = e0
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | REDUCE: (365), (2233) imply:
% 109.48/15.52 | | | | | | | | | | | (2235) ~ (all_53_13 = e0)
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | REDUCE: (2225), (2233) imply:
% 109.48/15.52 | | | | | | | | | | | (2236) ~ (e3 = e0)
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | BETA: splitting (78) gives:
% 109.48/15.52 | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | Case 1:
% 109.48/15.52 | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | (2237) ~ (all_32_2 = e0)
% 109.48/15.52 | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | REDUCE: (2234), (2237) imply:
% 109.48/15.52 | | | | | | | | | | | | (2238) $false
% 109.48/15.52 | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | CLOSE: (2238) is inconsistent.
% 109.48/15.52 | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | Case 2:
% 109.48/15.52 | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | (2239) op(e0, e0) = all_32_1 & $i(all_32_1) & ( ~
% 109.48/15.52 | | | | | | | | | | | | (all_32_1 = e3) | ( ~ (all_32_0 = e2) & op(e3,
% 109.48/15.52 | | | | | | | | | | | | e0) = all_32_0 & $i(all_32_0)))
% 109.48/15.52 | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | ALPHA: (2239) implies:
% 109.48/15.52 | | | | | | | | | | | | (2240) op(e0, e0) = all_32_1
% 109.48/15.52 | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | BETA: splitting (217) gives:
% 109.48/15.52 | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | Case 1:
% 109.48/15.52 | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | (2241) (all_57_96 = e0 & op(e3, e3) = e0) | (all_57_97 =
% 109.48/15.52 | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 109.48/15.52 | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | REF_CLOSE: (35), (174), (378), (2214), (2241),
% 109.48/15.52 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.48/15.52 | | | | | | | | | | | | | #155.
% 109.48/15.52 | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | Case 2:
% 109.48/15.52 | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | (2242) (all_57_98 = e0 & op(e3, e1) = e0) | (all_57_99 =
% 109.48/15.52 | | | | | | | | | | | | | e0 & op(e3, e0) = e0)
% 109.48/15.52 | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | BETA: splitting (2242) gives:
% 109.48/15.52 | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | Case 1:
% 109.48/15.52 | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | (2243) all_57_98 = e0 & op(e3, e1) = e0
% 109.48/15.52 | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | ALPHA: (2243) implies:
% 109.48/15.52 | | | | | | | | | | | | | | (2244) op(e3, e1) = e0
% 109.48/15.52 | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | REF_CLOSE: (173), (2235), (2244), (function-axioms) are
% 109.48/15.52 | | | | | | | | | | | | | | inconsistent by sub-proof #202.
% 109.48/15.52 | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | Case 2:
% 109.48/15.52 | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | (2245) all_57_99 = e0 & op(e3, e0) = e0
% 109.48/15.52 | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | ALPHA: (2245) implies:
% 109.48/15.52 | | | | | | | | | | | | | | (2246) op(e3, e0) = e0
% 109.48/15.52 | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_32_1,
% 109.48/15.52 | | | | | | | | | | | | | | e0, e0, simplifying with (1920), (2240) gives:
% 109.48/15.52 | | | | | | | | | | | | | | (2247) all_32_1 = e2
% 109.48/15.52 | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 109.48/15.52 | | | | | | | | | | | | | | all_32_1, e0, e0, simplifying with (2230), (2240)
% 109.48/15.52 | | | | | | | | | | | | | | gives:
% 109.48/15.52 | | | | | | | | | | | | | | (2248) all_32_1 = all_22_1
% 109.48/15.52 | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 109.48/15.52 | | | | | | | | | | | | | | e0, e0, e3, simplifying with (172), (2246) gives:
% 109.48/15.52 | | | | | | | | | | | | | | (2249) all_53_12 = e0
% 109.48/15.52 | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | COMBINE_EQS: (2247), (2248) imply:
% 109.48/15.52 | | | | | | | | | | | | | | (2250) all_22_1 = e2
% 109.48/15.52 | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | SIMP: (2250) implies:
% 109.48/15.52 | | | | | | | | | | | | | | (2251) all_22_1 = e2
% 109.48/15.52 | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | BETA: splitting (2231) gives:
% 109.48/15.52 | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | Case 1:
% 109.48/15.52 | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | (2252) ~ (all_22_1 = e2)
% 109.48/15.52 | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | REDUCE: (2251), (2252) imply:
% 109.48/15.52 | | | | | | | | | | | | | | | (2253) $false
% 109.48/15.52 | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | CLOSE: (2253) is inconsistent.
% 109.48/15.52 | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | Case 2:
% 109.48/15.52 | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | (2254) ~ (all_22_0 = e3) & op(e2, e0) = all_22_0 &
% 109.48/15.52 | | | | | | | | | | | | | | | $i(all_22_0)
% 109.48/15.52 | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | ALPHA: (2254) implies:
% 109.48/15.52 | | | | | | | | | | | | | | | (2255) ~ (all_22_0 = e3)
% 109.48/15.52 | | | | | | | | | | | | | | | (2256) op(e2, e0) = all_22_0
% 109.48/15.52 | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 109.48/15.52 | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | Case 1:
% 109.48/15.52 | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | (2257) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 109.48/15.52 | | | | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 109.48/15.52 | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | ALPHA: (2257) implies:
% 109.48/15.52 | | | | | | | | | | | | | | | | (2258) op(e3, e0) = e3
% 109.48/15.52 | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e0,
% 109.48/15.52 | | | | | | | | | | | | | | | | e3, simplifying with (2246), (2258) gives:
% 109.48/15.52 | | | | | | | | | | | | | | | | (2259) e3 = e0
% 109.48/15.52 | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | REDUCE: (6), (2259) imply:
% 109.48/15.52 | | | | | | | | | | | | | | | | (2260) $false
% 109.48/15.52 | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | CLOSE: (2260) is inconsistent.
% 109.48/15.52 | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | Case 2:
% 109.48/15.52 | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | (2261) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 109.48/15.52 | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 109.48/15.52 | | | | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 109.48/15.52 | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 109.48/15.52 | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | BETA: splitting (2261) gives:
% 109.48/15.52 | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | Case 1:
% 109.48/15.52 | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | (2262) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 109.48/15.52 | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 109.48/15.52 | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | ALPHA: (2262) implies:
% 109.48/15.52 | | | | | | | | | | | | | | | | | (2263) op(e2, e0) = e2
% 109.48/15.52 | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1918), (2263), (function-axioms) are
% 109.48/15.52 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #227.
% 109.48/15.52 | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | Case 2:
% 109.48/15.52 | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | (2264) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 109.48/15.52 | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 109.48/15.52 | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | ALPHA: (2264) implies:
% 109.48/15.52 | | | | | | | | | | | | | | | | | (2265) op(e1, e0) = e1
% 109.48/15.52 | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e1,
% 109.48/15.52 | | | | | | | | | | | | | | | | | e0, e1, simplifying with (164), (2265) gives:
% 109.48/15.52 | | | | | | | | | | | | | | | | | (2266) all_53_4 = e1
% 109.48/15.52 | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 109.48/15.52 | | | | | | | | | | | | | | | | | all_22_0, e0, e2, simplifying with (168), (2256)
% 109.48/15.52 | | | | | | | | | | | | | | | | | gives:
% 109.48/15.52 | | | | | | | | | | | | | | | | | (2267) all_53_8 = all_22_0
% 109.48/15.52 | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (2267) imply:
% 109.48/15.52 | | | | | | | | | | | | | | | | | (2268) all_55_8 = all_22_0
% 109.48/15.52 | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | REDUCE: (138), (2266), (2267) imply:
% 109.48/15.52 | | | | | | | | | | | | | | | | | (2269) ~ (all_22_0 = e1)
% 109.48/15.52 | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | SIMP: (2269) implies:
% 109.48/15.52 | | | | | | | | | | | | | | | | | (2270) ~ (all_22_0 = e1)
% 109.48/15.52 | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | REDUCE: (1918), (2267) imply:
% 109.48/15.52 | | | | | | | | | | | | | | | | | (2271) ~ (all_22_0 = e2)
% 109.48/15.52 | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | REDUCE: (2213), (2267) imply:
% 109.48/15.52 | | | | | | | | | | | | | | | | | (2272) ~ (all_22_0 = e0)
% 109.48/15.52 | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 109.48/15.52 | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | Case 1:
% 109.48/15.52 | | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | | (2273) all_55_8 = e3
% 109.48/15.52 | | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2268), (2273) imply:
% 109.48/15.52 | | | | | | | | | | | | | | | | | | (2274) all_22_0 = e3
% 109.48/15.52 | | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | | REDUCE: (2255), (2274) imply:
% 109.48/15.52 | | | | | | | | | | | | | | | | | | (2275) $false
% 109.48/15.52 | | | | | | | | | | | | | | | | | |
% 109.48/15.52 | | | | | | | | | | | | | | | | | | CLOSE: (2275) is inconsistent.
% 109.48/15.52 | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | Case 2:
% 109.48/15.53 | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | (2276) all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 109.48/15.53 | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | BETA: splitting (2276) gives:
% 109.48/15.53 | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | Case 1:
% 109.48/15.53 | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | (2277) all_55_8 = e2
% 109.48/15.53 | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2268), (2277) imply:
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | (2278) all_22_0 = e2
% 109.48/15.53 | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | REDUCE: (2271), (2278) imply:
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | (2279) $false
% 109.48/15.53 | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | CLOSE: (2279) is inconsistent.
% 109.48/15.53 | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | Case 2:
% 109.48/15.53 | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | (2280) all_55_8 = e1 | all_55_8 = e0
% 109.48/15.53 | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | BETA: splitting (2280) gives:
% 109.48/15.53 | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | Case 1:
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | | (2281) all_55_8 = e1
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2268), (2281) imply:
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | | (2282) all_22_0 = e1
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | | REDUCE: (2270), (2282) imply:
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | | (2283) $false
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | | CLOSE: (2283) is inconsistent.
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | Case 2:
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | | (2284) all_55_8 = e0
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2268), (2284) imply:
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | | (2285) all_22_0 = e0
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | | REDUCE: (2272), (2285) imply:
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | | (2286) $false
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | | CLOSE: (2286) is inconsistent.
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | Case 2:
% 109.48/15.53 | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | (2287) all_18_2 = e3
% 109.48/15.53 | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | COMBINE_EQS: (326), (2287) imply:
% 109.48/15.53 | | | | | | | | | | (2288) all_14_2 = e3
% 109.48/15.53 | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | SIMP: (2288) implies:
% 109.48/15.53 | | | | | | | | | | (2289) all_14_2 = e3
% 109.48/15.53 | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | REDUCE: (354), (2289) imply:
% 109.48/15.53 | | | | | | | | | | (2290) ~ (all_53_1 = e3)
% 109.48/15.53 | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | REDUCE: (363), (2289) imply:
% 109.48/15.53 | | | | | | | | | | (2291) ~ (all_53_9 = e3)
% 109.48/15.53 | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | BETA: splitting (69) gives:
% 109.48/15.53 | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | Case 1:
% 109.48/15.53 | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | (2292) ~ (all_26_2 = e2)
% 109.48/15.53 | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | REDUCE: (316), (2292) imply:
% 109.48/15.53 | | | | | | | | | | | (2293) ~ (all_4_2 = e2)
% 109.48/15.53 | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | BETA: splitting (81) gives:
% 109.48/15.53 | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | Case 1:
% 109.48/15.53 | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | (2294) ~ (all_34_2 = e1)
% 109.48/15.53 | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | REDUCE: (311), (2294) imply:
% 109.48/15.53 | | | | | | | | | | | | (2295) ~ (all_4_2 = e1)
% 109.48/15.53 | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | BETA: splitting (193) gives:
% 109.48/15.53 | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | Case 1:
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | (2296) all_55_15 = e3
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | COMBINE_EQS: (339), (2296) imply:
% 109.48/15.53 | | | | | | | | | | | | | (2297) all_4_2 = e3
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | REDUCE: (371), (2297) imply:
% 109.48/15.53 | | | | | | | | | | | | | (2298) ~ (all_53_10 = e3)
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | REDUCE: (374), (2297) imply:
% 109.48/15.53 | | | | | | | | | | | | | (2299) ~ (all_53_12 = e3)
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | REDUCE: (377), (2297) imply:
% 109.48/15.53 | | | | | | | | | | | | | (2300) ~ (all_53_15 = e3)
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | BETA: splitting (108) gives:
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | Case 1:
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | (2301) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 109.48/15.53 | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | ALPHA: (2301) implies:
% 109.48/15.53 | | | | | | | | | | | | | | (2302) op(e3, e2) = e3
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | REF_CLOSE: (174), (2300), (2302), (function-axioms) are
% 109.48/15.53 | | | | | | | | | | | | | | inconsistent by sub-proof #214.
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | Case 2:
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | (2303) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 109.48/15.53 | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 109.48/15.53 | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 109.48/15.53 | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | BETA: splitting (2303) gives:
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | Case 1:
% 109.48/15.53 | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | (2304) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 109.48/15.53 | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 109.48/15.53 | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | ALPHA: (2304) implies:
% 109.48/15.53 | | | | | | | | | | | | | | | (2305) op(e1, e2) = e1
% 109.48/15.53 | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 109.48/15.53 | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | Case 1:
% 109.48/15.53 | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | (2306) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 109.48/15.53 | | | | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 109.48/15.53 | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | ALPHA: (2306) implies:
% 109.48/15.53 | | | | | | | | | | | | | | | | (2307) op(e3, e0) = e3
% 109.48/15.53 | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | REF_CLOSE: (172), (2299), (2307), (function-axioms) are
% 109.48/15.53 | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 109.48/15.53 | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | Case 2:
% 109.48/15.53 | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | (2308) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 109.48/15.53 | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 109.48/15.53 | | | | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 109.48/15.53 | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 109.48/15.53 | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | BETA: splitting (2308) gives:
% 109.48/15.53 | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | Case 1:
% 109.48/15.53 | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | (2309) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 109.48/15.53 | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 109.48/15.53 | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (168), (169), (171), (219), (2215),
% 109.48/15.53 | | | | | | | | | | | | | | | | | (2291), (2298), (2309), (function-axioms) are
% 109.48/15.53 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #68.
% 109.48/15.53 | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | Case 2:
% 109.48/15.53 | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | (2310) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 109.48/15.53 | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 109.48/15.53 | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | | REF_CLOSE: (139), (164), (166), (2305), (2310),
% 109.48/15.53 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.48/15.53 | | | | | | | | | | | | | | | | | #100.
% 109.48/15.53 | | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | Case 2:
% 109.48/15.53 | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | (2311) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 109.48/15.53 | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 109.48/15.53 | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | ALPHA: (2311) implies:
% 109.48/15.53 | | | | | | | | | | | | | | | (2312) op(e0, e2) = e0
% 109.48/15.53 | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | | REF_CLOSE: (162), (2212), (2312), (function-axioms) are
% 109.48/15.53 | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 109.48/15.53 | | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | Case 2:
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | (2313) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | REF_CLOSE: (339), (378), (2293), (2295), (2313) are
% 109.48/15.53 | | | | | | | | | | | | | inconsistent by sub-proof #191.
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | Case 2:
% 109.48/15.53 | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | (2314) all_34_2 = e1
% 109.48/15.53 | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | COMBINE_EQS: (311), (2314) imply:
% 109.48/15.53 | | | | | | | | | | | | (2315) all_4_2 = e1
% 109.48/15.53 | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | REDUCE: (355), (2315) imply:
% 109.48/15.53 | | | | | | | | | | | | (2316) ~ (all_53_2 = e1)
% 109.48/15.53 | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | REDUCE: (371), (2315) imply:
% 109.48/15.53 | | | | | | | | | | | | (2317) ~ (all_53_10 = e1)
% 109.48/15.53 | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | BETA: splitting (110) gives:
% 109.48/15.53 | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | Case 1:
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | (2318) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 109.48/15.53 | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | ALPHA: (2318) implies:
% 109.48/15.53 | | | | | | | | | | | | | (2319) ~ (all_52_0 = e0)
% 109.48/15.53 | | | | | | | | | | | | | (2320) op(e0, e3) = all_52_0
% 109.48/15.53 | | | | | | | | | | | | | (2321) op(e3, e0) = e3
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2,
% 109.48/15.53 | | | | | | | | | | | | | all_52_0, e3, e0, simplifying with (163), (2320)
% 109.48/15.53 | | | | | | | | | | | | | gives:
% 109.48/15.53 | | | | | | | | | | | | | (2322) all_53_2 = all_52_0
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 109.48/15.53 | | | | | | | | | | | | | e3, e0, e3, simplifying with (172), (2321) gives:
% 109.48/15.53 | | | | | | | | | | | | | (2323) all_53_12 = e3
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | COMBINE_EQS: (251), (2322) imply:
% 109.48/15.53 | | | | | | | | | | | | | (2324) all_55_3 = all_52_0
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | REDUCE: (148), (2322) imply:
% 109.48/15.53 | | | | | | | | | | | | | (2325) ~ (all_53_3 = all_52_0)
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | SIMP: (2325) implies:
% 109.48/15.53 | | | | | | | | | | | | | (2326) ~ (all_53_3 = all_52_0)
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | REDUCE: (1915), (2322) imply:
% 109.48/15.53 | | | | | | | | | | | | | (2327) ~ (all_52_0 = e2)
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | REDUCE: (2316), (2322) imply:
% 109.48/15.53 | | | | | | | | | | | | | (2328) ~ (all_52_0 = e1)
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | REDUCE: (115), (2323) imply:
% 109.48/15.53 | | | | | | | | | | | | | (2329) ~ (all_53_15 = e3)
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | SIMP: (2329) implies:
% 109.48/15.53 | | | | | | | | | | | | | (2330) ~ (all_53_15 = e3)
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | BETA: splitting (205) gives:
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | Case 1:
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | (2331) all_55_3 = e3
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | COMBINE_EQS: (2324), (2331) imply:
% 109.48/15.53 | | | | | | | | | | | | | | (2332) all_52_0 = e3
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | REDUCE: (2326), (2332) imply:
% 109.48/15.53 | | | | | | | | | | | | | | (2333) ~ (all_53_3 = e3)
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | REF_CLOSE: (108), (144), (162), (166), (174), (206), (250),
% 109.48/15.53 | | | | | | | | | | | | | | (1916), (2212), (2330), (2333), (function-axioms)
% 109.48/15.53 | | | | | | | | | | | | | | are inconsistent by sub-proof #66.
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | Case 2:
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | (2334) all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | REF_CLOSE: (2319), (2324), (2327), (2328), (2334) are
% 109.48/15.53 | | | | | | | | | | | | | | inconsistent by sub-proof #65.
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | End of split
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | Case 2:
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | (2335) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 109.48/15.53 | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 109.48/15.53 | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 109.48/15.53 | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | BETA: splitting (2335) gives:
% 109.48/15.53 | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | Case 1:
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | (2336) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 109.48/15.53 | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | ALPHA: (2336) implies:
% 109.48/15.53 | | | | | | | | | | | | | | (2337) op(e2, e0) = e2
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | REF_CLOSE: (168), (1918), (2337), (function-axioms) are
% 109.48/15.53 | | | | | | | | | | | | | | inconsistent by sub-proof #227.
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | Case 2:
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | (2338) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 109.48/15.53 | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | ALPHA: (2338) implies:
% 109.48/15.53 | | | | | | | | | | | | | | (2339) ~ (all_52_4 = e0)
% 109.48/15.53 | | | | | | | | | | | | | | (2340) op(e0, e1) = all_52_4
% 109.48/15.53 | | | | | | | | | | | | | | (2341) op(e1, e0) = e1
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1,
% 109.48/15.53 | | | | | | | | | | | | | | all_52_4, e1, e0, simplifying with (161), (2340)
% 109.48/15.53 | | | | | | | | | | | | | | gives:
% 109.48/15.53 | | | | | | | | | | | | | | (2342) all_53_1 = all_52_4
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e1,
% 109.48/15.53 | | | | | | | | | | | | | | e0, e1, simplifying with (164), (2341) gives:
% 109.48/15.53 | | | | | | | | | | | | | | (2343) all_53_4 = e1
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | COMBINE_EQS: (249), (2342) imply:
% 109.48/15.53 | | | | | | | | | | | | | | (2344) all_55_1 = all_52_4
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | REDUCE: (2290), (2342) imply:
% 109.48/15.53 | | | | | | | | | | | | | | (2345) ~ (all_52_4 = e3)
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | REDUCE: (1914), (2342) imply:
% 109.48/15.53 | | | | | | | | | | | | | | (2346) ~ (all_52_4 = e2)
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | REDUCE: (140), (2343) imply:
% 109.48/15.53 | | | | | | | | | | | | | | (2347) ~ (all_53_6 = e1)
% 109.48/15.53 | | | | | | | | | | | | | |
% 109.48/15.53 | | | | | | | | | | | | | | SIMP: (2347) implies:
% 109.57/15.53 | | | | | | | | | | | | | | (2348) ~ (all_53_6 = e1)
% 109.57/15.53 | | | | | | | | | | | | | |
% 109.57/15.53 | | | | | | | | | | | | | | REDUCE: (138), (2343) imply:
% 109.57/15.54 | | | | | | | | | | | | | | (2349) ~ (all_53_8 = e1)
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | SIMP: (2349) implies:
% 109.57/15.54 | | | | | | | | | | | | | | (2350) ~ (all_53_8 = e1)
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | Case 1:
% 109.57/15.54 | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | (2351) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 109.57/15.54 | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 109.57/15.54 | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | ALPHA: (2351) implies:
% 109.57/15.54 | | | | | | | | | | | | | | | (2352) op(e3, e1) = e3
% 109.57/15.54 | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | REF_CLOSE: (108), (113), (139), (162), (164), (166), (173),
% 109.57/15.54 | | | | | | | | | | | | | | | (174), (2212), (2341), (2352), (function-axioms)
% 109.57/15.54 | | | | | | | | | | | | | | | are inconsistent by sub-proof #212.
% 109.57/15.54 | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | Case 2:
% 109.57/15.54 | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | (2353) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.57/15.54 | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 109.57/15.54 | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.57/15.54 | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 109.57/15.54 | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | BETA: splitting (2353) gives:
% 109.57/15.54 | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | Case 1:
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | (2354) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.57/15.54 | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | ALPHA: (2354) implies:
% 109.57/15.54 | | | | | | | | | | | | | | | | (2355) op(e2, e1) = e2
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | (2356) all_55_8 = e3
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (2356) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | | (2357) all_53_8 = e3
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | REDUCE: (126), (2357) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | | (2358) ~ (all_53_10 = e3)
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | SIMP: (2358) implies:
% 109.57/15.54 | | | | | | | | | | | | | | | | | (2359) ~ (all_53_10 = e3)
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (123), (146), (163), (167), (169), (171),
% 109.57/15.54 | | | | | | | | | | | | | | | | | (197), (205), (251), (271), (1915), (2316),
% 109.57/15.54 | | | | | | | | | | | | | | | | | (2317), (2348), (2355), (2359), (function-axioms)
% 109.57/15.54 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #64.
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | (2360) all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | REF_CLOSE: (262), (1918), (2213), (2350), (2360) are
% 109.57/15.54 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63.
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | End of split
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | Case 2:
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | (2361) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.57/15.54 | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | ALPHA: (2361) implies:
% 109.57/15.54 | | | | | | | | | | | | | | | | (2362) op(e0, e1) = e0
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | (2363) all_55_1 = e3
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2344), (2363) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | | (2364) all_52_4 = e3
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | REDUCE: (2345), (2364) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | | (2365) $false
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | CLOSE: (2365) is inconsistent.
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | (2366) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | BETA: splitting (2366) gives:
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.54 | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | (2367) all_55_1 = e2
% 109.57/15.54 | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2344), (2367) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | | | (2368) all_52_4 = e2
% 109.57/15.54 | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | REDUCE: (2346), (2368) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | | | (2369) $false
% 109.57/15.54 | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | CLOSE: (2369) is inconsistent.
% 109.57/15.54 | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.54 | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | (2370) all_55_1 = e1 | all_55_1 = e0
% 109.57/15.54 | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | BETA: splitting (2370) gives:
% 109.57/15.54 | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | (2371) all_55_1 = e1
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2344), (2371) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | (2372) all_52_4 = e1
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | SIMP: (2372) implies:
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | (2373) all_52_4 = e1
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | REDUCE: (2340), (2373) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | (2374) op(e0, e1) = e1
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_52_4,
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (2340), (2362) gives:
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | (2375) all_52_4 = e0
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2373), (2375) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | (2376) e1 = e0
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | SIMP: (2376) implies:
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | (2377) e1 = e0
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | REDUCE: (4), (2377) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | (2378) $false
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | CLOSE: (2378) is inconsistent.
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | (2379) all_55_1 = e0
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2344), (2379) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | (2380) all_52_4 = e0
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | SIMP: (2380) implies:
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | (2381) all_52_4 = e0
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | REDUCE: (2339), (2381) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | (2382) $false
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | | CLOSE: (2382) is inconsistent.
% 109.57/15.54 | | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.54 | | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | | End of split
% 109.57/15.54 | | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | End of split
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | End of split
% 109.57/15.54 | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | End of split
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | End of split
% 109.57/15.54 | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | End of split
% 109.57/15.54 | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | End of split
% 109.57/15.54 | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | Case 2:
% 109.57/15.54 | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | (2383) all_26_2 = e2
% 109.57/15.54 | | | | | | | | | | | (2384) op(e2, e2) = all_26_1 & $i(all_26_1) & ( ~
% 109.57/15.54 | | | | | | | | | | | (all_26_1 = e0) | ( ~ (all_26_0 = e1) & op(e0,
% 109.57/15.54 | | | | | | | | | | | e2) = all_26_0 & $i(all_26_0)))
% 109.57/15.54 | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | ALPHA: (2384) implies:
% 109.57/15.54 | | | | | | | | | | | (2385) op(e2, e2) = all_26_1
% 109.57/15.54 | | | | | | | | | | | (2386) ~ (all_26_1 = e0) | ( ~ (all_26_0 = e1) & op(e0,
% 109.57/15.54 | | | | | | | | | | | e2) = all_26_0 & $i(all_26_0))
% 109.57/15.54 | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | COMBINE_EQS: (316), (2383) imply:
% 109.57/15.54 | | | | | | | | | | | (2387) all_4_2 = e2
% 109.57/15.54 | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | COMBINE_EQS: (277), (2387) imply:
% 109.57/15.54 | | | | | | | | | | | (2388) all_50_2 = e2
% 109.57/15.54 | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | REDUCE: (377), (2387) imply:
% 109.57/15.54 | | | | | | | | | | | (2389) ~ (all_53_15 = e2)
% 109.57/15.54 | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | BETA: splitting (105) gives:
% 109.57/15.54 | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | Case 1:
% 109.57/15.54 | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | (2390) ~ (all_50_2 = e2)
% 109.57/15.54 | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | REDUCE: (2388), (2390) imply:
% 109.57/15.54 | | | | | | | | | | | | (2391) $false
% 109.57/15.54 | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | CLOSE: (2391) is inconsistent.
% 109.57/15.54 | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | Case 2:
% 109.57/15.54 | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | (2392) op(e2, e2) = all_50_1 & $i(all_50_1) & ( ~
% 109.57/15.54 | | | | | | | | | | | | (all_50_1 = e1) | ( ~ (all_50_0 = e0) & op(e1,
% 109.57/15.54 | | | | | | | | | | | | e2) = all_50_0 & $i(all_50_0)))
% 109.57/15.54 | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | ALPHA: (2392) implies:
% 109.57/15.54 | | | | | | | | | | | | (2393) op(e2, e2) = all_50_1
% 109.57/15.54 | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | BETA: splitting (220) gives:
% 109.57/15.54 | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | Case 1:
% 109.57/15.54 | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | (2394) (all_57_84 = e2 & op(e3, e2) = e2) | (all_57_85 =
% 109.57/15.54 | | | | | | | | | | | | | e2 & op(e2, e2) = e2)
% 109.57/15.54 | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | BETA: splitting (2394) gives:
% 109.57/15.54 | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | Case 1:
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | (2395) all_57_84 = e2 & op(e3, e2) = e2
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | ALPHA: (2395) implies:
% 109.57/15.54 | | | | | | | | | | | | | | (2396) op(e3, e2) = e2
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 109.57/15.54 | | | | | | | | | | | | | | e2, e2, e3, simplifying with (174), (2396) gives:
% 109.57/15.54 | | | | | | | | | | | | | | (2397) all_53_15 = e2
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | REDUCE: (2389), (2397) imply:
% 109.57/15.54 | | | | | | | | | | | | | | (2398) $false
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | CLOSE: (2398) is inconsistent.
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | Case 2:
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | (2399) all_57_85 = e2 & op(e2, e2) = e2
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | ALPHA: (2399) implies:
% 109.57/15.54 | | | | | | | | | | | | | | (2400) op(e2, e2) = e2
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_26_1,
% 109.57/15.54 | | | | | | | | | | | | | | e2, e2, simplifying with (2385), (2400) gives:
% 109.57/15.54 | | | | | | | | | | | | | | (2401) all_26_1 = e2
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_50_1,
% 109.57/15.54 | | | | | | | | | | | | | | e2, e2, simplifying with (2215), (2393) gives:
% 109.57/15.54 | | | | | | | | | | | | | | (2402) all_50_1 = e0
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_1,
% 109.57/15.54 | | | | | | | | | | | | | | all_50_1, e2, e2, simplifying with (2385), (2393)
% 109.57/15.54 | | | | | | | | | | | | | | gives:
% 109.57/15.54 | | | | | | | | | | | | | | (2403) all_50_1 = all_26_1
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | COMBINE_EQS: (2402), (2403) imply:
% 109.57/15.54 | | | | | | | | | | | | | | (2404) all_26_1 = e0
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | SIMP: (2404) implies:
% 109.57/15.54 | | | | | | | | | | | | | | (2405) all_26_1 = e0
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | COMBINE_EQS: (2401), (2405) imply:
% 109.57/15.54 | | | | | | | | | | | | | | (2406) e2 = e0
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | SIMP: (2406) implies:
% 109.57/15.54 | | | | | | | | | | | | | | (2407) e2 = e0
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | REDUCE: (5), (2407) imply:
% 109.57/15.54 | | | | | | | | | | | | | | (2408) $false
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | CLOSE: (2408) is inconsistent.
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | End of split
% 109.57/15.54 | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | Case 2:
% 109.57/15.54 | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | (2409) (all_57_86 = e2 & op(e1, e2) = e2) | (all_57_87 =
% 109.57/15.54 | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 109.57/15.54 | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | BETA: splitting (2409) gives:
% 109.57/15.54 | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | Case 1:
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | (2410) all_57_86 = e2 & op(e1, e2) = e2
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | ALPHA: (2410) implies:
% 109.57/15.54 | | | | | | | | | | | | | | (2411) op(e1, e2) = e2
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e2,
% 109.57/15.54 | | | | | | | | | | | | | | e2, e1, simplifying with (166), (2411) gives:
% 109.57/15.54 | | | | | | | | | | | | | | (2412) all_53_7 = e2
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_50_1,
% 109.57/15.54 | | | | | | | | | | | | | | e2, e2, simplifying with (2215), (2393) gives:
% 109.57/15.54 | | | | | | | | | | | | | | (2413) all_50_1 = e0
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_1,
% 109.57/15.54 | | | | | | | | | | | | | | all_50_1, e2, e2, simplifying with (2385), (2393)
% 109.57/15.54 | | | | | | | | | | | | | | gives:
% 109.57/15.54 | | | | | | | | | | | | | | (2414) all_50_1 = all_26_1
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | COMBINE_EQS: (2413), (2414) imply:
% 109.57/15.54 | | | | | | | | | | | | | | (2415) all_26_1 = e0
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 109.57/15.54 | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | Case 1:
% 109.57/15.54 | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | (2416) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 109.57/15.54 | | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 109.57/15.54 | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | ALPHA: (2416) implies:
% 109.57/15.54 | | | | | | | | | | | | | | | (2417) op(e3, e2) = e3
% 109.57/15.54 | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | BETA: splitting (2386) gives:
% 109.57/15.54 | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | Case 1:
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | (2418) ~ (all_26_1 = e0)
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | REDUCE: (2415), (2418) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | (2419) $false
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | CLOSE: (2419) is inconsistent.
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | Case 2:
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | (2420) ~ (all_26_0 = e1) & op(e0, e2) = all_26_0 &
% 109.57/15.54 | | | | | | | | | | | | | | | | $i(all_26_0)
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | ALPHA: (2420) implies:
% 109.57/15.54 | | | | | | | | | | | | | | | | (2421) ~ (all_26_0 = e1)
% 109.57/15.54 | | | | | | | | | | | | | | | | (2422) op(e0, e2) = all_26_0
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 109.57/15.54 | | | | | | | | | | | | | | | | all_26_0, e2, e0, simplifying with (162), (2422)
% 109.57/15.54 | | | | | | | | | | | | | | | | gives:
% 109.57/15.54 | | | | | | | | | | | | | | | | (2423) all_53_3 = all_26_0
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 109.57/15.54 | | | | | | | | | | | | | | | | e3, e2, e3, simplifying with (174), (2417) gives:
% 109.57/15.54 | | | | | | | | | | | | | | | | (2424) all_53_15 = e3
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (2423) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | (2425) all_55_2 = all_26_0
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | REDUCE: (142), (2423), (2424) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | (2426) ~ (all_26_0 = e3)
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.54 | | | | | | | | | | | | | | | | REDUCE: (1916), (2423) imply:
% 109.57/15.54 | | | | | | | | | | | | | | | | (2427) ~ (all_26_0 = e2)
% 109.57/15.54 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | REDUCE: (2212), (2423) imply:
% 109.57/15.55 | | | | | | | | | | | | | | | | (2428) ~ (all_26_0 = e0)
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.55 | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | (2429) all_55_2 = e3
% 109.57/15.55 | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2425), (2429) imply:
% 109.57/15.55 | | | | | | | | | | | | | | | | | (2430) all_26_0 = e3
% 109.57/15.55 | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | REDUCE: (2426), (2430) imply:
% 109.57/15.55 | | | | | | | | | | | | | | | | | (2431) $false
% 109.57/15.55 | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | CLOSE: (2431) is inconsistent.
% 109.57/15.55 | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.55 | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | (2432) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 109.57/15.55 | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | BETA: splitting (2432) gives:
% 109.57/15.55 | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.55 | | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | | (2433) all_55_2 = e2
% 109.57/15.55 | | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2425), (2433) imply:
% 109.57/15.55 | | | | | | | | | | | | | | | | | | (2434) all_26_0 = e2
% 109.57/15.55 | | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | | SIMP: (2434) implies:
% 109.57/15.55 | | | | | | | | | | | | | | | | | | (2435) all_26_0 = e2
% 109.57/15.55 | | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | | REDUCE: (2427), (2435) imply:
% 109.57/15.55 | | | | | | | | | | | | | | | | | | (2436) $false
% 109.57/15.55 | | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | | CLOSE: (2436) is inconsistent.
% 109.57/15.55 | | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.55 | | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | | (2437) all_55_2 = e1 | all_55_2 = e0
% 109.57/15.55 | | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2421), (2425), (2428), (2437) are inconsistent by
% 109.57/15.55 | | | | | | | | | | | | | | | | | | sub-proof #130.
% 109.57/15.55 | | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | Case 2:
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | (2438) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 109.57/15.55 | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 109.57/15.55 | | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 109.57/15.55 | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | BETA: splitting (2438) gives:
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | Case 1:
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | (2439) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 109.57/15.55 | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | ALPHA: (2439) implies:
% 109.57/15.55 | | | | | | | | | | | | | | | | (2440) op(e1, e2) = e1
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e1, e2,
% 109.57/15.55 | | | | | | | | | | | | | | | | e1, simplifying with (2411), (2440) gives:
% 109.57/15.55 | | | | | | | | | | | | | | | | (2441) e2 = e1
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | REDUCE: (1919), (2441) imply:
% 109.57/15.55 | | | | | | | | | | | | | | | | (2442) $false
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | CLOSE: (2442) is inconsistent.
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | Case 2:
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | (2443) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 109.57/15.55 | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | ALPHA: (2443) implies:
% 109.57/15.55 | | | | | | | | | | | | | | | | (2444) op(e0, e2) = e0
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2212), (2444), (function-axioms) are
% 109.57/15.55 | | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | Case 2:
% 109.57/15.55 | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | (2445) all_57_87 = e2 & op(e0, e2) = e2
% 109.57/15.55 | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | REF_CLOSE: (162), (1916), (2445), (function-axioms) are
% 109.57/15.55 | | | | | | | | | | | | | | inconsistent by sub-proof #71.
% 109.57/15.55 | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | |
% 109.57/15.55 | | | | | | | | Case 2:
% 109.57/15.55 | | | | | | | | |
% 109.57/15.55 | | | | | | | | | (2446) all_14_2 = e2
% 109.57/15.55 | | | | | | | | | (2447) op(e2, e2) = all_14_1 & $i(all_14_1) & ( ~ (all_14_1
% 109.57/15.55 | | | | | | | | | = e3) | ( ~ (all_14_0 = e0) & op(e3, e2) =
% 109.57/15.55 | | | | | | | | | all_14_0 & $i(all_14_0)))
% 109.57/15.55 | | | | | | | | |
% 109.57/15.55 | | | | | | | | | ALPHA: (2447) implies:
% 109.57/15.55 | | | | | | | | | (2448) op(e2, e2) = all_14_1
% 109.57/15.55 | | | | | | | | |
% 109.57/15.55 | | | | | | | | | COMBINE_EQS: (334), (2446) imply:
% 109.57/15.55 | | | | | | | | | (2449) all_44_2 = e2
% 109.57/15.55 | | | | | | | | |
% 109.57/15.55 | | | | | | | | | REDUCE: (361), (2446) imply:
% 109.57/15.55 | | | | | | | | | (2450) ~ (all_53_7 = e2)
% 109.57/15.55 | | | | | | | | |
% 109.57/15.55 | | | | | | | | | BETA: splitting (220) gives:
% 109.57/15.55 | | | | | | | | |
% 109.57/15.55 | | | | | | | | | Case 1:
% 109.57/15.55 | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | (2451) (all_57_84 = e2 & op(e3, e2) = e2) | (all_57_85 =
% 109.57/15.55 | | | | | | | | | | e2 & op(e2, e2) = e2)
% 109.57/15.55 | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | BETA: splitting (2451) gives:
% 109.57/15.55 | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | Case 1:
% 109.57/15.55 | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | (2452) all_57_84 = e2 & op(e3, e2) = e2
% 109.57/15.55 | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | ALPHA: (2452) implies:
% 109.57/15.55 | | | | | | | | | | | (2453) op(e3, e2) = e2
% 109.57/15.55 | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | BETA: splitting (96) gives:
% 109.57/15.55 | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | Case 1:
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | (2454) ~ (all_44_2 = e2)
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | REDUCE: (2449), (2454) imply:
% 109.57/15.55 | | | | | | | | | | | | (2455) $false
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | CLOSE: (2455) is inconsistent.
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | Case 2:
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | (2456) op(e2, e2) = all_44_1 & $i(all_44_1) & ( ~
% 109.57/15.55 | | | | | | | | | | | | (all_44_1 = e0) | ( ~ (all_44_0 = e3) & op(e0,
% 109.57/15.55 | | | | | | | | | | | | e2) = all_44_0 & $i(all_44_0)))
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | ALPHA: (2456) implies:
% 109.57/15.55 | | | | | | | | | | | | (2457) op(e2, e2) = all_44_1
% 109.57/15.55 | | | | | | | | | | | | (2458) ~ (all_44_1 = e0) | ( ~ (all_44_0 = e3) & op(e0,
% 109.57/15.55 | | | | | | | | | | | | e2) = all_44_0 & $i(all_44_0))
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_44_1,
% 109.57/15.55 | | | | | | | | | | | | e2, e2, simplifying with (2215), (2457) gives:
% 109.57/15.55 | | | | | | | | | | | | (2459) all_44_1 = e0
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 109.57/15.55 | | | | | | | | | | | | e2, e2, e3, simplifying with (174), (2453) gives:
% 109.57/15.55 | | | | | | | | | | | | (2460) all_53_15 = e2
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | BETA: splitting (2458) gives:
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | Case 1:
% 109.57/15.55 | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | (2461) ~ (all_44_1 = e0)
% 109.57/15.55 | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | REDUCE: (2459), (2461) imply:
% 109.57/15.55 | | | | | | | | | | | | | (2462) $false
% 109.57/15.55 | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | CLOSE: (2462) is inconsistent.
% 109.57/15.55 | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | Case 2:
% 109.57/15.55 | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | (2463) ~ (all_44_0 = e3) & op(e0, e2) = all_44_0 &
% 109.57/15.55 | | | | | | | | | | | | | $i(all_44_0)
% 109.57/15.55 | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | ALPHA: (2463) implies:
% 109.57/15.55 | | | | | | | | | | | | | (2464) ~ (all_44_0 = e3)
% 109.57/15.55 | | | | | | | | | | | | | (2465) op(e0, e2) = all_44_0
% 109.57/15.55 | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | BETA: splitting (108) gives:
% 109.57/15.55 | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | Case 1:
% 109.57/15.55 | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | (2466) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 109.57/15.55 | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 109.57/15.55 | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | REF_CLOSE: (8), (2453), (2466), (function-axioms) are
% 109.57/15.55 | | | | | | | | | | | | | | inconsistent by sub-proof #91.
% 109.57/15.55 | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | Case 2:
% 109.57/15.55 | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | (2467) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 109.57/15.55 | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 109.57/15.55 | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 109.57/15.55 | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 109.57/15.55 | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | BETA: splitting (2467) gives:
% 109.57/15.55 | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | Case 1:
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | (2468) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 109.57/15.55 | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | ALPHA: (2468) implies:
% 109.57/15.55 | | | | | | | | | | | | | | | (2469) op(e1, e2) = e1
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 109.57/15.55 | | | | | | | | | | | | | | | all_44_0, e2, e0, simplifying with (162), (2465)
% 109.57/15.55 | | | | | | | | | | | | | | | gives:
% 109.57/15.55 | | | | | | | | | | | | | | | (2470) all_53_3 = all_44_0
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e1,
% 109.57/15.55 | | | | | | | | | | | | | | | e2, e1, simplifying with (166), (2469) gives:
% 109.57/15.55 | | | | | | | | | | | | | | | (2471) all_53_7 = e1
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | COMBINE_EQS: (250), (2470) imply:
% 109.57/15.55 | | | | | | | | | | | | | | | (2472) all_55_2 = all_44_0
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | Case 1:
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | (2473) all_55_2 = e3
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | COMBINE_EQS: (2472), (2473) imply:
% 109.57/15.55 | | | | | | | | | | | | | | | | (2474) all_44_0 = e3
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | REDUCE: (2464), (2474) imply:
% 109.57/15.55 | | | | | | | | | | | | | | | | (2475) $false
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | CLOSE: (2475) is inconsistent.
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | Case 2:
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | (2476) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | | REF_CLOSE: (144), (166), (250), (1916), (2212), (2469),
% 109.57/15.55 | | | | | | | | | | | | | | | | (2476), (function-axioms) are inconsistent by
% 109.57/15.55 | | | | | | | | | | | | | | | | sub-proof #67.
% 109.57/15.55 | | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | Case 2:
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | (2477) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 109.57/15.55 | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | ALPHA: (2477) implies:
% 109.57/15.55 | | | | | | | | | | | | | | | (2478) op(e0, e2) = e0
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | | REF_CLOSE: (162), (2212), (2478), (function-axioms) are
% 109.57/15.55 | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 109.57/15.55 | | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | Case 2:
% 109.57/15.55 | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | (2479) all_57_85 = e2 & op(e2, e2) = e2
% 109.57/15.55 | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | ALPHA: (2479) implies:
% 109.57/15.55 | | | | | | | | | | | (2480) op(e2, e2) = e2
% 109.57/15.55 | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | BETA: splitting (96) gives:
% 109.57/15.55 | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | Case 1:
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | (2481) ~ (all_44_2 = e2)
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | REDUCE: (2449), (2481) imply:
% 109.57/15.55 | | | | | | | | | | | | (2482) $false
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | CLOSE: (2482) is inconsistent.
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | Case 2:
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | (2483) op(e2, e2) = all_44_1 & $i(all_44_1) & ( ~
% 109.57/15.55 | | | | | | | | | | | | (all_44_1 = e0) | ( ~ (all_44_0 = e3) & op(e0,
% 109.57/15.55 | | | | | | | | | | | | e2) = all_44_0 & $i(all_44_0)))
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | ALPHA: (2483) implies:
% 109.57/15.55 | | | | | | | | | | | | (2484) op(e2, e2) = all_44_1
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_14_1,
% 109.57/15.55 | | | | | | | | | | | | e2, e2, simplifying with (2448), (2480) gives:
% 109.57/15.55 | | | | | | | | | | | | (2485) all_14_1 = e2
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_44_1,
% 109.57/15.55 | | | | | | | | | | | | e2, e2, simplifying with (2215), (2484) gives:
% 109.57/15.55 | | | | | | | | | | | | (2486) all_44_1 = e0
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 109.57/15.55 | | | | | | | | | | | | all_44_1, e2, e2, simplifying with (2448), (2484)
% 109.57/15.55 | | | | | | | | | | | | gives:
% 109.57/15.55 | | | | | | | | | | | | (2487) all_44_1 = all_14_1
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | COMBINE_EQS: (2486), (2487) imply:
% 109.57/15.55 | | | | | | | | | | | | (2488) all_14_1 = e0
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | SIMP: (2488) implies:
% 109.57/15.55 | | | | | | | | | | | | (2489) all_14_1 = e0
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | COMBINE_EQS: (2485), (2489) imply:
% 109.57/15.55 | | | | | | | | | | | | (2490) e2 = e0
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | REDUCE: (5), (2490) imply:
% 109.57/15.55 | | | | | | | | | | | | (2491) $false
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | | CLOSE: (2491) is inconsistent.
% 109.57/15.55 | | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | Case 2:
% 109.57/15.55 | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | (2492) (all_57_86 = e2 & op(e1, e2) = e2) | (all_57_87 =
% 109.57/15.55 | | | | | | | | | | e2 & op(e0, e2) = e2)
% 109.57/15.55 | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | | REF_CLOSE: (162), (166), (1916), (2450), (2492),
% 109.57/15.55 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.57/15.55 | | | | | | | | | | #70.
% 109.57/15.55 | | | | | | | | | |
% 109.57/15.55 | | | | | | | | | End of split
% 109.57/15.55 | | | | | | | | |
% 109.57/15.55 | | | | | | | | End of split
% 109.57/15.55 | | | | | | | |
% 109.57/15.55 | | | | | | | End of split
% 109.57/15.55 | | | | | | |
% 109.57/15.55 | | | | | | End of split
% 109.57/15.55 | | | | | |
% 109.57/15.55 | | | | | Case 2:
% 109.57/15.55 | | | | | |
% 109.57/15.55 | | | | | | (2493) all_10_2 = e3
% 109.57/15.55 | | | | | | (2494) op(e3, e3) = all_10_1 & $i(all_10_1) & ( ~ (all_10_1 = e0)
% 109.57/15.55 | | | | | | | ( ~ (all_10_0 = e1) & op(e0, e3) = all_10_0 &
% 109.57/15.55 | | | | | | $i(all_10_0)))
% 109.57/15.55 | | | | | |
% 109.57/15.55 | | | | | | ALPHA: (2494) implies:
% 109.57/15.55 | | | | | | (2495) op(e3, e3) = all_10_1
% 109.57/15.55 | | | | | |
% 109.57/15.55 | | | | | | COMBINE_EQS: (1928), (2493) imply:
% 109.57/15.55 | | | | | | (2496) all_8_1 = e3
% 109.57/15.55 | | | | | |
% 109.57/15.55 | | | | | | SIMP: (2496) implies:
% 109.57/15.55 | | | | | | (2497) all_8_1 = e3
% 109.57/15.55 | | | | | |
% 109.57/15.55 | | | | | | COMBINE_EQS: (1927), (2497) imply:
% 109.57/15.55 | | | | | | (2498) all_16_1 = e3
% 109.57/15.55 | | | | | |
% 109.57/15.55 | | | | | | COMBINE_EQS: (1933), (2497) imply:
% 109.57/15.55 | | | | | | (2499) all_48_2 = e3
% 109.57/15.55 | | | | | |
% 109.57/15.55 | | | | | | REDUCE: (1935), (2497) imply:
% 109.57/15.56 | | | | | | (2500) ~ (all_53_3 = e3)
% 109.57/15.56 | | | | | |
% 109.57/15.56 | | | | | | REDUCE: (1937), (2497) imply:
% 109.57/15.56 | | | | | | (2501) ~ (all_53_8 = e3)
% 109.57/15.56 | | | | | |
% 109.57/15.56 | | | | | | REDUCE: (1939), (2497) imply:
% 109.57/15.56 | | | | | | (2502) ~ (all_53_10 = e3)
% 109.57/15.56 | | | | | |
% 109.57/15.56 | | | | | | REDUCE: (1940), (2497) imply:
% 109.57/15.56 | | | | | | (2503) ~ (all_53_15 = e3)
% 109.57/15.56 | | | | | |
% 109.57/15.56 | | | | | | REDUCE: (1909), (2497) imply:
% 109.57/15.56 | | | | | | (2504) op(e2, e2) = e3
% 109.57/15.56 | | | | | |
% 109.57/15.56 | | | | | | BETA: splitting (102) gives:
% 109.57/15.56 | | | | | |
% 109.57/15.56 | | | | | | Case 1:
% 109.57/15.56 | | | | | | |
% 109.57/15.56 | | | | | | | (2505) ~ (all_48_2 = e3)
% 109.57/15.56 | | | | | | |
% 109.57/15.56 | | | | | | | REDUCE: (2499), (2505) imply:
% 109.57/15.56 | | | | | | | (2506) $false
% 109.57/15.56 | | | | | | |
% 109.57/15.56 | | | | | | | CLOSE: (2506) is inconsistent.
% 109.57/15.56 | | | | | | |
% 109.57/15.56 | | | | | | Case 2:
% 109.57/15.56 | | | | | | |
% 109.57/15.56 | | | | | | | (2507) op(e3, e3) = all_48_1 & $i(all_48_1) & ( ~ (all_48_1 =
% 109.57/15.56 | | | | | | | e1) | ( ~ (all_48_0 = e0) & op(e1, e3) = all_48_0 &
% 109.57/15.56 | | | | | | | $i(all_48_0)))
% 109.57/15.56 | | | | | | |
% 109.57/15.56 | | | | | | | ALPHA: (2507) implies:
% 109.57/15.56 | | | | | | | (2508) op(e3, e3) = all_48_1
% 109.57/15.56 | | | | | | | (2509) ~ (all_48_1 = e1) | ( ~ (all_48_0 = e0) & op(e1, e3) =
% 109.57/15.56 | | | | | | | all_48_0 & $i(all_48_0))
% 109.57/15.56 | | | | | | |
% 109.57/15.56 | | | | | | | BETA: splitting (1925) gives:
% 109.57/15.56 | | | | | | |
% 109.57/15.56 | | | | | | | Case 1:
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | | (2510) ~ (all_16_1 = e3)
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | | REDUCE: (2498), (2510) imply:
% 109.57/15.56 | | | | | | | | (2511) $false
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | | CLOSE: (2511) is inconsistent.
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | Case 2:
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | | (2512) ~ (all_16_0 = e1) & op(e3, e2) = all_16_0 &
% 109.57/15.56 | | | | | | | | $i(all_16_0)
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | | ALPHA: (2512) implies:
% 109.57/15.56 | | | | | | | | (2513) ~ (all_16_0 = e1)
% 109.57/15.56 | | | | | | | | (2514) op(e3, e2) = all_16_0
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 109.57/15.56 | | | | | | | | all_16_0, e2, e3, simplifying with (174), (2514)
% 109.57/15.56 | | | | | | | | gives:
% 109.57/15.56 | | | | | | | | (2515) all_53_15 = all_16_0
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 109.57/15.56 | | | | | | | | all_48_1, e3, e3, simplifying with (35), (2508)
% 109.57/15.56 | | | | | | | | gives:
% 109.57/15.56 | | | | | | | | (2516) all_48_1 = all_4_2
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 109.57/15.56 | | | | | | | | all_48_1, e3, e3, simplifying with (2495), (2508)
% 109.57/15.56 | | | | | | | | gives:
% 109.57/15.56 | | | | | | | | (2517) all_48_1 = all_10_1
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | | COMBINE_EQS: (2516), (2517) imply:
% 109.57/15.56 | | | | | | | | (2518) all_10_1 = all_4_2
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | | COMBINE_EQS: (274), (2515) imply:
% 109.57/15.56 | | | | | | | | (2519) all_55_14 = all_16_0
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | | REDUCE: (142), (2515) imply:
% 109.57/15.56 | | | | | | | | (2520) ~ (all_53_3 = all_16_0)
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | | REDUCE: (377), (2515) imply:
% 109.57/15.56 | | | | | | | | (2521) ~ (all_16_0 = all_4_2)
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | | REDUCE: (2503), (2515) imply:
% 109.57/15.56 | | | | | | | | (2522) ~ (all_16_0 = e3)
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | | BETA: splitting (51) gives:
% 109.57/15.56 | | | | | | | |
% 109.57/15.56 | | | | | | | | Case 1:
% 109.57/15.56 | | | | | | | | |
% 109.57/15.56 | | | | | | | | | (2523) ~ (all_14_2 = e2)
% 109.57/15.56 | | | | | | | | |
% 109.57/15.56 | | | | | | | | | BETA: splitting (57) gives:
% 109.57/15.56 | | | | | | | | |
% 109.57/15.56 | | | | | | | | | Case 1:
% 109.57/15.56 | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | (2524) ~ (all_18_2 = e3)
% 109.57/15.56 | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | REDUCE: (326), (2524) imply:
% 109.57/15.56 | | | | | | | | | | (2525) ~ (all_14_2 = e3)
% 109.57/15.56 | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | BETA: splitting (63) gives:
% 109.57/15.56 | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | Case 1:
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | (2526) ~ (all_22_2 = e0)
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | REDUCE: (329), (2526) imply:
% 109.57/15.56 | | | | | | | | | | | (2527) ~ (all_14_2 = e0)
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (117), (123),
% 109.57/15.56 | | | | | | | | | | | (126), (127), (148), (152), (153), (161), (162),
% 109.57/15.56 | | | | | | | | | | | (163), (164), (166), (167), (168), (169), (171),
% 109.57/15.56 | | | | | | | | | | | (172), (173), (174), (203), (341), (357), (359),
% 109.57/15.56 | | | | | | | | | | | (361), (2523), (2525), (2527), (function-axioms)
% 109.57/15.56 | | | | | | | | | | | are inconsistent by sub-proof #216.
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | Case 2:
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | (2528) all_22_2 = e0
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | COMBINE_EQS: (329), (2528) imply:
% 109.57/15.56 | | | | | | | | | | | (2529) all_14_2 = e0
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | SIMP: (2529) implies:
% 109.57/15.56 | | | | | | | | | | | (2530) all_14_2 = e0
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | REDUCE: (354), (2530) imply:
% 109.57/15.56 | | | | | | | | | | | (2531) ~ (all_53_1 = e0)
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | BETA: splitting (69) gives:
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | Case 1:
% 109.57/15.56 | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | (2532) ~ (all_26_2 = e2)
% 109.57/15.56 | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | REDUCE: (316), (2532) imply:
% 109.57/15.56 | | | | | | | | | | | | (2533) ~ (all_4_2 = e2)
% 109.57/15.56 | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | BETA: splitting (81) gives:
% 109.57/15.56 | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | Case 1:
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | (2534) ~ (all_34_2 = e1)
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | REDUCE: (311), (2534) imply:
% 109.57/15.56 | | | | | | | | | | | | | (2535) ~ (all_4_2 = e1)
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | REF_CLOSE: (110), (164), (168), (172), (193), (234), (339),
% 109.57/15.56 | | | | | | | | | | | | | (374), (378), (1918), (1920), (2501), (2533),
% 109.57/15.56 | | | | | | | | | | | | | (2535), (function-axioms) are inconsistent by
% 109.57/15.56 | | | | | | | | | | | | | sub-proof #59.
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | Case 2:
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | (2536) all_34_2 = e1
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | COMBINE_EQS: (311), (2536) imply:
% 109.57/15.56 | | | | | | | | | | | | | (2537) all_4_2 = e1
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | REDUCE: (355), (2537) imply:
% 109.57/15.56 | | | | | | | | | | | | | (2538) ~ (all_53_2 = e1)
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | REDUCE: (366), (2537) imply:
% 109.57/15.56 | | | | | | | | | | | | | (2539) ~ (all_53_6 = e1)
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | REDUCE: (371), (2537) imply:
% 109.57/15.56 | | | | | | | | | | | | | (2540) ~ (all_53_10 = e1)
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | REDUCE: (375), (2537) imply:
% 109.57/15.56 | | | | | | | | | | | | | (2541) ~ (all_53_13 = e1)
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | BETA: splitting (109) gives:
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | Case 1:
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | (2542) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 109.57/15.56 | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | ALPHA: (2542) implies:
% 109.57/15.56 | | | | | | | | | | | | | | (2543) op(e3, e1) = e3
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 109.57/15.56 | | | | | | | | | | | | | | e3, e1, e3, simplifying with (173), (2543) gives:
% 109.57/15.56 | | | | | | | | | | | | | | (2544) all_53_13 = e3
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | REDUCE: (117), (2544) imply:
% 109.57/15.56 | | | | | | | | | | | | | | (2545) ~ (all_53_12 = e3)
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (110), (164), (168), (172), (234),
% 109.57/15.56 | | | | | | | | | | | | | | (1918), (1920), (2501), (2545), (function-axioms)
% 109.57/15.56 | | | | | | | | | | | | | | are inconsistent by sub-proof #60.
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | Case 2:
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | (2546) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.57/15.56 | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 109.57/15.56 | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.57/15.56 | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | BETA: splitting (2546) gives:
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | Case 1:
% 109.57/15.56 | | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | | (2547) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.57/15.56 | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)
% 109.57/15.56 | | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | | ALPHA: (2547) implies:
% 109.57/15.56 | | | | | | | | | | | | | | | (2548) op(e2, e1) = e2
% 109.57/15.56 | | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | | REF_CLOSE: (107), (123), (146), (163), (167), (169), (171),
% 109.57/15.56 | | | | | | | | | | | | | | | (197), (205), (251), (271), (1915), (2502),
% 109.57/15.56 | | | | | | | | | | | | | | | (2538), (2539), (2540), (2548), (function-axioms)
% 109.57/15.56 | | | | | | | | | | | | | | | are inconsistent by sub-proof #64.
% 109.57/15.56 | | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | Case 2:
% 109.57/15.56 | | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | | (2549) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.57/15.56 | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 109.57/15.56 | | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | | ALPHA: (2549) implies:
% 109.57/15.56 | | | | | | | | | | | | | | | (2550) op(e0, e1) = e0
% 109.57/15.56 | | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | | REF_CLOSE: (161), (2531), (2550), (function-axioms) are
% 109.57/15.56 | | | | | | | | | | | | | | | inconsistent by sub-proof #230.
% 109.57/15.56 | | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | End of split
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | End of split
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | End of split
% 109.57/15.56 | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | Case 2:
% 109.57/15.56 | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | (2551) all_26_2 = e2
% 109.57/15.56 | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | COMBINE_EQS: (316), (2551) imply:
% 109.57/15.56 | | | | | | | | | | | | (2552) all_4_2 = e2
% 109.57/15.56 | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | REDUCE: (2521), (2552) imply:
% 109.57/15.56 | | | | | | | | | | | | (2553) ~ (all_16_0 = e2)
% 109.57/15.56 | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | BETA: splitting (194) gives:
% 109.57/15.56 | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | Case 1:
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | (2554) all_55_14 = e3
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | REF_CLOSE: (2519), (2522), (2554) are inconsistent by
% 109.57/15.56 | | | | | | | | | | | | | sub-proof #58.
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | Case 2:
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | (2555) all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | BETA: splitting (2555) gives:
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | Case 1:
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | (2556) all_55_14 = e2
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | COMBINE_EQS: (2519), (2556) imply:
% 109.57/15.56 | | | | | | | | | | | | | | (2557) all_16_0 = e2
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | SIMP: (2557) implies:
% 109.57/15.56 | | | | | | | | | | | | | | (2558) all_16_0 = e2
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | REDUCE: (2553), (2558) imply:
% 109.57/15.56 | | | | | | | | | | | | | | (2559) $false
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | CLOSE: (2559) is inconsistent.
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | Case 2:
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | (2560) all_55_14 = e1 | all_55_14 = e0
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | REF_CLOSE: (108), (144), (162), (166), (174), (206), (250),
% 109.57/15.56 | | | | | | | | | | | | | | (1916), (2500), (2503), (2513), (2519), (2520),
% 109.57/15.56 | | | | | | | | | | | | | | (2560), (function-axioms) are inconsistent by
% 109.57/15.56 | | | | | | | | | | | | | | sub-proof #57.
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | End of split
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | End of split
% 109.57/15.56 | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | End of split
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | End of split
% 109.57/15.56 | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | Case 2:
% 109.57/15.56 | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | (2561) all_18_2 = e3
% 109.57/15.56 | | | | | | | | | | (2562) op(e3, e3) = all_18_1 & $i(all_18_1) & ( ~
% 109.57/15.56 | | | | | | | | | | (all_18_1 = e2) | ( ~ (all_18_0 = e0) & op(e2,
% 109.57/15.56 | | | | | | | | | | e3) = all_18_0 & $i(all_18_0)))
% 109.57/15.56 | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | ALPHA: (2562) implies:
% 109.57/15.56 | | | | | | | | | | (2563) op(e3, e3) = all_18_1
% 109.57/15.56 | | | | | | | | | | (2564) ~ (all_18_1 = e2) | ( ~ (all_18_0 = e0) & op(e2,
% 109.57/15.56 | | | | | | | | | | e3) = all_18_0 & $i(all_18_0))
% 109.57/15.56 | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | COMBINE_EQS: (326), (2561) imply:
% 109.57/15.56 | | | | | | | | | | (2565) all_14_2 = e3
% 109.57/15.56 | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | COMBINE_EQS: (253), (2565) imply:
% 109.57/15.56 | | | | | | | | | | (2566) all_20_2 = e3
% 109.57/15.56 | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | REDUCE: (354), (2565) imply:
% 109.57/15.56 | | | | | | | | | | (2567) ~ (all_53_1 = e3)
% 109.57/15.56 | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | REDUCE: (357), (2565) imply:
% 109.57/15.56 | | | | | | | | | | (2568) ~ (all_53_4 = e3)
% 109.57/15.56 | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | BETA: splitting (60) gives:
% 109.57/15.56 | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | Case 1:
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | (2569) ~ (all_20_2 = e3)
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | REDUCE: (2566), (2569) imply:
% 109.57/15.56 | | | | | | | | | | | (2570) $false
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | CLOSE: (2570) is inconsistent.
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | Case 2:
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | (2571) op(e3, e3) = all_20_1 & $i(all_20_1) & ( ~
% 109.57/15.56 | | | | | | | | | | | (all_20_1 = e0) | ( ~ (all_20_0 = e2) & op(e0,
% 109.57/15.56 | | | | | | | | | | | e3) = all_20_0 & $i(all_20_0)))
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | ALPHA: (2571) implies:
% 109.57/15.56 | | | | | | | | | | | (2572) op(e3, e3) = all_20_1
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | BETA: splitting (235) gives:
% 109.57/15.56 | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | Case 1:
% 109.57/15.56 | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | (2573) (all_57_24 = e3 & op(e0, e3) = e3) | (all_57_25 =
% 109.57/15.56 | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 109.57/15.56 | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | BETA: splitting (2573) gives:
% 109.57/15.56 | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | Case 1:
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | (2574) all_57_24 = e3 & op(e0, e3) = e3
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | ALPHA: (2574) implies:
% 109.57/15.56 | | | | | | | | | | | | | (2575) op(e0, e3) = e3
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | BETA: splitting (234) gives:
% 109.57/15.56 | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | Case 1:
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | (2576) (all_57_28 = e3 & op(e3, e0) = e3) | (all_57_29 =
% 109.57/15.56 | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | BETA: splitting (2576) gives:
% 109.57/15.56 | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | Case 1:
% 109.57/15.56 | | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | | (2577) all_57_28 = e3 & op(e3, e0) = e3
% 109.57/15.56 | | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | | ALPHA: (2577) implies:
% 109.57/15.56 | | | | | | | | | | | | | | | (2578) op(e3, e0) = e3
% 109.57/15.56 | | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e3,
% 109.57/15.56 | | | | | | | | | | | | | | | e3, e0, simplifying with (163), (2575) gives:
% 109.57/15.56 | | | | | | | | | | | | | | | (2579) all_53_2 = e3
% 109.57/15.56 | | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 109.57/15.56 | | | | | | | | | | | | | | | e3, e0, e3, simplifying with (172), (2578) gives:
% 109.57/15.56 | | | | | | | | | | | | | | | (2580) all_53_12 = e3
% 109.57/15.56 | | | | | | | | | | | | | | |
% 109.57/15.56 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 109.57/15.56 | | | | | | | | | | | | | | | all_20_1, e3, e3, simplifying with (35), (2572)
% 109.57/15.56 | | | | | | | | | | | | | | | gives:
% 109.57/15.57 | | | | | | | | | | | | | | | (2581) all_20_1 = all_4_2
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 109.57/15.57 | | | | | | | | | | | | | | | all_20_1, e3, e3, simplifying with (2563), (2572)
% 109.57/15.57 | | | | | | | | | | | | | | | gives:
% 109.57/15.57 | | | | | | | | | | | | | | | (2582) all_20_1 = all_18_1
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | COMBINE_EQS: (2581), (2582) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | (2583) all_18_1 = all_4_2
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | SIMP: (2583) implies:
% 109.57/15.57 | | | | | | | | | | | | | | | (2584) all_18_1 = all_4_2
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | REDUCE: (147), (2579) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | (2585) ~ (all_53_6 = e3)
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | SIMP: (2585) implies:
% 109.57/15.57 | | | | | | | | | | | | | | | (2586) ~ (all_53_6 = e3)
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | REDUCE: (146), (2579) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | (2587) ~ (all_53_10 = e3)
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | REDUCE: (374), (2580) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | (2588) ~ (all_4_2 = e3)
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | SIMP: (2588) implies:
% 109.57/15.57 | | | | | | | | | | | | | | | (2589) ~ (all_4_2 = e3)
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | Case 1:
% 109.57/15.57 | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | (2590) ~ (all_26_2 = e2)
% 109.57/15.57 | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | REDUCE: (316), (2590) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | | (2591) ~ (all_4_2 = e2)
% 109.57/15.57 | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 109.57/15.57 | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.57 | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | (2592) all_55_15 = e3
% 109.57/15.57 | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | REF_CLOSE: (339), (2589), (2592) are inconsistent by
% 109.57/15.57 | | | | | | | | | | | | | | | | | sub-proof #140.
% 109.57/15.57 | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | (2593) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 109.57/15.57 | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | BETA: splitting (2593) gives:
% 109.57/15.57 | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.57 | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | (2594) all_55_15 = e2
% 109.57/15.57 | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | REF_CLOSE: (339), (2591), (2594) are inconsistent by
% 109.57/15.57 | | | | | | | | | | | | | | | | | | sub-proof #193.
% 109.57/15.57 | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | (2595) all_55_15 = e1 | all_55_15 = e0
% 109.57/15.57 | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | BETA: splitting (2595) gives:
% 109.57/15.57 | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | (2596) all_55_15 = e1
% 109.57/15.57 | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (2596) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | (2597) all_4_2 = e1
% 109.57/15.57 | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | SIMP: (2597) implies:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | (2598) all_4_2 = e1
% 109.57/15.57 | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2516), (2598) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | (2599) all_48_1 = e1
% 109.57/15.57 | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | REDUCE: (366), (2598) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | (2600) ~ (all_53_6 = e1)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | (2601) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | = all_52_18 & op(e2, e3) = e2 & $i(all_52_18)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | ALPHA: (2601) implies:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | (2602) op(e2, e3) = e2
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2509) gives:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | (2603) ~ (all_48_1 = e1)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2599), (2603) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | (2604) $false
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | CLOSE: (2604) is inconsistent.
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | (2605) ~ (all_48_0 = e0) & op(e1, e3) = all_48_0 &
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | $i(all_48_0)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2605) implies:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | (2606) ~ (all_48_0 = e0)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | (2607) op(e1, e3) = all_48_0
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | all_48_0, e3, e1, simplifying with (167), (2607)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | gives:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | (2608) all_53_6 = all_48_0
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_10,
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | e2, e3, e2, simplifying with (171), (2602) gives:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | (2609) all_53_10 = e2
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (2608) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | (2610) all_55_7 = all_48_0
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (2608), (2609) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | (2611) ~ (all_48_0 = e2)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2586), (2608) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | (2612) ~ (all_48_0 = e3)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2600), (2608) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | (2613) ~ (all_48_0 = e1)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | | (2614) all_55_7 = e3
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2610), (2614) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | | (2615) all_48_0 = e3
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2612), (2615) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | | (2616) $false
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2616) is inconsistent.
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | | (2617) all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2606), (2610), (2611), (2613), (2617) are
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #56.
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | (2618) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | (all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22))
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2618) gives:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | (2619) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2619) implies:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | (2620) op(e1, e3) = e1
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2600), (2620), (function-axioms) are
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #223.
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | (2621) all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22)
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2621) implies:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | (2622) op(e0, e3) = e0
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2575), (2622), (function-axioms) are
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #122.
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | (2623) all_55_15 = e0
% 109.57/15.57 | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (339), (378), (2623) are inconsistent by sub-proof
% 109.57/15.57 | | | | | | | | | | | | | | | | | | | #192.
% 109.57/15.57 | | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | (2624) all_26_2 = e2
% 109.57/15.57 | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (2624) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | | (2625) all_4_2 = e2
% 109.57/15.57 | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | SIMP: (2625) implies:
% 109.57/15.57 | | | | | | | | | | | | | | | | (2626) all_4_2 = e2
% 109.57/15.57 | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | COMBINE_EQS: (2584), (2626) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | | (2627) all_18_1 = e2
% 109.57/15.57 | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | REDUCE: (371), (2626) imply:
% 109.57/15.57 | | | | | | | | | | | | | | | | (2628) ~ (all_53_10 = e2)
% 109.57/15.57 | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (107), (131), (167), (171), (197), (271),
% 109.57/15.57 | | | | | | | | | | | | | | | | (2502), (2564), (2575), (2627), (2628),
% 109.57/15.57 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.57/15.57 | | | | | | | | | | | | | | | | #54.
% 109.57/15.57 | | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | (2629) all_57_29 = e3 & op(e2, e0) = e3
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | ALPHA: (2629) implies:
% 109.57/15.57 | | | | | | | | | | | | | | | (2630) op(e2, e0) = e3
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | REF_CLOSE: (168), (2501), (2630), (function-axioms) are
% 109.57/15.57 | | | | | | | | | | | | | | | inconsistent by sub-proof #194.
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | (2631) (all_57_30 = e3 & op(e1, e0) = e3) | (all_57_31 =
% 109.57/15.57 | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 109.57/15.57 | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | BETA: splitting (2631) gives:
% 109.57/15.57 | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | Case 1:
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | (2632) all_57_30 = e3 & op(e1, e0) = e3
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | ALPHA: (2632) implies:
% 109.57/15.57 | | | | | | | | | | | | | | | (2633) op(e1, e0) = e3
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | REF_CLOSE: (164), (2568), (2633), (function-axioms) are
% 109.57/15.57 | | | | | | | | | | | | | | | inconsistent by sub-proof #126.
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | (2634) all_57_31 = e3 & op(e0, e0) = e3
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | ALPHA: (2634) implies:
% 109.57/15.57 | | | | | | | | | | | | | | | (2635) op(e0, e0) = e3
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | | REF_CLOSE: (8), (1920), (2635), (function-axioms) are
% 109.57/15.57 | | | | | | | | | | | | | | | inconsistent by sub-proof #61.
% 109.57/15.57 | | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | (2636) all_57_25 = e3 & op(e0, e2) = e3
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | ALPHA: (2636) implies:
% 109.57/15.57 | | | | | | | | | | | | | (2637) op(e0, e2) = e3
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | REF_CLOSE: (162), (2500), (2637), (function-axioms) are
% 109.57/15.57 | | | | | | | | | | | | | inconsistent by sub-proof #137.
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | (2638) (all_57_26 = e3 & op(e0, e1) = e3) | (all_57_27 =
% 109.57/15.57 | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 109.57/15.57 | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | BETA: splitting (2638) gives:
% 109.57/15.57 | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | Case 1:
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | (2639) all_57_26 = e3 & op(e0, e1) = e3
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | ALPHA: (2639) implies:
% 109.57/15.57 | | | | | | | | | | | | | (2640) op(e0, e1) = e3
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | REF_CLOSE: (161), (2567), (2640), (function-axioms) are
% 109.57/15.57 | | | | | | | | | | | | | inconsistent by sub-proof #145.
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | (2641) all_57_27 = e3 & op(e0, e0) = e3
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | ALPHA: (2641) implies:
% 109.57/15.57 | | | | | | | | | | | | | (2642) op(e0, e0) = e3
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | REF_CLOSE: (8), (1920), (2642), (function-axioms) are
% 109.57/15.57 | | | | | | | | | | | | | inconsistent by sub-proof #61.
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | End of split
% 109.57/15.57 | | | | | | | | |
% 109.57/15.57 | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | |
% 109.57/15.57 | | | | | | | | | (2643) all_14_2 = e2
% 109.57/15.57 | | | | | | | | | (2644) op(e2, e2) = all_14_1 & $i(all_14_1) & ( ~ (all_14_1
% 109.57/15.57 | | | | | | | | | = e3) | ( ~ (all_14_0 = e0) & op(e3, e2) =
% 109.57/15.57 | | | | | | | | | all_14_0 & $i(all_14_0)))
% 109.57/15.57 | | | | | | | | |
% 109.57/15.57 | | | | | | | | | ALPHA: (2644) implies:
% 109.57/15.57 | | | | | | | | | (2645) op(e2, e2) = all_14_1
% 109.57/15.57 | | | | | | | | |
% 109.57/15.57 | | | | | | | | | COMBINE_EQS: (334), (2643) imply:
% 109.57/15.57 | | | | | | | | | (2646) all_44_2 = e2
% 109.57/15.57 | | | | | | | | |
% 109.57/15.57 | | | | | | | | | REDUCE: (361), (2643) imply:
% 109.57/15.57 | | | | | | | | | (2647) ~ (all_53_7 = e2)
% 109.57/15.57 | | | | | | | | |
% 109.57/15.57 | | | | | | | | | REDUCE: (363), (2643) imply:
% 109.57/15.57 | | | | | | | | | (2648) ~ (all_53_9 = e2)
% 109.57/15.57 | | | | | | | | |
% 109.57/15.57 | | | | | | | | | BETA: splitting (220) gives:
% 109.57/15.57 | | | | | | | | |
% 109.57/15.57 | | | | | | | | | Case 1:
% 109.57/15.57 | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | (2649) (all_57_84 = e2 & op(e3, e2) = e2) | (all_57_85 =
% 109.57/15.57 | | | | | | | | | | e2 & op(e2, e2) = e2)
% 109.57/15.57 | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | BETA: splitting (2649) gives:
% 109.57/15.57 | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | Case 1:
% 109.57/15.57 | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | (2650) all_57_84 = e2 & op(e3, e2) = e2
% 109.57/15.57 | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | ALPHA: (2650) implies:
% 109.57/15.57 | | | | | | | | | | | (2651) op(e3, e2) = e2
% 109.57/15.57 | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | BETA: splitting (96) gives:
% 109.57/15.57 | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | Case 1:
% 109.57/15.57 | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | (2652) ~ (all_44_2 = e2)
% 109.57/15.57 | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | REDUCE: (2646), (2652) imply:
% 109.57/15.57 | | | | | | | | | | | | (2653) $false
% 109.57/15.57 | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | CLOSE: (2653) is inconsistent.
% 109.57/15.57 | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | Case 2:
% 109.57/15.57 | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | (2654) op(e2, e2) = all_44_1 & $i(all_44_1) & ( ~
% 109.57/15.57 | | | | | | | | | | | | (all_44_1 = e0) | ( ~ (all_44_0 = e3) & op(e0,
% 109.57/15.57 | | | | | | | | | | | | e2) = all_44_0 & $i(all_44_0)))
% 109.57/15.57 | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | ALPHA: (2654) implies:
% 109.57/15.57 | | | | | | | | | | | | (2655) op(e2, e2) = all_44_1
% 109.57/15.57 | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | BETA: splitting (221) gives:
% 109.57/15.57 | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | Case 1:
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | (2656) (all_57_80 = e2 & op(e2, e3) = e2) | (all_57_81 =
% 109.57/15.57 | | | | | | | | | | | | | e2 & op(e2, e2) = e2)
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | BETA: splitting (2656) gives:
% 109.57/15.57 | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | Case 1:
% 109.57/15.57 | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | (2657) all_57_80 = e2 & op(e2, e3) = e2
% 109.57/15.57 | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | ALPHA: (2657) implies:
% 109.57/15.57 | | | | | | | | | | | | | | (2658) op(e2, e3) = e2
% 109.57/15.57 | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_10,
% 109.57/15.57 | | | | | | | | | | | | | | e2, e3, e2, simplifying with (171), (2658) gives:
% 109.57/15.57 | | | | | | | | | | | | | | (2659) all_53_10 = e2
% 109.57/15.57 | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_0, e2,
% 109.57/15.57 | | | | | | | | | | | | | | e2, e3, simplifying with (2514), (2651) gives:
% 109.57/15.57 | | | | | | | | | | | | | | (2660) all_16_0 = e2
% 109.57/15.57 | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | REDUCE: (131), (2659) imply:
% 109.57/15.57 | | | | | | | | | | | | | | (2661) ~ (all_53_6 = e2)
% 109.57/15.57 | | | | | | | | | | | | | |
% 109.57/15.57 | | | | | | | | | | | | | | REDUCE: (2521), (2660) imply:
% 109.57/15.58 | | | | | | | | | | | | | | (2662) ~ (all_4_2 = e2)
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | SIMP: (2662) implies:
% 109.57/15.58 | | | | | | | | | | | | | | (2663) ~ (all_4_2 = e2)
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | Case 1:
% 109.57/15.58 | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | (2664) ~ (all_34_2 = e1)
% 109.57/15.58 | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | REDUCE: (311), (2664) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | (2665) ~ (all_4_2 = e1)
% 109.57/15.58 | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | REF_CLOSE: (110), (164), (168), (172), (193), (234), (339),
% 109.57/15.58 | | | | | | | | | | | | | | | (374), (378), (1918), (1920), (2501), (2663),
% 109.57/15.58 | | | | | | | | | | | | | | | (2665), (function-axioms) are inconsistent by
% 109.57/15.58 | | | | | | | | | | | | | | | sub-proof #59.
% 109.57/15.58 | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | Case 2:
% 109.57/15.58 | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | (2666) all_34_2 = e1
% 109.57/15.58 | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | COMBINE_EQS: (311), (2666) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | (2667) all_4_2 = e1
% 109.57/15.58 | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | SIMP: (2667) implies:
% 109.57/15.58 | | | | | | | | | | | | | | | (2668) all_4_2 = e1
% 109.57/15.58 | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | COMBINE_EQS: (2516), (2668) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | (2669) all_48_1 = e1
% 109.57/15.58 | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | REDUCE: (355), (2668) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | (2670) ~ (all_53_2 = e1)
% 109.57/15.58 | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | REDUCE: (366), (2668) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | (2671) ~ (all_53_6 = e1)
% 109.57/15.58 | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | REDUCE: (2663), (2668) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | (2672) ~ (e2 = e1)
% 109.57/15.58 | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | BETA: splitting (2509) gives:
% 109.57/15.58 | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | Case 1:
% 109.57/15.58 | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | (2673) ~ (all_48_1 = e1)
% 109.57/15.58 | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | REDUCE: (2669), (2673) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | | (2674) $false
% 109.57/15.58 | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | CLOSE: (2674) is inconsistent.
% 109.57/15.58 | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | Case 2:
% 109.57/15.58 | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | (2675) ~ (all_48_0 = e0) & op(e1, e3) = all_48_0 &
% 109.57/15.58 | | | | | | | | | | | | | | | | $i(all_48_0)
% 109.57/15.58 | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | ALPHA: (2675) implies:
% 109.57/15.58 | | | | | | | | | | | | | | | | (2676) ~ (all_48_0 = e0)
% 109.57/15.58 | | | | | | | | | | | | | | | | (2677) op(e1, e3) = all_48_0
% 109.57/15.58 | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 109.57/15.58 | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.58 | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | (2678) (all_57_108 = e1 & op(e3, e3) = e1) | (all_57_109
% 109.57/15.58 | | | | | | | | | | | | | | | | | = e1 & op(e2, e3) = e1)
% 109.57/15.58 | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | BETA: splitting (2678) gives:
% 109.57/15.58 | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 109.57/15.58 | | | | | | | | | | | | | | | | | | all_48_0, e3, e1, simplifying with (167), (2677)
% 109.57/15.58 | | | | | | | | | | | | | | | | | | gives:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | (2679) all_53_6 = all_48_0
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (2679) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | (2680) all_55_7 = all_48_0
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | REDUCE: (147), (2679) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | (2681) ~ (all_53_2 = all_48_0)
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | REDUCE: (2661), (2679) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | (2682) ~ (all_48_0 = e2)
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | REDUCE: (2671), (2679) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | (2683) ~ (all_48_0 = e1)
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | (2684) all_55_7 = e3
% 109.57/15.58 | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2680), (2684) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | (2685) all_48_0 = e3
% 109.57/15.58 | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | REDUCE: (2681), (2685) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | (2686) ~ (all_53_2 = e3)
% 109.57/15.58 | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | (2687) all_55_3 = e3
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (2687) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | (2688) all_53_2 = e3
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | SIMP: (2688) implies:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | (2689) all_53_2 = e3
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | REDUCE: (2686), (2689) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | (2690) $false
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | CLOSE: (2690) is inconsistent.
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | (2691) all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2691) gives:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | (2692) all_55_3 = e2
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (2692) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | (2693) all_53_2 = e2
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1915), (2693) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | (2694) $false
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | CLOSE: (2694) is inconsistent.
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | (2695) all_55_3 = e1 | all_55_3 = e0
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2695) gives:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | (2696) all_55_3 = e1
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (2696) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | (2697) all_53_2 = e1
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2670), (2697) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | (2698) $false
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2698) is inconsistent.
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | (2699) all_55_3 = e0
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (2699) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | (2700) all_53_2 = e0
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (2700) imply:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | (2701) ~ (all_53_3 = e0)
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2701) implies:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | (2702) ~ (all_53_3 = e0)
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (144), (162), (166), (174), (206), (250),
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | (1916), (2500), (2503), (2702), (function-axioms)
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #66.
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | (2703) all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 109.57/15.58 | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2676), (2680), (2682), (2683), (2703) are
% 109.57/15.58 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #56.
% 109.57/15.58 | | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | (2704) all_57_109 = e1 & op(e2, e3) = e1
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | ALPHA: (2704) implies:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | (2705) op(e2, e3) = e1
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1919), (2658), (2705), (function-axioms) are
% 109.57/15.58 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #53.
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.58 | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | (2706) (all_57_110 = e1 & op(e1, e3) = e1) | (all_57_111
% 109.57/15.58 | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 109.57/15.58 | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | BETA: splitting (2706) gives:
% 109.57/15.58 | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | (2707) all_57_110 = e1 & op(e1, e3) = e1
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | ALPHA: (2707) implies:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | (2708) op(e1, e3) = e1
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2671), (2708), (function-axioms) are
% 109.57/15.58 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #223.
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | (2709) all_57_111 = e1 & op(e0, e3) = e1
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | ALPHA: (2709) implies:
% 109.57/15.58 | | | | | | | | | | | | | | | | | | (2710) op(e0, e3) = e1
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2670), (2710), (function-axioms) are
% 109.57/15.58 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #166.
% 109.57/15.58 | | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | Case 2:
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | (2711) all_57_81 = e2 & op(e2, e2) = e2
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | ALPHA: (2711) implies:
% 109.57/15.58 | | | | | | | | | | | | | | (2712) op(e2, e2) = e2
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | REF_CLOSE: (8), (2504), (2645), (2655), (2712),
% 109.57/15.58 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.57/15.58 | | | | | | | | | | | | | | #52.
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | Case 2:
% 109.57/15.58 | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | (2713) (all_57_82 = e2 & op(e2, e1) = e2) | (all_57_83 =
% 109.57/15.58 | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 109.57/15.58 | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | BETA: splitting (2713) gives:
% 109.57/15.58 | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | Case 1:
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | (2714) all_57_82 = e2 & op(e2, e1) = e2
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | ALPHA: (2714) implies:
% 109.57/15.58 | | | | | | | | | | | | | | (2715) op(e2, e1) = e2
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | REF_CLOSE: (169), (2648), (2715), (function-axioms) are
% 109.57/15.58 | | | | | | | | | | | | | | inconsistent by sub-proof #231.
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | Case 2:
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | (2716) all_57_83 = e2 & op(e2, e0) = e2
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | ALPHA: (2716) implies:
% 109.57/15.58 | | | | | | | | | | | | | | (2717) op(e2, e0) = e2
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | | REF_CLOSE: (168), (1918), (2717), (function-axioms) are
% 109.57/15.58 | | | | | | | | | | | | | | inconsistent by sub-proof #227.
% 109.57/15.58 | | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | Case 2:
% 109.57/15.58 | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | (2718) all_57_85 = e2 & op(e2, e2) = e2
% 109.57/15.58 | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | ALPHA: (2718) implies:
% 109.57/15.58 | | | | | | | | | | | (2719) op(e2, e2) = e2
% 109.57/15.58 | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | BETA: splitting (96) gives:
% 109.57/15.58 | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | Case 1:
% 109.57/15.58 | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | (2720) ~ (all_44_2 = e2)
% 109.57/15.58 | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | REDUCE: (2646), (2720) imply:
% 109.57/15.58 | | | | | | | | | | | | (2721) $false
% 109.57/15.58 | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | CLOSE: (2721) is inconsistent.
% 109.57/15.58 | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | Case 2:
% 109.57/15.58 | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | (2722) op(e2, e2) = all_44_1 & $i(all_44_1) & ( ~
% 109.57/15.58 | | | | | | | | | | | | (all_44_1 = e0) | ( ~ (all_44_0 = e3) & op(e0,
% 109.57/15.58 | | | | | | | | | | | | e2) = all_44_0 & $i(all_44_0)))
% 109.57/15.58 | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | ALPHA: (2722) implies:
% 109.57/15.58 | | | | | | | | | | | | (2723) op(e2, e2) = all_44_1
% 109.57/15.58 | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | | REF_CLOSE: (8), (2504), (2645), (2719), (2723),
% 109.57/15.58 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.57/15.58 | | | | | | | | | | | | #52.
% 109.57/15.58 | | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | Case 2:
% 109.57/15.58 | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | (2724) (all_57_86 = e2 & op(e1, e2) = e2) | (all_57_87 =
% 109.57/15.58 | | | | | | | | | | e2 & op(e0, e2) = e2)
% 109.57/15.58 | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | | REF_CLOSE: (162), (166), (1916), (2647), (2724),
% 109.57/15.58 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.57/15.58 | | | | | | | | | | #70.
% 109.57/15.58 | | | | | | | | | |
% 109.57/15.58 | | | | | | | | | End of split
% 109.57/15.58 | | | | | | | | |
% 109.57/15.58 | | | | | | | | End of split
% 109.57/15.58 | | | | | | | |
% 109.57/15.58 | | | | | | | End of split
% 109.57/15.58 | | | | | | |
% 109.57/15.58 | | | | | | End of split
% 109.57/15.58 | | | | | |
% 109.57/15.58 | | | | | End of split
% 109.57/15.58 | | | | |
% 109.57/15.58 | | | | End of split
% 109.57/15.58 | | | |
% 109.57/15.58 | | | End of split
% 109.57/15.58 | | |
% 109.57/15.58 | | Case 2:
% 109.57/15.58 | | |
% 109.57/15.58 | | | (2725) all_6_2 = e1
% 109.57/15.58 | | | (2726) op(e1, e1) = all_6_1 & $i(all_6_1) & ( ~ (all_6_1 = e2) | ( ~
% 109.57/15.58 | | | (all_6_0 = e3) & op(e2, e1) = all_6_0 & $i(all_6_0)))
% 109.57/15.58 | | |
% 109.57/15.58 | | | ALPHA: (2726) implies:
% 109.57/15.58 | | | (2727) op(e1, e1) = all_6_1
% 109.57/15.58 | | | (2728) ~ (all_6_1 = e2) | ( ~ (all_6_0 = e3) & op(e2, e1) = all_6_0 &
% 109.57/15.58 | | | $i(all_6_0))
% 109.57/15.58 | | |
% 109.57/15.58 | | | COMBINE_EQS: (292), (2725) imply:
% 109.57/15.58 | | | (2729) all_38_2 = e1
% 109.57/15.58 | | |
% 109.57/15.58 | | | REDUCE: (343), (2725) imply:
% 109.57/15.58 | | | (2730) ~ (all_53_1 = e1)
% 109.57/15.58 | | |
% 109.57/15.58 | | | REDUCE: (345), (2725) imply:
% 109.57/15.58 | | | (2731) ~ (all_53_2 = e1)
% 109.57/15.58 | | |
% 109.57/15.58 | | | REDUCE: (347), (2725) imply:
% 109.57/15.58 | | | (2732) ~ (all_53_3 = e1)
% 109.57/15.58 | | |
% 109.57/15.58 | | | REDUCE: (349), (2725) imply:
% 109.57/15.58 | | | (2733) ~ (all_53_4 = e1)
% 109.57/15.58 | | |
% 109.57/15.58 | | | REDUCE: (351), (2725) imply:
% 109.57/15.58 | | | (2734) ~ (all_53_8 = e1)
% 109.57/15.58 | | |
% 109.57/15.58 | | | REDUCE: (353), (2725) imply:
% 109.57/15.58 | | | (2735) ~ (all_53_12 = e1)
% 109.57/15.58 | | |
% 109.57/15.58 | | | REDUCE: (38), (2725) imply:
% 109.57/15.58 | | | (2736) op(e0, e0) = e1
% 109.57/15.58 | | |
% 109.57/15.58 | | | BETA: splitting (87) gives:
% 109.57/15.58 | | |
% 109.57/15.58 | | | Case 1:
% 109.57/15.58 | | | |
% 109.57/15.58 | | | | (2737) ~ (all_38_2 = e1)
% 109.57/15.58 | | | |
% 109.57/15.58 | | | | REDUCE: (2729), (2737) imply:
% 109.57/15.58 | | | | (2738) $false
% 109.57/15.58 | | | |
% 109.57/15.58 | | | | CLOSE: (2738) is inconsistent.
% 109.57/15.58 | | | |
% 109.57/15.58 | | | Case 2:
% 109.57/15.58 | | | |
% 109.57/15.58 | | | | (2739) op(e1, e1) = all_38_1 & $i(all_38_1) & ( ~ (all_38_1 = e3) | (
% 109.57/15.58 | | | | ~ (all_38_0 = e2) & op(e3, e1) = all_38_0 & $i(all_38_0)))
% 109.57/15.58 | | | |
% 109.57/15.58 | | | | ALPHA: (2739) implies:
% 109.57/15.58 | | | | (2740) op(e1, e1) = all_38_1
% 109.57/15.58 | | | | (2741) ~ (all_38_1 = e3) | ( ~ (all_38_0 = e2) & op(e3, e1) =
% 109.57/15.58 | | | | all_38_0 & $i(all_38_0))
% 109.57/15.58 | | | |
% 109.57/15.58 | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, all_38_1,
% 109.57/15.58 | | | | e1, e1, simplifying with (50), (2740) gives:
% 109.57/15.58 | | | | (2742) all_38_1 = all_14_2
% 109.57/15.58 | | | |
% 109.57/15.58 | | | | GROUND_INST: instantiating (function-axioms) with all_6_1, all_38_1, e1,
% 109.57/15.58 | | | | e1, simplifying with (2727), (2740) gives:
% 109.57/15.58 | | | | (2743) all_38_1 = all_6_1
% 109.57/15.58 | | | |
% 109.57/15.58 | | | | COMBINE_EQS: (2742), (2743) imply:
% 109.57/15.58 | | | | (2744) all_14_2 = all_6_1
% 109.57/15.58 | | | |
% 109.57/15.58 | | | | SIMP: (2744) implies:
% 109.57/15.58 | | | | (2745) all_14_2 = all_6_1
% 109.57/15.58 | | | |
% 109.57/15.58 | | | | COMBINE_EQS: (326), (2745) imply:
% 109.57/15.59 | | | | (2746) all_18_2 = all_6_1
% 109.57/15.59 | | | |
% 109.57/15.59 | | | | COMBINE_EQS: (253), (2745) imply:
% 109.57/15.59 | | | | (2747) all_20_2 = all_6_1
% 109.57/15.59 | | | |
% 109.57/15.59 | | | | COMBINE_EQS: (329), (2745) imply:
% 109.57/15.59 | | | | (2748) all_22_2 = all_6_1
% 109.57/15.59 | | | |
% 109.57/15.59 | | | | COMBINE_EQS: (334), (2745) imply:
% 109.57/15.59 | | | | (2749) all_44_2 = all_6_1
% 109.57/15.59 | | | |
% 109.57/15.59 | | | | COMBINE_EQS: (341), (2745) imply:
% 109.57/15.59 | | | | (2750) all_55_5 = all_6_1
% 109.57/15.59 | | | |
% 109.57/15.59 | | | | REDUCE: (354), (2745) imply:
% 109.57/15.59 | | | | (2751) ~ (all_53_1 = all_6_1)
% 109.57/15.59 | | | |
% 109.57/15.59 | | | | REDUCE: (357), (2745) imply:
% 109.57/15.59 | | | | (2752) ~ (all_53_4 = all_6_1)
% 109.57/15.59 | | | |
% 109.57/15.59 | | | | REDUCE: (359), (2745) imply:
% 109.57/15.59 | | | | (2753) ~ (all_53_6 = all_6_1)
% 109.57/15.59 | | | |
% 109.57/15.59 | | | | REDUCE: (361), (2745) imply:
% 109.57/15.59 | | | | (2754) ~ (all_53_7 = all_6_1)
% 109.57/15.59 | | | |
% 109.57/15.59 | | | | REDUCE: (363), (2745) imply:
% 109.57/15.59 | | | | (2755) ~ (all_53_9 = all_6_1)
% 109.57/15.59 | | | |
% 109.57/15.59 | | | | REDUCE: (365), (2745) imply:
% 109.57/15.59 | | | | (2756) ~ (all_53_13 = all_6_1)
% 109.57/15.59 | | | |
% 109.57/15.59 | | | | BETA: splitting (45) gives:
% 109.57/15.59 | | | |
% 109.57/15.59 | | | | Case 1:
% 109.57/15.59 | | | | |
% 109.57/15.59 | | | | | (2757) ~ (all_10_2 = e3)
% 109.57/15.59 | | | | |
% 109.57/15.59 | | | | | BETA: splitting (48) gives:
% 109.57/15.59 | | | | |
% 109.57/15.59 | | | | | Case 1:
% 109.57/15.59 | | | | | |
% 109.57/15.59 | | | | | | (2758) ~ (all_12_2 = e0)
% 109.57/15.59 | | | | | |
% 109.57/15.59 | | | | | | REDUCE: (323), (2758) imply:
% 109.57/15.59 | | | | | | (2759) ~ (all_10_2 = e0)
% 109.57/15.59 | | | | | |
% 109.57/15.59 | | | | | | BETA: splitting (51) gives:
% 109.57/15.59 | | | | | |
% 109.57/15.59 | | | | | | Case 1:
% 109.57/15.59 | | | | | | |
% 109.57/15.59 | | | | | | | (2760) ~ (all_14_2 = e2)
% 109.57/15.59 | | | | | | |
% 109.57/15.59 | | | | | | | REDUCE: (2745), (2760) imply:
% 109.57/15.59 | | | | | | | (2761) ~ (all_6_1 = e2)
% 109.57/15.59 | | | | | | |
% 109.57/15.59 | | | | | | | REF_CLOSE: (35), (57), (60), (63), (66), (69), (99), (107), (108),
% 109.57/15.59 | | | | | | | (109), (110), (113), (117), (123), (126), (127), (131),
% 109.57/15.59 | | | | | | | (140), (146), (147), (148), (149), (150), (152), (153),
% 109.57/15.59 | | | | | | | (161), (162), (163), (164), (166), (167), (168), (169),
% 109.57/15.59 | | | | | | | (171), (172), (173), (174), (193), (197), (198), (203),
% 109.57/15.59 | | | | | | | (205), (207), (223), (228), (230), (231), (234), (249),
% 109.57/15.59 | | | | | | | (251), (265), (271), (303), (316), (339), (340), (355),
% 109.57/15.59 | | | | | | | (367), (368), (369), (370), (371), (374), (375), (378),
% 109.57/15.59 | | | | | | | (2727), (2730), (2733), (2736), (2741), (2743), (2746),
% 109.57/15.59 | | | | | | | (2747), (2748), (2750), (2751), (2752), (2753), (2754),
% 109.57/15.59 | | | | | | | (2756), (2757), (2759), (2761), (function-axioms) are
% 109.57/15.59 | | | | | | | inconsistent by sub-proof #39.
% 109.57/15.59 | | | | | | |
% 109.57/15.59 | | | | | | Case 2:
% 109.57/15.59 | | | | | | |
% 109.57/15.59 | | | | | | | (2762) all_14_2 = e2
% 109.57/15.59 | | | | | | |
% 109.57/15.59 | | | | | | | COMBINE_EQS: (2745), (2762) imply:
% 109.57/15.59 | | | | | | | (2763) all_6_1 = e2
% 109.57/15.59 | | | | | | |
% 109.57/15.59 | | | | | | | SIMP: (2763) implies:
% 109.57/15.59 | | | | | | | (2764) all_6_1 = e2
% 109.57/15.59 | | | | | | |
% 109.57/15.59 | | | | | | | REDUCE: (2751), (2764) imply:
% 109.57/15.59 | | | | | | | (2765) ~ (all_53_1 = e2)
% 109.57/15.59 | | | | | | |
% 109.57/15.59 | | | | | | | REDUCE: (2752), (2764) imply:
% 109.57/15.59 | | | | | | | (2766) ~ (all_53_4 = e2)
% 109.57/15.59 | | | | | | |
% 109.57/15.59 | | | | | | | REDUCE: (2755), (2764) imply:
% 109.57/15.59 | | | | | | | (2767) ~ (all_53_9 = e2)
% 109.57/15.59 | | | | | | |
% 109.57/15.59 | | | | | | | BETA: splitting (2728) gives:
% 109.57/15.59 | | | | | | |
% 109.57/15.59 | | | | | | | Case 1:
% 109.57/15.59 | | | | | | | |
% 109.57/15.59 | | | | | | | | (2768) ~ (all_6_1 = e2)
% 109.57/15.59 | | | | | | | |
% 109.57/15.59 | | | | | | | | REF_CLOSE: (35), (57), (60), (63), (66), (69), (99), (107),
% 109.57/15.59 | | | | | | | | (108), (109), (110), (113), (117), (123), (126),
% 109.57/15.59 | | | | | | | | (127), (131), (140), (146), (147), (148), (149),
% 109.57/15.59 | | | | | | | | (150), (152), (153), (161), (162), (163), (164),
% 109.57/15.59 | | | | | | | | (166), (167), (168), (169), (171), (172), (173),
% 109.57/15.59 | | | | | | | | (174), (193), (197), (198), (203), (205), (207),
% 109.57/15.59 | | | | | | | | (223), (228), (230), (231), (234), (249), (251),
% 109.57/15.59 | | | | | | | | (265), (271), (303), (316), (339), (340), (355),
% 109.57/15.59 | | | | | | | | (367), (368), (369), (370), (371), (374), (375),
% 109.57/15.59 | | | | | | | | (378), (2727), (2730), (2733), (2736), (2741),
% 109.57/15.59 | | | | | | | | (2743), (2746), (2747), (2748), (2750), (2751),
% 109.57/15.59 | | | | | | | | (2752), (2753), (2754), (2756), (2757), (2759),
% 109.57/15.59 | | | | | | | | (2768), (function-axioms) are inconsistent by
% 109.57/15.59 | | | | | | | | sub-proof #39.
% 109.57/15.59 | | | | | | | |
% 109.57/15.59 | | | | | | | Case 2:
% 109.57/15.59 | | | | | | | |
% 109.57/15.59 | | | | | | | | (2769) ~ (all_6_0 = e3) & op(e2, e1) = all_6_0 & $i(all_6_0)
% 109.57/15.59 | | | | | | | |
% 109.57/15.59 | | | | | | | | ALPHA: (2769) implies:
% 109.57/15.59 | | | | | | | | (2770) ~ (all_6_0 = e3)
% 109.57/15.59 | | | | | | | | (2771) op(e2, e1) = all_6_0
% 109.57/15.59 | | | | | | | |
% 109.57/15.59 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 109.57/15.59 | | | | | | | | all_6_0, e1, e2, simplifying with (169), (2771)
% 109.57/15.59 | | | | | | | | gives:
% 109.57/15.59 | | | | | | | | (2772) all_53_9 = all_6_0
% 109.57/15.59 | | | | | | | |
% 109.57/15.59 | | | | | | | | COMBINE_EQS: (263), (2772) imply:
% 109.57/15.59 | | | | | | | | (2773) all_55_9 = all_6_0
% 109.57/15.59 | | | | | | | |
% 109.57/15.59 | | | | | | | | REDUCE: (150), (2772) imply:
% 109.57/15.59 | | | | | | | | (2774) ~ (all_53_1 = all_6_0)
% 109.57/15.59 | | | | | | | |
% 109.57/15.59 | | | | | | | | REDUCE: (369), (2772) imply:
% 109.57/15.59 | | | | | | | | (2775) ~ (all_10_2 = all_6_0)
% 109.57/15.59 | | | | | | | |
% 109.57/15.59 | | | | | | | | SIMP: (2775) implies:
% 109.57/15.59 | | | | | | | | (2776) ~ (all_10_2 = all_6_0)
% 109.57/15.59 | | | | | | | |
% 109.57/15.59 | | | | | | | | REDUCE: (2767), (2772) imply:
% 109.57/15.59 | | | | | | | | (2777) ~ (all_6_0 = e2)
% 109.57/15.59 | | | | | | | |
% 109.57/15.59 | | | | | | | | BETA: splitting (66) gives:
% 109.57/15.59 | | | | | | | |
% 109.57/15.59 | | | | | | | | Case 1:
% 109.57/15.59 | | | | | | | | |
% 109.57/15.59 | | | | | | | | | (2778) ~ (all_24_2 = e1)
% 109.57/15.59 | | | | | | | | |
% 109.57/15.59 | | | | | | | | | REDUCE: (303), (2778) imply:
% 109.57/15.59 | | | | | | | | | (2779) ~ (all_10_2 = e1)
% 109.57/15.59 | | | | | | | | |
% 109.57/15.59 | | | | | | | | | BETA: splitting (198) gives:
% 109.57/15.59 | | | | | | | | |
% 109.57/15.59 | | | | | | | | | Case 1:
% 109.57/15.59 | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | (2780) all_55_10 = e3
% 109.57/15.59 | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | COMBINE_EQS: (340), (2780) imply:
% 109.57/15.59 | | | | | | | | | | (2781) all_10_2 = e3
% 109.57/15.59 | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | REDUCE: (2757), (2781) imply:
% 109.57/15.59 | | | | | | | | | | (2782) $false
% 109.57/15.59 | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | CLOSE: (2782) is inconsistent.
% 109.57/15.59 | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | Case 2:
% 109.57/15.59 | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | (2783) ~ (all_55_10 = e3)
% 109.57/15.59 | | | | | | | | | | (2784) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 109.57/15.59 | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | BETA: splitting (2784) gives:
% 109.57/15.59 | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | Case 1:
% 109.57/15.59 | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | (2785) all_55_10 = e2
% 109.57/15.59 | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | COMBINE_EQS: (340), (2785) imply:
% 109.57/15.59 | | | | | | | | | | | (2786) all_10_2 = e2
% 109.57/15.59 | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | REDUCE: (368), (2786) imply:
% 109.57/15.59 | | | | | | | | | | | (2787) ~ (all_53_8 = e2)
% 109.57/15.59 | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | REDUCE: (2757), (2786) imply:
% 109.57/15.59 | | | | | | | | | | | (2788) ~ (e3 = e2)
% 109.57/15.59 | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | REDUCE: (2779), (2786) imply:
% 109.57/15.59 | | | | | | | | | | | (2789) ~ (e2 = e1)
% 109.57/15.59 | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | BETA: splitting (236) gives:
% 109.57/15.59 | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | Case 1:
% 109.57/15.59 | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | (2790) (all_57_20 = e2 & op(e3, e0) = e2) | (all_57_21 =
% 109.57/15.59 | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 109.57/15.59 | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | BETA: splitting (2790) gives:
% 109.57/15.59 | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | Case 1:
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | (2791) all_57_20 = e2 & op(e3, e0) = e2
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | ALPHA: (2791) implies:
% 109.57/15.59 | | | | | | | | | | | | | (2792) op(e3, e0) = e2
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | BETA: splitting (110) gives:
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | Case 1:
% 109.57/15.59 | | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | | (2793) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 109.57/15.59 | | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 109.57/15.59 | | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | | ALPHA: (2793) implies:
% 109.57/15.59 | | | | | | | | | | | | | | (2794) op(e3, e0) = e3
% 109.57/15.59 | | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 109.57/15.59 | | | | | | | | | | | | | | e2, e0, e3, simplifying with (172), (2792) gives:
% 109.57/15.59 | | | | | | | | | | | | | | (2795) all_53_12 = e2
% 109.57/15.59 | | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 109.57/15.59 | | | | | | | | | | | | | | e3, e0, e3, simplifying with (172), (2794) gives:
% 109.57/15.59 | | | | | | | | | | | | | | (2796) all_53_12 = e3
% 109.57/15.59 | | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | | COMBINE_EQS: (2795), (2796) imply:
% 109.57/15.59 | | | | | | | | | | | | | | (2797) e3 = e2
% 109.57/15.59 | | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | | REDUCE: (8), (2797) imply:
% 109.57/15.59 | | | | | | | | | | | | | | (2798) $false
% 109.57/15.59 | | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | | CLOSE: (2798) is inconsistent.
% 109.57/15.59 | | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | Case 2:
% 109.57/15.59 | | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | | (2799) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 109.57/15.59 | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 109.57/15.59 | | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 109.57/15.59 | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 109.57/15.59 | | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (2733), (2787), (2799),
% 109.57/15.59 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.57/15.59 | | | | | | | | | | | | | | #225.
% 109.57/15.59 | | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | End of split
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | Case 2:
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | (2800) all_57_21 = e2 & op(e2, e0) = e2
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | ALPHA: (2800) implies:
% 109.57/15.59 | | | | | | | | | | | | | (2801) op(e2, e0) = e2
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | REF_CLOSE: (168), (2787), (2801), (function-axioms) are
% 109.57/15.59 | | | | | | | | | | | | | inconsistent by sub-proof #227.
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | End of split
% 109.57/15.59 | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | Case 2:
% 109.57/15.59 | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | (2802) (all_57_22 = e2 & op(e1, e0) = e2) | (all_57_23 =
% 109.57/15.59 | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 109.57/15.59 | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | BETA: splitting (2802) gives:
% 109.57/15.59 | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | Case 1:
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | (2803) all_57_22 = e2 & op(e1, e0) = e2
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | ALPHA: (2803) implies:
% 109.57/15.59 | | | | | | | | | | | | | (2804) op(e1, e0) = e2
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | REF_CLOSE: (164), (2766), (2804), (function-axioms) are
% 109.57/15.59 | | | | | | | | | | | | | inconsistent by sub-proof #112.
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | Case 2:
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | (2805) all_57_23 = e2 & op(e0, e0) = e2
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | ALPHA: (2805) implies:
% 109.57/15.59 | | | | | | | | | | | | | (2806) op(e0, e0) = e2
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e2, e0,
% 109.57/15.59 | | | | | | | | | | | | | e0, simplifying with (2736), (2806) gives:
% 109.57/15.59 | | | | | | | | | | | | | (2807) e2 = e1
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | REDUCE: (2789), (2807) imply:
% 109.57/15.59 | | | | | | | | | | | | | (2808) $false
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | | CLOSE: (2808) is inconsistent.
% 109.57/15.59 | | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | | End of split
% 109.57/15.59 | | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | End of split
% 109.57/15.59 | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | Case 2:
% 109.57/15.59 | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | (2809) all_55_10 = e1 | all_55_10 = e0
% 109.57/15.59 | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | | REF_CLOSE: (340), (2759), (2779), (2809) are inconsistent by
% 109.57/15.59 | | | | | | | | | | | sub-proof #208.
% 109.57/15.59 | | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | | End of split
% 109.57/15.59 | | | | | | | | | |
% 109.57/15.59 | | | | | | | | | End of split
% 109.57/15.59 | | | | | | | | |
% 109.57/15.59 | | | | | | | | Case 2:
% 109.57/15.59 | | | | | | | | |
% 109.57/15.59 | | | | | | | | | (2810) all_24_2 = e1
% 109.57/15.59 | | | | | | | | |
% 109.57/15.59 | | | | | | | | | COMBINE_EQS: (303), (2810) imply:
% 109.57/15.59 | | | | | | | | | (2811) all_10_2 = e1
% 109.57/15.59 | | | | | | | | |
% 109.57/15.59 | | | | | | | | | SIMP: (2811) implies:
% 109.57/15.59 | | | | | | | | | (2812) all_10_2 = e1
% 109.57/15.59 | | | | | | | | |
% 109.57/15.59 | | | | | | | | | REDUCE: (2776), (2812) imply:
% 109.57/15.59 | | | | | | | | | (2813) ~ (all_6_0 = e1)
% 109.57/15.59 | | | | | | | | |
% 109.57/15.59 | | | | | | | | | SIMP: (2813) implies:
% 109.57/15.59 | | | | | | | | | (2814) ~ (all_6_0 = e1)
% 109.57/15.59 | | | | | | | | |
% 109.57/15.59 | | | | | | | | | REF_CLOSE: (109), (149), (161), (169), (173), (199), (207),
% 109.57/15.59 | | | | | | | | | (249), (2730), (2765), (2767), (2770), (2771),
% 109.57/15.59 | | | | | | | | | (2773), (2774), (2777), (2814), (function-axioms)
% 109.57/15.59 | | | | | | | | | are inconsistent by sub-proof #36.
% 109.57/15.59 | | | | | | | | |
% 109.57/15.59 | | | | | | | | End of split
% 109.57/15.59 | | | | | | | |
% 109.57/15.59 | | | | | | | End of split
% 109.57/15.59 | | | | | | |
% 109.57/15.59 | | | | | | End of split
% 109.57/15.59 | | | | | |
% 109.57/15.59 | | | | | Case 2:
% 109.57/15.59 | | | | | |
% 109.57/15.59 | | | | | | (2815) all_12_2 = e0
% 109.57/15.59 | | | | | | (2816) op(e0, e0) = all_12_1 & $i(all_12_1) & ( ~ (all_12_1 = e1)
% 109.57/15.59 | | | | | | | ( ~ (all_12_0 = e3) & op(e1, e0) = all_12_0 &
% 109.57/15.59 | | | | | | $i(all_12_0)))
% 109.57/15.59 | | | | | |
% 109.57/15.59 | | | | | | ALPHA: (2816) implies:
% 109.57/15.60 | | | | | | (2817) op(e0, e0) = all_12_1
% 109.57/15.60 | | | | | | (2818) ~ (all_12_1 = e1) | ( ~ (all_12_0 = e3) & op(e1, e0) =
% 109.57/15.60 | | | | | | all_12_0 & $i(all_12_0))
% 109.57/15.60 | | | | | |
% 109.57/15.60 | | | | | | COMBINE_EQS: (323), (2815) imply:
% 109.57/15.60 | | | | | | (2819) all_10_2 = e0
% 109.57/15.60 | | | | | |
% 109.57/15.60 | | | | | | COMBINE_EQS: (330), (2819) imply:
% 109.57/15.60 | | | | | | (2820) all_30_2 = e0
% 109.57/15.60 | | | | | |
% 109.57/15.60 | | | | | | REDUCE: (356), (2819) imply:
% 109.57/15.60 | | | | | | (2821) ~ (all_53_3 = e0)
% 109.57/15.60 | | | | | |
% 109.57/15.60 | | | | | | REDUCE: (368), (2819) imply:
% 109.57/15.60 | | | | | | (2822) ~ (all_53_8 = e0)
% 109.57/15.60 | | | | | |
% 109.57/15.60 | | | | | | REDUCE: (369), (2819) imply:
% 109.57/15.60 | | | | | | (2823) ~ (all_53_9 = e0)
% 109.57/15.60 | | | | | |
% 109.57/15.60 | | | | | | REDUCE: (373), (2819) imply:
% 109.57/15.60 | | | | | | (2824) ~ (all_53_15 = e0)
% 109.57/15.60 | | | | | |
% 109.57/15.60 | | | | | | REDUCE: (44), (2819) imply:
% 109.57/15.60 | | | | | | (2825) op(e2, e2) = e0
% 109.57/15.60 | | | | | |
% 109.57/15.60 | | | | | | BETA: splitting (75) gives:
% 109.57/15.60 | | | | | |
% 109.57/15.60 | | | | | | Case 1:
% 109.57/15.60 | | | | | | |
% 109.57/15.60 | | | | | | | (2826) ~ (all_30_2 = e0)
% 109.57/15.60 | | | | | | |
% 109.57/15.60 | | | | | | | REDUCE: (2820), (2826) imply:
% 109.57/15.60 | | | | | | | (2827) $false
% 109.57/15.60 | | | | | | |
% 109.57/15.60 | | | | | | | CLOSE: (2827) is inconsistent.
% 109.57/15.60 | | | | | | |
% 109.57/15.60 | | | | | | Case 2:
% 109.57/15.60 | | | | | | |
% 109.57/15.60 | | | | | | | (2828) op(e0, e0) = all_30_1 & $i(all_30_1) & ( ~ (all_30_1 =
% 109.57/15.60 | | | | | | | e3) | ( ~ (all_30_0 = e1) & op(e3, e0) = all_30_0 &
% 109.57/15.60 | | | | | | | $i(all_30_0)))
% 109.57/15.60 | | | | | | |
% 109.57/15.60 | | | | | | | ALPHA: (2828) implies:
% 109.57/15.60 | | | | | | | (2829) op(e0, e0) = all_30_1
% 109.57/15.60 | | | | | | |
% 109.57/15.60 | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_30_1,
% 109.57/15.60 | | | | | | | e0, e0, simplifying with (2736), (2829) gives:
% 109.57/15.60 | | | | | | | (2830) all_30_1 = e1
% 109.57/15.60 | | | | | | |
% 109.57/15.60 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_1,
% 109.57/15.60 | | | | | | | all_30_1, e0, e0, simplifying with (2817), (2829)
% 109.57/15.60 | | | | | | | gives:
% 109.57/15.60 | | | | | | | (2831) all_30_1 = all_12_1
% 109.57/15.60 | | | | | | |
% 109.57/15.60 | | | | | | | COMBINE_EQS: (2830), (2831) imply:
% 109.57/15.60 | | | | | | | (2832) all_12_1 = e1
% 109.57/15.60 | | | | | | |
% 109.57/15.60 | | | | | | | BETA: splitting (2818) gives:
% 109.57/15.60 | | | | | | |
% 109.57/15.60 | | | | | | | Case 1:
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | | (2833) ~ (all_12_1 = e1)
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | | REDUCE: (2832), (2833) imply:
% 109.57/15.60 | | | | | | | | (2834) $false
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | | CLOSE: (2834) is inconsistent.
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | Case 2:
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | | (2835) ~ (all_12_0 = e3) & op(e1, e0) = all_12_0 &
% 109.57/15.60 | | | | | | | | $i(all_12_0)
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | | ALPHA: (2835) implies:
% 109.57/15.60 | | | | | | | | (2836) ~ (all_12_0 = e3)
% 109.57/15.60 | | | | | | | | (2837) op(e1, e0) = all_12_0
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4,
% 109.57/15.60 | | | | | | | | all_12_0, e0, e1, simplifying with (164), (2837)
% 109.57/15.60 | | | | | | | | gives:
% 109.57/15.60 | | | | | | | | (2838) all_53_4 = all_12_0
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | | COMBINE_EQS: (252), (2838) imply:
% 109.57/15.60 | | | | | | | | (2839) all_55_4 = all_12_0
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | | REDUCE: (138), (2838) imply:
% 109.57/15.60 | | | | | | | | (2840) ~ (all_53_8 = all_12_0)
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | | SIMP: (2840) implies:
% 109.57/15.60 | | | | | | | | (2841) ~ (all_53_8 = all_12_0)
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | | REDUCE: (137), (2838) imply:
% 109.57/15.60 | | | | | | | | (2842) ~ (all_53_12 = all_12_0)
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | | SIMP: (2842) implies:
% 109.57/15.60 | | | | | | | | (2843) ~ (all_53_12 = all_12_0)
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | | REDUCE: (2752), (2838) imply:
% 109.57/15.60 | | | | | | | | (2844) ~ (all_12_0 = all_6_1)
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | | REDUCE: (2733), (2838) imply:
% 109.57/15.60 | | | | | | | | (2845) ~ (all_12_0 = e1)
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | | BETA: splitting (51) gives:
% 109.57/15.60 | | | | | | | |
% 109.57/15.60 | | | | | | | | Case 1:
% 109.57/15.60 | | | | | | | | |
% 109.57/15.60 | | | | | | | | | (2846) ~ (all_14_2 = e2)
% 109.57/15.60 | | | | | | | | |
% 109.57/15.60 | | | | | | | | | REDUCE: (2745), (2846) imply:
% 109.57/15.60 | | | | | | | | | (2847) ~ (all_6_1 = e2)
% 109.57/15.60 | | | | | | | | |
% 109.57/15.60 | | | | | | | | | BETA: splitting (57) gives:
% 109.57/15.60 | | | | | | | | |
% 109.57/15.60 | | | | | | | | | Case 1:
% 109.57/15.60 | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | (2848) ~ (all_18_2 = e3)
% 109.57/15.60 | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | REDUCE: (2746), (2848) imply:
% 109.57/15.60 | | | | | | | | | | (2849) ~ (all_6_1 = e3)
% 109.57/15.60 | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | BETA: splitting (63) gives:
% 109.57/15.60 | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | Case 1:
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | (2850) ~ (all_22_2 = e0)
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | REDUCE: (2748), (2850) imply:
% 109.57/15.60 | | | | | | | | | | | (2851) ~ (all_6_1 = e0)
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | REF_CLOSE: (108), (162), (166), (174), (203), (222), (2732),
% 109.57/15.60 | | | | | | | | | | | (2750), (2754), (2821), (2825), (2847), (2849),
% 109.57/15.60 | | | | | | | | | | | (2851), (function-axioms) are inconsistent by
% 109.57/15.60 | | | | | | | | | | | sub-proof #34.
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | Case 2:
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | (2852) all_22_2 = e0
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | COMBINE_EQS: (2748), (2852) imply:
% 109.57/15.60 | | | | | | | | | | | (2853) all_6_1 = e0
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | SIMP: (2853) implies:
% 109.57/15.60 | | | | | | | | | | | (2854) all_6_1 = e0
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | REDUCE: (2844), (2854) imply:
% 109.57/15.60 | | | | | | | | | | | (2855) ~ (all_12_0 = e0)
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | BETA: splitting (204) gives:
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | Case 1:
% 109.57/15.60 | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | (2856) all_55_4 = e3
% 109.57/15.60 | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | COMBINE_EQS: (2839), (2856) imply:
% 109.57/15.60 | | | | | | | | | | | | (2857) all_12_0 = e3
% 109.57/15.60 | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | REDUCE: (2836), (2857) imply:
% 109.57/15.60 | | | | | | | | | | | | (2858) $false
% 109.57/15.60 | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | CLOSE: (2858) is inconsistent.
% 109.57/15.60 | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | Case 2:
% 109.57/15.60 | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | (2859) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 109.57/15.60 | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | BETA: splitting (2859) gives:
% 109.57/15.60 | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | Case 1:
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | (2860) all_55_4 = e2
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | COMBINE_EQS: (2839), (2860) imply:
% 109.57/15.60 | | | | | | | | | | | | | (2861) all_12_0 = e2
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | REDUCE: (2841), (2861) imply:
% 109.57/15.60 | | | | | | | | | | | | | (2862) ~ (all_53_8 = e2)
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | REF_CLOSE: (110), (124), (164), (168), (172), (200), (262),
% 109.57/15.60 | | | | | | | | | | | | | (2733), (2734), (2822), (2862), (function-axioms)
% 109.57/15.60 | | | | | | | | | | | | | are inconsistent by sub-proof #33.
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | Case 2:
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | (2863) all_55_4 = e1 | all_55_4 = e0
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | BETA: splitting (2863) gives:
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | Case 1:
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | (2864) all_55_4 = e1
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | COMBINE_EQS: (2839), (2864) imply:
% 109.57/15.60 | | | | | | | | | | | | | | (2865) all_12_0 = e1
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | REDUCE: (2845), (2865) imply:
% 109.57/15.60 | | | | | | | | | | | | | | (2866) $false
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | CLOSE: (2866) is inconsistent.
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | Case 2:
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | (2867) all_55_4 = e0
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | COMBINE_EQS: (2839), (2867) imply:
% 109.57/15.60 | | | | | | | | | | | | | | (2868) all_12_0 = e0
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | REDUCE: (2855), (2868) imply:
% 109.57/15.60 | | | | | | | | | | | | | | (2869) $false
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | CLOSE: (2869) is inconsistent.
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | End of split
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | End of split
% 109.57/15.60 | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | End of split
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | End of split
% 109.57/15.60 | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | Case 2:
% 109.57/15.60 | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | (2870) all_18_2 = e3
% 109.57/15.60 | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | COMBINE_EQS: (2746), (2870) imply:
% 109.57/15.60 | | | | | | | | | | (2871) all_6_1 = e3
% 109.57/15.60 | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | COMBINE_EQS: (2743), (2871) imply:
% 109.57/15.60 | | | | | | | | | | (2872) all_38_1 = e3
% 109.57/15.60 | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | REDUCE: (2751), (2871) imply:
% 109.57/15.60 | | | | | | | | | | (2873) ~ (all_53_1 = e3)
% 109.57/15.60 | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | REDUCE: (2755), (2871) imply:
% 109.57/15.60 | | | | | | | | | | (2874) ~ (all_53_9 = e3)
% 109.57/15.60 | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | REDUCE: (2756), (2871) imply:
% 109.57/15.60 | | | | | | | | | | (2875) ~ (all_53_13 = e3)
% 109.57/15.60 | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | BETA: splitting (2741) gives:
% 109.57/15.60 | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | Case 1:
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | (2876) ~ (all_38_1 = e3)
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | REDUCE: (2872), (2876) imply:
% 109.57/15.60 | | | | | | | | | | | (2877) $false
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | CLOSE: (2877) is inconsistent.
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | Case 2:
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | (2878) ~ (all_38_0 = e2) & op(e3, e1) = all_38_0 &
% 109.57/15.60 | | | | | | | | | | | $i(all_38_0)
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | ALPHA: (2878) implies:
% 109.57/15.60 | | | | | | | | | | | (2879) ~ (all_38_0 = e2)
% 109.57/15.60 | | | | | | | | | | | (2880) op(e3, e1) = all_38_0
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 109.57/15.60 | | | | | | | | | | | all_38_0, e1, e3, simplifying with (173), (2880)
% 109.57/15.60 | | | | | | | | | | | gives:
% 109.57/15.60 | | | | | | | | | | | (2881) all_53_13 = all_38_0
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | COMBINE_EQS: (273), (2881) imply:
% 109.57/15.60 | | | | | | | | | | | (2882) all_55_13 = all_38_0
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | REDUCE: (149), (2881) imply:
% 109.57/15.60 | | | | | | | | | | | (2883) ~ (all_53_1 = all_38_0)
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | REDUCE: (121), (2881) imply:
% 109.57/15.60 | | | | | | | | | | | (2884) ~ (all_53_9 = all_38_0)
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | REDUCE: (117), (2881) imply:
% 109.57/15.60 | | | | | | | | | | | (2885) ~ (all_53_12 = all_38_0)
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | REDUCE: (113), (2881) imply:
% 109.57/15.60 | | | | | | | | | | | (2886) ~ (all_53_15 = all_38_0)
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | SIMP: (2886) implies:
% 109.57/15.60 | | | | | | | | | | | (2887) ~ (all_53_15 = all_38_0)
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | REDUCE: (375), (2881) imply:
% 109.57/15.60 | | | | | | | | | | | (2888) ~ (all_38_0 = all_4_2)
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | REDUCE: (2875), (2881) imply:
% 109.57/15.60 | | | | | | | | | | | (2889) ~ (all_38_0 = e3)
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | BETA: splitting (69) gives:
% 109.57/15.60 | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | Case 1:
% 109.57/15.60 | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | (2890) ~ (all_26_2 = e2)
% 109.57/15.60 | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | REDUCE: (316), (2890) imply:
% 109.57/15.60 | | | | | | | | | | | | (2891) ~ (all_4_2 = e2)
% 109.57/15.60 | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | BETA: splitting (81) gives:
% 109.57/15.60 | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | Case 1:
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | (2892) ~ (all_34_2 = e1)
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | REDUCE: (311), (2892) imply:
% 109.57/15.60 | | | | | | | | | | | | | (2893) ~ (all_4_2 = e1)
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | BETA: splitting (193) gives:
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | Case 1:
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | (2894) all_55_15 = e3
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | COMBINE_EQS: (339), (2894) imply:
% 109.57/15.60 | | | | | | | | | | | | | | (2895) all_4_2 = e3
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | REDUCE: (371), (2895) imply:
% 109.57/15.60 | | | | | | | | | | | | | | (2896) ~ (all_53_10 = e3)
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | REDUCE: (374), (2895) imply:
% 109.57/15.60 | | | | | | | | | | | | | | (2897) ~ (all_53_12 = e3)
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (110), (164), (168), (169), (171),
% 109.57/15.60 | | | | | | | | | | | | | | (172), (219), (2733), (2825), (2874), (2896),
% 109.57/15.60 | | | | | | | | | | | | | | (2897), (function-axioms) are inconsistent by
% 109.57/15.60 | | | | | | | | | | | | | | sub-proof #32.
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | Case 2:
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | (2898) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | REF_CLOSE: (339), (378), (2891), (2893), (2898) are
% 109.57/15.60 | | | | | | | | | | | | | | inconsistent by sub-proof #191.
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | End of split
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | Case 2:
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | (2899) all_34_2 = e1
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | COMBINE_EQS: (311), (2899) imply:
% 109.57/15.60 | | | | | | | | | | | | | (2900) all_4_2 = e1
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | REDUCE: (2888), (2900) imply:
% 109.57/15.60 | | | | | | | | | | | | | (2901) ~ (all_38_0 = e1)
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | BETA: splitting (195) gives:
% 109.57/15.60 | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | Case 1:
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | (2902) all_55_13 = e3
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | COMBINE_EQS: (2882), (2902) imply:
% 109.57/15.60 | | | | | | | | | | | | | | (2903) all_38_0 = e3
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | REDUCE: (2889), (2903) imply:
% 109.57/15.60 | | | | | | | | | | | | | | (2904) $false
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | CLOSE: (2904) is inconsistent.
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | Case 2:
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | (2905) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | BETA: splitting (2905) gives:
% 109.57/15.60 | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | Case 1:
% 109.57/15.60 | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | (2906) all_55_13 = e2
% 109.57/15.60 | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | COMBINE_EQS: (2882), (2906) imply:
% 109.57/15.60 | | | | | | | | | | | | | | | (2907) all_38_0 = e2
% 109.57/15.60 | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | REDUCE: (2879), (2907) imply:
% 109.57/15.60 | | | | | | | | | | | | | | | (2908) $false
% 109.57/15.60 | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | CLOSE: (2908) is inconsistent.
% 109.57/15.60 | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | Case 2:
% 109.57/15.60 | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | (2909) all_55_13 = e1 | all_55_13 = e0
% 109.57/15.60 | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | BETA: splitting (2909) gives:
% 109.57/15.60 | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | Case 1:
% 109.57/15.60 | | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | | (2910) all_55_13 = e1
% 109.57/15.60 | | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | | COMBINE_EQS: (2882), (2910) imply:
% 109.57/15.60 | | | | | | | | | | | | | | | | (2911) all_38_0 = e1
% 109.57/15.60 | | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | | REDUCE: (2901), (2911) imply:
% 109.57/15.60 | | | | | | | | | | | | | | | | (2912) $false
% 109.57/15.60 | | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | | CLOSE: (2912) is inconsistent.
% 109.57/15.60 | | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | Case 2:
% 109.57/15.60 | | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | | (2913) all_55_13 = e0
% 109.57/15.60 | | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | | COMBINE_EQS: (2882), (2913) imply:
% 109.57/15.60 | | | | | | | | | | | | | | | | (2914) all_38_0 = e0
% 109.57/15.60 | | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | | REDUCE: (2883), (2914) imply:
% 109.57/15.60 | | | | | | | | | | | | | | | | (2915) ~ (all_53_1 = e0)
% 109.57/15.60 | | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 109.57/15.60 | | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.60 | | | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | | | (2916) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 109.57/15.60 | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 109.57/15.60 | | | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | | | ALPHA: (2916) implies:
% 109.57/15.60 | | | | | | | | | | | | | | | | | (2917) op(e3, e1) = e3
% 109.57/15.60 | | | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (2875), (2917), (function-axioms) are
% 109.57/15.60 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #232.
% 109.57/15.60 | | | | | | | | | | | | | | | | |
% 109.57/15.60 | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.60 | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | (2918) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.57/15.61 | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 109.57/15.61 | | | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.57/15.61 | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 109.57/15.61 | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | BETA: splitting (2918) gives:
% 109.57/15.61 | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.61 | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | (2919) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.57/15.61 | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)
% 109.57/15.61 | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | ALPHA: (2919) implies:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | (2920) op(e2, e1) = e2
% 109.57/15.61 | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 109.57/15.61 | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | (2921) all_55_1 = e3
% 109.57/15.61 | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (2873), (2921) are inconsistent by
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | sub-proof #78.
% 109.57/15.61 | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | (2922) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 109.57/15.61 | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | BETA: splitting (2922) gives:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | (2923) all_55_1 = e2
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (2923) imply:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | (2924) all_53_1 = e2
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (2924) imply:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | (2925) ~ (all_53_9 = e2)
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | SIMP: (2925) implies:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | (2926) ~ (all_53_9 = e2)
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | (2927) all_55_9 = e3
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (2874), (2927) are inconsistent by
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | sub-proof #176.
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | (2928) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2928) gives:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | (2929) all_55_9 = e2
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (2926), (2929) are inconsistent by
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | sub-proof #175.
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | (2930) ~ (all_55_9 = e2)
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | (2931) all_55_9 = e1 | all_55_9 = e0
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2931) gives:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | (2932) all_55_9 = e1
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (2932) imply:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | (2933) all_53_9 = e1
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2933) implies:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | (2934) all_53_9 = e1
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2926), (2934) imply:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | (2935) ~ (e2 = e1)
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2935) implies:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | (2936) ~ (e2 = e1)
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (2934) imply:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | (2937) op(e2, e1) = e1
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2920), (2936), (2937), (function-axioms) are
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #31.
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | (2938) all_55_9 = e0
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (2938) imply:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | (2939) all_53_9 = e0
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2939) implies:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | (2940) all_53_9 = e0
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2823), (2940) imply:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | (2941) $false
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2941) is inconsistent.
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | (2942) all_55_1 = e1 | all_55_1 = e0
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (2730), (2915), (2942) are inconsistent by
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | | sub-proof #49.
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | (2943) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.57/15.61 | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 109.57/15.61 | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | ALPHA: (2943) implies:
% 109.57/15.61 | | | | | | | | | | | | | | | | | | (2944) op(e0, e1) = e0
% 109.57/15.61 | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2915), (2944), (function-axioms) are
% 109.57/15.61 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #230.
% 109.57/15.61 | | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | (2945) all_26_2 = e2
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | COMBINE_EQS: (316), (2945) imply:
% 109.57/15.61 | | | | | | | | | | | | (2946) all_4_2 = e2
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | REDUCE: (374), (2946) imply:
% 109.57/15.61 | | | | | | | | | | | | (2947) ~ (all_53_12 = e2)
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | REDUCE: (377), (2946) imply:
% 109.57/15.61 | | | | | | | | | | | | (2948) ~ (all_53_15 = e2)
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | BETA: splitting (108) gives:
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | Case 1:
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | (2949) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 109.57/15.61 | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | ALPHA: (2949) implies:
% 109.57/15.61 | | | | | | | | | | | | | (2950) op(e3, e2) = e3
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 109.57/15.61 | | | | | | | | | | | | | e3, e2, e3, simplifying with (174), (2950) gives:
% 109.57/15.61 | | | | | | | | | | | | | (2951) all_53_15 = e3
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | REF_CLOSE: (110), (115), (127), (164), (168), (169), (172),
% 109.57/15.61 | | | | | | | | | | | | | (195), (196), (199), (263), (272), (2733), (2735),
% 109.57/15.61 | | | | | | | | | | | | | (2823), (2874), (2879), (2882), (2884), (2885),
% 109.57/15.61 | | | | | | | | | | | | | (2887), (2947), (2951), (function-axioms) are
% 109.57/15.61 | | | | | | | | | | | | | inconsistent by sub-proof #27.
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | (2952) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 109.57/15.61 | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 109.57/15.61 | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 109.57/15.61 | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | BETA: splitting (2952) gives:
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | Case 1:
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | (2953) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 109.57/15.61 | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | ALPHA: (2953) implies:
% 109.57/15.61 | | | | | | | | | | | | | | (2954) op(e1, e2) = e1
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e1,
% 109.57/15.61 | | | | | | | | | | | | | | e2, e1, simplifying with (166), (2954) gives:
% 109.57/15.61 | | | | | | | | | | | | | | (2955) all_53_7 = e1
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | REDUCE: (128), (2955) imply:
% 109.57/15.61 | | | | | | | | | | | | | | (2956) ~ (all_53_15 = e1)
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | SIMP: (2956) implies:
% 109.57/15.61 | | | | | | | | | | | | | | (2957) ~ (all_53_15 = e1)
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | Case 1:
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | (2958) all_55_14 = e3
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | COMBINE_EQS: (274), (2958) imply:
% 109.57/15.61 | | | | | | | | | | | | | | | (2959) all_53_15 = e3
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | REF_CLOSE: (110), (115), (127), (164), (168), (169), (172),
% 109.57/15.61 | | | | | | | | | | | | | | | (195), (196), (199), (263), (272), (2733), (2735),
% 109.57/15.61 | | | | | | | | | | | | | | | (2823), (2874), (2879), (2882), (2884), (2885),
% 109.57/15.61 | | | | | | | | | | | | | | | (2887), (2947), (2959), (function-axioms) are
% 109.57/15.61 | | | | | | | | | | | | | | | inconsistent by sub-proof #27.
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | (2960) all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | REF_CLOSE: (274), (2824), (2948), (2957), (2960) are
% 109.57/15.61 | | | | | | | | | | | | | | | inconsistent by sub-proof #26.
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | (2961) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 109.57/15.61 | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | ALPHA: (2961) implies:
% 109.57/15.61 | | | | | | | | | | | | | | (2962) op(e0, e2) = e0
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | REF_CLOSE: (162), (2821), (2962), (function-axioms) are
% 109.57/15.61 | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | End of split
% 109.57/15.61 | | | | | | | | |
% 109.57/15.61 | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | |
% 109.57/15.61 | | | | | | | | | (2963) all_14_2 = e2
% 109.57/15.61 | | | | | | | | |
% 109.57/15.61 | | | | | | | | | COMBINE_EQS: (2745), (2963) imply:
% 109.57/15.61 | | | | | | | | | (2964) all_6_1 = e2
% 109.57/15.61 | | | | | | | | |
% 109.57/15.61 | | | | | | | | | REDUCE: (2751), (2964) imply:
% 109.57/15.61 | | | | | | | | | (2965) ~ (all_53_1 = e2)
% 109.57/15.61 | | | | | | | | |
% 109.57/15.61 | | | | | | | | | REDUCE: (2755), (2964) imply:
% 109.57/15.61 | | | | | | | | | (2966) ~ (all_53_9 = e2)
% 109.57/15.61 | | | | | | | | |
% 109.57/15.61 | | | | | | | | | REDUCE: (2844), (2964) imply:
% 109.57/15.61 | | | | | | | | | (2967) ~ (all_12_0 = e2)
% 109.57/15.61 | | | | | | | | |
% 109.57/15.61 | | | | | | | | | BETA: splitting (2728) gives:
% 109.57/15.61 | | | | | | | | |
% 109.57/15.61 | | | | | | | | | Case 1:
% 109.57/15.61 | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | (2968) ~ (all_6_1 = e2)
% 109.57/15.61 | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | REDUCE: (2964), (2968) imply:
% 109.57/15.61 | | | | | | | | | | (2969) $false
% 109.57/15.61 | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | CLOSE: (2969) is inconsistent.
% 109.57/15.61 | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | (2970) ~ (all_6_0 = e3) & op(e2, e1) = all_6_0 &
% 109.57/15.61 | | | | | | | | | | $i(all_6_0)
% 109.57/15.61 | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | ALPHA: (2970) implies:
% 109.57/15.61 | | | | | | | | | | (2971) ~ (all_6_0 = e3)
% 109.57/15.61 | | | | | | | | | | (2972) op(e2, e1) = all_6_0
% 109.57/15.61 | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | BETA: splitting (204) gives:
% 109.57/15.61 | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | Case 1:
% 109.57/15.61 | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | (2973) all_55_4 = e3
% 109.57/15.61 | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | COMBINE_EQS: (2839), (2973) imply:
% 109.57/15.61 | | | | | | | | | | | (2974) all_12_0 = e3
% 109.57/15.61 | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | REDUCE: (2836), (2974) imply:
% 109.57/15.61 | | | | | | | | | | | (2975) $false
% 109.57/15.61 | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | CLOSE: (2975) is inconsistent.
% 109.57/15.61 | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | (2976) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 109.57/15.61 | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | BETA: splitting (2976) gives:
% 109.57/15.61 | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | Case 1:
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | (2977) all_55_4 = e2
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | COMBINE_EQS: (2839), (2977) imply:
% 109.57/15.61 | | | | | | | | | | | | (2978) all_12_0 = e2
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | REDUCE: (2967), (2978) imply:
% 109.57/15.61 | | | | | | | | | | | | (2979) $false
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | CLOSE: (2979) is inconsistent.
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | (2980) all_55_4 = e1 | all_55_4 = e0
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | BETA: splitting (2980) gives:
% 109.57/15.61 | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | Case 1:
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | (2981) all_55_4 = e1
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | COMBINE_EQS: (2839), (2981) imply:
% 109.57/15.61 | | | | | | | | | | | | | (2982) all_12_0 = e1
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | REDUCE: (2845), (2982) imply:
% 109.57/15.61 | | | | | | | | | | | | | (2983) $false
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | CLOSE: (2983) is inconsistent.
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | (2984) all_55_4 = e0
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | COMBINE_EQS: (2839), (2984) imply:
% 109.57/15.61 | | | | | | | | | | | | | (2985) all_12_0 = e0
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | REDUCE: (2843), (2985) imply:
% 109.57/15.61 | | | | | | | | | | | | | (2986) ~ (all_53_12 = e0)
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | BETA: splitting (217) gives:
% 109.57/15.61 | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | Case 1:
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | (2987) (all_57_96 = e0 & op(e3, e3) = e0) | (all_57_97 =
% 109.57/15.61 | | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | REF_CLOSE: (35), (174), (378), (2824), (2987),
% 109.57/15.61 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.57/15.61 | | | | | | | | | | | | | | #155.
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | Case 2:
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | (2988) (all_57_98 = e0 & op(e3, e1) = e0) | (all_57_99 =
% 109.57/15.61 | | | | | | | | | | | | | | e0 & op(e3, e0) = e0)
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | BETA: splitting (2988) gives:
% 109.57/15.61 | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | Case 1:
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | (2989) all_57_98 = e0 & op(e3, e1) = e0
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | ALPHA: (2989) implies:
% 109.57/15.61 | | | | | | | | | | | | | | | (2990) op(e3, e1) = e0
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 109.57/15.61 | | | | | | | | | | | | | | | all_6_0, e1, e2, simplifying with (169), (2972)
% 109.57/15.61 | | | | | | | | | | | | | | | gives:
% 109.57/15.61 | | | | | | | | | | | | | | | (2991) all_53_9 = all_6_0
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 109.57/15.61 | | | | | | | | | | | | | | | e0, e1, e3, simplifying with (173), (2990) gives:
% 109.57/15.61 | | | | | | | | | | | | | | | (2992) all_53_13 = e0
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | COMBINE_EQS: (263), (2991) imply:
% 109.57/15.61 | | | | | | | | | | | | | | | (2993) all_55_9 = all_6_0
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | REDUCE: (150), (2991) imply:
% 109.57/15.61 | | | | | | | | | | | | | | | (2994) ~ (all_53_1 = all_6_0)
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | REDUCE: (149), (2992) imply:
% 109.57/15.61 | | | | | | | | | | | | | | | (2995) ~ (all_53_1 = e0)
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | REDUCE: (2966), (2991) imply:
% 109.57/15.61 | | | | | | | | | | | | | | | (2996) ~ (all_6_0 = e2)
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | REDUCE: (2823), (2991) imply:
% 109.57/15.61 | | | | | | | | | | | | | | | (2997) ~ (all_6_0 = e0)
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 109.57/15.61 | | | | | | | | | | | | | | |
% 109.57/15.61 | | | | | | | | | | | | | | | Case 1:
% 109.57/15.62 | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | (2998) all_55_9 = e3
% 109.57/15.62 | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | COMBINE_EQS: (2993), (2998) imply:
% 109.57/15.62 | | | | | | | | | | | | | | | | (2999) all_6_0 = e3
% 109.57/15.62 | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | REDUCE: (2971), (2999) imply:
% 109.57/15.62 | | | | | | | | | | | | | | | | (3000) $false
% 109.57/15.62 | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | CLOSE: (3000) is inconsistent.
% 109.57/15.62 | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | Case 2:
% 109.57/15.62 | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | (3001) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 109.57/15.62 | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | BETA: splitting (3001) gives:
% 109.57/15.62 | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.62 | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | (3002) all_55_9 = e2
% 109.57/15.62 | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2993), (3002) imply:
% 109.57/15.62 | | | | | | | | | | | | | | | | | (3003) all_6_0 = e2
% 109.57/15.62 | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | REDUCE: (2996), (3003) imply:
% 109.57/15.62 | | | | | | | | | | | | | | | | | (3004) $false
% 109.57/15.62 | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | CLOSE: (3004) is inconsistent.
% 109.57/15.62 | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.62 | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | (3005) ~ (all_55_9 = e2)
% 109.57/15.62 | | | | | | | | | | | | | | | | | (3006) all_55_9 = e1 | all_55_9 = e0
% 109.57/15.62 | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | BETA: splitting (3006) gives:
% 109.57/15.62 | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.62 | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | (3007) all_55_9 = e1
% 109.57/15.62 | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2993), (3007) imply:
% 109.57/15.62 | | | | | | | | | | | | | | | | | | (3008) all_6_0 = e1
% 109.57/15.62 | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | REDUCE: (2996), (3008) imply:
% 109.57/15.62 | | | | | | | | | | | | | | | | | | (3009) ~ (e2 = e1)
% 109.57/15.62 | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | SIMP: (3009) implies:
% 109.57/15.62 | | | | | | | | | | | | | | | | | | (3010) ~ (e2 = e1)
% 109.57/15.62 | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | REDUCE: (2972), (3008) imply:
% 109.57/15.62 | | | | | | | | | | | | | | | | | | (3011) op(e2, e1) = e1
% 109.57/15.62 | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 109.57/15.62 | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | Case 1:
% 109.57/15.62 | | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | | (3012) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 109.57/15.62 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 109.57/15.62 | | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (173), (207), (249), (2730), (2965),
% 109.57/15.62 | | | | | | | | | | | | | | | | | | | (2995), (3012), (function-axioms) are inconsistent
% 109.57/15.62 | | | | | | | | | | | | | | | | | | | by sub-proof #38.
% 109.57/15.62 | | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.62 | | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | | (3013) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.57/15.62 | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.57/15.62 | | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 109.57/15.62 | | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2995), (3010), (3011), (3013),
% 109.57/15.62 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.57/15.62 | | | | | | | | | | | | | | | | | | | #25.
% 109.57/15.62 | | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | End of split
% 109.57/15.62 | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | Case 2:
% 109.57/15.62 | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | (3014) all_55_9 = e0
% 109.57/15.62 | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2993), (3014) imply:
% 109.57/15.62 | | | | | | | | | | | | | | | | | | (3015) all_6_0 = e0
% 109.57/15.62 | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | REDUCE: (2997), (3015) imply:
% 109.57/15.62 | | | | | | | | | | | | | | | | | | (3016) $false
% 109.57/15.62 | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | | CLOSE: (3016) is inconsistent.
% 109.57/15.62 | | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | | End of split
% 109.57/15.62 | | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | | End of split
% 109.57/15.62 | | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | End of split
% 109.57/15.62 | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | Case 2:
% 109.57/15.62 | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | (3017) all_57_99 = e0 & op(e3, e0) = e0
% 109.57/15.62 | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | ALPHA: (3017) implies:
% 109.57/15.62 | | | | | | | | | | | | | | | (3018) op(e3, e0) = e0
% 109.57/15.62 | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | | REF_CLOSE: (172), (2986), (3018), (function-axioms) are
% 109.57/15.62 | | | | | | | | | | | | | | | inconsistent by sub-proof #201.
% 109.57/15.62 | | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | | End of split
% 109.57/15.62 | | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | | End of split
% 109.57/15.62 | | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | | End of split
% 109.57/15.62 | | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | | End of split
% 109.57/15.62 | | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | | End of split
% 109.57/15.62 | | | | | | | | | |
% 109.57/15.62 | | | | | | | | | End of split
% 109.57/15.62 | | | | | | | | |
% 109.57/15.62 | | | | | | | | End of split
% 109.57/15.62 | | | | | | | |
% 109.57/15.62 | | | | | | | End of split
% 109.57/15.62 | | | | | | |
% 109.57/15.62 | | | | | | End of split
% 109.57/15.62 | | | | | |
% 109.57/15.62 | | | | | End of split
% 109.57/15.62 | | | | |
% 109.57/15.62 | | | | Case 2:
% 109.57/15.62 | | | | |
% 109.57/15.62 | | | | | (3019) all_10_2 = e3
% 109.57/15.62 | | | | | (3020) op(e3, e3) = all_10_1 & $i(all_10_1) & ( ~ (all_10_1 = e0) |
% 109.57/15.62 | | | | | ( ~ (all_10_0 = e1) & op(e0, e3) = all_10_0 &
% 109.57/15.62 | | | | | $i(all_10_0)))
% 109.57/15.62 | | | | |
% 109.57/15.62 | | | | | ALPHA: (3020) implies:
% 109.57/15.62 | | | | | (3021) op(e3, e3) = all_10_1
% 109.57/15.62 | | | | |
% 109.57/15.62 | | | | | COMBINE_EQS: (335), (3019) imply:
% 109.57/15.62 | | | | | (3022) all_48_2 = e3
% 109.57/15.62 | | | | |
% 109.57/15.62 | | | | | REDUCE: (356), (3019) imply:
% 109.57/15.62 | | | | | (3023) ~ (all_53_3 = e3)
% 109.57/15.62 | | | | |
% 109.57/15.62 | | | | | REDUCE: (367), (3019) imply:
% 109.57/15.62 | | | | | (3024) ~ (all_53_7 = e3)
% 109.57/15.62 | | | | |
% 109.57/15.62 | | | | | REDUCE: (368), (3019) imply:
% 109.57/15.62 | | | | | (3025) ~ (all_53_8 = e3)
% 109.57/15.62 | | | | |
% 109.57/15.62 | | | | | REDUCE: (369), (3019) imply:
% 109.57/15.62 | | | | | (3026) ~ (all_53_9 = e3)
% 109.57/15.62 | | | | |
% 109.57/15.62 | | | | | REDUCE: (373), (3019) imply:
% 109.57/15.62 | | | | | (3027) ~ (all_53_15 = e3)
% 109.57/15.62 | | | | |
% 109.57/15.62 | | | | | REDUCE: (44), (3019) imply:
% 109.57/15.62 | | | | | (3028) op(e2, e2) = e3
% 109.57/15.62 | | | | |
% 109.57/15.62 | | | | | BETA: splitting (102) gives:
% 109.57/15.62 | | | | |
% 109.57/15.62 | | | | | Case 1:
% 109.57/15.62 | | | | | |
% 109.57/15.62 | | | | | | (3029) ~ (all_48_2 = e3)
% 109.57/15.62 | | | | | |
% 109.57/15.62 | | | | | | REDUCE: (3022), (3029) imply:
% 109.57/15.62 | | | | | | (3030) $false
% 109.57/15.62 | | | | | |
% 109.57/15.62 | | | | | | CLOSE: (3030) is inconsistent.
% 109.57/15.62 | | | | | |
% 109.57/15.62 | | | | | Case 2:
% 109.57/15.62 | | | | | |
% 109.57/15.62 | | | | | | (3031) op(e3, e3) = all_48_1 & $i(all_48_1) & ( ~ (all_48_1 = e1)
% 109.57/15.62 | | | | | | | ( ~ (all_48_0 = e0) & op(e1, e3) = all_48_0 &
% 109.57/15.62 | | | | | | $i(all_48_0)))
% 109.57/15.62 | | | | | |
% 109.57/15.62 | | | | | | ALPHA: (3031) implies:
% 109.57/15.62 | | | | | | (3032) op(e3, e3) = all_48_1
% 109.57/15.62 | | | | | |
% 109.57/15.62 | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, all_48_1,
% 109.57/15.62 | | | | | | e3, e3, simplifying with (35), (3032) gives:
% 109.57/15.62 | | | | | | (3033) all_48_1 = all_4_2
% 109.57/15.62 | | | | | |
% 109.57/15.62 | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 109.57/15.62 | | | | | | all_48_1, e3, e3, simplifying with (3021), (3032)
% 109.57/15.62 | | | | | | gives:
% 109.57/15.62 | | | | | | (3034) all_48_1 = all_10_1
% 109.57/15.62 | | | | | |
% 109.57/15.62 | | | | | | COMBINE_EQS: (3033), (3034) imply:
% 109.57/15.62 | | | | | | (3035) all_10_1 = all_4_2
% 109.57/15.62 | | | | | |
% 109.57/15.62 | | | | | | BETA: splitting (51) gives:
% 109.57/15.62 | | | | | |
% 109.57/15.62 | | | | | | Case 1:
% 109.57/15.62 | | | | | | |
% 109.57/15.62 | | | | | | | (3036) ~ (all_14_2 = e2)
% 109.57/15.62 | | | | | | |
% 109.57/15.62 | | | | | | | REDUCE: (2745), (3036) imply:
% 109.92/15.62 | | | | | | | (3037) ~ (all_6_1 = e2)
% 109.92/15.62 | | | | | | |
% 109.92/15.62 | | | | | | | BETA: splitting (57) gives:
% 109.92/15.62 | | | | | | |
% 109.92/15.62 | | | | | | | Case 1:
% 109.92/15.62 | | | | | | | |
% 109.92/15.62 | | | | | | | | (3038) ~ (all_18_2 = e3)
% 109.92/15.62 | | | | | | | |
% 109.92/15.62 | | | | | | | | REDUCE: (2746), (3038) imply:
% 109.92/15.62 | | | | | | | | (3039) ~ (all_6_1 = e3)
% 109.92/15.62 | | | | | | | |
% 109.92/15.62 | | | | | | | | BETA: splitting (63) gives:
% 109.92/15.62 | | | | | | | |
% 109.92/15.62 | | | | | | | | Case 1:
% 109.92/15.62 | | | | | | | | |
% 109.92/15.62 | | | | | | | | | (3040) ~ (all_22_2 = e0)
% 109.92/15.62 | | | | | | | | |
% 109.92/15.62 | | | | | | | | | REDUCE: (2748), (3040) imply:
% 109.92/15.62 | | | | | | | | | (3041) ~ (all_6_1 = e0)
% 109.92/15.62 | | | | | | | | |
% 109.92/15.62 | | | | | | | | | BETA: splitting (203) gives:
% 109.92/15.62 | | | | | | | | |
% 109.92/15.62 | | | | | | | | | Case 1:
% 109.92/15.62 | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | (3042) all_55_5 = e3
% 109.92/15.62 | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | COMBINE_EQS: (2750), (3042) imply:
% 109.92/15.62 | | | | | | | | | | (3043) all_6_1 = e3
% 109.92/15.62 | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | REDUCE: (3039), (3043) imply:
% 109.92/15.62 | | | | | | | | | | (3044) $false
% 109.92/15.62 | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | CLOSE: (3044) is inconsistent.
% 109.92/15.62 | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | Case 2:
% 109.92/15.62 | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | (3045) ~ (all_55_5 = e3)
% 109.92/15.62 | | | | | | | | | | (3046) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 109.92/15.62 | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | BETA: splitting (3046) gives:
% 109.92/15.62 | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | Case 1:
% 109.92/15.62 | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | (3047) all_55_5 = e2
% 109.92/15.62 | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | COMBINE_EQS: (2750), (3047) imply:
% 109.92/15.62 | | | | | | | | | | | (3048) all_6_1 = e2
% 109.92/15.62 | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | REDUCE: (3037), (3048) imply:
% 109.92/15.62 | | | | | | | | | | | (3049) $false
% 109.92/15.62 | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | CLOSE: (3049) is inconsistent.
% 109.92/15.62 | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | Case 2:
% 109.92/15.62 | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | (3050) all_55_5 = e1 | all_55_5 = e0
% 109.92/15.62 | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | BETA: splitting (3050) gives:
% 109.92/15.62 | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | Case 1:
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | (3051) all_55_5 = e1
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | COMBINE_EQS: (2750), (3051) imply:
% 109.92/15.62 | | | | | | | | | | | | (3052) all_6_1 = e1
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | REDUCE: (2754), (3052) imply:
% 109.92/15.62 | | | | | | | | | | | | (3053) ~ (all_53_7 = e1)
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | REDUCE: (2755), (3052) imply:
% 109.92/15.62 | | | | | | | | | | | | (3054) ~ (all_53_9 = e1)
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | REDUCE: (3039), (3052) imply:
% 109.92/15.62 | | | | | | | | | | | | (3055) ~ (e3 = e1)
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | REF_CLOSE: (7), (108), (110), (123), (127), (128), (137),
% 109.92/15.62 | | | | | | | | | | | | (138), (139), (144), (162), (164), (166), (168),
% 109.92/15.62 | | | | | | | | | | | | (169), (171), (172), (174), (199), (200), (202),
% 109.92/15.62 | | | | | | | | | | | | (204), (222), (223), (252), (260), (262), (263),
% 109.92/15.62 | | | | | | | | | | | | (2732), (2733), (2734), (3024), (3025), (3026),
% 109.92/15.62 | | | | | | | | | | | | (3027), (3028), (3053), (3054), (function-axioms)
% 109.92/15.62 | | | | | | | | | | | | are inconsistent by sub-proof #23.
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | Case 2:
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | (3056) all_55_5 = e0
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | COMBINE_EQS: (2750), (3056) imply:
% 109.92/15.62 | | | | | | | | | | | | (3057) all_6_1 = e0
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | REDUCE: (3041), (3057) imply:
% 109.92/15.62 | | | | | | | | | | | | (3058) $false
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | CLOSE: (3058) is inconsistent.
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | End of split
% 109.92/15.62 | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | End of split
% 109.92/15.62 | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | End of split
% 109.92/15.62 | | | | | | | | |
% 109.92/15.62 | | | | | | | | Case 2:
% 109.92/15.62 | | | | | | | | |
% 109.92/15.62 | | | | | | | | | (3059) all_22_2 = e0
% 109.92/15.62 | | | | | | | | |
% 109.92/15.62 | | | | | | | | | COMBINE_EQS: (2748), (3059) imply:
% 109.92/15.62 | | | | | | | | | (3060) all_6_1 = e0
% 109.92/15.62 | | | | | | | | |
% 109.92/15.62 | | | | | | | | | SIMP: (3060) implies:
% 109.92/15.62 | | | | | | | | | (3061) all_6_1 = e0
% 109.92/15.62 | | | | | | | | |
% 109.92/15.62 | | | | | | | | | REDUCE: (2751), (3061) imply:
% 109.92/15.62 | | | | | | | | | (3062) ~ (all_53_1 = e0)
% 109.92/15.62 | | | | | | | | |
% 109.92/15.62 | | | | | | | | | REDUCE: (2752), (3061) imply:
% 109.92/15.62 | | | | | | | | | (3063) ~ (all_53_4 = e0)
% 109.92/15.62 | | | | | | | | |
% 109.92/15.62 | | | | | | | | | REDUCE: (2753), (3061) imply:
% 109.92/15.62 | | | | | | | | | (3064) ~ (all_53_6 = e0)
% 109.92/15.62 | | | | | | | | |
% 109.92/15.62 | | | | | | | | | REDUCE: (2754), (3061) imply:
% 109.92/15.62 | | | | | | | | | (3065) ~ (all_53_7 = e0)
% 109.92/15.62 | | | | | | | | |
% 109.92/15.62 | | | | | | | | | REDUCE: (2727), (3061) imply:
% 109.92/15.62 | | | | | | | | | (3066) op(e1, e1) = e0
% 109.92/15.62 | | | | | | | | |
% 109.92/15.62 | | | | | | | | | BETA: splitting (69) gives:
% 109.92/15.62 | | | | | | | | |
% 109.92/15.62 | | | | | | | | | Case 1:
% 109.92/15.62 | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | (3067) ~ (all_26_2 = e2)
% 109.92/15.62 | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | REDUCE: (316), (3067) imply:
% 109.92/15.62 | | | | | | | | | | (3068) ~ (all_4_2 = e2)
% 109.92/15.62 | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | BETA: splitting (81) gives:
% 109.92/15.62 | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | Case 1:
% 109.92/15.62 | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | (3069) ~ (all_34_2 = e1)
% 109.92/15.62 | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | REDUCE: (311), (3069) imply:
% 109.92/15.62 | | | | | | | | | | | (3070) ~ (all_4_2 = e1)
% 109.92/15.62 | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | BETA: splitting (193) gives:
% 109.92/15.62 | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | Case 1:
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | (3071) all_55_15 = e3
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | COMBINE_EQS: (339), (3071) imply:
% 109.92/15.62 | | | | | | | | | | | | (3072) all_4_2 = e3
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | SIMP: (3072) implies:
% 109.92/15.62 | | | | | | | | | | | | (3073) all_4_2 = e3
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | REDUCE: (374), (3073) imply:
% 109.92/15.62 | | | | | | | | | | | | (3074) ~ (all_53_12 = e3)
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | REDUCE: (375), (3073) imply:
% 109.92/15.62 | | | | | | | | | | | | (3075) ~ (all_53_13 = e3)
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | BETA: splitting (109) gives:
% 109.92/15.62 | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | Case 1:
% 109.92/15.62 | | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | | (3076) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 109.92/15.62 | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 109.92/15.62 | | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | | ALPHA: (3076) implies:
% 109.92/15.62 | | | | | | | | | | | | | (3077) op(e3, e1) = e3
% 109.92/15.62 | | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | | REF_CLOSE: (173), (3075), (3077), (function-axioms) are
% 109.92/15.62 | | | | | | | | | | | | | inconsistent by sub-proof #232.
% 109.92/15.62 | | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | Case 2:
% 109.92/15.62 | | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | | (3078) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.92/15.62 | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 109.92/15.62 | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.92/15.62 | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 109.92/15.62 | | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | | BETA: splitting (3078) gives:
% 109.92/15.62 | | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | | Case 1:
% 109.92/15.62 | | | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | | | (3079) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.92/15.62 | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)
% 109.92/15.62 | | | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | | | ALPHA: (3079) implies:
% 109.92/15.62 | | | | | | | | | | | | | | (3080) op(e2, e1) = e2
% 109.92/15.62 | | | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | | | REF_CLOSE: (110), (127), (164), (168), (169), (172), (2733),
% 109.92/15.62 | | | | | | | | | | | | | | (3074), (3080), (function-axioms) are inconsistent
% 109.92/15.62 | | | | | | | | | | | | | | by sub-proof #133.
% 109.92/15.62 | | | | | | | | | | | | | |
% 109.92/15.62 | | | | | | | | | | | | | Case 2:
% 109.92/15.62 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | (3081) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.92/15.63 | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | ALPHA: (3081) implies:
% 109.92/15.63 | | | | | | | | | | | | | | (3082) op(e0, e1) = e0
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | REF_CLOSE: (161), (3062), (3082), (function-axioms) are
% 109.92/15.63 | | | | | | | | | | | | | | inconsistent by sub-proof #230.
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | End of split
% 109.92/15.63 | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | End of split
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | Case 2:
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | (3083) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | REF_CLOSE: (339), (378), (3068), (3070), (3083) are
% 109.92/15.63 | | | | | | | | | | | | inconsistent by sub-proof #191.
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | End of split
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | Case 2:
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | (3084) all_34_2 = e1
% 109.92/15.63 | | | | | | | | | | | (3085) op(e1, e1) = all_34_1 & $i(all_34_1) & ( ~
% 109.92/15.63 | | | | | | | | | | | (all_34_1 = e2) | ( ~ (all_34_0 = e0) & op(e2,
% 109.92/15.63 | | | | | | | | | | | e1) = all_34_0 & $i(all_34_0)))
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | ALPHA: (3085) implies:
% 109.92/15.63 | | | | | | | | | | | (3086) op(e1, e1) = all_34_1
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | COMBINE_EQS: (311), (3084) imply:
% 109.92/15.63 | | | | | | | | | | | (3087) all_4_2 = e1
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | COMBINE_EQS: (333), (3087) imply:
% 109.92/15.63 | | | | | | | | | | | (3088) all_42_2 = e1
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | REDUCE: (375), (3087) imply:
% 109.92/15.63 | | | | | | | | | | | (3089) ~ (all_53_13 = e1)
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | REDUCE: (3068), (3087) imply:
% 109.92/15.63 | | | | | | | | | | | (3090) ~ (e2 = e1)
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | SIMP: (3090) implies:
% 109.92/15.63 | | | | | | | | | | | (3091) ~ (e2 = e1)
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | BETA: splitting (93) gives:
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | Case 1:
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | (3092) ~ (all_42_2 = e1)
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | REDUCE: (3088), (3092) imply:
% 109.92/15.63 | | | | | | | | | | | | (3093) $false
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | CLOSE: (3093) is inconsistent.
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | Case 2:
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | (3094) op(e1, e1) = all_42_1 & $i(all_42_1) & ( ~
% 109.92/15.63 | | | | | | | | | | | | (all_42_1 = e0) | ( ~ (all_42_0 = e2) & op(e0,
% 109.92/15.63 | | | | | | | | | | | | e1) = all_42_0 & $i(all_42_0)))
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | ALPHA: (3094) implies:
% 109.92/15.63 | | | | | | | | | | | | (3095) op(e1, e1) = all_42_1
% 109.92/15.63 | | | | | | | | | | | | (3096) ~ (all_42_1 = e0) | ( ~ (all_42_0 = e2) & op(e0,
% 109.92/15.63 | | | | | | | | | | | | e1) = all_42_0 & $i(all_42_0))
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | BETA: splitting (230) gives:
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | Case 1:
% 109.92/15.63 | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | (3097) (all_57_44 = e1 & op(e3, e1) = e1) | (all_57_45 =
% 109.92/15.63 | | | | | | | | | | | | | e1 & op(e2, e1) = e1)
% 109.92/15.63 | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | BETA: splitting (3097) gives:
% 109.92/15.63 | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | Case 1:
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | (3098) all_57_44 = e1 & op(e3, e1) = e1
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | ALPHA: (3098) implies:
% 109.92/15.63 | | | | | | | | | | | | | | (3099) op(e3, e1) = e1
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | REF_CLOSE: (173), (3089), (3099), (function-axioms) are
% 109.92/15.63 | | | | | | | | | | | | | | inconsistent by sub-proof #118.
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | Case 2:
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | (3100) all_57_45 = e1 & op(e2, e1) = e1
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | ALPHA: (3100) implies:
% 109.92/15.63 | | | | | | | | | | | | | | (3101) op(e2, e1) = e1
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_42_1,
% 109.92/15.63 | | | | | | | | | | | | | | e1, e1, simplifying with (3066), (3095) gives:
% 109.92/15.63 | | | | | | | | | | | | | | (3102) all_42_1 = e0
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_34_1,
% 109.92/15.63 | | | | | | | | | | | | | | all_42_1, e1, e1, simplifying with (3086), (3095)
% 109.92/15.63 | | | | | | | | | | | | | | gives:
% 109.92/15.63 | | | | | | | | | | | | | | (3103) all_42_1 = all_34_1
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e1,
% 109.92/15.63 | | | | | | | | | | | | | | e1, e2, simplifying with (169), (3101) gives:
% 109.92/15.63 | | | | | | | | | | | | | | (3104) all_53_9 = e1
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | COMBINE_EQS: (3102), (3103) imply:
% 109.92/15.63 | | | | | | | | | | | | | | (3105) all_34_1 = e0
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | Case 1:
% 109.92/15.63 | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | (3106) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 109.92/15.63 | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 109.92/15.63 | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | ALPHA: (3106) implies:
% 109.92/15.63 | | | | | | | | | | | | | | | (3107) op(e3, e1) = e3
% 109.92/15.63 | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | BETA: splitting (3096) gives:
% 109.92/15.63 | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | Case 1:
% 109.92/15.63 | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | (3108) ~ (all_42_1 = e0)
% 109.92/15.63 | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | REDUCE: (3102), (3108) imply:
% 109.92/15.63 | | | | | | | | | | | | | | | | (3109) $false
% 109.92/15.63 | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | CLOSE: (3109) is inconsistent.
% 109.92/15.63 | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | Case 2:
% 109.92/15.63 | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | (3110) ~ (all_42_0 = e2) & op(e0, e1) = all_42_0 &
% 109.92/15.63 | | | | | | | | | | | | | | | | $i(all_42_0)
% 109.92/15.63 | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | ALPHA: (3110) implies:
% 109.92/15.63 | | | | | | | | | | | | | | | | (3111) ~ (all_42_0 = e2)
% 109.92/15.63 | | | | | | | | | | | | | | | | (3112) op(e0, e1) = all_42_0
% 109.92/15.63 | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1,
% 109.92/15.63 | | | | | | | | | | | | | | | | all_42_0, e1, e0, simplifying with (161), (3112)
% 109.92/15.63 | | | | | | | | | | | | | | | | gives:
% 109.92/15.63 | | | | | | | | | | | | | | | | (3113) all_53_1 = all_42_0
% 109.92/15.63 | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 109.92/15.63 | | | | | | | | | | | | | | | | e3, e1, e3, simplifying with (173), (3107) gives:
% 109.92/15.63 | | | | | | | | | | | | | | | | (3114) all_53_13 = e3
% 109.92/15.63 | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (3113) imply:
% 109.92/15.63 | | | | | | | | | | | | | | | | (3115) all_55_1 = all_42_0
% 109.92/15.63 | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | REDUCE: (149), (3113), (3114) imply:
% 109.92/15.63 | | | | | | | | | | | | | | | | (3116) ~ (all_42_0 = e3)
% 109.92/15.63 | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | REDUCE: (2730), (3113) imply:
% 109.92/15.63 | | | | | | | | | | | | | | | | (3117) ~ (all_42_0 = e1)
% 109.92/15.63 | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | REDUCE: (3062), (3113) imply:
% 109.92/15.63 | | | | | | | | | | | | | | | | (3118) ~ (all_42_0 = e0)
% 109.92/15.63 | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 109.92/15.63 | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.63 | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | (3119) all_55_1 = e3
% 109.92/15.63 | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | COMBINE_EQS: (3115), (3119) imply:
% 109.92/15.63 | | | | | | | | | | | | | | | | | (3120) all_42_0 = e3
% 109.92/15.63 | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | SIMP: (3120) implies:
% 109.92/15.63 | | | | | | | | | | | | | | | | | (3121) all_42_0 = e3
% 109.92/15.63 | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | REDUCE: (3116), (3121) imply:
% 109.92/15.63 | | | | | | | | | | | | | | | | | (3122) $false
% 109.92/15.63 | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | CLOSE: (3122) is inconsistent.
% 109.92/15.63 | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.63 | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | (3123) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 109.92/15.63 | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | BETA: splitting (3123) gives:
% 109.92/15.63 | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.63 | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | (3124) all_55_1 = e2
% 109.92/15.63 | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3115), (3124) imply:
% 109.92/15.63 | | | | | | | | | | | | | | | | | | (3125) all_42_0 = e2
% 109.92/15.63 | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | SIMP: (3125) implies:
% 109.92/15.63 | | | | | | | | | | | | | | | | | | (3126) all_42_0 = e2
% 109.92/15.63 | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | REDUCE: (3111), (3126) imply:
% 109.92/15.63 | | | | | | | | | | | | | | | | | | (3127) $false
% 109.92/15.63 | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | CLOSE: (3127) is inconsistent.
% 109.92/15.63 | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.63 | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | (3128) all_55_1 = e1 | all_55_1 = e0
% 109.92/15.63 | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | BETA: splitting (3128) gives:
% 109.92/15.63 | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.63 | | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | (3129) all_55_1 = e1
% 109.92/15.63 | | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3115), (3129) imply:
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | (3130) all_42_0 = e1
% 109.92/15.63 | | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | SIMP: (3130) implies:
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | (3131) all_42_0 = e1
% 109.92/15.63 | | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | REDUCE: (3117), (3131) imply:
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | (3132) $false
% 109.92/15.63 | | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | CLOSE: (3132) is inconsistent.
% 109.92/15.63 | | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.63 | | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | (3133) all_55_1 = e0
% 109.92/15.63 | | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3115), (3133) imply:
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | (3134) all_42_0 = e0
% 109.92/15.63 | | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | SIMP: (3134) implies:
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | (3135) all_42_0 = e0
% 109.92/15.63 | | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | REDUCE: (3118), (3135) imply:
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | (3136) $false
% 109.92/15.63 | | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | | CLOSE: (3136) is inconsistent.
% 109.92/15.63 | | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.63 | | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | | End of split
% 109.92/15.63 | | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | | End of split
% 109.92/15.63 | | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | End of split
% 109.92/15.63 | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | Case 2:
% 109.92/15.63 | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | (3137) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.92/15.63 | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 109.92/15.63 | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.92/15.63 | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 109.92/15.63 | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | | REF_CLOSE: (161), (3062), (3091), (3101), (3137),
% 109.92/15.63 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.92/15.63 | | | | | | | | | | | | | | | #25.
% 109.92/15.63 | | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | End of split
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | End of split
% 109.92/15.63 | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | Case 2:
% 109.92/15.63 | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | (3138) (all_57_46 = e1 & op(e1, e1) = e1) | (all_57_47 =
% 109.92/15.63 | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 109.92/15.63 | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | BETA: splitting (3138) gives:
% 109.92/15.63 | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | Case 1:
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | (3139) all_57_46 = e1 & op(e1, e1) = e1
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | ALPHA: (3139) implies:
% 109.92/15.63 | | | | | | | | | | | | | | (3140) op(e1, e1) = e1
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_34_1,
% 109.92/15.63 | | | | | | | | | | | | | | e1, e1, simplifying with (3086), (3140) gives:
% 109.92/15.63 | | | | | | | | | | | | | | (3141) all_34_1 = e1
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_42_1,
% 109.92/15.63 | | | | | | | | | | | | | | e1, e1, simplifying with (3066), (3095) gives:
% 109.92/15.63 | | | | | | | | | | | | | | (3142) all_42_1 = e0
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_34_1,
% 109.92/15.63 | | | | | | | | | | | | | | all_42_1, e1, e1, simplifying with (3086), (3095)
% 109.92/15.63 | | | | | | | | | | | | | | gives:
% 109.92/15.63 | | | | | | | | | | | | | | (3143) all_42_1 = all_34_1
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | COMBINE_EQS: (3142), (3143) imply:
% 109.92/15.63 | | | | | | | | | | | | | | (3144) all_34_1 = e0
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | SIMP: (3144) implies:
% 109.92/15.63 | | | | | | | | | | | | | | (3145) all_34_1 = e0
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | COMBINE_EQS: (3141), (3145) imply:
% 109.92/15.63 | | | | | | | | | | | | | | (3146) e1 = e0
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | REDUCE: (4), (3146) imply:
% 109.92/15.63 | | | | | | | | | | | | | | (3147) $false
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | CLOSE: (3147) is inconsistent.
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | Case 2:
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | (3148) all_57_47 = e1 & op(e0, e1) = e1
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | ALPHA: (3148) implies:
% 109.92/15.63 | | | | | | | | | | | | | | (3149) op(e0, e1) = e1
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | | REF_CLOSE: (161), (2730), (3149), (function-axioms) are
% 109.92/15.63 | | | | | | | | | | | | | | inconsistent by sub-proof #170.
% 109.92/15.63 | | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | | End of split
% 109.92/15.63 | | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | End of split
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | End of split
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | End of split
% 109.92/15.63 | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | Case 2:
% 109.92/15.63 | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | (3150) all_26_2 = e2
% 109.92/15.63 | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | COMBINE_EQS: (316), (3150) imply:
% 109.92/15.63 | | | | | | | | | | (3151) all_4_2 = e2
% 109.92/15.63 | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | REDUCE: (355), (3151) imply:
% 109.92/15.63 | | | | | | | | | | (3152) ~ (all_53_2 = e2)
% 109.92/15.63 | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | REDUCE: (366), (3151) imply:
% 109.92/15.63 | | | | | | | | | | (3153) ~ (all_53_6 = e2)
% 109.92/15.63 | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | BETA: splitting (110) gives:
% 109.92/15.63 | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | Case 1:
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | (3154) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 109.92/15.63 | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | ALPHA: (3154) implies:
% 109.92/15.63 | | | | | | | | | | | (3155) ~ (all_52_0 = e0)
% 109.92/15.63 | | | | | | | | | | | (3156) op(e0, e3) = all_52_0
% 109.92/15.63 | | | | | | | | | | | (3157) op(e3, e0) = e3
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2,
% 109.92/15.63 | | | | | | | | | | | all_52_0, e3, e0, simplifying with (163), (3156)
% 109.92/15.63 | | | | | | | | | | | gives:
% 109.92/15.63 | | | | | | | | | | | (3158) all_53_2 = all_52_0
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 109.92/15.63 | | | | | | | | | | | e3, e0, e3, simplifying with (172), (3157) gives:
% 109.92/15.63 | | | | | | | | | | | (3159) all_53_12 = e3
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | COMBINE_EQS: (251), (3158) imply:
% 109.92/15.63 | | | | | | | | | | | (3160) all_55_3 = all_52_0
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | REDUCE: (147), (3158) imply:
% 109.92/15.63 | | | | | | | | | | | (3161) ~ (all_53_6 = all_52_0)
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | SIMP: (3161) implies:
% 109.92/15.63 | | | | | | | | | | | (3162) ~ (all_53_6 = all_52_0)
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | REDUCE: (3152), (3158) imply:
% 109.92/15.63 | | | | | | | | | | | (3163) ~ (all_52_0 = e2)
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | REDUCE: (2731), (3158) imply:
% 109.92/15.63 | | | | | | | | | | | (3164) ~ (all_52_0 = e1)
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | REDUCE: (137), (3159) imply:
% 109.92/15.63 | | | | | | | | | | | (3165) ~ (all_53_4 = e3)
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | BETA: splitting (204) gives:
% 109.92/15.63 | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | Case 1:
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | (3166) all_55_4 = e3
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | COMBINE_EQS: (252), (3166) imply:
% 109.92/15.63 | | | | | | | | | | | | (3167) all_53_4 = e3
% 109.92/15.63 | | | | | | | | | | | |
% 109.92/15.63 | | | | | | | | | | | | REDUCE: (3165), (3167) imply:
% 109.92/15.63 | | | | | | | | | | | | (3168) $false
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | CLOSE: (3168) is inconsistent.
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | Case 2:
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | (3169) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | BETA: splitting (205) gives:
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | Case 1:
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | (3170) all_55_3 = e3
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | COMBINE_EQS: (3160), (3170) imply:
% 109.92/15.64 | | | | | | | | | | | | | (3171) all_52_0 = e3
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | REDUCE: (3162), (3171) imply:
% 109.92/15.64 | | | | | | | | | | | | | (3172) ~ (all_53_6 = e3)
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | BETA: splitting (3169) gives:
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | Case 1:
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | (3173) all_55_4 = e2
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | COMBINE_EQS: (252), (3173) imply:
% 109.92/15.64 | | | | | | | | | | | | | | (3174) all_53_4 = e2
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | REDUCE: (140), (3174) imply:
% 109.92/15.64 | | | | | | | | | | | | | | (3175) ~ (all_53_6 = e2)
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | REDUCE: (139), (3174) imply:
% 109.92/15.64 | | | | | | | | | | | | | | (3176) ~ (all_53_7 = e2)
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | SIMP: (3176) implies:
% 109.92/15.64 | | | | | | | | | | | | | | (3177) ~ (all_53_7 = e2)
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | REF_CLOSE: (132), (201), (202), (260), (261), (3024), (3064),
% 109.92/15.64 | | | | | | | | | | | | | | (3065), (3153), (3172), (3177) are inconsistent by
% 109.92/15.64 | | | | | | | | | | | | | | sub-proof #22.
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | Case 2:
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | (3178) all_55_4 = e1 | all_55_4 = e0
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | REF_CLOSE: (252), (2733), (3063), (3178) are inconsistent by
% 109.92/15.64 | | | | | | | | | | | | | | sub-proof #104.
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | End of split
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | Case 2:
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | (3179) all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | REF_CLOSE: (3155), (3160), (3163), (3164), (3179) are
% 109.92/15.64 | | | | | | | | | | | | | inconsistent by sub-proof #65.
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | End of split
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | End of split
% 109.92/15.64 | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | Case 2:
% 109.92/15.64 | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | (3180) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 109.92/15.64 | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 109.92/15.64 | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 109.92/15.64 | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 109.92/15.64 | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | BETA: splitting (3180) gives:
% 109.92/15.64 | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | Case 1:
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | (3181) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 109.92/15.64 | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | ALPHA: (3181) implies:
% 109.92/15.64 | | | | | | | | | | | | (3182) ~ (all_52_2 = e0)
% 109.92/15.64 | | | | | | | | | | | | (3183) op(e0, e2) = all_52_2
% 109.92/15.64 | | | | | | | | | | | | (3184) op(e2, e0) = e2
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 109.92/15.64 | | | | | | | | | | | | all_52_2, e2, e0, simplifying with (162), (3183)
% 109.92/15.64 | | | | | | | | | | | | gives:
% 109.92/15.64 | | | | | | | | | | | | (3185) all_53_3 = all_52_2
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e2,
% 109.92/15.64 | | | | | | | | | | | | e0, e2, simplifying with (168), (3184) gives:
% 109.92/15.64 | | | | | | | | | | | | (3186) all_53_8 = e2
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | COMBINE_EQS: (250), (3185) imply:
% 109.92/15.64 | | | | | | | | | | | | (3187) all_55_2 = all_52_2
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | REDUCE: (144), (3185) imply:
% 109.92/15.64 | | | | | | | | | | | | (3188) ~ (all_53_7 = all_52_2)
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | SIMP: (3188) implies:
% 109.92/15.64 | | | | | | | | | | | | (3189) ~ (all_53_7 = all_52_2)
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | REDUCE: (3023), (3185) imply:
% 109.92/15.64 | | | | | | | | | | | | (3190) ~ (all_52_2 = e3)
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | REDUCE: (2732), (3185) imply:
% 109.92/15.64 | | | | | | | | | | | | (3191) ~ (all_52_2 = e1)
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | REDUCE: (138), (3186) imply:
% 109.92/15.64 | | | | | | | | | | | | (3192) ~ (all_53_4 = e2)
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | BETA: splitting (204) gives:
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | Case 1:
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | (3193) all_55_4 = e3
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | COMBINE_EQS: (252), (3193) imply:
% 109.92/15.64 | | | | | | | | | | | | | (3194) all_53_4 = e3
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | REDUCE: (140), (3194) imply:
% 109.92/15.64 | | | | | | | | | | | | | (3195) ~ (all_53_6 = e3)
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | SIMP: (3195) implies:
% 109.92/15.64 | | | | | | | | | | | | | (3196) ~ (all_53_6 = e3)
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | REDUCE: (139), (3194) imply:
% 109.92/15.64 | | | | | | | | | | | | | (3197) ~ (all_53_7 = e3)
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | BETA: splitting (206) gives:
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | Case 1:
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | (3198) all_55_2 = e3
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | COMBINE_EQS: (3187), (3198) imply:
% 109.92/15.64 | | | | | | | | | | | | | | (3199) all_52_2 = e3
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | REDUCE: (3190), (3199) imply:
% 109.92/15.64 | | | | | | | | | | | | | | (3200) $false
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | CLOSE: (3200) is inconsistent.
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | Case 2:
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | (3201) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | BETA: splitting (3201) gives:
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | Case 1:
% 109.92/15.64 | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | (3202) all_55_2 = e2
% 109.92/15.64 | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | COMBINE_EQS: (3187), (3202) imply:
% 109.92/15.64 | | | | | | | | | | | | | | | (3203) all_52_2 = e2
% 109.92/15.64 | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | REDUCE: (3189), (3203) imply:
% 109.92/15.64 | | | | | | | | | | | | | | | (3204) ~ (all_53_7 = e2)
% 109.92/15.64 | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | REF_CLOSE: (132), (201), (202), (260), (261), (3024), (3064),
% 109.92/15.64 | | | | | | | | | | | | | | | (3065), (3153), (3196), (3204) are inconsistent by
% 109.92/15.64 | | | | | | | | | | | | | | | sub-proof #22.
% 109.92/15.64 | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | Case 2:
% 109.92/15.64 | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | (3205) all_55_2 = e1 | all_55_2 = e0
% 109.92/15.64 | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | REF_CLOSE: (3182), (3187), (3191), (3205) are inconsistent by
% 109.92/15.64 | | | | | | | | | | | | | | | sub-proof #21.
% 109.92/15.64 | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | End of split
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | End of split
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | Case 2:
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | (3206) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | REF_CLOSE: (252), (2733), (3063), (3192), (3206) are
% 109.92/15.64 | | | | | | | | | | | | | inconsistent by sub-proof #24.
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | End of split
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | Case 2:
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | (3207) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 109.92/15.64 | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | ALPHA: (3207) implies:
% 109.92/15.64 | | | | | | | | | | | | (3208) op(e1, e0) = e1
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | REF_CLOSE: (164), (2733), (3208), (function-axioms) are
% 109.92/15.64 | | | | | | | | | | | | inconsistent by sub-proof #226.
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | End of split
% 109.92/15.64 | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | End of split
% 109.92/15.64 | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | End of split
% 109.92/15.64 | | | | | | | | |
% 109.92/15.64 | | | | | | | | End of split
% 109.92/15.64 | | | | | | | |
% 109.92/15.64 | | | | | | | Case 2:
% 109.92/15.64 | | | | | | | |
% 109.92/15.64 | | | | | | | | (3209) all_18_2 = e3
% 109.92/15.64 | | | | | | | | (3210) op(e3, e3) = all_18_1 & $i(all_18_1) & ( ~ (all_18_1 =
% 109.92/15.64 | | | | | | | | e2) | ( ~ (all_18_0 = e0) & op(e2, e3) = all_18_0
% 109.92/15.64 | | | | | | | | & $i(all_18_0)))
% 109.92/15.64 | | | | | | | |
% 109.92/15.64 | | | | | | | | ALPHA: (3210) implies:
% 109.92/15.64 | | | | | | | | (3211) op(e3, e3) = all_18_1
% 109.92/15.64 | | | | | | | | (3212) ~ (all_18_1 = e2) | ( ~ (all_18_0 = e0) & op(e2, e3)
% 109.92/15.64 | | | | | | | | = all_18_0 & $i(all_18_0))
% 109.92/15.64 | | | | | | | |
% 109.92/15.64 | | | | | | | | COMBINE_EQS: (2746), (3209) imply:
% 109.92/15.64 | | | | | | | | (3213) all_6_1 = e3
% 109.92/15.64 | | | | | | | |
% 109.92/15.64 | | | | | | | | SIMP: (3213) implies:
% 109.92/15.64 | | | | | | | | (3214) all_6_1 = e3
% 109.92/15.64 | | | | | | | |
% 109.92/15.64 | | | | | | | | COMBINE_EQS: (2747), (3214) imply:
% 109.92/15.64 | | | | | | | | (3215) all_20_2 = e3
% 109.92/15.64 | | | | | | | |
% 109.92/15.64 | | | | | | | | COMBINE_EQS: (2743), (3214) imply:
% 109.92/15.64 | | | | | | | | (3216) all_38_1 = e3
% 109.92/15.64 | | | | | | | |
% 109.92/15.64 | | | | | | | | REDUCE: (2751), (3214) imply:
% 109.92/15.64 | | | | | | | | (3217) ~ (all_53_1 = e3)
% 109.92/15.64 | | | | | | | |
% 109.92/15.64 | | | | | | | | REDUCE: (2752), (3214) imply:
% 109.92/15.64 | | | | | | | | (3218) ~ (all_53_4 = e3)
% 109.92/15.64 | | | | | | | |
% 109.92/15.64 | | | | | | | | REDUCE: (2756), (3214) imply:
% 109.92/15.64 | | | | | | | | (3219) ~ (all_53_13 = e3)
% 109.92/15.64 | | | | | | | |
% 109.92/15.64 | | | | | | | | BETA: splitting (60) gives:
% 109.92/15.64 | | | | | | | |
% 109.92/15.64 | | | | | | | | Case 1:
% 109.92/15.64 | | | | | | | | |
% 109.92/15.64 | | | | | | | | | (3220) ~ (all_20_2 = e3)
% 109.92/15.64 | | | | | | | | |
% 109.92/15.64 | | | | | | | | | REDUCE: (3215), (3220) imply:
% 109.92/15.64 | | | | | | | | | (3221) $false
% 109.92/15.64 | | | | | | | | |
% 109.92/15.64 | | | | | | | | | CLOSE: (3221) is inconsistent.
% 109.92/15.64 | | | | | | | | |
% 109.92/15.64 | | | | | | | | Case 2:
% 109.92/15.64 | | | | | | | | |
% 109.92/15.64 | | | | | | | | | (3222) op(e3, e3) = all_20_1 & $i(all_20_1) & ( ~ (all_20_1
% 109.92/15.64 | | | | | | | | | = e0) | ( ~ (all_20_0 = e2) & op(e0, e3) =
% 109.92/15.64 | | | | | | | | | all_20_0 & $i(all_20_0)))
% 109.92/15.64 | | | | | | | | |
% 109.92/15.64 | | | | | | | | | ALPHA: (3222) implies:
% 109.92/15.64 | | | | | | | | | (3223) op(e3, e3) = all_20_1
% 109.92/15.64 | | | | | | | | |
% 109.92/15.64 | | | | | | | | | BETA: splitting (234) gives:
% 109.92/15.64 | | | | | | | | |
% 109.92/15.64 | | | | | | | | | Case 1:
% 109.92/15.64 | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | (3224) (all_57_28 = e3 & op(e3, e0) = e3) | (all_57_29 =
% 109.92/15.64 | | | | | | | | | | e3 & op(e2, e0) = e3)
% 109.92/15.64 | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | BETA: splitting (3224) gives:
% 109.92/15.64 | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | Case 1:
% 109.92/15.64 | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | (3225) all_57_28 = e3 & op(e3, e0) = e3
% 109.92/15.64 | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | ALPHA: (3225) implies:
% 109.92/15.64 | | | | | | | | | | | (3226) op(e3, e0) = e3
% 109.92/15.64 | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | BETA: splitting (2741) gives:
% 109.92/15.64 | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | Case 1:
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | (3227) ~ (all_38_1 = e3)
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | REDUCE: (3216), (3227) imply:
% 109.92/15.64 | | | | | | | | | | | | (3228) $false
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | CLOSE: (3228) is inconsistent.
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | Case 2:
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | (3229) ~ (all_38_0 = e2) & op(e3, e1) = all_38_0 &
% 109.92/15.64 | | | | | | | | | | | | $i(all_38_0)
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | ALPHA: (3229) implies:
% 109.92/15.64 | | | | | | | | | | | | (3230) ~ (all_38_0 = e2)
% 109.92/15.64 | | | | | | | | | | | | (3231) op(e3, e1) = all_38_0
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | BETA: splitting (235) gives:
% 109.92/15.64 | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | Case 1:
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | (3232) (all_57_24 = e3 & op(e0, e3) = e3) | (all_57_25 =
% 109.92/15.64 | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | BETA: splitting (3232) gives:
% 109.92/15.64 | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | Case 1:
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | (3233) all_57_24 = e3 & op(e0, e3) = e3
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | ALPHA: (3233) implies:
% 109.92/15.64 | | | | | | | | | | | | | | (3234) op(e0, e3) = e3
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e3,
% 109.92/15.64 | | | | | | | | | | | | | | e3, e0, simplifying with (163), (3234) gives:
% 109.92/15.64 | | | | | | | | | | | | | | (3235) all_53_2 = e3
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 109.92/15.64 | | | | | | | | | | | | | | e3, e0, e3, simplifying with (172), (3226) gives:
% 109.92/15.64 | | | | | | | | | | | | | | (3236) all_53_12 = e3
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 109.92/15.64 | | | | | | | | | | | | | | all_38_0, e1, e3, simplifying with (173), (3231)
% 109.92/15.64 | | | | | | | | | | | | | | gives:
% 109.92/15.64 | | | | | | | | | | | | | | (3237) all_53_13 = all_38_0
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 109.92/15.64 | | | | | | | | | | | | | | all_20_1, e3, e3, simplifying with (35), (3223)
% 109.92/15.64 | | | | | | | | | | | | | | gives:
% 109.92/15.64 | | | | | | | | | | | | | | (3238) all_20_1 = all_4_2
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 109.92/15.64 | | | | | | | | | | | | | | all_20_1, e3, e3, simplifying with (3211), (3223)
% 109.92/15.64 | | | | | | | | | | | | | | gives:
% 109.92/15.64 | | | | | | | | | | | | | | (3239) all_20_1 = all_18_1
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | COMBINE_EQS: (3238), (3239) imply:
% 109.92/15.64 | | | | | | | | | | | | | | (3240) all_18_1 = all_4_2
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | COMBINE_EQS: (273), (3237) imply:
% 109.92/15.64 | | | | | | | | | | | | | | (3241) all_55_13 = all_38_0
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | REDUCE: (149), (3237) imply:
% 109.92/15.64 | | | | | | | | | | | | | | (3242) ~ (all_53_1 = all_38_0)
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | REDUCE: (146), (3235) imply:
% 109.92/15.64 | | | | | | | | | | | | | | (3243) ~ (all_53_10 = e3)
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | SIMP: (3243) implies:
% 109.92/15.64 | | | | | | | | | | | | | | (3244) ~ (all_53_10 = e3)
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | REDUCE: (374), (3236) imply:
% 109.92/15.64 | | | | | | | | | | | | | | (3245) ~ (all_4_2 = e3)
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | SIMP: (3245) implies:
% 109.92/15.64 | | | | | | | | | | | | | | (3246) ~ (all_4_2 = e3)
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | REDUCE: (375), (3237) imply:
% 109.92/15.64 | | | | | | | | | | | | | | (3247) ~ (all_38_0 = all_4_2)
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | REDUCE: (3219), (3237) imply:
% 109.92/15.64 | | | | | | | | | | | | | | (3248) ~ (all_38_0 = e3)
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 109.92/15.64 | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | Case 1:
% 109.92/15.64 | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | (3249) ~ (all_26_2 = e2)
% 109.92/15.64 | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | REDUCE: (316), (3249) imply:
% 109.92/15.64 | | | | | | | | | | | | | | | (3250) ~ (all_4_2 = e2)
% 109.92/15.64 | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 109.92/15.64 | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | Case 1:
% 109.92/15.64 | | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | | (3251) all_55_15 = e3
% 109.92/15.64 | | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | | REF_CLOSE: (339), (3246), (3251) are inconsistent by
% 109.92/15.64 | | | | | | | | | | | | | | | | sub-proof #140.
% 109.92/15.64 | | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | Case 2:
% 109.92/15.64 | | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | | (3252) ~ (all_55_15 = e3)
% 109.92/15.64 | | | | | | | | | | | | | | | | (3253) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 109.92/15.64 | | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | | BETA: splitting (3253) gives:
% 109.92/15.64 | | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.64 | | | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | | | (3254) all_55_15 = e2
% 109.92/15.64 | | | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | | | REF_CLOSE: (339), (3250), (3254) are inconsistent by
% 109.92/15.64 | | | | | | | | | | | | | | | | | sub-proof #193.
% 109.92/15.64 | | | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.64 | | | | | | | | | | | | | | | | |
% 109.92/15.64 | | | | | | | | | | | | | | | | | (3255) ~ (all_55_15 = e2)
% 109.92/15.65 | | | | | | | | | | | | | | | | | (3256) all_55_15 = e1 | all_55_15 = e0
% 109.92/15.65 | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | BETA: splitting (3256) gives:
% 109.92/15.65 | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.65 | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | (3257) all_55_15 = e1
% 109.92/15.65 | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (3257) imply:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | (3258) all_4_2 = e1
% 109.92/15.65 | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | SIMP: (3258) implies:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | (3259) all_4_2 = e1
% 109.92/15.65 | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | REDUCE: (371), (3259) imply:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | (3260) ~ (all_53_10 = e1)
% 109.92/15.65 | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | REDUCE: (3247), (3259) imply:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | (3261) ~ (all_38_0 = e1)
% 109.92/15.65 | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | REDUCE: (3246), (3259) imply:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | (3262) ~ (e3 = e1)
% 109.92/15.65 | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | REDUCE: (3250), (3259) imply:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | (3263) ~ (e2 = e1)
% 109.92/15.65 | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | SIMP: (3263) implies:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | (3264) ~ (e2 = e1)
% 109.92/15.65 | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 109.92/15.65 | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | (3265) all_55_13 = e3
% 109.92/15.65 | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3241), (3248), (3265) are inconsistent by
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | sub-proof #30.
% 109.92/15.65 | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | (3266) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 109.92/15.65 | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | (3267) (all_57_72 = e1 & op(e2, e3) = e1) | (all_57_73 =
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e2) = e1)
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (171), (3028), (3260), (3267),
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | #20.
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | (3268) (all_57_74 = e1 & op(e2, e1) = e1) | (all_57_75 =
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3268) gives:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | (3269) all_57_74 = e1 & op(e2, e1) = e1
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3269) implies:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | (3270) op(e2, e1) = e1
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3266) gives:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | (3271) all_55_13 = e2
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3230), (3241), (3271) are inconsistent by
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | sub-proof #29.
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | (3272) all_55_13 = e1 | all_55_13 = e0
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3272) gives:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | (3273) all_55_13 = e1
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3241), (3273) imply:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | (3274) all_38_0 = e1
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3274) implies:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | (3275) all_38_0 = e1
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3261), (3275) imply:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | (3276) $false
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3276) is inconsistent.
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | (3277) all_55_13 = e0
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3241), (3277) imply:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | (3278) all_38_0 = e0
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3278) implies:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | (3279) all_38_0 = e0
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3242), (3279) imply:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | (3280) ~ (all_53_1 = e0)
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | | (3281) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3281) implies:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | | (3282) op(e3, e1) = e3
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (3219), (3282), (function-axioms) are
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #232.
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | | (3283) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3264), (3270), (3280), (3283),
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | | #25.
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | (3284) all_57_75 = e1 & op(e2, e0) = e1
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3284) implies:
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | (3285) op(e2, e0) = e1
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (2734), (3285), (function-axioms) are
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #173.
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.65 | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | (3286) all_55_15 = e0
% 109.92/15.65 | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | | REF_CLOSE: (339), (378), (3286) are inconsistent by sub-proof
% 109.92/15.65 | | | | | | | | | | | | | | | | | | #192.
% 109.92/15.65 | | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | Case 2:
% 109.92/15.65 | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | (3287) all_26_2 = e2
% 109.92/15.65 | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | COMBINE_EQS: (316), (3287) imply:
% 109.92/15.65 | | | | | | | | | | | | | | | (3288) all_4_2 = e2
% 109.92/15.65 | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | SIMP: (3288) implies:
% 109.92/15.65 | | | | | | | | | | | | | | | (3289) all_4_2 = e2
% 109.92/15.65 | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | COMBINE_EQS: (3240), (3289) imply:
% 109.92/15.65 | | | | | | | | | | | | | | | (3290) all_18_1 = e2
% 109.92/15.65 | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | REDUCE: (371), (3289) imply:
% 109.92/15.65 | | | | | | | | | | | | | | | (3291) ~ (all_53_10 = e2)
% 109.92/15.65 | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | | REF_CLOSE: (6), (107), (131), (167), (171), (197), (271),
% 109.92/15.65 | | | | | | | | | | | | | | | (3212), (3234), (3244), (3290), (3291),
% 109.92/15.65 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.92/15.65 | | | | | | | | | | | | | | | #54.
% 109.92/15.65 | | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | Case 2:
% 109.92/15.65 | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | (3292) all_57_25 = e3 & op(e0, e2) = e3
% 109.92/15.65 | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | ALPHA: (3292) implies:
% 109.92/15.65 | | | | | | | | | | | | | | (3293) op(e0, e2) = e3
% 109.92/15.65 | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | REF_CLOSE: (162), (3023), (3293), (function-axioms) are
% 109.92/15.65 | | | | | | | | | | | | | | inconsistent by sub-proof #137.
% 109.92/15.65 | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | Case 2:
% 109.92/15.65 | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | (3294) (all_57_26 = e3 & op(e0, e1) = e3) | (all_57_27 =
% 109.92/15.65 | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 109.92/15.65 | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | BETA: splitting (3294) gives:
% 109.92/15.65 | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | Case 1:
% 109.92/15.65 | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | (3295) all_57_26 = e3 & op(e0, e1) = e3
% 109.92/15.65 | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | ALPHA: (3295) implies:
% 109.92/15.65 | | | | | | | | | | | | | | (3296) op(e0, e1) = e3
% 109.92/15.65 | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | REF_CLOSE: (161), (3217), (3296), (function-axioms) are
% 109.92/15.65 | | | | | | | | | | | | | | inconsistent by sub-proof #145.
% 109.92/15.65 | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | Case 2:
% 109.92/15.65 | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | (3297) all_57_27 = e3 & op(e0, e0) = e3
% 109.92/15.65 | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | ALPHA: (3297) implies:
% 109.92/15.65 | | | | | | | | | | | | | | (3298) op(e0, e0) = e3
% 109.92/15.65 | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | | REF_CLOSE: (7), (2736), (3298), (function-axioms) are
% 109.92/15.65 | | | | | | | | | | | | | | inconsistent by sub-proof #165.
% 109.92/15.65 | | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | Case 2:
% 109.92/15.65 | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | (3299) all_57_29 = e3 & op(e2, e0) = e3
% 109.92/15.65 | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | ALPHA: (3299) implies:
% 109.92/15.65 | | | | | | | | | | | (3300) op(e2, e0) = e3
% 109.92/15.65 | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | REF_CLOSE: (168), (3025), (3300), (function-axioms) are
% 109.92/15.65 | | | | | | | | | | | inconsistent by sub-proof #194.
% 109.92/15.65 | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | Case 2:
% 109.92/15.65 | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | (3301) (all_57_30 = e3 & op(e1, e0) = e3) | (all_57_31 =
% 109.92/15.65 | | | | | | | | | | e3 & op(e0, e0) = e3)
% 109.92/15.65 | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | REF_CLOSE: (7), (164), (2736), (3218), (3301),
% 109.92/15.65 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.92/15.65 | | | | | | | | | | #42.
% 109.92/15.65 | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | End of split
% 109.92/15.65 | | | | | | | | |
% 109.92/15.65 | | | | | | | | End of split
% 109.92/15.65 | | | | | | | |
% 109.92/15.65 | | | | | | | End of split
% 109.92/15.65 | | | | | | |
% 109.92/15.65 | | | | | | Case 2:
% 109.92/15.65 | | | | | | |
% 109.92/15.65 | | | | | | | (3302) all_14_2 = e2
% 109.92/15.65 | | | | | | | (3303) op(e2, e2) = all_14_1 & $i(all_14_1) & ( ~ (all_14_1 =
% 109.92/15.65 | | | | | | | e3) | ( ~ (all_14_0 = e0) & op(e3, e2) = all_14_0 &
% 109.92/15.65 | | | | | | | $i(all_14_0)))
% 109.92/15.65 | | | | | | |
% 109.92/15.65 | | | | | | | ALPHA: (3303) implies:
% 109.92/15.65 | | | | | | | (3304) op(e2, e2) = all_14_1
% 109.92/15.65 | | | | | | | (3305) ~ (all_14_1 = e3) | ( ~ (all_14_0 = e0) & op(e3, e2) =
% 109.92/15.65 | | | | | | | all_14_0 & $i(all_14_0))
% 109.92/15.65 | | | | | | |
% 109.92/15.65 | | | | | | | COMBINE_EQS: (2745), (3302) imply:
% 109.92/15.65 | | | | | | | (3306) all_6_1 = e2
% 109.92/15.65 | | | | | | |
% 109.92/15.65 | | | | | | | SIMP: (3306) implies:
% 109.92/15.65 | | | | | | | (3307) all_6_1 = e2
% 109.92/15.65 | | | | | | |
% 109.92/15.65 | | | | | | | COMBINE_EQS: (2749), (3307) imply:
% 109.92/15.65 | | | | | | | (3308) all_44_2 = e2
% 109.92/15.65 | | | | | | |
% 109.92/15.65 | | | | | | | REDUCE: (2751), (3307) imply:
% 109.92/15.65 | | | | | | | (3309) ~ (all_53_1 = e2)
% 109.92/15.65 | | | | | | |
% 109.92/15.65 | | | | | | | REDUCE: (2752), (3307) imply:
% 109.92/15.65 | | | | | | | (3310) ~ (all_53_4 = e2)
% 109.92/15.65 | | | | | | |
% 109.92/15.65 | | | | | | | REDUCE: (2754), (3307) imply:
% 109.92/15.65 | | | | | | | (3311) ~ (all_53_7 = e2)
% 109.92/15.65 | | | | | | |
% 109.92/15.65 | | | | | | | REDUCE: (2727), (3307) imply:
% 109.92/15.65 | | | | | | | (3312) op(e1, e1) = e2
% 109.92/15.65 | | | | | | |
% 109.92/15.65 | | | | | | | BETA: splitting (96) gives:
% 109.92/15.65 | | | | | | |
% 109.92/15.65 | | | | | | | Case 1:
% 109.92/15.65 | | | | | | | |
% 109.92/15.65 | | | | | | | | (3313) ~ (all_44_2 = e2)
% 109.92/15.65 | | | | | | | |
% 109.92/15.65 | | | | | | | | REDUCE: (3308), (3313) imply:
% 109.92/15.65 | | | | | | | | (3314) $false
% 109.92/15.65 | | | | | | | |
% 109.92/15.65 | | | | | | | | CLOSE: (3314) is inconsistent.
% 109.92/15.65 | | | | | | | |
% 109.92/15.65 | | | | | | | Case 2:
% 109.92/15.65 | | | | | | | |
% 109.92/15.65 | | | | | | | | (3315) op(e2, e2) = all_44_1 & $i(all_44_1) & ( ~ (all_44_1 =
% 109.92/15.65 | | | | | | | | e0) | ( ~ (all_44_0 = e3) & op(e0, e2) = all_44_0
% 109.92/15.65 | | | | | | | | & $i(all_44_0)))
% 109.92/15.65 | | | | | | | |
% 109.92/15.65 | | | | | | | | ALPHA: (3315) implies:
% 109.92/15.65 | | | | | | | | (3316) op(e2, e2) = all_44_1
% 109.92/15.65 | | | | | | | |
% 109.92/15.65 | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_44_1,
% 109.92/15.65 | | | | | | | | e2, e2, simplifying with (3028), (3316) gives:
% 109.92/15.65 | | | | | | | | (3317) all_44_1 = e3
% 109.92/15.65 | | | | | | | |
% 109.92/15.65 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 109.92/15.65 | | | | | | | | all_44_1, e2, e2, simplifying with (3304), (3316)
% 109.92/15.65 | | | | | | | | gives:
% 109.92/15.65 | | | | | | | | (3318) all_44_1 = all_14_1
% 109.92/15.65 | | | | | | | |
% 109.92/15.65 | | | | | | | | COMBINE_EQS: (3317), (3318) imply:
% 109.92/15.65 | | | | | | | | (3319) all_14_1 = e3
% 109.92/15.65 | | | | | | | |
% 109.92/15.65 | | | | | | | | BETA: splitting (3305) gives:
% 109.92/15.65 | | | | | | | |
% 109.92/15.65 | | | | | | | | Case 1:
% 109.92/15.65 | | | | | | | | |
% 109.92/15.65 | | | | | | | | | (3320) ~ (all_14_1 = e3)
% 109.92/15.65 | | | | | | | | |
% 109.92/15.65 | | | | | | | | | REDUCE: (3319), (3320) imply:
% 109.92/15.65 | | | | | | | | | (3321) $false
% 109.92/15.65 | | | | | | | | |
% 109.92/15.65 | | | | | | | | | CLOSE: (3321) is inconsistent.
% 109.92/15.65 | | | | | | | | |
% 109.92/15.65 | | | | | | | | Case 2:
% 109.92/15.65 | | | | | | | | |
% 109.92/15.65 | | | | | | | | | (3322) ~ (all_14_0 = e0) & op(e3, e2) = all_14_0 &
% 109.92/15.65 | | | | | | | | | $i(all_14_0)
% 109.92/15.65 | | | | | | | | |
% 109.92/15.65 | | | | | | | | | ALPHA: (3322) implies:
% 109.92/15.65 | | | | | | | | | (3323) ~ (all_14_0 = e0)
% 109.92/15.65 | | | | | | | | | (3324) op(e3, e2) = all_14_0
% 109.92/15.65 | | | | | | | | |
% 109.92/15.65 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 109.92/15.65 | | | | | | | | | all_14_0, e2, e3, simplifying with (174), (3324)
% 109.92/15.65 | | | | | | | | | gives:
% 109.92/15.65 | | | | | | | | | (3325) all_53_15 = all_14_0
% 109.92/15.65 | | | | | | | | |
% 109.92/15.65 | | | | | | | | | COMBINE_EQS: (274), (3325) imply:
% 109.92/15.65 | | | | | | | | | (3326) all_55_14 = all_14_0
% 109.92/15.65 | | | | | | | | |
% 109.92/15.65 | | | | | | | | | REDUCE: (142), (3325) imply:
% 109.92/15.65 | | | | | | | | | (3327) ~ (all_53_3 = all_14_0)
% 109.92/15.65 | | | | | | | | |
% 109.92/15.65 | | | | | | | | | REDUCE: (128), (3325) imply:
% 109.92/15.65 | | | | | | | | | (3328) ~ (all_53_7 = all_14_0)
% 109.92/15.65 | | | | | | | | |
% 109.92/15.65 | | | | | | | | | REDUCE: (377), (3325) imply:
% 109.92/15.65 | | | | | | | | | (3329) ~ (all_14_0 = all_4_2)
% 109.92/15.65 | | | | | | | | |
% 109.92/15.65 | | | | | | | | | REDUCE: (3027), (3325) imply:
% 109.92/15.65 | | | | | | | | | (3330) ~ (all_14_0 = e3)
% 109.92/15.65 | | | | | | | | |
% 109.92/15.65 | | | | | | | | | BETA: splitting (69) gives:
% 109.92/15.65 | | | | | | | | |
% 109.92/15.65 | | | | | | | | | Case 1:
% 109.92/15.65 | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | (3331) ~ (all_26_2 = e2)
% 109.92/15.65 | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | REDUCE: (316), (3331) imply:
% 109.92/15.65 | | | | | | | | | | (3332) ~ (all_4_2 = e2)
% 109.92/15.65 | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | BETA: splitting (81) gives:
% 109.92/15.65 | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | Case 1:
% 109.92/15.65 | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | (3333) ~ (all_34_2 = e1)
% 109.92/15.65 | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | REDUCE: (311), (3333) imply:
% 109.92/15.65 | | | | | | | | | | | (3334) ~ (all_4_2 = e1)
% 109.92/15.65 | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | BETA: splitting (193) gives:
% 109.92/15.65 | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | Case 1:
% 109.92/15.65 | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | (3335) all_55_15 = e3
% 109.92/15.65 | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | COMBINE_EQS: (339), (3335) imply:
% 109.92/15.65 | | | | | | | | | | | | (3336) all_4_2 = e3
% 109.92/15.65 | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | SIMP: (3336) implies:
% 109.92/15.65 | | | | | | | | | | | | (3337) all_4_2 = e3
% 109.92/15.65 | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | REDUCE: (374), (3337) imply:
% 109.92/15.65 | | | | | | | | | | | | (3338) ~ (all_53_12 = e3)
% 109.92/15.65 | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | REDUCE: (375), (3337) imply:
% 109.92/15.65 | | | | | | | | | | | | (3339) ~ (all_53_13 = e3)
% 109.92/15.65 | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | BETA: splitting (110) gives:
% 109.92/15.65 | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | Case 1:
% 109.92/15.65 | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | (3340) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 109.92/15.65 | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 109.92/15.65 | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | ALPHA: (3340) implies:
% 109.92/15.65 | | | | | | | | | | | | | (3341) op(e3, e0) = e3
% 109.92/15.65 | | | | | | | | | | | | |
% 109.92/15.65 | | | | | | | | | | | | | REF_CLOSE: (172), (3338), (3341), (function-axioms) are
% 109.92/15.65 | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 109.92/15.65 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | (3342) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 109.92/15.66 | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 109.92/15.66 | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 109.92/15.66 | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | BETA: splitting (3342) gives:
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | (3343) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 109.92/15.66 | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | ALPHA: (3343) implies:
% 109.92/15.66 | | | | | | | | | | | | | | (3344) op(e2, e0) = e2
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | (3345) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 109.92/15.66 | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | ALPHA: (3345) implies:
% 109.92/15.66 | | | | | | | | | | | | | | | (3346) op(e3, e1) = e3
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | REF_CLOSE: (173), (3339), (3346), (function-axioms) are
% 109.92/15.66 | | | | | | | | | | | | | | | inconsistent by sub-proof #232.
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | (3347) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.92/15.66 | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 109.92/15.66 | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.92/15.66 | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | BETA: splitting (3347) gives:
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | (3348) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.92/15.66 | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | ALPHA: (3348) implies:
% 109.92/15.66 | | | | | | | | | | | | | | | | (3349) op(e2, e1) = e2
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | REF_CLOSE: (127), (168), (169), (3344), (3349),
% 109.92/15.66 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.92/15.66 | | | | | | | | | | | | | | | | #186.
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | (3350) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.92/15.66 | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | ALPHA: (3350) implies:
% 109.92/15.66 | | | | | | | | | | | | | | | | (3351) op(e0, e1) = e0
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (161), (169), (173), (226), (3026),
% 109.92/15.66 | | | | | | | | | | | | | | | | (3312), (3339), (3351), (function-axioms) are
% 109.92/15.66 | | | | | | | | | | | | | | | | inconsistent by sub-proof #79.
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | End of split
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | End of split
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | (3352) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 109.92/15.66 | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | ALPHA: (3352) implies:
% 109.92/15.66 | | | | | | | | | | | | | | (3353) op(e1, e0) = e1
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | REF_CLOSE: (164), (2733), (3353), (function-axioms) are
% 109.92/15.66 | | | | | | | | | | | | | | inconsistent by sub-proof #226.
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | End of split
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | End of split
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | (3354) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | REF_CLOSE: (339), (378), (3332), (3334), (3354) are
% 109.92/15.66 | | | | | | | | | | | | inconsistent by sub-proof #191.
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | End of split
% 109.92/15.66 | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | (3355) all_34_2 = e1
% 109.92/15.66 | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | COMBINE_EQS: (311), (3355) imply:
% 109.92/15.66 | | | | | | | | | | | (3356) all_4_2 = e1
% 109.92/15.66 | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | REDUCE: (371), (3356) imply:
% 109.92/15.66 | | | | | | | | | | | (3357) ~ (all_53_10 = e1)
% 109.92/15.66 | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | REDUCE: (3329), (3356) imply:
% 109.92/15.66 | | | | | | | | | | | (3358) ~ (all_14_0 = e1)
% 109.92/15.66 | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | BETA: splitting (194) gives:
% 109.92/15.66 | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | (3359) all_55_14 = e3
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | REF_CLOSE: (3326), (3330), (3359) are inconsistent by
% 109.92/15.66 | | | | | | | | | | | | sub-proof #95.
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | (3360) all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | BETA: splitting (223) gives:
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | (3361) (all_57_72 = e1 & op(e2, e3) = e1) | (all_57_73 =
% 109.92/15.66 | | | | | | | | | | | | | e1 & op(e2, e2) = e1)
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | REF_CLOSE: (7), (171), (3028), (3357), (3361),
% 109.92/15.66 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.92/15.66 | | | | | | | | | | | | | #20.
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | (3362) (all_57_74 = e1 & op(e2, e1) = e1) | (all_57_75 =
% 109.92/15.66 | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | BETA: splitting (3362) gives:
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | (3363) all_57_74 = e1 & op(e2, e1) = e1
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | ALPHA: (3363) implies:
% 109.92/15.66 | | | | | | | | | | | | | | (3364) op(e2, e1) = e1
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | BETA: splitting (3360) gives:
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | (3365) all_55_14 = e2
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | COMBINE_EQS: (3326), (3365) imply:
% 109.92/15.66 | | | | | | | | | | | | | | | (3366) all_14_0 = e2
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | REDUCE: (3327), (3366) imply:
% 109.92/15.66 | | | | | | | | | | | | | | | (3367) ~ (all_53_3 = e2)
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | REDUCE: (3358), (3366) imply:
% 109.92/15.66 | | | | | | | | | | | | | | | (3368) ~ (e2 = e1)
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | (3369) all_55_2 = e3
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (3369) imply:
% 109.92/15.66 | | | | | | | | | | | | | | | | (3370) all_53_3 = e3
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | REDUCE: (3023), (3370) imply:
% 109.92/15.66 | | | | | | | | | | | | | | | | (3371) $false
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | CLOSE: (3371) is inconsistent.
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | (3372) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | BETA: splitting (3372) gives:
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | (3373) all_55_2 = e2
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (3373) imply:
% 109.92/15.66 | | | | | | | | | | | | | | | | | (3374) all_53_3 = e2
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | REDUCE: (3367), (3374) imply:
% 109.92/15.66 | | | | | | | | | | | | | | | | | (3375) $false
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | CLOSE: (3375) is inconsistent.
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | (3376) all_55_2 = e1 | all_55_2 = e0
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | BETA: splitting (3376) gives:
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | (3377) all_55_2 = e1
% 109.92/15.66 | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (3377) imply:
% 109.92/15.66 | | | | | | | | | | | | | | | | | | (3378) all_53_3 = e1
% 109.92/15.66 | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | REDUCE: (2732), (3378) imply:
% 109.92/15.66 | | | | | | | | | | | | | | | | | | (3379) $false
% 109.92/15.66 | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | CLOSE: (3379) is inconsistent.
% 109.92/15.66 | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | (3380) all_55_2 = e0
% 109.92/15.66 | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (3380) imply:
% 109.92/15.66 | | | | | | | | | | | | | | | | | | (3381) all_53_3 = e0
% 109.92/15.66 | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | REDUCE: (152), (3381) imply:
% 109.92/15.66 | | | | | | | | | | | | | | | | | | (3382) ~ (all_53_1 = e0)
% 109.92/15.66 | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 109.92/15.66 | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | | (3383) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 109.92/15.66 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 109.92/15.66 | | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (173), (207), (249), (2730), (3309),
% 109.92/15.66 | | | | | | | | | | | | | | | | | | | (3382), (3383), (function-axioms) are inconsistent
% 109.92/15.66 | | | | | | | | | | | | | | | | | | | by sub-proof #38.
% 109.92/15.66 | | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | | (3384) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.92/15.66 | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.92/15.66 | | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 109.92/15.66 | | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3364), (3368), (3382), (3384),
% 109.92/15.66 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.92/15.66 | | | | | | | | | | | | | | | | | | | #25.
% 109.92/15.66 | | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.66 | | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | End of split
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | End of split
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | End of split
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | (3385) all_55_14 = e1 | all_55_14 = e0
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | REF_CLOSE: (3323), (3326), (3358), (3385) are inconsistent by
% 109.92/15.66 | | | | | | | | | | | | | | | sub-proof #90.
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | End of split
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | (3386) all_57_75 = e1 & op(e2, e0) = e1
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | ALPHA: (3386) implies:
% 109.92/15.66 | | | | | | | | | | | | | | (3387) op(e2, e0) = e1
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | REF_CLOSE: (168), (2734), (3387), (function-axioms) are
% 109.92/15.66 | | | | | | | | | | | | | | inconsistent by sub-proof #173.
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | End of split
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | End of split
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | End of split
% 109.92/15.66 | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | End of split
% 109.92/15.66 | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | (3388) all_26_2 = e2
% 109.92/15.66 | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | COMBINE_EQS: (316), (3388) imply:
% 109.92/15.66 | | | | | | | | | | (3389) all_4_2 = e2
% 109.92/15.66 | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | REDUCE: (3329), (3389) imply:
% 109.92/15.66 | | | | | | | | | | (3390) ~ (all_14_0 = e2)
% 109.92/15.66 | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | BETA: splitting (194) gives:
% 109.92/15.66 | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | (3391) all_55_14 = e3
% 109.92/15.66 | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | REF_CLOSE: (3326), (3330), (3391) are inconsistent by
% 109.92/15.66 | | | | | | | | | | | sub-proof #95.
% 109.92/15.66 | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | (3392) all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 109.92/15.66 | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | BETA: splitting (3392) gives:
% 109.92/15.66 | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | (3393) all_55_14 = e2
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | REF_CLOSE: (3326), (3390), (3393) are inconsistent by
% 109.92/15.66 | | | | | | | | | | | | sub-proof #88.
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | (3394) all_55_14 = e1 | all_55_14 = e0
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | BETA: splitting (3394) gives:
% 109.92/15.66 | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | (3395) all_55_14 = e1
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | COMBINE_EQS: (3326), (3395) imply:
% 109.92/15.66 | | | | | | | | | | | | | (3396) all_14_0 = e1
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | SIMP: (3396) implies:
% 109.92/15.66 | | | | | | | | | | | | | (3397) all_14_0 = e1
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | REDUCE: (3328), (3397) imply:
% 109.92/15.66 | | | | | | | | | | | | | (3398) ~ (all_53_7 = e1)
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | BETA: splitting (108) gives:
% 109.92/15.66 | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | (3399) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 109.92/15.66 | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | ALPHA: (3399) implies:
% 109.92/15.66 | | | | | | | | | | | | | | (3400) op(e3, e2) = e3
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | REF_CLOSE: (174), (3027), (3400), (function-axioms) are
% 109.92/15.66 | | | | | | | | | | | | | | inconsistent by sub-proof #214.
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | (3401) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 109.92/15.66 | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 109.92/15.66 | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 109.92/15.66 | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | BETA: splitting (3401) gives:
% 109.92/15.66 | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | (3402) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 109.92/15.66 | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | ALPHA: (3402) implies:
% 109.92/15.66 | | | | | | | | | | | | | | | (3403) op(e1, e2) = e1
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | REF_CLOSE: (166), (3398), (3403), (function-axioms) are
% 109.92/15.66 | | | | | | | | | | | | | | | inconsistent by sub-proof #233.
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | (3404) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 109.92/15.66 | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | ALPHA: (3404) implies:
% 109.92/15.66 | | | | | | | | | | | | | | | (3405) op(e0, e2) = e0
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 109.92/15.66 | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | (3406) all_55_6 = e3
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3406) imply:
% 109.92/15.66 | | | | | | | | | | | | | | | | (3407) all_53_7 = e3
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | REDUCE: (3024), (3407) imply:
% 109.92/15.66 | | | | | | | | | | | | | | | | (3408) $false
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | CLOSE: (3408) is inconsistent.
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | (3409) all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | BETA: splitting (3409) gives:
% 109.92/15.66 | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | (3410) all_55_6 = e2
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3410) imply:
% 109.92/15.66 | | | | | | | | | | | | | | | | | (3411) all_53_7 = e2
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | REDUCE: (3311), (3411) imply:
% 109.92/15.66 | | | | | | | | | | | | | | | | | (3412) $false
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | CLOSE: (3412) is inconsistent.
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.66 | | | | | | | | | | | | | | | | | (3413) all_55_6 = e1 | all_55_6 = e0
% 109.92/15.66 | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | BETA: splitting (3413) gives:
% 109.92/15.67 | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.67 | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | (3414) all_55_6 = e1
% 109.92/15.67 | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3414) imply:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | (3415) all_53_7 = e1
% 109.92/15.67 | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | REDUCE: (3398), (3415) imply:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | (3416) $false
% 109.92/15.67 | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | CLOSE: (3416) is inconsistent.
% 109.92/15.67 | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.67 | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | (3417) all_55_6 = e0
% 109.92/15.67 | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3417) imply:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | (3418) all_53_7 = e0
% 109.92/15.67 | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | REDUCE: (144), (3418) imply:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | (3419) ~ (all_53_3 = e0)
% 109.92/15.67 | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | REDUCE: (139), (3418) imply:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | (3420) ~ (all_53_4 = e0)
% 109.92/15.67 | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 109.92/15.67 | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | (3421) all_55_4 = e3
% 109.92/15.67 | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (3421) imply:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | (3422) all_53_4 = e3
% 109.92/15.67 | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | SIMP: (3422) implies:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | (3423) all_53_4 = e3
% 109.92/15.67 | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | REDUCE: (137), (3423) imply:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | (3424) ~ (all_53_12 = e3)
% 109.92/15.67 | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | SIMP: (3424) implies:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | (3425) ~ (all_53_12 = e3)
% 109.92/15.67 | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | (3426) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | ALPHA: (3426) implies:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | (3427) op(e3, e0) = e3
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (3425), (3427), (function-axioms) are
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | (3428) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3428) gives:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | (3429) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3429) implies:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | (3430) op(e0, e2) = all_52_2
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | (3431) op(e2, e0) = e2
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | (3432) all_55_2 = e3
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (3023), (3432) are inconsistent by
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | sub-proof #111.
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | (3433) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3433) gives:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | (3434) all_55_2 = e2
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (3434) imply:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | (3435) all_53_3 = e2
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (3435) imply:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | (3436) op(e0, e2) = e2
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_52_2,
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (3430), (3436) gives:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | (3437) all_52_2 = e2
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_52_2,
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (3405), (3430) gives:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | (3438) all_52_2 = e0
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3437), (3438) imply:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | (3439) e2 = e0
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3439) implies:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | (3440) e2 = e0
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (3440) imply:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | (3441) $false
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3441) is inconsistent.
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | (3442) all_55_2 = e1 | all_55_2 = e0
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3442) gives:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | (3443) all_55_2 = e1
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (3443) imply:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | (3444) all_53_3 = e1
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2732), (3444) imply:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | (3445) $false
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3445) is inconsistent.
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | (3446) all_55_2 = e0
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (3446) imply:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | (3447) all_53_3 = e0
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (152), (3447) imply:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | (3448) ~ (all_53_1 = e0)
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | (3449) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (173), (207), (249), (2730), (3309),
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | (3448), (3449), (function-axioms) are inconsistent
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #38.
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | (3450) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3450) gives:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (3451) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3451) implies:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (3452) op(e2, e1) = e2
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (168), (169), (3431), (3452),
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | | #186.
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (3453) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3453) implies:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (3454) op(e0, e1) = e0
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3448), (3454), (function-axioms) are
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #230.
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | (3455) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3455) implies:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | (3456) op(e1, e0) = e1
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2733), (3456), (function-axioms) are
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #226.
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.67 | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | (3457) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 109.92/15.67 | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (252), (2733), (3310), (3420), (3457) are
% 109.92/15.67 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #24.
% 109.92/15.67 | | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | Case 2:
% 109.92/15.67 | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | (3458) all_55_14 = e0
% 109.92/15.67 | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | | REF_CLOSE: (3323), (3326), (3458) are inconsistent by
% 109.92/15.67 | | | | | | | | | | | | | sub-proof #86.
% 109.92/15.67 | | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | | |
% 109.92/15.67 | | | | | | | | | End of split
% 109.92/15.67 | | | | | | | | |
% 109.92/15.67 | | | | | | | | End of split
% 109.92/15.67 | | | | | | | |
% 109.92/15.67 | | | | | | | End of split
% 109.92/15.67 | | | | | | |
% 109.92/15.67 | | | | | | End of split
% 109.92/15.67 | | | | | |
% 109.92/15.67 | | | | | End of split
% 109.92/15.67 | | | | |
% 109.92/15.67 | | | | End of split
% 109.92/15.67 | | | |
% 109.92/15.67 | | | End of split
% 109.92/15.67 | | |
% 109.92/15.67 | | End of split
% 109.92/15.67 | |
% 109.92/15.67 | Case 2:
% 109.92/15.67 | |
% 109.92/15.67 | | (3459) all_4_2 = e0
% 109.92/15.67 | | (3460) op(e0, e0) = all_4_1 & $i(all_4_1) & ( ~ (all_4_1 = e1) | ( ~
% 109.92/15.67 | | (all_4_0 = e2) & op(e1, e0) = all_4_0 & $i(all_4_0)))
% 109.92/15.67 | |
% 109.92/15.67 | | ALPHA: (3460) implies:
% 109.92/15.67 | | (3461) op(e0, e0) = all_4_1
% 109.92/15.67 | | (3462) ~ (all_4_1 = e1) | ( ~ (all_4_0 = e2) & op(e1, e0) = all_4_0 &
% 109.92/15.67 | | $i(all_4_0))
% 109.92/15.67 | |
% 109.92/15.67 | | COMBINE_EQS: (300), (3459) imply:
% 109.92/15.67 | | (3463) all_40_2 = e0
% 109.92/15.67 | |
% 109.92/15.67 | | REDUCE: (355), (3459) imply:
% 109.92/15.67 | | (3464) ~ (all_53_2 = e0)
% 109.92/15.67 | |
% 109.92/15.67 | | REDUCE: (366), (3459) imply:
% 109.92/15.67 | | (3465) ~ (all_53_6 = e0)
% 109.92/15.67 | |
% 109.92/15.67 | | REDUCE: (371), (3459) imply:
% 109.92/15.67 | | (3466) ~ (all_53_10 = e0)
% 109.92/15.67 | |
% 109.92/15.67 | | REDUCE: (374), (3459) imply:
% 109.92/15.67 | | (3467) ~ (all_53_12 = e0)
% 109.92/15.67 | |
% 109.92/15.67 | | REDUCE: (375), (3459) imply:
% 109.92/15.67 | | (3468) ~ (all_53_13 = e0)
% 109.92/15.67 | |
% 109.92/15.67 | | REDUCE: (377), (3459) imply:
% 109.92/15.67 | | (3469) ~ (all_53_15 = e0)
% 109.92/15.67 | |
% 109.92/15.67 | | REDUCE: (35), (3459) imply:
% 109.92/15.67 | | (3470) op(e3, e3) = e0
% 109.92/15.67 | |
% 109.92/15.67 | | BETA: splitting (90) gives:
% 109.92/15.67 | |
% 109.92/15.67 | | Case 1:
% 109.92/15.67 | | |
% 109.92/15.67 | | | (3471) ~ (all_40_2 = e0)
% 109.92/15.67 | | |
% 109.92/15.67 | | | REDUCE: (3463), (3471) imply:
% 109.92/15.67 | | | (3472) $false
% 109.92/15.67 | | |
% 109.92/15.67 | | | CLOSE: (3472) is inconsistent.
% 109.92/15.67 | | |
% 109.92/15.67 | | Case 2:
% 109.92/15.67 | | |
% 109.92/15.67 | | | (3473) op(e0, e0) = all_40_1 & $i(all_40_1) & ( ~ (all_40_1 = e2) | ( ~
% 109.92/15.67 | | | (all_40_0 = e1) & op(e2, e0) = all_40_0 & $i(all_40_0)))
% 109.92/15.67 | | |
% 109.92/15.67 | | | ALPHA: (3473) implies:
% 109.92/15.67 | | | (3474) op(e0, e0) = all_40_1
% 109.92/15.67 | | | (3475) ~ (all_40_1 = e2) | ( ~ (all_40_0 = e1) & op(e2, e0) = all_40_0
% 109.92/15.67 | | | & $i(all_40_0))
% 109.92/15.67 | | |
% 109.92/15.67 | | | GROUND_INST: instantiating (function-axioms) with all_6_2, all_40_1, e0,
% 109.92/15.67 | | | e0, simplifying with (38), (3474) gives:
% 109.92/15.67 | | | (3476) all_40_1 = all_6_2
% 109.92/15.67 | | |
% 109.92/15.67 | | | GROUND_INST: instantiating (function-axioms) with all_4_1, all_40_1, e0,
% 109.92/15.67 | | | e0, simplifying with (3461), (3474) gives:
% 109.92/15.67 | | | (3477) all_40_1 = all_4_1
% 109.92/15.67 | | |
% 109.92/15.67 | | | COMBINE_EQS: (3476), (3477) imply:
% 109.92/15.67 | | | (3478) all_6_2 = all_4_1
% 109.92/15.67 | | |
% 109.92/15.67 | | | SIMP: (3478) implies:
% 109.92/15.67 | | | (3479) all_6_2 = all_4_1
% 109.92/15.67 | | |
% 109.92/15.67 | | | COMBINE_EQS: (328), (3479) imply:
% 109.92/15.67 | | | (3480) all_8_2 = all_4_1
% 109.92/15.67 | | |
% 109.92/15.67 | | | COMBINE_EQS: (322), (3479) imply:
% 109.92/15.67 | | | (3481) all_16_2 = all_4_1
% 109.92/15.67 | | |
% 109.92/15.67 | | | COMBINE_EQS: (313), (3479) imply:
% 109.92/15.67 | | | (3482) all_28_2 = all_4_1
% 109.92/15.67 | | |
% 109.92/15.67 | | | COMBINE_EQS: (332), (3479) imply:
% 109.92/15.67 | | | (3483) all_36_2 = all_4_1
% 109.92/15.67 | | |
% 109.92/15.67 | | | COMBINE_EQS: (292), (3479) imply:
% 109.92/15.67 | | | (3484) all_38_2 = all_4_1
% 109.92/15.67 | | |
% 109.92/15.67 | | | COMBINE_EQS: (248), (3479) imply:
% 109.92/15.67 | | | (3485) all_55_0 = all_4_1
% 109.92/15.67 | | |
% 109.92/15.67 | | | REDUCE: (343), (3479) imply:
% 109.92/15.67 | | | (3486) ~ (all_53_1 = all_4_1)
% 109.92/15.67 | | |
% 109.92/15.67 | | | REDUCE: (345), (3479) imply:
% 109.92/15.67 | | | (3487) ~ (all_53_2 = all_4_1)
% 109.92/15.67 | | |
% 109.92/15.67 | | | REDUCE: (347), (3479) imply:
% 109.92/15.67 | | | (3488) ~ (all_53_3 = all_4_1)
% 109.92/15.67 | | |
% 109.92/15.67 | | | REDUCE: (349), (3479) imply:
% 109.92/15.67 | | | (3489) ~ (all_53_4 = all_4_1)
% 109.92/15.67 | | |
% 109.92/15.67 | | | REDUCE: (351), (3479) imply:
% 109.92/15.67 | | | (3490) ~ (all_53_8 = all_4_1)
% 109.92/15.67 | | |
% 109.92/15.67 | | | REDUCE: (353), (3479) imply:
% 109.92/15.67 | | | (3491) ~ (all_53_12 = all_4_1)
% 109.92/15.67 | | |
% 109.92/15.67 | | | BETA: splitting (39) gives:
% 109.92/15.67 | | |
% 109.92/15.67 | | | Case 1:
% 109.92/15.67 | | | |
% 109.92/15.67 | | | | (3492) ~ (all_6_2 = e1)
% 109.92/15.67 | | | |
% 109.92/15.67 | | | | REDUCE: (3479), (3492) imply:
% 109.92/15.67 | | | | (3493) ~ (all_4_1 = e1)
% 109.92/15.67 | | | |
% 109.92/15.67 | | | | BETA: splitting (42) gives:
% 109.92/15.67 | | | |
% 109.92/15.67 | | | | Case 1:
% 109.92/15.67 | | | | |
% 109.92/15.67 | | | | | (3494) ~ (all_8_2 = e2)
% 109.92/15.67 | | | | |
% 109.92/15.67 | | | | | REDUCE: (3480), (3494) imply:
% 109.92/15.67 | | | | | (3495) ~ (all_4_1 = e2)
% 109.92/15.67 | | | | |
% 109.92/15.67 | | | | | BETA: splitting (45) gives:
% 109.92/15.67 | | | | |
% 109.92/15.67 | | | | | Case 1:
% 109.92/15.67 | | | | | |
% 109.92/15.67 | | | | | | (3496) ~ (all_10_2 = e3)
% 109.92/15.68 | | | | | |
% 109.92/15.68 | | | | | | BETA: splitting (48) gives:
% 109.92/15.68 | | | | | |
% 109.92/15.68 | | | | | | Case 1:
% 109.92/15.68 | | | | | | |
% 109.92/15.68 | | | | | | | (3497) ~ (all_12_2 = e0)
% 109.92/15.68 | | | | | | |
% 109.92/15.68 | | | | | | | REDUCE: (323), (3497) imply:
% 109.92/15.68 | | | | | | | (3498) ~ (all_10_2 = e0)
% 109.92/15.68 | | | | | | |
% 109.92/15.68 | | | | | | | BETA: splitting (51) gives:
% 109.92/15.68 | | | | | | |
% 109.92/15.68 | | | | | | | Case 1:
% 109.92/15.68 | | | | | | | |
% 109.92/15.68 | | | | | | | | (3499) ~ (all_14_2 = e2)
% 109.92/15.68 | | | | | | | |
% 109.92/15.68 | | | | | | | | BETA: splitting (57) gives:
% 109.92/15.68 | | | | | | | |
% 109.92/15.68 | | | | | | | | Case 1:
% 109.92/15.68 | | | | | | | | |
% 109.92/15.68 | | | | | | | | | (3500) ~ (all_18_2 = e3)
% 109.92/15.68 | | | | | | | | |
% 109.92/15.68 | | | | | | | | | REDUCE: (326), (3500) imply:
% 109.92/15.68 | | | | | | | | | (3501) ~ (all_14_2 = e3)
% 109.92/15.68 | | | | | | | | |
% 109.92/15.68 | | | | | | | | | BETA: splitting (63) gives:
% 109.92/15.68 | | | | | | | | |
% 109.92/15.68 | | | | | | | | | Case 1:
% 109.92/15.68 | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | (3502) ~ (all_22_2 = e0)
% 109.92/15.68 | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | REDUCE: (329), (3502) imply:
% 109.92/15.68 | | | | | | | | | | (3503) ~ (all_14_2 = e0)
% 109.92/15.68 | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (117), (123),
% 109.92/15.68 | | | | | | | | | | (126), (127), (148), (152), (153), (161), (162),
% 109.92/15.68 | | | | | | | | | | (163), (164), (166), (167), (168), (169), (171),
% 109.92/15.68 | | | | | | | | | | (172), (173), (174), (203), (341), (357), (359),
% 109.92/15.68 | | | | | | | | | | (361), (3499), (3501), (3503), (function-axioms)
% 109.92/15.68 | | | | | | | | | | are inconsistent by sub-proof #216.
% 109.92/15.68 | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | Case 2:
% 109.92/15.68 | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | (3504) all_22_2 = e0
% 109.92/15.68 | | | | | | | | | | (3505) op(e0, e0) = all_22_1 & $i(all_22_1) & ( ~
% 109.92/15.68 | | | | | | | | | | (all_22_1 = e2) | ( ~ (all_22_0 = e3) & op(e2,
% 109.92/15.68 | | | | | | | | | | e0) = all_22_0 & $i(all_22_0)))
% 109.92/15.68 | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | ALPHA: (3505) implies:
% 109.92/15.68 | | | | | | | | | | (3506) op(e0, e0) = all_22_1
% 109.92/15.68 | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | COMBINE_EQS: (329), (3504) imply:
% 109.92/15.68 | | | | | | | | | | (3507) all_14_2 = e0
% 109.92/15.68 | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | SIMP: (3507) implies:
% 109.92/15.68 | | | | | | | | | | (3508) all_14_2 = e0
% 109.92/15.68 | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | COMBINE_EQS: (331), (3508) imply:
% 109.92/15.68 | | | | | | | | | | (3509) all_32_2 = e0
% 109.92/15.68 | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | REDUCE: (361), (3508) imply:
% 109.92/15.68 | | | | | | | | | | (3510) ~ (all_53_7 = e0)
% 109.92/15.68 | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | REDUCE: (363), (3508) imply:
% 109.92/15.68 | | | | | | | | | | (3511) ~ (all_53_9 = e0)
% 109.92/15.68 | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | REDUCE: (3499), (3508) imply:
% 109.92/15.68 | | | | | | | | | | (3512) ~ (e2 = e0)
% 109.92/15.68 | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | BETA: splitting (78) gives:
% 109.92/15.68 | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | Case 1:
% 109.92/15.68 | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | (3513) ~ (all_32_2 = e0)
% 109.92/15.68 | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | REDUCE: (3509), (3513) imply:
% 109.92/15.68 | | | | | | | | | | | (3514) $false
% 109.92/15.68 | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | CLOSE: (3514) is inconsistent.
% 109.92/15.68 | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | Case 2:
% 109.92/15.68 | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | (3515) op(e0, e0) = all_32_1 & $i(all_32_1) & ( ~
% 109.92/15.68 | | | | | | | | | | | (all_32_1 = e3) | ( ~ (all_32_0 = e2) & op(e3,
% 109.92/15.68 | | | | | | | | | | | e0) = all_32_0 & $i(all_32_0)))
% 109.92/15.68 | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | ALPHA: (3515) implies:
% 109.92/15.68 | | | | | | | | | | | (3516) op(e0, e0) = all_32_1
% 109.92/15.68 | | | | | | | | | | | (3517) ~ (all_32_1 = e3) | ( ~ (all_32_0 = e2) & op(e3,
% 109.92/15.68 | | | | | | | | | | | e0) = all_32_0 & $i(all_32_0))
% 109.92/15.68 | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | BETA: splitting (224) gives:
% 109.92/15.68 | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | Case 1:
% 109.92/15.68 | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | (3518) (all_57_68 = e0 & op(e3, e2) = e0) | (all_57_69 =
% 109.92/15.68 | | | | | | | | | | | | e0 & op(e2, e2) = e0)
% 109.92/15.68 | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | BETA: splitting (3518) gives:
% 109.92/15.68 | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | Case 1:
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | (3519) all_57_68 = e0 & op(e3, e2) = e0
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | ALPHA: (3519) implies:
% 109.92/15.68 | | | | | | | | | | | | | (3520) op(e3, e2) = e0
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | REF_CLOSE: (174), (3469), (3520), (function-axioms) are
% 109.92/15.68 | | | | | | | | | | | | | inconsistent by sub-proof #156.
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | Case 2:
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | (3521) all_57_69 = e0 & op(e2, e2) = e0
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | ALPHA: (3521) implies:
% 109.92/15.68 | | | | | | | | | | | | | (3522) op(e2, e2) = e0
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | REF_CLOSE: (44), (3498), (3522), (function-axioms) are
% 109.92/15.68 | | | | | | | | | | | | | inconsistent by sub-proof #19.
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | End of split
% 109.92/15.68 | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | Case 2:
% 109.92/15.68 | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | (3523) (all_57_70 = e0 & op(e1, e2) = e0) | (all_57_71 =
% 109.92/15.68 | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 109.92/15.68 | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | BETA: splitting (3523) gives:
% 109.92/15.68 | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | Case 1:
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | (3524) all_57_70 = e0 & op(e1, e2) = e0
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | ALPHA: (3524) implies:
% 109.92/15.68 | | | | | | | | | | | | | (3525) op(e1, e2) = e0
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | REF_CLOSE: (166), (3510), (3525), (function-axioms) are
% 109.92/15.68 | | | | | | | | | | | | | inconsistent by sub-proof #153.
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | Case 2:
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | (3526) all_57_71 = e0 & op(e0, e2) = e0
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | ALPHA: (3526) implies:
% 109.92/15.68 | | | | | | | | | | | | | (3527) op(e0, e2) = e0
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | BETA: splitting (225) gives:
% 109.92/15.68 | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | Case 1:
% 109.92/15.68 | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | (3528) (all_57_64 = e0 & op(e2, e3) = e0) | (all_57_65 =
% 109.92/15.68 | | | | | | | | | | | | | | e0 & op(e2, e2) = e0)
% 109.92/15.68 | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | REF_CLOSE: (44), (171), (3466), (3498), (3528),
% 109.92/15.68 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.92/15.68 | | | | | | | | | | | | | | #18.
% 109.92/15.68 | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | Case 2:
% 109.92/15.68 | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | (3529) (all_57_66 = e0 & op(e2, e1) = e0) | (all_57_67 =
% 109.92/15.68 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 109.92/15.68 | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | BETA: splitting (3529) gives:
% 109.92/15.68 | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | Case 1:
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | (3530) all_57_66 = e0 & op(e2, e1) = e0
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | ALPHA: (3530) implies:
% 109.92/15.68 | | | | | | | | | | | | | | | (3531) op(e2, e1) = e0
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | REF_CLOSE: (169), (3511), (3531), (function-axioms) are
% 109.92/15.68 | | | | | | | | | | | | | | | inconsistent by sub-proof #147.
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | Case 2:
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | (3532) all_57_67 = e0 & op(e2, e0) = e0
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | ALPHA: (3532) implies:
% 109.92/15.68 | | | | | | | | | | | | | | | (3533) op(e2, e0) = e0
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 109.92/15.68 | | | | | | | | | | | | | | | all_32_1, e0, e0, simplifying with (3461), (3516)
% 109.92/15.68 | | | | | | | | | | | | | | | gives:
% 109.92/15.68 | | | | | | | | | | | | | | | (3534) all_32_1 = all_4_1
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 109.92/15.68 | | | | | | | | | | | | | | | all_32_1, e0, e0, simplifying with (3506), (3516)
% 109.92/15.68 | | | | | | | | | | | | | | | gives:
% 109.92/15.68 | | | | | | | | | | | | | | | (3535) all_32_1 = all_22_1
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e0,
% 109.92/15.68 | | | | | | | | | | | | | | | e2, e0, simplifying with (162), (3527) gives:
% 109.92/15.68 | | | | | | | | | | | | | | | (3536) all_53_3 = e0
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e0,
% 109.92/15.68 | | | | | | | | | | | | | | | e0, e2, simplifying with (168), (3533) gives:
% 109.92/15.68 | | | | | | | | | | | | | | | (3537) all_53_8 = e0
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | COMBINE_EQS: (3534), (3535) imply:
% 109.92/15.68 | | | | | | | | | | | | | | | (3538) all_22_1 = all_4_1
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | REDUCE: (152), (3536) imply:
% 109.92/15.68 | | | | | | | | | | | | | | | (3539) ~ (all_53_1 = e0)
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | REDUCE: (124), (3537) imply:
% 109.92/15.68 | | | | | | | | | | | | | | | (3540) ~ (all_53_12 = e0)
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | REDUCE: (3490), (3537) imply:
% 109.92/15.68 | | | | | | | | | | | | | | | (3541) ~ (all_4_1 = e0)
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | SIMP: (3541) implies:
% 109.92/15.68 | | | | | | | | | | | | | | | (3542) ~ (all_4_1 = e0)
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 109.92/15.68 | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | Case 1:
% 109.92/15.68 | | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | | (3543) all_55_0 = e3
% 109.92/15.68 | | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | | COMBINE_EQS: (3485), (3543) imply:
% 109.92/15.68 | | | | | | | | | | | | | | | | (3544) all_4_1 = e3
% 109.92/15.68 | | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | | COMBINE_EQS: (3534), (3544) imply:
% 109.92/15.68 | | | | | | | | | | | | | | | | (3545) all_32_1 = e3
% 109.92/15.68 | | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | | REDUCE: (3491), (3544) imply:
% 109.92/15.68 | | | | | | | | | | | | | | | | (3546) ~ (all_53_12 = e3)
% 109.92/15.68 | | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | | REDUCE: (3461), (3544) imply:
% 109.92/15.68 | | | | | | | | | | | | | | | | (3547) op(e0, e0) = e3
% 109.92/15.68 | | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | | BETA: splitting (3517) gives:
% 109.92/15.68 | | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | | Case 1:
% 109.92/15.68 | | | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | | | (3548) ~ (all_32_1 = e3)
% 109.92/15.68 | | | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | | | REDUCE: (3545), (3548) imply:
% 109.92/15.68 | | | | | | | | | | | | | | | | | (3549) $false
% 109.92/15.68 | | | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | | | CLOSE: (3549) is inconsistent.
% 109.92/15.68 | | | | | | | | | | | | | | | | |
% 109.92/15.68 | | | | | | | | | | | | | | | | Case 2:
% 109.92/15.68 | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | (3550) ~ (all_32_0 = e2) & op(e3, e0) = all_32_0 &
% 110.16/15.68 | | | | | | | | | | | | | | | | | $i(all_32_0)
% 110.16/15.68 | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | ALPHA: (3550) implies:
% 110.16/15.68 | | | | | | | | | | | | | | | | | (3551) ~ (all_32_0 = e2)
% 110.16/15.68 | | | | | | | | | | | | | | | | | (3552) op(e3, e0) = all_32_0
% 110.16/15.68 | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 110.16/15.68 | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.68 | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | (3553) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 110.16/15.68 | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 110.16/15.68 | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | ALPHA: (3553) implies:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | (3554) op(e3, e0) = e3
% 110.16/15.68 | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (3546), (3554), (function-axioms) are
% 110.16/15.68 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 110.16/15.68 | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.68 | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | (3555) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 110.16/15.68 | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 110.16/15.68 | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 110.16/15.68 | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | BETA: splitting (3555) gives:
% 110.16/15.68 | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | (3556) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 110.16/15.68 | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | ALPHA: (3556) implies:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | (3557) op(e2, e0) = e2
% 110.16/15.68 | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e0,
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | e2, simplifying with (3533), (3557) gives:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | (3558) e2 = e0
% 110.16/15.68 | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | REDUCE: (5), (3558) imply:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | (3559) $false
% 110.16/15.68 | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | CLOSE: (3559) is inconsistent.
% 110.16/15.68 | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | (3560) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 110.16/15.68 | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | ALPHA: (3560) implies:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | (3561) op(e1, e0) = e1
% 110.16/15.68 | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | (3562) (all_57_0 = e0 & op(e0, e3) = e0) | (all_57_1 = e0
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0)
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3562) gives:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | (3563) all_57_0 = e0 & op(e0, e3) = e0
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3563) implies:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | (3564) op(e0, e3) = e0
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3464), (3564), (function-axioms) are
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #149.
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e1,
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | e0, e1, simplifying with (164), (3561) gives:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | (3565) all_53_4 = e1
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | all_32_0, e0, e3, simplifying with (172), (3552)
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | gives:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | (3566) all_53_12 = all_32_0
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (3566) imply:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | (3567) all_55_12 = all_32_0
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3546), (3566) imply:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | (3568) ~ (all_32_0 = e3)
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | | (3569) all_55_12 = e3
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3567), (3568), (3569) are inconsistent by
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | | sub-proof #190.
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | | (3570) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3570) gives:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | | | (3571) all_55_12 = e2
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3551), (3567), (3571) are inconsistent by
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #189.
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.68 | | | | | | | | | | | | | | | | | | | | | | | (3572) all_55_12 = e1 | all_55_12 = e0
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (164), (272), (3467), (3561), (3572),
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | | | #16.
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | (3573) (all_57_2 = e0 & op(e0, e1) = e0) | (all_57_3 = e0
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e0)
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3573) gives:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | (3574) all_57_2 = e0 & op(e0, e1) = e0
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3574) implies:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | (3575) op(e0, e1) = e0
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3539), (3575), (function-axioms) are
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #230.
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | (3576) all_57_3 = e0 & op(e0, e0) = e0
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3576) implies:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | (3577) op(e0, e0) = e0
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e0,
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (3547), (3577) gives:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | (3578) e3 = e0
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (3578) imply:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | (3579) $false
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3579) is inconsistent.
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.69 | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.69 | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | End of split
% 110.16/15.69 | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | End of split
% 110.16/15.69 | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | Case 2:
% 110.16/15.69 | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | (3580) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 110.16/15.69 | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | REF_CLOSE: (3485), (3493), (3495), (3542), (3580) are
% 110.16/15.69 | | | | | | | | | | | | | | | | inconsistent by sub-proof #15.
% 110.16/15.69 | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | End of split
% 110.16/15.69 | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | End of split
% 110.16/15.69 | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | End of split
% 110.16/15.69 | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | End of split
% 110.16/15.69 | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | End of split
% 110.16/15.69 | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | End of split
% 110.16/15.69 | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | End of split
% 110.16/15.69 | | | | | | | | |
% 110.16/15.69 | | | | | | | | Case 2:
% 110.16/15.69 | | | | | | | | |
% 110.16/15.69 | | | | | | | | | (3581) all_18_2 = e3
% 110.16/15.69 | | | | | | | | | (3582) op(e3, e3) = all_18_1 & $i(all_18_1) & ( ~ (all_18_1
% 110.16/15.69 | | | | | | | | | = e2) | ( ~ (all_18_0 = e0) & op(e2, e3) =
% 110.16/15.69 | | | | | | | | | all_18_0 & $i(all_18_0)))
% 110.16/15.69 | | | | | | | | |
% 110.16/15.69 | | | | | | | | | ALPHA: (3582) implies:
% 110.16/15.69 | | | | | | | | | (3583) op(e3, e3) = all_18_1
% 110.16/15.69 | | | | | | | | |
% 110.16/15.69 | | | | | | | | | COMBINE_EQS: (326), (3581) imply:
% 110.16/15.69 | | | | | | | | | (3584) all_14_2 = e3
% 110.16/15.69 | | | | | | | | |
% 110.16/15.69 | | | | | | | | | COMBINE_EQS: (253), (3584) imply:
% 110.16/15.69 | | | | | | | | | (3585) all_20_2 = e3
% 110.16/15.69 | | | | | | | | |
% 110.16/15.69 | | | | | | | | | REDUCE: (365), (3584) imply:
% 110.16/15.69 | | | | | | | | | (3586) ~ (all_53_13 = e3)
% 110.16/15.69 | | | | | | | | |
% 110.16/15.69 | | | | | | | | | BETA: splitting (60) gives:
% 110.16/15.69 | | | | | | | | |
% 110.16/15.69 | | | | | | | | | Case 1:
% 110.16/15.69 | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | (3587) ~ (all_20_2 = e3)
% 110.16/15.69 | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | REDUCE: (3585), (3587) imply:
% 110.16/15.69 | | | | | | | | | | (3588) $false
% 110.16/15.69 | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | CLOSE: (3588) is inconsistent.
% 110.16/15.69 | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | Case 2:
% 110.16/15.69 | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | (3589) op(e3, e3) = all_20_1 & $i(all_20_1) & ( ~
% 110.16/15.69 | | | | | | | | | | (all_20_1 = e0) | ( ~ (all_20_0 = e2) & op(e0,
% 110.16/15.69 | | | | | | | | | | e3) = all_20_0 & $i(all_20_0)))
% 110.16/15.69 | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | ALPHA: (3589) implies:
% 110.16/15.69 | | | | | | | | | | (3590) op(e3, e3) = all_20_1
% 110.16/15.69 | | | | | | | | | | (3591) ~ (all_20_1 = e0) | ( ~ (all_20_0 = e2) & op(e0,
% 110.16/15.69 | | | | | | | | | | e3) = all_20_0 & $i(all_20_0))
% 110.16/15.69 | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_20_1,
% 110.16/15.69 | | | | | | | | | | e3, e3, simplifying with (3470), (3590) gives:
% 110.16/15.69 | | | | | | | | | | (3592) all_20_1 = e0
% 110.16/15.69 | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 110.16/15.69 | | | | | | | | | | all_20_1, e3, e3, simplifying with (3583), (3590)
% 110.16/15.69 | | | | | | | | | | gives:
% 110.16/15.69 | | | | | | | | | | (3593) all_20_1 = all_18_1
% 110.16/15.69 | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | COMBINE_EQS: (3592), (3593) imply:
% 110.16/15.69 | | | | | | | | | | (3594) all_18_1 = e0
% 110.16/15.69 | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | BETA: splitting (3591) gives:
% 110.16/15.69 | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | Case 1:
% 110.16/15.69 | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | (3595) ~ (all_20_1 = e0)
% 110.16/15.69 | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | REDUCE: (3592), (3595) imply:
% 110.16/15.69 | | | | | | | | | | | (3596) $false
% 110.16/15.69 | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | CLOSE: (3596) is inconsistent.
% 110.16/15.69 | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | Case 2:
% 110.16/15.69 | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | (3597) ~ (all_20_0 = e2) & op(e0, e3) = all_20_0 &
% 110.16/15.69 | | | | | | | | | | | $i(all_20_0)
% 110.16/15.69 | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | ALPHA: (3597) implies:
% 110.16/15.69 | | | | | | | | | | | (3598) ~ (all_20_0 = e2)
% 110.16/15.69 | | | | | | | | | | | (3599) op(e0, e3) = all_20_0
% 110.16/15.69 | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2,
% 110.16/15.69 | | | | | | | | | | | all_20_0, e3, e0, simplifying with (163), (3599)
% 110.16/15.69 | | | | | | | | | | | gives:
% 110.16/15.69 | | | | | | | | | | | (3600) all_53_2 = all_20_0
% 110.16/15.69 | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | COMBINE_EQS: (251), (3600) imply:
% 110.16/15.69 | | | | | | | | | | | (3601) all_55_3 = all_20_0
% 110.16/15.69 | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | REDUCE: (147), (3600) imply:
% 110.16/15.69 | | | | | | | | | | | (3602) ~ (all_53_6 = all_20_0)
% 110.16/15.69 | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | SIMP: (3602) implies:
% 110.16/15.69 | | | | | | | | | | | (3603) ~ (all_53_6 = all_20_0)
% 110.16/15.69 | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | REDUCE: (3487), (3600) imply:
% 110.16/15.69 | | | | | | | | | | | (3604) ~ (all_20_0 = all_4_1)
% 110.16/15.69 | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | REDUCE: (3464), (3600) imply:
% 110.16/15.69 | | | | | | | | | | | (3605) ~ (all_20_0 = e0)
% 110.16/15.69 | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | BETA: splitting (66) gives:
% 110.16/15.69 | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | Case 1:
% 110.16/15.69 | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | (3606) ~ (all_24_2 = e1)
% 110.16/15.69 | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | REDUCE: (303), (3606) imply:
% 110.16/15.69 | | | | | | | | | | | | (3607) ~ (all_10_2 = e1)
% 110.16/15.69 | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (115), (117),
% 110.16/15.69 | | | | | | | | | | | | (132), (139), (140), (148), (152), (153), (161),
% 110.16/15.69 | | | | | | | | | | | | (162), (163), (164), (166), (167), (168), (169),
% 110.16/15.69 | | | | | | | | | | | | (171), (172), (173), (174), (198), (340), (368),
% 110.16/15.69 | | | | | | | | | | | | (369), (370), (3496), (3498), (3607),
% 110.16/15.69 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.69 | | | | | | | | | | | | #207.
% 110.16/15.69 | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | Case 2:
% 110.16/15.69 | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | (3608) all_24_2 = e1
% 110.16/15.69 | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | COMBINE_EQS: (303), (3608) imply:
% 110.16/15.69 | | | | | | | | | | | | (3609) all_10_2 = e1
% 110.16/15.69 | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | REDUCE: (356), (3609) imply:
% 110.16/15.69 | | | | | | | | | | | | (3610) ~ (all_53_3 = e1)
% 110.16/15.69 | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | REDUCE: (367), (3609) imply:
% 110.16/15.69 | | | | | | | | | | | | (3611) ~ (all_53_7 = e1)
% 110.16/15.69 | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | REDUCE: (3496), (3609) imply:
% 110.16/15.69 | | | | | | | | | | | | (3612) ~ (e3 = e1)
% 110.16/15.69 | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | BETA: splitting (72) gives:
% 110.16/15.69 | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | Case 1:
% 110.16/15.69 | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | (3613) ~ (all_28_2 = e3)
% 110.16/15.69 | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | REDUCE: (3482), (3613) imply:
% 110.16/15.69 | | | | | | | | | | | | | (3614) ~ (all_4_1 = e3)
% 110.16/15.69 | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | REF_CLOSE: (7), (108), (109), (113), (161), (162), (166),
% 110.16/15.69 | | | | | | | | | | | | | (168), (169), (171), (173), (174), (208), (222),
% 110.16/15.69 | | | | | | | | | | | | | (225), (3466), (3485), (3486), (3488), (3490),
% 110.16/15.69 | | | | | | | | | | | | | (3493), (3495), (3610), (3611), (3614),
% 110.16/15.69 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.69 | | | | | | | | | | | | | #13.
% 110.16/15.69 | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | Case 2:
% 110.16/15.69 | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | (3615) all_28_2 = e3
% 110.16/15.69 | | | | | | | | | | | | | (3616) op(e3, e3) = all_28_1 & $i(all_28_1) & ( ~
% 110.16/15.69 | | | | | | | | | | | | | (all_28_1 = e1) | ( ~ (all_28_0 = e2) & op(e1,
% 110.16/15.69 | | | | | | | | | | | | | e3) = all_28_0 & $i(all_28_0)))
% 110.16/15.69 | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | ALPHA: (3616) implies:
% 110.16/15.69 | | | | | | | | | | | | | (3617) op(e3, e3) = all_28_1
% 110.16/15.69 | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | COMBINE_EQS: (3482), (3615) imply:
% 110.16/15.69 | | | | | | | | | | | | | (3618) all_4_1 = e3
% 110.16/15.69 | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | COMBINE_EQS: (3483), (3618) imply:
% 110.16/15.69 | | | | | | | | | | | | | (3619) all_36_2 = e3
% 110.16/15.69 | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | REDUCE: (3491), (3618) imply:
% 110.16/15.69 | | | | | | | | | | | | | (3620) ~ (all_53_12 = e3)
% 110.16/15.69 | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | REDUCE: (3604), (3618) imply:
% 110.16/15.69 | | | | | | | | | | | | | (3621) ~ (all_20_0 = e3)
% 110.16/15.69 | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | BETA: splitting (84) gives:
% 110.16/15.69 | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | Case 1:
% 110.16/15.69 | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | (3622) ~ (all_36_2 = e3)
% 110.16/15.69 | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | REDUCE: (3619), (3622) imply:
% 110.16/15.69 | | | | | | | | | | | | | | (3623) $false
% 110.16/15.69 | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | CLOSE: (3623) is inconsistent.
% 110.16/15.69 | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | Case 2:
% 110.16/15.69 | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | (3624) op(e3, e3) = all_36_1 & $i(all_36_1) & ( ~
% 110.16/15.69 | | | | | | | | | | | | | | (all_36_1 = e2) | ( ~ (all_36_0 = e1) & op(e2,
% 110.16/15.69 | | | | | | | | | | | | | | e3) = all_36_0 & $i(all_36_0)))
% 110.16/15.69 | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | ALPHA: (3624) implies:
% 110.16/15.69 | | | | | | | | | | | | | | (3625) op(e3, e3) = all_36_1
% 110.16/15.69 | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 110.16/15.69 | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | Case 1:
% 110.16/15.69 | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | (3626) (all_57_120 = e3 & op(e3, e3) = e3) | (all_57_121
% 110.16/15.69 | | | | | | | | | | | | | | | = e3 & op(e3, e2) = e3)
% 110.16/15.69 | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | BETA: splitting (3626) gives:
% 110.16/15.69 | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | Case 1:
% 110.16/15.69 | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | (3627) all_57_120 = e3 & op(e3, e3) = e3
% 110.16/15.69 | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | ALPHA: (3627) implies:
% 110.16/15.69 | | | | | | | | | | | | | | | | (3628) op(e3, e3) = e3
% 110.16/15.69 | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | REF_CLOSE: (35), (107), (108), (109), (110), (123), (126),
% 110.16/15.69 | | | | | | | | | | | | | | | | (127), (132), (139), (140), (148), (152), (153),
% 110.16/15.69 | | | | | | | | | | | | | | | | (161), (162), (163), (164), (166), (167), (168),
% 110.16/15.69 | | | | | | | | | | | | | | | | (169), (171), (172), (173), (174), (374), (375),
% 110.16/15.69 | | | | | | | | | | | | | | | | (377), (3617), (3625), (3628), (function-axioms)
% 110.16/15.69 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #97.
% 110.16/15.69 | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | Case 2:
% 110.16/15.69 | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | (3629) all_57_121 = e3 & op(e3, e2) = e3
% 110.16/15.69 | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | ALPHA: (3629) implies:
% 110.16/15.69 | | | | | | | | | | | | | | | | (3630) op(e3, e2) = e3
% 110.16/15.69 | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 110.16/15.69 | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.69 | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | (3631) all_55_3 = e3
% 110.16/15.69 | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | COMBINE_EQS: (3601), (3631) imply:
% 110.16/15.69 | | | | | | | | | | | | | | | | | (3632) all_20_0 = e3
% 110.16/15.69 | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | REDUCE: (3621), (3632) imply:
% 110.16/15.69 | | | | | | | | | | | | | | | | | (3633) $false
% 110.16/15.69 | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | CLOSE: (3633) is inconsistent.
% 110.16/15.69 | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.69 | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | (3634) all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 110.16/15.69 | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | BETA: splitting (3634) gives:
% 110.16/15.69 | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.69 | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | (3635) all_55_3 = e2
% 110.16/15.69 | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3601), (3635) imply:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | (3636) all_20_0 = e2
% 110.16/15.69 | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | REDUCE: (3598), (3636) imply:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | (3637) $false
% 110.16/15.69 | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | CLOSE: (3637) is inconsistent.
% 110.16/15.69 | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.69 | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | (3638) all_55_3 = e1 | all_55_3 = e0
% 110.16/15.69 | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | BETA: splitting (3638) gives:
% 110.16/15.69 | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | (3639) all_55_3 = e1
% 110.16/15.69 | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3601), (3639) imply:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | (3640) all_20_0 = e1
% 110.16/15.69 | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | REDUCE: (3603), (3640) imply:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | (3641) ~ (all_53_6 = e1)
% 110.16/15.69 | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | REDUCE: (3599), (3640) imply:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | (3642) op(e0, e3) = e1
% 110.16/15.69 | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | (3643) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2)
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | = all_52_18 & op(e2, e3) = e2 & $i(all_52_18)
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | ALPHA: (3643) implies:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | (3644) ~ (all_52_18 = e3)
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | (3645) op(e3, e2) = all_52_18
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3630), (3644), (3645), (function-axioms) are
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #234.
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.69 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | | (3646) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | | (all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22))
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (3641), (3642), (3646),
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | | #172.
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | (3647) all_55_3 = e0
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3601), (3647) imply:
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | (3648) all_20_0 = e0
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | REDUCE: (3605), (3648) imply:
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | (3649) $false
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | CLOSE: (3649) is inconsistent.
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | Case 2:
% 110.16/15.70 | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | (3650) (all_57_122 = e3 & op(e3, e1) = e3) | (all_57_123
% 110.16/15.70 | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3)
% 110.16/15.70 | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | REF_CLOSE: (172), (173), (3586), (3620), (3650),
% 110.16/15.70 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.70 | | | | | | | | | | | | | | | #96.
% 110.16/15.70 | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | |
% 110.16/15.70 | | | | | | | | End of split
% 110.16/15.70 | | | | | | | |
% 110.16/15.70 | | | | | | | Case 2:
% 110.16/15.70 | | | | | | | |
% 110.16/15.70 | | | | | | | | (3651) all_14_2 = e2
% 110.16/15.70 | | | | | | | |
% 110.16/15.70 | | | | | | | | REDUCE: (354), (3651) imply:
% 110.16/15.70 | | | | | | | | (3652) ~ (all_53_1 = e2)
% 110.16/15.70 | | | | | | | |
% 110.16/15.70 | | | | | | | | REDUCE: (357), (3651) imply:
% 110.16/15.70 | | | | | | | | (3653) ~ (all_53_4 = e2)
% 110.16/15.70 | | | | | | | |
% 110.16/15.70 | | | | | | | | REDUCE: (361), (3651) imply:
% 110.16/15.70 | | | | | | | | (3654) ~ (all_53_7 = e2)
% 110.16/15.70 | | | | | | | |
% 110.16/15.70 | | | | | | | | REDUCE: (363), (3651) imply:
% 110.16/15.70 | | | | | | | | (3655) ~ (all_53_9 = e2)
% 110.16/15.70 | | | | | | | |
% 110.16/15.70 | | | | | | | | BETA: splitting (66) gives:
% 110.16/15.70 | | | | | | | |
% 110.16/15.70 | | | | | | | | Case 1:
% 110.16/15.70 | | | | | | | | |
% 110.16/15.70 | | | | | | | | | (3656) ~ (all_24_2 = e1)
% 110.16/15.70 | | | | | | | | |
% 110.16/15.70 | | | | | | | | | REDUCE: (303), (3656) imply:
% 110.16/15.70 | | | | | | | | | (3657) ~ (all_10_2 = e1)
% 110.16/15.70 | | | | | | | | |
% 110.16/15.70 | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (115), (117),
% 110.16/15.70 | | | | | | | | | (132), (139), (140), (148), (152), (153), (161),
% 110.16/15.70 | | | | | | | | | (162), (163), (164), (166), (167), (168), (169),
% 110.16/15.70 | | | | | | | | | (171), (172), (173), (174), (198), (340), (368),
% 110.16/15.70 | | | | | | | | | (369), (370), (3496), (3498), (3657),
% 110.16/15.70 | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.70 | | | | | | | | | #207.
% 110.16/15.70 | | | | | | | | |
% 110.16/15.70 | | | | | | | | Case 2:
% 110.16/15.70 | | | | | | | | |
% 110.16/15.70 | | | | | | | | | (3658) all_24_2 = e1
% 110.16/15.70 | | | | | | | | |
% 110.16/15.70 | | | | | | | | | COMBINE_EQS: (303), (3658) imply:
% 110.16/15.70 | | | | | | | | | (3659) all_10_2 = e1
% 110.16/15.70 | | | | | | | | |
% 110.16/15.70 | | | | | | | | | REDUCE: (356), (3659) imply:
% 110.16/15.70 | | | | | | | | | (3660) ~ (all_53_3 = e1)
% 110.16/15.70 | | | | | | | | |
% 110.16/15.70 | | | | | | | | | REDUCE: (367), (3659) imply:
% 110.16/15.70 | | | | | | | | | (3661) ~ (all_53_7 = e1)
% 110.16/15.70 | | | | | | | | |
% 110.16/15.70 | | | | | | | | | REDUCE: (3496), (3659) imply:
% 110.16/15.70 | | | | | | | | | (3662) ~ (e3 = e1)
% 110.16/15.70 | | | | | | | | |
% 110.16/15.70 | | | | | | | | | BETA: splitting (72) gives:
% 110.16/15.70 | | | | | | | | |
% 110.16/15.70 | | | | | | | | | Case 1:
% 110.16/15.70 | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | (3663) ~ (all_28_2 = e3)
% 110.16/15.70 | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | REDUCE: (3482), (3663) imply:
% 110.16/15.70 | | | | | | | | | | (3664) ~ (all_4_1 = e3)
% 110.16/15.70 | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | REF_CLOSE: (7), (108), (109), (113), (161), (162), (166),
% 110.16/15.70 | | | | | | | | | | (168), (169), (171), (173), (174), (208), (222),
% 110.16/15.70 | | | | | | | | | | (225), (3466), (3485), (3486), (3488), (3490),
% 110.16/15.70 | | | | | | | | | | (3493), (3495), (3660), (3661), (3664),
% 110.16/15.70 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.70 | | | | | | | | | | #13.
% 110.16/15.70 | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | Case 2:
% 110.16/15.70 | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | (3665) all_28_2 = e3
% 110.16/15.70 | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | COMBINE_EQS: (3482), (3665) imply:
% 110.16/15.70 | | | | | | | | | | (3666) all_4_1 = e3
% 110.16/15.70 | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | REDUCE: (3488), (3666) imply:
% 110.16/15.70 | | | | | | | | | | (3667) ~ (all_53_3 = e3)
% 110.16/15.70 | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | REDUCE: (3489), (3666) imply:
% 110.16/15.70 | | | | | | | | | | (3668) ~ (all_53_4 = e3)
% 110.16/15.70 | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | REDUCE: (3491), (3666) imply:
% 110.16/15.70 | | | | | | | | | | (3669) ~ (all_53_12 = e3)
% 110.16/15.70 | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | BETA: splitting (108) gives:
% 110.16/15.70 | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | Case 1:
% 110.16/15.70 | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | (3670) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 110.16/15.70 | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 110.16/15.70 | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | ALPHA: (3670) implies:
% 110.16/15.70 | | | | | | | | | | | (3671) op(e3, e2) = e3
% 110.16/15.70 | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 110.16/15.70 | | | | | | | | | | | e3, e2, e3, simplifying with (174), (3671) gives:
% 110.16/15.70 | | | | | | | | | | | (3672) all_53_15 = e3
% 110.16/15.70 | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | REDUCE: (128), (3672) imply:
% 110.16/15.70 | | | | | | | | | | | (3673) ~ (all_53_7 = e3)
% 110.16/15.70 | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | BETA: splitting (107) gives:
% 110.16/15.70 | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | Case 1:
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | (3674) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2)
% 110.16/15.70 | | | | | | | | | | | | = all_52_18 & op(e2, e3) = e2 & $i(all_52_18)
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | ALPHA: (3674) implies:
% 110.16/15.70 | | | | | | | | | | | | (3675) ~ (all_52_18 = e3)
% 110.16/15.70 | | | | | | | | | | | | (3676) op(e3, e2) = all_52_18
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | REF_CLOSE: (3671), (3675), (3676), (function-axioms) are
% 110.16/15.70 | | | | | | | | | | | | inconsistent by sub-proof #234.
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | Case 2:
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | (3677) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 110.16/15.70 | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) |
% 110.16/15.70 | | | | | | | | | | | | (all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 110.16/15.70 | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22))
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | BETA: splitting (3677) gives:
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | Case 1:
% 110.16/15.70 | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | (3678) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 110.16/15.70 | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)
% 110.16/15.70 | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | ALPHA: (3678) implies:
% 110.16/15.70 | | | | | | | | | | | | | (3679) op(e1, e3) = e1
% 110.16/15.70 | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | BETA: splitting (202) gives:
% 110.16/15.70 | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | Case 1:
% 110.16/15.70 | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | (3680) all_55_6 = e3
% 110.16/15.70 | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | REF_CLOSE: (260), (3673), (3680) are inconsistent by
% 110.16/15.70 | | | | | | | | | | | | | | sub-proof #135.
% 110.16/15.70 | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | Case 2:
% 110.16/15.70 | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | (3681) all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 110.16/15.70 | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | BETA: splitting (3681) gives:
% 110.16/15.70 | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | Case 1:
% 110.16/15.70 | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | (3682) all_55_6 = e2
% 110.16/15.70 | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | REF_CLOSE: (260), (3654), (3682) are inconsistent by
% 110.16/15.70 | | | | | | | | | | | | | | | sub-proof #134.
% 110.16/15.70 | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | Case 2:
% 110.16/15.70 | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | (3683) all_55_6 = e1 | all_55_6 = e0
% 110.16/15.70 | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | BETA: splitting (3683) gives:
% 110.16/15.70 | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | Case 1:
% 110.16/15.70 | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | (3684) all_55_6 = e1
% 110.16/15.70 | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3684) imply:
% 110.16/15.70 | | | | | | | | | | | | | | | | (3685) all_53_7 = e1
% 110.16/15.70 | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | REDUCE: (3661), (3685) imply:
% 110.16/15.70 | | | | | | | | | | | | | | | | (3686) $false
% 110.16/15.70 | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | CLOSE: (3686) is inconsistent.
% 110.16/15.70 | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | Case 2:
% 110.16/15.70 | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | (3687) all_55_6 = e0
% 110.16/15.70 | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3687) imply:
% 110.16/15.70 | | | | | | | | | | | | | | | | (3688) all_53_7 = e0
% 110.16/15.70 | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | REDUCE: (139), (3688) imply:
% 110.16/15.70 | | | | | | | | | | | | | | | | (3689) ~ (all_53_4 = e0)
% 110.16/15.70 | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 110.16/15.70 | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.70 | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | (3690) all_55_4 = e3
% 110.16/15.70 | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (3690) imply:
% 110.16/15.70 | | | | | | | | | | | | | | | | | (3691) all_53_4 = e3
% 110.16/15.70 | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | REDUCE: (3668), (3691) imply:
% 110.16/15.70 | | | | | | | | | | | | | | | | | (3692) $false
% 110.16/15.70 | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | CLOSE: (3692) is inconsistent.
% 110.16/15.70 | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.70 | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | (3693) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 110.16/15.70 | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | BETA: splitting (3693) gives:
% 110.16/15.70 | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.70 | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | (3694) all_55_4 = e2
% 110.16/15.70 | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (3694) imply:
% 110.16/15.70 | | | | | | | | | | | | | | | | | | (3695) all_53_4 = e2
% 110.16/15.70 | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | REDUCE: (3653), (3695) imply:
% 110.16/15.70 | | | | | | | | | | | | | | | | | | (3696) $false
% 110.16/15.70 | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | CLOSE: (3696) is inconsistent.
% 110.16/15.70 | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.70 | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | (3697) all_55_4 = e1 | all_55_4 = e0
% 110.16/15.70 | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | BETA: splitting (3697) gives:
% 110.16/15.70 | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | (3698) all_55_4 = e1
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (3698) imply:
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | (3699) all_53_4 = e1
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | REDUCE: (140), (3699) imply:
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | (3700) ~ (all_53_6 = e1)
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | SIMP: (3700) implies:
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | (3701) ~ (all_53_6 = e1)
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (3679), (3701), (function-axioms) are
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #223.
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | (3702) all_55_4 = e0
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (3702) imply:
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | (3703) all_53_4 = e0
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | REDUCE: (3689), (3703) imply:
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | (3704) $false
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | | CLOSE: (3704) is inconsistent.
% 110.16/15.70 | | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | Case 2:
% 110.16/15.70 | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | (3705) all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 110.16/15.70 | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22)
% 110.16/15.70 | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | ALPHA: (3705) implies:
% 110.16/15.70 | | | | | | | | | | | | | (3706) op(e0, e3) = e0
% 110.16/15.70 | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | REF_CLOSE: (163), (3464), (3706), (function-axioms) are
% 110.16/15.70 | | | | | | | | | | | | | inconsistent by sub-proof #149.
% 110.16/15.70 | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | End of split
% 110.16/15.70 | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | Case 2:
% 110.16/15.70 | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | (3707) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 110.16/15.70 | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 110.16/15.70 | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 110.16/15.70 | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 110.16/15.70 | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | BETA: splitting (3707) gives:
% 110.16/15.70 | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | Case 1:
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | (3708) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 110.16/15.70 | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | ALPHA: (3708) implies:
% 110.16/15.70 | | | | | | | | | | | | (3709) op(e1, e2) = e1
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | REF_CLOSE: (107), (110), (126), (132), (139), (163), (164),
% 110.16/15.70 | | | | | | | | | | | | (166), (167), (168), (171), (172), (3464), (3669),
% 110.16/15.70 | | | | | | | | | | | | (3709), (function-axioms) are inconsistent by
% 110.16/15.70 | | | | | | | | | | | | sub-proof #99.
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | Case 2:
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | (3710) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 110.16/15.70 | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | ALPHA: (3710) implies:
% 110.16/15.70 | | | | | | | | | | | | (3711) op(e0, e2) = e0
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e0,
% 110.16/15.70 | | | | | | | | | | | | e2, e0, simplifying with (162), (3711) gives:
% 110.16/15.70 | | | | | | | | | | | | (3712) all_53_3 = e0
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | REDUCE: (152), (3712) imply:
% 110.16/15.70 | | | | | | | | | | | | (3713) ~ (all_53_1 = e0)
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | REDUCE: (144), (3712) imply:
% 110.16/15.70 | | | | | | | | | | | | (3714) ~ (all_53_7 = e0)
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | SIMP: (3714) implies:
% 110.16/15.70 | | | | | | | | | | | | (3715) ~ (all_53_7 = e0)
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | REDUCE: (3660), (3712) imply:
% 110.16/15.70 | | | | | | | | | | | | (3716) ~ (e1 = e0)
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | BETA: splitting (110) gives:
% 110.16/15.70 | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | Case 1:
% 110.16/15.70 | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | (3717) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 110.16/15.70 | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 110.16/15.70 | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | ALPHA: (3717) implies:
% 110.16/15.70 | | | | | | | | | | | | | (3718) op(e3, e0) = e3
% 110.16/15.70 | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | | REF_CLOSE: (109), (117), (161), (169), (172), (173), (3655),
% 110.16/15.70 | | | | | | | | | | | | | (3713), (3718), (function-axioms) are inconsistent
% 110.16/15.70 | | | | | | | | | | | | | by sub-proof #51.
% 110.16/15.70 | | | | | | | | | | | | |
% 110.16/15.70 | | | | | | | | | | | | Case 2:
% 110.16/15.71 | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | (3719) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 110.16/15.71 | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 110.16/15.71 | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 110.16/15.71 | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 110.16/15.71 | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | BETA: splitting (3719) gives:
% 110.16/15.71 | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | Case 1:
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | (3720) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 110.16/15.71 | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | ALPHA: (3720) implies:
% 110.16/15.71 | | | | | | | | | | | | | | (3721) ~ (all_52_2 = e0)
% 110.16/15.71 | | | | | | | | | | | | | | (3722) op(e0, e2) = all_52_2
% 110.16/15.71 | | | | | | | | | | | | | | (3723) op(e2, e0) = e2
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | Case 1:
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | (3724) all_55_6 = e3
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3724) imply:
% 110.16/15.71 | | | | | | | | | | | | | | | (3725) all_53_7 = e3
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | SIMP: (3725) implies:
% 110.16/15.71 | | | | | | | | | | | | | | | (3726) all_53_7 = e3
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | REDUCE: (128), (3726) imply:
% 110.16/15.71 | | | | | | | | | | | | | | | (3727) ~ (all_53_15 = e3)
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | SIMP: (3727) implies:
% 110.16/15.71 | | | | | | | | | | | | | | | (3728) ~ (all_53_15 = e3)
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | REF_CLOSE: (107), (108), (126), (132), (162), (163), (166),
% 110.16/15.71 | | | | | | | | | | | | | | | (167), (168), (171), (174), (206), (250), (3464),
% 110.16/15.71 | | | | | | | | | | | | | | | (3660), (3667), (3721), (3722), (3723), (3728),
% 110.16/15.71 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.71 | | | | | | | | | | | | | | | #12.
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | Case 2:
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | (3729) all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | REF_CLOSE: (260), (3654), (3661), (3715), (3729) are
% 110.16/15.71 | | | | | | | | | | | | | | | inconsistent by sub-proof #114.
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | End of split
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | Case 2:
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | (3730) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 110.16/15.71 | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | ALPHA: (3730) implies:
% 110.16/15.71 | | | | | | | | | | | | | | (3731) op(e1, e0) = e1
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | Case 1:
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | (3732) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 110.16/15.71 | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | ALPHA: (3732) implies:
% 110.16/15.71 | | | | | | | | | | | | | | | (3733) op(e3, e1) = e3
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | Case 1:
% 110.16/15.71 | | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | | (3734) (all_57_32 = e0 & op(e1, e3) = e0) | (all_57_33 =
% 110.16/15.71 | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0)
% 110.16/15.71 | | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | | REF_CLOSE: (166), (167), (3465), (3715), (3734),
% 110.16/15.71 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.71 | | | | | | | | | | | | | | | | #11.
% 110.16/15.71 | | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | Case 2:
% 110.16/15.71 | | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | | (3735) (all_57_34 = e0 & op(e1, e1) = e0) | (all_57_35 =
% 110.16/15.71 | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 110.16/15.71 | | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | | BETA: splitting (3735) gives:
% 110.16/15.71 | | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.71 | | | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | | | (3736) all_57_34 = e0 & op(e1, e1) = e0
% 110.16/15.71 | | | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | | | ALPHA: (3736) implies:
% 110.16/15.71 | | | | | | | | | | | | | | | | | (3737) op(e1, e1) = e0
% 110.16/15.71 | | | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (161), (169), (173), (228), (3652),
% 110.16/15.71 | | | | | | | | | | | | | | | | | (3655), (3733), (3737), (function-axioms) are
% 110.16/15.71 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #85.
% 110.16/15.71 | | | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.71 | | | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | | | (3738) all_57_35 = e0 & op(e1, e0) = e0
% 110.16/15.71 | | | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | | | ALPHA: (3738) implies:
% 110.16/15.71 | | | | | | | | | | | | | | | | | (3739) op(e1, e0) = e0
% 110.16/15.71 | | | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3731), (3739), (function-axioms) are
% 110.16/15.71 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #81.
% 110.16/15.71 | | | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | | End of split
% 110.16/15.71 | | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | End of split
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | Case 2:
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | (3740) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 110.16/15.71 | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 110.16/15.71 | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 110.16/15.71 | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | | REF_CLOSE: (161), (169), (3655), (3713), (3740),
% 110.16/15.71 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.71 | | | | | | | | | | | | | | | #229.
% 110.16/15.71 | | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | End of split
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | End of split
% 110.16/15.71 | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | End of split
% 110.16/15.71 | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | End of split
% 110.16/15.71 | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | End of split
% 110.16/15.71 | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | End of split
% 110.16/15.71 | | | | | | | | |
% 110.16/15.71 | | | | | | | | End of split
% 110.16/15.71 | | | | | | | |
% 110.16/15.71 | | | | | | | End of split
% 110.16/15.71 | | | | | | |
% 110.16/15.71 | | | | | | Case 2:
% 110.16/15.71 | | | | | | |
% 110.16/15.71 | | | | | | | (3741) all_12_2 = e0
% 110.16/15.71 | | | | | | | (3742) op(e0, e0) = all_12_1 & $i(all_12_1) & ( ~ (all_12_1 =
% 110.16/15.71 | | | | | | | e1) | ( ~ (all_12_0 = e3) & op(e1, e0) = all_12_0 &
% 110.16/15.71 | | | | | | | $i(all_12_0)))
% 110.16/15.71 | | | | | | |
% 110.16/15.71 | | | | | | | ALPHA: (3742) implies:
% 110.16/15.71 | | | | | | | (3743) op(e0, e0) = all_12_1
% 110.16/15.71 | | | | | | |
% 110.16/15.71 | | | | | | | COMBINE_EQS: (323), (3741) imply:
% 110.16/15.71 | | | | | | | (3744) all_10_2 = e0
% 110.16/15.71 | | | | | | |
% 110.16/15.71 | | | | | | | SIMP: (3744) implies:
% 110.16/15.71 | | | | | | | (3745) all_10_2 = e0
% 110.16/15.71 | | | | | | |
% 110.16/15.71 | | | | | | | COMBINE_EQS: (330), (3745) imply:
% 110.16/15.71 | | | | | | | (3746) all_30_2 = e0
% 110.16/15.71 | | | | | | |
% 110.16/15.71 | | | | | | | REDUCE: (367), (3745) imply:
% 110.16/15.71 | | | | | | | (3747) ~ (all_53_7 = e0)
% 110.16/15.71 | | | | | | |
% 110.16/15.71 | | | | | | | REDUCE: (368), (3745) imply:
% 110.16/15.71 | | | | | | | (3748) ~ (all_53_8 = e0)
% 110.16/15.71 | | | | | | |
% 110.16/15.71 | | | | | | | REDUCE: (369), (3745) imply:
% 110.16/15.71 | | | | | | | (3749) ~ (all_53_9 = e0)
% 110.16/15.71 | | | | | | |
% 110.16/15.71 | | | | | | | REDUCE: (3496), (3745) imply:
% 110.16/15.71 | | | | | | | (3750) ~ (e3 = e0)
% 110.16/15.71 | | | | | | |
% 110.16/15.71 | | | | | | | BETA: splitting (75) gives:
% 110.16/15.71 | | | | | | |
% 110.16/15.71 | | | | | | | Case 1:
% 110.16/15.71 | | | | | | | |
% 110.16/15.71 | | | | | | | | (3751) ~ (all_30_2 = e0)
% 110.16/15.71 | | | | | | | |
% 110.16/15.71 | | | | | | | | REDUCE: (3746), (3751) imply:
% 110.16/15.71 | | | | | | | | (3752) $false
% 110.16/15.71 | | | | | | | |
% 110.16/15.71 | | | | | | | | CLOSE: (3752) is inconsistent.
% 110.16/15.71 | | | | | | | |
% 110.16/15.71 | | | | | | | Case 2:
% 110.16/15.71 | | | | | | | |
% 110.16/15.71 | | | | | | | | (3753) op(e0, e0) = all_30_1 & $i(all_30_1) & ( ~ (all_30_1 =
% 110.16/15.71 | | | | | | | | e3) | ( ~ (all_30_0 = e1) & op(e3, e0) = all_30_0
% 110.16/15.71 | | | | | | | | & $i(all_30_0)))
% 110.16/15.71 | | | | | | | |
% 110.16/15.71 | | | | | | | | ALPHA: (3753) implies:
% 110.16/15.71 | | | | | | | | (3754) op(e0, e0) = all_30_1
% 110.16/15.71 | | | | | | | | (3755) ~ (all_30_1 = e3) | ( ~ (all_30_0 = e1) & op(e3, e0)
% 110.16/15.71 | | | | | | | | = all_30_0 & $i(all_30_0))
% 110.16/15.71 | | | | | | | |
% 110.16/15.71 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 110.16/15.71 | | | | | | | | all_30_1, e0, e0, simplifying with (3461), (3754)
% 110.16/15.71 | | | | | | | | gives:
% 110.16/15.71 | | | | | | | | (3756) all_30_1 = all_4_1
% 110.16/15.71 | | | | | | | |
% 110.16/15.71 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_1,
% 110.16/15.71 | | | | | | | | all_30_1, e0, e0, simplifying with (3743), (3754)
% 110.16/15.71 | | | | | | | | gives:
% 110.16/15.71 | | | | | | | | (3757) all_30_1 = all_12_1
% 110.16/15.71 | | | | | | | |
% 110.16/15.71 | | | | | | | | COMBINE_EQS: (3756), (3757) imply:
% 110.16/15.71 | | | | | | | | (3758) all_12_1 = all_4_1
% 110.16/15.71 | | | | | | | |
% 110.16/15.71 | | | | | | | | SIMP: (3758) implies:
% 110.16/15.71 | | | | | | | | (3759) all_12_1 = all_4_1
% 110.16/15.71 | | | | | | | |
% 110.16/15.71 | | | | | | | | BETA: splitting (51) gives:
% 110.16/15.71 | | | | | | | |
% 110.16/15.71 | | | | | | | | Case 1:
% 110.16/15.71 | | | | | | | | |
% 110.16/15.71 | | | | | | | | | (3760) ~ (all_14_2 = e2)
% 110.16/15.71 | | | | | | | | |
% 110.16/15.71 | | | | | | | | | BETA: splitting (57) gives:
% 110.16/15.71 | | | | | | | | |
% 110.16/15.71 | | | | | | | | | Case 1:
% 110.16/15.71 | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | (3761) ~ (all_18_2 = e3)
% 110.16/15.71 | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | REDUCE: (326), (3761) imply:
% 110.16/15.71 | | | | | | | | | | (3762) ~ (all_14_2 = e3)
% 110.16/15.71 | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | BETA: splitting (63) gives:
% 110.16/15.71 | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | Case 1:
% 110.16/15.71 | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | (3763) ~ (all_22_2 = e0)
% 110.16/15.71 | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | REDUCE: (329), (3763) imply:
% 110.16/15.71 | | | | | | | | | | | (3764) ~ (all_14_2 = e0)
% 110.16/15.71 | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (117), (123),
% 110.16/15.71 | | | | | | | | | | | (126), (127), (148), (152), (153), (161), (162),
% 110.16/15.71 | | | | | | | | | | | (163), (164), (166), (167), (168), (169), (171),
% 110.16/15.71 | | | | | | | | | | | (172), (173), (174), (203), (341), (357), (359),
% 110.16/15.71 | | | | | | | | | | | (361), (3760), (3762), (3764), (function-axioms)
% 110.16/15.71 | | | | | | | | | | | are inconsistent by sub-proof #216.
% 110.16/15.71 | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | Case 2:
% 110.16/15.71 | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | (3765) all_22_2 = e0
% 110.16/15.71 | | | | | | | | | | | (3766) op(e0, e0) = all_22_1 & $i(all_22_1) & ( ~
% 110.16/15.71 | | | | | | | | | | | (all_22_1 = e2) | ( ~ (all_22_0 = e3) & op(e2,
% 110.16/15.71 | | | | | | | | | | | e0) = all_22_0 & $i(all_22_0)))
% 110.16/15.71 | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | ALPHA: (3766) implies:
% 110.16/15.71 | | | | | | | | | | | (3767) op(e0, e0) = all_22_1
% 110.16/15.71 | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | COMBINE_EQS: (329), (3765) imply:
% 110.16/15.71 | | | | | | | | | | | (3768) all_14_2 = e0
% 110.16/15.71 | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | COMBINE_EQS: (331), (3768) imply:
% 110.16/15.71 | | | | | | | | | | | (3769) all_32_2 = e0
% 110.16/15.71 | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | REDUCE: (357), (3768) imply:
% 110.16/15.71 | | | | | | | | | | | (3770) ~ (all_53_4 = e0)
% 110.16/15.71 | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | BETA: splitting (240) gives:
% 110.16/15.71 | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | Case 1:
% 110.16/15.71 | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | (3771) (all_57_4 = e0 & op(e3, e0) = e0) | (all_57_5 = e0
% 110.16/15.71 | | | | | | | | | | | | & op(e2, e0) = e0)
% 110.16/15.71 | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | REF_CLOSE: (168), (172), (3467), (3748), (3771),
% 110.16/15.71 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.71 | | | | | | | | | | | | #10.
% 110.16/15.71 | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | Case 2:
% 110.16/15.71 | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | (3772) (all_57_6 = e0 & op(e1, e0) = e0) | (all_57_7 = e0
% 110.16/15.71 | | | | | | | | | | | | & op(e0, e0) = e0)
% 110.16/15.71 | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | BETA: splitting (3772) gives:
% 110.16/15.71 | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | Case 1:
% 110.16/15.71 | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | (3773) all_57_6 = e0 & op(e1, e0) = e0
% 110.16/15.71 | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | ALPHA: (3773) implies:
% 110.16/15.71 | | | | | | | | | | | | | (3774) op(e1, e0) = e0
% 110.16/15.71 | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | REF_CLOSE: (164), (3770), (3774), (function-axioms) are
% 110.16/15.71 | | | | | | | | | | | | | inconsistent by sub-proof #151.
% 110.16/15.71 | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | Case 2:
% 110.16/15.71 | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | (3775) all_57_7 = e0 & op(e0, e0) = e0
% 110.16/15.71 | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | ALPHA: (3775) implies:
% 110.16/15.71 | | | | | | | | | | | | | (3776) op(e0, e0) = e0
% 110.16/15.71 | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | BETA: splitting (78) gives:
% 110.16/15.71 | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | Case 1:
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | (3777) ~ (all_32_2 = e0)
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | REDUCE: (3769), (3777) imply:
% 110.16/15.71 | | | | | | | | | | | | | | (3778) $false
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | CLOSE: (3778) is inconsistent.
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | Case 2:
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | (3779) op(e0, e0) = all_32_1 & $i(all_32_1) & ( ~
% 110.16/15.71 | | | | | | | | | | | | | | (all_32_1 = e3) | ( ~ (all_32_0 = e2) & op(e3,
% 110.16/15.71 | | | | | | | | | | | | | | e0) = all_32_0 & $i(all_32_0)))
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | ALPHA: (3779) implies:
% 110.16/15.71 | | | | | | | | | | | | | | (3780) op(e0, e0) = all_32_1
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 110.16/15.71 | | | | | | | | | | | | | | all_22_1, e0, e0, simplifying with (3461), (3767)
% 110.16/15.71 | | | | | | | | | | | | | | gives:
% 110.16/15.71 | | | | | | | | | | | | | | (3781) all_22_1 = all_4_1
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 110.16/15.71 | | | | | | | | | | | | | | all_32_1, e0, e0, simplifying with (3767), (3780)
% 110.16/15.71 | | | | | | | | | | | | | | gives:
% 110.16/15.71 | | | | | | | | | | | | | | (3782) all_32_1 = all_22_1
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_32_1,
% 110.16/15.71 | | | | | | | | | | | | | | e0, e0, simplifying with (3776), (3780) gives:
% 110.16/15.71 | | | | | | | | | | | | | | (3783) all_32_1 = e0
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | COMBINE_EQS: (3782), (3783) imply:
% 110.16/15.71 | | | | | | | | | | | | | | (3784) all_22_1 = e0
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | SIMP: (3784) implies:
% 110.16/15.71 | | | | | | | | | | | | | | (3785) all_22_1 = e0
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | COMBINE_EQS: (3781), (3785) imply:
% 110.16/15.71 | | | | | | | | | | | | | | (3786) all_4_1 = e0
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | SIMP: (3786) implies:
% 110.16/15.71 | | | | | | | | | | | | | | (3787) all_4_1 = e0
% 110.16/15.71 | | | | | | | | | | | | | |
% 110.16/15.71 | | | | | | | | | | | | | | REDUCE: (3486), (3787) imply:
% 110.16/15.72 | | | | | | | | | | | | | | (3788) ~ (all_53_1 = e0)
% 110.16/15.72 | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | REDUCE: (3488), (3787) imply:
% 110.16/15.72 | | | | | | | | | | | | | | (3789) ~ (all_53_3 = e0)
% 110.16/15.72 | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 110.16/15.72 | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | Case 1:
% 110.16/15.72 | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | (3790) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2)
% 110.16/15.72 | | | | | | | | | | | | | | | = all_52_18 & op(e2, e3) = e2 & $i(all_52_18)
% 110.16/15.72 | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | ALPHA: (3790) implies:
% 110.16/15.72 | | | | | | | | | | | | | | | (3791) ~ (all_52_18 = e3)
% 110.16/15.72 | | | | | | | | | | | | | | | (3792) op(e2, e3) = e2
% 110.16/15.72 | | | | | | | | | | | | | | | (3793) op(e3, e2) = all_52_18
% 110.16/15.72 | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_10,
% 110.16/15.72 | | | | | | | | | | | | | | | e2, e3, e2, simplifying with (171), (3792) gives:
% 110.16/15.72 | | | | | | | | | | | | | | | (3794) all_53_10 = e2
% 110.16/15.72 | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 110.16/15.72 | | | | | | | | | | | | | | | all_52_18, e2, e3, simplifying with (174), (3793)
% 110.16/15.72 | | | | | | | | | | | | | | | gives:
% 110.16/15.72 | | | | | | | | | | | | | | | (3795) all_53_15 = all_52_18
% 110.16/15.72 | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | REDUCE: (126), (3794) imply:
% 110.16/15.72 | | | | | | | | | | | | | | | (3796) ~ (all_53_8 = e2)
% 110.16/15.72 | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 110.16/15.72 | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | Case 1:
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | (3797) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 110.16/15.72 | | | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | ALPHA: (3797) implies:
% 110.16/15.72 | | | | | | | | | | | | | | | | (3798) op(e3, e2) = e3
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | REF_CLOSE: (3791), (3793), (3798), (function-axioms) are
% 110.16/15.72 | | | | | | | | | | | | | | | | inconsistent by sub-proof #234.
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | Case 2:
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | (3799) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 110.16/15.72 | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 110.16/15.72 | | | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 110.16/15.72 | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | BETA: splitting (3799) gives:
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | (3800) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 110.16/15.72 | | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | ALPHA: (3800) implies:
% 110.16/15.72 | | | | | | | | | | | | | | | | | (3801) ~ (all_52_14 = e2)
% 110.16/15.72 | | | | | | | | | | | | | | | | | (3802) op(e2, e1) = all_52_14
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.72 | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | (3803) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 110.16/15.72 | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 110.16/15.72 | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | ALPHA: (3803) implies:
% 110.16/15.72 | | | | | | | | | | | | | | | | | | (3804) op(e3, e1) = e3
% 110.16/15.72 | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (110), (113), (117), (139), (162), (164),
% 110.16/15.72 | | | | | | | | | | | | | | | | | | (166), (168), (172), (173), (174), (3789), (3796),
% 110.16/15.72 | | | | | | | | | | | | | | | | | | (3804), (function-axioms) are inconsistent by
% 110.16/15.72 | | | | | | | | | | | | | | | | | | sub-proof #211.
% 110.16/15.72 | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.72 | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | (3805) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 110.16/15.72 | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 110.16/15.72 | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 110.16/15.72 | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (169), (3788), (3801), (3802), (3805),
% 110.16/15.72 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.72 | | | | | | | | | | | | | | | | | | #107.
% 110.16/15.72 | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | End of split
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | (3806) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 110.16/15.72 | | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | ALPHA: (3806) implies:
% 110.16/15.72 | | | | | | | | | | | | | | | | | (3807) op(e0, e2) = e0
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (3789), (3807), (function-axioms) are
% 110.16/15.72 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | End of split
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | End of split
% 110.16/15.72 | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | Case 2:
% 110.16/15.72 | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | (3808) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 110.16/15.72 | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) |
% 110.16/15.72 | | | | | | | | | | | | | | | (all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 110.16/15.72 | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22))
% 110.16/15.72 | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | BETA: splitting (3808) gives:
% 110.16/15.72 | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | Case 1:
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | (3809) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 110.16/15.72 | | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | ALPHA: (3809) implies:
% 110.16/15.72 | | | | | | | | | | | | | | | | (3810) op(e1, e3) = e1
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e1,
% 110.16/15.72 | | | | | | | | | | | | | | | | e3, e1, simplifying with (167), (3810) gives:
% 110.16/15.72 | | | | | | | | | | | | | | | | (3811) all_53_6 = e1
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | REDUCE: (140), (3811) imply:
% 110.16/15.72 | | | | | | | | | | | | | | | | (3812) ~ (all_53_4 = e1)
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | REDUCE: (132), (3811) imply:
% 110.16/15.72 | | | | | | | | | | | | | | | | (3813) ~ (all_53_7 = e1)
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | SIMP: (3813) implies:
% 110.16/15.72 | | | | | | | | | | | | | | | | (3814) ~ (all_53_7 = e1)
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | (3815) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 110.16/15.72 | | | | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | ALPHA: (3815) implies:
% 110.16/15.72 | | | | | | | | | | | | | | | | | (3816) op(e3, e2) = e3
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.72 | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | (3817) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 110.16/15.72 | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 110.16/15.72 | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | ALPHA: (3817) implies:
% 110.16/15.72 | | | | | | | | | | | | | | | | | | (3818) op(e3, e1) = e3
% 110.16/15.72 | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (173), (174), (3816), (3818),
% 110.16/15.72 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.72 | | | | | | | | | | | | | | | | | | #169.
% 110.16/15.72 | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.72 | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | (3819) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 110.16/15.72 | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 110.16/15.72 | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 110.16/15.72 | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | BETA: splitting (3819) gives:
% 110.16/15.72 | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.72 | | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | (3820) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)
% 110.16/15.72 | | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | ALPHA: (3820) implies:
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | (3821) op(e2, e1) = e2
% 110.16/15.72 | | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e2,
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (169), (3821) gives:
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | (3822) all_53_9 = e2
% 110.16/15.72 | | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | e3, e2, e3, simplifying with (174), (3816) gives:
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | (3823) all_53_15 = e3
% 110.16/15.72 | | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | REDUCE: (115), (3823) imply:
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | (3824) ~ (all_53_12 = e3)
% 110.16/15.72 | | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (127), (164), (168), (169), (172), (3812),
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | (3821), (3824), (function-axioms) are inconsistent
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | by sub-proof #133.
% 110.16/15.72 | | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.72 | | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | (3825) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 110.16/15.72 | | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | ALPHA: (3825) implies:
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | (3826) op(e0, e1) = e0
% 110.16/15.72 | | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3788), (3826), (function-axioms) are
% 110.16/15.72 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #230.
% 110.16/15.72 | | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.72 | | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | End of split
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | (3827) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 110.16/15.72 | | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 110.16/15.72 | | | | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 110.16/15.72 | | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (166), (3789), (3814), (3827),
% 110.16/15.72 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.72 | | | | | | | | | | | | | | | | | #218.
% 110.16/15.72 | | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | End of split
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | Case 2:
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | (3828) all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 110.16/15.72 | | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22)
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | ALPHA: (3828) implies:
% 110.16/15.72 | | | | | | | | | | | | | | | | (3829) op(e0, e3) = e0
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3464), (3829), (function-axioms) are
% 110.16/15.72 | | | | | | | | | | | | | | | | inconsistent by sub-proof #149.
% 110.16/15.72 | | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | | End of split
% 110.16/15.72 | | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | End of split
% 110.16/15.72 | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | End of split
% 110.16/15.72 | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | End of split
% 110.16/15.72 | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | End of split
% 110.16/15.72 | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | End of split
% 110.16/15.72 | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | Case 2:
% 110.16/15.72 | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | (3830) all_18_2 = e3
% 110.16/15.72 | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | COMBINE_EQS: (326), (3830) imply:
% 110.16/15.72 | | | | | | | | | | (3831) all_14_2 = e3
% 110.16/15.72 | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | SIMP: (3831) implies:
% 110.16/15.72 | | | | | | | | | | (3832) all_14_2 = e3
% 110.16/15.72 | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | REDUCE: (359), (3832) imply:
% 110.16/15.72 | | | | | | | | | | (3833) ~ (all_53_6 = e3)
% 110.16/15.72 | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | REDUCE: (361), (3832) imply:
% 110.16/15.72 | | | | | | | | | | (3834) ~ (all_53_7 = e3)
% 110.16/15.72 | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | REDUCE: (50), (3832) imply:
% 110.16/15.72 | | | | | | | | | | (3835) op(e1, e1) = e3
% 110.16/15.72 | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | BETA: splitting (233) gives:
% 110.16/15.72 | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | Case 1:
% 110.16/15.72 | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | (3836) (all_57_32 = e0 & op(e1, e3) = e0) | (all_57_33 =
% 110.16/15.72 | | | | | | | | | | | e0 & op(e1, e2) = e0)
% 110.16/15.72 | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | REF_CLOSE: (166), (167), (3465), (3747), (3836),
% 110.16/15.72 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.72 | | | | | | | | | | | #11.
% 110.16/15.72 | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | Case 2:
% 110.16/15.72 | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | (3837) (all_57_34 = e0 & op(e1, e1) = e0) | (all_57_35 =
% 110.16/15.72 | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 110.16/15.72 | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | BETA: splitting (3837) gives:
% 110.16/15.72 | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | Case 1:
% 110.16/15.72 | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | (3838) all_57_34 = e0 & op(e1, e1) = e0
% 110.16/15.72 | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | ALPHA: (3838) implies:
% 110.16/15.72 | | | | | | | | | | | | (3839) op(e1, e1) = e0
% 110.16/15.72 | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | REF_CLOSE: (6), (3835), (3839), (function-axioms) are
% 110.16/15.72 | | | | | | | | | | | | inconsistent by sub-proof #152.
% 110.16/15.72 | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | Case 2:
% 110.16/15.72 | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | (3840) all_57_35 = e0 & op(e1, e0) = e0
% 110.16/15.72 | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | ALPHA: (3840) implies:
% 110.16/15.72 | | | | | | | | | | | | (3841) op(e1, e0) = e0
% 110.16/15.72 | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | BETA: splitting (227) gives:
% 110.16/15.72 | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | Case 1:
% 110.16/15.72 | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | (3842) (all_57_56 = e3 & op(e1, e3) = e3) | (all_57_57 =
% 110.16/15.72 | | | | | | | | | | | | | e3 & op(e1, e2) = e3)
% 110.16/15.72 | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | BETA: splitting (3842) gives:
% 110.16/15.72 | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | Case 1:
% 110.16/15.72 | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | (3843) all_57_56 = e3 & op(e1, e3) = e3
% 110.16/15.72 | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | REF_CLOSE: (167), (3833), (3843), (function-axioms) are
% 110.16/15.72 | | | | | | | | | | | | | | inconsistent by sub-proof #127.
% 110.16/15.72 | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | Case 2:
% 110.16/15.72 | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | (3844) all_57_57 = e3 & op(e1, e2) = e3
% 110.16/15.72 | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | ALPHA: (3844) implies:
% 110.16/15.72 | | | | | | | | | | | | | | (3845) op(e1, e2) = e3
% 110.16/15.72 | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | | REF_CLOSE: (166), (3834), (3845), (function-axioms) are
% 110.16/15.72 | | | | | | | | | | | | | | inconsistent by sub-proof #179.
% 110.16/15.72 | | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | | End of split
% 110.16/15.72 | | | | | | | | | | | | |
% 110.16/15.72 | | | | | | | | | | | | Case 2:
% 110.16/15.72 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | (3846) (all_57_58 = e3 & op(e1, e1) = e3) | (all_57_59 =
% 110.16/15.73 | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | BETA: splitting (3846) gives:
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | Case 1:
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | REF_CLOSE: (4), (110), (124), (137), (164), (168), (172),
% 110.16/15.73 | | | | | | | | | | | | | | (196), (208), (272), (3485), (3489), (3491),
% 110.16/15.73 | | | | | | | | | | | | | | (3493), (3495), (3755), (3756), (3841),
% 110.16/15.73 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.73 | | | | | | | | | | | | | | #9.
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | Case 2:
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | (3847) all_57_59 = e3 & op(e1, e0) = e3
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | ALPHA: (3847) implies:
% 110.16/15.73 | | | | | | | | | | | | | | (3848) op(e1, e0) = e3
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e0,
% 110.16/15.73 | | | | | | | | | | | | | | e1, simplifying with (3841), (3848) gives:
% 110.16/15.73 | | | | | | | | | | | | | | (3849) e3 = e0
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | REDUCE: (6), (3849) imply:
% 110.16/15.73 | | | | | | | | | | | | | | (3850) $false
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | CLOSE: (3850) is inconsistent.
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | End of split
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | End of split
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | End of split
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | End of split
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | End of split
% 110.16/15.73 | | | | | | | | |
% 110.16/15.73 | | | | | | | | Case 2:
% 110.16/15.73 | | | | | | | | |
% 110.16/15.73 | | | | | | | | | (3851) all_14_2 = e2
% 110.16/15.73 | | | | | | | | |
% 110.16/15.73 | | | | | | | | | REDUCE: (363), (3851) imply:
% 110.16/15.73 | | | | | | | | | (3852) ~ (all_53_9 = e2)
% 110.16/15.73 | | | | | | | | |
% 110.16/15.73 | | | | | | | | | REDUCE: (365), (3851) imply:
% 110.16/15.73 | | | | | | | | | (3853) ~ (all_53_13 = e2)
% 110.16/15.73 | | | | | | | | |
% 110.16/15.73 | | | | | | | | | REDUCE: (50), (3851) imply:
% 110.16/15.73 | | | | | | | | | (3854) op(e1, e1) = e2
% 110.16/15.73 | | | | | | | | |
% 110.16/15.73 | | | | | | | | | BETA: splitting (232) gives:
% 110.16/15.73 | | | | | | | | |
% 110.16/15.73 | | | | | | | | | Case 1:
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | (3855) (all_57_36 = e0 & op(e3, e1) = e0) | (all_57_37 =
% 110.16/15.73 | | | | | | | | | | e0 & op(e2, e1) = e0)
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | BETA: splitting (3855) gives:
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | Case 1:
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | (3856) all_57_36 = e0 & op(e3, e1) = e0
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | ALPHA: (3856) implies:
% 110.16/15.73 | | | | | | | | | | | (3857) op(e3, e1) = e0
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | REF_CLOSE: (173), (3468), (3857), (function-axioms) are
% 110.16/15.73 | | | | | | | | | | | inconsistent by sub-proof #202.
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | Case 2:
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | (3858) all_57_37 = e0 & op(e2, e1) = e0
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | ALPHA: (3858) implies:
% 110.16/15.73 | | | | | | | | | | | (3859) op(e2, e1) = e0
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | REF_CLOSE: (169), (3749), (3859), (function-axioms) are
% 110.16/15.73 | | | | | | | | | | | inconsistent by sub-proof #147.
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | End of split
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | Case 2:
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | (3860) (all_57_38 = e0 & op(e1, e1) = e0) | (all_57_39 =
% 110.16/15.73 | | | | | | | | | | e0 & op(e0, e1) = e0)
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | BETA: splitting (3860) gives:
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | Case 1:
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | (3861) all_57_38 = e0 & op(e1, e1) = e0
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | ALPHA: (3861) implies:
% 110.16/15.73 | | | | | | | | | | | (3862) op(e1, e1) = e0
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | REF_CLOSE: (5), (3854), (3862), (function-axioms) are
% 110.16/15.73 | | | | | | | | | | | inconsistent by sub-proof #109.
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | Case 2:
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | (3863) all_57_39 = e0 & op(e0, e1) = e0
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | ALPHA: (3863) implies:
% 110.16/15.73 | | | | | | | | | | | (3864) op(e0, e1) = e0
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | BETA: splitting (233) gives:
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | Case 1:
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | (3865) (all_57_32 = e0 & op(e1, e3) = e0) | (all_57_33 =
% 110.16/15.73 | | | | | | | | | | | | e0 & op(e1, e2) = e0)
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | REF_CLOSE: (166), (167), (3465), (3747), (3865),
% 110.16/15.73 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.73 | | | | | | | | | | | | #11.
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | Case 2:
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | (3866) (all_57_34 = e0 & op(e1, e1) = e0) | (all_57_35 =
% 110.16/15.73 | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | BETA: splitting (3866) gives:
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | Case 1:
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | (3867) all_57_34 = e0 & op(e1, e1) = e0
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | ALPHA: (3867) implies:
% 110.16/15.73 | | | | | | | | | | | | | (3868) op(e1, e1) = e0
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | REF_CLOSE: (5), (3854), (3868), (function-axioms) are
% 110.16/15.73 | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | Case 2:
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | (3869) all_57_35 = e0 & op(e1, e0) = e0
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | ALPHA: (3869) implies:
% 110.16/15.73 | | | | | | | | | | | | | (3870) op(e1, e0) = e0
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | BETA: splitting (228) gives:
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | Case 1:
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | (3871) (all_57_52 = e2 & op(e3, e1) = e2) | (all_57_53 =
% 110.16/15.73 | | | | | | | | | | | | | | e2 & op(e2, e1) = e2)
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | BETA: splitting (3871) gives:
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | Case 1:
% 110.16/15.73 | | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | | (3872) all_57_52 = e2 & op(e3, e1) = e2
% 110.16/15.73 | | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | | ALPHA: (3872) implies:
% 110.16/15.73 | | | | | | | | | | | | | | | (3873) op(e3, e1) = e2
% 110.16/15.73 | | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | | REF_CLOSE: (173), (3853), (3873), (function-axioms) are
% 110.16/15.73 | | | | | | | | | | | | | | | inconsistent by sub-proof #136.
% 110.16/15.73 | | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | Case 2:
% 110.16/15.73 | | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | | (3874) all_57_53 = e2 & op(e2, e1) = e2
% 110.16/15.73 | | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | | ALPHA: (3874) implies:
% 110.16/15.73 | | | | | | | | | | | | | | | (3875) op(e2, e1) = e2
% 110.16/15.73 | | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | | REF_CLOSE: (169), (3852), (3875), (function-axioms) are
% 110.16/15.73 | | | | | | | | | | | | | | | inconsistent by sub-proof #231.
% 110.16/15.73 | | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | End of split
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | Case 2:
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | (3876) (all_57_54 = e2 & op(e1, e1) = e2) | (all_57_55 =
% 110.16/15.73 | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | BETA: splitting (3876) gives:
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | Case 1:
% 110.16/15.73 | | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | | REF_CLOSE: (4), (110), (124), (137), (164), (168), (172),
% 110.16/15.73 | | | | | | | | | | | | | | | (196), (208), (272), (3485), (3489), (3491),
% 110.16/15.73 | | | | | | | | | | | | | | | (3493), (3495), (3755), (3756), (3870),
% 110.16/15.73 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.73 | | | | | | | | | | | | | | | #9.
% 110.16/15.73 | | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | Case 2:
% 110.16/15.73 | | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | | (3877) all_57_55 = e2 & op(e0, e1) = e2
% 110.16/15.73 | | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | | ALPHA: (3877) implies:
% 110.16/15.73 | | | | | | | | | | | | | | | (3878) op(e0, e1) = e2
% 110.16/15.73 | | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | | REF_CLOSE: (5), (161), (3864), (3878), (function-axioms) are
% 110.16/15.73 | | | | | | | | | | | | | | | inconsistent by sub-proof #45.
% 110.16/15.73 | | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | | End of split
% 110.16/15.73 | | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | End of split
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | End of split
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | End of split
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | End of split
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | End of split
% 110.16/15.73 | | | | | | | | |
% 110.16/15.73 | | | | | | | | End of split
% 110.16/15.73 | | | | | | | |
% 110.16/15.73 | | | | | | | End of split
% 110.16/15.73 | | | | | | |
% 110.16/15.73 | | | | | | End of split
% 110.16/15.73 | | | | | |
% 110.16/15.73 | | | | | Case 2:
% 110.16/15.73 | | | | | |
% 110.16/15.73 | | | | | | (3879) all_10_2 = e3
% 110.16/15.73 | | | | | | (3880) op(e3, e3) = all_10_1 & $i(all_10_1) & ( ~ (all_10_1 = e0)
% 110.16/15.73 | | | | | | | ( ~ (all_10_0 = e1) & op(e0, e3) = all_10_0 &
% 110.16/15.73 | | | | | | $i(all_10_0)))
% 110.16/15.73 | | | | | |
% 110.16/15.73 | | | | | | ALPHA: (3880) implies:
% 110.16/15.73 | | | | | | (3881) op(e3, e3) = all_10_1
% 110.16/15.73 | | | | | | (3882) ~ (all_10_1 = e0) | ( ~ (all_10_0 = e1) & op(e0, e3) =
% 110.16/15.73 | | | | | | all_10_0 & $i(all_10_0))
% 110.16/15.73 | | | | | |
% 110.16/15.73 | | | | | | COMBINE_EQS: (335), (3879) imply:
% 110.16/15.73 | | | | | | (3883) all_48_2 = e3
% 110.16/15.73 | | | | | |
% 110.16/15.73 | | | | | | REDUCE: (370), (3879) imply:
% 110.16/15.73 | | | | | | (3884) ~ (all_53_10 = e3)
% 110.16/15.73 | | | | | |
% 110.16/15.73 | | | | | | REDUCE: (373), (3879) imply:
% 110.16/15.73 | | | | | | (3885) ~ (all_53_15 = e3)
% 110.16/15.73 | | | | | |
% 110.16/15.73 | | | | | | REDUCE: (44), (3879) imply:
% 110.16/15.73 | | | | | | (3886) op(e2, e2) = e3
% 110.16/15.73 | | | | | |
% 110.16/15.73 | | | | | | BETA: splitting (102) gives:
% 110.16/15.73 | | | | | |
% 110.16/15.73 | | | | | | Case 1:
% 110.16/15.73 | | | | | | |
% 110.16/15.73 | | | | | | | (3887) ~ (all_48_2 = e3)
% 110.16/15.73 | | | | | | |
% 110.16/15.73 | | | | | | | REDUCE: (3883), (3887) imply:
% 110.16/15.73 | | | | | | | (3888) $false
% 110.16/15.73 | | | | | | |
% 110.16/15.73 | | | | | | | CLOSE: (3888) is inconsistent.
% 110.16/15.73 | | | | | | |
% 110.16/15.73 | | | | | | Case 2:
% 110.16/15.73 | | | | | | |
% 110.16/15.73 | | | | | | | (3889) op(e3, e3) = all_48_1 & $i(all_48_1) & ( ~ (all_48_1 =
% 110.16/15.73 | | | | | | | e1) | ( ~ (all_48_0 = e0) & op(e1, e3) = all_48_0 &
% 110.16/15.73 | | | | | | | $i(all_48_0)))
% 110.16/15.73 | | | | | | |
% 110.16/15.73 | | | | | | | ALPHA: (3889) implies:
% 110.16/15.73 | | | | | | | (3890) op(e3, e3) = all_48_1
% 110.16/15.73 | | | | | | |
% 110.16/15.73 | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_48_1,
% 110.16/15.73 | | | | | | | e3, e3, simplifying with (3470), (3890) gives:
% 110.16/15.73 | | | | | | | (3891) all_48_1 = e0
% 110.16/15.73 | | | | | | |
% 110.16/15.73 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 110.16/15.73 | | | | | | | all_48_1, e3, e3, simplifying with (3881), (3890)
% 110.16/15.73 | | | | | | | gives:
% 110.16/15.73 | | | | | | | (3892) all_48_1 = all_10_1
% 110.16/15.73 | | | | | | |
% 110.16/15.73 | | | | | | | COMBINE_EQS: (3891), (3892) imply:
% 110.16/15.73 | | | | | | | (3893) all_10_1 = e0
% 110.16/15.73 | | | | | | |
% 110.16/15.73 | | | | | | | SIMP: (3893) implies:
% 110.16/15.73 | | | | | | | (3894) all_10_1 = e0
% 110.16/15.73 | | | | | | |
% 110.16/15.73 | | | | | | | BETA: splitting (3882) gives:
% 110.16/15.73 | | | | | | |
% 110.16/15.73 | | | | | | | Case 1:
% 110.16/15.73 | | | | | | | |
% 110.16/15.73 | | | | | | | | (3895) ~ (all_10_1 = e0)
% 110.16/15.73 | | | | | | | |
% 110.16/15.73 | | | | | | | | REDUCE: (3894), (3895) imply:
% 110.16/15.73 | | | | | | | | (3896) $false
% 110.16/15.73 | | | | | | | |
% 110.16/15.73 | | | | | | | | CLOSE: (3896) is inconsistent.
% 110.16/15.73 | | | | | | | |
% 110.16/15.73 | | | | | | | Case 2:
% 110.16/15.73 | | | | | | | |
% 110.16/15.73 | | | | | | | | (3897) ~ (all_10_0 = e1) & op(e0, e3) = all_10_0 &
% 110.16/15.73 | | | | | | | | $i(all_10_0)
% 110.16/15.73 | | | | | | | |
% 110.16/15.73 | | | | | | | | ALPHA: (3897) implies:
% 110.16/15.73 | | | | | | | | (3898) ~ (all_10_0 = e1)
% 110.16/15.73 | | | | | | | | (3899) op(e0, e3) = all_10_0
% 110.16/15.73 | | | | | | | |
% 110.16/15.73 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2,
% 110.16/15.73 | | | | | | | | all_10_0, e3, e0, simplifying with (163), (3899)
% 110.16/15.73 | | | | | | | | gives:
% 110.16/15.73 | | | | | | | | (3900) all_53_2 = all_10_0
% 110.16/15.73 | | | | | | | |
% 110.16/15.73 | | | | | | | | COMBINE_EQS: (251), (3900) imply:
% 110.16/15.73 | | | | | | | | (3901) all_55_3 = all_10_0
% 110.16/15.73 | | | | | | | |
% 110.16/15.73 | | | | | | | | REDUCE: (146), (3900) imply:
% 110.16/15.73 | | | | | | | | (3902) ~ (all_53_10 = all_10_0)
% 110.16/15.73 | | | | | | | |
% 110.16/15.73 | | | | | | | | SIMP: (3902) implies:
% 110.16/15.73 | | | | | | | | (3903) ~ (all_53_10 = all_10_0)
% 110.16/15.73 | | | | | | | |
% 110.16/15.73 | | | | | | | | REDUCE: (3487), (3900) imply:
% 110.16/15.73 | | | | | | | | (3904) ~ (all_10_0 = all_4_1)
% 110.16/15.73 | | | | | | | |
% 110.16/15.73 | | | | | | | | REDUCE: (3464), (3900) imply:
% 110.16/15.73 | | | | | | | | (3905) ~ (all_10_0 = e0)
% 110.16/15.73 | | | | | | | |
% 110.16/15.73 | | | | | | | | BETA: splitting (72) gives:
% 110.16/15.73 | | | | | | | |
% 110.16/15.73 | | | | | | | | Case 1:
% 110.16/15.73 | | | | | | | | |
% 110.16/15.73 | | | | | | | | | (3906) ~ (all_28_2 = e3)
% 110.16/15.73 | | | | | | | | |
% 110.16/15.73 | | | | | | | | | REDUCE: (3482), (3906) imply:
% 110.16/15.73 | | | | | | | | | (3907) ~ (all_4_1 = e3)
% 110.16/15.73 | | | | | | | | |
% 110.16/15.73 | | | | | | | | | BETA: splitting (208) gives:
% 110.16/15.73 | | | | | | | | |
% 110.16/15.73 | | | | | | | | | Case 1:
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | (3908) all_55_0 = e3
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | COMBINE_EQS: (3485), (3908) imply:
% 110.16/15.73 | | | | | | | | | | (3909) all_4_1 = e3
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | REDUCE: (3907), (3909) imply:
% 110.16/15.73 | | | | | | | | | | (3910) $false
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | CLOSE: (3910) is inconsistent.
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | Case 2:
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | (3911) ~ (all_55_0 = e3)
% 110.16/15.73 | | | | | | | | | | (3912) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | BETA: splitting (3912) gives:
% 110.16/15.73 | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | Case 1:
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | (3913) all_55_0 = e2
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | COMBINE_EQS: (3485), (3913) imply:
% 110.16/15.73 | | | | | | | | | | | (3914) all_4_1 = e2
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | REDUCE: (3495), (3914) imply:
% 110.16/15.73 | | | | | | | | | | | (3915) $false
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | CLOSE: (3915) is inconsistent.
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | Case 2:
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | (3916) all_55_0 = e1 | all_55_0 = e0
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | BETA: splitting (3916) gives:
% 110.16/15.73 | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | Case 1:
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | (3917) all_55_0 = e1
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | COMBINE_EQS: (3485), (3917) imply:
% 110.16/15.73 | | | | | | | | | | | | (3918) all_4_1 = e1
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | REDUCE: (3493), (3918) imply:
% 110.16/15.73 | | | | | | | | | | | | (3919) $false
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | CLOSE: (3919) is inconsistent.
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | Case 2:
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | (3920) all_55_0 = e0
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | COMBINE_EQS: (3485), (3920) imply:
% 110.16/15.73 | | | | | | | | | | | | (3921) all_4_1 = e0
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | REDUCE: (3488), (3921) imply:
% 110.16/15.73 | | | | | | | | | | | | (3922) ~ (all_53_3 = e0)
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | REDUCE: (3907), (3921) imply:
% 110.16/15.73 | | | | | | | | | | | | (3923) ~ (e3 = e0)
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | REDUCE: (3493), (3921) imply:
% 110.16/15.73 | | | | | | | | | | | | (3924) ~ (e1 = e0)
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | BETA: splitting (108) gives:
% 110.16/15.73 | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | Case 1:
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | (3925) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 110.16/15.73 | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | ALPHA: (3925) implies:
% 110.16/15.73 | | | | | | | | | | | | | (3926) op(e3, e2) = e3
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | | REF_CLOSE: (174), (3885), (3926), (function-axioms) are
% 110.16/15.73 | | | | | | | | | | | | | inconsistent by sub-proof #214.
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.73 | | | | | | | | | | | | Case 2:
% 110.16/15.73 | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | (3927) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 110.16/15.74 | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 110.16/15.74 | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 110.16/15.74 | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 110.16/15.74 | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | BETA: splitting (3927) gives:
% 110.16/15.74 | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | Case 1:
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | (3928) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 110.16/15.74 | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | ALPHA: (3928) implies:
% 110.16/15.74 | | | | | | | | | | | | | | (3929) op(e1, e2) = e1
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | Case 1:
% 110.16/15.74 | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | (3930) (all_57_68 = e0 & op(e3, e2) = e0) | (all_57_69 =
% 110.16/15.74 | | | | | | | | | | | | | | | e0 & op(e2, e2) = e0)
% 110.16/15.74 | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | BETA: splitting (3930) gives:
% 110.16/15.74 | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | Case 1:
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | (3931) all_57_68 = e0 & op(e3, e2) = e0
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | ALPHA: (3931) implies:
% 110.16/15.74 | | | | | | | | | | | | | | | | (3932) op(e3, e2) = e0
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | REF_CLOSE: (174), (3469), (3932), (function-axioms) are
% 110.16/15.74 | | | | | | | | | | | | | | | | inconsistent by sub-proof #156.
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | Case 2:
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | (3933) all_57_69 = e0 & op(e2, e2) = e0
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | ALPHA: (3933) implies:
% 110.16/15.74 | | | | | | | | | | | | | | | | (3934) op(e2, e2) = e0
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3886), (3934), (function-axioms) are
% 110.16/15.74 | | | | | | | | | | | | | | | | inconsistent by sub-proof #139.
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | End of split
% 110.16/15.74 | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | Case 2:
% 110.16/15.74 | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | (3935) (all_57_70 = e0 & op(e1, e2) = e0) | (all_57_71 =
% 110.16/15.74 | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 110.16/15.74 | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | BETA: splitting (3935) gives:
% 110.16/15.74 | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | Case 1:
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | (3936) all_57_70 = e0 & op(e1, e2) = e0
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | ALPHA: (3936) implies:
% 110.16/15.74 | | | | | | | | | | | | | | | | (3937) op(e1, e2) = e0
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e0,
% 110.16/15.74 | | | | | | | | | | | | | | | | e2, e1, simplifying with (166), (3937) gives:
% 110.16/15.74 | | | | | | | | | | | | | | | | (3938) all_53_7 = e0
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e1,
% 110.16/15.74 | | | | | | | | | | | | | | | | e2, e1, simplifying with (166), (3929) gives:
% 110.16/15.74 | | | | | | | | | | | | | | | | (3939) all_53_7 = e1
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | COMBINE_EQS: (3938), (3939) imply:
% 110.16/15.74 | | | | | | | | | | | | | | | | (3940) e1 = e0
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | SIMP: (3940) implies:
% 110.16/15.74 | | | | | | | | | | | | | | | | (3941) e1 = e0
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | REDUCE: (4), (3941) imply:
% 110.16/15.74 | | | | | | | | | | | | | | | | (3942) $false
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | CLOSE: (3942) is inconsistent.
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | Case 2:
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | (3943) all_57_71 = e0 & op(e0, e2) = e0
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | ALPHA: (3943) implies:
% 110.16/15.74 | | | | | | | | | | | | | | | | (3944) op(e0, e2) = e0
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | | REF_CLOSE: (162), (3922), (3944), (function-axioms) are
% 110.16/15.74 | | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 110.16/15.74 | | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | End of split
% 110.16/15.74 | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | End of split
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | Case 2:
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | (3945) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 110.16/15.74 | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | ALPHA: (3945) implies:
% 110.16/15.74 | | | | | | | | | | | | | | (3946) op(e0, e2) = e0
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | REF_CLOSE: (162), (3922), (3946), (function-axioms) are
% 110.16/15.74 | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | End of split
% 110.16/15.74 | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | End of split
% 110.16/15.74 | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | End of split
% 110.16/15.74 | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | End of split
% 110.16/15.74 | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | End of split
% 110.16/15.74 | | | | | | | | |
% 110.16/15.74 | | | | | | | | Case 2:
% 110.16/15.74 | | | | | | | | |
% 110.16/15.74 | | | | | | | | | (3947) all_28_2 = e3
% 110.16/15.74 | | | | | | | | |
% 110.16/15.74 | | | | | | | | | COMBINE_EQS: (3482), (3947) imply:
% 110.16/15.74 | | | | | | | | | (3948) all_4_1 = e3
% 110.16/15.74 | | | | | | | | |
% 110.16/15.74 | | | | | | | | | REDUCE: (3904), (3948) imply:
% 110.16/15.74 | | | | | | | | | (3949) ~ (all_10_0 = e3)
% 110.16/15.74 | | | | | | | | |
% 110.16/15.74 | | | | | | | | | BETA: splitting (205) gives:
% 110.16/15.74 | | | | | | | | |
% 110.16/15.74 | | | | | | | | | Case 1:
% 110.16/15.74 | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | (3950) all_55_3 = e3
% 110.16/15.74 | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | COMBINE_EQS: (3901), (3950) imply:
% 110.16/15.74 | | | | | | | | | | (3951) all_10_0 = e3
% 110.16/15.74 | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | REDUCE: (3949), (3951) imply:
% 110.16/15.74 | | | | | | | | | | (3952) $false
% 110.16/15.74 | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | CLOSE: (3952) is inconsistent.
% 110.16/15.74 | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | Case 2:
% 110.16/15.74 | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | (3953) all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 110.16/15.74 | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | BETA: splitting (3953) gives:
% 110.16/15.74 | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | Case 1:
% 110.16/15.74 | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | (3954) all_55_3 = e2
% 110.16/15.74 | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | COMBINE_EQS: (3901), (3954) imply:
% 110.16/15.74 | | | | | | | | | | | (3955) all_10_0 = e2
% 110.16/15.74 | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | REDUCE: (3903), (3955) imply:
% 110.16/15.74 | | | | | | | | | | | (3956) ~ (all_53_10 = e2)
% 110.16/15.74 | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | BETA: splitting (197) gives:
% 110.16/15.74 | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | Case 1:
% 110.16/15.74 | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | (3957) all_55_11 = e3
% 110.16/15.74 | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | REF_CLOSE: (271), (3884), (3957) are inconsistent by
% 110.16/15.74 | | | | | | | | | | | | sub-proof #144.
% 110.16/15.74 | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | Case 2:
% 110.16/15.74 | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | (3958) all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 110.16/15.74 | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | BETA: splitting (3958) gives:
% 110.16/15.74 | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | Case 1:
% 110.16/15.74 | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | (3959) all_55_11 = e2
% 110.16/15.74 | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | COMBINE_EQS: (271), (3959) imply:
% 110.16/15.74 | | | | | | | | | | | | | (3960) all_53_10 = e2
% 110.16/15.74 | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | SIMP: (3960) implies:
% 110.16/15.74 | | | | | | | | | | | | | (3961) all_53_10 = e2
% 110.16/15.74 | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | REDUCE: (3956), (3961) imply:
% 110.16/15.74 | | | | | | | | | | | | | (3962) $false
% 110.16/15.74 | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | CLOSE: (3962) is inconsistent.
% 110.16/15.74 | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | Case 2:
% 110.16/15.74 | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | (3963) ~ (all_55_11 = e2)
% 110.16/15.74 | | | | | | | | | | | | | (3964) all_55_11 = e1 | all_55_11 = e0
% 110.16/15.74 | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | BETA: splitting (3964) gives:
% 110.16/15.74 | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | Case 1:
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | (3965) all_55_11 = e1
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | COMBINE_EQS: (271), (3965) imply:
% 110.16/15.74 | | | | | | | | | | | | | | (3966) all_53_10 = e1
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | SIMP: (3966) implies:
% 110.16/15.74 | | | | | | | | | | | | | | (3967) all_53_10 = e1
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | REDUCE: (131), (3967) imply:
% 110.16/15.74 | | | | | | | | | | | | | | (3968) ~ (all_53_6 = e1)
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | REDUCE: (3956), (3967) imply:
% 110.16/15.74 | | | | | | | | | | | | | | (3969) ~ (e2 = e1)
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | SIMP: (3969) implies:
% 110.16/15.74 | | | | | | | | | | | | | | (3970) ~ (e2 = e1)
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | REDUCE: (171), (3967) imply:
% 110.16/15.74 | | | | | | | | | | | | | | (3971) op(e2, e3) = e1
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | Case 1:
% 110.16/15.74 | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | (3972) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2)
% 110.16/15.74 | | | | | | | | | | | | | | | = all_52_18 & op(e2, e3) = e2 & $i(all_52_18)
% 110.16/15.74 | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | ALPHA: (3972) implies:
% 110.16/15.74 | | | | | | | | | | | | | | | (3973) op(e2, e3) = e2
% 110.16/15.74 | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | REF_CLOSE: (3970), (3971), (3973), (function-axioms) are
% 110.16/15.74 | | | | | | | | | | | | | | | inconsistent by sub-proof #53.
% 110.16/15.74 | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | Case 2:
% 110.16/15.74 | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | (3974) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 110.16/15.74 | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) |
% 110.16/15.74 | | | | | | | | | | | | | | | (all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 110.16/15.74 | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22))
% 110.16/15.74 | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (3464), (3968), (3974),
% 110.16/15.74 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.74 | | | | | | | | | | | | | | | #102.
% 110.16/15.74 | | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | End of split
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | Case 2:
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | (3975) all_55_11 = e0
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | | REF_CLOSE: (271), (3466), (3975) are inconsistent by
% 110.16/15.74 | | | | | | | | | | | | | | sub-proof #143.
% 110.16/15.74 | | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | | End of split
% 110.16/15.74 | | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | | End of split
% 110.16/15.74 | | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | End of split
% 110.16/15.74 | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | Case 2:
% 110.16/15.74 | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | (3976) all_55_3 = e1 | all_55_3 = e0
% 110.16/15.74 | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | | REF_CLOSE: (3898), (3901), (3905), (3976) are inconsistent by
% 110.16/15.74 | | | | | | | | | | | sub-proof #8.
% 110.16/15.74 | | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | | End of split
% 110.16/15.74 | | | | | | | | | |
% 110.16/15.74 | | | | | | | | | End of split
% 110.16/15.74 | | | | | | | | |
% 110.16/15.74 | | | | | | | | End of split
% 110.16/15.74 | | | | | | | |
% 110.16/15.74 | | | | | | | End of split
% 110.16/15.74 | | | | | | |
% 110.16/15.74 | | | | | | End of split
% 110.16/15.74 | | | | | |
% 110.16/15.74 | | | | | End of split
% 110.16/15.74 | | | | |
% 110.16/15.74 | | | | Case 2:
% 110.16/15.74 | | | | |
% 110.16/15.74 | | | | | (3977) all_8_2 = e2
% 110.16/15.74 | | | | | (3978) op(e2, e2) = all_8_1 & $i(all_8_1) & ( ~ (all_8_1 = e1) | (
% 110.16/15.74 | | | | | ~ (all_8_0 = e3) & op(e1, e2) = all_8_0 & $i(all_8_0)))
% 110.16/15.74 | | | | |
% 110.16/15.74 | | | | | ALPHA: (3978) implies:
% 110.16/15.74 | | | | | (3979) op(e2, e2) = all_8_1
% 110.16/15.74 | | | | | (3980) ~ (all_8_1 = e1) | ( ~ (all_8_0 = e3) & op(e1, e2) =
% 110.16/15.74 | | | | | all_8_0 & $i(all_8_0))
% 110.16/15.74 | | | | |
% 110.16/15.74 | | | | | COMBINE_EQS: (3480), (3977) imply:
% 110.16/15.74 | | | | | (3981) all_4_1 = e2
% 110.16/15.74 | | | | |
% 110.16/15.74 | | | | | COMBINE_EQS: (3481), (3981) imply:
% 110.16/15.74 | | | | | (3982) all_16_2 = e2
% 110.16/15.74 | | | | |
% 110.16/15.74 | | | | | COMBINE_EQS: (3477), (3981) imply:
% 110.16/15.74 | | | | | (3983) all_40_1 = e2
% 110.16/15.74 | | | | |
% 110.16/15.74 | | | | | REDUCE: (3486), (3981) imply:
% 110.16/15.74 | | | | | (3984) ~ (all_53_1 = e2)
% 110.16/15.74 | | | | |
% 110.16/15.74 | | | | | REDUCE: (3487), (3981) imply:
% 110.16/15.74 | | | | | (3985) ~ (all_53_2 = e2)
% 110.16/15.74 | | | | |
% 110.16/15.74 | | | | | REDUCE: (3488), (3981) imply:
% 110.16/15.74 | | | | | (3986) ~ (all_53_3 = e2)
% 110.16/15.74 | | | | |
% 110.16/15.74 | | | | | REDUCE: (3489), (3981) imply:
% 110.16/15.74 | | | | | (3987) ~ (all_53_4 = e2)
% 110.16/15.74 | | | | |
% 110.16/15.74 | | | | | REDUCE: (3490), (3981) imply:
% 110.16/15.74 | | | | | (3988) ~ (all_53_8 = e2)
% 110.16/15.74 | | | | |
% 110.16/15.74 | | | | | REDUCE: (3491), (3981) imply:
% 110.16/15.74 | | | | | (3989) ~ (all_53_12 = e2)
% 110.16/15.74 | | | | |
% 110.16/15.74 | | | | | REDUCE: (3461), (3981) imply:
% 110.16/15.74 | | | | | (3990) op(e0, e0) = e2
% 110.16/15.74 | | | | |
% 110.16/15.74 | | | | | BETA: splitting (54) gives:
% 110.16/15.74 | | | | |
% 110.16/15.74 | | | | | Case 1:
% 110.16/15.74 | | | | | |
% 110.16/15.74 | | | | | | (3991) ~ (all_16_2 = e2)
% 110.16/15.74 | | | | | |
% 110.16/15.74 | | | | | | REDUCE: (3982), (3991) imply:
% 110.16/15.74 | | | | | | (3992) $false
% 110.16/15.74 | | | | | |
% 110.16/15.74 | | | | | | CLOSE: (3992) is inconsistent.
% 110.16/15.74 | | | | | |
% 110.16/15.74 | | | | | Case 2:
% 110.16/15.74 | | | | | |
% 110.16/15.74 | | | | | | (3993) op(e2, e2) = all_16_1 & $i(all_16_1) & ( ~ (all_16_1 = e3)
% 110.16/15.74 | | | | | | | ( ~ (all_16_0 = e1) & op(e3, e2) = all_16_0 &
% 110.16/15.74 | | | | | | $i(all_16_0)))
% 110.16/15.74 | | | | | |
% 110.16/15.74 | | | | | | ALPHA: (3993) implies:
% 110.16/15.74 | | | | | | (3994) op(e2, e2) = all_16_1
% 110.16/15.74 | | | | | | (3995) ~ (all_16_1 = e3) | ( ~ (all_16_0 = e1) & op(e3, e2) =
% 110.16/15.74 | | | | | | all_16_0 & $i(all_16_0))
% 110.16/15.74 | | | | | |
% 110.16/15.74 | | | | | | BETA: splitting (3475) gives:
% 110.16/15.74 | | | | | |
% 110.16/15.74 | | | | | | Case 1:
% 110.16/15.74 | | | | | | |
% 110.16/15.74 | | | | | | | (3996) ~ (all_40_1 = e2)
% 110.16/15.74 | | | | | | |
% 110.16/15.74 | | | | | | | REDUCE: (3983), (3996) imply:
% 110.16/15.74 | | | | | | | (3997) $false
% 110.16/15.74 | | | | | | |
% 110.16/15.74 | | | | | | | CLOSE: (3997) is inconsistent.
% 110.16/15.74 | | | | | | |
% 110.16/15.74 | | | | | | Case 2:
% 110.16/15.74 | | | | | | |
% 110.16/15.74 | | | | | | | (3998) ~ (all_40_0 = e1) & op(e2, e0) = all_40_0 &
% 110.16/15.74 | | | | | | | $i(all_40_0)
% 110.16/15.74 | | | | | | |
% 110.16/15.74 | | | | | | | ALPHA: (3998) implies:
% 110.16/15.74 | | | | | | | (3999) ~ (all_40_0 = e1)
% 110.16/15.74 | | | | | | | (4000) op(e2, e0) = all_40_0
% 110.16/15.74 | | | | | | |
% 110.16/15.74 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 110.16/15.74 | | | | | | | all_40_0, e0, e2, simplifying with (168), (4000)
% 110.16/15.74 | | | | | | | gives:
% 110.16/15.74 | | | | | | | (4001) all_53_8 = all_40_0
% 110.16/15.74 | | | | | | |
% 110.16/15.74 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 110.16/15.74 | | | | | | | all_16_1, e2, e2, simplifying with (44), (3994)
% 110.16/15.74 | | | | | | | gives:
% 110.16/15.74 | | | | | | | (4002) all_16_1 = all_10_2
% 110.16/15.74 | | | | | | |
% 110.16/15.74 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1,
% 110.16/15.74 | | | | | | | all_16_1, e2, e2, simplifying with (3979), (3994)
% 110.16/15.74 | | | | | | | gives:
% 110.16/15.74 | | | | | | | (4003) all_16_1 = all_8_1
% 110.16/15.74 | | | | | | |
% 110.16/15.74 | | | | | | | COMBINE_EQS: (4002), (4003) imply:
% 110.16/15.74 | | | | | | | (4004) all_10_2 = all_8_1
% 110.16/15.74 | | | | | | |
% 110.16/15.74 | | | | | | | COMBINE_EQS: (323), (4004) imply:
% 110.16/15.74 | | | | | | | (4005) all_12_2 = all_8_1
% 110.16/15.74 | | | | | | |
% 110.16/15.74 | | | | | | | COMBINE_EQS: (303), (4004) imply:
% 110.16/15.74 | | | | | | | (4006) all_24_2 = all_8_1
% 110.16/15.74 | | | | | | |
% 110.16/15.74 | | | | | | | COMBINE_EQS: (335), (4004) imply:
% 110.16/15.74 | | | | | | | (4007) all_48_2 = all_8_1
% 110.16/15.74 | | | | | | |
% 110.16/15.74 | | | | | | | COMBINE_EQS: (340), (4004) imply:
% 110.16/15.75 | | | | | | | (4008) all_55_10 = all_8_1
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | COMBINE_EQS: (262), (4001) imply:
% 110.16/15.75 | | | | | | | (4009) all_55_8 = all_40_0
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | REDUCE: (356), (4004) imply:
% 110.16/15.75 | | | | | | | (4010) ~ (all_53_3 = all_8_1)
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | REDUCE: (367), (4004) imply:
% 110.16/15.75 | | | | | | | (4011) ~ (all_53_7 = all_8_1)
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | REDUCE: (127), (4001) imply:
% 110.16/15.75 | | | | | | | (4012) ~ (all_53_9 = all_40_0)
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | SIMP: (4012) implies:
% 110.16/15.75 | | | | | | | (4013) ~ (all_53_9 = all_40_0)
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | REDUCE: (126), (4001) imply:
% 110.16/15.75 | | | | | | | (4014) ~ (all_53_10 = all_40_0)
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | SIMP: (4014) implies:
% 110.16/15.75 | | | | | | | (4015) ~ (all_53_10 = all_40_0)
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | REDUCE: (124), (4001) imply:
% 110.16/15.75 | | | | | | | (4016) ~ (all_53_12 = all_40_0)
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | SIMP: (4016) implies:
% 110.16/15.75 | | | | | | | (4017) ~ (all_53_12 = all_40_0)
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | REDUCE: (368), (4001), (4004) imply:
% 110.16/15.75 | | | | | | | (4018) ~ (all_40_0 = all_8_1)
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | REDUCE: (3988), (4001) imply:
% 110.16/15.75 | | | | | | | (4019) ~ (all_40_0 = e2)
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | REDUCE: (369), (4004) imply:
% 110.16/15.75 | | | | | | | (4020) ~ (all_53_9 = all_8_1)
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | REDUCE: (370), (4004) imply:
% 110.16/15.75 | | | | | | | (4021) ~ (all_53_10 = all_8_1)
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | REDUCE: (373), (4004) imply:
% 110.16/15.75 | | | | | | | (4022) ~ (all_53_15 = all_8_1)
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | BETA: splitting (45) gives:
% 110.16/15.75 | | | | | | |
% 110.16/15.75 | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | |
% 110.16/15.75 | | | | | | | | (4023) ~ (all_10_2 = e3)
% 110.16/15.75 | | | | | | | |
% 110.16/15.75 | | | | | | | | REDUCE: (4004), (4023) imply:
% 110.16/15.75 | | | | | | | | (4024) ~ (all_8_1 = e3)
% 110.16/15.75 | | | | | | | |
% 110.16/15.75 | | | | | | | | BETA: splitting (48) gives:
% 110.16/15.75 | | | | | | | |
% 110.16/15.75 | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | |
% 110.16/15.75 | | | | | | | | | (4025) ~ (all_12_2 = e0)
% 110.16/15.75 | | | | | | | | |
% 110.16/15.75 | | | | | | | | | REDUCE: (4005), (4025) imply:
% 110.16/15.75 | | | | | | | | | (4026) ~ (all_8_1 = e0)
% 110.16/15.75 | | | | | | | | |
% 110.16/15.75 | | | | | | | | | BETA: splitting (51) gives:
% 110.16/15.75 | | | | | | | | |
% 110.16/15.75 | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | (4027) ~ (all_14_2 = e2)
% 110.16/15.75 | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | BETA: splitting (57) gives:
% 110.16/15.75 | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | (4028) ~ (all_18_2 = e3)
% 110.16/15.75 | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | REDUCE: (326), (4028) imply:
% 110.16/15.75 | | | | | | | | | | | (4029) ~ (all_14_2 = e3)
% 110.16/15.75 | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | BETA: splitting (63) gives:
% 110.16/15.75 | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | (4030) ~ (all_22_2 = e0)
% 110.16/15.75 | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | REDUCE: (329), (4030) imply:
% 110.16/15.75 | | | | | | | | | | | | (4031) ~ (all_14_2 = e0)
% 110.16/15.75 | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (117), (123),
% 110.16/15.75 | | | | | | | | | | | | (126), (127), (148), (152), (153), (161), (162),
% 110.16/15.75 | | | | | | | | | | | | (163), (164), (166), (167), (168), (169), (171),
% 110.16/15.75 | | | | | | | | | | | | (172), (173), (174), (203), (341), (357), (359),
% 110.16/15.75 | | | | | | | | | | | | (361), (4027), (4029), (4031), (function-axioms)
% 110.16/15.75 | | | | | | | | | | | | are inconsistent by sub-proof #216.
% 110.16/15.75 | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | Case 2:
% 110.16/15.75 | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | (4032) all_22_2 = e0
% 110.16/15.75 | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | COMBINE_EQS: (329), (4032) imply:
% 110.16/15.75 | | | | | | | | | | | | (4033) all_14_2 = e0
% 110.16/15.75 | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | REDUCE: (354), (4033) imply:
% 110.16/15.75 | | | | | | | | | | | | (4034) ~ (all_53_1 = e0)
% 110.16/15.75 | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | REDUCE: (361), (4033) imply:
% 110.16/15.75 | | | | | | | | | | | | (4035) ~ (all_53_7 = e0)
% 110.16/15.75 | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | REDUCE: (50), (4033) imply:
% 110.16/15.75 | | | | | | | | | | | | (4036) op(e1, e1) = e0
% 110.16/15.75 | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | BETA: splitting (66) gives:
% 110.16/15.75 | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | (4037) ~ (all_24_2 = e1)
% 110.16/15.75 | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | REDUCE: (4006), (4037) imply:
% 110.16/15.75 | | | | | | | | | | | | | (4038) ~ (all_8_1 = e1)
% 110.16/15.75 | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | REF_CLOSE: (109), (161), (169), (173), (198), (228), (3984),
% 110.16/15.75 | | | | | | | | | | | | | (4008), (4020), (4024), (4026), (4034), (4036),
% 110.16/15.75 | | | | | | | | | | | | | (4038), (function-axioms) are inconsistent by
% 110.16/15.75 | | | | | | | | | | | | | sub-proof #83.
% 110.16/15.75 | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | Case 2:
% 110.16/15.75 | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | (4039) all_24_2 = e1
% 110.16/15.75 | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | COMBINE_EQS: (4006), (4039) imply:
% 110.16/15.75 | | | | | | | | | | | | | (4040) all_8_1 = e1
% 110.16/15.75 | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | REDUCE: (4011), (4040) imply:
% 110.16/15.75 | | | | | | | | | | | | | (4041) ~ (all_53_7 = e1)
% 110.16/15.75 | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | REDUCE: (4022), (4040) imply:
% 110.16/15.75 | | | | | | | | | | | | | (4042) ~ (all_53_15 = e1)
% 110.16/15.75 | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | BETA: splitting (3980) gives:
% 110.16/15.75 | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | (4043) ~ (all_8_1 = e1)
% 110.16/15.75 | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | REF_CLOSE: (109), (161), (169), (173), (198), (228), (3984),
% 110.16/15.75 | | | | | | | | | | | | | | (4008), (4020), (4024), (4026), (4034), (4036),
% 110.16/15.75 | | | | | | | | | | | | | | (4043), (function-axioms) are inconsistent by
% 110.16/15.75 | | | | | | | | | | | | | | sub-proof #83.
% 110.16/15.75 | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | Case 2:
% 110.16/15.75 | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | (4044) ~ (all_8_0 = e3) & op(e1, e2) = all_8_0 &
% 110.16/15.75 | | | | | | | | | | | | | | $i(all_8_0)
% 110.16/15.75 | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | ALPHA: (4044) implies:
% 110.16/15.75 | | | | | | | | | | | | | | (4045) ~ (all_8_0 = e3)
% 110.16/15.75 | | | | | | | | | | | | | | (4046) op(e1, e2) = all_8_0
% 110.16/15.75 | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7,
% 110.16/15.75 | | | | | | | | | | | | | | all_8_0, e2, e1, simplifying with (166), (4046)
% 110.16/15.75 | | | | | | | | | | | | | | gives:
% 110.16/15.75 | | | | | | | | | | | | | | (4047) all_53_7 = all_8_0
% 110.16/15.75 | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | COMBINE_EQS: (260), (4047) imply:
% 110.16/15.75 | | | | | | | | | | | | | | (4048) all_55_6 = all_8_0
% 110.16/15.75 | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | REDUCE: (128), (4047) imply:
% 110.16/15.75 | | | | | | | | | | | | | | (4049) ~ (all_53_15 = all_8_0)
% 110.16/15.75 | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | SIMP: (4049) implies:
% 110.16/15.75 | | | | | | | | | | | | | | (4050) ~ (all_53_15 = all_8_0)
% 110.16/15.75 | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 110.16/15.75 | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | (4051) all_55_6 = e3
% 110.16/15.75 | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | REF_CLOSE: (4045), (4048), (4051) are inconsistent by
% 110.16/15.75 | | | | | | | | | | | | | | | sub-proof #74.
% 110.16/15.75 | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | Case 2:
% 110.16/15.75 | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | (4052) all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 110.16/15.75 | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | BETA: splitting (4052) gives:
% 110.16/15.75 | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | (4053) all_55_6 = e2
% 110.16/15.75 | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | COMBINE_EQS: (4048), (4053) imply:
% 110.16/15.75 | | | | | | | | | | | | | | | | (4054) all_8_0 = e2
% 110.16/15.75 | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | SIMP: (4054) implies:
% 110.16/15.75 | | | | | | | | | | | | | | | | (4055) all_8_0 = e2
% 110.16/15.75 | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | REDUCE: (4050), (4055) imply:
% 110.16/15.75 | | | | | | | | | | | | | | | | (4056) ~ (all_53_15 = e2)
% 110.16/15.75 | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 110.16/15.75 | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | (4057) all_55_14 = e3
% 110.16/15.75 | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (4057) imply:
% 110.16/15.75 | | | | | | | | | | | | | | | | | (4058) all_53_15 = e3
% 110.16/15.75 | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | SIMP: (4058) implies:
% 110.16/15.75 | | | | | | | | | | | | | | | | | (4059) all_53_15 = e3
% 110.16/15.75 | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | REDUCE: (115), (4059) imply:
% 110.16/15.75 | | | | | | | | | | | | | | | | | (4060) ~ (all_53_12 = e3)
% 110.16/15.75 | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | REDUCE: (174), (4059) imply:
% 110.16/15.75 | | | | | | | | | | | | | | | | | (4061) op(e3, e2) = e3
% 110.16/15.75 | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 110.16/15.75 | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | (4062) all_55_12 = e3
% 110.16/15.75 | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (4060), (4062) are inconsistent by
% 110.16/15.75 | | | | | | | | | | | | | | | | | | sub-proof #94.
% 110.16/15.75 | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.75 | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | (4063) ~ (all_55_12 = e3)
% 110.16/15.75 | | | | | | | | | | | | | | | | | | (4064) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 110.16/15.75 | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | BETA: splitting (4064) gives:
% 110.16/15.75 | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | (4065) all_55_12 = e2
% 110.16/15.75 | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (3989), (4065) are inconsistent by
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | sub-proof #93.
% 110.16/15.75 | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | (4066) all_55_12 = e1 | all_55_12 = e0
% 110.16/15.75 | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | (4067) (all_57_28 = e3 & op(e3, e0) = e3) | (all_57_29 =
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4067) gives:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | (4068) all_57_28 = e3 & op(e3, e0) = e3
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4068) implies:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | (4069) op(e3, e0) = e3
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (4060), (4069), (function-axioms) are
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | (4070) all_57_29 = e3 & op(e2, e0) = e3
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4070) implies:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | (4071) op(e2, e0) = e3
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | (4072) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4072) implies:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | (4073) op(e3, e0) = e3
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (4060), (4073), (function-axioms) are
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | (4074) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4074) gives:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | (4075) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4075) implies:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | (4076) op(e2, e0) = e2
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (4071), (4076), (function-axioms) are
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #69.
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | (4077) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4077) implies:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | (4078) op(e1, e0) = e1
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (164), (272), (3467), (4066), (4078),
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | #16.
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | (4079) (all_57_30 = e3 & op(e1, e0) = e3) | (all_57_31 =
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4079) gives:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | (4080) all_57_30 = e3 & op(e1, e0) = e3
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4080) implies:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | (4081) op(e1, e0) = e3
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | (4082) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4082) implies:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | (4083) op(e3, e0) = e3
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (4060), (4083), (function-axioms) are
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | (4084) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4084) gives:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | (4085) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (113), (127), (161), (168), (169), (173),
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | (174), (4034), (4061), (4085), (function-axioms)
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #221.
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | (4086) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4086) implies:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | (4087) op(e1, e0) = e1
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (164), (4081), (4087), (function-axioms) are
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #62.
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | (4088) all_57_31 = e3 & op(e0, e0) = e3
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4088) implies:
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | (4089) op(e0, e0) = e3
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3990), (4089), (function-axioms) are
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #61.
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.75 | | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | | End of split
% 110.16/15.75 | | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | | End of split
% 110.16/15.75 | | | | | | | | | | | | | | | | |
% 110.16/15.75 | | | | | | | | | | | | | | | | Case 2:
% 110.16/15.75 | | | | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | | | | (4090) all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 110.16/15.76 | | | | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | | | | REF_CLOSE: (274), (3469), (4042), (4056), (4090) are
% 110.16/15.76 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #26.
% 110.16/15.76 | | | | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | | | End of split
% 110.16/15.76 | | | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | | Case 2:
% 110.16/15.76 | | | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | | | (4091) all_55_6 = e1 | all_55_6 = e0
% 110.16/15.76 | | | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | | | REF_CLOSE: (260), (4035), (4041), (4091) are inconsistent by
% 110.16/15.76 | | | | | | | | | | | | | | | | sub-proof #115.
% 110.16/15.76 | | | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | | End of split
% 110.16/15.76 | | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | End of split
% 110.16/15.76 | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | End of split
% 110.16/15.76 | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | End of split
% 110.16/15.76 | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | End of split
% 110.16/15.76 | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | Case 2:
% 110.16/15.76 | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | (4092) all_18_2 = e3
% 110.16/15.76 | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | COMBINE_EQS: (326), (4092) imply:
% 110.16/15.76 | | | | | | | | | | | (4093) all_14_2 = e3
% 110.16/15.76 | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | SIMP: (4093) implies:
% 110.16/15.76 | | | | | | | | | | | (4094) all_14_2 = e3
% 110.16/15.76 | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | REDUCE: (361), (4094) imply:
% 110.16/15.76 | | | | | | | | | | | (4095) ~ (all_53_7 = e3)
% 110.16/15.76 | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | BETA: splitting (66) gives:
% 110.16/15.76 | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | Case 1:
% 110.16/15.76 | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | (4096) ~ (all_24_2 = e1)
% 110.16/15.76 | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | REDUCE: (4006), (4096) imply:
% 110.16/15.76 | | | | | | | | | | | | (4097) ~ (all_8_1 = e1)
% 110.16/15.76 | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | BETA: splitting (198) gives:
% 110.16/15.76 | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | Case 1:
% 110.16/15.76 | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | (4098) all_55_10 = e3
% 110.16/15.76 | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | COMBINE_EQS: (4008), (4098) imply:
% 110.16/15.76 | | | | | | | | | | | | | (4099) all_8_1 = e3
% 110.16/15.76 | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | SIMP: (4099) implies:
% 110.16/15.76 | | | | | | | | | | | | | (4100) all_8_1 = e3
% 110.16/15.76 | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | REDUCE: (4024), (4100) imply:
% 110.16/15.76 | | | | | | | | | | | | | (4101) $false
% 110.16/15.76 | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | CLOSE: (4101) is inconsistent.
% 110.16/15.76 | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | Case 2:
% 110.16/15.76 | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | (4102) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 110.16/15.76 | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | BETA: splitting (4102) gives:
% 110.16/15.76 | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | Case 1:
% 110.16/15.76 | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | (4103) all_55_10 = e2
% 110.16/15.76 | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | COMBINE_EQS: (4008), (4103) imply:
% 110.16/15.76 | | | | | | | | | | | | | | (4104) all_8_1 = e2
% 110.16/15.76 | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | SIMP: (4104) implies:
% 110.16/15.76 | | | | | | | | | | | | | | (4105) all_8_1 = e2
% 110.16/15.76 | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | REDUCE: (4020), (4105) imply:
% 110.16/15.76 | | | | | | | | | | | | | | (4106) ~ (all_53_9 = e2)
% 110.16/15.76 | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | REDUCE: (4021), (4105) imply:
% 110.16/15.76 | | | | | | | | | | | | | | (4107) ~ (all_53_10 = e2)
% 110.16/15.76 | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (115), (117),
% 110.16/15.76 | | | | | | | | | | | | | | (132), (139), (140), (148), (152), (153), (161),
% 110.16/15.76 | | | | | | | | | | | | | | (162), (163), (164), (166), (167), (168), (169),
% 110.16/15.76 | | | | | | | | | | | | | | (171), (172), (173), (174), (3988), (4106),
% 110.16/15.76 | | | | | | | | | | | | | | (4107), (function-axioms) are inconsistent by
% 110.16/15.76 | | | | | | | | | | | | | | sub-proof #209.
% 110.16/15.76 | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | Case 2:
% 110.16/15.76 | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | (4108) all_55_10 = e1 | all_55_10 = e0
% 110.16/15.76 | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | | REF_CLOSE: (4008), (4026), (4097), (4108) are inconsistent by
% 110.16/15.76 | | | | | | | | | | | | | | sub-proof #84.
% 110.16/15.76 | | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | | End of split
% 110.16/15.76 | | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | End of split
% 110.16/15.76 | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | Case 2:
% 110.16/15.76 | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | (4109) all_24_2 = e1
% 110.16/15.76 | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | COMBINE_EQS: (4006), (4109) imply:
% 110.16/15.76 | | | | | | | | | | | | (4110) all_8_1 = e1
% 110.16/15.76 | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | REDUCE: (4011), (4110) imply:
% 110.16/15.76 | | | | | | | | | | | | (4111) ~ (all_53_7 = e1)
% 110.16/15.76 | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | REDUCE: (4024), (4110) imply:
% 110.16/15.76 | | | | | | | | | | | | (4112) ~ (e3 = e1)
% 110.16/15.76 | | | | | | | | | | | |
% 110.16/15.76 | | | | | | | | | | | | REDUCE: (3979), (4110) imply:
% 110.16/15.76 | | | | | | | | | | | | (4113) op(e2, e2) = e1
% 110.16/15.76 | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | BETA: splitting (110) gives:
% 110.47/15.76 | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | Case 1:
% 110.47/15.76 | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | (4114) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 110.47/15.76 | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 110.47/15.76 | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | ALPHA: (4114) implies:
% 110.47/15.76 | | | | | | | | | | | | | (4115) op(e3, e0) = e3
% 110.47/15.76 | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 110.47/15.76 | | | | | | | | | | | | | e3, e0, e3, simplifying with (172), (4115) gives:
% 110.47/15.76 | | | | | | | | | | | | | (4116) all_53_12 = e3
% 110.47/15.76 | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | REDUCE: (115), (4116) imply:
% 110.47/15.76 | | | | | | | | | | | | | (4117) ~ (all_53_15 = e3)
% 110.47/15.76 | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | SIMP: (4117) implies:
% 110.47/15.76 | | | | | | | | | | | | | (4118) ~ (all_53_15 = e3)
% 110.47/15.76 | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | REF_CLOSE: (6), (7), (108), (162), (166), (174), (218),
% 110.47/15.76 | | | | | | | | | | | | | (4095), (4111), (4113), (4118), (function-axioms)
% 110.47/15.76 | | | | | | | | | | | | | are inconsistent by sub-proof #178.
% 110.47/15.76 | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | Case 2:
% 110.47/15.76 | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | (4119) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 110.47/15.76 | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 110.47/15.76 | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 110.47/15.76 | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 110.47/15.76 | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | BETA: splitting (4119) gives:
% 110.47/15.76 | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | Case 1:
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | (4120) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 110.47/15.76 | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | ALPHA: (4120) implies:
% 110.47/15.76 | | | | | | | | | | | | | | (4121) op(e2, e0) = e2
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | REF_CLOSE: (168), (3988), (4121), (function-axioms) are
% 110.47/15.76 | | | | | | | | | | | | | | inconsistent by sub-proof #227.
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | Case 2:
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | (4122) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 110.47/15.76 | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | ALPHA: (4122) implies:
% 110.47/15.76 | | | | | | | | | | | | | | (4123) op(e1, e0) = e1
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e1,
% 110.47/15.76 | | | | | | | | | | | | | | e0, e1, simplifying with (164), (4123) gives:
% 110.47/15.76 | | | | | | | | | | | | | | (4124) all_53_4 = e1
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | REDUCE: (137), (4124) imply:
% 110.47/15.76 | | | | | | | | | | | | | | (4125) ~ (all_53_12 = e1)
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | SIMP: (4125) implies:
% 110.47/15.76 | | | | | | | | | | | | | | (4126) ~ (all_53_12 = e1)
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | Case 1:
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | (4127) all_55_12 = e3
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | COMBINE_EQS: (272), (4127) imply:
% 110.47/15.76 | | | | | | | | | | | | | | | (4128) all_53_12 = e3
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | SIMP: (4128) implies:
% 110.47/15.76 | | | | | | | | | | | | | | | (4129) all_53_12 = e3
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | REDUCE: (115), (4129) imply:
% 110.47/15.76 | | | | | | | | | | | | | | | (4130) ~ (all_53_15 = e3)
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | SIMP: (4130) implies:
% 110.47/15.76 | | | | | | | | | | | | | | | (4131) ~ (all_53_15 = e3)
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (108), (162), (166), (174), (218),
% 110.47/15.76 | | | | | | | | | | | | | | | (4095), (4111), (4113), (4131), (function-axioms)
% 110.47/15.76 | | | | | | | | | | | | | | | are inconsistent by sub-proof #178.
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | Case 2:
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | (4132) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | BETA: splitting (4132) gives:
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | Case 1:
% 110.47/15.76 | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | (4133) all_55_12 = e2
% 110.47/15.76 | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | REF_CLOSE: (272), (3989), (4133) are inconsistent by
% 110.47/15.76 | | | | | | | | | | | | | | | | sub-proof #93.
% 110.47/15.76 | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | Case 2:
% 110.47/15.76 | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | (4134) all_55_12 = e1 | all_55_12 = e0
% 110.47/15.76 | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | REF_CLOSE: (137), (164), (272), (3467), (4123), (4134),
% 110.47/15.76 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.47/15.76 | | | | | | | | | | | | | | | | #16.
% 110.47/15.76 | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | End of split
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | End of split
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | End of split
% 110.47/15.76 | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | End of split
% 110.47/15.76 | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | End of split
% 110.47/15.76 | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | End of split
% 110.47/15.76 | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | Case 2:
% 110.47/15.76 | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | (4135) all_14_2 = e2
% 110.47/15.76 | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | REDUCE: (359), (4135) imply:
% 110.47/15.76 | | | | | | | | | | (4136) ~ (all_53_6 = e2)
% 110.47/15.76 | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | REDUCE: (365), (4135) imply:
% 110.47/15.76 | | | | | | | | | | (4137) ~ (all_53_13 = e2)
% 110.47/15.76 | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | BETA: splitting (212) gives:
% 110.47/15.76 | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | Case 1:
% 110.47/15.76 | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | (4138) (all_57_116 = e2 & op(e3, e3) = e2) | (all_57_117
% 110.47/15.76 | | | | | | | | | | | = e2 & op(e2, e3) = e2)
% 110.47/15.76 | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | BETA: splitting (4138) gives:
% 110.47/15.76 | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | Case 1:
% 110.47/15.76 | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | (4139) all_57_116 = e2 & op(e3, e3) = e2
% 110.47/15.76 | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | ALPHA: (4139) implies:
% 110.47/15.76 | | | | | | | | | | | | (4140) op(e3, e3) = e2
% 110.47/15.76 | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | REF_CLOSE: (5), (3470), (4140), (function-axioms) are
% 110.47/15.76 | | | | | | | | | | | | inconsistent by sub-proof #7.
% 110.47/15.76 | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | Case 2:
% 110.47/15.76 | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | (4141) all_57_117 = e2 & op(e2, e3) = e2
% 110.47/15.76 | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | ALPHA: (4141) implies:
% 110.47/15.76 | | | | | | | | | | | | (4142) op(e2, e3) = e2
% 110.47/15.76 | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | BETA: splitting (213) gives:
% 110.47/15.76 | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | Case 1:
% 110.47/15.76 | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | (4143) (all_57_112 = e2 & op(e3, e3) = e2) | (all_57_113
% 110.47/15.76 | | | | | | | | | | | | | = e2 & op(e3, e2) = e2)
% 110.47/15.76 | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | BETA: splitting (4143) gives:
% 110.47/15.76 | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | Case 1:
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | (4144) all_57_112 = e2 & op(e3, e3) = e2
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | ALPHA: (4144) implies:
% 110.47/15.76 | | | | | | | | | | | | | | (4145) op(e3, e3) = e2
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | REF_CLOSE: (5), (3470), (4145), (function-axioms) are
% 110.47/15.76 | | | | | | | | | | | | | | inconsistent by sub-proof #7.
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | Case 2:
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | (4146) all_57_113 = e2 & op(e3, e2) = e2
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | ALPHA: (4146) implies:
% 110.47/15.76 | | | | | | | | | | | | | | (4147) op(e3, e2) = e2
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_10,
% 110.47/15.76 | | | | | | | | | | | | | | e2, e3, e2, simplifying with (171), (4142) gives:
% 110.47/15.76 | | | | | | | | | | | | | | (4148) all_53_10 = e2
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 110.47/15.76 | | | | | | | | | | | | | | e2, e2, e3, simplifying with (174), (4147) gives:
% 110.47/15.76 | | | | | | | | | | | | | | (4149) all_53_15 = e2
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | REDUCE: (123), (4148) imply:
% 110.47/15.76 | | | | | | | | | | | | | | (4150) ~ (all_53_9 = e2)
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | REDUCE: (4022), (4149) imply:
% 110.47/15.76 | | | | | | | | | | | | | | (4151) ~ (all_8_1 = e2)
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | SIMP: (4151) implies:
% 110.47/15.76 | | | | | | | | | | | | | | (4152) ~ (all_8_1 = e2)
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 110.47/15.76 | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | Case 1:
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | (4153) all_55_10 = e3
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | COMBINE_EQS: (4008), (4153) imply:
% 110.47/15.76 | | | | | | | | | | | | | | | (4154) all_8_1 = e3
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | REDUCE: (4024), (4154) imply:
% 110.47/15.76 | | | | | | | | | | | | | | | (4155) $false
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | CLOSE: (4155) is inconsistent.
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | Case 2:
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | (4156) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | BETA: splitting (4156) gives:
% 110.47/15.76 | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | Case 1:
% 110.47/15.76 | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | (4157) all_55_10 = e2
% 110.47/15.76 | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | COMBINE_EQS: (4008), (4157) imply:
% 110.47/15.76 | | | | | | | | | | | | | | | | (4158) all_8_1 = e2
% 110.47/15.76 | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | SIMP: (4158) implies:
% 110.47/15.76 | | | | | | | | | | | | | | | | (4159) all_8_1 = e2
% 110.47/15.76 | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | REDUCE: (4152), (4159) imply:
% 110.47/15.76 | | | | | | | | | | | | | | | | (4160) $false
% 110.47/15.76 | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | CLOSE: (4160) is inconsistent.
% 110.47/15.76 | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | Case 2:
% 110.47/15.76 | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | (4161) all_55_10 = e1 | all_55_10 = e0
% 110.47/15.76 | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | BETA: splitting (4161) gives:
% 110.47/15.76 | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | Case 1:
% 110.47/15.76 | | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | | (4162) all_55_10 = e1
% 110.47/15.76 | | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | | COMBINE_EQS: (4008), (4162) imply:
% 110.47/15.76 | | | | | | | | | | | | | | | | | (4163) all_8_1 = e1
% 110.47/15.76 | | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | | SIMP: (4163) implies:
% 110.47/15.76 | | | | | | | | | | | | | | | | | (4164) all_8_1 = e1
% 110.47/15.76 | | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | | REDUCE: (4011), (4164) imply:
% 110.47/15.76 | | | | | | | | | | | | | | | | | (4165) ~ (all_53_7 = e1)
% 110.47/15.76 | | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 110.47/15.76 | | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | | Case 1:
% 110.47/15.76 | | | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | | | (4166) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2)
% 110.47/15.76 | | | | | | | | | | | | | | | | | | = e3 & op(e2, e3) = all_52_12 & $i(all_52_12)
% 110.47/15.76 | | | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4147), (4166), (function-axioms) are
% 110.47/15.76 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #91.
% 110.47/15.76 | | | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | | Case 2:
% 110.47/15.76 | | | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | | | (4167) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 110.47/15.76 | | | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) |
% 110.47/15.76 | | | | | | | | | | | | | | | | | | (all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 110.47/15.76 | | | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 110.47/15.76 | | | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | | | BETA: splitting (4167) gives:
% 110.47/15.76 | | | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | | | Case 1:
% 110.47/15.76 | | | | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | | | | (4168) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1)
% 110.47/15.76 | | | | | | | | | | | | | | | | | | | = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 110.47/15.76 | | | | | | | | | | | | | | | | | | |
% 110.47/15.76 | | | | | | | | | | | | | | | | | | | ALPHA: (4168) implies:
% 110.47/15.76 | | | | | | | | | | | | | | | | | | | (4169) op(e1, e2) = e1
% 110.47/15.76 | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (4165), (4169), (function-axioms) are
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #233.
% 110.47/15.77 | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | (4170) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0)
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | = all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 110.47/15.77 | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | ALPHA: (4170) implies:
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | (4171) op(e0, e2) = e0
% 110.47/15.77 | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e0,
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (162), (4171) gives:
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | (4172) all_53_3 = e0
% 110.47/15.77 | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | REDUCE: (152), (4172) imply:
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | (4173) ~ (all_53_1 = e0)
% 110.47/15.77 | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 110.47/15.77 | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | Case 1:
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | | (4174) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | | ALPHA: (4174) implies:
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | | (4175) op(e3, e1) = e3
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (117), (137), (164), (168), (172), (173),
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | | (195), (196), (272), (273), (3467), (3988),
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | | (3989), (4175), (function-axioms) are inconsistent
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | | by sub-proof #6.
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | | (4176) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (169), (4150), (4173), (4176),
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | | #229.
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | (4177) all_55_10 = e0
% 110.47/15.77 | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | COMBINE_EQS: (4008), (4177) imply:
% 110.47/15.77 | | | | | | | | | | | | | | | | | (4178) all_8_1 = e0
% 110.47/15.77 | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | SIMP: (4178) implies:
% 110.47/15.77 | | | | | | | | | | | | | | | | | (4179) all_8_1 = e0
% 110.47/15.77 | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | REDUCE: (4026), (4179) imply:
% 110.47/15.77 | | | | | | | | | | | | | | | | | (4180) $false
% 110.47/15.77 | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | | CLOSE: (4180) is inconsistent.
% 110.47/15.77 | | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | (4181) (all_57_114 = e2 & op(e3, e1) = e2) | (all_57_115
% 110.47/15.77 | | | | | | | | | | | | | = e2 & op(e3, e0) = e2)
% 110.47/15.77 | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | BETA: splitting (4181) gives:
% 110.47/15.77 | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | Case 1:
% 110.47/15.77 | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | (4182) all_57_114 = e2 & op(e3, e1) = e2
% 110.47/15.77 | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | ALPHA: (4182) implies:
% 110.47/15.77 | | | | | | | | | | | | | | (4183) op(e3, e1) = e2
% 110.47/15.77 | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | REF_CLOSE: (173), (4137), (4183), (function-axioms) are
% 110.47/15.77 | | | | | | | | | | | | | | inconsistent by sub-proof #136.
% 110.47/15.77 | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | (4184) all_57_115 = e2 & op(e3, e0) = e2
% 110.47/15.77 | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | ALPHA: (4184) implies:
% 110.47/15.77 | | | | | | | | | | | | | | (4185) op(e3, e0) = e2
% 110.47/15.77 | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | | REF_CLOSE: (172), (3989), (4185), (function-axioms) are
% 110.47/15.77 | | | | | | | | | | | | | | inconsistent by sub-proof #117.
% 110.47/15.77 | | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | (4186) (all_57_118 = e2 & op(e1, e3) = e2) | (all_57_119
% 110.47/15.77 | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | BETA: splitting (4186) gives:
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | Case 1:
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | (4187) all_57_118 = e2 & op(e1, e3) = e2
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | ALPHA: (4187) implies:
% 110.47/15.77 | | | | | | | | | | | | (4188) op(e1, e3) = e2
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e2,
% 110.47/15.77 | | | | | | | | | | | | e3, e1, simplifying with (167), (4188) gives:
% 110.47/15.77 | | | | | | | | | | | | (4189) all_53_6 = e2
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | REDUCE: (4136), (4189) imply:
% 110.47/15.77 | | | | | | | | | | | | (4190) $false
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | CLOSE: (4190) is inconsistent.
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | (4191) all_57_119 = e2 & op(e0, e3) = e2
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | ALPHA: (4191) implies:
% 110.47/15.77 | | | | | | | | | | | | (4192) op(e0, e3) = e2
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | REF_CLOSE: (163), (3985), (4192), (function-axioms) are
% 110.47/15.77 | | | | | | | | | | | | inconsistent by sub-proof #164.
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | | (4193) all_12_2 = e0
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | | COMBINE_EQS: (4005), (4193) imply:
% 110.47/15.77 | | | | | | | | | (4194) all_8_1 = e0
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | | REDUCE: (4018), (4194) imply:
% 110.47/15.77 | | | | | | | | | (4195) ~ (all_40_0 = e0)
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | | REDUCE: (3979), (4194) imply:
% 110.47/15.77 | | | | | | | | | (4196) op(e2, e2) = e0
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | | BETA: splitting (200) gives:
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | | Case 1:
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | (4197) all_55_8 = e3
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | COMBINE_EQS: (4009), (4197) imply:
% 110.47/15.77 | | | | | | | | | | (4198) all_40_0 = e3
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | REDUCE: (4013), (4198) imply:
% 110.47/15.77 | | | | | | | | | | (4199) ~ (all_53_9 = e3)
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | REDUCE: (4015), (4198) imply:
% 110.47/15.77 | | | | | | | | | | (4200) ~ (all_53_10 = e3)
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | REDUCE: (4017), (4198) imply:
% 110.47/15.77 | | | | | | | | | | (4201) ~ (all_53_12 = e3)
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | BETA: splitting (196) gives:
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | Case 1:
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | (4202) all_55_12 = e3
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | REF_CLOSE: (272), (4201), (4202) are inconsistent by
% 110.47/15.77 | | | | | | | | | | | sub-proof #94.
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | (4203) ~ (all_55_12 = e3)
% 110.47/15.77 | | | | | | | | | | | (4204) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | BETA: splitting (4204) gives:
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | Case 1:
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | (4205) all_55_12 = e2
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | REF_CLOSE: (272), (3989), (4205) are inconsistent by
% 110.47/15.77 | | | | | | | | | | | | sub-proof #93.
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | (4206) all_55_12 = e1 | all_55_12 = e0
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | BETA: splitting (4206) gives:
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | Case 1:
% 110.47/15.77 | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | (4207) all_55_12 = e1
% 110.47/15.77 | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | COMBINE_EQS: (272), (4207) imply:
% 110.47/15.77 | | | | | | | | | | | | | (4208) all_53_12 = e1
% 110.47/15.77 | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | SIMP: (4208) implies:
% 110.47/15.77 | | | | | | | | | | | | | (4209) all_53_12 = e1
% 110.47/15.77 | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | REDUCE: (137), (4209) imply:
% 110.47/15.77 | | | | | | | | | | | | | (4210) ~ (all_53_4 = e1)
% 110.47/15.77 | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | REF_CLOSE: (6), (8), (110), (164), (168), (169), (171),
% 110.47/15.77 | | | | | | | | | | | | | (172), (219), (4196), (4199), (4200), (4201),
% 110.47/15.77 | | | | | | | | | | | | | (4210), (function-axioms) are inconsistent by
% 110.47/15.77 | | | | | | | | | | | | | sub-proof #32.
% 110.47/15.77 | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | (4211) all_55_12 = e0
% 110.47/15.77 | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | | REF_CLOSE: (272), (3467), (4211) are inconsistent by
% 110.47/15.77 | | | | | | | | | | | | | sub-proof #17.
% 110.47/15.77 | | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | (4212) all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | BETA: splitting (4212) gives:
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | Case 1:
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | (4213) all_55_8 = e2
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | COMBINE_EQS: (4009), (4213) imply:
% 110.47/15.77 | | | | | | | | | | | (4214) all_40_0 = e2
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | REDUCE: (4019), (4214) imply:
% 110.47/15.77 | | | | | | | | | | | (4215) $false
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | CLOSE: (4215) is inconsistent.
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | (4216) all_55_8 = e1 | all_55_8 = e0
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | BETA: splitting (4216) gives:
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | Case 1:
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | (4217) all_55_8 = e1
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | COMBINE_EQS: (4009), (4217) imply:
% 110.47/15.77 | | | | | | | | | | | | (4218) all_40_0 = e1
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | REDUCE: (3999), (4218) imply:
% 110.47/15.77 | | | | | | | | | | | | (4219) $false
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | CLOSE: (4219) is inconsistent.
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | (4220) all_55_8 = e0
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | COMBINE_EQS: (4009), (4220) imply:
% 110.47/15.77 | | | | | | | | | | | | (4221) all_40_0 = e0
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | REDUCE: (4195), (4221) imply:
% 110.47/15.77 | | | | | | | | | | | | (4222) $false
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | | CLOSE: (4222) is inconsistent.
% 110.47/15.77 | | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | End of split
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | End of split
% 110.47/15.77 | | | | | | | |
% 110.47/15.77 | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | |
% 110.47/15.77 | | | | | | | | (4223) all_10_2 = e3
% 110.47/15.77 | | | | | | | | (4224) op(e3, e3) = all_10_1 & $i(all_10_1) & ( ~ (all_10_1 =
% 110.47/15.77 | | | | | | | | e0) | ( ~ (all_10_0 = e1) & op(e0, e3) = all_10_0
% 110.47/15.77 | | | | | | | | & $i(all_10_0)))
% 110.47/15.77 | | | | | | | |
% 110.47/15.77 | | | | | | | | ALPHA: (4224) implies:
% 110.47/15.77 | | | | | | | | (4225) op(e3, e3) = all_10_1
% 110.47/15.77 | | | | | | | | (4226) ~ (all_10_1 = e0) | ( ~ (all_10_0 = e1) & op(e0, e3)
% 110.47/15.77 | | | | | | | | = all_10_0 & $i(all_10_0))
% 110.47/15.77 | | | | | | | |
% 110.47/15.77 | | | | | | | | COMBINE_EQS: (4004), (4223) imply:
% 110.47/15.77 | | | | | | | | (4227) all_8_1 = e3
% 110.47/15.77 | | | | | | | |
% 110.47/15.77 | | | | | | | | SIMP: (4227) implies:
% 110.47/15.77 | | | | | | | | (4228) all_8_1 = e3
% 110.47/15.77 | | | | | | | |
% 110.47/15.77 | | | | | | | | COMBINE_EQS: (4003), (4228) imply:
% 110.47/15.77 | | | | | | | | (4229) all_16_1 = e3
% 110.47/15.77 | | | | | | | |
% 110.47/15.77 | | | | | | | | COMBINE_EQS: (4007), (4228) imply:
% 110.47/15.77 | | | | | | | | (4230) all_48_2 = e3
% 110.47/15.77 | | | | | | | |
% 110.47/15.77 | | | | | | | | REDUCE: (4010), (4228) imply:
% 110.47/15.77 | | | | | | | | (4231) ~ (all_53_3 = e3)
% 110.47/15.77 | | | | | | | |
% 110.47/15.77 | | | | | | | | REDUCE: (4020), (4228) imply:
% 110.47/15.77 | | | | | | | | (4232) ~ (all_53_9 = e3)
% 110.47/15.77 | | | | | | | |
% 110.47/15.77 | | | | | | | | REDUCE: (4022), (4228) imply:
% 110.47/15.77 | | | | | | | | (4233) ~ (all_53_15 = e3)
% 110.47/15.77 | | | | | | | |
% 110.47/15.77 | | | | | | | | BETA: splitting (102) gives:
% 110.47/15.77 | | | | | | | |
% 110.47/15.77 | | | | | | | | Case 1:
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | | (4234) ~ (all_48_2 = e3)
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | | REDUCE: (4230), (4234) imply:
% 110.47/15.77 | | | | | | | | | (4235) $false
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | | CLOSE: (4235) is inconsistent.
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | | (4236) op(e3, e3) = all_48_1 & $i(all_48_1) & ( ~ (all_48_1
% 110.47/15.77 | | | | | | | | | = e1) | ( ~ (all_48_0 = e0) & op(e1, e3) =
% 110.47/15.77 | | | | | | | | | all_48_0 & $i(all_48_0)))
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | | ALPHA: (4236) implies:
% 110.47/15.77 | | | | | | | | | (4237) op(e3, e3) = all_48_1
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | | BETA: splitting (3995) gives:
% 110.47/15.77 | | | | | | | | |
% 110.47/15.77 | | | | | | | | | Case 1:
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | (4238) ~ (all_16_1 = e3)
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | REDUCE: (4229), (4238) imply:
% 110.47/15.77 | | | | | | | | | | (4239) $false
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | CLOSE: (4239) is inconsistent.
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | Case 2:
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | (4240) ~ (all_16_0 = e1) & op(e3, e2) = all_16_0 &
% 110.47/15.77 | | | | | | | | | | $i(all_16_0)
% 110.47/15.77 | | | | | | | | | |
% 110.47/15.77 | | | | | | | | | | ALPHA: (4240) implies:
% 110.47/15.77 | | | | | | | | | | (4241) ~ (all_16_0 = e1)
% 110.53/15.77 | | | | | | | | | | (4242) op(e3, e2) = all_16_0
% 110.53/15.77 | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_15,
% 110.53/15.77 | | | | | | | | | | all_16_0, e2, e3, simplifying with (174), (4242)
% 110.53/15.77 | | | | | | | | | | gives:
% 110.53/15.77 | | | | | | | | | | (4243) all_53_15 = all_16_0
% 110.53/15.77 | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_48_1,
% 110.53/15.77 | | | | | | | | | | e3, e3, simplifying with (3470), (4237) gives:
% 110.53/15.77 | | | | | | | | | | (4244) all_48_1 = e0
% 110.53/15.77 | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 110.53/15.77 | | | | | | | | | | all_48_1, e3, e3, simplifying with (4225), (4237)
% 110.53/15.77 | | | | | | | | | | gives:
% 110.53/15.77 | | | | | | | | | | (4245) all_48_1 = all_10_1
% 110.53/15.77 | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | COMBINE_EQS: (4244), (4245) imply:
% 110.53/15.77 | | | | | | | | | | (4246) all_10_1 = e0
% 110.53/15.77 | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | COMBINE_EQS: (274), (4243) imply:
% 110.53/15.77 | | | | | | | | | | (4247) all_55_14 = all_16_0
% 110.53/15.77 | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | REDUCE: (142), (4243) imply:
% 110.53/15.77 | | | | | | | | | | (4248) ~ (all_53_3 = all_16_0)
% 110.53/15.77 | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | REDUCE: (128), (4243) imply:
% 110.53/15.77 | | | | | | | | | | (4249) ~ (all_53_7 = all_16_0)
% 110.53/15.77 | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | REDUCE: (115), (4243) imply:
% 110.53/15.77 | | | | | | | | | | (4250) ~ (all_53_12 = all_16_0)
% 110.53/15.77 | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | REDUCE: (113), (4243) imply:
% 110.53/15.77 | | | | | | | | | | (4251) ~ (all_53_13 = all_16_0)
% 110.53/15.77 | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | REDUCE: (4233), (4243) imply:
% 110.53/15.77 | | | | | | | | | | (4252) ~ (all_16_0 = e3)
% 110.53/15.77 | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | BETA: splitting (194) gives:
% 110.53/15.77 | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | Case 1:
% 110.53/15.77 | | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | | (4253) all_55_14 = e3
% 110.53/15.77 | | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | | REF_CLOSE: (4247), (4252), (4253) are inconsistent by
% 110.53/15.77 | | | | | | | | | | | sub-proof #58.
% 110.53/15.77 | | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | Case 2:
% 110.53/15.77 | | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | | (4254) all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 110.53/15.77 | | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | | BETA: splitting (4226) gives:
% 110.53/15.77 | | | | | | | | | | |
% 110.53/15.77 | | | | | | | | | | | Case 1:
% 110.53/15.77 | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | (4255) ~ (all_10_1 = e0)
% 110.53/15.78 | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | REDUCE: (4246), (4255) imply:
% 110.53/15.78 | | | | | | | | | | | | (4256) $false
% 110.53/15.78 | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | CLOSE: (4256) is inconsistent.
% 110.53/15.78 | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | Case 2:
% 110.53/15.78 | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | (4257) ~ (all_10_0 = e1) & op(e0, e3) = all_10_0 &
% 110.53/15.78 | | | | | | | | | | | | $i(all_10_0)
% 110.53/15.78 | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | ALPHA: (4257) implies:
% 110.53/15.78 | | | | | | | | | | | | (4258) ~ (all_10_0 = e1)
% 110.53/15.78 | | | | | | | | | | | | (4259) op(e0, e3) = all_10_0
% 110.53/15.78 | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | BETA: splitting (4254) gives:
% 110.53/15.78 | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | Case 1:
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | (4260) all_55_14 = e2
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | COMBINE_EQS: (4247), (4260) imply:
% 110.53/15.78 | | | | | | | | | | | | | (4261) all_16_0 = e2
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | SIMP: (4261) implies:
% 110.53/15.78 | | | | | | | | | | | | | (4262) all_16_0 = e2
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | REDUCE: (4249), (4262) imply:
% 110.53/15.78 | | | | | | | | | | | | | (4263) ~ (all_53_7 = e2)
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | REDUCE: (4251), (4262) imply:
% 110.53/15.78 | | | | | | | | | | | | | (4264) ~ (all_53_13 = e2)
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | REDUCE: (4241), (4262) imply:
% 110.53/15.78 | | | | | | | | | | | | | (4265) ~ (e2 = e1)
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2,
% 110.53/15.78 | | | | | | | | | | | | | all_10_0, e3, e0, simplifying with (163), (4259)
% 110.53/15.78 | | | | | | | | | | | | | gives:
% 110.53/15.78 | | | | | | | | | | | | | (4266) all_53_2 = all_10_0
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | COMBINE_EQS: (251), (4266) imply:
% 110.53/15.78 | | | | | | | | | | | | | (4267) all_55_3 = all_10_0
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | REDUCE: (153), (4266) imply:
% 110.53/15.78 | | | | | | | | | | | | | (4268) ~ (all_53_1 = all_10_0)
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | REDUCE: (3985), (4266) imply:
% 110.53/15.78 | | | | | | | | | | | | | (4269) ~ (all_10_0 = e2)
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | REDUCE: (3464), (4266) imply:
% 110.53/15.78 | | | | | | | | | | | | | (4270) ~ (all_10_0 = e0)
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | BETA: splitting (205) gives:
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | Case 1:
% 110.53/15.78 | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | (4271) all_55_3 = e3
% 110.53/15.78 | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | COMBINE_EQS: (4267), (4271) imply:
% 110.53/15.78 | | | | | | | | | | | | | | (4272) all_10_0 = e3
% 110.53/15.78 | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | REDUCE: (4268), (4272) imply:
% 110.53/15.78 | | | | | | | | | | | | | | (4273) ~ (all_53_1 = e3)
% 110.53/15.78 | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 110.53/15.78 | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | Case 1:
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | (4274) ~ (all_14_2 = e2)
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | Case 1:
% 110.53/15.78 | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | (4275) (all_57_48 = e2 & op(e1, e3) = e2) | (all_57_49 =
% 110.53/15.78 | | | | | | | | | | | | | | | | e2 & op(e1, e2) = e2)
% 110.53/15.78 | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | BETA: splitting (4275) gives:
% 110.53/15.78 | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | Case 1:
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | (4276) all_57_48 = e2 & op(e1, e3) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | ALPHA: (4276) implies:
% 110.53/15.78 | | | | | | | | | | | | | | | | | (4277) op(e1, e3) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | Case 1:
% 110.53/15.78 | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | (4278) (all_57_52 = e2 & op(e3, e1) = e2) | (all_57_53 =
% 110.53/15.78 | | | | | | | | | | | | | | | | | | e2 & op(e2, e1) = e2)
% 110.53/15.78 | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | BETA: splitting (4278) gives:
% 110.53/15.78 | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | Case 1:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | (4279) all_57_52 = e2 & op(e3, e1) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | ALPHA: (4279) implies:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | (4280) op(e3, e1) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (4264), (4280), (function-axioms) are
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #136.
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | Case 2:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | (4281) all_57_53 = e2 & op(e2, e1) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | ALPHA: (4281) implies:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | (4282) op(e2, e1) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e2,
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (167), (4277) gives:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | (4283) all_53_6 = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e2,
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (169), (4282) gives:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | (4284) all_53_9 = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | REDUCE: (123), (4284) imply:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | (4285) ~ (all_53_10 = e2)
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | SIMP: (4285) implies:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | (4286) ~ (all_53_10 = e2)
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | Case 1:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | (4287) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2)
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | = all_52_18 & op(e2, e3) = e2 & $i(all_52_18)
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (4286), (4287), (function-axioms) are
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #215.
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | Case 2:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | (4288) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | (all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22))
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4288) gives:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | | (4289) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1)
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | | = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4265), (4277), (4289), (function-axioms) are
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #82.
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | | (4290) all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0)
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | | = all_52_22 & op(e0, e3) = e0 & $i(all_52_22)
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4290) implies:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | | (4291) op(e0, e3) = e0
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3464), (4291), (function-axioms) are
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #149.
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | Case 2:
% 110.53/15.78 | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | (4292) (all_57_54 = e2 & op(e1, e1) = e2) | (all_57_55 =
% 110.53/15.78 | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 110.53/15.78 | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | BETA: splitting (4292) gives:
% 110.53/15.78 | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | Case 1:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | (4293) all_57_54 = e2 & op(e1, e1) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | ALPHA: (4293) implies:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | (4294) op(e1, e1) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e2,
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (50), (4294) gives:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | (4295) all_14_2 = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | REDUCE: (4274), (4295) imply:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | (4296) $false
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | CLOSE: (4296) is inconsistent.
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | Case 2:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | (4297) all_57_55 = e2 & op(e0, e1) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | ALPHA: (4297) implies:
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | (4298) op(e0, e1) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3984), (4298), (function-axioms) are
% 110.53/15.78 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #161.
% 110.53/15.78 | | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | Case 2:
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | (4299) all_57_49 = e2 & op(e1, e2) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | ALPHA: (4299) implies:
% 110.53/15.78 | | | | | | | | | | | | | | | | | (4300) op(e1, e2) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (4263), (4300), (function-axioms) are
% 110.53/15.78 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #80.
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | Case 2:
% 110.53/15.78 | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | (4301) (all_57_50 = e2 & op(e1, e1) = e2) | (all_57_51 =
% 110.53/15.78 | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 110.53/15.78 | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | BETA: splitting (4301) gives:
% 110.53/15.78 | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | Case 1:
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | (4302) all_57_50 = e2 & op(e1, e1) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | ALPHA: (4302) implies:
% 110.53/15.78 | | | | | | | | | | | | | | | | | (4303) op(e1, e1) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e2,
% 110.53/15.78 | | | | | | | | | | | | | | | | | e1, e1, simplifying with (50), (4303) gives:
% 110.53/15.78 | | | | | | | | | | | | | | | | | (4304) all_14_2 = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | REDUCE: (4274), (4304) imply:
% 110.53/15.78 | | | | | | | | | | | | | | | | | (4305) $false
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | CLOSE: (4305) is inconsistent.
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | Case 2:
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | (4306) all_57_51 = e2 & op(e1, e0) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | ALPHA: (4306) implies:
% 110.53/15.78 | | | | | | | | | | | | | | | | | (4307) op(e1, e0) = e2
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (3987), (4307), (function-axioms) are
% 110.53/15.78 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #112.
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | Case 2:
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | (4308) all_14_2 = e2
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | REDUCE: (50), (4308) imply:
% 110.53/15.78 | | | | | | | | | | | | | | | (4309) op(e1, e1) = e2
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | Case 1:
% 110.53/15.78 | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | (4310) (all_57_60 = e3 & op(e3, e1) = e3) | (all_57_61 =
% 110.53/15.78 | | | | | | | | | | | | | | | | e3 & op(e2, e1) = e3)
% 110.53/15.78 | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | BETA: splitting (4310) gives:
% 110.53/15.78 | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | Case 1:
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | (4311) all_57_60 = e3 & op(e3, e1) = e3
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | ALPHA: (4311) implies:
% 110.53/15.78 | | | | | | | | | | | | | | | | | (4312) op(e3, e1) = e3
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (117), (137), (164), (168), (172), (173),
% 110.53/15.78 | | | | | | | | | | | | | | | | | (195), (196), (272), (273), (3467), (3988),
% 110.53/15.78 | | | | | | | | | | | | | | | | | (3989), (4312), (function-axioms) are inconsistent
% 110.53/15.78 | | | | | | | | | | | | | | | | | by sub-proof #6.
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | Case 2:
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | (4313) all_57_61 = e3 & op(e2, e1) = e3
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | ALPHA: (4313) implies:
% 110.53/15.78 | | | | | | | | | | | | | | | | | (4314) op(e2, e1) = e3
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4232), (4314), (function-axioms) are
% 110.53/15.78 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #138.
% 110.53/15.78 | | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | Case 2:
% 110.53/15.78 | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | (4315) (all_57_62 = e3 & op(e1, e1) = e3) | (all_57_63 =
% 110.53/15.78 | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 110.53/15.78 | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (161), (4273), (4309), (4315),
% 110.53/15.78 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.53/15.78 | | | | | | | | | | | | | | | | #89.
% 110.53/15.78 | | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | Case 2:
% 110.53/15.78 | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | (4316) all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 110.53/15.78 | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | BETA: splitting (4316) gives:
% 110.53/15.78 | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | Case 1:
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | (4317) all_55_3 = e2
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | COMBINE_EQS: (4267), (4317) imply:
% 110.53/15.78 | | | | | | | | | | | | | | | (4318) all_10_0 = e2
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | SIMP: (4318) implies:
% 110.53/15.78 | | | | | | | | | | | | | | | (4319) all_10_0 = e2
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | REDUCE: (4269), (4319) imply:
% 110.53/15.78 | | | | | | | | | | | | | | | (4320) $false
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | CLOSE: (4320) is inconsistent.
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | Case 2:
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | (4321) all_55_3 = e1 | all_55_3 = e0
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | | REF_CLOSE: (4258), (4267), (4270), (4321) are inconsistent by
% 110.53/15.78 | | | | | | | | | | | | | | | sub-proof #8.
% 110.53/15.78 | | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | Case 2:
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | (4322) all_55_14 = e1 | all_55_14 = e0
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | | REF_CLOSE: (108), (144), (162), (166), (174), (206), (250),
% 110.53/15.78 | | | | | | | | | | | | | (3986), (4231), (4233), (4241), (4247), (4248),
% 110.53/15.78 | | | | | | | | | | | | | (4322), (function-axioms) are inconsistent by
% 110.53/15.78 | | | | | | | | | | | | | sub-proof #57.
% 110.53/15.78 | | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | | |
% 110.53/15.78 | | | | | | | | | End of split
% 110.53/15.78 | | | | | | | | |
% 110.53/15.78 | | | | | | | | End of split
% 110.53/15.78 | | | | | | | |
% 110.53/15.78 | | | | | | | End of split
% 110.53/15.78 | | | | | | |
% 110.53/15.78 | | | | | | End of split
% 110.53/15.78 | | | | | |
% 110.53/15.78 | | | | | End of split
% 110.53/15.78 | | | | |
% 110.53/15.78 | | | | End of split
% 110.53/15.78 | | | |
% 110.53/15.78 | | | Case 2:
% 110.53/15.78 | | | |
% 110.53/15.78 | | | | (4323) all_6_2 = e1
% 110.53/15.79 | | | | (4324) op(e1, e1) = all_6_1 & $i(all_6_1) & ( ~ (all_6_1 = e2) | ( ~
% 110.53/15.79 | | | | (all_6_0 = e3) & op(e2, e1) = all_6_0 & $i(all_6_0)))
% 110.53/15.79 | | | |
% 110.53/15.79 | | | | ALPHA: (4324) implies:
% 110.53/15.79 | | | | (4325) op(e1, e1) = all_6_1
% 110.53/15.79 | | | | (4326) ~ (all_6_1 = e2) | ( ~ (all_6_0 = e3) & op(e2, e1) = all_6_0
% 110.53/15.79 | | | | & $i(all_6_0))
% 110.53/15.79 | | | |
% 110.53/15.79 | | | | COMBINE_EQS: (3479), (4323) imply:
% 110.53/15.79 | | | | (4327) all_4_1 = e1
% 110.53/15.79 | | | |
% 110.53/15.79 | | | | SIMP: (4327) implies:
% 110.53/15.79 | | | | (4328) all_4_1 = e1
% 110.53/15.79 | | | |
% 110.53/15.79 | | | | COMBINE_EQS: (3484), (4328) imply:
% 110.53/15.79 | | | | (4329) all_38_2 = e1
% 110.53/15.79 | | | |
% 110.53/15.79 | | | | REDUCE: (3486), (4328) imply:
% 110.53/15.79 | | | | (4330) ~ (all_53_1 = e1)
% 110.53/15.79 | | | |
% 110.53/15.79 | | | | REDUCE: (3488), (4328) imply:
% 110.53/15.79 | | | | (4331) ~ (all_53_3 = e1)
% 110.53/15.79 | | | |
% 110.53/15.79 | | | | REDUCE: (3489), (4328) imply:
% 110.53/15.79 | | | | (4332) ~ (all_53_4 = e1)
% 110.53/15.79 | | | |
% 110.53/15.79 | | | | REDUCE: (3490), (4328) imply:
% 110.53/15.79 | | | | (4333) ~ (all_53_8 = e1)
% 110.53/15.79 | | | |
% 110.53/15.79 | | | | REDUCE: (3461), (4328) imply:
% 110.53/15.79 | | | | (4334) op(e0, e0) = e1
% 110.53/15.79 | | | |
% 110.53/15.79 | | | | BETA: splitting (3462) gives:
% 110.53/15.79 | | | |
% 110.53/15.79 | | | | Case 1:
% 110.53/15.79 | | | | |
% 110.53/15.79 | | | | | (4335) ~ (all_4_1 = e1)
% 110.53/15.79 | | | | |
% 110.53/15.79 | | | | | REDUCE: (4328), (4335) imply:
% 110.53/15.79 | | | | | (4336) $false
% 110.53/15.79 | | | | |
% 110.53/15.79 | | | | | CLOSE: (4336) is inconsistent.
% 110.53/15.79 | | | | |
% 110.53/15.79 | | | | Case 2:
% 110.53/15.79 | | | | |
% 110.53/15.79 | | | | | (4337) ~ (all_4_0 = e2) & op(e1, e0) = all_4_0 & $i(all_4_0)
% 110.53/15.79 | | | | |
% 110.53/15.79 | | | | | ALPHA: (4337) implies:
% 110.53/15.79 | | | | | (4338) ~ (all_4_0 = e2)
% 110.53/15.79 | | | | | (4339) op(e1, e0) = all_4_0
% 110.53/15.79 | | | | |
% 110.53/15.79 | | | | | BETA: splitting (87) gives:
% 110.53/15.79 | | | | |
% 110.53/15.79 | | | | | Case 1:
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | (4340) ~ (all_38_2 = e1)
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | REDUCE: (4329), (4340) imply:
% 110.53/15.79 | | | | | | (4341) $false
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | CLOSE: (4341) is inconsistent.
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | Case 2:
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | (4342) op(e1, e1) = all_38_1 & $i(all_38_1) & ( ~ (all_38_1 = e3)
% 110.53/15.79 | | | | | | | ( ~ (all_38_0 = e2) & op(e3, e1) = all_38_0 &
% 110.53/15.79 | | | | | | $i(all_38_0)))
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | ALPHA: (4342) implies:
% 110.53/15.79 | | | | | | (4343) op(e1, e1) = all_38_1
% 110.53/15.79 | | | | | | (4344) ~ (all_38_1 = e3) | ( ~ (all_38_0 = e2) & op(e3, e1) =
% 110.53/15.79 | | | | | | all_38_0 & $i(all_38_0))
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, all_4_0,
% 110.53/15.79 | | | | | | e0, e1, simplifying with (164), (4339) gives:
% 110.53/15.79 | | | | | | (4345) all_53_4 = all_4_0
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2,
% 110.53/15.79 | | | | | | all_38_1, e1, e1, simplifying with (50), (4343) gives:
% 110.53/15.79 | | | | | | (4346) all_38_1 = all_14_2
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1, all_38_1,
% 110.53/15.79 | | | | | | e1, e1, simplifying with (4325), (4343) gives:
% 110.53/15.79 | | | | | | (4347) all_38_1 = all_6_1
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | COMBINE_EQS: (4346), (4347) imply:
% 110.53/15.79 | | | | | | (4348) all_14_2 = all_6_1
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | SIMP: (4348) implies:
% 110.53/15.79 | | | | | | (4349) all_14_2 = all_6_1
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | COMBINE_EQS: (326), (4349) imply:
% 110.53/15.79 | | | | | | (4350) all_18_2 = all_6_1
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | COMBINE_EQS: (329), (4349) imply:
% 110.53/15.79 | | | | | | (4351) all_22_2 = all_6_1
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | COMBINE_EQS: (341), (4349) imply:
% 110.53/15.79 | | | | | | (4352) all_55_5 = all_6_1
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | COMBINE_EQS: (252), (4345) imply:
% 110.53/15.79 | | | | | | (4353) all_55_4 = all_4_0
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | REDUCE: (354), (4349) imply:
% 110.53/15.79 | | | | | | (4354) ~ (all_53_1 = all_6_1)
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | REDUCE: (138), (4345) imply:
% 110.53/15.79 | | | | | | (4355) ~ (all_53_8 = all_4_0)
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | SIMP: (4355) implies:
% 110.53/15.79 | | | | | | (4356) ~ (all_53_8 = all_4_0)
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | REDUCE: (137), (4345) imply:
% 110.53/15.79 | | | | | | (4357) ~ (all_53_12 = all_4_0)
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | SIMP: (4357) implies:
% 110.53/15.79 | | | | | | (4358) ~ (all_53_12 = all_4_0)
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | REDUCE: (357), (4345), (4349) imply:
% 110.53/15.79 | | | | | | (4359) ~ (all_6_1 = all_4_0)
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | SIMP: (4359) implies:
% 110.53/15.79 | | | | | | (4360) ~ (all_6_1 = all_4_0)
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | REDUCE: (4332), (4345) imply:
% 110.53/15.79 | | | | | | (4361) ~ (all_4_0 = e1)
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | REDUCE: (359), (4349) imply:
% 110.53/15.79 | | | | | | (4362) ~ (all_53_6 = all_6_1)
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | REDUCE: (361), (4349) imply:
% 110.53/15.79 | | | | | | (4363) ~ (all_53_7 = all_6_1)
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | REDUCE: (363), (4349) imply:
% 110.53/15.79 | | | | | | (4364) ~ (all_53_9 = all_6_1)
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | REDUCE: (365), (4349) imply:
% 110.53/15.79 | | | | | | (4365) ~ (all_53_13 = all_6_1)
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | BETA: splitting (45) gives:
% 110.53/15.79 | | | | | |
% 110.53/15.79 | | | | | | Case 1:
% 110.53/15.79 | | | | | | |
% 110.53/15.79 | | | | | | | (4366) ~ (all_10_2 = e3)
% 110.53/15.79 | | | | | | |
% 110.53/15.79 | | | | | | | BETA: splitting (48) gives:
% 110.53/15.79 | | | | | | |
% 110.53/15.79 | | | | | | | Case 1:
% 110.53/15.79 | | | | | | | |
% 110.53/15.79 | | | | | | | | (4367) ~ (all_12_2 = e0)
% 110.53/15.79 | | | | | | | |
% 110.53/15.79 | | | | | | | | REDUCE: (323), (4367) imply:
% 110.53/15.79 | | | | | | | | (4368) ~ (all_10_2 = e0)
% 110.53/15.79 | | | | | | | |
% 110.53/15.79 | | | | | | | | BETA: splitting (51) gives:
% 110.53/15.79 | | | | | | | |
% 110.53/15.79 | | | | | | | | Case 1:
% 110.53/15.79 | | | | | | | | |
% 110.53/15.79 | | | | | | | | | (4369) ~ (all_14_2 = e2)
% 110.53/15.79 | | | | | | | | |
% 110.53/15.79 | | | | | | | | | REDUCE: (4349), (4369) imply:
% 110.53/15.79 | | | | | | | | | (4370) ~ (all_6_1 = e2)
% 110.53/15.79 | | | | | | | | |
% 110.53/15.79 | | | | | | | | | BETA: splitting (57) gives:
% 110.53/15.79 | | | | | | | | |
% 110.53/15.79 | | | | | | | | | Case 1:
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | (4371) ~ (all_18_2 = e3)
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | REDUCE: (4350), (4371) imply:
% 110.53/15.79 | | | | | | | | | | (4372) ~ (all_6_1 = e3)
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | BETA: splitting (63) gives:
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | Case 1:
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | (4373) ~ (all_22_2 = e0)
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | REDUCE: (4351), (4373) imply:
% 110.53/15.79 | | | | | | | | | | | (4374) ~ (all_6_1 = e0)
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | BETA: splitting (203) gives:
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | Case 1:
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | (4375) all_55_5 = e3
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | REF_CLOSE: (4352), (4372), (4375) are inconsistent by
% 110.53/15.79 | | | | | | | | | | | | sub-proof #5.
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | Case 2:
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | (4376) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | BETA: splitting (4376) gives:
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | Case 1:
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | (4377) all_55_5 = e2
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | REF_CLOSE: (4352), (4370), (4377) are inconsistent by
% 110.53/15.79 | | | | | | | | | | | | | sub-proof #4.
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | Case 2:
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | (4378) all_55_5 = e1 | all_55_5 = e0
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | BETA: splitting (4378) gives:
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | Case 1:
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | (4379) all_55_5 = e1
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | COMBINE_EQS: (4352), (4379) imply:
% 110.53/15.79 | | | | | | | | | | | | | | (4380) all_6_1 = e1
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | SIMP: (4380) implies:
% 110.53/15.79 | | | | | | | | | | | | | | (4381) all_6_1 = e1
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | REDUCE: (4362), (4381) imply:
% 110.53/15.79 | | | | | | | | | | | | | | (4382) ~ (all_53_6 = e1)
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | REDUCE: (4363), (4381) imply:
% 110.53/15.79 | | | | | | | | | | | | | | (4383) ~ (all_53_7 = e1)
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (117), (123),
% 110.53/15.79 | | | | | | | | | | | | | | (126), (127), (148), (152), (153), (161), (162),
% 110.53/15.79 | | | | | | | | | | | | | | (163), (164), (166), (167), (168), (169), (171),
% 110.53/15.79 | | | | | | | | | | | | | | (172), (173), (174), (4332), (4382), (4383),
% 110.53/15.79 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.53/15.79 | | | | | | | | | | | | | | #217.
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | Case 2:
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | (4384) all_55_5 = e0
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | REF_CLOSE: (4352), (4374), (4384) are inconsistent by
% 110.53/15.79 | | | | | | | | | | | | | | sub-proof #3.
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | End of split
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | End of split
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | End of split
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | Case 2:
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | (4385) all_22_2 = e0
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | REF_CLOSE: (66), (99), (109), (110), (117), (149), (150),
% 110.53/15.79 | | | | | | | | | | | (161), (164), (168), (169), (171), (172), (173),
% 110.53/15.79 | | | | | | | | | | | (198), (207), (223), (230), (249), (265), (303),
% 110.53/15.79 | | | | | | | | | | | (340), (368), (369), (370), (4325), (4330),
% 110.53/15.79 | | | | | | | | | | | (4332), (4351), (4354), (4366), (4368), (4385),
% 110.53/15.79 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.53/15.79 | | | | | | | | | | | #46.
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | End of split
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | Case 2:
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | (4386) all_18_2 = e3
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | COMBINE_EQS: (4350), (4386) imply:
% 110.53/15.79 | | | | | | | | | | (4387) all_6_1 = e3
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | SIMP: (4387) implies:
% 110.53/15.79 | | | | | | | | | | (4388) all_6_1 = e3
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | REDUCE: (4354), (4388) imply:
% 110.53/15.79 | | | | | | | | | | (4389) ~ (all_53_1 = e3)
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | REDUCE: (4365), (4388) imply:
% 110.53/15.79 | | | | | | | | | | (4390) ~ (all_53_13 = e3)
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | REDUCE: (4360), (4388) imply:
% 110.53/15.79 | | | | | | | | | | (4391) ~ (all_4_0 = e3)
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | SIMP: (4391) implies:
% 110.53/15.79 | | | | | | | | | | (4392) ~ (all_4_0 = e3)
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | BETA: splitting (204) gives:
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | Case 1:
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | (4393) all_55_4 = e3
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | COMBINE_EQS: (4353), (4393) imply:
% 110.53/15.79 | | | | | | | | | | | (4394) all_4_0 = e3
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | REDUCE: (4392), (4394) imply:
% 110.53/15.79 | | | | | | | | | | | (4395) $false
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | CLOSE: (4395) is inconsistent.
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | Case 2:
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | (4396) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | BETA: splitting (4396) gives:
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | Case 1:
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | (4397) all_55_4 = e2
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | COMBINE_EQS: (4353), (4397) imply:
% 110.53/15.79 | | | | | | | | | | | | (4398) all_4_0 = e2
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | REDUCE: (4338), (4398) imply:
% 110.53/15.79 | | | | | | | | | | | | (4399) $false
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | CLOSE: (4399) is inconsistent.
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | Case 2:
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | (4400) all_55_4 = e1 | all_55_4 = e0
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | BETA: splitting (4400) gives:
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | Case 1:
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | (4401) all_55_4 = e1
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | COMBINE_EQS: (4353), (4401) imply:
% 110.53/15.79 | | | | | | | | | | | | | (4402) all_4_0 = e1
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | REDUCE: (4361), (4402) imply:
% 110.53/15.79 | | | | | | | | | | | | | (4403) $false
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | CLOSE: (4403) is inconsistent.
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | Case 2:
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | (4404) all_55_4 = e0
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | COMBINE_EQS: (4353), (4404) imply:
% 110.53/15.79 | | | | | | | | | | | | | (4405) all_4_0 = e0
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | REDUCE: (4356), (4405) imply:
% 110.53/15.79 | | | | | | | | | | | | | (4406) ~ (all_53_8 = e0)
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | BETA: splitting (225) gives:
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | Case 1:
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | (4407) (all_57_64 = e0 & op(e2, e3) = e0) | (all_57_65 =
% 110.53/15.79 | | | | | | | | | | | | | | e0 & op(e2, e2) = e0)
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | REF_CLOSE: (44), (171), (3466), (4368), (4407),
% 110.53/15.79 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.53/15.79 | | | | | | | | | | | | | | #18.
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | Case 2:
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | (4408) (all_57_66 = e0 & op(e2, e1) = e0) | (all_57_67 =
% 110.53/15.79 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | BETA: splitting (4408) gives:
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | Case 1:
% 110.53/15.79 | | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | | (4409) all_57_66 = e0 & op(e2, e1) = e0
% 110.53/15.79 | | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | | ALPHA: (4409) implies:
% 110.53/15.79 | | | | | | | | | | | | | | | (4410) op(e2, e1) = e0
% 110.53/15.79 | | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e0,
% 110.53/15.79 | | | | | | | | | | | | | | | e1, e2, simplifying with (169), (4410) gives:
% 110.53/15.79 | | | | | | | | | | | | | | | (4411) all_53_9 = e0
% 110.53/15.79 | | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | | REDUCE: (150), (4411) imply:
% 110.53/15.79 | | | | | | | | | | | | | | | (4412) ~ (all_53_1 = e0)
% 110.53/15.79 | | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | | REF_CLOSE: (109), (150), (161), (169), (173), (207), (249),
% 110.53/15.79 | | | | | | | | | | | | | | | (4330), (4389), (4390), (4412), (function-axioms)
% 110.53/15.79 | | | | | | | | | | | | | | | are inconsistent by sub-proof #41.
% 110.53/15.79 | | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | Case 2:
% 110.53/15.79 | | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | | (4413) all_57_67 = e0 & op(e2, e0) = e0
% 110.53/15.79 | | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | | ALPHA: (4413) implies:
% 110.53/15.79 | | | | | | | | | | | | | | | (4414) op(e2, e0) = e0
% 110.53/15.79 | | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | | REF_CLOSE: (168), (4406), (4414), (function-axioms) are
% 110.53/15.79 | | | | | | | | | | | | | | | inconsistent by sub-proof #14.
% 110.53/15.79 | | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | | End of split
% 110.53/15.79 | | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | | End of split
% 110.53/15.79 | | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | | End of split
% 110.53/15.79 | | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | | End of split
% 110.53/15.79 | | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | End of split
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | End of split
% 110.53/15.79 | | | | | | | | |
% 110.53/15.79 | | | | | | | | Case 2:
% 110.53/15.79 | | | | | | | | |
% 110.53/15.79 | | | | | | | | | (4415) all_14_2 = e2
% 110.53/15.79 | | | | | | | | |
% 110.53/15.79 | | | | | | | | | COMBINE_EQS: (4349), (4415) imply:
% 110.53/15.79 | | | | | | | | | (4416) all_6_1 = e2
% 110.53/15.79 | | | | | | | | |
% 110.53/15.79 | | | | | | | | | REDUCE: (4354), (4416) imply:
% 110.53/15.79 | | | | | | | | | (4417) ~ (all_53_1 = e2)
% 110.53/15.79 | | | | | | | | |
% 110.53/15.79 | | | | | | | | | REDUCE: (4364), (4416) imply:
% 110.53/15.79 | | | | | | | | | (4418) ~ (all_53_9 = e2)
% 110.53/15.79 | | | | | | | | |
% 110.53/15.79 | | | | | | | | | BETA: splitting (4326) gives:
% 110.53/15.79 | | | | | | | | |
% 110.53/15.79 | | | | | | | | | Case 1:
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | (4419) ~ (all_6_1 = e2)
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | REDUCE: (4416), (4419) imply:
% 110.53/15.79 | | | | | | | | | | (4420) $false
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | CLOSE: (4420) is inconsistent.
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | Case 2:
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | (4421) ~ (all_6_0 = e3) & op(e2, e1) = all_6_0 &
% 110.53/15.79 | | | | | | | | | | $i(all_6_0)
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | ALPHA: (4421) implies:
% 110.53/15.79 | | | | | | | | | | (4422) ~ (all_6_0 = e3)
% 110.53/15.79 | | | | | | | | | | (4423) op(e2, e1) = all_6_0
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 110.53/15.79 | | | | | | | | | | all_6_0, e1, e2, simplifying with (169), (4423)
% 110.53/15.79 | | | | | | | | | | gives:
% 110.53/15.79 | | | | | | | | | | (4424) all_53_9 = all_6_0
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.79 | | | | | | | | | | COMBINE_EQS: (263), (4424) imply:
% 110.53/15.79 | | | | | | | | | | (4425) all_55_9 = all_6_0
% 110.53/15.79 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | REDUCE: (150), (4424) imply:
% 110.53/15.80 | | | | | | | | | | (4426) ~ (all_53_1 = all_6_0)
% 110.53/15.80 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | REDUCE: (369), (4424) imply:
% 110.53/15.80 | | | | | | | | | | (4427) ~ (all_10_2 = all_6_0)
% 110.53/15.80 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | SIMP: (4427) implies:
% 110.53/15.80 | | | | | | | | | | (4428) ~ (all_10_2 = all_6_0)
% 110.53/15.80 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | REDUCE: (4418), (4424) imply:
% 110.53/15.80 | | | | | | | | | | (4429) ~ (all_6_0 = e2)
% 110.53/15.80 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | BETA: splitting (66) gives:
% 110.53/15.80 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | Case 1:
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | (4430) ~ (all_24_2 = e1)
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | REDUCE: (303), (4430) imply:
% 110.53/15.80 | | | | | | | | | | | (4431) ~ (all_10_2 = e1)
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | REF_CLOSE: (107), (108), (109), (110), (113), (115), (117),
% 110.53/15.80 | | | | | | | | | | | (132), (139), (140), (148), (152), (153), (161),
% 110.53/15.80 | | | | | | | | | | | (162), (163), (164), (166), (167), (168), (169),
% 110.53/15.80 | | | | | | | | | | | (171), (172), (173), (174), (198), (340), (368),
% 110.53/15.80 | | | | | | | | | | | (369), (370), (4366), (4368), (4431),
% 110.53/15.80 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.53/15.80 | | | | | | | | | | | #207.
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | Case 2:
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | (4432) all_24_2 = e1
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | COMBINE_EQS: (303), (4432) imply:
% 110.53/15.80 | | | | | | | | | | | (4433) all_10_2 = e1
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | REDUCE: (4428), (4433) imply:
% 110.53/15.80 | | | | | | | | | | | (4434) ~ (all_6_0 = e1)
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | SIMP: (4434) implies:
% 110.53/15.80 | | | | | | | | | | | (4435) ~ (all_6_0 = e1)
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | REF_CLOSE: (109), (149), (161), (169), (173), (199), (207),
% 110.53/15.80 | | | | | | | | | | | (249), (4330), (4417), (4418), (4422), (4423),
% 110.53/15.80 | | | | | | | | | | | (4425), (4426), (4429), (4435), (function-axioms)
% 110.53/15.80 | | | | | | | | | | | are inconsistent by sub-proof #36.
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | End of split
% 110.53/15.80 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | End of split
% 110.53/15.80 | | | | | | | | |
% 110.53/15.80 | | | | | | | | End of split
% 110.53/15.80 | | | | | | | |
% 110.53/15.80 | | | | | | | Case 2:
% 110.53/15.80 | | | | | | | |
% 110.53/15.80 | | | | | | | | (4436) all_12_2 = e0
% 110.53/15.80 | | | | | | | |
% 110.53/15.80 | | | | | | | | COMBINE_EQS: (323), (4436) imply:
% 110.53/15.80 | | | | | | | | (4437) all_10_2 = e0
% 110.53/15.80 | | | | | | | |
% 110.53/15.80 | | | | | | | | REDUCE: (356), (4437) imply:
% 110.53/15.80 | | | | | | | | (4438) ~ (all_53_3 = e0)
% 110.53/15.80 | | | | | | | |
% 110.53/15.80 | | | | | | | | REDUCE: (368), (4437) imply:
% 110.53/15.80 | | | | | | | | (4439) ~ (all_53_8 = e0)
% 110.53/15.80 | | | | | | | |
% 110.53/15.80 | | | | | | | | REDUCE: (44), (4437) imply:
% 110.53/15.80 | | | | | | | | (4440) op(e2, e2) = e0
% 110.53/15.80 | | | | | | | |
% 110.53/15.80 | | | | | | | | BETA: splitting (240) gives:
% 110.53/15.80 | | | | | | | |
% 110.53/15.80 | | | | | | | | Case 1:
% 110.53/15.80 | | | | | | | | |
% 110.53/15.80 | | | | | | | | | (4441) (all_57_4 = e0 & op(e3, e0) = e0) | (all_57_5 = e0 &
% 110.53/15.80 | | | | | | | | | op(e2, e0) = e0)
% 110.53/15.80 | | | | | | | | |
% 110.53/15.80 | | | | | | | | | REF_CLOSE: (168), (172), (3467), (4439), (4441),
% 110.53/15.80 | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.53/15.80 | | | | | | | | | #10.
% 110.53/15.80 | | | | | | | | |
% 110.53/15.80 | | | | | | | | Case 2:
% 110.53/15.80 | | | | | | | | |
% 110.53/15.80 | | | | | | | | | (4442) (all_57_6 = e0 & op(e1, e0) = e0) | (all_57_7 = e0 &
% 110.53/15.80 | | | | | | | | | op(e0, e0) = e0)
% 110.53/15.80 | | | | | | | | |
% 110.53/15.80 | | | | | | | | | BETA: splitting (4442) gives:
% 110.53/15.80 | | | | | | | | |
% 110.53/15.80 | | | | | | | | | Case 1:
% 110.53/15.80 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | (4443) all_57_6 = e0 & op(e1, e0) = e0
% 110.53/15.80 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | ALPHA: (4443) implies:
% 110.53/15.80 | | | | | | | | | | (4444) op(e1, e0) = e0
% 110.53/15.80 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | BETA: splitting (241) gives:
% 110.53/15.80 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | Case 1:
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | (4445) (all_57_0 = e0 & op(e0, e3) = e0) | (all_57_1 = e0
% 110.53/15.80 | | | | | | | | | | | & op(e0, e2) = e0)
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | BETA: splitting (4445) gives:
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | Case 1:
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | (4446) all_57_0 = e0 & op(e0, e3) = e0
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | ALPHA: (4446) implies:
% 110.53/15.80 | | | | | | | | | | | | (4447) op(e0, e3) = e0
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | REF_CLOSE: (163), (3464), (4447), (function-axioms) are
% 110.53/15.80 | | | | | | | | | | | | inconsistent by sub-proof #149.
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | Case 2:
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | (4448) all_57_1 = e0 & op(e0, e2) = e0
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | ALPHA: (4448) implies:
% 110.53/15.80 | | | | | | | | | | | | (4449) op(e0, e2) = e0
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | REF_CLOSE: (162), (4438), (4449), (function-axioms) are
% 110.53/15.80 | | | | | | | | | | | | inconsistent by sub-proof #219.
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | End of split
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | Case 2:
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | (4450) (all_57_2 = e0 & op(e0, e1) = e0) | (all_57_3 = e0
% 110.53/15.80 | | | | | | | | | | | & op(e0, e0) = e0)
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | BETA: splitting (4450) gives:
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | Case 1:
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | (4451) all_57_2 = e0 & op(e0, e1) = e0
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | ALPHA: (4451) implies:
% 110.53/15.80 | | | | | | | | | | | | (4452) op(e0, e1) = e0
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e0,
% 110.53/15.80 | | | | | | | | | | | | e1, e0, simplifying with (161), (4452) gives:
% 110.53/15.80 | | | | | | | | | | | | (4453) all_53_1 = e0
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_0, e0,
% 110.53/15.80 | | | | | | | | | | | | e0, e1, simplifying with (4339), (4444) gives:
% 110.53/15.80 | | | | | | | | | | | | (4454) all_4_0 = e0
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | REDUCE: (152), (4453) imply:
% 110.53/15.80 | | | | | | | | | | | | (4455) ~ (all_53_3 = e0)
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | REDUCE: (150), (4453) imply:
% 110.53/15.80 | | | | | | | | | | | | (4456) ~ (all_53_9 = e0)
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | SIMP: (4456) implies:
% 110.53/15.80 | | | | | | | | | | | | (4457) ~ (all_53_9 = e0)
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | REDUCE: (149), (4453) imply:
% 110.53/15.80 | | | | | | | | | | | | (4458) ~ (all_53_13 = e0)
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | REDUCE: (4360), (4454) imply:
% 110.53/15.80 | | | | | | | | | | | | (4459) ~ (all_6_1 = e0)
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | BETA: splitting (51) gives:
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | Case 1:
% 110.53/15.80 | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | (4460) ~ (all_14_2 = e2)
% 110.53/15.80 | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | REDUCE: (4349), (4460) imply:
% 110.53/15.80 | | | | | | | | | | | | | (4461) ~ (all_6_1 = e2)
% 110.53/15.80 | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | REF_CLOSE: (57), (108), (110), (121), (124), (127), (162),
% 110.53/15.80 | | | | | | | | | | | | | (164), (166), (168), (172), (173), (174), (195),
% 110.53/15.80 | | | | | | | | | | | | | (199), (200), (203), (222), (262), (263), (273),
% 110.53/15.80 | | | | | | | | | | | | | (3468), (4331), (4332), (4333), (4344), (4347),
% 110.53/15.80 | | | | | | | | | | | | | (4350), (4352), (4363), (4364), (4365), (4438),
% 110.53/15.80 | | | | | | | | | | | | | (4439), (4440), (4457), (4459), (4461),
% 110.53/15.80 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.53/15.80 | | | | | | | | | | | | | #2.
% 110.53/15.80 | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | Case 2:
% 110.53/15.80 | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | (4462) all_14_2 = e2
% 110.53/15.80 | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | COMBINE_EQS: (4349), (4462) imply:
% 110.53/15.80 | | | | | | | | | | | | | (4463) all_6_1 = e2
% 110.53/15.80 | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | REDUCE: (4364), (4463) imply:
% 110.53/15.80 | | | | | | | | | | | | | (4464) ~ (all_53_9 = e2)
% 110.53/15.80 | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | REDUCE: (4365), (4463) imply:
% 110.53/15.80 | | | | | | | | | | | | | (4465) ~ (all_53_13 = e2)
% 110.53/15.80 | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | BETA: splitting (4326) gives:
% 110.53/15.80 | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | Case 1:
% 110.53/15.80 | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | (4466) ~ (all_6_1 = e2)
% 110.53/15.80 | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | REF_CLOSE: (57), (108), (110), (121), (124), (127), (162),
% 110.53/15.80 | | | | | | | | | | | | | | (164), (166), (168), (172), (173), (174), (195),
% 110.53/15.80 | | | | | | | | | | | | | | (199), (200), (203), (222), (262), (263), (273),
% 110.53/15.80 | | | | | | | | | | | | | | (3468), (4331), (4332), (4333), (4344), (4347),
% 110.53/15.80 | | | | | | | | | | | | | | (4350), (4352), (4363), (4364), (4365), (4438),
% 110.53/15.80 | | | | | | | | | | | | | | (4439), (4440), (4457), (4459), (4466),
% 110.53/15.80 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.53/15.80 | | | | | | | | | | | | | | #2.
% 110.53/15.80 | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | Case 2:
% 110.53/15.80 | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | (4467) ~ (all_6_0 = e3) & op(e2, e1) = all_6_0 &
% 110.53/15.80 | | | | | | | | | | | | | | $i(all_6_0)
% 110.53/15.80 | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | ALPHA: (4467) implies:
% 110.53/15.80 | | | | | | | | | | | | | | (4468) ~ (all_6_0 = e3)
% 110.53/15.80 | | | | | | | | | | | | | | (4469) op(e2, e1) = all_6_0
% 110.53/15.80 | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 110.53/15.80 | | | | | | | | | | | | | | all_6_0, e1, e2, simplifying with (169), (4469)
% 110.53/15.80 | | | | | | | | | | | | | | gives:
% 110.53/15.80 | | | | | | | | | | | | | | (4470) all_53_9 = all_6_0
% 110.53/15.80 | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | COMBINE_EQS: (263), (4470) imply:
% 110.53/15.80 | | | | | | | | | | | | | | (4471) all_55_9 = all_6_0
% 110.53/15.80 | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | REDUCE: (121), (4470) imply:
% 110.53/15.80 | | | | | | | | | | | | | | (4472) ~ (all_53_13 = all_6_0)
% 110.53/15.80 | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | SIMP: (4472) implies:
% 110.53/15.80 | | | | | | | | | | | | | | (4473) ~ (all_53_13 = all_6_0)
% 110.53/15.80 | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | REDUCE: (4464), (4470) imply:
% 110.53/15.80 | | | | | | | | | | | | | | (4474) ~ (all_6_0 = e2)
% 110.53/15.80 | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | REDUCE: (4457), (4470) imply:
% 110.53/15.80 | | | | | | | | | | | | | | (4475) ~ (all_6_0 = e0)
% 110.53/15.80 | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 110.53/15.80 | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | Case 1:
% 110.53/15.80 | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | (4476) all_55_9 = e3
% 110.53/15.80 | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | COMBINE_EQS: (4471), (4476) imply:
% 110.53/15.80 | | | | | | | | | | | | | | | (4477) all_6_0 = e3
% 110.53/15.80 | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | REDUCE: (4468), (4477) imply:
% 110.53/15.80 | | | | | | | | | | | | | | | (4478) $false
% 110.53/15.80 | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | CLOSE: (4478) is inconsistent.
% 110.53/15.80 | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | Case 2:
% 110.53/15.80 | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | (4479) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 110.53/15.80 | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | BETA: splitting (4479) gives:
% 110.53/15.80 | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | Case 1:
% 110.53/15.80 | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | (4480) all_55_9 = e2
% 110.53/15.80 | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | COMBINE_EQS: (4471), (4480) imply:
% 110.53/15.80 | | | | | | | | | | | | | | | | (4481) all_6_0 = e2
% 110.53/15.80 | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | REDUCE: (4474), (4481) imply:
% 110.53/15.80 | | | | | | | | | | | | | | | | (4482) $false
% 110.53/15.80 | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | CLOSE: (4482) is inconsistent.
% 110.53/15.80 | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | Case 2:
% 110.53/15.80 | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | (4483) all_55_9 = e1 | all_55_9 = e0
% 110.53/15.80 | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | BETA: splitting (4483) gives:
% 110.53/15.80 | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | Case 1:
% 110.53/15.80 | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | (4484) all_55_9 = e1
% 110.53/15.80 | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | COMBINE_EQS: (4471), (4484) imply:
% 110.53/15.80 | | | | | | | | | | | | | | | | | (4485) all_6_0 = e1
% 110.53/15.80 | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | REDUCE: (4473), (4485) imply:
% 110.53/15.80 | | | | | | | | | | | | | | | | | (4486) ~ (all_53_13 = e1)
% 110.53/15.80 | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 110.53/15.80 | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | Case 1:
% 110.53/15.80 | | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | | (4487) all_55_13 = e3
% 110.53/15.80 | | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (4487) imply:
% 110.53/15.80 | | | | | | | | | | | | | | | | | | (4488) all_53_13 = e3
% 110.53/15.80 | | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | | SIMP: (4488) implies:
% 110.53/15.80 | | | | | | | | | | | | | | | | | | (4489) all_53_13 = e3
% 110.53/15.80 | | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | | REDUCE: (117), (4489) imply:
% 110.53/15.80 | | | | | | | | | | | | | | | | | | (4490) ~ (all_53_12 = e3)
% 110.53/15.80 | | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | | REDUCE: (113), (4489) imply:
% 110.53/15.80 | | | | | | | | | | | | | | | | | | (4491) ~ (all_53_15 = e3)
% 110.53/15.80 | | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | | SIMP: (4491) implies:
% 110.53/15.80 | | | | | | | | | | | | | | | | | | (4492) ~ (all_53_15 = e3)
% 110.53/15.80 | | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (108), (110), (126), (132), (139), (152),
% 110.53/15.80 | | | | | | | | | | | | | | | | | | (153), (161), (162), (163), (164), (166), (167),
% 110.53/15.80 | | | | | | | | | | | | | | | | | | (168), (171), (172), (174), (4452), (4490),
% 110.53/15.80 | | | | | | | | | | | | | | | | | | (4492), (function-axioms) are inconsistent by
% 110.53/15.80 | | | | | | | | | | | | | | | | | | sub-proof #98.
% 110.53/15.80 | | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | Case 2:
% 110.53/15.80 | | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | | (4493) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 110.53/15.80 | | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (161), (273), (4452), (4465), (4486),
% 110.53/15.80 | | | | | | | | | | | | | | | | | | (4493), (function-axioms) are inconsistent by
% 110.53/15.80 | | | | | | | | | | | | | | | | | | sub-proof #124.
% 110.53/15.80 | | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | End of split
% 110.53/15.80 | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | Case 2:
% 110.53/15.80 | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | (4494) all_55_9 = e0
% 110.53/15.80 | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | COMBINE_EQS: (4471), (4494) imply:
% 110.53/15.80 | | | | | | | | | | | | | | | | | (4495) all_6_0 = e0
% 110.53/15.80 | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | REDUCE: (4475), (4495) imply:
% 110.53/15.80 | | | | | | | | | | | | | | | | | (4496) $false
% 110.53/15.80 | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | | CLOSE: (4496) is inconsistent.
% 110.53/15.80 | | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | | End of split
% 110.53/15.80 | | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | | End of split
% 110.53/15.80 | | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | | End of split
% 110.53/15.80 | | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | | End of split
% 110.53/15.80 | | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | End of split
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | Case 2:
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | (4497) all_57_3 = e0 & op(e0, e0) = e0
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | ALPHA: (4497) implies:
% 110.53/15.80 | | | | | | | | | | | | (4498) op(e0, e0) = e0
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | | REF_CLOSE: (4), (4334), (4498), (function-axioms) are
% 110.53/15.80 | | | | | | | | | | | | inconsistent by sub-proof #1.
% 110.53/15.80 | | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | | End of split
% 110.53/15.80 | | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | End of split
% 110.53/15.80 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | Case 2:
% 110.53/15.80 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | (4499) all_57_7 = e0 & op(e0, e0) = e0
% 110.53/15.80 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | ALPHA: (4499) implies:
% 110.53/15.80 | | | | | | | | | | (4500) op(e0, e0) = e0
% 110.53/15.80 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | | REF_CLOSE: (4), (4334), (4500), (function-axioms) are
% 110.53/15.80 | | | | | | | | | | inconsistent by sub-proof #1.
% 110.53/15.80 | | | | | | | | | |
% 110.53/15.80 | | | | | | | | | End of split
% 110.53/15.80 | | | | | | | | |
% 110.53/15.80 | | | | | | | | End of split
% 110.53/15.80 | | | | | | | |
% 110.53/15.80 | | | | | | | End of split
% 110.53/15.80 | | | | | | |
% 110.53/15.80 | | | | | | Case 2:
% 110.53/15.80 | | | | | | |
% 110.53/15.80 | | | | | | | (4501) all_10_2 = e3
% 110.53/15.80 | | | | | | |
% 110.53/15.80 | | | | | | | REDUCE: (356), (4501) imply:
% 110.53/15.80 | | | | | | | (4502) ~ (all_53_3 = e3)
% 110.53/15.80 | | | | | | |
% 110.53/15.80 | | | | | | | REDUCE: (367), (4501) imply:
% 110.53/15.80 | | | | | | | (4503) ~ (all_53_7 = e3)
% 110.53/15.80 | | | | | | |
% 110.53/15.80 | | | | | | | REDUCE: (368), (4501) imply:
% 110.53/15.80 | | | | | | | (4504) ~ (all_53_8 = e3)
% 110.53/15.80 | | | | | | |
% 110.53/15.80 | | | | | | | REDUCE: (369), (4501) imply:
% 110.53/15.80 | | | | | | | (4505) ~ (all_53_9 = e3)
% 110.53/15.80 | | | | | | |
% 110.53/15.80 | | | | | | | REDUCE: (373), (4501) imply:
% 110.53/15.80 | | | | | | | (4506) ~ (all_53_15 = e3)
% 110.53/15.80 | | | | | | |
% 110.53/15.80 | | | | | | | REDUCE: (44), (4501) imply:
% 110.53/15.80 | | | | | | | (4507) op(e2, e2) = e3
% 110.53/15.81 | | | | | | |
% 110.53/15.81 | | | | | | | BETA: splitting (51) gives:
% 110.53/15.81 | | | | | | |
% 110.53/15.81 | | | | | | | Case 1:
% 110.53/15.81 | | | | | | | |
% 110.53/15.81 | | | | | | | | (4508) ~ (all_14_2 = e2)
% 110.53/15.81 | | | | | | | |
% 110.53/15.81 | | | | | | | | REDUCE: (4349), (4508) imply:
% 110.53/15.81 | | | | | | | | (4509) ~ (all_6_1 = e2)
% 110.53/15.81 | | | | | | | |
% 110.53/15.81 | | | | | | | | BETA: splitting (57) gives:
% 110.53/15.81 | | | | | | | |
% 110.53/15.81 | | | | | | | | Case 1:
% 110.53/15.81 | | | | | | | | |
% 110.53/15.81 | | | | | | | | | (4510) ~ (all_18_2 = e3)
% 110.53/15.81 | | | | | | | | |
% 110.53/15.81 | | | | | | | | | REDUCE: (4350), (4510) imply:
% 110.53/15.81 | | | | | | | | | (4511) ~ (all_6_1 = e3)
% 110.53/15.81 | | | | | | | | |
% 110.53/15.81 | | | | | | | | | BETA: splitting (63) gives:
% 110.53/15.81 | | | | | | | | |
% 110.53/15.81 | | | | | | | | | Case 1:
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | (4512) ~ (all_22_2 = e0)
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | REDUCE: (4351), (4512) imply:
% 110.53/15.81 | | | | | | | | | | (4513) ~ (all_6_1 = e0)
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | BETA: splitting (203) gives:
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | Case 1:
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | (4514) all_55_5 = e3
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | REF_CLOSE: (4352), (4511), (4514) are inconsistent by
% 110.53/15.81 | | | | | | | | | | | sub-proof #5.
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | Case 2:
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | (4515) ~ (all_55_5 = e3)
% 110.53/15.81 | | | | | | | | | | | (4516) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | BETA: splitting (4516) gives:
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | Case 1:
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | (4517) all_55_5 = e2
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | REF_CLOSE: (4352), (4509), (4517) are inconsistent by
% 110.53/15.81 | | | | | | | | | | | | sub-proof #4.
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | Case 2:
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | (4518) all_55_5 = e1 | all_55_5 = e0
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | BETA: splitting (4518) gives:
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | Case 1:
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | (4519) all_55_5 = e1
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | COMBINE_EQS: (4352), (4519) imply:
% 110.53/15.81 | | | | | | | | | | | | | (4520) all_6_1 = e1
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | SIMP: (4520) implies:
% 110.53/15.81 | | | | | | | | | | | | | (4521) all_6_1 = e1
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | REDUCE: (4363), (4521) imply:
% 110.53/15.81 | | | | | | | | | | | | | (4522) ~ (all_53_7 = e1)
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | REDUCE: (4364), (4521) imply:
% 110.53/15.81 | | | | | | | | | | | | | (4523) ~ (all_53_9 = e1)
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | REDUCE: (4511), (4521) imply:
% 110.53/15.81 | | | | | | | | | | | | | (4524) ~ (e3 = e1)
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | REF_CLOSE: (7), (108), (110), (123), (127), (128), (137),
% 110.53/15.81 | | | | | | | | | | | | | (138), (139), (144), (162), (164), (166), (168),
% 110.53/15.81 | | | | | | | | | | | | | (169), (171), (172), (174), (199), (200), (202),
% 110.53/15.81 | | | | | | | | | | | | | (204), (222), (223), (252), (260), (262), (263),
% 110.53/15.81 | | | | | | | | | | | | | (4331), (4332), (4333), (4503), (4504), (4505),
% 110.53/15.81 | | | | | | | | | | | | | (4506), (4507), (4522), (4523), (function-axioms)
% 110.53/15.81 | | | | | | | | | | | | | are inconsistent by sub-proof #23.
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | Case 2:
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | (4525) all_55_5 = e0
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | REF_CLOSE: (4352), (4513), (4525) are inconsistent by
% 110.53/15.81 | | | | | | | | | | | | | sub-proof #3.
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | End of split
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | End of split
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | End of split
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | Case 2:
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | (4526) all_22_2 = e0
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | COMBINE_EQS: (4351), (4526) imply:
% 110.53/15.81 | | | | | | | | | | (4527) all_6_1 = e0
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | REDUCE: (4360), (4527) imply:
% 110.53/15.81 | | | | | | | | | | (4528) ~ (all_4_0 = e0)
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | SIMP: (4528) implies:
% 110.53/15.81 | | | | | | | | | | (4529) ~ (all_4_0 = e0)
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | BETA: splitting (204) gives:
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | Case 1:
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | (4530) all_55_4 = e3
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | COMBINE_EQS: (4353), (4530) imply:
% 110.53/15.81 | | | | | | | | | | | (4531) all_4_0 = e3
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | SIMP: (4531) implies:
% 110.53/15.81 | | | | | | | | | | | (4532) all_4_0 = e3
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | REDUCE: (4358), (4532) imply:
% 110.53/15.81 | | | | | | | | | | | (4533) ~ (all_53_12 = e3)
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | REDUCE: (4339), (4532) imply:
% 110.53/15.81 | | | | | | | | | | | (4534) op(e1, e0) = e3
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | BETA: splitting (110) gives:
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | Case 1:
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | (4535) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 110.53/15.81 | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | ALPHA: (4535) implies:
% 110.53/15.81 | | | | | | | | | | | | (4536) op(e3, e0) = e3
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | REF_CLOSE: (172), (4533), (4536), (function-axioms) are
% 110.53/15.81 | | | | | | | | | | | | inconsistent by sub-proof #180.
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | Case 2:
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | (4537) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 110.53/15.81 | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 110.53/15.81 | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 110.53/15.81 | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | BETA: splitting (4537) gives:
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | Case 1:
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | (4538) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 110.53/15.81 | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | ALPHA: (4538) implies:
% 110.53/15.81 | | | | | | | | | | | | | (4539) ~ (all_52_2 = e0)
% 110.53/15.81 | | | | | | | | | | | | | (4540) op(e0, e2) = all_52_2
% 110.53/15.81 | | | | | | | | | | | | | (4541) op(e2, e0) = e2
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | REF_CLOSE: (107), (108), (126), (132), (162), (163), (166),
% 110.53/15.81 | | | | | | | | | | | | | (167), (168), (171), (174), (206), (250), (3464),
% 110.53/15.81 | | | | | | | | | | | | | (4331), (4502), (4506), (4539), (4540), (4541),
% 110.53/15.81 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.53/15.81 | | | | | | | | | | | | | #12.
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | Case 2:
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | (4542) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 110.53/15.81 | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | ALPHA: (4542) implies:
% 110.53/15.81 | | | | | | | | | | | | | (4543) op(e1, e0) = e1
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | REF_CLOSE: (7), (164), (4534), (4543), (function-axioms) are
% 110.53/15.81 | | | | | | | | | | | | | inconsistent by sub-proof #62.
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | End of split
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | End of split
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | Case 2:
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | (4544) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | BETA: splitting (4544) gives:
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | Case 1:
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | (4545) all_55_4 = e2
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | COMBINE_EQS: (4353), (4545) imply:
% 110.53/15.81 | | | | | | | | | | | | (4546) all_4_0 = e2
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | SIMP: (4546) implies:
% 110.53/15.81 | | | | | | | | | | | | (4547) all_4_0 = e2
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | REDUCE: (4338), (4547) imply:
% 110.53/15.81 | | | | | | | | | | | | (4548) $false
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | CLOSE: (4548) is inconsistent.
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | Case 2:
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | (4549) all_55_4 = e1 | all_55_4 = e0
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | BETA: splitting (4549) gives:
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | Case 1:
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | (4550) all_55_4 = e1
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | COMBINE_EQS: (4353), (4550) imply:
% 110.53/15.81 | | | | | | | | | | | | | (4551) all_4_0 = e1
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | SIMP: (4551) implies:
% 110.53/15.81 | | | | | | | | | | | | | (4552) all_4_0 = e1
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | REDUCE: (4361), (4552) imply:
% 110.53/15.81 | | | | | | | | | | | | | (4553) $false
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | CLOSE: (4553) is inconsistent.
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | Case 2:
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | (4554) all_55_4 = e0
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | COMBINE_EQS: (4353), (4554) imply:
% 110.53/15.81 | | | | | | | | | | | | | (4555) all_4_0 = e0
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | SIMP: (4555) implies:
% 110.53/15.81 | | | | | | | | | | | | | (4556) all_4_0 = e0
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | REDUCE: (4529), (4556) imply:
% 110.53/15.81 | | | | | | | | | | | | | (4557) $false
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | | CLOSE: (4557) is inconsistent.
% 110.53/15.81 | | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | | End of split
% 110.53/15.81 | | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | End of split
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | End of split
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | End of split
% 110.53/15.81 | | | | | | | | |
% 110.53/15.81 | | | | | | | | Case 2:
% 110.53/15.81 | | | | | | | | |
% 110.53/15.81 | | | | | | | | | (4558) all_18_2 = e3
% 110.53/15.81 | | | | | | | | |
% 110.53/15.81 | | | | | | | | | COMBINE_EQS: (4350), (4558) imply:
% 110.53/15.81 | | | | | | | | | (4559) all_6_1 = e3
% 110.53/15.81 | | | | | | | | |
% 110.53/15.81 | | | | | | | | | COMBINE_EQS: (4347), (4559) imply:
% 110.53/15.81 | | | | | | | | | (4560) all_38_1 = e3
% 110.53/15.81 | | | | | | | | |
% 110.53/15.81 | | | | | | | | | REDUCE: (4365), (4559) imply:
% 110.53/15.81 | | | | | | | | | (4561) ~ (all_53_13 = e3)
% 110.53/15.81 | | | | | | | | |
% 110.53/15.81 | | | | | | | | | REDUCE: (4360), (4559) imply:
% 110.53/15.81 | | | | | | | | | (4562) ~ (all_4_0 = e3)
% 110.53/15.81 | | | | | | | | |
% 110.53/15.81 | | | | | | | | | SIMP: (4562) implies:
% 110.53/15.81 | | | | | | | | | (4563) ~ (all_4_0 = e3)
% 110.53/15.81 | | | | | | | | |
% 110.53/15.81 | | | | | | | | | REDUCE: (4325), (4559) imply:
% 110.53/15.81 | | | | | | | | | (4564) op(e1, e1) = e3
% 110.53/15.81 | | | | | | | | |
% 110.53/15.81 | | | | | | | | | BETA: splitting (4344) gives:
% 110.53/15.81 | | | | | | | | |
% 110.53/15.81 | | | | | | | | | Case 1:
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | (4565) ~ (all_38_1 = e3)
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | REDUCE: (4560), (4565) imply:
% 110.53/15.81 | | | | | | | | | | (4566) $false
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | CLOSE: (4566) is inconsistent.
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | Case 2:
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | (4567) ~ (all_38_0 = e2) & op(e3, e1) = all_38_0 &
% 110.53/15.81 | | | | | | | | | | $i(all_38_0)
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | ALPHA: (4567) implies:
% 110.53/15.81 | | | | | | | | | | (4568) ~ (all_38_0 = e2)
% 110.53/15.81 | | | | | | | | | | (4569) op(e3, e1) = all_38_0
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | BETA: splitting (204) gives:
% 110.53/15.81 | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | Case 1:
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | (4570) all_55_4 = e3
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | COMBINE_EQS: (4353), (4570) imply:
% 110.53/15.81 | | | | | | | | | | | (4571) all_4_0 = e3
% 110.53/15.81 | | | | | | | | | | |
% 110.53/15.81 | | | | | | | | | | | SIMP: (4571) implies:
% 110.68/15.81 | | | | | | | | | | | (4572) all_4_0 = e3
% 110.68/15.81 | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | REDUCE: (4563), (4572) imply:
% 110.68/15.81 | | | | | | | | | | | (4573) $false
% 110.68/15.81 | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | CLOSE: (4573) is inconsistent.
% 110.68/15.81 | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | Case 2:
% 110.68/15.81 | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | (4574) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 110.68/15.81 | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | BETA: splitting (4574) gives:
% 110.68/15.81 | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | Case 1:
% 110.68/15.81 | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | (4575) all_55_4 = e2
% 110.68/15.81 | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | COMBINE_EQS: (4353), (4575) imply:
% 110.68/15.81 | | | | | | | | | | | | (4576) all_4_0 = e2
% 110.68/15.81 | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | REDUCE: (4338), (4576) imply:
% 110.68/15.81 | | | | | | | | | | | | (4577) $false
% 110.68/15.81 | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | CLOSE: (4577) is inconsistent.
% 110.68/15.81 | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | Case 2:
% 110.68/15.81 | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | (4578) all_55_4 = e1 | all_55_4 = e0
% 110.68/15.81 | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | BETA: splitting (4578) gives:
% 110.68/15.81 | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | Case 1:
% 110.68/15.81 | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | (4579) all_55_4 = e1
% 110.68/15.81 | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | COMBINE_EQS: (4353), (4579) imply:
% 110.68/15.81 | | | | | | | | | | | | | (4580) all_4_0 = e1
% 110.68/15.81 | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | REDUCE: (4361), (4580) imply:
% 110.68/15.81 | | | | | | | | | | | | | (4581) $false
% 110.68/15.81 | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | CLOSE: (4581) is inconsistent.
% 110.68/15.81 | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | Case 2:
% 110.68/15.81 | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | (4582) all_55_4 = e0
% 110.68/15.81 | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | COMBINE_EQS: (4353), (4582) imply:
% 110.68/15.81 | | | | | | | | | | | | | (4583) all_4_0 = e0
% 110.68/15.81 | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | REDUCE: (4356), (4583) imply:
% 110.68/15.81 | | | | | | | | | | | | | (4584) ~ (all_53_8 = e0)
% 110.68/15.81 | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | BETA: splitting (200) gives:
% 110.68/15.81 | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | Case 1:
% 110.68/15.81 | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | (4585) all_55_8 = e3
% 110.68/15.81 | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | REF_CLOSE: (262), (4504), (4585) are inconsistent by
% 110.68/15.81 | | | | | | | | | | | | | | sub-proof #187.
% 110.68/15.81 | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | Case 2:
% 110.68/15.81 | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | (4586) ~ (all_55_8 = e3)
% 110.68/15.81 | | | | | | | | | | | | | | (4587) all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 110.68/15.81 | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | BETA: splitting (4587) gives:
% 110.68/15.81 | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | Case 1:
% 110.68/15.81 | | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | | (4588) all_55_8 = e2
% 110.68/15.81 | | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | | COMBINE_EQS: (262), (4588) imply:
% 110.68/15.81 | | | | | | | | | | | | | | | (4589) all_53_8 = e2
% 110.68/15.81 | | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | | SIMP: (4589) implies:
% 110.68/15.81 | | | | | | | | | | | | | | | (4590) all_53_8 = e2
% 110.68/15.81 | | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | | REDUCE: (127), (4590) imply:
% 110.68/15.81 | | | | | | | | | | | | | | | (4591) ~ (all_53_9 = e2)
% 110.68/15.81 | | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | | SIMP: (4591) implies:
% 110.68/15.81 | | | | | | | | | | | | | | | (4592) ~ (all_53_9 = e2)
% 110.68/15.81 | | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | | REDUCE: (4504), (4590) imply:
% 110.68/15.81 | | | | | | | | | | | | | | | (4593) ~ (e3 = e2)
% 110.68/15.81 | | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (109), (161), (169), (173), (228),
% 110.68/15.81 | | | | | | | | | | | | | | | (4561), (4564), (4568), (4569), (4592),
% 110.68/15.81 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.68/15.81 | | | | | | | | | | | | | | | #43.
% 110.68/15.81 | | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | Case 2:
% 110.68/15.81 | | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | | (4594) all_55_8 = e1 | all_55_8 = e0
% 110.68/15.81 | | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | | REF_CLOSE: (262), (4333), (4584), (4594) are inconsistent by
% 110.68/15.81 | | | | | | | | | | | | | | | sub-proof #182.
% 110.68/15.81 | | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | | End of split
% 110.68/15.81 | | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | | End of split
% 110.68/15.81 | | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | | End of split
% 110.68/15.81 | | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | | End of split
% 110.68/15.81 | | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | | End of split
% 110.68/15.81 | | | | | | | | | |
% 110.68/15.81 | | | | | | | | | End of split
% 110.68/15.81 | | | | | | | | |
% 110.68/15.81 | | | | | | | | End of split
% 110.68/15.81 | | | | | | | |
% 110.68/15.81 | | | | | | | Case 2:
% 110.68/15.81 | | | | | | | |
% 110.68/15.81 | | | | | | | | (4595) all_14_2 = e2
% 110.68/15.81 | | | | | | | |
% 110.68/15.81 | | | | | | | | COMBINE_EQS: (4349), (4595) imply:
% 110.68/15.81 | | | | | | | | (4596) all_6_1 = e2
% 110.68/15.81 | | | | | | | |
% 110.68/15.81 | | | | | | | | SIMP: (4596) implies:
% 110.68/15.81 | | | | | | | | (4597) all_6_1 = e2
% 110.68/15.81 | | | | | | | |
% 110.68/15.81 | | | | | | | | REDUCE: (4364), (4597) imply:
% 110.68/15.81 | | | | | | | | (4598) ~ (all_53_9 = e2)
% 110.68/15.81 | | | | | | | |
% 110.68/15.81 | | | | | | | | REDUCE: (4325), (4597) imply:
% 110.68/15.81 | | | | | | | | (4599) op(e1, e1) = e2
% 110.68/15.81 | | | | | | | |
% 110.68/15.81 | | | | | | | | BETA: splitting (4326) gives:
% 110.68/15.81 | | | | | | | |
% 110.68/15.81 | | | | | | | | Case 1:
% 110.68/15.81 | | | | | | | | |
% 110.68/15.81 | | | | | | | | | (4600) ~ (all_6_1 = e2)
% 110.68/15.81 | | | | | | | | |
% 110.68/15.81 | | | | | | | | | REDUCE: (4597), (4600) imply:
% 110.68/15.81 | | | | | | | | | (4601) $false
% 110.68/15.81 | | | | | | | | |
% 110.68/15.81 | | | | | | | | | CLOSE: (4601) is inconsistent.
% 110.68/15.81 | | | | | | | | |
% 110.68/15.81 | | | | | | | | Case 2:
% 110.68/15.81 | | | | | | | | |
% 110.68/15.81 | | | | | | | | | (4602) ~ (all_6_0 = e3) & op(e2, e1) = all_6_0 &
% 110.68/15.81 | | | | | | | | | $i(all_6_0)
% 110.68/15.81 | | | | | | | | |
% 110.68/15.81 | | | | | | | | | ALPHA: (4602) implies:
% 110.68/15.82 | | | | | | | | | (4603) op(e2, e1) = all_6_0
% 110.68/15.82 | | | | | | | | |
% 110.68/15.82 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 110.68/15.82 | | | | | | | | | all_6_0, e1, e2, simplifying with (169), (4603)
% 110.68/15.82 | | | | | | | | | gives:
% 110.68/15.82 | | | | | | | | | (4604) all_53_9 = all_6_0
% 110.68/15.82 | | | | | | | | |
% 110.68/15.82 | | | | | | | | | BETA: splitting (110) gives:
% 110.68/15.82 | | | | | | | | |
% 110.68/15.82 | | | | | | | | | Case 1:
% 110.68/15.82 | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | (4605) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 110.68/15.82 | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 110.68/15.82 | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | ALPHA: (4605) implies:
% 110.68/15.82 | | | | | | | | | | (4606) op(e3, e0) = e3
% 110.68/15.82 | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 110.68/15.82 | | | | | | | | | | e3, e0, e3, simplifying with (172), (4606) gives:
% 110.68/15.82 | | | | | | | | | | (4607) all_53_12 = e3
% 110.68/15.82 | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | REDUCE: (117), (4607) imply:
% 110.68/15.82 | | | | | | | | | | (4608) ~ (all_53_13 = e3)
% 110.68/15.82 | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | SIMP: (4608) implies:
% 110.68/15.82 | | | | | | | | | | (4609) ~ (all_53_13 = e3)
% 110.68/15.82 | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | BETA: splitting (109) gives:
% 110.68/15.82 | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | Case 1:
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | (4610) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) =
% 110.68/15.82 | | | | | | | | | | | e3 & op(e1, e3) = all_52_6 & $i(all_52_6)
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | ALPHA: (4610) implies:
% 110.68/15.82 | | | | | | | | | | | (4611) op(e3, e1) = e3
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | REF_CLOSE: (173), (4609), (4611), (function-axioms) are
% 110.68/15.82 | | | | | | | | | | | inconsistent by sub-proof #232.
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | Case 2:
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | (4612) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 110.68/15.82 | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) |
% 110.68/15.82 | | | | | | | | | | | (all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 110.68/15.82 | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | BETA: splitting (4612) gives:
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | Case 1:
% 110.68/15.82 | | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | | (4613) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) =
% 110.68/15.82 | | | | | | | | | | | | e2 & op(e1, e2) = all_52_8 & $i(all_52_8)
% 110.68/15.82 | | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | | REF_CLOSE: (169), (4598), (4603), (4613), (function-axioms)
% 110.68/15.82 | | | | | | | | | | | | are inconsistent by sub-proof #37.
% 110.68/15.82 | | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | Case 2:
% 110.68/15.82 | | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | | (4614) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0)
% 110.68/15.82 | | | | | | | | | | | | = all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 110.68/15.82 | | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | | ALPHA: (4614) implies:
% 110.68/15.82 | | | | | | | | | | | | (4615) op(e0, e1) = e0
% 110.68/15.82 | | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | | REF_CLOSE: (6), (8), (161), (169), (173), (226), (4505),
% 110.68/15.82 | | | | | | | | | | | | (4599), (4609), (4615), (function-axioms) are
% 110.68/15.82 | | | | | | | | | | | | inconsistent by sub-proof #79.
% 110.68/15.82 | | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | End of split
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | End of split
% 110.68/15.82 | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | Case 2:
% 110.68/15.82 | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | (4616) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 110.68/15.82 | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 110.68/15.82 | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 110.68/15.82 | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 110.68/15.82 | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | BETA: splitting (4616) gives:
% 110.68/15.82 | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | Case 1:
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | (4617) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 110.68/15.82 | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | ALPHA: (4617) implies:
% 110.68/15.82 | | | | | | | | | | | (4618) ~ (all_52_2 = e0)
% 110.68/15.82 | | | | | | | | | | | (4619) op(e0, e2) = all_52_2
% 110.68/15.82 | | | | | | | | | | | (4620) op(e2, e0) = e2
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | REF_CLOSE: (107), (108), (126), (132), (162), (163), (166),
% 110.68/15.82 | | | | | | | | | | | (167), (168), (171), (174), (206), (250), (3464),
% 110.68/15.82 | | | | | | | | | | | (4331), (4502), (4506), (4618), (4619), (4620),
% 110.68/15.82 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.68/15.82 | | | | | | | | | | | #12.
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | Case 2:
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | (4621) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 110.68/15.82 | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | ALPHA: (4621) implies:
% 110.68/15.82 | | | | | | | | | | | (4622) op(e1, e0) = e1
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | | REF_CLOSE: (164), (4332), (4622), (function-axioms) are
% 110.68/15.82 | | | | | | | | | | | inconsistent by sub-proof #226.
% 110.68/15.82 | | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | | End of split
% 110.68/15.82 | | | | | | | | | |
% 110.68/15.82 | | | | | | | | | End of split
% 110.68/15.82 | | | | | | | | |
% 110.68/15.82 | | | | | | | | End of split
% 110.68/15.82 | | | | | | | |
% 110.68/15.82 | | | | | | | End of split
% 110.68/15.82 | | | | | | |
% 110.68/15.82 | | | | | | End of split
% 110.68/15.82 | | | | | |
% 110.68/15.82 | | | | | End of split
% 110.68/15.82 | | | | |
% 110.68/15.82 | | | | End of split
% 110.68/15.82 | | | |
% 110.68/15.82 | | | End of split
% 110.68/15.82 | | |
% 110.68/15.82 | | End of split
% 110.68/15.82 | |
% 110.68/15.82 | End of split
% 110.68/15.82 |
% 110.68/15.82 End of proof
% 110.68/15.82
% 110.68/15.82 Sub-proof #1 shows that the following formulas are inconsistent:
% 110.68/15.82 ----------------------------------------------------------------
% 110.68/15.82 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.68/15.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.68/15.82 (2) op(e0, e0) = e1
% 110.68/15.82 (3) op(e0, e0) = e0
% 110.68/15.82 (4) ~ (e1 = e0)
% 110.68/15.82
% 110.68/15.82 Begin of proof
% 110.68/15.82 |
% 110.68/15.82 | GROUND_INST: instantiating (1) with e1, e0, e0, e0, simplifying with (2), (3)
% 110.68/15.82 | gives:
% 110.68/15.82 | (5) e1 = e0
% 110.68/15.82 |
% 110.68/15.82 | REDUCE: (4), (5) imply:
% 110.68/15.82 | (6) $false
% 110.68/15.82 |
% 110.68/15.82 | CLOSE: (6) is inconsistent.
% 110.68/15.82 |
% 110.68/15.82 End of proof
% 110.68/15.82
% 110.68/15.82 Sub-proof #2 shows that the following formulas are inconsistent:
% 110.68/15.82 ----------------------------------------------------------------
% 110.68/15.82 (1) all_18_2 = all_6_1
% 110.68/15.82 (2) ~ (all_18_2 = e3) | (op(e3, e3) = all_18_1 & $i(all_18_1) & ( ~
% 110.68/15.82 (all_18_1 = e2) | ( ~ (all_18_0 = e0) & op(e2, e3) = all_18_0 &
% 110.68/15.82 $i(all_18_0))))
% 110.68/15.82 (3) op(e2, e2) = e0
% 110.68/15.82 (4) op(e3, e0) = all_53_12
% 110.68/15.82 (5) op(e1, e0) = all_53_4
% 110.68/15.82 (6) all_38_1 = all_6_1
% 110.68/15.82 (7) ~ (all_53_7 = all_6_1)
% 110.68/15.82 (8) ~ (all_53_8 = e0)
% 110.68/15.82 (9) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 110.68/15.82 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 110.68/15.82 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 110.68/15.82 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 110.68/15.82 $i(all_52_16))
% 110.68/15.82 (10) op(e3, e2) = all_53_15
% 110.68/15.82 (11) ~ (all_38_1 = e3) | ( ~ (all_38_0 = e2) & op(e3, e1) = all_38_0 &
% 110.68/15.82 $i(all_38_0))
% 110.68/15.82 (12) all_55_5 = all_6_1
% 110.68/15.82 (13) ~ (all_53_4 = e1)
% 110.68/15.82 (14) op(e1, e2) = all_53_7
% 110.68/15.82 (15) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 110.68/15.82 (16) ~ (all_53_8 = all_53_12)
% 110.68/15.82 (17) ~ (all_53_9 = all_6_1)
% 110.68/15.82 (18) ~ (all_6_1 = e2)
% 110.68/15.82 (19) ~ (all_53_9 = all_53_13)
% 110.68/15.82 (20) ~ (all_53_8 = e1)
% 110.68/15.82 (21) all_55_13 = all_53_13
% 110.68/15.82 (22) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 110.68/15.82 (23) ~ (all_53_3 = e1)
% 110.68/15.82 (24) (all_57_76 = e1 & op(e3, e2) = e1) | (all_57_77 = e1 & op(e2, e2) = e1)
% 110.68/15.82 | (all_57_78 = e1 & op(e1, e2) = e1) | (all_57_79 = e1 & op(e0, e2) =
% 110.68/15.82 e1)
% 110.68/15.82 (25) op(e2, e0) = all_53_8
% 110.68/15.82 (26) op(e3, e1) = all_53_13
% 110.68/15.82 (27) all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 110.68/15.82 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.68/15.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.68/15.82 (29) ~ (all_6_1 = e0)
% 110.68/15.82 (30) all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 110.68/15.82 (31) ~ (all_53_13 = e0)
% 110.68/15.82 (32) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 110.68/15.82 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 110.68/15.82 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 110.68/15.82 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 110.68/15.82 $i(all_52_4))
% 110.68/15.82 (33) ~ (all_53_13 = all_6_1)
% 110.68/15.82 (34) ~ (all_53_9 = e0)
% 110.68/15.82 (35) all_55_8 = all_53_8
% 110.68/15.82 (36) all_55_9 = all_53_9
% 110.68/15.82 (37) ~ (all_53_8 = all_53_9)
% 110.68/15.82 (38) op(e0, e2) = all_53_3
% 110.68/15.82 (39) ~ (all_53_3 = e0)
% 110.68/15.82
% 110.68/15.82 Begin of proof
% 110.68/15.82 |
% 110.68/15.82 | BETA: splitting (2) gives:
% 110.68/15.82 |
% 110.68/15.82 | Case 1:
% 110.68/15.82 | |
% 110.68/15.82 | | (40) ~ (all_18_2 = e3)
% 110.68/15.82 | |
% 110.68/15.82 | | REDUCE: (1), (40) imply:
% 110.68/15.82 | | (41) ~ (all_6_1 = e3)
% 110.68/15.82 | |
% 110.68/15.82 | | REF_CLOSE: (3), (7), (9), (10), (12), (14), (18), (22), (23), (24), (28),
% 110.68/15.82 | | (29), (38), (39), (41) are inconsistent by sub-proof #34.
% 110.68/15.82 | |
% 110.68/15.83 | Case 2:
% 110.68/15.83 | |
% 110.68/15.83 | | (42) all_18_2 = e3
% 110.68/15.83 | |
% 110.68/15.83 | | COMBINE_EQS: (1), (42) imply:
% 110.68/15.83 | | (43) all_6_1 = e3
% 110.68/15.83 | |
% 110.68/15.83 | | SIMP: (43) implies:
% 110.68/15.83 | | (44) all_6_1 = e3
% 110.68/15.83 | |
% 110.68/15.83 | | COMBINE_EQS: (6), (44) imply:
% 110.68/15.83 | | (45) all_38_1 = e3
% 110.68/15.83 | |
% 110.68/15.83 | | REDUCE: (17), (44) imply:
% 110.68/15.83 | | (46) ~ (all_53_9 = e3)
% 110.68/15.83 | |
% 110.68/15.83 | | REDUCE: (33), (44) imply:
% 110.68/15.83 | | (47) ~ (all_53_13 = e3)
% 110.68/15.83 | |
% 110.68/15.83 | | BETA: splitting (11) gives:
% 110.68/15.83 | |
% 110.68/15.83 | | Case 1:
% 110.68/15.83 | | |
% 110.68/15.83 | | | (48) ~ (all_38_1 = e3)
% 110.68/15.83 | | |
% 110.68/15.83 | | | REDUCE: (45), (48) imply:
% 110.68/15.83 | | | (49) $false
% 110.68/15.83 | | |
% 110.68/15.83 | | | CLOSE: (49) is inconsistent.
% 110.68/15.83 | | |
% 110.68/15.83 | | Case 2:
% 110.68/15.83 | | |
% 110.68/15.83 | | | (50) ~ (all_38_0 = e2) & op(e3, e1) = all_38_0 & $i(all_38_0)
% 110.68/15.83 | | |
% 110.68/15.83 | | | ALPHA: (50) implies:
% 110.68/15.83 | | | (51) ~ (all_38_0 = e2)
% 110.68/15.83 | | | (52) op(e3, e1) = all_38_0
% 110.68/15.83 | | |
% 110.68/15.83 | | | GROUND_INST: instantiating (28) with all_53_13, all_38_0, e1, e3,
% 110.68/15.83 | | | simplifying with (26), (52) gives:
% 110.68/15.83 | | | (53) all_53_13 = all_38_0
% 110.68/15.83 | | |
% 110.68/15.83 | | | COMBINE_EQS: (21), (53) imply:
% 110.68/15.83 | | | (54) all_55_13 = all_38_0
% 110.68/15.83 | | |
% 110.68/15.83 | | | REDUCE: (19), (53) imply:
% 110.68/15.83 | | | (55) ~ (all_53_9 = all_38_0)
% 110.68/15.83 | | |
% 110.68/15.83 | | | REDUCE: (47), (53) imply:
% 110.68/15.83 | | | (56) ~ (all_38_0 = e3)
% 110.68/15.83 | | |
% 110.68/15.83 | | | REDUCE: (31), (53) imply:
% 110.68/15.83 | | | (57) ~ (all_38_0 = e0)
% 110.68/15.83 | | |
% 110.68/15.83 | | | BETA: splitting (27) gives:
% 110.68/15.83 | | |
% 110.68/15.83 | | | Case 1:
% 110.68/15.83 | | | |
% 110.68/15.83 | | | | (58) all_55_13 = e3
% 110.68/15.83 | | | |
% 110.68/15.83 | | | | REF_CLOSE: (54), (56), (58) are inconsistent by sub-proof #30.
% 110.68/15.83 | | | |
% 110.68/15.83 | | | Case 2:
% 110.68/15.83 | | | |
% 110.68/15.83 | | | | (59) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 110.68/15.83 | | | |
% 110.68/15.83 | | | | BETA: splitting (59) gives:
% 110.68/15.83 | | | |
% 110.68/15.83 | | | | Case 1:
% 110.68/15.83 | | | | |
% 110.68/15.83 | | | | | (60) all_55_13 = e2
% 110.68/15.83 | | | | |
% 110.68/15.83 | | | | | REF_CLOSE: (51), (54), (60) are inconsistent by sub-proof #29.
% 110.68/15.83 | | | | |
% 110.68/15.83 | | | | Case 2:
% 110.68/15.83 | | | | |
% 110.68/15.83 | | | | | (61) all_55_13 = e1 | all_55_13 = e0
% 110.68/15.83 | | | | |
% 110.68/15.83 | | | | | BETA: splitting (61) gives:
% 110.68/15.83 | | | | |
% 110.68/15.83 | | | | | Case 1:
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | | (62) all_55_13 = e1
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | | COMBINE_EQS: (54), (62) imply:
% 110.68/15.83 | | | | | | (63) all_38_0 = e1
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | | SIMP: (63) implies:
% 110.68/15.83 | | | | | | (64) all_38_0 = e1
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | | REDUCE: (55), (64) imply:
% 110.68/15.83 | | | | | | (65) ~ (all_53_9 = e1)
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | | BETA: splitting (15) gives:
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | | Case 1:
% 110.68/15.83 | | | | | | |
% 110.68/15.83 | | | | | | | (66) all_55_9 = e3
% 110.68/15.83 | | | | | | |
% 110.68/15.83 | | | | | | | COMBINE_EQS: (36), (66) imply:
% 110.68/15.83 | | | | | | | (67) all_53_9 = e3
% 110.68/15.83 | | | | | | |
% 110.68/15.83 | | | | | | | REDUCE: (46), (67) imply:
% 110.68/15.83 | | | | | | | (68) $false
% 110.68/15.83 | | | | | | |
% 110.68/15.83 | | | | | | | CLOSE: (68) is inconsistent.
% 110.68/15.83 | | | | | | |
% 110.68/15.83 | | | | | | Case 2:
% 110.68/15.83 | | | | | | |
% 110.68/15.83 | | | | | | | (69) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 110.68/15.83 | | | | | | |
% 110.68/15.83 | | | | | | | BETA: splitting (69) gives:
% 110.68/15.83 | | | | | | |
% 110.68/15.83 | | | | | | | Case 1:
% 110.68/15.83 | | | | | | | |
% 110.68/15.83 | | | | | | | | (70) all_55_9 = e2
% 110.68/15.83 | | | | | | | |
% 110.68/15.83 | | | | | | | | COMBINE_EQS: (36), (70) imply:
% 110.68/15.83 | | | | | | | | (71) all_53_9 = e2
% 110.68/15.83 | | | | | | | |
% 110.68/15.83 | | | | | | | | REDUCE: (37), (71) imply:
% 110.68/15.83 | | | | | | | | (72) ~ (all_53_8 = e2)
% 110.68/15.83 | | | | | | | |
% 110.68/15.83 | | | | | | | | REF_CLOSE: (4), (5), (8), (13), (16), (20), (25), (28), (30),
% 110.68/15.83 | | | | | | | | (32), (35), (72) are inconsistent by sub-proof #33.
% 110.68/15.83 | | | | | | | |
% 110.68/15.83 | | | | | | | Case 2:
% 110.68/15.83 | | | | | | | |
% 110.68/15.83 | | | | | | | | (73) all_55_9 = e1 | all_55_9 = e0
% 110.68/15.83 | | | | | | | |
% 110.68/15.83 | | | | | | | | REF_CLOSE: (34), (36), (65), (73) are inconsistent by sub-proof
% 110.68/15.83 | | | | | | | | #185.
% 110.68/15.83 | | | | | | | |
% 110.68/15.83 | | | | | | | End of split
% 110.68/15.83 | | | | | | |
% 110.68/15.83 | | | | | | End of split
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | Case 2:
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | | (74) all_55_13 = e0
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | | REF_CLOSE: (54), (57), (74) are inconsistent by sub-proof #28.
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | End of split
% 110.68/15.83 | | | | |
% 110.68/15.83 | | | | End of split
% 110.68/15.83 | | | |
% 110.68/15.83 | | | End of split
% 110.68/15.83 | | |
% 110.68/15.83 | | End of split
% 110.68/15.83 | |
% 110.68/15.83 | End of split
% 110.68/15.83 |
% 110.68/15.83 End of proof
% 110.68/15.83
% 110.68/15.83 Sub-proof #3 shows that the following formulas are inconsistent:
% 110.68/15.83 ----------------------------------------------------------------
% 110.68/15.83 (1) all_55_5 = all_6_1
% 110.68/15.83 (2) all_55_5 = e0
% 110.68/15.83 (3) ~ (all_6_1 = e0)
% 110.68/15.83
% 110.68/15.83 Begin of proof
% 110.68/15.83 |
% 110.68/15.83 | COMBINE_EQS: (1), (2) imply:
% 110.68/15.83 | (4) all_6_1 = e0
% 110.68/15.83 |
% 110.68/15.83 | SIMP: (4) implies:
% 110.68/15.83 | (5) all_6_1 = e0
% 110.68/15.83 |
% 110.68/15.83 | REDUCE: (3), (5) imply:
% 110.68/15.83 | (6) $false
% 110.68/15.83 |
% 110.68/15.83 | CLOSE: (6) is inconsistent.
% 110.68/15.83 |
% 110.68/15.83 End of proof
% 110.68/15.83
% 110.68/15.83 Sub-proof #4 shows that the following formulas are inconsistent:
% 110.68/15.83 ----------------------------------------------------------------
% 110.68/15.83 (1) all_55_5 = all_6_1
% 110.68/15.83 (2) all_55_5 = e2
% 110.68/15.83 (3) ~ (all_6_1 = e2)
% 110.68/15.83
% 110.68/15.83 Begin of proof
% 110.68/15.83 |
% 110.68/15.83 | COMBINE_EQS: (1), (2) imply:
% 110.68/15.83 | (4) all_6_1 = e2
% 110.68/15.83 |
% 110.68/15.83 | SIMP: (4) implies:
% 110.68/15.83 | (5) all_6_1 = e2
% 110.68/15.83 |
% 110.68/15.83 | REDUCE: (3), (5) imply:
% 110.68/15.83 | (6) $false
% 110.68/15.83 |
% 110.68/15.83 | CLOSE: (6) is inconsistent.
% 110.68/15.83 |
% 110.68/15.83 End of proof
% 110.68/15.83
% 110.68/15.83 Sub-proof #5 shows that the following formulas are inconsistent:
% 110.68/15.83 ----------------------------------------------------------------
% 110.68/15.83 (1) all_55_5 = all_6_1
% 110.68/15.83 (2) all_55_5 = e3
% 110.68/15.83 (3) ~ (all_6_1 = e3)
% 110.68/15.83
% 110.68/15.83 Begin of proof
% 110.68/15.83 |
% 110.68/15.83 | COMBINE_EQS: (1), (2) imply:
% 110.68/15.83 | (4) all_6_1 = e3
% 110.68/15.83 |
% 110.68/15.83 | SIMP: (4) implies:
% 110.68/15.83 | (5) all_6_1 = e3
% 110.68/15.83 |
% 110.68/15.83 | REDUCE: (3), (5) imply:
% 110.68/15.83 | (6) $false
% 110.68/15.83 |
% 110.68/15.83 | CLOSE: (6) is inconsistent.
% 110.68/15.83 |
% 110.68/15.83 End of proof
% 110.68/15.83
% 110.68/15.83 Sub-proof #6 shows that the following formulas are inconsistent:
% 110.68/15.83 ----------------------------------------------------------------
% 110.68/15.83 (1) ~ (all_53_12 = e2)
% 110.68/15.83 (2) op(e3, e0) = all_53_12
% 110.68/15.83 (3) op(e1, e0) = all_53_4
% 110.68/15.83 (4) all_55_12 = all_53_12
% 110.68/15.83 (5) ~ (all_53_4 = all_53_12)
% 110.68/15.83 (6) ~ (all_53_12 = all_53_13)
% 110.68/15.83 (7) ~ (all_53_8 = e2)
% 110.68/15.83 (8) all_55_13 = all_53_13
% 110.68/15.83 (9) ~ (all_53_12 = e0)
% 110.68/15.83 (10) all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 110.68/15.83 (11) op(e2, e0) = all_53_8
% 110.68/15.83 (12) op(e3, e1) = all_53_13
% 110.68/15.83 (13) all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 110.68/15.83 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.68/15.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.68/15.83 (15) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 110.68/15.83 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 110.68/15.83 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 110.68/15.83 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 110.68/15.83 $i(all_52_4))
% 110.68/15.83 (16) op(e3, e1) = e3
% 110.68/15.83
% 110.68/15.83 Begin of proof
% 110.68/15.83 |
% 110.68/15.83 | BETA: splitting (13) gives:
% 110.68/15.83 |
% 110.68/15.83 | Case 1:
% 110.68/15.83 | |
% 110.68/15.83 | | (17) all_55_13 = e3
% 110.68/15.83 | |
% 110.68/15.83 | | COMBINE_EQS: (8), (17) imply:
% 110.68/15.83 | | (18) all_53_13 = e3
% 110.68/15.83 | |
% 110.68/15.83 | | SIMP: (18) implies:
% 110.68/15.83 | | (19) all_53_13 = e3
% 110.68/15.83 | |
% 110.68/15.83 | | REDUCE: (6), (19) imply:
% 110.68/15.83 | | (20) ~ (all_53_12 = e3)
% 110.68/15.83 | |
% 110.68/15.83 | | BETA: splitting (15) gives:
% 110.68/15.83 | |
% 110.68/15.83 | | Case 1:
% 110.68/15.83 | | |
% 110.68/15.83 | | | (21) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 110.68/15.83 | | | = all_52_0 & $i(all_52_0)
% 110.68/15.83 | | |
% 110.68/15.83 | | | ALPHA: (21) implies:
% 110.68/15.83 | | | (22) op(e3, e0) = e3
% 110.68/15.83 | | |
% 110.68/15.83 | | | REF_CLOSE: (2), (6), (12), (14), (16), (22) are inconsistent by sub-proof
% 110.68/15.83 | | | #213.
% 110.68/15.83 | | |
% 110.68/15.83 | | Case 2:
% 110.68/15.83 | | |
% 110.68/15.83 | | | (23) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 110.68/15.83 | | | = all_52_2 & $i(all_52_2)) | (all_52_5 = e1 & ~ (all_52_4 = e0)
% 110.68/15.83 | | | & op(e1, e0) = e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 110.68/15.83 | | |
% 110.68/15.83 | | | BETA: splitting (23) gives:
% 110.68/15.83 | | |
% 110.68/15.83 | | | Case 1:
% 110.68/15.83 | | | |
% 110.68/15.83 | | | | (24) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0,
% 110.68/15.83 | | | | e2) = all_52_2 & $i(all_52_2)
% 110.68/15.83 | | | |
% 110.68/15.83 | | | | ALPHA: (24) implies:
% 110.68/15.83 | | | | (25) op(e2, e0) = e2
% 110.68/15.83 | | | |
% 110.68/15.83 | | | | REF_CLOSE: (7), (11), (14), (25) are inconsistent by sub-proof #227.
% 110.68/15.83 | | | |
% 110.68/15.83 | | | Case 2:
% 110.68/15.83 | | | |
% 110.68/15.83 | | | | (26) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0,
% 110.68/15.83 | | | | e1) = all_52_4 & $i(all_52_4)
% 110.68/15.83 | | | |
% 110.68/15.83 | | | | ALPHA: (26) implies:
% 110.68/15.83 | | | | (27) op(e1, e0) = e1
% 110.68/15.83 | | | |
% 110.68/15.83 | | | | BETA: splitting (10) gives:
% 110.68/15.83 | | | |
% 110.68/15.83 | | | | Case 1:
% 110.68/15.83 | | | | |
% 110.68/15.83 | | | | | (28) all_55_12 = e3
% 110.68/15.83 | | | | |
% 110.68/15.83 | | | | | REF_CLOSE: (4), (20), (28) are inconsistent by sub-proof #94.
% 110.68/15.83 | | | | |
% 110.68/15.83 | | | | Case 2:
% 110.68/15.83 | | | | |
% 110.68/15.83 | | | | | (29) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 110.68/15.83 | | | | |
% 110.68/15.83 | | | | | BETA: splitting (29) gives:
% 110.68/15.83 | | | | |
% 110.68/15.83 | | | | | Case 1:
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | | (30) all_55_12 = e2
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | | REF_CLOSE: (1), (4), (30) are inconsistent by sub-proof #93.
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | Case 2:
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | | (31) all_55_12 = e1 | all_55_12 = e0
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | | REF_CLOSE: (3), (4), (5), (9), (14), (27), (31) are inconsistent by
% 110.68/15.83 | | | | | | sub-proof #16.
% 110.68/15.83 | | | | | |
% 110.68/15.83 | | | | | End of split
% 110.68/15.83 | | | | |
% 110.68/15.83 | | | | End of split
% 110.68/15.83 | | | |
% 110.68/15.83 | | | End of split
% 110.68/15.83 | | |
% 110.68/15.83 | | End of split
% 110.68/15.83 | |
% 110.68/15.83 | Case 2:
% 110.68/15.83 | |
% 110.68/15.83 | | (32) ~ (all_55_13 = e3)
% 110.68/15.83 | |
% 110.68/15.83 | | REDUCE: (8), (32) imply:
% 110.68/15.83 | | (33) ~ (all_53_13 = e3)
% 110.68/15.83 | |
% 110.68/15.83 | | REF_CLOSE: (12), (14), (16), (33) are inconsistent by sub-proof #232.
% 110.68/15.83 | |
% 110.68/15.83 | End of split
% 110.68/15.83 |
% 110.68/15.83 End of proof
% 110.68/15.83
% 110.68/15.83 Sub-proof #7 shows that the following formulas are inconsistent:
% 110.68/15.83 ----------------------------------------------------------------
% 110.68/15.83 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.68/15.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.68/15.83 (2) op(e3, e3) = e2
% 110.68/15.83 (3) op(e3, e3) = e0
% 110.68/15.83 (4) ~ (e2 = e0)
% 110.68/15.83
% 110.68/15.83 Begin of proof
% 110.68/15.83 |
% 110.68/15.83 | GROUND_INST: instantiating (1) with e0, e2, e3, e3, simplifying with (2), (3)
% 110.68/15.83 | gives:
% 110.68/15.83 | (5) e2 = e0
% 110.68/15.83 |
% 110.68/15.83 | REDUCE: (4), (5) imply:
% 110.68/15.83 | (6) $false
% 110.68/15.83 |
% 110.68/15.83 | CLOSE: (6) is inconsistent.
% 110.68/15.83 |
% 110.68/15.83 End of proof
% 110.68/15.83
% 110.68/15.83 Sub-proof #8 shows that the following formulas are inconsistent:
% 110.68/15.83 ----------------------------------------------------------------
% 110.68/15.83 (1) all_55_3 = e1 | all_55_3 = e0
% 110.68/15.83 (2) all_55_3 = all_10_0
% 110.68/15.83 (3) ~ (all_10_0 = e1)
% 110.68/15.83 (4) ~ (all_10_0 = e0)
% 110.68/15.83
% 110.68/15.83 Begin of proof
% 110.68/15.83 |
% 110.68/15.83 | BETA: splitting (1) gives:
% 110.68/15.83 |
% 110.68/15.83 | Case 1:
% 110.68/15.83 | |
% 110.68/15.83 | | (5) all_55_3 = e1
% 110.68/15.83 | |
% 110.68/15.83 | | COMBINE_EQS: (2), (5) imply:
% 110.68/15.83 | | (6) all_10_0 = e1
% 110.68/15.83 | |
% 110.68/15.83 | | SIMP: (6) implies:
% 110.68/15.83 | | (7) all_10_0 = e1
% 110.68/15.83 | |
% 110.68/15.83 | | REDUCE: (3), (7) imply:
% 110.68/15.83 | | (8) $false
% 110.68/15.83 | |
% 110.68/15.83 | | CLOSE: (8) is inconsistent.
% 110.68/15.83 | |
% 110.68/15.83 | Case 2:
% 110.68/15.83 | |
% 110.68/15.83 | | (9) all_55_3 = e0
% 110.68/15.83 | |
% 110.68/15.83 | | COMBINE_EQS: (2), (9) imply:
% 110.68/15.83 | | (10) all_10_0 = e0
% 110.68/15.83 | |
% 110.68/15.83 | | SIMP: (10) implies:
% 110.68/15.83 | | (11) all_10_0 = e0
% 110.68/15.83 | |
% 110.68/15.83 | | REDUCE: (4), (11) imply:
% 110.68/15.83 | | (12) $false
% 110.68/15.83 | |
% 110.68/15.83 | | CLOSE: (12) is inconsistent.
% 110.68/15.83 | |
% 110.68/15.83 | End of split
% 110.68/15.83 |
% 110.68/15.83 End of proof
% 110.68/15.83
% 110.68/15.83 Sub-proof #9 shows that the following formulas are inconsistent:
% 110.68/15.83 ----------------------------------------------------------------
% 110.68/15.83 (1) op(e3, e0) = all_53_12
% 110.68/15.83 (2) op(e1, e0) = all_53_4
% 110.68/15.83 (3) ~ (all_4_1 = e1)
% 110.68/15.83 (4) all_55_12 = all_53_12
% 110.68/15.83 (5) ~ (all_30_1 = e3) | ( ~ (all_30_0 = e1) & op(e3, e0) = all_30_0 &
% 110.68/15.83 $i(all_30_0))
% 110.68/15.84 (6) ~ (all_53_4 = all_53_12)
% 110.68/15.84 (7) ~ (e1 = e0)
% 110.68/15.84 (8) ~ (all_53_8 = all_53_12)
% 110.68/15.84 (9) ~ (all_53_12 = all_4_1)
% 110.68/15.84 (10) all_30_1 = all_4_1
% 110.79/15.84 (11) all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 110.79/15.84 (12) op(e2, e0) = all_53_8
% 110.79/15.84 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.84 (14) op(e1, e0) = e0
% 110.79/15.84 (15) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 110.79/15.84 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 110.79/15.84 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 110.79/15.84 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 110.79/15.84 $i(all_52_4))
% 110.79/15.84 (16) ~ (all_53_4 = all_4_1)
% 110.79/15.84 (17) all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 110.79/15.84 (18) ~ (all_4_1 = e2)
% 110.79/15.84 (19) all_55_0 = all_4_1
% 110.79/15.84
% 110.79/15.84 Begin of proof
% 110.79/15.84 |
% 110.79/15.84 | GROUND_INST: instantiating (13) with all_53_4, e0, e0, e1, simplifying with
% 110.79/15.84 | (2), (14) gives:
% 110.79/15.84 | (20) all_53_4 = e0
% 110.79/15.84 |
% 110.79/15.84 | REDUCE: (6), (20) imply:
% 110.79/15.84 | (21) ~ (all_53_12 = e0)
% 110.79/15.84 |
% 110.79/15.84 | SIMP: (21) implies:
% 110.79/15.84 | (22) ~ (all_53_12 = e0)
% 110.79/15.84 |
% 110.79/15.84 | REDUCE: (16), (20) imply:
% 110.79/15.84 | (23) ~ (all_4_1 = e0)
% 110.79/15.84 |
% 110.79/15.84 | SIMP: (23) implies:
% 110.79/15.84 | (24) ~ (all_4_1 = e0)
% 110.79/15.84 |
% 110.79/15.84 | BETA: splitting (17) gives:
% 110.79/15.84 |
% 110.79/15.84 | Case 1:
% 110.79/15.84 | |
% 110.79/15.84 | | (25) all_55_0 = e3
% 110.79/15.84 | |
% 110.79/15.84 | | COMBINE_EQS: (19), (25) imply:
% 110.79/15.84 | | (26) all_4_1 = e3
% 110.79/15.84 | |
% 110.79/15.84 | | SIMP: (26) implies:
% 110.79/15.84 | | (27) all_4_1 = e3
% 110.79/15.84 | |
% 110.79/15.84 | | COMBINE_EQS: (10), (27) imply:
% 110.79/15.84 | | (28) all_30_1 = e3
% 110.79/15.84 | |
% 110.79/15.84 | | REDUCE: (9), (27) imply:
% 110.79/15.84 | | (29) ~ (all_53_12 = e3)
% 110.79/15.84 | |
% 110.79/15.84 | | BETA: splitting (15) gives:
% 110.79/15.84 | |
% 110.79/15.84 | | Case 1:
% 110.79/15.84 | | |
% 110.79/15.84 | | | (30) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 110.79/15.84 | | | = all_52_0 & $i(all_52_0)
% 110.79/15.84 | | |
% 110.79/15.84 | | | ALPHA: (30) implies:
% 110.79/15.84 | | | (31) op(e3, e0) = e3
% 110.79/15.84 | | |
% 110.79/15.84 | | | REF_CLOSE: (1), (13), (29), (31) are inconsistent by sub-proof #180.
% 110.79/15.84 | | |
% 110.79/15.84 | | Case 2:
% 110.79/15.84 | | |
% 110.79/15.84 | | | (32) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 110.79/15.84 | | | = all_52_2 & $i(all_52_2)) | (all_52_5 = e1 & ~ (all_52_4 = e0)
% 110.79/15.84 | | | & op(e1, e0) = e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 110.79/15.84 | | |
% 110.79/15.84 | | | BETA: splitting (32) gives:
% 110.79/15.84 | | |
% 110.79/15.84 | | | Case 1:
% 110.79/15.84 | | | |
% 110.79/15.84 | | | | (33) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0,
% 110.79/15.84 | | | | e2) = all_52_2 & $i(all_52_2)
% 110.79/15.84 | | | |
% 110.79/15.84 | | | | ALPHA: (33) implies:
% 110.79/15.84 | | | | (34) op(e2, e0) = e2
% 110.79/15.84 | | | |
% 110.79/15.84 | | | | BETA: splitting (5) gives:
% 110.79/15.84 | | | |
% 110.79/15.84 | | | | Case 1:
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | | (35) ~ (all_30_1 = e3)
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | | REDUCE: (28), (35) imply:
% 110.79/15.84 | | | | | (36) $false
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | | CLOSE: (36) is inconsistent.
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | Case 2:
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | | (37) ~ (all_30_0 = e1) & op(e3, e0) = all_30_0 & $i(all_30_0)
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | | ALPHA: (37) implies:
% 110.79/15.84 | | | | | (38) ~ (all_30_0 = e1)
% 110.79/15.84 | | | | | (39) op(e3, e0) = all_30_0
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | | GROUND_INST: instantiating (13) with all_53_8, e2, e0, e2, simplifying
% 110.79/15.84 | | | | | with (12), (34) gives:
% 110.79/15.84 | | | | | (40) all_53_8 = e2
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | | GROUND_INST: instantiating (13) with all_53_12, all_30_0, e0, e3,
% 110.79/15.84 | | | | | simplifying with (1), (39) gives:
% 110.79/15.84 | | | | | (41) all_53_12 = all_30_0
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | | COMBINE_EQS: (4), (41) imply:
% 110.79/15.84 | | | | | (42) all_55_12 = all_30_0
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | | REDUCE: (8), (40), (41) imply:
% 110.79/15.84 | | | | | (43) ~ (all_30_0 = e2)
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | | SIMP: (43) implies:
% 110.79/15.84 | | | | | (44) ~ (all_30_0 = e2)
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | | REDUCE: (29), (41) imply:
% 110.79/15.84 | | | | | (45) ~ (all_30_0 = e3)
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | | REDUCE: (22), (41) imply:
% 110.79/15.84 | | | | | (46) ~ (all_30_0 = e0)
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | | BETA: splitting (11) gives:
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | | Case 1:
% 110.79/15.84 | | | | | |
% 110.79/15.84 | | | | | | (47) all_55_12 = e3
% 110.79/15.84 | | | | | |
% 110.79/15.84 | | | | | | COMBINE_EQS: (42), (47) imply:
% 110.79/15.84 | | | | | | (48) all_30_0 = e3
% 110.79/15.84 | | | | | |
% 110.79/15.84 | | | | | | REDUCE: (45), (48) imply:
% 110.79/15.84 | | | | | | (49) $false
% 110.79/15.84 | | | | | |
% 110.79/15.84 | | | | | | CLOSE: (49) is inconsistent.
% 110.79/15.84 | | | | | |
% 110.79/15.84 | | | | | Case 2:
% 110.79/15.84 | | | | | |
% 110.79/15.84 | | | | | | (50) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 110.79/15.84 | | | | | |
% 110.79/15.84 | | | | | | BETA: splitting (50) gives:
% 110.79/15.84 | | | | | |
% 110.79/15.84 | | | | | | Case 1:
% 110.79/15.84 | | | | | | |
% 110.79/15.84 | | | | | | | (51) all_55_12 = e2
% 110.79/15.84 | | | | | | |
% 110.79/15.84 | | | | | | | COMBINE_EQS: (42), (51) imply:
% 110.79/15.84 | | | | | | | (52) all_30_0 = e2
% 110.79/15.84 | | | | | | |
% 110.79/15.84 | | | | | | | REDUCE: (44), (52) imply:
% 110.79/15.84 | | | | | | | (53) $false
% 110.79/15.84 | | | | | | |
% 110.79/15.84 | | | | | | | CLOSE: (53) is inconsistent.
% 110.79/15.84 | | | | | | |
% 110.79/15.84 | | | | | | Case 2:
% 110.79/15.84 | | | | | | |
% 110.79/15.84 | | | | | | | (54) all_55_12 = e1 | all_55_12 = e0
% 110.79/15.84 | | | | | | |
% 110.79/15.84 | | | | | | | BETA: splitting (54) gives:
% 110.79/15.84 | | | | | | |
% 110.79/15.84 | | | | | | | Case 1:
% 110.79/15.84 | | | | | | | |
% 110.79/15.84 | | | | | | | | (55) all_55_12 = e1
% 110.79/15.84 | | | | | | | |
% 110.79/15.84 | | | | | | | | COMBINE_EQS: (42), (55) imply:
% 110.79/15.84 | | | | | | | | (56) all_30_0 = e1
% 110.79/15.84 | | | | | | | |
% 110.79/15.84 | | | | | | | | REDUCE: (38), (56) imply:
% 110.79/15.84 | | | | | | | | (57) $false
% 110.79/15.84 | | | | | | | |
% 110.79/15.84 | | | | | | | | CLOSE: (57) is inconsistent.
% 110.79/15.84 | | | | | | | |
% 110.79/15.84 | | | | | | | Case 2:
% 110.79/15.84 | | | | | | | |
% 110.79/15.84 | | | | | | | | (58) all_55_12 = e0
% 110.79/15.84 | | | | | | | |
% 110.79/15.84 | | | | | | | | COMBINE_EQS: (42), (58) imply:
% 110.79/15.84 | | | | | | | | (59) all_30_0 = e0
% 110.79/15.84 | | | | | | | |
% 110.79/15.84 | | | | | | | | REDUCE: (46), (59) imply:
% 110.79/15.84 | | | | | | | | (60) $false
% 110.79/15.84 | | | | | | | |
% 110.79/15.84 | | | | | | | | CLOSE: (60) is inconsistent.
% 110.79/15.84 | | | | | | | |
% 110.79/15.84 | | | | | | | End of split
% 110.79/15.84 | | | | | | |
% 110.79/15.84 | | | | | | End of split
% 110.79/15.84 | | | | | |
% 110.79/15.84 | | | | | End of split
% 110.79/15.84 | | | | |
% 110.79/15.84 | | | | End of split
% 110.79/15.84 | | | |
% 110.79/15.84 | | | Case 2:
% 110.79/15.84 | | | |
% 110.79/15.84 | | | | (61) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0,
% 110.79/15.84 | | | | e1) = all_52_4 & $i(all_52_4)
% 110.79/15.84 | | | |
% 110.79/15.84 | | | | ALPHA: (61) implies:
% 110.79/15.84 | | | | (62) op(e1, e0) = e1
% 110.79/15.84 | | | |
% 110.79/15.84 | | | | REF_CLOSE: (7), (13), (14), (62) are inconsistent by sub-proof #81.
% 110.79/15.84 | | | |
% 110.79/15.84 | | | End of split
% 110.79/15.84 | | |
% 110.79/15.84 | | End of split
% 110.79/15.84 | |
% 110.79/15.84 | Case 2:
% 110.79/15.84 | |
% 110.79/15.84 | | (63) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 110.79/15.84 | |
% 110.79/15.84 | | REF_CLOSE: (3), (18), (19), (24), (63) are inconsistent by sub-proof #15.
% 110.79/15.84 | |
% 110.79/15.84 | End of split
% 110.79/15.84 |
% 110.79/15.84 End of proof
% 110.79/15.84
% 110.79/15.84 Sub-proof #10 shows that the following formulas are inconsistent:
% 110.79/15.84 ----------------------------------------------------------------
% 110.79/15.84 (1) op(e3, e0) = all_53_12
% 110.79/15.84 (2) (all_57_4 = e0 & op(e3, e0) = e0) | (all_57_5 = e0 & op(e2, e0) = e0)
% 110.79/15.84 (3) ~ (all_53_8 = e0)
% 110.79/15.84 (4) ~ (all_53_12 = e0)
% 110.79/15.84 (5) op(e2, e0) = all_53_8
% 110.79/15.84 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.84
% 110.79/15.84 Begin of proof
% 110.79/15.84 |
% 110.79/15.84 | BETA: splitting (2) gives:
% 110.79/15.84 |
% 110.79/15.84 | Case 1:
% 110.79/15.84 | |
% 110.79/15.84 | | (7) all_57_4 = e0 & op(e3, e0) = e0
% 110.79/15.84 | |
% 110.79/15.84 | | ALPHA: (7) implies:
% 110.79/15.84 | | (8) op(e3, e0) = e0
% 110.79/15.84 | |
% 110.79/15.84 | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #201.
% 110.79/15.84 | |
% 110.79/15.84 | Case 2:
% 110.79/15.84 | |
% 110.79/15.84 | | (9) all_57_5 = e0 & op(e2, e0) = e0
% 110.79/15.84 | |
% 110.79/15.84 | | ALPHA: (9) implies:
% 110.79/15.84 | | (10) op(e2, e0) = e0
% 110.79/15.84 | |
% 110.79/15.84 | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #14.
% 110.79/15.84 | |
% 110.79/15.84 | End of split
% 110.79/15.84 |
% 110.79/15.84 End of proof
% 110.79/15.84
% 110.79/15.84 Sub-proof #11 shows that the following formulas are inconsistent:
% 110.79/15.84 ----------------------------------------------------------------
% 110.79/15.84 (1) op(e1, e2) = all_53_7
% 110.79/15.84 (2) ~ (all_53_7 = e0)
% 110.79/15.84 (3) op(e1, e3) = all_53_6
% 110.79/15.84 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.84 (5) ~ (all_53_6 = e0)
% 110.79/15.84 (6) (all_57_32 = e0 & op(e1, e3) = e0) | (all_57_33 = e0 & op(e1, e2) = e0)
% 110.79/15.84
% 110.79/15.84 Begin of proof
% 110.79/15.84 |
% 110.79/15.84 | BETA: splitting (6) gives:
% 110.79/15.84 |
% 110.79/15.84 | Case 1:
% 110.79/15.84 | |
% 110.79/15.84 | | (7) all_57_32 = e0 & op(e1, e3) = e0
% 110.79/15.84 | |
% 110.79/15.84 | | ALPHA: (7) implies:
% 110.79/15.84 | | (8) op(e1, e3) = e0
% 110.79/15.84 | |
% 110.79/15.84 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #157.
% 110.79/15.84 | |
% 110.79/15.84 | Case 2:
% 110.79/15.84 | |
% 110.79/15.84 | | (9) all_57_33 = e0 & op(e1, e2) = e0
% 110.79/15.84 | |
% 110.79/15.84 | | ALPHA: (9) implies:
% 110.79/15.84 | | (10) op(e1, e2) = e0
% 110.79/15.84 | |
% 110.79/15.84 | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #153.
% 110.79/15.84 | |
% 110.79/15.84 | End of split
% 110.79/15.84 |
% 110.79/15.84 End of proof
% 110.79/15.84
% 110.79/15.84 Sub-proof #12 shows that the following formulas are inconsistent:
% 110.79/15.84 ----------------------------------------------------------------
% 110.79/15.84 (1) all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 110.79/15.84 (2) ~ (all_53_15 = e3)
% 110.79/15.84 (3) op(e2, e3) = all_53_10
% 110.79/15.84 (4) ~ (all_53_3 = e3)
% 110.79/15.84 (5) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 110.79/15.84 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 110.79/15.84 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 110.79/15.84 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 110.79/15.84 $i(all_52_16))
% 110.79/15.84 (6) op(e3, e2) = all_53_15
% 110.79/15.84 (7) op(e1, e2) = all_53_7
% 110.79/15.84 (8) op(e2, e0) = e2
% 110.79/15.84 (9) op(e0, e3) = all_53_2
% 110.79/15.84 (10) ~ (all_53_6 = all_53_7)
% 110.79/15.84 (11) ~ (all_53_8 = all_53_10)
% 110.79/15.84 (12) ~ (all_53_3 = e1)
% 110.79/15.84 (13) op(e0, e2) = all_52_2
% 110.79/15.84 (14) op(e1, e3) = all_53_6
% 110.79/15.84 (15) all_55_2 = all_53_3
% 110.79/15.84 (16) op(e2, e0) = all_53_8
% 110.79/15.85 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.85 (18) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 110.79/15.85 e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20 = e3) &
% 110.79/15.85 op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23
% 110.79/15.85 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0
% 110.79/15.85 & $i(all_52_22))
% 110.79/15.85 (19) ~ (all_52_2 = e0)
% 110.79/15.85 (20) ~ (all_53_2 = e0)
% 110.79/15.85 (21) op(e0, e2) = all_53_3
% 110.79/15.85
% 110.79/15.85 Begin of proof
% 110.79/15.85 |
% 110.79/15.85 | GROUND_INST: instantiating (17) with all_53_3, all_52_2, e2, e0, simplifying
% 110.79/15.85 | with (13), (21) gives:
% 110.79/15.85 | (22) all_53_3 = all_52_2
% 110.79/15.85 |
% 110.79/15.85 | GROUND_INST: instantiating (17) with all_53_8, e2, e0, e2, simplifying with
% 110.79/15.85 | (8), (16) gives:
% 110.79/15.85 | (23) all_53_8 = e2
% 110.79/15.85 |
% 110.79/15.85 | COMBINE_EQS: (15), (22) imply:
% 110.79/15.85 | (24) all_55_2 = all_52_2
% 110.79/15.85 |
% 110.79/15.85 | REDUCE: (4), (22) imply:
% 110.79/15.85 | (25) ~ (all_52_2 = e3)
% 110.79/15.85 |
% 110.79/15.85 | REDUCE: (12), (22) imply:
% 110.79/15.85 | (26) ~ (all_52_2 = e1)
% 110.79/15.85 |
% 110.79/15.85 | BETA: splitting (5) gives:
% 110.79/15.85 |
% 110.79/15.85 | Case 1:
% 110.79/15.85 | |
% 110.79/15.85 | | (27) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3)
% 110.79/15.85 | | = all_52_12 & $i(all_52_12)
% 110.79/15.85 | |
% 110.79/15.85 | | ALPHA: (27) implies:
% 110.79/15.85 | | (28) op(e3, e2) = e3
% 110.79/15.85 | |
% 110.79/15.85 | | REF_CLOSE: (2), (6), (17), (28) are inconsistent by sub-proof #214.
% 110.79/15.85 | |
% 110.79/15.85 | Case 2:
% 110.79/15.85 | |
% 110.79/15.85 | | (29) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 110.79/15.85 | | op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~ (all_52_16
% 110.79/15.85 | | = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 110.79/15.85 | | $i(all_52_16))
% 110.79/15.85 | |
% 110.79/15.85 | | BETA: splitting (29) gives:
% 110.79/15.85 | |
% 110.79/15.85 | | Case 1:
% 110.79/15.85 | | |
% 110.79/15.85 | | | (30) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 110.79/15.85 | | | op(e1, e2) = e1 & $i(all_52_14)
% 110.79/15.85 | | |
% 110.79/15.85 | | | ALPHA: (30) implies:
% 110.79/15.85 | | | (31) op(e1, e2) = e1
% 110.79/15.85 | | |
% 110.79/15.85 | | | REF_CLOSE: (3), (7), (8), (9), (10), (11), (14), (16), (17), (18), (20),
% 110.79/15.85 | | | (31) are inconsistent by sub-proof #101.
% 110.79/15.85 | | |
% 110.79/15.85 | | Case 2:
% 110.79/15.85 | | |
% 110.79/15.85 | | | (32) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 &
% 110.79/15.85 | | | op(e0, e2) = e0 & $i(all_52_16)
% 110.79/15.85 | | |
% 110.79/15.85 | | | ALPHA: (32) implies:
% 110.79/15.85 | | | (33) op(e0, e2) = e0
% 110.79/15.85 | | |
% 110.79/15.85 | | | BETA: splitting (1) gives:
% 110.79/15.85 | | |
% 110.79/15.85 | | | Case 1:
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | (34) all_55_2 = e3
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | COMBINE_EQS: (24), (34) imply:
% 110.79/15.85 | | | | (35) all_52_2 = e3
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | SIMP: (35) implies:
% 110.79/15.85 | | | | (36) all_52_2 = e3
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | REDUCE: (25), (36) imply:
% 110.79/15.85 | | | | (37) $false
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | CLOSE: (37) is inconsistent.
% 110.79/15.85 | | | |
% 110.79/15.85 | | | Case 2:
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | (38) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | BETA: splitting (38) gives:
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | Case 1:
% 110.79/15.85 | | | | |
% 110.79/15.85 | | | | | (39) all_55_2 = e2
% 110.79/15.85 | | | | |
% 110.79/15.85 | | | | | COMBINE_EQS: (24), (39) imply:
% 110.79/15.85 | | | | | (40) all_52_2 = e2
% 110.79/15.85 | | | | |
% 110.79/15.85 | | | | | REDUCE: (19), (40) imply:
% 110.79/15.85 | | | | | (41) ~ (e2 = e0)
% 110.79/15.85 | | | | |
% 110.79/15.85 | | | | | REDUCE: (13), (40) imply:
% 110.79/15.85 | | | | | (42) op(e0, e2) = e2
% 110.79/15.85 | | | | |
% 110.79/15.85 | | | | | REF_CLOSE: (17), (33), (41), (42) are inconsistent by sub-proof #163.
% 110.79/15.85 | | | | |
% 110.79/15.85 | | | | Case 2:
% 110.79/15.85 | | | | |
% 110.79/15.85 | | | | | (43) all_55_2 = e1 | all_55_2 = e0
% 110.79/15.85 | | | | |
% 110.79/15.85 | | | | | REF_CLOSE: (19), (24), (26), (43) are inconsistent by sub-proof #21.
% 110.79/15.85 | | | | |
% 110.79/15.85 | | | | End of split
% 110.79/15.85 | | | |
% 110.79/15.85 | | | End of split
% 110.79/15.85 | | |
% 110.79/15.85 | | End of split
% 110.79/15.85 | |
% 110.79/15.85 | End of split
% 110.79/15.85 |
% 110.79/15.85 End of proof
% 110.79/15.85
% 110.79/15.85 Sub-proof #13 shows that the following formulas are inconsistent:
% 110.79/15.85 ----------------------------------------------------------------
% 110.79/15.85 (1) ~ (all_4_1 = e3)
% 110.79/15.85 (2) ~ (all_53_3 = all_4_1)
% 110.79/15.85 (3) op(e2, e3) = all_53_10
% 110.79/15.85 (4) ~ (all_4_1 = e1)
% 110.79/15.85 (5) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 110.79/15.85 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 110.79/15.85 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 110.79/15.85 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 110.79/15.85 $i(all_52_16))
% 110.79/15.85 (6) op(e3, e2) = all_53_15
% 110.79/15.85 (7) op(e1, e2) = all_53_7
% 110.79/15.85 (8) ~ (e3 = e1)
% 110.79/15.85 (9) op(e0, e1) = all_53_1
% 110.79/15.85 (10) op(e2, e1) = all_53_9
% 110.79/15.85 (11) ~ (all_53_1 = all_4_1)
% 110.79/15.85 (12) ~ (all_53_10 = e0)
% 110.79/15.85 (13) ~ (all_53_3 = e1)
% 110.79/15.85 (14) (all_57_76 = e1 & op(e3, e2) = e1) | (all_57_77 = e1 & op(e2, e2) = e1)
% 110.79/15.85 | (all_57_78 = e1 & op(e1, e2) = e1) | (all_57_79 = e1 & op(e0, e2) =
% 110.79/15.85 e1)
% 110.79/15.85 (15) op(e2, e0) = all_53_8
% 110.79/15.85 (16) op(e3, e1) = all_53_13
% 110.79/15.85 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.85 (18) ~ (all_53_13 = all_53_15)
% 110.79/15.85 (19) (all_57_64 = e0 & op(e2, e3) = e0) | (all_57_65 = e0 & op(e2, e2) = e0)
% 110.79/15.85 | (all_57_66 = e0 & op(e2, e1) = e0) | (all_57_67 = e0 & op(e2, e0) =
% 110.79/15.85 e0)
% 110.79/15.85 (20) ~ (all_53_7 = e1)
% 110.79/15.85 (21) all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 110.79/15.85 (22) ~ (all_53_8 = all_4_1)
% 110.79/15.85 (23) ~ (all_4_1 = e2)
% 110.79/15.85 (24) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 110.79/15.85 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 110.79/15.85 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 110.79/15.85 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 110.79/15.85 $i(all_52_10))
% 110.79/15.85 (25) all_55_0 = all_4_1
% 110.79/15.85 (26) op(e0, e2) = all_53_3
% 110.79/15.85
% 110.79/15.85 Begin of proof
% 110.79/15.85 |
% 110.79/15.85 | BETA: splitting (21) gives:
% 110.79/15.85 |
% 110.79/15.85 | Case 1:
% 110.79/15.85 | |
% 110.79/15.85 | | (27) all_55_0 = e3
% 110.79/15.85 | |
% 110.79/15.85 | | COMBINE_EQS: (25), (27) imply:
% 110.79/15.85 | | (28) all_4_1 = e3
% 110.79/15.85 | |
% 110.79/15.85 | | REDUCE: (1), (28) imply:
% 110.79/15.85 | | (29) $false
% 110.79/15.85 | |
% 110.79/15.85 | | CLOSE: (29) is inconsistent.
% 110.79/15.85 | |
% 110.79/15.85 | Case 2:
% 110.79/15.85 | |
% 110.79/15.85 | | (30) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 110.79/15.85 | |
% 110.79/15.85 | | BETA: splitting (30) gives:
% 110.79/15.85 | |
% 110.79/15.85 | | Case 1:
% 110.79/15.85 | | |
% 110.79/15.85 | | | (31) all_55_0 = e2
% 110.79/15.85 | | |
% 110.79/15.85 | | | COMBINE_EQS: (25), (31) imply:
% 110.79/15.85 | | | (32) all_4_1 = e2
% 110.79/15.85 | | |
% 110.79/15.85 | | | REDUCE: (23), (32) imply:
% 110.79/15.85 | | | (33) $false
% 110.79/15.85 | | |
% 110.79/15.85 | | | CLOSE: (33) is inconsistent.
% 110.79/15.85 | | |
% 110.79/15.85 | | Case 2:
% 110.79/15.85 | | |
% 110.79/15.85 | | | (34) ~ (all_55_0 = e2)
% 110.79/15.85 | | | (35) all_55_0 = e1 | all_55_0 = e0
% 110.79/15.85 | | |
% 110.79/15.85 | | | BETA: splitting (35) gives:
% 110.79/15.85 | | |
% 110.79/15.85 | | | Case 1:
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | (36) all_55_0 = e1
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | COMBINE_EQS: (25), (36) imply:
% 110.79/15.85 | | | | (37) all_4_1 = e1
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | REDUCE: (4), (37) imply:
% 110.79/15.85 | | | | (38) $false
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | CLOSE: (38) is inconsistent.
% 110.79/15.85 | | | |
% 110.79/15.85 | | | Case 2:
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | (39) all_55_0 = e0
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | COMBINE_EQS: (25), (39) imply:
% 110.79/15.85 | | | | (40) all_4_1 = e0
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | REDUCE: (11), (40) imply:
% 110.79/15.85 | | | | (41) ~ (all_53_1 = e0)
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | REDUCE: (2), (40) imply:
% 110.79/15.85 | | | | (42) ~ (all_53_3 = e0)
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | REDUCE: (22), (40) imply:
% 110.79/15.85 | | | | (43) ~ (all_53_8 = e0)
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | REDUCE: (23), (40) imply:
% 110.79/15.85 | | | | (44) ~ (e2 = e0)
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | SIMP: (44) implies:
% 110.79/15.85 | | | | (45) ~ (e2 = e0)
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | REDUCE: (4), (40) imply:
% 110.79/15.85 | | | | (46) ~ (e1 = e0)
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | SIMP: (46) implies:
% 110.79/15.85 | | | | (47) ~ (e1 = e0)
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | BETA: splitting (5) gives:
% 110.79/15.85 | | | |
% 110.79/15.85 | | | | Case 1:
% 110.79/15.85 | | | | |
% 110.79/15.85 | | | | | (48) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 &
% 110.79/15.85 | | | | | op(e2, e3) = all_52_12 & $i(all_52_12)
% 110.79/15.85 | | | | |
% 110.79/15.85 | | | | | ALPHA: (48) implies:
% 110.79/15.85 | | | | | (49) op(e3, e2) = e3
% 110.79/15.85 | | | | |
% 110.79/15.85 | | | | | BETA: splitting (24) gives:
% 110.79/15.85 | | | | |
% 110.79/15.85 | | | | | Case 1:
% 110.79/15.85 | | | | | |
% 110.79/15.85 | | | | | | (50) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 &
% 110.79/15.85 | | | | | | op(e1, e3) = all_52_6 & $i(all_52_6)
% 110.79/15.85 | | | | | |
% 110.79/15.85 | | | | | | REF_CLOSE: (5), (6), (7), (16), (17), (18), (20), (26), (42), (50)
% 110.79/15.85 | | | | | | are inconsistent by sub-proof #168.
% 110.79/15.85 | | | | | |
% 110.79/15.85 | | | | | Case 2:
% 110.79/15.85 | | | | | |
% 110.79/15.85 | | | | | | (51) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 &
% 110.79/15.85 | | | | | | op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 = e0 &
% 110.79/15.85 | | | | | | ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) =
% 110.79/15.85 | | | | | | e0 & $i(all_52_10))
% 110.79/15.85 | | | | | |
% 110.79/15.85 | | | | | | BETA: splitting (51) gives:
% 110.79/15.85 | | | | | |
% 110.79/15.85 | | | | | | Case 1:
% 110.79/15.85 | | | | | | |
% 110.79/15.85 | | | | | | | (52) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 &
% 110.79/15.85 | | | | | | | op(e1, e2) = all_52_8 & $i(all_52_8)
% 110.79/15.85 | | | | | | |
% 110.79/15.85 | | | | | | | ALPHA: (52) implies:
% 110.79/15.85 | | | | | | | (53) op(e2, e1) = e2
% 110.79/15.85 | | | | | | |
% 110.79/15.85 | | | | | | | BETA: splitting (19) gives:
% 110.79/15.85 | | | | | | |
% 110.79/15.85 | | | | | | | Case 1:
% 110.79/15.85 | | | | | | | |
% 110.79/15.85 | | | | | | | | (54) (all_57_64 = e0 & op(e2, e3) = e0) | (all_57_65 = e0 &
% 110.79/15.85 | | | | | | | | op(e2, e2) = e0)
% 110.79/15.85 | | | | | | | |
% 110.79/15.85 | | | | | | | | BETA: splitting (54) gives:
% 110.79/15.85 | | | | | | | |
% 110.79/15.85 | | | | | | | | Case 1:
% 110.79/15.85 | | | | | | | | |
% 110.79/15.85 | | | | | | | | | (55) all_57_64 = e0 & op(e2, e3) = e0
% 110.79/15.85 | | | | | | | | |
% 110.79/15.85 | | | | | | | | | ALPHA: (55) implies:
% 110.79/15.85 | | | | | | | | | (56) op(e2, e3) = e0
% 110.79/15.85 | | | | | | | | |
% 110.79/15.85 | | | | | | | | | REF_CLOSE: (3), (12), (17), (56) are inconsistent by sub-proof
% 110.79/15.85 | | | | | | | | | #158.
% 110.79/15.85 | | | | | | | | |
% 110.79/15.85 | | | | | | | | Case 2:
% 110.79/15.85 | | | | | | | | |
% 110.79/15.85 | | | | | | | | | (57) all_57_65 = e0 & op(e2, e2) = e0
% 110.79/15.85 | | | | | | | | |
% 110.79/15.85 | | | | | | | | | ALPHA: (57) implies:
% 110.79/15.85 | | | | | | | | | (58) op(e2, e2) = e0
% 110.79/15.85 | | | | | | | | |
% 110.79/15.85 | | | | | | | | | REF_CLOSE: (6), (7), (8), (13), (14), (17), (20), (26), (47),
% 110.79/15.85 | | | | | | | | | (49), (58) are inconsistent by sub-proof #35.
% 110.79/15.85 | | | | | | | | |
% 110.79/15.85 | | | | | | | | End of split
% 110.79/15.85 | | | | | | | |
% 110.79/15.85 | | | | | | | Case 2:
% 110.79/15.85 | | | | | | | |
% 110.79/15.85 | | | | | | | | (59) (all_57_66 = e0 & op(e2, e1) = e0) | (all_57_67 = e0 &
% 110.79/15.85 | | | | | | | | op(e2, e0) = e0)
% 110.79/15.85 | | | | | | | |
% 110.79/15.85 | | | | | | | | BETA: splitting (59) gives:
% 110.79/15.85 | | | | | | | |
% 110.79/15.85 | | | | | | | | Case 1:
% 110.79/15.85 | | | | | | | | |
% 110.79/15.86 | | | | | | | | | (60) all_57_66 = e0 & op(e2, e1) = e0
% 110.79/15.86 | | | | | | | | |
% 110.79/15.86 | | | | | | | | | ALPHA: (60) implies:
% 110.79/15.86 | | | | | | | | | (61) op(e2, e1) = e0
% 110.79/15.86 | | | | | | | | |
% 110.79/15.86 | | | | | | | | | GROUND_INST: instantiating (17) with all_53_9, e0, e1, e2,
% 110.79/15.86 | | | | | | | | | simplifying with (10), (61) gives:
% 110.79/15.86 | | | | | | | | | (62) all_53_9 = e0
% 110.79/15.86 | | | | | | | | |
% 110.79/15.86 | | | | | | | | | GROUND_INST: instantiating (17) with all_53_9, e2, e1, e2,
% 110.79/15.86 | | | | | | | | | simplifying with (10), (53) gives:
% 110.79/15.86 | | | | | | | | | (63) all_53_9 = e2
% 110.79/15.86 | | | | | | | | |
% 110.79/15.86 | | | | | | | | | COMBINE_EQS: (62), (63) imply:
% 110.79/15.86 | | | | | | | | | (64) e2 = e0
% 110.79/15.86 | | | | | | | | |
% 110.79/15.86 | | | | | | | | | SIMP: (64) implies:
% 110.79/15.86 | | | | | | | | | (65) e2 = e0
% 110.79/15.86 | | | | | | | | |
% 110.79/15.86 | | | | | | | | | REDUCE: (45), (65) imply:
% 110.79/15.86 | | | | | | | | | (66) $false
% 110.79/15.86 | | | | | | | | |
% 110.79/15.86 | | | | | | | | | CLOSE: (66) is inconsistent.
% 110.79/15.86 | | | | | | | | |
% 110.79/15.86 | | | | | | | | Case 2:
% 110.79/15.86 | | | | | | | | |
% 110.79/15.86 | | | | | | | | | (67) all_57_67 = e0 & op(e2, e0) = e0
% 110.79/15.86 | | | | | | | | |
% 110.79/15.86 | | | | | | | | | ALPHA: (67) implies:
% 110.79/15.86 | | | | | | | | | (68) op(e2, e0) = e0
% 110.79/15.86 | | | | | | | | |
% 110.79/15.86 | | | | | | | | | REF_CLOSE: (15), (17), (43), (68) are inconsistent by
% 110.79/15.86 | | | | | | | | | sub-proof #14.
% 110.79/15.86 | | | | | | | | |
% 110.79/15.86 | | | | | | | | End of split
% 110.79/15.86 | | | | | | | |
% 110.79/15.86 | | | | | | | End of split
% 110.79/15.86 | | | | | | |
% 110.79/15.86 | | | | | | Case 2:
% 110.79/15.86 | | | | | | |
% 110.79/15.86 | | | | | | | (69) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0) =
% 110.79/15.86 | | | | | | | all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 110.79/15.86 | | | | | | |
% 110.79/15.86 | | | | | | | ALPHA: (69) implies:
% 110.79/15.86 | | | | | | | (70) op(e0, e1) = e0
% 110.79/15.86 | | | | | | |
% 110.79/15.86 | | | | | | | REF_CLOSE: (9), (17), (41), (70) are inconsistent by sub-proof
% 110.79/15.86 | | | | | | | #230.
% 110.79/15.86 | | | | | | |
% 110.79/15.86 | | | | | | End of split
% 110.79/15.86 | | | | | |
% 110.79/15.86 | | | | | End of split
% 110.79/15.86 | | | | |
% 110.79/15.86 | | | | Case 2:
% 110.79/15.86 | | | | |
% 110.79/15.86 | | | | | (71) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14
% 110.79/15.86 | | | | | & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~
% 110.79/15.86 | | | | | (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0
% 110.79/15.86 | | | | | & $i(all_52_16))
% 110.79/15.86 | | | | |
% 110.79/15.86 | | | | | REF_CLOSE: (7), (17), (20), (26), (42), (71) are inconsistent by
% 110.79/15.86 | | | | | sub-proof #218.
% 110.79/15.86 | | | | |
% 110.79/15.86 | | | | End of split
% 110.79/15.86 | | | |
% 110.79/15.86 | | | End of split
% 110.79/15.86 | | |
% 110.79/15.86 | | End of split
% 110.79/15.86 | |
% 110.79/15.86 | End of split
% 110.79/15.86 |
% 110.79/15.86 End of proof
% 110.79/15.86
% 110.79/15.86 Sub-proof #14 shows that the following formulas are inconsistent:
% 110.79/15.86 ----------------------------------------------------------------
% 110.79/15.86 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.86 (2) op(e2, e0) = all_53_8
% 110.79/15.86 (3) op(e2, e0) = e0
% 110.79/15.86 (4) ~ (all_53_8 = e0)
% 110.79/15.86
% 110.79/15.86 Begin of proof
% 110.79/15.86 |
% 110.79/15.86 | GROUND_INST: instantiating (1) with all_53_8, e0, e0, e2, simplifying with
% 110.79/15.86 | (2), (3) gives:
% 110.79/15.86 | (5) all_53_8 = e0
% 110.79/15.86 |
% 110.79/15.86 | REDUCE: (4), (5) imply:
% 110.79/15.86 | (6) $false
% 110.79/15.86 |
% 110.79/15.86 | CLOSE: (6) is inconsistent.
% 110.79/15.86 |
% 110.79/15.86 End of proof
% 110.79/15.86
% 110.79/15.86 Sub-proof #15 shows that the following formulas are inconsistent:
% 110.79/15.86 ----------------------------------------------------------------
% 110.79/15.86 (1) ~ (all_4_1 = e1)
% 110.79/15.86 (2) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 110.79/15.86 (3) ~ (all_4_1 = e0)
% 110.79/15.86 (4) ~ (all_4_1 = e2)
% 110.79/15.86 (5) all_55_0 = all_4_1
% 110.79/15.86
% 110.79/15.86 Begin of proof
% 110.79/15.86 |
% 110.79/15.86 | BETA: splitting (2) gives:
% 110.79/15.86 |
% 110.79/15.86 | Case 1:
% 110.79/15.86 | |
% 110.79/15.86 | | (6) all_55_0 = e2
% 110.79/15.86 | |
% 110.79/15.86 | | COMBINE_EQS: (5), (6) imply:
% 110.79/15.86 | | (7) all_4_1 = e2
% 110.79/15.86 | |
% 110.79/15.86 | | SIMP: (7) implies:
% 110.79/15.86 | | (8) all_4_1 = e2
% 110.79/15.86 | |
% 110.79/15.86 | | REDUCE: (4), (8) imply:
% 110.79/15.86 | | (9) $false
% 110.79/15.86 | |
% 110.79/15.86 | | CLOSE: (9) is inconsistent.
% 110.79/15.86 | |
% 110.79/15.86 | Case 2:
% 110.79/15.86 | |
% 110.79/15.86 | | (10) all_55_0 = e1 | all_55_0 = e0
% 110.79/15.86 | |
% 110.79/15.86 | | BETA: splitting (10) gives:
% 110.79/15.86 | |
% 110.79/15.86 | | Case 1:
% 110.79/15.86 | | |
% 110.79/15.86 | | | (11) all_55_0 = e1
% 110.79/15.86 | | |
% 110.79/15.86 | | | COMBINE_EQS: (5), (11) imply:
% 110.79/15.86 | | | (12) all_4_1 = e1
% 110.79/15.86 | | |
% 110.79/15.86 | | | SIMP: (12) implies:
% 110.79/15.86 | | | (13) all_4_1 = e1
% 110.79/15.86 | | |
% 110.79/15.86 | | | REDUCE: (1), (13) imply:
% 110.79/15.86 | | | (14) $false
% 110.79/15.86 | | |
% 110.79/15.86 | | | CLOSE: (14) is inconsistent.
% 110.79/15.86 | | |
% 110.79/15.86 | | Case 2:
% 110.79/15.86 | | |
% 110.79/15.86 | | | (15) all_55_0 = e0
% 110.79/15.86 | | |
% 110.79/15.86 | | | COMBINE_EQS: (5), (15) imply:
% 110.79/15.86 | | | (16) all_4_1 = e0
% 110.79/15.86 | | |
% 110.79/15.86 | | | SIMP: (16) implies:
% 110.79/15.86 | | | (17) all_4_1 = e0
% 110.79/15.86 | | |
% 110.79/15.86 | | | REDUCE: (3), (17) imply:
% 110.79/15.86 | | | (18) $false
% 110.79/15.86 | | |
% 110.79/15.86 | | | CLOSE: (18) is inconsistent.
% 110.79/15.86 | | |
% 110.79/15.86 | | End of split
% 110.79/15.86 | |
% 110.79/15.86 | End of split
% 110.79/15.86 |
% 110.79/15.86 End of proof
% 110.79/15.86
% 110.79/15.86 Sub-proof #16 shows that the following formulas are inconsistent:
% 110.79/15.86 ----------------------------------------------------------------
% 110.79/15.86 (1) all_55_12 = e1 | all_55_12 = e0
% 110.79/15.86 (2) op(e1, e0) = all_53_4
% 110.79/15.86 (3) all_55_12 = all_53_12
% 110.79/15.86 (4) ~ (all_53_4 = all_53_12)
% 110.79/15.86 (5) ~ (all_53_12 = e0)
% 110.79/15.86 (6) op(e1, e0) = e1
% 110.79/15.86 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.86
% 110.79/15.86 Begin of proof
% 110.79/15.86 |
% 110.79/15.86 | BETA: splitting (1) gives:
% 110.79/15.86 |
% 110.79/15.86 | Case 1:
% 110.79/15.86 | |
% 110.79/15.86 | | (8) all_55_12 = e1
% 110.79/15.86 | |
% 110.79/15.86 | | COMBINE_EQS: (3), (8) imply:
% 110.79/15.86 | | (9) all_53_12 = e1
% 110.79/15.86 | |
% 110.79/15.86 | | SIMP: (9) implies:
% 110.79/15.86 | | (10) all_53_12 = e1
% 110.79/15.86 | |
% 110.79/15.86 | | REDUCE: (4), (10) imply:
% 110.79/15.86 | | (11) ~ (all_53_4 = e1)
% 110.79/15.86 | |
% 110.79/15.86 | | REF_CLOSE: (2), (6), (7), (11) are inconsistent by sub-proof #226.
% 110.79/15.86 | |
% 110.79/15.86 | Case 2:
% 110.79/15.86 | |
% 110.79/15.86 | | (12) all_55_12 = e0
% 110.79/15.86 | |
% 110.79/15.86 | | REF_CLOSE: (3), (5), (12) are inconsistent by sub-proof #17.
% 110.79/15.86 | |
% 110.79/15.86 | End of split
% 110.79/15.86 |
% 110.79/15.86 End of proof
% 110.79/15.86
% 110.79/15.86 Sub-proof #17 shows that the following formulas are inconsistent:
% 110.79/15.86 ----------------------------------------------------------------
% 110.79/15.86 (1) all_55_12 = all_53_12
% 110.79/15.86 (2) all_55_12 = e0
% 110.79/15.86 (3) ~ (all_53_12 = e0)
% 110.79/15.86
% 110.79/15.86 Begin of proof
% 110.79/15.86 |
% 110.79/15.86 | COMBINE_EQS: (1), (2) imply:
% 110.79/15.86 | (4) all_53_12 = e0
% 110.79/15.86 |
% 110.79/15.86 | SIMP: (4) implies:
% 110.79/15.86 | (5) all_53_12 = e0
% 110.79/15.86 |
% 110.79/15.86 | REDUCE: (3), (5) imply:
% 110.79/15.86 | (6) $false
% 110.79/15.86 |
% 110.79/15.86 | CLOSE: (6) is inconsistent.
% 110.79/15.86 |
% 110.79/15.86 End of proof
% 110.79/15.86
% 110.79/15.86 Sub-proof #18 shows that the following formulas are inconsistent:
% 110.79/15.86 ----------------------------------------------------------------
% 110.79/15.86 (1) op(e2, e3) = all_53_10
% 110.79/15.86 (2) ~ (all_10_2 = e0)
% 110.79/15.86 (3) ~ (all_53_10 = e0)
% 110.79/15.86 (4) op(e2, e2) = all_10_2
% 110.79/15.86 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.86 (6) (all_57_64 = e0 & op(e2, e3) = e0) | (all_57_65 = e0 & op(e2, e2) = e0)
% 110.79/15.86
% 110.79/15.86 Begin of proof
% 110.79/15.86 |
% 110.79/15.86 | BETA: splitting (6) gives:
% 110.79/15.86 |
% 110.79/15.86 | Case 1:
% 110.79/15.86 | |
% 110.79/15.86 | | (7) all_57_64 = e0 & op(e2, e3) = e0
% 110.79/15.86 | |
% 110.79/15.86 | | ALPHA: (7) implies:
% 110.79/15.86 | | (8) op(e2, e3) = e0
% 110.79/15.86 | |
% 110.79/15.86 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #158.
% 110.79/15.86 | |
% 110.79/15.86 | Case 2:
% 110.79/15.86 | |
% 110.79/15.86 | | (9) all_57_65 = e0 & op(e2, e2) = e0
% 110.79/15.86 | |
% 110.79/15.86 | | ALPHA: (9) implies:
% 110.79/15.86 | | (10) op(e2, e2) = e0
% 110.79/15.86 | |
% 110.79/15.86 | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #19.
% 110.79/15.86 | |
% 110.79/15.86 | End of split
% 110.79/15.86 |
% 110.79/15.86 End of proof
% 110.79/15.86
% 110.79/15.86 Sub-proof #19 shows that the following formulas are inconsistent:
% 110.79/15.86 ----------------------------------------------------------------
% 110.79/15.86 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.86 (2) op(e2, e2) = all_10_2
% 110.79/15.86 (3) op(e2, e2) = e0
% 110.79/15.86 (4) ~ (all_10_2 = e0)
% 110.79/15.86
% 110.79/15.86 Begin of proof
% 110.79/15.86 |
% 110.79/15.86 | GROUND_INST: instantiating (1) with all_10_2, e0, e2, e2, simplifying with
% 110.79/15.86 | (2), (3) gives:
% 110.79/15.86 | (5) all_10_2 = e0
% 110.79/15.86 |
% 110.79/15.86 | REDUCE: (4), (5) imply:
% 110.79/15.86 | (6) $false
% 110.79/15.86 |
% 110.79/15.86 | CLOSE: (6) is inconsistent.
% 110.79/15.86 |
% 110.79/15.86 End of proof
% 110.79/15.86
% 110.79/15.86 Sub-proof #20 shows that the following formulas are inconsistent:
% 110.79/15.86 ----------------------------------------------------------------
% 110.79/15.86 (1) ~ (all_53_10 = e1)
% 110.79/15.86 (2) op(e2, e3) = all_53_10
% 110.79/15.86 (3) ~ (e3 = e1)
% 110.79/15.86 (4) (all_57_72 = e1 & op(e2, e3) = e1) | (all_57_73 = e1 & op(e2, e2) = e1)
% 110.79/15.86 (5) op(e2, e2) = e3
% 110.79/15.86 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.86
% 110.79/15.86 Begin of proof
% 110.79/15.86 |
% 110.79/15.86 | BETA: splitting (4) gives:
% 110.79/15.86 |
% 110.79/15.86 | Case 1:
% 110.79/15.86 | |
% 110.79/15.86 | | (7) all_57_72 = e1 & op(e2, e3) = e1
% 110.79/15.86 | |
% 110.79/15.86 | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #50.
% 110.79/15.86 | |
% 110.79/15.86 | Case 2:
% 110.79/15.86 | |
% 110.79/15.86 | | (8) all_57_73 = e1 & op(e2, e2) = e1
% 110.79/15.86 | |
% 110.79/15.86 | | ALPHA: (8) implies:
% 110.79/15.86 | | (9) op(e2, e2) = e1
% 110.79/15.86 | |
% 110.79/15.86 | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #197.
% 110.79/15.86 | |
% 110.79/15.86 | End of split
% 110.79/15.86 |
% 110.79/15.86 End of proof
% 110.79/15.86
% 110.79/15.86 Sub-proof #21 shows that the following formulas are inconsistent:
% 110.79/15.86 ----------------------------------------------------------------
% 110.79/15.86 (1) all_55_2 = e1 | all_55_2 = e0
% 110.79/15.86 (2) all_55_2 = all_52_2
% 110.79/15.86 (3) ~ (all_52_2 = e1)
% 110.79/15.86 (4) ~ (all_52_2 = e0)
% 110.79/15.86
% 110.79/15.86 Begin of proof
% 110.79/15.86 |
% 110.79/15.86 | BETA: splitting (1) gives:
% 110.79/15.86 |
% 110.79/15.86 | Case 1:
% 110.79/15.86 | |
% 110.79/15.86 | | (5) all_55_2 = e1
% 110.79/15.86 | |
% 110.79/15.86 | | COMBINE_EQS: (2), (5) imply:
% 110.79/15.86 | | (6) all_52_2 = e1
% 110.79/15.86 | |
% 110.79/15.86 | | REDUCE: (3), (6) imply:
% 110.79/15.86 | | (7) $false
% 110.79/15.86 | |
% 110.79/15.86 | | CLOSE: (7) is inconsistent.
% 110.79/15.86 | |
% 110.79/15.86 | Case 2:
% 110.79/15.86 | |
% 110.79/15.86 | | (8) all_55_2 = e0
% 110.79/15.86 | |
% 110.79/15.86 | | COMBINE_EQS: (2), (8) imply:
% 110.79/15.86 | | (9) all_52_2 = e0
% 110.79/15.86 | |
% 110.79/15.86 | | REDUCE: (4), (9) imply:
% 110.79/15.86 | | (10) $false
% 110.79/15.86 | |
% 110.79/15.86 | | CLOSE: (10) is inconsistent.
% 110.79/15.86 | |
% 110.79/15.86 | End of split
% 110.79/15.86 |
% 110.79/15.86 End of proof
% 110.79/15.86
% 110.79/15.86 Sub-proof #22 shows that the following formulas are inconsistent:
% 110.79/15.86 ----------------------------------------------------------------
% 110.79/15.86 (1) ~ (all_53_7 = e2)
% 110.79/15.86 (2) ~ (all_53_7 = e3)
% 110.79/15.86 (3) ~ (all_53_6 = e3)
% 110.79/15.86 (4) all_55_7 = all_53_6
% 110.79/15.86 (5) ~ (all_53_6 = all_53_7)
% 110.79/15.86 (6) all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 110.79/15.86 (7) ~ (all_53_7 = e0)
% 110.79/15.86 (8) all_55_6 = all_53_7
% 110.79/15.86 (9) ~ (all_53_6 = e2)
% 110.79/15.86 (10) all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 110.79/15.86 (11) ~ (all_53_6 = e0)
% 110.79/15.86
% 110.79/15.86 Begin of proof
% 110.79/15.86 |
% 110.79/15.86 | BETA: splitting (6) gives:
% 110.79/15.86 |
% 110.79/15.86 | Case 1:
% 110.79/15.86 | |
% 110.79/15.86 | | (12) all_55_6 = e3
% 110.79/15.86 | |
% 110.79/15.86 | | REF_CLOSE: (2), (8), (12) are inconsistent by sub-proof #135.
% 110.79/15.86 | |
% 110.79/15.86 | Case 2:
% 110.79/15.86 | |
% 110.79/15.86 | | (13) all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 110.79/15.86 | |
% 110.79/15.86 | | BETA: splitting (10) gives:
% 110.79/15.86 | |
% 110.79/15.86 | | Case 1:
% 110.79/15.86 | | |
% 110.79/15.86 | | | (14) all_55_7 = e3
% 110.79/15.86 | | |
% 110.79/15.86 | | | COMBINE_EQS: (4), (14) imply:
% 110.79/15.86 | | | (15) all_53_6 = e3
% 110.79/15.86 | | |
% 110.79/15.86 | | | REDUCE: (3), (15) imply:
% 110.79/15.86 | | | (16) $false
% 110.79/15.86 | | |
% 110.79/15.86 | | | CLOSE: (16) is inconsistent.
% 110.79/15.86 | | |
% 110.79/15.86 | | Case 2:
% 110.79/15.86 | | |
% 110.79/15.87 | | | (17) all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 110.79/15.87 | | |
% 110.79/15.87 | | | BETA: splitting (13) gives:
% 110.79/15.87 | | |
% 110.79/15.87 | | | Case 1:
% 110.79/15.87 | | | |
% 110.79/15.87 | | | | (18) all_55_6 = e2
% 110.79/15.87 | | | |
% 110.79/15.87 | | | | COMBINE_EQS: (8), (18) imply:
% 110.79/15.87 | | | | (19) all_53_7 = e2
% 110.79/15.87 | | | |
% 110.79/15.87 | | | | REDUCE: (1), (19) imply:
% 110.79/15.87 | | | | (20) $false
% 110.79/15.87 | | | |
% 110.79/15.87 | | | | CLOSE: (20) is inconsistent.
% 110.79/15.87 | | | |
% 110.79/15.87 | | | Case 2:
% 110.79/15.87 | | | |
% 110.79/15.87 | | | | (21) all_55_6 = e1 | all_55_6 = e0
% 110.79/15.87 | | | |
% 110.79/15.87 | | | | BETA: splitting (17) gives:
% 110.79/15.87 | | | |
% 110.79/15.87 | | | | Case 1:
% 110.79/15.87 | | | | |
% 110.79/15.87 | | | | | (22) all_55_7 = e2
% 110.79/15.87 | | | | |
% 110.79/15.87 | | | | | COMBINE_EQS: (4), (22) imply:
% 110.79/15.87 | | | | | (23) all_53_6 = e2
% 110.79/15.87 | | | | |
% 110.79/15.87 | | | | | SIMP: (23) implies:
% 110.79/15.87 | | | | | (24) all_53_6 = e2
% 110.79/15.87 | | | | |
% 110.79/15.87 | | | | | REDUCE: (9), (24) imply:
% 110.79/15.87 | | | | | (25) $false
% 110.79/15.87 | | | | |
% 110.79/15.87 | | | | | CLOSE: (25) is inconsistent.
% 110.79/15.87 | | | | |
% 110.79/15.87 | | | | Case 2:
% 110.79/15.87 | | | | |
% 110.79/15.87 | | | | | (26) all_55_7 = e1 | all_55_7 = e0
% 110.79/15.87 | | | | |
% 110.79/15.87 | | | | | BETA: splitting (26) gives:
% 110.79/15.87 | | | | |
% 110.79/15.87 | | | | | Case 1:
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | | (27) all_55_7 = e1
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | | COMBINE_EQS: (4), (27) imply:
% 110.79/15.87 | | | | | | (28) all_53_6 = e1
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | | SIMP: (28) implies:
% 110.79/15.87 | | | | | | (29) all_53_6 = e1
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | | REDUCE: (5), (29) imply:
% 110.79/15.87 | | | | | | (30) ~ (all_53_7 = e1)
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | | SIMP: (30) implies:
% 110.79/15.87 | | | | | | (31) ~ (all_53_7 = e1)
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | | REF_CLOSE: (7), (8), (21), (31) are inconsistent by sub-proof #115.
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | Case 2:
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | | (32) all_55_7 = e0
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | | COMBINE_EQS: (4), (32) imply:
% 110.79/15.87 | | | | | | (33) all_53_6 = e0
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | | SIMP: (33) implies:
% 110.79/15.87 | | | | | | (34) all_53_6 = e0
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | | REDUCE: (11), (34) imply:
% 110.79/15.87 | | | | | | (35) $false
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | | CLOSE: (35) is inconsistent.
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | End of split
% 110.79/15.87 | | | | |
% 110.79/15.87 | | | | End of split
% 110.79/15.87 | | | |
% 110.79/15.87 | | | End of split
% 110.79/15.87 | | |
% 110.79/15.87 | | End of split
% 110.79/15.87 | |
% 110.79/15.87 | End of split
% 110.79/15.87 |
% 110.79/15.87 End of proof
% 110.79/15.87
% 110.79/15.87 Sub-proof #23 shows that the following formulas are inconsistent:
% 110.79/15.87 ----------------------------------------------------------------
% 110.79/15.87 (1) ~ (all_53_3 = all_53_7)
% 110.79/15.87 (2) ~ (all_53_9 = e1)
% 110.79/15.87 (3) op(e3, e0) = all_53_12
% 110.79/15.87 (4) ~ (all_53_9 = e3)
% 110.79/15.87 (5) ~ (all_53_15 = e3)
% 110.79/15.87 (6) op(e2, e3) = all_53_10
% 110.79/15.87 (7) ~ (all_53_7 = e3)
% 110.79/15.87 (8) op(e1, e0) = all_53_4
% 110.79/15.87 (9) ~ (all_53_4 = all_53_12)
% 110.79/15.87 (10) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 110.79/15.87 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 110.79/15.87 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 110.79/15.87 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0
% 110.79/15.87 & $i(all_52_16))
% 110.79/15.87 (11) op(e3, e2) = all_53_15
% 110.79/15.87 (12) ~ (all_53_4 = e1)
% 110.79/15.87 (13) op(e1, e2) = all_53_7
% 110.79/15.87 (14) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 110.79/15.87 (15) ~ (e3 = e1)
% 110.79/15.87 (16) ~ (all_53_4 = all_53_8)
% 110.79/15.87 (17) all_55_4 = all_53_4
% 110.79/15.87 (18) ~ (all_53_8 = e1)
% 110.79/15.87 (19) all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 110.79/15.87 (20) op(e2, e1) = all_53_9
% 110.79/15.87 (21) ~ (all_53_7 = all_53_15)
% 110.79/15.87 (22) (all_57_72 = e1 & op(e2, e3) = e1) | (all_57_73 = e1 & op(e2, e2) = e1)
% 110.79/15.87 | (all_57_74 = e1 & op(e2, e1) = e1) | (all_57_75 = e1 & op(e2, e0) =
% 110.79/15.87 e1)
% 110.79/15.87 (23) all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 110.79/15.87 (24) all_55_6 = all_53_7
% 110.79/15.87 (25) ~ (all_53_3 = e1)
% 110.79/15.87 (26) (all_57_76 = e1 & op(e3, e2) = e1) | (all_57_77 = e1 & op(e2, e2) = e1)
% 110.79/15.87 | (all_57_78 = e1 & op(e1, e2) = e1) | (all_57_79 = e1 & op(e0, e2) =
% 110.79/15.87 e1)
% 110.79/15.87 (27) op(e2, e0) = all_53_8
% 110.79/15.87 (28) ~ (all_53_9 = all_53_10)
% 110.79/15.87 (29) op(e2, e2) = e3
% 110.79/15.87 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.87 (31) all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 110.79/15.87 (32) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 110.79/15.87 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 110.79/15.87 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 110.79/15.87 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 110.79/15.87 $i(all_52_4))
% 110.79/15.87 (33) ~ (all_53_8 = e3)
% 110.79/15.87 (34) ~ (all_53_4 = all_53_7)
% 110.79/15.87 (35) ~ (all_53_7 = e1)
% 110.79/15.87 (36) all_55_8 = all_53_8
% 110.79/15.87 (37) all_55_9 = all_53_9
% 110.79/15.87 (38) ~ (all_53_8 = all_53_9)
% 110.79/15.87 (39) op(e0, e2) = all_53_3
% 110.79/15.87
% 110.79/15.87 Begin of proof
% 110.79/15.87 |
% 110.79/15.87 | BETA: splitting (10) gives:
% 110.79/15.87 |
% 110.79/15.87 | Case 1:
% 110.79/15.87 | |
% 110.79/15.87 | | (40) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3)
% 110.79/15.87 | | = all_52_12 & $i(all_52_12)
% 110.79/15.87 | |
% 110.79/15.87 | | ALPHA: (40) implies:
% 110.79/15.87 | | (41) op(e3, e2) = e3
% 110.79/15.87 | |
% 110.79/15.87 | | REF_CLOSE: (5), (11), (30), (41) are inconsistent by sub-proof #214.
% 110.79/15.87 | |
% 110.79/15.87 | Case 2:
% 110.79/15.87 | |
% 110.79/15.87 | | (42) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 110.79/15.87 | | op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~ (all_52_16
% 110.79/15.87 | | = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 110.79/15.87 | | $i(all_52_16))
% 110.79/15.87 | |
% 110.79/15.87 | | BETA: splitting (42) gives:
% 110.79/15.87 | |
% 110.79/15.87 | | Case 1:
% 110.79/15.87 | | |
% 110.79/15.87 | | | (43) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 110.79/15.87 | | | op(e1, e2) = e1 & $i(all_52_14)
% 110.79/15.87 | | |
% 110.79/15.87 | | | ALPHA: (43) implies:
% 110.79/15.87 | | | (44) op(e1, e2) = e1
% 110.79/15.87 | | |
% 110.79/15.87 | | | REF_CLOSE: (13), (30), (35), (44) are inconsistent by sub-proof #233.
% 110.79/15.87 | | |
% 110.79/15.87 | | Case 2:
% 110.79/15.87 | | |
% 110.79/15.87 | | | (45) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 &
% 110.79/15.87 | | | op(e0, e2) = e0 & $i(all_52_16)
% 110.79/15.87 | | |
% 110.79/15.87 | | | ALPHA: (45) implies:
% 110.79/15.87 | | | (46) ~ (all_52_16 = e2)
% 110.79/15.87 | | | (47) op(e0, e2) = e0
% 110.79/15.87 | | | (48) op(e2, e0) = all_52_16
% 110.79/15.87 | | |
% 110.79/15.87 | | | BETA: splitting (26) gives:
% 110.79/15.87 | | |
% 110.79/15.87 | | | Case 1:
% 110.79/15.87 | | | |
% 110.79/15.87 | | | | (49) (all_57_76 = e1 & op(e3, e2) = e1) | (all_57_77 = e1 & op(e2,
% 110.79/15.87 | | | | e2) = e1)
% 110.79/15.87 | | | |
% 110.79/15.87 | | | | BETA: splitting (49) gives:
% 110.79/15.87 | | | |
% 110.79/15.87 | | | | Case 1:
% 110.79/15.87 | | | | |
% 110.79/15.87 | | | | | (50) all_57_76 = e1 & op(e3, e2) = e1
% 110.79/15.87 | | | | |
% 110.79/15.87 | | | | | ALPHA: (50) implies:
% 110.79/15.87 | | | | | (51) op(e3, e2) = e1
% 110.79/15.87 | | | | |
% 110.79/15.87 | | | | | BETA: splitting (22) gives:
% 110.79/15.87 | | | | |
% 110.79/15.87 | | | | | Case 1:
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | | (52) (all_57_72 = e1 & op(e2, e3) = e1) | (all_57_73 = e1 &
% 110.79/15.87 | | | | | | op(e2, e2) = e1)
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | | BETA: splitting (52) gives:
% 110.79/15.87 | | | | | |
% 110.79/15.87 | | | | | | Case 1:
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | (53) all_57_72 = e1 & op(e2, e3) = e1
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | ALPHA: (53) implies:
% 110.79/15.87 | | | | | | | (54) op(e2, e3) = e1
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | GROUND_INST: instantiating (30) with all_53_3, e0, e2, e0,
% 110.79/15.87 | | | | | | | simplifying with (39), (47) gives:
% 110.79/15.87 | | | | | | | (55) all_53_3 = e0
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | GROUND_INST: instantiating (30) with all_53_8, all_52_16, e0, e2,
% 110.79/15.87 | | | | | | | simplifying with (27), (48) gives:
% 110.79/15.87 | | | | | | | (56) all_53_8 = all_52_16
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | GROUND_INST: instantiating (30) with all_53_10, e1, e3, e2,
% 110.79/15.87 | | | | | | | simplifying with (6), (54) gives:
% 110.79/15.87 | | | | | | | (57) all_53_10 = e1
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | GROUND_INST: instantiating (30) with all_53_15, e1, e2, e3,
% 110.79/15.87 | | | | | | | simplifying with (11), (51) gives:
% 110.79/15.87 | | | | | | | (58) all_53_15 = e1
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | COMBINE_EQS: (36), (56) imply:
% 110.79/15.87 | | | | | | | (59) all_55_8 = all_52_16
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | REDUCE: (1), (55) imply:
% 110.79/15.87 | | | | | | | (60) ~ (all_53_7 = e0)
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | SIMP: (60) implies:
% 110.79/15.87 | | | | | | | (61) ~ (all_53_7 = e0)
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | REDUCE: (16), (56) imply:
% 110.79/15.87 | | | | | | | (62) ~ (all_53_4 = all_52_16)
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | REDUCE: (38), (56) imply:
% 110.79/15.87 | | | | | | | (63) ~ (all_53_9 = all_52_16)
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | SIMP: (63) implies:
% 110.79/15.87 | | | | | | | (64) ~ (all_53_9 = all_52_16)
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | REDUCE: (33), (56) imply:
% 110.79/15.87 | | | | | | | (65) ~ (all_52_16 = e3)
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | REDUCE: (18), (56) imply:
% 110.79/15.87 | | | | | | | (66) ~ (all_52_16 = e1)
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | BETA: splitting (23) gives:
% 110.79/15.87 | | | | | | |
% 110.79/15.87 | | | | | | | Case 1:
% 110.79/15.87 | | | | | | | |
% 110.79/15.87 | | | | | | | | (67) all_55_6 = e3
% 110.79/15.87 | | | | | | | |
% 110.79/15.87 | | | | | | | | REF_CLOSE: (7), (24), (67) are inconsistent by sub-proof #135.
% 110.79/15.87 | | | | | | | |
% 110.79/15.87 | | | | | | | Case 2:
% 110.79/15.87 | | | | | | | |
% 110.79/15.87 | | | | | | | | (68) all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 110.79/15.87 | | | | | | | |
% 110.79/15.87 | | | | | | | | BETA: splitting (31) gives:
% 110.79/15.87 | | | | | | | |
% 110.79/15.87 | | | | | | | | Case 1:
% 110.79/15.87 | | | | | | | | |
% 110.79/15.87 | | | | | | | | | (69) all_55_8 = e3
% 110.79/15.87 | | | | | | | | |
% 110.79/15.87 | | | | | | | | | COMBINE_EQS: (59), (69) imply:
% 110.79/15.87 | | | | | | | | | (70) all_52_16 = e3
% 110.79/15.87 | | | | | | | | |
% 110.79/15.87 | | | | | | | | | SIMP: (70) implies:
% 110.79/15.87 | | | | | | | | | (71) all_52_16 = e3
% 110.79/15.87 | | | | | | | | |
% 110.79/15.87 | | | | | | | | | REDUCE: (65), (71) imply:
% 110.79/15.87 | | | | | | | | | (72) $false
% 110.79/15.87 | | | | | | | | |
% 110.79/15.87 | | | | | | | | | CLOSE: (72) is inconsistent.
% 110.79/15.87 | | | | | | | | |
% 110.79/15.87 | | | | | | | | Case 2:
% 110.79/15.87 | | | | | | | | |
% 110.79/15.87 | | | | | | | | | (73) all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 110.79/15.87 | | | | | | | | |
% 110.79/15.87 | | | | | | | | | BETA: splitting (73) gives:
% 110.79/15.87 | | | | | | | | |
% 110.79/15.87 | | | | | | | | | Case 1:
% 110.79/15.87 | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | (74) all_55_8 = e2
% 110.79/15.87 | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | COMBINE_EQS: (59), (74) imply:
% 110.79/15.87 | | | | | | | | | | (75) all_52_16 = e2
% 110.79/15.87 | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | REDUCE: (46), (75) imply:
% 110.79/15.87 | | | | | | | | | | (76) $false
% 110.79/15.87 | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | CLOSE: (76) is inconsistent.
% 110.79/15.87 | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | Case 2:
% 110.79/15.87 | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | (77) all_55_8 = e1 | all_55_8 = e0
% 110.79/15.87 | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | BETA: splitting (68) gives:
% 110.79/15.87 | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | Case 1:
% 110.79/15.87 | | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | | (78) all_55_6 = e2
% 110.79/15.87 | | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | | COMBINE_EQS: (24), (78) imply:
% 110.79/15.87 | | | | | | | | | | | (79) all_53_7 = e2
% 110.79/15.87 | | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | | REDUCE: (34), (79) imply:
% 110.79/15.87 | | | | | | | | | | | (80) ~ (all_53_4 = e2)
% 110.79/15.87 | | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | | BETA: splitting (77) gives:
% 110.79/15.87 | | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | | Case 1:
% 110.79/15.87 | | | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | | | (81) all_55_8 = e1
% 110.79/15.87 | | | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | | | COMBINE_EQS: (59), (81) imply:
% 110.79/15.87 | | | | | | | | | | | | (82) all_52_16 = e1
% 110.79/15.87 | | | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | | | REDUCE: (66), (82) imply:
% 110.79/15.87 | | | | | | | | | | | | (83) $false
% 110.79/15.87 | | | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | | | CLOSE: (83) is inconsistent.
% 110.79/15.87 | | | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | | Case 2:
% 110.79/15.87 | | | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | | | (84) all_55_8 = e0
% 110.79/15.87 | | | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | | | COMBINE_EQS: (59), (84) imply:
% 110.79/15.87 | | | | | | | | | | | | (85) all_52_16 = e0
% 110.79/15.87 | | | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | | | REDUCE: (62), (85) imply:
% 110.79/15.87 | | | | | | | | | | | | (86) ~ (all_53_4 = e0)
% 110.79/15.87 | | | | | | | | | | | |
% 110.79/15.87 | | | | | | | | | | | | REDUCE: (64), (85) imply:
% 110.79/15.87 | | | | | | | | | | | | (87) ~ (all_53_9 = e0)
% 110.79/15.87 | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | BETA: splitting (14) gives:
% 110.79/15.88 | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | Case 1:
% 110.79/15.88 | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | (88) all_55_9 = e3
% 110.79/15.88 | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | COMBINE_EQS: (37), (88) imply:
% 110.79/15.88 | | | | | | | | | | | | | (89) all_53_9 = e3
% 110.79/15.88 | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | REDUCE: (4), (89) imply:
% 110.79/15.88 | | | | | | | | | | | | | (90) $false
% 110.79/15.88 | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | CLOSE: (90) is inconsistent.
% 110.79/15.88 | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | Case 2:
% 110.79/15.88 | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | (91) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 110.79/15.88 | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | BETA: splitting (91) gives:
% 110.79/15.88 | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | Case 1:
% 110.79/15.88 | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | (92) all_55_9 = e2
% 110.79/15.88 | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | COMBINE_EQS: (37), (92) imply:
% 110.79/15.88 | | | | | | | | | | | | | | (93) all_53_9 = e2
% 110.79/15.88 | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | REDUCE: (20), (93) imply:
% 110.79/15.88 | | | | | | | | | | | | | | (94) op(e2, e1) = e2
% 110.79/15.88 | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 110.79/15.88 | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | Case 1:
% 110.79/15.88 | | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | | (95) all_55_4 = e3
% 110.79/15.88 | | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | | COMBINE_EQS: (17), (95) imply:
% 110.79/15.88 | | | | | | | | | | | | | | | (96) all_53_4 = e3
% 110.79/15.88 | | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | | REDUCE: (9), (96) imply:
% 110.79/15.88 | | | | | | | | | | | | | | | (97) ~ (all_53_12 = e3)
% 110.79/15.88 | | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | | SIMP: (97) implies:
% 110.79/15.88 | | | | | | | | | | | | | | | (98) ~ (all_53_12 = e3)
% 110.79/15.88 | | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (12), (20), (27), (30), (32), (38),
% 110.79/15.88 | | | | | | | | | | | | | | | (94), (98) are inconsistent by sub-proof #133.
% 110.79/15.88 | | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | Case 2:
% 110.79/15.88 | | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | | (99) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 110.79/15.88 | | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (80), (86), (99) are inconsistent by
% 110.79/15.88 | | | | | | | | | | | | | | | sub-proof #24.
% 110.79/15.88 | | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | End of split
% 110.79/15.88 | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | Case 2:
% 110.79/15.88 | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | (100) all_55_9 = e1 | all_55_9 = e0
% 110.79/15.88 | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | | REF_CLOSE: (2), (37), (87), (100) are inconsistent by
% 110.79/15.88 | | | | | | | | | | | | | | sub-proof #185.
% 110.79/15.88 | | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | | End of split
% 110.79/15.88 | | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | | End of split
% 110.79/15.88 | | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | End of split
% 110.79/15.88 | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | Case 2:
% 110.79/15.88 | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | (101) all_55_6 = e1 | all_55_6 = e0
% 110.79/15.88 | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | | REF_CLOSE: (24), (35), (61), (101) are inconsistent by
% 110.79/15.88 | | | | | | | | | | | sub-proof #115.
% 110.79/15.88 | | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | | End of split
% 110.79/15.88 | | | | | | | | | |
% 110.79/15.88 | | | | | | | | | End of split
% 110.79/15.88 | | | | | | | | |
% 110.79/15.88 | | | | | | | | End of split
% 110.79/15.88 | | | | | | | |
% 110.79/15.88 | | | | | | | End of split
% 110.79/15.88 | | | | | | |
% 110.79/15.88 | | | | | | Case 2:
% 110.79/15.88 | | | | | | |
% 110.79/15.88 | | | | | | | (102) all_57_73 = e1 & op(e2, e2) = e1
% 110.79/15.88 | | | | | | |
% 110.79/15.88 | | | | | | | ALPHA: (102) implies:
% 110.79/15.88 | | | | | | | (103) op(e2, e2) = e1
% 110.79/15.88 | | | | | | |
% 110.79/15.88 | | | | | | | REF_CLOSE: (15), (29), (30), (103) are inconsistent by sub-proof
% 110.79/15.88 | | | | | | | #197.
% 110.79/15.88 | | | | | | |
% 110.79/15.88 | | | | | | End of split
% 110.79/15.88 | | | | | |
% 110.79/15.88 | | | | | Case 2:
% 110.79/15.88 | | | | | |
% 110.79/15.88 | | | | | | (104) (all_57_74 = e1 & op(e2, e1) = e1) | (all_57_75 = e1 &
% 110.79/15.88 | | | | | | op(e2, e0) = e1)
% 110.79/15.88 | | | | | |
% 110.79/15.88 | | | | | | REF_CLOSE: (2), (18), (20), (27), (30), (104) are inconsistent by
% 110.79/15.88 | | | | | | sub-proof #47.
% 110.79/15.88 | | | | | |
% 110.79/15.88 | | | | | End of split
% 110.79/15.88 | | | | |
% 110.79/15.88 | | | | Case 2:
% 110.79/15.88 | | | | |
% 110.79/15.88 | | | | | (105) all_57_77 = e1 & op(e2, e2) = e1
% 110.79/15.88 | | | | |
% 110.79/15.88 | | | | | ALPHA: (105) implies:
% 110.79/15.88 | | | | | (106) op(e2, e2) = e1
% 110.79/15.88 | | | | |
% 110.79/15.88 | | | | | REF_CLOSE: (15), (29), (30), (106) are inconsistent by sub-proof #197.
% 110.79/15.88 | | | | |
% 110.79/15.88 | | | | End of split
% 110.79/15.88 | | | |
% 110.79/15.88 | | | Case 2:
% 110.79/15.88 | | | |
% 110.79/15.88 | | | | (107) (all_57_78 = e1 & op(e1, e2) = e1) | (all_57_79 = e1 & op(e0,
% 110.79/15.88 | | | | e2) = e1)
% 110.79/15.88 | | | |
% 110.79/15.88 | | | | REF_CLOSE: (13), (25), (30), (35), (39), (107) are inconsistent by
% 110.79/15.88 | | | | sub-proof #203.
% 110.79/15.88 | | | |
% 110.79/15.88 | | | End of split
% 110.79/15.88 | | |
% 110.79/15.88 | | End of split
% 110.79/15.88 | |
% 110.79/15.88 | End of split
% 110.79/15.88 |
% 110.79/15.88 End of proof
% 110.79/15.88
% 110.79/15.88 Sub-proof #24 shows that the following formulas are inconsistent:
% 110.79/15.88 ----------------------------------------------------------------
% 110.79/15.88 (1) ~ (all_53_4 = e2)
% 110.79/15.88 (2) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 110.79/15.88 (3) ~ (all_53_4 = e1)
% 110.79/15.88 (4) all_55_4 = all_53_4
% 110.79/15.88 (5) ~ (all_53_4 = e0)
% 110.79/15.88
% 110.79/15.88 Begin of proof
% 110.79/15.88 |
% 110.79/15.88 | BETA: splitting (2) gives:
% 110.79/15.88 |
% 110.79/15.88 | Case 1:
% 110.79/15.88 | |
% 110.79/15.88 | | (6) all_55_4 = e2
% 110.79/15.88 | |
% 110.79/15.88 | | COMBINE_EQS: (4), (6) imply:
% 110.79/15.88 | | (7) all_53_4 = e2
% 110.79/15.88 | |
% 110.79/15.88 | | REDUCE: (1), (7) imply:
% 110.79/15.88 | | (8) $false
% 110.79/15.88 | |
% 110.79/15.88 | | CLOSE: (8) is inconsistent.
% 110.79/15.88 | |
% 110.79/15.88 | Case 2:
% 110.79/15.88 | |
% 110.79/15.88 | | (9) all_55_4 = e1 | all_55_4 = e0
% 110.79/15.88 | |
% 110.79/15.88 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #104.
% 110.79/15.88 | |
% 110.79/15.88 | End of split
% 110.79/15.88 |
% 110.79/15.88 End of proof
% 110.79/15.88
% 110.79/15.88 Sub-proof #25 shows that the following formulas are inconsistent:
% 110.79/15.88 ----------------------------------------------------------------
% 110.79/15.88 (1) ~ (all_53_1 = e0)
% 110.79/15.88 (2) ~ (e2 = e1)
% 110.79/15.88 (3) op(e0, e1) = all_53_1
% 110.79/15.88 (4) op(e2, e1) = e1
% 110.79/15.88 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.88 (6) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 110.79/15.88 all_52_8 & $i(all_52_8)) | (all_52_11 = e0 & ~ (all_52_10 = e1) &
% 110.79/15.88 op(e1, e0) = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 110.79/15.88
% 110.79/15.88 Begin of proof
% 110.79/15.88 |
% 110.79/15.88 | BETA: splitting (6) gives:
% 110.79/15.88 |
% 110.79/15.88 | Case 1:
% 110.79/15.88 | |
% 110.79/15.88 | | (7) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 110.79/15.88 | | all_52_8 & $i(all_52_8)
% 110.79/15.88 | |
% 110.79/15.88 | | ALPHA: (7) implies:
% 110.79/15.88 | | (8) op(e2, e1) = e2
% 110.79/15.88 | |
% 110.79/15.88 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #31.
% 110.79/15.88 | |
% 110.79/15.88 | Case 2:
% 110.79/15.88 | |
% 110.79/15.88 | | (9) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 &
% 110.79/15.88 | | op(e0, e1) = e0 & $i(all_52_10)
% 110.79/15.88 | |
% 110.79/15.88 | | ALPHA: (9) implies:
% 110.79/15.88 | | (10) op(e0, e1) = e0
% 110.79/15.88 | |
% 110.79/15.88 | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #230.
% 110.79/15.88 | |
% 110.79/15.88 | End of split
% 110.79/15.88 |
% 110.79/15.88 End of proof
% 110.79/15.88
% 110.79/15.88 Sub-proof #26 shows that the following formulas are inconsistent:
% 110.79/15.88 ----------------------------------------------------------------
% 110.79/15.88 (1) ~ (all_53_15 = e0)
% 110.79/15.88 (2) ~ (all_53_15 = e1)
% 110.79/15.88 (3) ~ (all_53_15 = e2)
% 110.79/15.88 (4) all_55_14 = all_53_15
% 110.79/15.88 (5) all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 110.79/15.88
% 110.79/15.88 Begin of proof
% 110.79/15.88 |
% 110.79/15.88 | BETA: splitting (5) gives:
% 110.79/15.88 |
% 110.79/15.88 | Case 1:
% 110.79/15.88 | |
% 110.79/15.88 | | (6) all_55_14 = e2
% 110.79/15.88 | |
% 110.79/15.88 | | COMBINE_EQS: (4), (6) imply:
% 110.79/15.88 | | (7) all_53_15 = e2
% 110.79/15.88 | |
% 110.79/15.88 | | REDUCE: (3), (7) imply:
% 110.79/15.88 | | (8) $false
% 110.79/15.88 | |
% 110.79/15.88 | | CLOSE: (8) is inconsistent.
% 110.79/15.88 | |
% 110.79/15.88 | Case 2:
% 110.79/15.88 | |
% 110.79/15.88 | | (9) all_55_14 = e1 | all_55_14 = e0
% 110.79/15.88 | |
% 110.79/15.88 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #103.
% 110.79/15.88 | |
% 110.79/15.88 | End of split
% 110.79/15.88 |
% 110.79/15.88 End of proof
% 110.79/15.88
% 110.79/15.88 Sub-proof #27 shows that the following formulas are inconsistent:
% 110.79/15.88 ----------------------------------------------------------------
% 110.79/15.88 (1) ~ (all_53_12 = e2)
% 110.79/15.88 (2) op(e3, e0) = all_53_12
% 110.79/15.88 (3) ~ (all_53_9 = e3)
% 110.79/15.88 (4) ~ (all_38_0 = e2)
% 110.79/15.88 (5) all_53_15 = e3
% 110.79/15.88 (6) op(e1, e0) = all_53_4
% 110.79/15.88 (7) all_55_12 = all_53_12
% 110.79/15.88 (8) all_55_13 = all_38_0
% 110.79/15.88 (9) ~ (all_53_12 = all_53_15)
% 110.79/15.88 (10) ~ (all_53_4 = e1)
% 110.79/15.88 (11) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 110.79/15.88 (12) op(e2, e1) = all_53_9
% 110.79/15.88 (13) all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 110.79/15.88 (14) op(e2, e0) = all_53_8
% 110.79/15.88 (15) all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 110.79/15.88 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.88 (17) ~ (all_53_15 = all_38_0)
% 110.79/15.88 (18) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 110.79/15.88 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 110.79/15.88 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 110.79/15.88 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 110.79/15.88 $i(all_52_4))
% 110.79/15.88 (19) ~ (all_53_9 = all_38_0)
% 110.79/15.88 (20) ~ (all_53_9 = e0)
% 110.79/15.88 (21) ~ (all_53_12 = e1)
% 110.79/15.88 (22) all_55_9 = all_53_9
% 110.79/15.88 (23) ~ (all_53_8 = all_53_9)
% 110.79/15.88 (24) ~ (all_53_12 = all_38_0)
% 110.79/15.88
% 110.79/15.88 Begin of proof
% 110.79/15.88 |
% 110.79/15.88 | REDUCE: (5), (9) imply:
% 110.79/15.88 | (25) ~ (all_53_12 = e3)
% 110.79/15.88 |
% 110.79/15.88 | REDUCE: (5), (17) imply:
% 110.79/15.88 | (26) ~ (all_38_0 = e3)
% 110.79/15.88 |
% 110.79/15.88 | SIMP: (26) implies:
% 110.79/15.88 | (27) ~ (all_38_0 = e3)
% 110.79/15.88 |
% 110.79/15.88 | BETA: splitting (18) gives:
% 110.79/15.88 |
% 110.79/15.88 | Case 1:
% 110.79/15.88 | |
% 110.79/15.88 | | (28) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 110.79/15.88 | | all_52_0 & $i(all_52_0)
% 110.79/15.88 | |
% 110.79/15.88 | | ALPHA: (28) implies:
% 110.79/15.88 | | (29) op(e3, e0) = e3
% 110.79/15.88 | |
% 110.79/15.88 | | REF_CLOSE: (2), (16), (25), (29) are inconsistent by sub-proof #180.
% 110.79/15.88 | |
% 110.79/15.88 | Case 2:
% 110.79/15.88 | |
% 110.79/15.88 | | (30) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 110.79/15.88 | | all_52_2 & $i(all_52_2)) | (all_52_5 = e1 & ~ (all_52_4 = e0) &
% 110.79/15.88 | | op(e1, e0) = e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 110.79/15.88 | |
% 110.79/15.88 | | BETA: splitting (30) gives:
% 110.79/15.88 | |
% 110.79/15.88 | | Case 1:
% 110.79/15.88 | | |
% 110.79/15.88 | | | (31) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 110.79/15.88 | | | = all_52_2 & $i(all_52_2)
% 110.79/15.88 | | |
% 110.79/15.88 | | | ALPHA: (31) implies:
% 110.79/15.88 | | | (32) op(e2, e0) = e2
% 110.79/15.88 | | |
% 110.79/15.88 | | | BETA: splitting (13) gives:
% 110.79/15.88 | | |
% 110.79/15.88 | | | Case 1:
% 110.79/15.88 | | | |
% 110.79/15.88 | | | | (33) all_55_12 = e3
% 110.79/15.88 | | | |
% 110.79/15.88 | | | | REF_CLOSE: (7), (25), (33) are inconsistent by sub-proof #94.
% 110.79/15.88 | | | |
% 110.79/15.88 | | | Case 2:
% 110.79/15.88 | | | |
% 110.79/15.88 | | | | (34) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 110.79/15.88 | | | |
% 110.79/15.88 | | | | BETA: splitting (34) gives:
% 110.79/15.88 | | | |
% 110.79/15.88 | | | | Case 1:
% 110.79/15.88 | | | | |
% 110.79/15.88 | | | | | (35) all_55_12 = e2
% 110.79/15.88 | | | | |
% 110.79/15.88 | | | | | REF_CLOSE: (1), (7), (35) are inconsistent by sub-proof #93.
% 110.79/15.88 | | | | |
% 110.79/15.88 | | | | Case 2:
% 110.79/15.88 | | | | |
% 110.79/15.88 | | | | | (36) all_55_12 = e1 | all_55_12 = e0
% 110.79/15.88 | | | | |
% 110.79/15.88 | | | | | BETA: splitting (36) gives:
% 110.79/15.88 | | | | |
% 110.79/15.88 | | | | | Case 1:
% 110.79/15.88 | | | | | |
% 110.79/15.88 | | | | | | (37) all_55_12 = e1
% 110.79/15.88 | | | | | |
% 110.79/15.88 | | | | | | REF_CLOSE: (7), (21), (37) are inconsistent by sub-proof #92.
% 110.79/15.88 | | | | | |
% 110.79/15.88 | | | | | Case 2:
% 110.79/15.88 | | | | | |
% 110.79/15.88 | | | | | | (38) all_55_12 = e0
% 110.79/15.88 | | | | | |
% 110.79/15.88 | | | | | | COMBINE_EQS: (7), (38) imply:
% 110.79/15.88 | | | | | | (39) all_53_12 = e0
% 110.79/15.88 | | | | | |
% 110.79/15.88 | | | | | | SIMP: (39) implies:
% 110.79/15.88 | | | | | | (40) all_53_12 = e0
% 110.79/15.88 | | | | | |
% 110.79/15.88 | | | | | | REDUCE: (24), (40) imply:
% 110.79/15.88 | | | | | | (41) ~ (all_38_0 = e0)
% 110.79/15.88 | | | | | |
% 110.79/15.88 | | | | | | SIMP: (41) implies:
% 110.79/15.88 | | | | | | (42) ~ (all_38_0 = e0)
% 110.79/15.88 | | | | | |
% 110.79/15.88 | | | | | | BETA: splitting (15) gives:
% 110.79/15.88 | | | | | |
% 110.79/15.88 | | | | | | Case 1:
% 110.79/15.88 | | | | | | |
% 110.79/15.88 | | | | | | | (43) all_55_13 = e3
% 110.79/15.88 | | | | | | |
% 110.79/15.88 | | | | | | | REF_CLOSE: (8), (27), (43) are inconsistent by sub-proof #30.
% 110.79/15.88 | | | | | | |
% 110.79/15.88 | | | | | | Case 2:
% 110.79/15.88 | | | | | | |
% 110.79/15.88 | | | | | | | (44) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 110.79/15.88 | | | | | | |
% 110.79/15.88 | | | | | | | BETA: splitting (44) gives:
% 110.79/15.88 | | | | | | |
% 110.79/15.88 | | | | | | | Case 1:
% 110.79/15.88 | | | | | | | |
% 110.79/15.88 | | | | | | | | (45) all_55_13 = e2
% 110.79/15.88 | | | | | | | |
% 110.79/15.88 | | | | | | | | REF_CLOSE: (4), (8), (45) are inconsistent by sub-proof #29.
% 110.79/15.88 | | | | | | | |
% 110.79/15.88 | | | | | | | Case 2:
% 110.79/15.88 | | | | | | | |
% 110.79/15.88 | | | | | | | | (46) all_55_13 = e1 | all_55_13 = e0
% 110.79/15.88 | | | | | | | |
% 110.79/15.88 | | | | | | | | BETA: splitting (46) gives:
% 110.79/15.88 | | | | | | | |
% 110.79/15.88 | | | | | | | | Case 1:
% 110.79/15.88 | | | | | | | | |
% 110.79/15.88 | | | | | | | | | (47) all_55_13 = e1
% 110.79/15.88 | | | | | | | | |
% 110.79/15.88 | | | | | | | | | COMBINE_EQS: (8), (47) imply:
% 110.79/15.88 | | | | | | | | | (48) all_38_0 = e1
% 110.79/15.88 | | | | | | | | |
% 110.79/15.88 | | | | | | | | | SIMP: (48) implies:
% 110.79/15.88 | | | | | | | | | (49) all_38_0 = e1
% 110.79/15.88 | | | | | | | | |
% 110.79/15.88 | | | | | | | | | REDUCE: (19), (49) imply:
% 110.79/15.88 | | | | | | | | | (50) ~ (all_53_9 = e1)
% 110.79/15.88 | | | | | | | | |
% 110.79/15.88 | | | | | | | | | BETA: splitting (11) gives:
% 110.79/15.89 | | | | | | | | |
% 110.79/15.89 | | | | | | | | | Case 1:
% 110.79/15.89 | | | | | | | | | |
% 110.79/15.89 | | | | | | | | | | (51) all_55_9 = e3
% 110.79/15.89 | | | | | | | | | |
% 110.79/15.89 | | | | | | | | | | COMBINE_EQS: (22), (51) imply:
% 110.79/15.89 | | | | | | | | | | (52) all_53_9 = e3
% 110.79/15.89 | | | | | | | | | |
% 110.79/15.89 | | | | | | | | | | REDUCE: (3), (52) imply:
% 110.79/15.89 | | | | | | | | | | (53) $false
% 110.79/15.89 | | | | | | | | | |
% 110.79/15.89 | | | | | | | | | | CLOSE: (53) is inconsistent.
% 110.79/15.89 | | | | | | | | | |
% 110.79/15.89 | | | | | | | | | Case 2:
% 110.79/15.89 | | | | | | | | | |
% 110.79/15.89 | | | | | | | | | | (54) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 110.79/15.89 | | | | | | | | | |
% 110.79/15.89 | | | | | | | | | | REF_CLOSE: (12), (14), (16), (20), (22), (23), (32), (50),
% 110.79/15.89 | | | | | | | | | | (54) are inconsistent by sub-proof #184.
% 110.79/15.89 | | | | | | | | | |
% 110.79/15.89 | | | | | | | | | End of split
% 110.79/15.89 | | | | | | | | |
% 110.79/15.89 | | | | | | | | Case 2:
% 110.79/15.89 | | | | | | | | |
% 110.79/15.89 | | | | | | | | | (55) all_55_13 = e0
% 110.79/15.89 | | | | | | | | |
% 110.79/15.89 | | | | | | | | | REF_CLOSE: (8), (42), (55) are inconsistent by sub-proof #28.
% 110.79/15.89 | | | | | | | | |
% 110.79/15.89 | | | | | | | | End of split
% 110.79/15.89 | | | | | | | |
% 110.79/15.89 | | | | | | | End of split
% 110.79/15.89 | | | | | | |
% 110.79/15.89 | | | | | | End of split
% 110.79/15.89 | | | | | |
% 110.79/15.89 | | | | | End of split
% 110.79/15.89 | | | | |
% 110.79/15.89 | | | | End of split
% 110.79/15.89 | | | |
% 110.79/15.89 | | | End of split
% 110.79/15.89 | | |
% 110.79/15.89 | | Case 2:
% 110.79/15.89 | | |
% 110.79/15.89 | | | (56) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 110.79/15.89 | | | = all_52_4 & $i(all_52_4)
% 110.79/15.89 | | |
% 110.79/15.89 | | | ALPHA: (56) implies:
% 110.79/15.89 | | | (57) op(e1, e0) = e1
% 110.79/15.89 | | |
% 110.79/15.89 | | | REF_CLOSE: (6), (10), (16), (57) are inconsistent by sub-proof #226.
% 110.79/15.89 | | |
% 110.79/15.89 | | End of split
% 110.79/15.89 | |
% 110.79/15.89 | End of split
% 110.79/15.89 |
% 110.79/15.89 End of proof
% 110.79/15.89
% 110.79/15.89 Sub-proof #28 shows that the following formulas are inconsistent:
% 110.79/15.89 ----------------------------------------------------------------
% 110.79/15.89 (1) all_55_13 = all_38_0
% 110.79/15.89 (2) all_55_13 = e0
% 110.79/15.89 (3) ~ (all_38_0 = e0)
% 110.79/15.89
% 110.79/15.89 Begin of proof
% 110.79/15.89 |
% 110.79/15.89 | COMBINE_EQS: (1), (2) imply:
% 110.79/15.89 | (4) all_38_0 = e0
% 110.79/15.89 |
% 110.79/15.89 | SIMP: (4) implies:
% 110.79/15.89 | (5) all_38_0 = e0
% 110.79/15.89 |
% 110.79/15.89 | REDUCE: (3), (5) imply:
% 110.79/15.89 | (6) $false
% 110.79/15.89 |
% 110.79/15.89 | CLOSE: (6) is inconsistent.
% 110.79/15.89 |
% 110.79/15.89 End of proof
% 110.79/15.89
% 110.79/15.89 Sub-proof #29 shows that the following formulas are inconsistent:
% 110.79/15.89 ----------------------------------------------------------------
% 110.79/15.89 (1) all_55_13 = all_38_0
% 110.79/15.89 (2) all_55_13 = e2
% 110.79/15.89 (3) ~ (all_38_0 = e2)
% 110.79/15.89
% 110.79/15.89 Begin of proof
% 110.79/15.89 |
% 110.79/15.89 | COMBINE_EQS: (1), (2) imply:
% 110.79/15.89 | (4) all_38_0 = e2
% 110.79/15.89 |
% 110.79/15.89 | SIMP: (4) implies:
% 110.79/15.89 | (5) all_38_0 = e2
% 110.79/15.89 |
% 110.79/15.89 | REDUCE: (3), (5) imply:
% 110.79/15.89 | (6) $false
% 110.79/15.89 |
% 110.79/15.89 | CLOSE: (6) is inconsistent.
% 110.79/15.89 |
% 110.79/15.89 End of proof
% 110.79/15.89
% 110.79/15.89 Sub-proof #30 shows that the following formulas are inconsistent:
% 110.79/15.89 ----------------------------------------------------------------
% 110.79/15.89 (1) all_55_13 = all_38_0
% 110.79/15.89 (2) all_55_13 = e3
% 110.79/15.89 (3) ~ (all_38_0 = e3)
% 110.79/15.89
% 110.79/15.89 Begin of proof
% 110.79/15.89 |
% 110.79/15.89 | COMBINE_EQS: (1), (2) imply:
% 110.79/15.89 | (4) all_38_0 = e3
% 110.79/15.89 |
% 110.79/15.89 | SIMP: (4) implies:
% 110.79/15.89 | (5) all_38_0 = e3
% 110.79/15.89 |
% 110.79/15.89 | REDUCE: (3), (5) imply:
% 110.79/15.89 | (6) $false
% 110.79/15.89 |
% 110.79/15.89 | CLOSE: (6) is inconsistent.
% 110.79/15.89 |
% 110.79/15.89 End of proof
% 110.79/15.89
% 110.79/15.89 Sub-proof #31 shows that the following formulas are inconsistent:
% 110.79/15.89 ----------------------------------------------------------------
% 110.79/15.89 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.89 (2) op(e2, e1) = e2
% 110.79/15.89 (3) op(e2, e1) = e1
% 110.79/15.89 (4) ~ (e2 = e1)
% 110.79/15.89
% 110.79/15.89 Begin of proof
% 110.79/15.89 |
% 110.79/15.89 | GROUND_INST: instantiating (1) with e1, e2, e1, e2, simplifying with (2), (3)
% 110.79/15.89 | gives:
% 110.79/15.89 | (5) e2 = e1
% 110.79/15.89 |
% 110.79/15.89 | REDUCE: (4), (5) imply:
% 110.79/15.89 | (6) $false
% 110.79/15.89 |
% 110.79/15.89 | CLOSE: (6) is inconsistent.
% 110.79/15.89 |
% 110.79/15.89 End of proof
% 110.79/15.89
% 110.79/15.89 Sub-proof #32 shows that the following formulas are inconsistent:
% 110.79/15.89 ----------------------------------------------------------------
% 110.79/15.89 (1) op(e2, e2) = e0
% 110.79/15.89 (2) ~ (all_53_10 = e3)
% 110.79/15.89 (3) op(e3, e0) = all_53_12
% 110.79/15.89 (4) ~ (all_53_9 = e3)
% 110.79/15.89 (5) op(e2, e3) = all_53_10
% 110.79/15.89 (6) op(e1, e0) = all_53_4
% 110.79/15.89 (7) (all_57_88 = e3 & op(e2, e3) = e3) | (all_57_89 = e3 & op(e2, e2) = e3) |
% 110.79/15.89 (all_57_90 = e3 & op(e2, e1) = e3) | (all_57_91 = e3 & op(e2, e0) = e3)
% 110.79/15.89 (8) ~ (all_53_4 = e1)
% 110.79/15.89 (9) ~ (e3 = e0)
% 110.79/15.89 (10) ~ (all_53_12 = e3)
% 110.79/15.89 (11) op(e2, e1) = all_53_9
% 110.79/15.89 (12) op(e2, e0) = all_53_8
% 110.79/15.89 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.89 (14) ~ (e3 = e2)
% 110.79/15.89 (15) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 110.79/15.89 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 110.79/15.89 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 110.79/15.89 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 110.79/15.89 $i(all_52_4))
% 110.79/15.89
% 110.79/15.89 Begin of proof
% 110.79/15.89 |
% 110.79/15.89 | BETA: splitting (15) gives:
% 110.79/15.89 |
% 110.79/15.89 | Case 1:
% 110.79/15.89 | |
% 110.79/15.89 | | (16) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 110.79/15.89 | | all_52_0 & $i(all_52_0)
% 110.79/15.89 | |
% 110.79/15.89 | | ALPHA: (16) implies:
% 110.79/15.89 | | (17) op(e3, e0) = e3
% 110.79/15.89 | |
% 110.79/15.89 | | REF_CLOSE: (3), (10), (13), (17) are inconsistent by sub-proof #180.
% 110.79/15.89 | |
% 110.79/15.89 | Case 2:
% 110.79/15.89 | |
% 110.79/15.89 | | (18) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 110.79/15.89 | | all_52_2 & $i(all_52_2)) | (all_52_5 = e1 & ~ (all_52_4 = e0) &
% 110.79/15.89 | | op(e1, e0) = e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 110.79/15.89 | |
% 110.79/15.89 | | BETA: splitting (18) gives:
% 110.79/15.89 | |
% 110.79/15.89 | | Case 1:
% 110.79/15.89 | | |
% 110.79/15.89 | | | (19) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 110.79/15.89 | | | = all_52_2 & $i(all_52_2)
% 110.79/15.89 | | |
% 110.79/15.89 | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (11), (12), (13), (14), (19) are
% 110.79/15.89 | | | inconsistent by sub-proof #68.
% 110.79/15.89 | | |
% 110.79/15.89 | | Case 2:
% 110.79/15.89 | | |
% 110.79/15.89 | | | (20) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 110.79/15.89 | | | = all_52_4 & $i(all_52_4)
% 110.79/15.89 | | |
% 110.79/15.89 | | | ALPHA: (20) implies:
% 110.79/15.89 | | | (21) op(e1, e0) = e1
% 110.79/15.89 | | |
% 110.79/15.89 | | | REF_CLOSE: (6), (8), (13), (21) are inconsistent by sub-proof #226.
% 110.79/15.89 | | |
% 110.79/15.89 | | End of split
% 110.79/15.89 | |
% 110.79/15.89 | End of split
% 110.79/15.89 |
% 110.79/15.89 End of proof
% 110.79/15.89
% 110.79/15.89 Sub-proof #33 shows that the following formulas are inconsistent:
% 110.79/15.89 ----------------------------------------------------------------
% 110.79/15.89 (1) op(e3, e0) = all_53_12
% 110.79/15.89 (2) op(e1, e0) = all_53_4
% 110.79/15.89 (3) ~ (all_53_8 = e0)
% 110.79/15.89 (4) ~ (all_53_4 = e1)
% 110.79/15.89 (5) ~ (all_53_8 = all_53_12)
% 110.79/15.89 (6) ~ (all_53_8 = e2)
% 110.79/15.89 (7) ~ (all_53_8 = e1)
% 110.79/15.89 (8) op(e2, e0) = all_53_8
% 110.79/15.89 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.89 (10) all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 110.79/15.89 (11) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 110.79/15.89 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 110.79/15.89 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 110.79/15.89 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 110.79/15.89 $i(all_52_4))
% 110.79/15.89 (12) all_55_8 = all_53_8
% 110.79/15.89
% 110.79/15.89 Begin of proof
% 110.79/15.89 |
% 110.79/15.89 | BETA: splitting (11) gives:
% 110.79/15.89 |
% 110.79/15.89 | Case 1:
% 110.79/15.89 | |
% 110.79/15.89 | | (13) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 110.79/15.89 | | all_52_0 & $i(all_52_0)
% 110.79/15.89 | |
% 110.79/15.89 | | ALPHA: (13) implies:
% 110.79/15.89 | | (14) op(e3, e0) = e3
% 110.79/15.89 | |
% 110.79/15.89 | | BETA: splitting (10) gives:
% 110.79/15.89 | |
% 110.79/15.89 | | Case 1:
% 110.79/15.89 | | |
% 110.79/15.89 | | | (15) all_55_8 = e3
% 110.79/15.89 | | |
% 110.79/15.89 | | | COMBINE_EQS: (12), (15) imply:
% 110.79/15.89 | | | (16) all_53_8 = e3
% 110.79/15.89 | | |
% 110.79/15.89 | | | SIMP: (16) implies:
% 110.79/15.89 | | | (17) all_53_8 = e3
% 110.79/15.89 | | |
% 110.79/15.89 | | | REDUCE: (5), (17) imply:
% 110.79/15.89 | | | (18) ~ (all_53_12 = e3)
% 110.79/15.89 | | |
% 110.79/15.89 | | | SIMP: (18) implies:
% 110.79/15.89 | | | (19) ~ (all_53_12 = e3)
% 110.79/15.89 | | |
% 110.79/15.89 | | | REF_CLOSE: (1), (9), (14), (19) are inconsistent by sub-proof #180.
% 110.79/15.89 | | |
% 110.79/15.89 | | Case 2:
% 110.79/15.89 | | |
% 110.79/15.89 | | | (20) all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 110.79/15.89 | | |
% 110.79/15.89 | | | REF_CLOSE: (3), (6), (7), (12), (20) are inconsistent by sub-proof #63.
% 110.79/15.89 | | |
% 110.79/15.89 | | End of split
% 110.79/15.89 | |
% 110.79/15.89 | Case 2:
% 110.79/15.89 | |
% 110.79/15.89 | | (21) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 110.79/15.89 | | all_52_2 & $i(all_52_2)) | (all_52_5 = e1 & ~ (all_52_4 = e0) &
% 110.79/15.89 | | op(e1, e0) = e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 110.79/15.89 | |
% 110.79/15.89 | | BETA: splitting (21) gives:
% 110.79/15.89 | |
% 110.79/15.89 | | Case 1:
% 110.79/15.89 | | |
% 110.79/15.89 | | | (22) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 110.79/15.89 | | | = all_52_2 & $i(all_52_2)
% 110.79/15.89 | | |
% 110.79/15.89 | | | ALPHA: (22) implies:
% 110.79/15.89 | | | (23) op(e2, e0) = e2
% 110.79/15.89 | | |
% 110.79/15.89 | | | BETA: splitting (10) gives:
% 110.79/15.89 | | |
% 110.79/15.89 | | | Case 1:
% 110.79/15.89 | | | |
% 110.79/15.89 | | | | (24) all_55_8 = e3
% 110.79/15.89 | | | |
% 110.79/15.89 | | | | COMBINE_EQS: (12), (24) imply:
% 110.79/15.89 | | | | (25) all_53_8 = e3
% 110.79/15.89 | | | |
% 110.79/15.89 | | | | SIMP: (25) implies:
% 110.79/15.89 | | | | (26) all_53_8 = e3
% 110.79/15.89 | | | |
% 110.79/15.89 | | | | REDUCE: (6), (26) imply:
% 110.79/15.89 | | | | (27) ~ (e3 = e2)
% 110.79/15.89 | | | |
% 110.79/15.89 | | | | REDUCE: (8), (26) imply:
% 110.79/15.89 | | | | (28) op(e2, e0) = e3
% 110.79/15.89 | | | |
% 110.79/15.89 | | | | REF_CLOSE: (8), (9), (23), (27), (28) are inconsistent by sub-proof #69.
% 110.79/15.89 | | | |
% 110.79/15.89 | | | Case 2:
% 110.79/15.89 | | | |
% 110.79/15.89 | | | | (29) all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 110.79/15.89 | | | |
% 110.79/15.89 | | | | REF_CLOSE: (3), (6), (7), (12), (29) are inconsistent by sub-proof #63.
% 110.79/15.89 | | | |
% 110.79/15.89 | | | End of split
% 110.79/15.89 | | |
% 110.79/15.89 | | Case 2:
% 110.79/15.89 | | |
% 110.79/15.89 | | | (30) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 110.79/15.89 | | | = all_52_4 & $i(all_52_4)
% 110.79/15.89 | | |
% 110.79/15.89 | | | ALPHA: (30) implies:
% 110.79/15.89 | | | (31) op(e1, e0) = e1
% 110.79/15.89 | | |
% 110.79/15.89 | | | REF_CLOSE: (2), (4), (9), (31) are inconsistent by sub-proof #226.
% 110.79/15.89 | | |
% 110.79/15.89 | | End of split
% 110.79/15.89 | |
% 110.79/15.89 | End of split
% 110.79/15.89 |
% 110.79/15.89 End of proof
% 110.79/15.89
% 110.79/15.89 Sub-proof #34 shows that the following formulas are inconsistent:
% 110.79/15.89 ----------------------------------------------------------------
% 110.79/15.89 (1) op(e2, e2) = e0
% 110.79/15.89 (2) ~ (all_53_7 = all_6_1)
% 110.79/15.90 (3) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 110.79/15.90 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 110.79/15.90 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 110.79/15.90 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 110.79/15.90 $i(all_52_16))
% 110.79/15.90 (4) op(e3, e2) = all_53_15
% 110.79/15.90 (5) all_55_5 = all_6_1
% 110.79/15.90 (6) op(e1, e2) = all_53_7
% 110.79/15.90 (7) ~ (all_6_1 = e2)
% 110.79/15.90 (8) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 110.79/15.90 (9) ~ (all_53_3 = e1)
% 110.79/15.90 (10) (all_57_76 = e1 & op(e3, e2) = e1) | (all_57_77 = e1 & op(e2, e2) = e1)
% 110.79/15.90 | (all_57_78 = e1 & op(e1, e2) = e1) | (all_57_79 = e1 & op(e0, e2) =
% 110.79/15.90 e1)
% 110.79/15.90 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.90 (12) ~ (all_6_1 = e0)
% 110.79/15.90 (13) ~ (all_6_1 = e3)
% 110.79/15.90 (14) op(e0, e2) = all_53_3
% 110.79/15.90 (15) ~ (all_53_3 = e0)
% 110.79/15.90
% 110.79/15.90 Begin of proof
% 110.79/15.90 |
% 110.79/15.90 | BETA: splitting (8) gives:
% 110.79/15.90 |
% 110.79/15.90 | Case 1:
% 110.79/15.90 | |
% 110.79/15.90 | | (16) all_55_5 = e3
% 110.79/15.90 | |
% 110.79/15.90 | | COMBINE_EQS: (5), (16) imply:
% 110.79/15.90 | | (17) all_6_1 = e3
% 110.79/15.90 | |
% 110.79/15.90 | | REDUCE: (13), (17) imply:
% 110.79/15.90 | | (18) $false
% 110.79/15.90 | |
% 110.79/15.90 | | CLOSE: (18) is inconsistent.
% 110.79/15.90 | |
% 110.79/15.90 | Case 2:
% 110.79/15.90 | |
% 110.79/15.90 | | (19) ~ (all_55_5 = e3)
% 110.79/15.90 | | (20) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 110.79/15.90 | |
% 110.79/15.90 | | BETA: splitting (20) gives:
% 110.79/15.90 | |
% 110.79/15.90 | | Case 1:
% 110.79/15.90 | | |
% 110.79/15.90 | | | (21) all_55_5 = e2
% 110.79/15.90 | | |
% 110.79/15.90 | | | COMBINE_EQS: (5), (21) imply:
% 110.79/15.90 | | | (22) all_6_1 = e2
% 110.79/15.90 | | |
% 110.79/15.90 | | | REDUCE: (7), (22) imply:
% 110.79/15.90 | | | (23) $false
% 110.79/15.90 | | |
% 110.79/15.90 | | | CLOSE: (23) is inconsistent.
% 110.79/15.90 | | |
% 110.79/15.90 | | Case 2:
% 110.79/15.90 | | |
% 110.79/15.90 | | | (24) all_55_5 = e1 | all_55_5 = e0
% 110.79/15.90 | | |
% 110.79/15.90 | | | BETA: splitting (24) gives:
% 110.79/15.90 | | |
% 110.79/15.90 | | | Case 1:
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | (25) all_55_5 = e1
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | COMBINE_EQS: (5), (25) imply:
% 110.79/15.90 | | | | (26) all_6_1 = e1
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | REDUCE: (2), (26) imply:
% 110.79/15.90 | | | | (27) ~ (all_53_7 = e1)
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | REDUCE: (13), (26) imply:
% 110.79/15.90 | | | | (28) ~ (e3 = e1)
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | SIMP: (28) implies:
% 110.79/15.90 | | | | (29) ~ (e3 = e1)
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | REDUCE: (12), (26) imply:
% 110.79/15.90 | | | | (30) ~ (e1 = e0)
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | BETA: splitting (3) gives:
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | Case 1:
% 110.79/15.90 | | | | |
% 110.79/15.90 | | | | | (31) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 &
% 110.79/15.90 | | | | | op(e2, e3) = all_52_12 & $i(all_52_12)
% 110.79/15.90 | | | | |
% 110.79/15.90 | | | | | ALPHA: (31) implies:
% 110.79/15.90 | | | | | (32) op(e3, e2) = e3
% 110.79/15.90 | | | | |
% 110.79/15.90 | | | | | REF_CLOSE: (1), (4), (6), (9), (10), (11), (14), (27), (29), (30),
% 110.79/15.90 | | | | | (32) are inconsistent by sub-proof #35.
% 110.79/15.90 | | | | |
% 110.79/15.90 | | | | Case 2:
% 110.79/15.90 | | | | |
% 110.79/15.90 | | | | | (33) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14
% 110.79/15.90 | | | | | & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~
% 110.79/15.90 | | | | | (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0
% 110.79/15.90 | | | | | & $i(all_52_16))
% 110.79/15.90 | | | | |
% 110.79/15.90 | | | | | REF_CLOSE: (6), (11), (14), (15), (27), (33) are inconsistent by
% 110.79/15.90 | | | | | sub-proof #218.
% 110.79/15.90 | | | | |
% 110.79/15.90 | | | | End of split
% 110.79/15.90 | | | |
% 110.79/15.90 | | | Case 2:
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | (34) all_55_5 = e0
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | COMBINE_EQS: (5), (34) imply:
% 110.79/15.90 | | | | (35) all_6_1 = e0
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | REDUCE: (12), (35) imply:
% 110.79/15.90 | | | | (36) $false
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | CLOSE: (36) is inconsistent.
% 110.79/15.90 | | | |
% 110.79/15.90 | | | End of split
% 110.79/15.90 | | |
% 110.79/15.90 | | End of split
% 110.79/15.90 | |
% 110.79/15.90 | End of split
% 110.79/15.90 |
% 110.79/15.90 End of proof
% 110.79/15.90
% 110.79/15.90 Sub-proof #35 shows that the following formulas are inconsistent:
% 110.79/15.90 ----------------------------------------------------------------
% 110.79/15.90 (1) op(e3, e2) = e3
% 110.79/15.90 (2) op(e2, e2) = e0
% 110.79/15.90 (3) op(e3, e2) = all_53_15
% 110.79/15.90 (4) op(e1, e2) = all_53_7
% 110.79/15.90 (5) ~ (e1 = e0)
% 110.79/15.90 (6) ~ (e3 = e1)
% 110.79/15.90 (7) ~ (all_53_3 = e1)
% 110.79/15.90 (8) (all_57_76 = e1 & op(e3, e2) = e1) | (all_57_77 = e1 & op(e2, e2) = e1) |
% 110.79/15.90 (all_57_78 = e1 & op(e1, e2) = e1) | (all_57_79 = e1 & op(e0, e2) = e1)
% 110.79/15.90 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.90 (10) ~ (all_53_7 = e1)
% 110.79/15.90 (11) op(e0, e2) = all_53_3
% 110.79/15.90
% 110.79/15.90 Begin of proof
% 110.79/15.90 |
% 110.79/15.90 | BETA: splitting (8) gives:
% 110.79/15.90 |
% 110.79/15.90 | Case 1:
% 110.79/15.90 | |
% 110.79/15.90 | | (12) (all_57_76 = e1 & op(e3, e2) = e1) | (all_57_77 = e1 & op(e2, e2) =
% 110.79/15.90 | | e1)
% 110.79/15.90 | |
% 110.79/15.90 | | BETA: splitting (12) gives:
% 110.79/15.90 | |
% 110.79/15.90 | | Case 1:
% 110.79/15.90 | | |
% 110.79/15.90 | | | (13) all_57_76 = e1 & op(e3, e2) = e1
% 110.79/15.90 | | |
% 110.79/15.90 | | | ALPHA: (13) implies:
% 110.79/15.90 | | | (14) op(e3, e2) = e1
% 110.79/15.90 | | |
% 110.79/15.90 | | | REF_CLOSE: (1), (3), (6), (9), (14) are inconsistent by sub-proof #87.
% 110.79/15.90 | | |
% 110.79/15.90 | | Case 2:
% 110.79/15.90 | | |
% 110.79/15.90 | | | (15) all_57_77 = e1 & op(e2, e2) = e1
% 110.79/15.90 | | |
% 110.79/15.90 | | | ALPHA: (15) implies:
% 110.79/15.90 | | | (16) op(e2, e2) = e1
% 110.79/15.90 | | |
% 110.79/15.90 | | | GROUND_INST: instantiating (9) with e0, e1, e2, e2, simplifying with (2),
% 110.79/15.90 | | | (16) gives:
% 110.79/15.90 | | | (17) e1 = e0
% 110.79/15.90 | | |
% 110.79/15.90 | | | REDUCE: (5), (17) imply:
% 110.79/15.90 | | | (18) $false
% 110.79/15.90 | | |
% 110.79/15.90 | | | CLOSE: (18) is inconsistent.
% 110.79/15.90 | | |
% 110.79/15.90 | | End of split
% 110.79/15.90 | |
% 110.79/15.90 | Case 2:
% 110.79/15.90 | |
% 110.79/15.90 | | (19) (all_57_78 = e1 & op(e1, e2) = e1) | (all_57_79 = e1 & op(e0, e2) =
% 110.79/15.90 | | e1)
% 110.79/15.90 | |
% 110.79/15.90 | | REF_CLOSE: (4), (7), (9), (10), (11), (19) are inconsistent by sub-proof
% 110.79/15.90 | | #203.
% 110.79/15.90 | |
% 110.79/15.90 | End of split
% 110.79/15.90 |
% 110.79/15.90 End of proof
% 110.79/15.90
% 110.79/15.90 Sub-proof #36 shows that the following formulas are inconsistent:
% 110.79/15.90 ----------------------------------------------------------------
% 110.79/15.90 (1) ~ (all_53_9 = e2)
% 110.79/15.90 (2) ~ (all_53_1 = e2)
% 110.79/15.90 (3) ~ (all_6_0 = e3)
% 110.79/15.90 (4) ~ (all_53_1 = all_6_0)
% 110.79/15.90 (5) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 110.79/15.90 (6) op(e2, e1) = all_6_0
% 110.79/15.90 (7) op(e0, e1) = all_53_1
% 110.79/15.90 (8) op(e2, e1) = all_53_9
% 110.79/15.90 (9) ~ (all_53_1 = e1)
% 110.79/15.90 (10) op(e3, e1) = all_53_13
% 110.79/15.90 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.90 (12) ~ (all_53_1 = all_53_13)
% 110.79/15.90 (13) ~ (all_6_0 = e2)
% 110.79/15.90 (14) all_55_9 = all_6_0
% 110.79/15.90 (15) ~ (all_6_0 = e1)
% 110.79/15.90 (16) all_55_1 = all_53_1
% 110.79/15.90 (17) all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 110.79/15.90 (18) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 110.79/15.90 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 110.79/15.90 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 110.79/15.90 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 110.79/15.90 $i(all_52_10))
% 110.79/15.90
% 110.79/15.90 Begin of proof
% 110.79/15.90 |
% 110.79/15.90 | BETA: splitting (5) gives:
% 110.79/15.90 |
% 110.79/15.90 | Case 1:
% 110.79/15.90 | |
% 110.79/15.90 | | (19) all_55_9 = e3
% 110.79/15.90 | |
% 110.79/15.90 | | COMBINE_EQS: (14), (19) imply:
% 110.79/15.90 | | (20) all_6_0 = e3
% 110.79/15.90 | |
% 110.79/15.90 | | REDUCE: (3), (20) imply:
% 110.79/15.90 | | (21) $false
% 110.79/15.90 | |
% 110.79/15.90 | | CLOSE: (21) is inconsistent.
% 110.79/15.90 | |
% 110.79/15.90 | Case 2:
% 110.79/15.90 | |
% 110.79/15.90 | | (22) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 110.79/15.90 | |
% 110.79/15.90 | | BETA: splitting (22) gives:
% 110.79/15.90 | |
% 110.79/15.90 | | Case 1:
% 110.79/15.90 | | |
% 110.79/15.90 | | | (23) all_55_9 = e2
% 110.79/15.90 | | |
% 110.79/15.90 | | | COMBINE_EQS: (14), (23) imply:
% 110.79/15.90 | | | (24) all_6_0 = e2
% 110.79/15.90 | | |
% 110.79/15.90 | | | REDUCE: (13), (24) imply:
% 110.79/15.90 | | | (25) $false
% 110.79/15.90 | | |
% 110.79/15.90 | | | CLOSE: (25) is inconsistent.
% 110.79/15.90 | | |
% 110.79/15.90 | | Case 2:
% 110.79/15.90 | | |
% 110.79/15.90 | | | (26) all_55_9 = e1 | all_55_9 = e0
% 110.79/15.90 | | |
% 110.79/15.90 | | | BETA: splitting (26) gives:
% 110.79/15.90 | | |
% 110.79/15.90 | | | Case 1:
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | (27) all_55_9 = e1
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | COMBINE_EQS: (14), (27) imply:
% 110.79/15.90 | | | | (28) all_6_0 = e1
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | REDUCE: (15), (28) imply:
% 110.79/15.90 | | | | (29) $false
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | CLOSE: (29) is inconsistent.
% 110.79/15.90 | | | |
% 110.79/15.90 | | | Case 2:
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | (30) all_55_9 = e0
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | COMBINE_EQS: (14), (30) imply:
% 110.79/15.90 | | | | (31) all_6_0 = e0
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | REDUCE: (4), (31) imply:
% 110.79/15.90 | | | | (32) ~ (all_53_1 = e0)
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | BETA: splitting (18) gives:
% 110.79/15.90 | | | |
% 110.79/15.90 | | | | Case 1:
% 110.79/15.90 | | | | |
% 110.79/15.90 | | | | | (33) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1,
% 110.79/15.90 | | | | | e3) = all_52_6 & $i(all_52_6)
% 110.79/15.90 | | | | |
% 110.79/15.90 | | | | | REF_CLOSE: (2), (9), (10), (11), (12), (16), (17), (32), (33) are
% 110.79/15.90 | | | | | inconsistent by sub-proof #38.
% 110.79/15.90 | | | | |
% 110.79/15.90 | | | | Case 2:
% 110.79/15.90 | | | | |
% 110.79/15.90 | | | | | (34) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1,
% 110.79/15.90 | | | | | e2) = all_52_8 & $i(all_52_8)) | (all_52_11 = e0 & ~
% 110.79/15.90 | | | | | (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0
% 110.79/15.90 | | | | | & $i(all_52_10))
% 110.79/15.90 | | | | |
% 110.79/15.90 | | | | | BETA: splitting (34) gives:
% 110.79/15.90 | | | | |
% 110.79/15.90 | | | | | Case 1:
% 110.79/15.90 | | | | | |
% 110.79/15.90 | | | | | | (35) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 &
% 110.79/15.90 | | | | | | op(e1, e2) = all_52_8 & $i(all_52_8)
% 110.79/15.90 | | | | | |
% 110.79/15.90 | | | | | | REF_CLOSE: (1), (6), (8), (11), (35) are inconsistent by sub-proof
% 110.79/15.90 | | | | | | #37.
% 110.79/15.90 | | | | | |
% 110.79/15.90 | | | | | Case 2:
% 110.79/15.90 | | | | | |
% 110.79/15.90 | | | | | | (36) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0) =
% 110.79/15.90 | | | | | | all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 110.79/15.90 | | | | | |
% 110.79/15.90 | | | | | | ALPHA: (36) implies:
% 110.79/15.90 | | | | | | (37) op(e0, e1) = e0
% 110.79/15.90 | | | | | |
% 110.79/15.90 | | | | | | REF_CLOSE: (7), (11), (32), (37) are inconsistent by sub-proof #230.
% 110.79/15.90 | | | | | |
% 110.79/15.90 | | | | | End of split
% 110.79/15.90 | | | | |
% 110.79/15.90 | | | | End of split
% 110.79/15.90 | | | |
% 110.79/15.90 | | | End of split
% 110.79/15.90 | | |
% 110.79/15.90 | | End of split
% 110.79/15.90 | |
% 110.79/15.90 | End of split
% 110.79/15.90 |
% 110.79/15.90 End of proof
% 110.79/15.90
% 110.79/15.90 Sub-proof #37 shows that the following formulas are inconsistent:
% 110.79/15.90 ----------------------------------------------------------------
% 110.79/15.90 (1) ~ (all_53_9 = e2)
% 110.79/15.90 (2) op(e2, e1) = all_6_0
% 110.79/15.90 (3) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 110.79/15.90 all_52_8 & $i(all_52_8)
% 110.79/15.90 (4) op(e2, e1) = all_53_9
% 110.79/15.90 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.90
% 110.79/15.90 Begin of proof
% 110.79/15.91 |
% 110.79/15.91 | ALPHA: (3) implies:
% 110.79/15.91 | (6) op(e2, e1) = e2
% 110.79/15.91 |
% 110.79/15.91 | GROUND_INST: instantiating (5) with all_53_9, e2, e1, e2, simplifying with
% 110.79/15.91 | (4), (6) gives:
% 110.79/15.91 | (7) all_53_9 = e2
% 110.79/15.91 |
% 110.79/15.91 | GROUND_INST: instantiating (5) with all_53_9, all_6_0, e1, e2, simplifying
% 110.79/15.91 | with (2), (4) gives:
% 110.79/15.91 | (8) all_53_9 = all_6_0
% 110.79/15.91 |
% 110.79/15.91 | COMBINE_EQS: (7), (8) imply:
% 110.79/15.91 | (9) all_6_0 = e2
% 110.79/15.91 |
% 110.79/15.91 | REDUCE: (1), (7) imply:
% 110.79/15.91 | (10) $false
% 110.79/15.91 |
% 110.79/15.91 | CLOSE: (10) is inconsistent.
% 110.79/15.91 |
% 110.79/15.91 End of proof
% 110.79/15.91
% 110.79/15.91 Sub-proof #38 shows that the following formulas are inconsistent:
% 110.79/15.91 ----------------------------------------------------------------
% 110.79/15.91 (1) ~ (all_53_1 = e0)
% 110.79/15.91 (2) ~ (all_53_1 = e2)
% 110.79/15.91 (3) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 110.79/15.91 all_52_6 & $i(all_52_6)
% 110.79/15.91 (4) ~ (all_53_1 = e1)
% 110.79/15.91 (5) op(e3, e1) = all_53_13
% 110.79/15.91 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.91 (7) ~ (all_53_1 = all_53_13)
% 110.79/15.91 (8) all_55_1 = all_53_1
% 110.79/15.91 (9) all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 110.79/15.91
% 110.79/15.91 Begin of proof
% 110.79/15.91 |
% 110.79/15.91 | ALPHA: (3) implies:
% 110.79/15.91 | (10) op(e3, e1) = e3
% 110.79/15.91 |
% 110.79/15.91 | BETA: splitting (9) gives:
% 110.79/15.91 |
% 110.79/15.91 | Case 1:
% 110.79/15.91 | |
% 110.79/15.91 | | (11) all_55_1 = e3
% 110.79/15.91 | |
% 110.79/15.91 | | COMBINE_EQS: (8), (11) imply:
% 110.79/15.91 | | (12) all_53_1 = e3
% 110.79/15.91 | |
% 110.79/15.91 | | SIMP: (12) implies:
% 110.79/15.91 | | (13) all_53_1 = e3
% 110.79/15.91 | |
% 110.79/15.91 | | REDUCE: (7), (13) imply:
% 110.79/15.91 | | (14) ~ (all_53_13 = e3)
% 110.79/15.91 | |
% 110.79/15.91 | | SIMP: (14) implies:
% 110.79/15.91 | | (15) ~ (all_53_13 = e3)
% 110.79/15.91 | |
% 110.79/15.91 | | REF_CLOSE: (5), (6), (10), (15) are inconsistent by sub-proof #232.
% 110.79/15.91 | |
% 110.79/15.91 | Case 2:
% 110.79/15.91 | |
% 110.79/15.91 | | (16) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 110.79/15.91 | |
% 110.79/15.91 | | BETA: splitting (16) gives:
% 110.79/15.91 | |
% 110.79/15.91 | | Case 1:
% 110.79/15.91 | | |
% 110.79/15.91 | | | (17) all_55_1 = e2
% 110.79/15.91 | | |
% 110.79/15.91 | | | REF_CLOSE: (2), (8), (17) are inconsistent by sub-proof #77.
% 110.79/15.91 | | |
% 110.79/15.91 | | Case 2:
% 110.79/15.91 | | |
% 110.79/15.91 | | | (18) all_55_1 = e1 | all_55_1 = e0
% 110.79/15.91 | | |
% 110.79/15.91 | | | REF_CLOSE: (1), (4), (8), (18) are inconsistent by sub-proof #49.
% 110.79/15.91 | | |
% 110.79/15.91 | | End of split
% 110.79/15.91 | |
% 110.79/15.91 | End of split
% 110.79/15.91 |
% 110.79/15.91 End of proof
% 110.79/15.91
% 110.79/15.91 Sub-proof #39 shows that the following formulas are inconsistent:
% 110.79/15.91 ----------------------------------------------------------------
% 110.79/15.91 (1) ~ (all_53_2 = all_53_6)
% 110.79/15.91 (2) all_18_2 = all_6_1
% 110.79/15.91 (3) op(e1, e1) = all_6_1
% 110.79/15.91 (4) op(e0, e0) = e1
% 110.79/15.91 (5) all_20_2 = all_6_1
% 110.79/15.91 (6) ~ (all_18_2 = e3) | (op(e3, e3) = all_18_1 & $i(all_18_1) & ( ~
% 110.79/15.91 (all_18_1 = e2) | ( ~ (all_18_0 = e0) & op(e2, e3) = all_18_0 &
% 110.79/15.91 $i(all_18_0))))
% 110.79/15.91 (7) all_55_15 = all_4_2
% 110.79/15.91 (8) ~ (all_53_6 = all_53_10)
% 110.79/15.91 (9) all_22_2 = all_6_1
% 110.79/15.91 (10) (all_57_40 = e1 & op(e1, e3) = e1) | (all_57_41 = e1 & op(e1, e2) = e1)
% 110.79/15.91 | (all_57_42 = e1 & op(e1, e1) = e1) | (all_57_43 = e1 & op(e1, e0) =
% 110.79/15.91 e1)
% 110.79/15.91 (11) ~ (all_22_2 = e0) | (op(e0, e0) = all_22_1 & $i(all_22_1) & ( ~
% 110.79/15.91 (all_22_1 = e2) | ( ~ (all_22_0 = e3) & op(e2, e0) = all_22_0 &
% 110.79/15.91 $i(all_22_0))))
% 110.79/15.91 (12) ~ (all_20_2 = e3) | (op(e3, e3) = all_20_1 & $i(all_20_1) & ( ~
% 110.79/15.91 (all_20_1 = e0) | ( ~ (all_20_0 = e2) & op(e0, e3) = all_20_0 &
% 110.79/15.91 $i(all_20_0))))
% 110.79/15.91 (13) op(e3, e0) = all_53_12
% 110.79/15.91 (14) ~ (all_10_2 = e3)
% 110.79/15.91 (15) ~ (all_46_2 = e1) | (op(e1, e1) = all_46_1 & $i(all_46_1) & ( ~
% 110.79/15.91 (all_46_1 = e0) | ( ~ (all_46_0 = e3) & op(e0, e1) = all_46_0 &
% 110.79/15.91 $i(all_46_0))))
% 110.79/15.91 (16) op(e2, e3) = all_53_10
% 110.79/15.91 (17) op(e1, e0) = all_53_4
% 110.79/15.91 (18) all_38_1 = all_6_1
% 110.79/15.91 (19) all_55_11 = all_53_10
% 110.79/15.91 (20) ~ (all_53_6 = all_6_1)
% 110.79/15.91 (21) all_55_10 = all_10_2
% 110.79/15.91 (22) all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 110.79/15.91 (23) all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 110.79/15.91 (24) ~ (all_53_7 = all_6_1)
% 110.79/15.91 (25) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 110.79/15.91 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 110.79/15.91 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 110.79/15.91 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0
% 110.79/15.91 & $i(all_52_16))
% 110.79/15.91 (26) op(e3, e2) = all_53_15
% 110.79/15.91 (27) all_55_3 = all_53_2
% 110.79/15.91 (28) ~ (all_38_1 = e3) | ( ~ (all_38_0 = e2) & op(e3, e1) = all_38_0 &
% 110.79/15.91 $i(all_38_0))
% 110.79/15.91 (29) all_55_5 = all_6_1
% 110.79/15.91 (30) ~ (all_53_4 = e1)
% 110.79/15.91 (31) ~ (all_53_1 = all_53_9)
% 110.79/15.91 (32) op(e1, e2) = all_53_7
% 110.79/15.91 (33) ~ (all_53_2 = all_4_2)
% 110.79/15.91 (34) ~ (all_53_12 = all_53_13)
% 110.79/15.91 (35) ~ (all_53_8 = all_10_2)
% 110.79/15.91 (36) ~ (all_6_1 = e2)
% 110.79/15.91 (37) ~ (all_53_12 = all_4_2)
% 110.79/15.91 (38) all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 110.79/15.91 (39) op(e0, e3) = all_53_2
% 110.79/15.91 (40) (all_57_44 = e1 & op(e3, e1) = e1) | (all_57_45 = e1 & op(e2, e1) = e1)
% 110.79/15.91 | (all_57_46 = e1 & op(e1, e1) = e1) | (all_57_47 = e1 & op(e0, e1) =
% 110.79/15.91 e1)
% 110.79/15.91 (41) ~ (all_10_2 = e0)
% 110.79/15.91 (42) (all_57_28 = e3 & op(e3, e0) = e3) | (all_57_29 = e3 & op(e2, e0) = e3)
% 110.79/15.91 | (all_57_30 = e3 & op(e1, e0) = e3) | (all_57_31 = e3 & op(e0, e0) =
% 110.79/15.91 e3)
% 110.79/15.91 (43) op(e0, e1) = all_53_1
% 110.79/15.91 (44) (all_57_52 = e2 & op(e3, e1) = e2) | (all_57_53 = e2 & op(e2, e1) = e2)
% 110.79/15.91 | (all_57_54 = e2 & op(e1, e1) = e2) | (all_57_55 = e2 & op(e0, e1) =
% 110.79/15.91 e2)
% 110.79/15.91 (45) op(e2, e1) = all_53_9
% 110.79/15.91 (46) ~ (all_4_2 = e0)
% 110.79/15.91 (47) (all_57_72 = e1 & op(e2, e3) = e1) | (all_57_73 = e1 & op(e2, e2) = e1)
% 110.79/15.91 | (all_57_74 = e1 & op(e2, e1) = e1) | (all_57_75 = e1 & op(e2, e0) =
% 110.79/15.91 e1)
% 110.79/15.91 (48) ~ (all_53_2 = all_53_3)
% 110.79/15.91 (49) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 110.79/15.91 (50) ~ (all_53_8 = all_53_10)
% 110.79/15.91 (51) ~ (all_53_4 = all_53_6)
% 110.79/15.91 (52) ~ (all_53_9 = all_10_2)
% 110.79/15.91 (53) op(e1, e3) = all_53_6
% 110.79/15.91 (54) ~ (all_53_1 = e1)
% 110.79/15.91 (55) ~ (all_53_7 = all_10_2)
% 110.79/15.91 (56) op(e2, e0) = all_53_8
% 110.79/15.91 (57) op(e3, e1) = all_53_13
% 110.79/15.91 (58) ~ (all_53_9 = all_53_10)
% 110.79/15.91 (59) ~ (all_53_10 = all_4_2)
% 110.79/15.91 (60) all_26_2 = all_4_2
% 110.79/15.91 (61) ~ (all_53_13 = all_4_2)
% 110.79/15.91 (62) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.79/15.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 110.79/15.91 (63) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 110.79/15.91 e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20 = e3) &
% 110.79/15.91 op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23
% 110.79/15.91 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0
% 110.79/15.91 & $i(all_52_22))
% 110.79/15.91 (64) ~ (all_24_2 = e1) | (op(e1, e1) = all_24_1 & $i(all_24_1) & ( ~
% 110.79/15.91 (all_24_1 = e3) | ( ~ (all_24_0 = e0) & op(e3, e1) = all_24_0 &
% 110.79/15.91 $i(all_24_0))))
% 110.79/15.91 (65) ~ (all_53_13 = all_53_15)
% 110.79/15.91 (66) all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 110.79/15.91 (67) ~ (all_53_1 = all_53_13)
% 110.79/15.91 (68) all_46_2 = all_10_2
% 110.79/15.91 (69) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 110.79/15.91 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 110.79/15.91 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 110.79/15.91 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 110.79/15.91 $i(all_52_4))
% 110.79/15.91 (70) ~ (all_53_1 = all_6_1)
% 110.79/15.91 (71) ~ (all_53_10 = all_10_2)
% 110.79/15.91 (72) ~ (all_53_1 = all_53_3)
% 110.79/15.91 (73) ~ (all_53_13 = all_6_1)
% 110.79/15.91 (74) all_55_1 = all_53_1
% 110.79/15.91 (75) ~ (all_53_2 = all_53_10)
% 110.79/15.91 (76) all_24_2 = all_10_2
% 110.79/15.91 (77) ~ (all_26_2 = e2) | (op(e2, e2) = all_26_1 & $i(all_26_1) & ( ~
% 110.79/15.91 (all_26_1 = e0) | ( ~ (all_26_0 = e1) & op(e0, e2) = all_26_0 &
% 110.79/15.91 $i(all_26_0))))
% 110.79/15.91 (78) ~ (all_53_4 = all_6_1)
% 110.79/15.91 (79) all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 110.79/15.92 (80) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 110.79/15.92 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 110.79/15.92 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 110.79/15.92 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 110.79/15.92 $i(all_52_10))
% 110.79/15.92 (81) op(e3, e3) = all_4_2
% 110.79/15.92 (82) ~ (all_53_8 = all_53_9)
% 110.79/15.92 (83) op(e0, e2) = all_53_3
% 110.79/15.92 (84) ~ (all_53_1 = all_53_2)
% 110.79/15.92
% 110.79/15.92 Begin of proof
% 110.79/15.92 |
% 110.79/15.92 | BETA: splitting (6) gives:
% 110.79/15.92 |
% 110.79/15.92 | Case 1:
% 110.79/15.92 | |
% 110.79/15.92 | | (85) ~ (all_18_2 = e3)
% 110.79/15.92 | |
% 110.79/15.92 | | REDUCE: (2), (85) imply:
% 110.79/15.92 | | (86) ~ (all_6_1 = e3)
% 110.79/15.92 | |
% 110.79/15.92 | | BETA: splitting (11) gives:
% 110.79/15.92 | |
% 110.79/15.92 | | Case 1:
% 110.79/15.92 | | |
% 110.79/15.92 | | | (87) ~ (all_22_2 = e0)
% 110.79/15.92 | | |
% 110.79/15.92 | | | REDUCE: (9), (87) imply:
% 110.79/15.92 | | | (88) ~ (all_6_1 = e0)
% 110.79/15.92 | | |
% 110.79/15.92 | | | BETA: splitting (49) gives:
% 110.79/15.92 | | |
% 110.79/15.92 | | | Case 1:
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | (89) all_55_5 = e3
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | COMBINE_EQS: (29), (89) imply:
% 110.79/15.92 | | | | (90) all_6_1 = e3
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | REDUCE: (86), (90) imply:
% 110.79/15.92 | | | | (91) $false
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | CLOSE: (91) is inconsistent.
% 110.79/15.92 | | | |
% 110.79/15.92 | | | Case 2:
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | (92) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | BETA: splitting (92) gives:
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | Case 1:
% 110.79/15.92 | | | | |
% 110.79/15.92 | | | | | (93) all_55_5 = e2
% 110.79/15.92 | | | | |
% 110.79/15.92 | | | | | COMBINE_EQS: (29), (93) imply:
% 110.79/15.92 | | | | | (94) all_6_1 = e2
% 110.79/15.92 | | | | |
% 110.79/15.92 | | | | | REDUCE: (36), (94) imply:
% 110.79/15.92 | | | | | (95) $false
% 110.79/15.92 | | | | |
% 110.79/15.92 | | | | | CLOSE: (95) is inconsistent.
% 110.79/15.92 | | | | |
% 110.79/15.92 | | | | Case 2:
% 110.79/15.92 | | | | |
% 110.79/15.92 | | | | | (96) all_55_5 = e1 | all_55_5 = e0
% 110.79/15.92 | | | | |
% 110.79/15.92 | | | | | BETA: splitting (96) gives:
% 110.79/15.92 | | | | |
% 110.79/15.92 | | | | | Case 1:
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | | (97) all_55_5 = e1
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | | COMBINE_EQS: (29), (97) imply:
% 110.79/15.92 | | | | | | (98) all_6_1 = e1
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | | REDUCE: (20), (98) imply:
% 110.79/15.92 | | | | | | (99) ~ (all_53_6 = e1)
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | | REDUCE: (24), (98) imply:
% 110.79/15.92 | | | | | | (100) ~ (all_53_7 = e1)
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | | REF_CLOSE: (13), (16), (17), (25), (26), (30), (32), (34), (39),
% 110.79/15.92 | | | | | | (43), (45), (48), (50), (53), (56), (57), (58), (62),
% 110.79/15.92 | | | | | | (63), (65), (69), (72), (80), (82), (83), (84), (99),
% 110.79/15.92 | | | | | | (100) are inconsistent by sub-proof #217.
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | Case 2:
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | | (101) all_55_5 = e0
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | | COMBINE_EQS: (29), (101) imply:
% 110.79/15.92 | | | | | | (102) all_6_1 = e0
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | | REDUCE: (88), (102) imply:
% 110.79/15.92 | | | | | | (103) $false
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | | CLOSE: (103) is inconsistent.
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | End of split
% 110.79/15.92 | | | | |
% 110.79/15.92 | | | | End of split
% 110.79/15.92 | | | |
% 110.79/15.92 | | | End of split
% 110.79/15.92 | | |
% 110.79/15.92 | | Case 2:
% 110.79/15.92 | | |
% 110.79/15.92 | | | (104) all_22_2 = e0
% 110.79/15.92 | | |
% 110.79/15.92 | | | REF_CLOSE: (3), (9), (13), (14), (15), (16), (17), (21), (30), (31), (34),
% 110.79/15.92 | | | (35), (38), (40), (41), (43), (45), (47), (52), (54), (56),
% 110.79/15.92 | | | (57), (62), (64), (67), (68), (69), (70), (71), (74), (76),
% 110.79/15.92 | | | (79), (80), (104) are inconsistent by sub-proof #46.
% 110.79/15.92 | | |
% 110.79/15.92 | | End of split
% 110.79/15.92 | |
% 110.79/15.92 | Case 2:
% 110.79/15.92 | |
% 110.79/15.92 | | (105) all_18_2 = e3
% 110.79/15.92 | | (106) op(e3, e3) = all_18_1 & $i(all_18_1) & ( ~ (all_18_1 = e2) | ( ~
% 110.79/15.92 | | (all_18_0 = e0) & op(e2, e3) = all_18_0 & $i(all_18_0)))
% 110.79/15.92 | |
% 110.79/15.92 | | ALPHA: (106) implies:
% 110.79/15.92 | | (107) op(e3, e3) = all_18_1
% 110.79/15.92 | | (108) ~ (all_18_1 = e2) | ( ~ (all_18_0 = e0) & op(e2, e3) = all_18_0 &
% 110.79/15.92 | | $i(all_18_0))
% 110.79/15.92 | |
% 110.79/15.92 | | COMBINE_EQS: (2), (105) imply:
% 110.79/15.92 | | (109) all_6_1 = e3
% 110.79/15.92 | |
% 110.79/15.92 | | SIMP: (109) implies:
% 110.79/15.92 | | (110) all_6_1 = e3
% 110.79/15.92 | |
% 110.79/15.92 | | COMBINE_EQS: (5), (110) imply:
% 110.79/15.92 | | (111) all_20_2 = e3
% 110.79/15.92 | |
% 110.79/15.92 | | COMBINE_EQS: (18), (110) imply:
% 110.79/15.92 | | (112) all_38_1 = e3
% 110.79/15.92 | |
% 110.79/15.92 | | REDUCE: (70), (110) imply:
% 110.79/15.92 | | (113) ~ (all_53_1 = e3)
% 110.79/15.92 | |
% 110.79/15.92 | | REDUCE: (78), (110) imply:
% 110.79/15.92 | | (114) ~ (all_53_4 = e3)
% 110.79/15.92 | |
% 110.79/15.92 | | REDUCE: (73), (110) imply:
% 110.79/15.92 | | (115) ~ (all_53_13 = e3)
% 110.79/15.92 | |
% 110.79/15.92 | | REDUCE: (3), (110) imply:
% 110.79/15.92 | | (116) op(e1, e1) = e3
% 110.79/15.92 | |
% 110.79/15.92 | | BETA: splitting (12) gives:
% 110.79/15.92 | |
% 110.79/15.92 | | Case 1:
% 110.79/15.92 | | |
% 110.79/15.92 | | | (117) ~ (all_20_2 = e3)
% 110.79/15.92 | | |
% 110.79/15.92 | | | REDUCE: (111), (117) imply:
% 110.79/15.92 | | | (118) $false
% 110.79/15.92 | | |
% 110.79/15.92 | | | CLOSE: (118) is inconsistent.
% 110.79/15.92 | | |
% 110.79/15.92 | | Case 2:
% 110.79/15.92 | | |
% 110.79/15.92 | | | (119) op(e3, e3) = all_20_1 & $i(all_20_1) & ( ~ (all_20_1 = e0) | ( ~
% 110.79/15.92 | | | (all_20_0 = e2) & op(e0, e3) = all_20_0 & $i(all_20_0)))
% 110.79/15.92 | | |
% 110.79/15.92 | | | ALPHA: (119) implies:
% 110.79/15.92 | | | (120) op(e3, e3) = all_20_1
% 110.79/15.92 | | |
% 110.79/15.92 | | | BETA: splitting (28) gives:
% 110.79/15.92 | | |
% 110.79/15.92 | | | Case 1:
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | (121) ~ (all_38_1 = e3)
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | REDUCE: (112), (121) imply:
% 110.79/15.92 | | | | (122) $false
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | CLOSE: (122) is inconsistent.
% 110.79/15.92 | | | |
% 110.79/15.92 | | | Case 2:
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | (123) ~ (all_38_0 = e2) & op(e3, e1) = all_38_0 & $i(all_38_0)
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | ALPHA: (123) implies:
% 110.79/15.92 | | | | (124) ~ (all_38_0 = e2)
% 110.79/15.92 | | | | (125) op(e3, e1) = all_38_0
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | GROUND_INST: instantiating (62) with all_53_13, all_38_0, e1, e3,
% 110.79/15.92 | | | | simplifying with (57), (125) gives:
% 110.79/15.92 | | | | (126) all_53_13 = all_38_0
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | GROUND_INST: instantiating (62) with all_4_2, all_20_1, e3, e3,
% 110.79/15.92 | | | | simplifying with (81), (120) gives:
% 110.79/15.92 | | | | (127) all_20_1 = all_4_2
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | GROUND_INST: instantiating (62) with all_18_1, all_20_1, e3, e3,
% 110.79/15.92 | | | | simplifying with (107), (120) gives:
% 110.79/15.92 | | | | (128) all_20_1 = all_18_1
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | COMBINE_EQS: (127), (128) imply:
% 110.79/15.92 | | | | (129) all_18_1 = all_4_2
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | REDUCE: (67), (126) imply:
% 110.79/15.92 | | | | (130) ~ (all_53_1 = all_38_0)
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | REDUCE: (61), (126) imply:
% 110.79/15.92 | | | | (131) ~ (all_38_0 = all_4_2)
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | BETA: splitting (64) gives:
% 110.79/15.92 | | | |
% 110.79/15.92 | | | | Case 1:
% 110.79/15.92 | | | | |
% 110.79/15.92 | | | | | (132) ~ (all_24_2 = e1)
% 110.79/15.92 | | | | |
% 110.79/15.92 | | | | | REDUCE: (76), (132) imply:
% 110.79/15.92 | | | | | (133) ~ (all_10_2 = e1)
% 110.79/15.92 | | | | |
% 110.79/15.92 | | | | | BETA: splitting (38) gives:
% 110.79/15.92 | | | | |
% 110.79/15.92 | | | | | Case 1:
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | | (134) all_55_10 = e3
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | | COMBINE_EQS: (21), (134) imply:
% 110.79/15.92 | | | | | | (135) all_10_2 = e3
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | | REDUCE: (14), (135) imply:
% 110.79/15.92 | | | | | | (136) $false
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | | CLOSE: (136) is inconsistent.
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | Case 2:
% 110.79/15.92 | | | | | |
% 110.79/15.92 | | | | | | (137) ~ (all_55_10 = e3)
% 110.79/15.92 | | | | | | (138) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 110.79/15.92 | | | | | |
% 111.13/15.92 | | | | | | BETA: splitting (138) gives:
% 111.13/15.92 | | | | | |
% 111.13/15.92 | | | | | | Case 1:
% 111.13/15.92 | | | | | | |
% 111.13/15.92 | | | | | | | (139) all_55_10 = e2
% 111.13/15.92 | | | | | | |
% 111.13/15.92 | | | | | | | COMBINE_EQS: (21), (139) imply:
% 111.13/15.92 | | | | | | | (140) all_10_2 = e2
% 111.13/15.92 | | | | | | |
% 111.13/15.92 | | | | | | | REDUCE: (52), (140) imply:
% 111.13/15.92 | | | | | | | (141) ~ (all_53_9 = e2)
% 111.13/15.92 | | | | | | |
% 111.13/15.92 | | | | | | | REDUCE: (14), (140) imply:
% 111.13/15.92 | | | | | | | (142) ~ (e3 = e2)
% 111.13/15.92 | | | | | | |
% 111.13/15.92 | | | | | | | SIMP: (142) implies:
% 111.13/15.92 | | | | | | | (143) ~ (e3 = e2)
% 111.13/15.92 | | | | | | |
% 111.13/15.92 | | | | | | | REDUCE: (41), (140) imply:
% 111.13/15.92 | | | | | | | (144) ~ (e2 = e0)
% 111.13/15.92 | | | | | | |
% 111.13/15.92 | | | | | | | REF_CLOSE: (43), (44), (45), (57), (62), (80), (115), (116),
% 111.13/15.92 | | | | | | | (124), (125), (141), (143), (144) are inconsistent by
% 111.13/15.92 | | | | | | | sub-proof #43.
% 111.13/15.92 | | | | | | |
% 111.13/15.92 | | | | | | Case 2:
% 111.13/15.92 | | | | | | |
% 111.13/15.92 | | | | | | | (145) all_55_10 = e1 | all_55_10 = e0
% 111.13/15.92 | | | | | | |
% 111.13/15.92 | | | | | | | REF_CLOSE: (21), (41), (133), (145) are inconsistent by sub-proof
% 111.13/15.92 | | | | | | | #208.
% 111.13/15.92 | | | | | | |
% 111.13/15.92 | | | | | | End of split
% 111.13/15.92 | | | | | |
% 111.13/15.92 | | | | | End of split
% 111.13/15.92 | | | | |
% 111.13/15.92 | | | | Case 2:
% 111.13/15.92 | | | | |
% 111.13/15.92 | | | | | (146) all_24_2 = e1
% 111.13/15.92 | | | | | (147) op(e1, e1) = all_24_1 & $i(all_24_1) & ( ~ (all_24_1 = e3) |
% 111.13/15.92 | | | | | ( ~ (all_24_0 = e0) & op(e3, e1) = all_24_0 &
% 111.13/15.92 | | | | | $i(all_24_0)))
% 111.13/15.92 | | | | |
% 111.13/15.92 | | | | | ALPHA: (147) implies:
% 111.13/15.92 | | | | | (148) op(e1, e1) = all_24_1
% 111.13/15.92 | | | | |
% 111.13/15.92 | | | | | COMBINE_EQS: (76), (146) imply:
% 111.13/15.92 | | | | | (149) all_10_2 = e1
% 111.13/15.92 | | | | |
% 111.13/15.92 | | | | | COMBINE_EQS: (68), (149) imply:
% 111.13/15.92 | | | | | (150) all_46_2 = e1
% 111.13/15.92 | | | | |
% 111.13/15.92 | | | | | REDUCE: (55), (149) imply:
% 111.13/15.92 | | | | | (151) ~ (all_53_7 = e1)
% 111.13/15.92 | | | | |
% 111.13/15.92 | | | | | REDUCE: (52), (149) imply:
% 111.13/15.92 | | | | | (152) ~ (all_53_9 = e1)
% 111.13/15.92 | | | | |
% 111.13/15.92 | | | | | REDUCE: (14), (149) imply:
% 111.13/15.92 | | | | | (153) ~ (e3 = e1)
% 111.13/15.92 | | | | |
% 111.13/15.92 | | | | | SIMP: (153) implies:
% 111.13/15.92 | | | | | (154) ~ (e3 = e1)
% 111.13/15.92 | | | | |
% 111.13/15.92 | | | | | BETA: splitting (15) gives:
% 111.13/15.92 | | | | |
% 111.13/15.92 | | | | | Case 1:
% 111.13/15.92 | | | | | |
% 111.13/15.92 | | | | | | (155) ~ (all_46_2 = e1)
% 111.13/15.92 | | | | | |
% 111.13/15.92 | | | | | | REDUCE: (150), (155) imply:
% 111.13/15.92 | | | | | | (156) $false
% 111.13/15.92 | | | | | |
% 111.13/15.92 | | | | | | CLOSE: (156) is inconsistent.
% 111.13/15.92 | | | | | |
% 111.13/15.92 | | | | | Case 2:
% 111.13/15.92 | | | | | |
% 111.13/15.92 | | | | | | (157) op(e1, e1) = all_46_1 & $i(all_46_1) & ( ~ (all_46_1 = e0)
% 111.13/15.92 | | | | | | | ( ~ (all_46_0 = e3) & op(e0, e1) = all_46_0 &
% 111.13/15.92 | | | | | | $i(all_46_0)))
% 111.13/15.92 | | | | | |
% 111.13/15.92 | | | | | | ALPHA: (157) implies:
% 111.13/15.92 | | | | | | (158) op(e1, e1) = all_46_1
% 111.13/15.92 | | | | | |
% 111.13/15.92 | | | | | | BETA: splitting (10) gives:
% 111.13/15.92 | | | | | |
% 111.13/15.92 | | | | | | Case 1:
% 111.13/15.92 | | | | | | |
% 111.13/15.92 | | | | | | | (159) (all_57_40 = e1 & op(e1, e3) = e1) | (all_57_41 = e1 &
% 111.13/15.92 | | | | | | | op(e1, e2) = e1)
% 111.13/15.92 | | | | | | |
% 111.13/15.92 | | | | | | | BETA: splitting (159) gives:
% 111.13/15.92 | | | | | | |
% 111.13/15.92 | | | | | | | Case 1:
% 111.13/15.92 | | | | | | | |
% 111.13/15.92 | | | | | | | | (160) all_57_40 = e1 & op(e1, e3) = e1
% 111.13/15.92 | | | | | | | |
% 111.13/15.92 | | | | | | | | ALPHA: (160) implies:
% 111.13/15.92 | | | | | | | | (161) op(e1, e3) = e1
% 111.13/15.92 | | | | | | | |
% 111.13/15.92 | | | | | | | | BETA: splitting (40) gives:
% 111.13/15.92 | | | | | | | |
% 111.13/15.92 | | | | | | | | Case 1:
% 111.13/15.92 | | | | | | | | |
% 111.13/15.92 | | | | | | | | | (162) (all_57_44 = e1 & op(e3, e1) = e1) | (all_57_45 = e1
% 111.13/15.92 | | | | | | | | | & op(e2, e1) = e1)
% 111.13/15.92 | | | | | | | | |
% 111.13/15.92 | | | | | | | | | BETA: splitting (162) gives:
% 111.13/15.92 | | | | | | | | |
% 111.13/15.92 | | | | | | | | | Case 1:
% 111.13/15.92 | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | (163) all_57_44 = e1 & op(e3, e1) = e1
% 111.13/15.92 | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | ALPHA: (163) implies:
% 111.13/15.92 | | | | | | | | | | (164) op(e3, e1) = e1
% 111.13/15.92 | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | GROUND_INST: instantiating (62) with all_53_6, e1, e3, e1,
% 111.13/15.92 | | | | | | | | | | simplifying with (53), (161) gives:
% 111.13/15.92 | | | | | | | | | | (165) all_53_6 = e1
% 111.13/15.92 | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | GROUND_INST: instantiating (62) with all_38_0, e1, e1, e3,
% 111.13/15.92 | | | | | | | | | | simplifying with (125), (164) gives:
% 111.13/15.92 | | | | | | | | | | (166) all_38_0 = e1
% 111.13/15.92 | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | REDUCE: (1), (165) imply:
% 111.13/15.92 | | | | | | | | | | (167) ~ (all_53_2 = e1)
% 111.13/15.92 | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | REDUCE: (8), (165) imply:
% 111.13/15.92 | | | | | | | | | | (168) ~ (all_53_10 = e1)
% 111.13/15.92 | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | SIMP: (168) implies:
% 111.13/15.92 | | | | | | | | | | (169) ~ (all_53_10 = e1)
% 111.13/15.92 | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | REDUCE: (131), (166) imply:
% 111.13/15.92 | | | | | | | | | | (170) ~ (all_4_2 = e1)
% 111.13/15.92 | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | SIMP: (170) implies:
% 111.13/15.92 | | | | | | | | | | (171) ~ (all_4_2 = e1)
% 111.13/15.92 | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | BETA: splitting (77) gives:
% 111.13/15.92 | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | Case 1:
% 111.13/15.92 | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | (172) ~ (all_26_2 = e2)
% 111.13/15.92 | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | REDUCE: (60), (172) imply:
% 111.13/15.92 | | | | | | | | | | | (173) ~ (all_4_2 = e2)
% 111.13/15.92 | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | BETA: splitting (22) gives:
% 111.13/15.92 | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | Case 1:
% 111.13/15.92 | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | (174) all_55_15 = e3
% 111.13/15.92 | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | COMBINE_EQS: (7), (174) imply:
% 111.13/15.92 | | | | | | | | | | | | (175) all_4_2 = e3
% 111.13/15.92 | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | SIMP: (175) implies:
% 111.13/15.92 | | | | | | | | | | | | (176) all_4_2 = e3
% 111.13/15.92 | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | REDUCE: (37), (176) imply:
% 111.13/15.92 | | | | | | | | | | | | (177) ~ (all_53_12 = e3)
% 111.13/15.92 | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | REDUCE: (173), (176) imply:
% 111.13/15.92 | | | | | | | | | | | | (178) ~ (e3 = e2)
% 111.13/15.92 | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | BETA: splitting (69) gives:
% 111.13/15.92 | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | Case 1:
% 111.13/15.92 | | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | | (179) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) =
% 111.13/15.92 | | | | | | | | | | | | | e3 & op(e0, e3) = all_52_0 & $i(all_52_0)
% 111.13/15.92 | | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | | ALPHA: (179) implies:
% 111.13/15.92 | | | | | | | | | | | | | (180) op(e3, e0) = e3
% 111.13/15.92 | | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | | REF_CLOSE: (13), (62), (177), (180) are inconsistent by
% 111.13/15.92 | | | | | | | | | | | | | sub-proof #180.
% 111.13/15.92 | | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | Case 2:
% 111.13/15.92 | | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | | (181) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 111.13/15.92 | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) |
% 111.13/15.92 | | | | | | | | | | | | | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 111.13/15.92 | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 111.13/15.92 | | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | | BETA: splitting (181) gives:
% 111.13/15.92 | | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | | Case 1:
% 111.13/15.92 | | | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | | | (182) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) =
% 111.13/15.92 | | | | | | | | | | | | | | e2 & op(e0, e2) = all_52_2 & $i(all_52_2)
% 111.13/15.92 | | | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | | | ALPHA: (182) implies:
% 111.13/15.92 | | | | | | | | | | | | | | (183) op(e2, e0) = e2
% 111.13/15.92 | | | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 111.13/15.92 | | | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | | | Case 1:
% 111.13/15.92 | | | | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | | | | (184) (all_57_28 = e3 & op(e3, e0) = e3) | (all_57_29 =
% 111.13/15.92 | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 111.13/15.92 | | | | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 111.13/15.92 | | | | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | | | | Case 1:
% 111.13/15.92 | | | | | | | | | | | | | | | |
% 111.13/15.92 | | | | | | | | | | | | | | | | (185) all_57_28 = e3 & op(e3, e0) = e3
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 111.13/15.93 | | | | | | | | | | | | | | | | (186) op(e3, e0) = e3
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (62), (177), (186) are inconsistent by
% 111.13/15.93 | | | | | | | | | | | | | | | | sub-proof #180.
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | Case 2:
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | | (187) all_57_29 = e3 & op(e2, e0) = e3
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 111.13/15.93 | | | | | | | | | | | | | | | | (188) op(e2, e0) = e3
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | | REF_CLOSE: (56), (62), (178), (183), (188) are inconsistent
% 111.13/15.93 | | | | | | | | | | | | | | | | by sub-proof #69.
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | End of split
% 111.13/15.93 | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | Case 2:
% 111.13/15.93 | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | (189) (all_57_30 = e3 & op(e1, e0) = e3) | (all_57_31 =
% 111.13/15.93 | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 111.13/15.93 | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | REF_CLOSE: (4), (17), (62), (114), (154), (189) are
% 111.13/15.93 | | | | | | | | | | | | | | | inconsistent by sub-proof #42.
% 111.13/15.93 | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | End of split
% 111.13/15.93 | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | Case 2:
% 111.13/15.93 | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | (190) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) =
% 111.13/15.93 | | | | | | | | | | | | | | e1 & op(e0, e1) = all_52_4 & $i(all_52_4)
% 111.13/15.93 | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | ALPHA: (190) implies:
% 111.13/15.93 | | | | | | | | | | | | | | (191) op(e1, e0) = e1
% 111.13/15.93 | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | REF_CLOSE: (17), (30), (62), (191) are inconsistent by
% 111.13/15.93 | | | | | | | | | | | | | | sub-proof #226.
% 111.13/15.93 | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | End of split
% 111.13/15.93 | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | End of split
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | Case 2:
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | (192) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | REF_CLOSE: (7), (46), (171), (173), (192) are inconsistent by
% 111.13/15.93 | | | | | | | | | | | | sub-proof #191.
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | End of split
% 111.13/15.93 | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | Case 2:
% 111.13/15.93 | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | (193) all_26_2 = e2
% 111.13/15.93 | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | COMBINE_EQS: (60), (193) imply:
% 111.13/15.93 | | | | | | | | | | | (194) all_4_2 = e2
% 111.13/15.93 | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | SIMP: (194) implies:
% 111.13/15.93 | | | | | | | | | | | (195) all_4_2 = e2
% 111.13/15.93 | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | COMBINE_EQS: (129), (195) imply:
% 111.13/15.93 | | | | | | | | | | | (196) all_18_1 = e2
% 111.13/15.93 | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | REDUCE: (33), (195) imply:
% 111.13/15.93 | | | | | | | | | | | (197) ~ (all_53_2 = e2)
% 111.13/15.93 | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | REDUCE: (59), (195) imply:
% 111.13/15.93 | | | | | | | | | | | (198) ~ (all_53_10 = e2)
% 111.13/15.93 | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | BETA: splitting (108) gives:
% 111.13/15.93 | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | Case 1:
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | (199) ~ (all_18_1 = e2)
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | REDUCE: (196), (199) imply:
% 111.13/15.93 | | | | | | | | | | | | (200) $false
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | CLOSE: (200) is inconsistent.
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | Case 2:
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | (201) ~ (all_18_0 = e0) & op(e2, e3) = all_18_0 &
% 111.13/15.93 | | | | | | | | | | | | $i(all_18_0)
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | ALPHA: (201) implies:
% 111.13/15.93 | | | | | | | | | | | | (202) ~ (all_18_0 = e0)
% 111.13/15.93 | | | | | | | | | | | | (203) op(e2, e3) = all_18_0
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | GROUND_INST: instantiating (62) with all_53_10, all_18_0, e3,
% 111.13/15.93 | | | | | | | | | | | | e2, simplifying with (16), (203) gives:
% 111.13/15.93 | | | | | | | | | | | | (204) all_53_10 = all_18_0
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | COMBINE_EQS: (19), (204) imply:
% 111.13/15.93 | | | | | | | | | | | | (205) all_55_11 = all_18_0
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | REDUCE: (75), (204) imply:
% 111.13/15.93 | | | | | | | | | | | | (206) ~ (all_53_2 = all_18_0)
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | REDUCE: (198), (204) imply:
% 111.13/15.93 | | | | | | | | | | | | (207) ~ (all_18_0 = e2)
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | REDUCE: (169), (204) imply:
% 111.13/15.93 | | | | | | | | | | | | (208) ~ (all_18_0 = e1)
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | BETA: splitting (66) gives:
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | Case 1:
% 111.13/15.93 | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | (209) all_55_11 = e3
% 111.13/15.93 | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | COMBINE_EQS: (205), (209) imply:
% 111.13/15.93 | | | | | | | | | | | | | (210) all_18_0 = e3
% 111.13/15.93 | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | SIMP: (210) implies:
% 111.13/15.93 | | | | | | | | | | | | | (211) all_18_0 = e3
% 111.13/15.93 | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | REDUCE: (206), (211) imply:
% 111.13/15.93 | | | | | | | | | | | | | (212) ~ (all_53_2 = e3)
% 111.13/15.93 | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | BETA: splitting (23) gives:
% 111.13/15.93 | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | Case 1:
% 111.13/15.93 | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | (213) all_55_3 = e3
% 111.13/15.93 | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | COMBINE_EQS: (27), (213) imply:
% 111.13/15.93 | | | | | | | | | | | | | | (214) all_53_2 = e3
% 111.13/15.93 | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | REDUCE: (212), (214) imply:
% 111.13/15.93 | | | | | | | | | | | | | | (215) $false
% 111.13/15.93 | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | CLOSE: (215) is inconsistent.
% 111.13/15.93 | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | Case 2:
% 111.13/15.93 | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | (216) all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 111.13/15.93 | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 111.13/15.93 | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | Case 1:
% 111.13/15.93 | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | (217) all_55_3 = e2
% 111.13/15.93 | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | COMBINE_EQS: (27), (217) imply:
% 111.13/15.93 | | | | | | | | | | | | | | | (218) all_53_2 = e2
% 111.13/15.93 | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | REDUCE: (197), (218) imply:
% 111.13/15.93 | | | | | | | | | | | | | | | (219) $false
% 111.13/15.93 | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent.
% 111.13/15.93 | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | Case 2:
% 111.13/15.93 | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | (220) all_55_3 = e1 | all_55_3 = e0
% 111.13/15.93 | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 111.13/15.93 | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | Case 1:
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | | (221) all_55_3 = e1
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (167), (221) are inconsistent by sub-proof
% 111.13/15.93 | | | | | | | | | | | | | | | | #121.
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | Case 2:
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | | (222) all_55_3 = e0
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (222) imply:
% 111.13/15.93 | | | | | | | | | | | | | | | | (223) all_53_2 = e0
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | | SIMP: (223) implies:
% 111.13/15.93 | | | | | | | | | | | | | | | | (224) all_53_2 = e0
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | | REDUCE: (84), (224) imply:
% 111.13/15.93 | | | | | | | | | | | | | | | | (225) ~ (all_53_1 = e0)
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | | REF_CLOSE: (31), (43), (45), (54), (57), (62), (74), (79),
% 111.13/15.93 | | | | | | | | | | | | | | | | (80), (113), (115), (225) are inconsistent by
% 111.13/15.93 | | | | | | | | | | | | | | | | sub-proof #41.
% 111.13/15.93 | | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | | End of split
% 111.13/15.93 | | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | | End of split
% 111.13/15.93 | | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | End of split
% 111.13/15.93 | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | Case 2:
% 111.13/15.93 | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | (226) all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 111.13/15.93 | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | | REF_CLOSE: (202), (205), (207), (208), (226) are inconsistent
% 111.13/15.93 | | | | | | | | | | | | | by sub-proof #55.
% 111.13/15.93 | | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | | End of split
% 111.13/15.93 | | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | | End of split
% 111.13/15.93 | | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | End of split
% 111.13/15.93 | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | Case 2:
% 111.13/15.93 | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | (227) all_57_45 = e1 & op(e2, e1) = e1
% 111.13/15.93 | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | ALPHA: (227) implies:
% 111.13/15.93 | | | | | | | | | | (228) op(e2, e1) = e1
% 111.13/15.93 | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | REF_CLOSE: (45), (62), (152), (228) are inconsistent by
% 111.13/15.93 | | | | | | | | | | sub-proof #48.
% 111.13/15.93 | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | End of split
% 111.13/15.93 | | | | | | | | |
% 111.13/15.93 | | | | | | | | Case 2:
% 111.13/15.93 | | | | | | | | |
% 111.13/15.93 | | | | | | | | | (229) (all_57_46 = e1 & op(e1, e1) = e1) | (all_57_47 = e1
% 111.13/15.93 | | | | | | | | | & op(e0, e1) = e1)
% 111.13/15.93 | | | | | | | | |
% 111.13/15.93 | | | | | | | | | BETA: splitting (229) gives:
% 111.13/15.93 | | | | | | | | |
% 111.13/15.93 | | | | | | | | | Case 1:
% 111.13/15.93 | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | (230) all_57_46 = e1 & op(e1, e1) = e1
% 111.13/15.93 | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | ALPHA: (230) implies:
% 111.13/15.93 | | | | | | | | | | (231) op(e1, e1) = e1
% 111.13/15.93 | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | REF_CLOSE: (62), (116), (148), (154), (158), (231) are
% 111.13/15.93 | | | | | | | | | | inconsistent by sub-proof #40.
% 111.13/15.93 | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | Case 2:
% 111.13/15.93 | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | (232) all_57_47 = e1 & op(e0, e1) = e1
% 111.13/15.93 | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | ALPHA: (232) implies:
% 111.13/15.93 | | | | | | | | | | (233) op(e0, e1) = e1
% 111.13/15.93 | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | | REF_CLOSE: (43), (54), (62), (233) are inconsistent by
% 111.13/15.93 | | | | | | | | | | sub-proof #170.
% 111.13/15.93 | | | | | | | | | |
% 111.13/15.93 | | | | | | | | | End of split
% 111.13/15.93 | | | | | | | | |
% 111.13/15.93 | | | | | | | | End of split
% 111.13/15.93 | | | | | | | |
% 111.13/15.93 | | | | | | | Case 2:
% 111.13/15.93 | | | | | | | |
% 111.13/15.93 | | | | | | | | (234) all_57_41 = e1 & op(e1, e2) = e1
% 111.13/15.93 | | | | | | | |
% 111.13/15.93 | | | | | | | | ALPHA: (234) implies:
% 111.13/15.93 | | | | | | | | (235) op(e1, e2) = e1
% 111.13/15.93 | | | | | | | |
% 111.13/15.93 | | | | | | | | REF_CLOSE: (32), (62), (151), (235) are inconsistent by
% 111.13/15.93 | | | | | | | | sub-proof #233.
% 111.13/15.93 | | | | | | | |
% 111.13/15.93 | | | | | | | End of split
% 111.13/15.93 | | | | | | |
% 111.13/15.93 | | | | | | Case 2:
% 111.13/15.93 | | | | | | |
% 111.13/15.93 | | | | | | | (236) (all_57_42 = e1 & op(e1, e1) = e1) | (all_57_43 = e1 &
% 111.13/15.93 | | | | | | | op(e1, e0) = e1)
% 111.13/15.93 | | | | | | |
% 111.13/15.93 | | | | | | | BETA: splitting (236) gives:
% 111.13/15.93 | | | | | | |
% 111.13/15.93 | | | | | | | Case 1:
% 111.13/15.93 | | | | | | | |
% 111.13/15.93 | | | | | | | | (237) all_57_42 = e1 & op(e1, e1) = e1
% 111.13/15.93 | | | | | | | |
% 111.13/15.93 | | | | | | | | ALPHA: (237) implies:
% 111.13/15.93 | | | | | | | | (238) op(e1, e1) = e1
% 111.13/15.93 | | | | | | | |
% 111.13/15.93 | | | | | | | | REF_CLOSE: (62), (116), (148), (154), (158), (238) are
% 111.13/15.93 | | | | | | | | inconsistent by sub-proof #40.
% 111.13/15.93 | | | | | | | |
% 111.13/15.93 | | | | | | | Case 2:
% 111.13/15.93 | | | | | | | |
% 111.13/15.93 | | | | | | | | (239) all_57_43 = e1 & op(e1, e0) = e1
% 111.13/15.93 | | | | | | | |
% 111.13/15.93 | | | | | | | | ALPHA: (239) implies:
% 111.13/15.93 | | | | | | | | (240) op(e1, e0) = e1
% 111.13/15.93 | | | | | | | |
% 111.13/15.93 | | | | | | | | REF_CLOSE: (17), (30), (62), (240) are inconsistent by sub-proof
% 111.13/15.93 | | | | | | | | #226.
% 111.13/15.93 | | | | | | | |
% 111.13/15.93 | | | | | | | End of split
% 111.13/15.93 | | | | | | |
% 111.13/15.93 | | | | | | End of split
% 111.13/15.93 | | | | | |
% 111.13/15.93 | | | | | End of split
% 111.13/15.93 | | | | |
% 111.13/15.93 | | | | End of split
% 111.13/15.93 | | | |
% 111.13/15.93 | | | End of split
% 111.13/15.93 | | |
% 111.13/15.93 | | End of split
% 111.13/15.93 | |
% 111.13/15.93 | End of split
% 111.13/15.93 |
% 111.13/15.93 End of proof
% 111.13/15.93
% 111.13/15.93 Sub-proof #40 shows that the following formulas are inconsistent:
% 111.13/15.93 ----------------------------------------------------------------
% 111.13/15.93 (1) op(e1, e1) = e3
% 111.13/15.93 (2) op(e1, e1) = all_24_1
% 111.13/15.93 (3) op(e1, e1) = all_46_1
% 111.13/15.93 (4) ~ (e3 = e1)
% 111.13/15.93 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/15.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/15.93 (6) op(e1, e1) = e1
% 111.13/15.93
% 111.13/15.93 Begin of proof
% 111.13/15.93 |
% 111.13/15.93 | GROUND_INST: instantiating (5) with e3, all_24_1, e1, e1, simplifying with
% 111.13/15.93 | (1), (2) gives:
% 111.13/15.93 | (7) all_24_1 = e3
% 111.13/15.93 |
% 111.13/15.93 | GROUND_INST: instantiating (5) with all_24_1, all_46_1, e1, e1, simplifying
% 111.13/15.93 | with (2), (3) gives:
% 111.13/15.93 | (8) all_46_1 = all_24_1
% 111.13/15.93 |
% 111.13/15.93 | GROUND_INST: instantiating (5) with e1, all_46_1, e1, e1, simplifying with
% 111.13/15.93 | (3), (6) gives:
% 111.13/15.93 | (9) all_46_1 = e1
% 111.13/15.93 |
% 111.13/15.93 | COMBINE_EQS: (8), (9) imply:
% 111.13/15.93 | (10) all_24_1 = e1
% 111.13/15.93 |
% 111.13/15.93 | SIMP: (10) implies:
% 111.13/15.93 | (11) all_24_1 = e1
% 111.13/15.93 |
% 111.13/15.93 | COMBINE_EQS: (7), (11) imply:
% 111.13/15.93 | (12) e3 = e1
% 111.13/15.93 |
% 111.13/15.93 | REDUCE: (4), (12) imply:
% 111.13/15.93 | (13) $false
% 111.13/15.93 |
% 111.13/15.93 | CLOSE: (13) is inconsistent.
% 111.13/15.93 |
% 111.13/15.93 End of proof
% 111.13/15.93
% 111.13/15.93 Sub-proof #41 shows that the following formulas are inconsistent:
% 111.13/15.93 ----------------------------------------------------------------
% 111.13/15.93 (1) ~ (all_53_13 = e3)
% 111.13/15.93 (2) ~ (all_53_1 = e0)
% 111.13/15.93 (3) ~ (all_53_1 = all_53_9)
% 111.13/15.93 (4) op(e0, e1) = all_53_1
% 111.13/15.93 (5) op(e2, e1) = all_53_9
% 111.13/15.93 (6) ~ (all_53_1 = e1)
% 111.13/15.93 (7) op(e3, e1) = all_53_13
% 111.13/15.93 (8) ~ (all_53_1 = e3)
% 111.13/15.93 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/15.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/15.93 (10) all_55_1 = all_53_1
% 111.13/15.93 (11) all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 111.13/15.93 (12) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.13/15.93 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 111.13/15.93 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 111.13/15.93 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.13/15.93 $i(all_52_10))
% 111.13/15.93
% 111.13/15.93 Begin of proof
% 111.13/15.93 |
% 111.13/15.93 | BETA: splitting (11) gives:
% 111.13/15.93 |
% 111.13/15.93 | Case 1:
% 111.13/15.93 | |
% 111.13/15.93 | | (13) all_55_1 = e3
% 111.13/15.93 | |
% 111.13/15.93 | | COMBINE_EQS: (10), (13) imply:
% 111.13/15.93 | | (14) all_53_1 = e3
% 111.13/15.93 | |
% 111.13/15.93 | | REDUCE: (8), (14) imply:
% 111.13/15.93 | | (15) $false
% 111.13/15.93 | |
% 111.13/15.93 | | CLOSE: (15) is inconsistent.
% 111.13/15.93 | |
% 111.13/15.93 | Case 2:
% 111.13/15.93 | |
% 111.13/15.93 | | (16) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 111.13/15.93 | |
% 111.13/15.93 | | BETA: splitting (16) gives:
% 111.13/15.93 | |
% 111.13/15.93 | | Case 1:
% 111.13/15.93 | | |
% 111.13/15.93 | | | (17) all_55_1 = e2
% 111.13/15.93 | | |
% 111.13/15.93 | | | COMBINE_EQS: (10), (17) imply:
% 111.13/15.93 | | | (18) all_53_1 = e2
% 111.13/15.93 | | |
% 111.13/15.93 | | | REDUCE: (3), (18) imply:
% 111.13/15.93 | | | (19) ~ (all_53_9 = e2)
% 111.13/15.93 | | |
% 111.13/15.93 | | | SIMP: (19) implies:
% 111.13/15.93 | | | (20) ~ (all_53_9 = e2)
% 111.13/15.93 | | |
% 111.13/15.93 | | | REDUCE: (2), (18) imply:
% 111.13/15.93 | | | (21) ~ (e2 = e0)
% 111.13/15.93 | | |
% 111.13/15.93 | | | REDUCE: (4), (18) imply:
% 111.13/15.93 | | | (22) op(e0, e1) = e2
% 111.13/15.93 | | |
% 111.13/15.93 | | | REF_CLOSE: (1), (4), (5), (7), (9), (12), (20), (21), (22) are
% 111.13/15.93 | | | inconsistent by sub-proof #44.
% 111.13/15.93 | | |
% 111.13/15.93 | | Case 2:
% 111.13/15.93 | | |
% 111.13/15.93 | | | (23) all_55_1 = e1 | all_55_1 = e0
% 111.13/15.93 | | |
% 111.13/15.93 | | | REF_CLOSE: (2), (6), (10), (23) are inconsistent by sub-proof #49.
% 111.13/15.93 | | |
% 111.13/15.93 | | End of split
% 111.13/15.93 | |
% 111.13/15.93 | End of split
% 111.13/15.93 |
% 111.13/15.93 End of proof
% 111.13/15.93
% 111.13/15.93 Sub-proof #42 shows that the following formulas are inconsistent:
% 111.13/15.93 ----------------------------------------------------------------
% 111.13/15.93 (1) op(e0, e0) = e1
% 111.13/15.93 (2) (all_57_30 = e3 & op(e1, e0) = e3) | (all_57_31 = e3 & op(e0, e0) = e3)
% 111.13/15.93 (3) op(e1, e0) = all_53_4
% 111.13/15.93 (4) ~ (e3 = e1)
% 111.13/15.93 (5) ~ (all_53_4 = e3)
% 111.13/15.93 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/15.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/15.93
% 111.13/15.93 Begin of proof
% 111.13/15.93 |
% 111.13/15.93 | BETA: splitting (2) gives:
% 111.13/15.93 |
% 111.13/15.93 | Case 1:
% 111.13/15.93 | |
% 111.13/15.93 | | (7) all_57_30 = e3 & op(e1, e0) = e3
% 111.13/15.94 | |
% 111.13/15.94 | | ALPHA: (7) implies:
% 111.13/15.94 | | (8) op(e1, e0) = e3
% 111.13/15.94 | |
% 111.13/15.94 | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #126.
% 111.13/15.94 | |
% 111.13/15.94 | Case 2:
% 111.13/15.94 | |
% 111.13/15.94 | | (9) all_57_31 = e3 & op(e0, e0) = e3
% 111.13/15.94 | |
% 111.13/15.94 | | ALPHA: (9) implies:
% 111.13/15.94 | | (10) op(e0, e0) = e3
% 111.13/15.94 | |
% 111.13/15.94 | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #165.
% 111.13/15.94 | |
% 111.13/15.94 | End of split
% 111.13/15.94 |
% 111.13/15.94 End of proof
% 111.13/15.94
% 111.13/15.94 Sub-proof #43 shows that the following formulas are inconsistent:
% 111.13/15.94 ----------------------------------------------------------------
% 111.13/15.94 (1) ~ (all_53_9 = e2)
% 111.13/15.94 (2) ~ (all_53_13 = e3)
% 111.13/15.94 (3) op(e1, e1) = e3
% 111.13/15.94 (4) ~ (all_38_0 = e2)
% 111.13/15.94 (5) ~ (e2 = e0)
% 111.13/15.94 (6) op(e0, e1) = all_53_1
% 111.13/15.94 (7) (all_57_52 = e2 & op(e3, e1) = e2) | (all_57_53 = e2 & op(e2, e1) = e2) |
% 111.13/15.94 (all_57_54 = e2 & op(e1, e1) = e2) | (all_57_55 = e2 & op(e0, e1) = e2)
% 111.13/15.94 (8) op(e2, e1) = all_53_9
% 111.13/15.94 (9) op(e3, e1) = all_53_13
% 111.13/15.94 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/15.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/15.94 (11) op(e3, e1) = all_38_0
% 111.13/15.94 (12) ~ (e3 = e2)
% 111.13/15.94 (13) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.13/15.94 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 111.13/15.94 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 111.13/15.94 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.13/15.94 $i(all_52_10))
% 111.13/15.94
% 111.13/15.94 Begin of proof
% 111.13/15.94 |
% 111.13/15.94 | BETA: splitting (7) gives:
% 111.13/15.94 |
% 111.13/15.94 | Case 1:
% 111.13/15.94 | |
% 111.13/15.94 | | (14) (all_57_52 = e2 & op(e3, e1) = e2) | (all_57_53 = e2 & op(e2, e1) =
% 111.13/15.94 | | e2)
% 111.13/15.94 | |
% 111.13/15.94 | | BETA: splitting (14) gives:
% 111.13/15.94 | |
% 111.13/15.94 | | Case 1:
% 111.13/15.94 | | |
% 111.13/15.94 | | | (15) all_57_52 = e2 & op(e3, e1) = e2
% 111.13/15.94 | | |
% 111.13/15.94 | | | ALPHA: (15) implies:
% 111.13/15.94 | | | (16) op(e3, e1) = e2
% 111.13/15.94 | | |
% 111.13/15.94 | | | GROUND_INST: instantiating (10) with all_38_0, e2, e1, e3, simplifying
% 111.13/15.94 | | | with (11), (16) gives:
% 111.13/15.94 | | | (17) all_38_0 = e2
% 111.13/15.94 | | |
% 111.13/15.94 | | | REDUCE: (4), (17) imply:
% 111.13/15.94 | | | (18) $false
% 111.13/15.94 | | |
% 111.13/15.94 | | | CLOSE: (18) is inconsistent.
% 111.13/15.94 | | |
% 111.13/15.94 | | Case 2:
% 111.13/15.94 | | |
% 111.13/15.94 | | | (19) all_57_53 = e2 & op(e2, e1) = e2
% 111.13/15.94 | | |
% 111.13/15.94 | | | ALPHA: (19) implies:
% 111.13/15.94 | | | (20) op(e2, e1) = e2
% 111.13/15.94 | | |
% 111.13/15.94 | | | REF_CLOSE: (1), (8), (10), (20) are inconsistent by sub-proof #231.
% 111.13/15.94 | | |
% 111.13/15.94 | | End of split
% 111.13/15.94 | |
% 111.13/15.94 | Case 2:
% 111.13/15.94 | |
% 111.13/15.94 | | (21) (all_57_54 = e2 & op(e1, e1) = e2) | (all_57_55 = e2 & op(e0, e1) =
% 111.13/15.94 | | e2)
% 111.13/15.94 | |
% 111.13/15.94 | | BETA: splitting (21) gives:
% 111.13/15.94 | |
% 111.13/15.94 | | Case 1:
% 111.13/15.94 | | |
% 111.13/15.94 | | | (22) all_57_54 = e2 & op(e1, e1) = e2
% 111.13/15.94 | | |
% 111.13/15.94 | | | ALPHA: (22) implies:
% 111.13/15.94 | | | (23) op(e1, e1) = e2
% 111.13/15.94 | | |
% 111.13/15.94 | | | REF_CLOSE: (3), (10), (12), (23) are inconsistent by sub-proof #131.
% 111.13/15.94 | | |
% 111.13/15.94 | | Case 2:
% 111.13/15.94 | | |
% 111.13/15.94 | | | (24) all_57_55 = e2 & op(e0, e1) = e2
% 111.13/15.94 | | |
% 111.13/15.94 | | | ALPHA: (24) implies:
% 111.13/15.94 | | | (25) op(e0, e1) = e2
% 111.13/15.94 | | |
% 111.13/15.94 | | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (10), (13), (25) are inconsistent
% 111.13/15.94 | | | by sub-proof #44.
% 111.13/15.94 | | |
% 111.13/15.94 | | End of split
% 111.13/15.94 | |
% 111.13/15.94 | End of split
% 111.13/15.94 |
% 111.13/15.94 End of proof
% 111.13/15.94
% 111.13/15.94 Sub-proof #44 shows that the following formulas are inconsistent:
% 111.13/15.94 ----------------------------------------------------------------
% 111.13/15.94 (1) ~ (all_53_9 = e2)
% 111.13/15.94 (2) ~ (all_53_13 = e3)
% 111.13/15.94 (3) ~ (e2 = e0)
% 111.13/15.94 (4) op(e0, e1) = e2
% 111.13/15.94 (5) op(e0, e1) = all_53_1
% 111.13/15.94 (6) op(e2, e1) = all_53_9
% 111.13/15.94 (7) op(e3, e1) = all_53_13
% 111.13/15.94 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/15.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/15.94 (9) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.13/15.94 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2,
% 111.13/15.94 e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 = e0 &
% 111.13/15.94 ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.13/15.94 $i(all_52_10))
% 111.13/15.94
% 111.13/15.94 Begin of proof
% 111.13/15.94 |
% 111.13/15.94 | BETA: splitting (9) gives:
% 111.13/15.94 |
% 111.13/15.94 | Case 1:
% 111.13/15.94 | |
% 111.13/15.94 | | (10) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.13/15.94 | | all_52_6 & $i(all_52_6)
% 111.13/15.94 | |
% 111.13/15.94 | | ALPHA: (10) implies:
% 111.13/15.94 | | (11) op(e3, e1) = e3
% 111.13/15.94 | |
% 111.13/15.94 | | REF_CLOSE: (2), (7), (8), (11) are inconsistent by sub-proof #232.
% 111.13/15.94 | |
% 111.13/15.94 | Case 2:
% 111.13/15.94 | |
% 111.13/15.94 | | (12) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 111.13/15.94 | | all_52_8 & $i(all_52_8)) | (all_52_11 = e0 & ~ (all_52_10 = e1) &
% 111.13/15.94 | | op(e1, e0) = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 111.13/15.94 | |
% 111.13/15.94 | | BETA: splitting (12) gives:
% 111.13/15.94 | |
% 111.13/15.94 | | Case 1:
% 111.13/15.94 | | |
% 111.13/15.94 | | | (13) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 111.13/15.94 | | | = all_52_8 & $i(all_52_8)
% 111.13/15.94 | | |
% 111.13/15.94 | | | ALPHA: (13) implies:
% 111.13/15.94 | | | (14) op(e2, e1) = e2
% 111.13/15.94 | | |
% 111.13/15.94 | | | REF_CLOSE: (1), (6), (8), (14) are inconsistent by sub-proof #231.
% 111.13/15.94 | | |
% 111.13/15.94 | | Case 2:
% 111.13/15.94 | | |
% 111.13/15.94 | | | (15) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 &
% 111.13/15.94 | | | op(e0, e1) = e0 & $i(all_52_10)
% 111.13/15.94 | | |
% 111.13/15.94 | | | ALPHA: (15) implies:
% 111.13/15.94 | | | (16) op(e0, e1) = e0
% 111.13/15.94 | | |
% 111.13/15.94 | | | REF_CLOSE: (3), (4), (5), (8), (16) are inconsistent by sub-proof #45.
% 111.13/15.94 | | |
% 111.13/15.94 | | End of split
% 111.13/15.94 | |
% 111.13/15.94 | End of split
% 111.13/15.94 |
% 111.13/15.94 End of proof
% 111.13/15.94
% 111.13/15.94 Sub-proof #45 shows that the following formulas are inconsistent:
% 111.13/15.94 ----------------------------------------------------------------
% 111.13/15.94 (1) ~ (e2 = e0)
% 111.13/15.94 (2) op(e0, e1) = e2
% 111.13/15.94 (3) op(e0, e1) = all_53_1
% 111.13/15.94 (4) op(e0, e1) = e0
% 111.13/15.94 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/15.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/15.94
% 111.13/15.94 Begin of proof
% 111.13/15.94 |
% 111.13/15.94 | GROUND_INST: instantiating (5) with all_53_1, e0, e1, e0, simplifying with
% 111.13/15.94 | (3), (4) gives:
% 111.13/15.94 | (6) all_53_1 = e0
% 111.13/15.94 |
% 111.13/15.94 | GROUND_INST: instantiating (5) with all_53_1, e2, e1, e0, simplifying with
% 111.13/15.94 | (2), (3) gives:
% 111.13/15.94 | (7) all_53_1 = e2
% 111.13/15.94 |
% 111.13/15.94 | COMBINE_EQS: (6), (7) imply:
% 111.13/15.94 | (8) e2 = e0
% 111.13/15.94 |
% 111.13/15.94 | SIMP: (8) implies:
% 111.13/15.94 | (9) e2 = e0
% 111.13/15.94 |
% 111.13/15.94 | REDUCE: (1), (9) imply:
% 111.13/15.94 | (10) $false
% 111.13/15.94 |
% 111.13/15.94 | CLOSE: (10) is inconsistent.
% 111.13/15.94 |
% 111.13/15.94 End of proof
% 111.13/15.94
% 111.13/15.94 Sub-proof #46 shows that the following formulas are inconsistent:
% 111.13/15.94 ----------------------------------------------------------------
% 111.13/15.94 (1) op(e1, e1) = all_6_1
% 111.13/15.94 (2) all_22_2 = all_6_1
% 111.13/15.94 (3) op(e3, e0) = all_53_12
% 111.13/15.94 (4) ~ (all_10_2 = e3)
% 111.13/15.94 (5) ~ (all_46_2 = e1) | (op(e1, e1) = all_46_1 & $i(all_46_1) & ( ~
% 111.13/15.94 (all_46_1 = e0) | ( ~ (all_46_0 = e3) & op(e0, e1) = all_46_0 &
% 111.13/15.94 $i(all_46_0))))
% 111.13/15.94 (6) op(e2, e3) = all_53_10
% 111.13/15.94 (7) op(e1, e0) = all_53_4
% 111.13/15.94 (8) all_55_10 = all_10_2
% 111.13/15.94 (9) ~ (all_53_4 = e1)
% 111.13/15.94 (10) ~ (all_53_1 = all_53_9)
% 111.13/15.94 (11) ~ (all_53_12 = all_53_13)
% 111.13/15.94 (12) ~ (all_53_8 = all_10_2)
% 111.13/15.94 (13) all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 111.13/15.94 (14) (all_57_44 = e1 & op(e3, e1) = e1) | (all_57_45 = e1 & op(e2, e1) = e1)
% 111.13/15.94 | (all_57_46 = e1 & op(e1, e1) = e1) | (all_57_47 = e1 & op(e0, e1) =
% 111.13/15.94 e1)
% 111.13/15.94 (15) ~ (all_10_2 = e0)
% 111.13/15.94 (16) op(e0, e1) = all_53_1
% 111.13/15.94 (17) op(e2, e1) = all_53_9
% 111.13/15.94 (18) (all_57_72 = e1 & op(e2, e3) = e1) | (all_57_73 = e1 & op(e2, e2) = e1)
% 111.13/15.94 | (all_57_74 = e1 & op(e2, e1) = e1) | (all_57_75 = e1 & op(e2, e0) =
% 111.13/15.94 e1)
% 111.13/15.94 (19) ~ (all_53_9 = all_10_2)
% 111.13/15.94 (20) ~ (all_53_1 = e1)
% 111.13/15.94 (21) op(e2, e0) = all_53_8
% 111.13/15.94 (22) op(e3, e1) = all_53_13
% 111.13/15.94 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/15.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/15.94 (24) ~ (all_24_2 = e1) | (op(e1, e1) = all_24_1 & $i(all_24_1) & ( ~
% 111.13/15.94 (all_24_1 = e3) | ( ~ (all_24_0 = e0) & op(e3, e1) = all_24_0 &
% 111.13/15.94 $i(all_24_0))))
% 111.13/15.94 (25) ~ (all_53_1 = all_53_13)
% 111.13/15.94 (26) all_46_2 = all_10_2
% 111.13/15.94 (27) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 111.13/15.94 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 111.13/15.94 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 111.13/15.94 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 111.13/15.94 $i(all_52_4))
% 111.13/15.94 (28) ~ (all_53_1 = all_6_1)
% 111.13/15.94 (29) ~ (all_53_10 = all_10_2)
% 111.13/15.94 (30) all_55_1 = all_53_1
% 111.13/15.94 (31) all_24_2 = all_10_2
% 111.13/15.94 (32) all_22_2 = e0
% 111.13/15.94 (33) all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 111.13/15.94 (34) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.13/15.94 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 111.13/15.94 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 111.13/15.94 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.13/15.94 $i(all_52_10))
% 111.13/15.94
% 111.13/15.94 Begin of proof
% 111.13/15.94 |
% 111.13/15.94 | COMBINE_EQS: (2), (32) imply:
% 111.13/15.94 | (35) all_6_1 = e0
% 111.13/15.94 |
% 111.13/15.94 | REDUCE: (28), (35) imply:
% 111.13/15.94 | (36) ~ (all_53_1 = e0)
% 111.13/15.95 |
% 111.13/15.95 | REDUCE: (1), (35) imply:
% 111.13/15.95 | (37) op(e1, e1) = e0
% 111.13/15.95 |
% 111.13/15.95 | BETA: splitting (24) gives:
% 111.13/15.95 |
% 111.13/15.95 | Case 1:
% 111.13/15.95 | |
% 111.13/15.95 | | (38) ~ (all_24_2 = e1)
% 111.13/15.95 | |
% 111.13/15.95 | | REDUCE: (31), (38) imply:
% 111.13/15.95 | | (39) ~ (all_10_2 = e1)
% 111.13/15.95 | |
% 111.13/15.95 | | BETA: splitting (13) gives:
% 111.13/15.95 | |
% 111.13/15.95 | | Case 1:
% 111.13/15.95 | | |
% 111.13/15.95 | | | (40) all_55_10 = e3
% 111.13/15.95 | | |
% 111.13/15.95 | | | COMBINE_EQS: (8), (40) imply:
% 111.13/15.95 | | | (41) all_10_2 = e3
% 111.13/15.95 | | |
% 111.13/15.95 | | | REDUCE: (4), (41) imply:
% 111.13/15.95 | | | (42) $false
% 111.13/15.95 | | |
% 111.13/15.95 | | | CLOSE: (42) is inconsistent.
% 111.13/15.95 | | |
% 111.13/15.95 | | Case 2:
% 111.13/15.95 | | |
% 111.13/15.95 | | | (43) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 111.13/15.95 | | |
% 111.13/15.95 | | | BETA: splitting (43) gives:
% 111.13/15.95 | | |
% 111.13/15.95 | | | Case 1:
% 111.13/15.95 | | | |
% 111.13/15.95 | | | | (44) all_55_10 = e2
% 111.13/15.95 | | | |
% 111.13/15.95 | | | | COMBINE_EQS: (8), (44) imply:
% 111.13/15.95 | | | | (45) all_10_2 = e2
% 111.13/15.95 | | | |
% 111.13/15.95 | | | | REDUCE: (12), (45) imply:
% 111.13/15.95 | | | | (46) ~ (all_53_8 = e2)
% 111.13/15.95 | | | |
% 111.13/15.95 | | | | REDUCE: (19), (45) imply:
% 111.13/15.95 | | | | (47) ~ (all_53_9 = e2)
% 111.13/15.95 | | | |
% 111.13/15.95 | | | | BETA: splitting (27) gives:
% 111.13/15.95 | | | |
% 111.13/15.95 | | | | Case 1:
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | (48) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0,
% 111.13/15.95 | | | | | e3) = all_52_0 & $i(all_52_0)
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | ALPHA: (48) implies:
% 111.13/15.95 | | | | | (49) op(e3, e0) = e3
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | REF_CLOSE: (3), (11), (16), (17), (22), (23), (34), (36), (47), (49)
% 111.13/15.95 | | | | | are inconsistent by sub-proof #51.
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | Case 2:
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | (50) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0,
% 111.13/15.95 | | | | | e2) = all_52_2 & $i(all_52_2)) | (all_52_5 = e1 & ~
% 111.13/15.95 | | | | | (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 111.13/15.95 | | | | | $i(all_52_4))
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | REF_CLOSE: (7), (9), (21), (23), (46), (50) are inconsistent by
% 111.13/15.95 | | | | | sub-proof #225.
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | End of split
% 111.13/15.95 | | | |
% 111.13/15.95 | | | Case 2:
% 111.13/15.95 | | | |
% 111.13/15.95 | | | | (51) all_55_10 = e1 | all_55_10 = e0
% 111.13/15.95 | | | |
% 111.13/15.95 | | | | REF_CLOSE: (8), (15), (39), (51) are inconsistent by sub-proof #208.
% 111.13/15.95 | | | |
% 111.13/15.95 | | | End of split
% 111.13/15.95 | | |
% 111.13/15.95 | | End of split
% 111.13/15.95 | |
% 111.13/15.95 | Case 2:
% 111.13/15.95 | |
% 111.13/15.95 | | (52) all_24_2 = e1
% 111.13/15.95 | | (53) op(e1, e1) = all_24_1 & $i(all_24_1) & ( ~ (all_24_1 = e3) | ( ~
% 111.13/15.95 | | (all_24_0 = e0) & op(e3, e1) = all_24_0 & $i(all_24_0)))
% 111.13/15.95 | |
% 111.13/15.95 | | ALPHA: (53) implies:
% 111.13/15.95 | | (54) op(e1, e1) = all_24_1
% 111.13/15.95 | |
% 111.13/15.95 | | COMBINE_EQS: (31), (52) imply:
% 111.13/15.95 | | (55) all_10_2 = e1
% 111.13/15.95 | |
% 111.13/15.95 | | SIMP: (55) implies:
% 111.13/15.95 | | (56) all_10_2 = e1
% 111.13/15.95 | |
% 111.13/15.95 | | COMBINE_EQS: (26), (56) imply:
% 111.13/15.95 | | (57) all_46_2 = e1
% 111.13/15.95 | |
% 111.13/15.95 | | REDUCE: (12), (56) imply:
% 111.13/15.95 | | (58) ~ (all_53_8 = e1)
% 111.13/15.95 | |
% 111.13/15.95 | | REDUCE: (19), (56) imply:
% 111.13/15.95 | | (59) ~ (all_53_9 = e1)
% 111.13/15.95 | |
% 111.13/15.95 | | REDUCE: (29), (56) imply:
% 111.13/15.95 | | (60) ~ (all_53_10 = e1)
% 111.13/15.95 | |
% 111.13/15.95 | | REDUCE: (4), (56) imply:
% 111.13/15.95 | | (61) ~ (e3 = e1)
% 111.13/15.95 | |
% 111.13/15.95 | | SIMP: (61) implies:
% 111.13/15.95 | | (62) ~ (e3 = e1)
% 111.13/15.95 | |
% 111.13/15.95 | | REDUCE: (15), (56) imply:
% 111.13/15.95 | | (63) ~ (e1 = e0)
% 111.13/15.95 | |
% 111.13/15.95 | | BETA: splitting (5) gives:
% 111.13/15.95 | |
% 111.13/15.95 | | Case 1:
% 111.13/15.95 | | |
% 111.13/15.95 | | | (64) ~ (all_46_2 = e1)
% 111.13/15.95 | | |
% 111.13/15.95 | | | REDUCE: (57), (64) imply:
% 111.13/15.95 | | | (65) $false
% 111.13/15.95 | | |
% 111.13/15.95 | | | CLOSE: (65) is inconsistent.
% 111.13/15.95 | | |
% 111.13/15.95 | | Case 2:
% 111.13/15.95 | | |
% 111.13/15.95 | | | (66) op(e1, e1) = all_46_1 & $i(all_46_1) & ( ~ (all_46_1 = e0) | ( ~
% 111.13/15.95 | | | (all_46_0 = e3) & op(e0, e1) = all_46_0 & $i(all_46_0)))
% 111.13/15.95 | | |
% 111.13/15.95 | | | ALPHA: (66) implies:
% 111.13/15.95 | | | (67) op(e1, e1) = all_46_1
% 111.13/15.95 | | | (68) ~ (all_46_1 = e0) | ( ~ (all_46_0 = e3) & op(e0, e1) = all_46_0 &
% 111.13/15.95 | | | $i(all_46_0))
% 111.13/15.95 | | |
% 111.13/15.95 | | | BETA: splitting (14) gives:
% 111.13/15.95 | | |
% 111.13/15.95 | | | Case 1:
% 111.13/15.95 | | | |
% 111.13/15.95 | | | | (69) (all_57_44 = e1 & op(e3, e1) = e1) | (all_57_45 = e1 & op(e2,
% 111.13/15.95 | | | | e1) = e1)
% 111.13/15.95 | | | |
% 111.13/15.95 | | | | BETA: splitting (69) gives:
% 111.13/15.95 | | | |
% 111.13/15.95 | | | | Case 1:
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | (70) all_57_44 = e1 & op(e3, e1) = e1
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | ALPHA: (70) implies:
% 111.13/15.95 | | | | | (71) op(e3, e1) = e1
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | BETA: splitting (18) gives:
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | Case 1:
% 111.13/15.95 | | | | | |
% 111.13/15.95 | | | | | | (72) (all_57_72 = e1 & op(e2, e3) = e1) | (all_57_73 = e1 &
% 111.13/15.95 | | | | | | op(e2, e2) = e1)
% 111.13/15.95 | | | | | |
% 111.13/15.95 | | | | | | BETA: splitting (72) gives:
% 111.13/15.95 | | | | | |
% 111.13/15.95 | | | | | | Case 1:
% 111.13/15.95 | | | | | | |
% 111.13/15.95 | | | | | | | (73) all_57_72 = e1 & op(e2, e3) = e1
% 111.13/15.95 | | | | | | |
% 111.13/15.95 | | | | | | | REF_CLOSE: (6), (23), (60), (73) are inconsistent by sub-proof
% 111.13/15.95 | | | | | | | #50.
% 111.13/15.95 | | | | | | |
% 111.13/15.95 | | | | | | Case 2:
% 111.13/15.95 | | | | | | |
% 111.13/15.95 | | | | | | |
% 111.13/15.95 | | | | | | | GROUND_INST: instantiating (23) with e0, all_46_1, e1, e1,
% 111.13/15.95 | | | | | | | simplifying with (37), (67) gives:
% 111.13/15.95 | | | | | | | (74) all_46_1 = e0
% 111.13/15.95 | | | | | | |
% 111.13/15.95 | | | | | | | GROUND_INST: instantiating (23) with all_24_1, all_46_1, e1, e1,
% 111.13/15.95 | | | | | | | simplifying with (54), (67) gives:
% 111.13/15.95 | | | | | | | (75) all_46_1 = all_24_1
% 111.13/15.95 | | | | | | |
% 111.13/15.95 | | | | | | | GROUND_INST: instantiating (23) with all_53_13, e1, e1, e3,
% 111.13/15.95 | | | | | | | simplifying with (22), (71) gives:
% 111.13/15.95 | | | | | | | (76) all_53_13 = e1
% 111.13/15.95 | | | | | | |
% 111.13/15.95 | | | | | | | COMBINE_EQS: (74), (75) imply:
% 111.13/15.95 | | | | | | | (77) all_24_1 = e0
% 111.13/15.95 | | | | | | |
% 111.13/15.95 | | | | | | | BETA: splitting (34) gives:
% 111.13/15.95 | | | | | | |
% 111.13/15.95 | | | | | | | Case 1:
% 111.13/15.95 | | | | | | | |
% 111.13/15.95 | | | | | | | | (78) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 &
% 111.13/15.95 | | | | | | | | op(e1, e3) = all_52_6 & $i(all_52_6)
% 111.13/15.95 | | | | | | | |
% 111.13/15.95 | | | | | | | | ALPHA: (78) implies:
% 111.13/15.95 | | | | | | | | (79) op(e3, e1) = e3
% 111.13/15.95 | | | | | | | |
% 111.13/15.95 | | | | | | | | GROUND_INST: instantiating (23) with e1, e3, e1, e3, simplifying
% 111.13/15.95 | | | | | | | | with (71), (79) gives:
% 111.13/15.95 | | | | | | | | (80) e3 = e1
% 111.13/15.95 | | | | | | | |
% 111.13/15.95 | | | | | | | | REDUCE: (62), (80) imply:
% 111.13/15.95 | | | | | | | | (81) $false
% 111.13/15.95 | | | | | | | |
% 111.13/15.95 | | | | | | | | CLOSE: (81) is inconsistent.
% 111.13/15.95 | | | | | | | |
% 111.13/15.95 | | | | | | | Case 2:
% 111.13/15.95 | | | | | | | |
% 111.13/15.95 | | | | | | | | (82) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 &
% 111.13/15.95 | | | | | | | | op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 111.13/15.95 | | | | | | | | e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 &
% 111.13/15.95 | | | | | | | | op(e0, e1) = e0 & $i(all_52_10))
% 111.13/15.95 | | | | | | | |
% 111.13/15.95 | | | | | | | | BETA: splitting (82) gives:
% 111.13/15.95 | | | | | | | |
% 111.13/15.95 | | | | | | | | Case 1:
% 111.13/15.95 | | | | | | | | |
% 111.13/15.95 | | | | | | | | | (83) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 &
% 111.13/15.95 | | | | | | | | | op(e1, e2) = all_52_8 & $i(all_52_8)
% 111.13/15.95 | | | | | | | | |
% 111.13/15.95 | | | | | | | | | ALPHA: (83) implies:
% 111.13/15.95 | | | | | | | | | (84) op(e2, e1) = e2
% 111.13/15.95 | | | | | | | | |
% 111.13/15.95 | | | | | | | | | BETA: splitting (68) gives:
% 111.13/15.95 | | | | | | | | |
% 111.13/15.95 | | | | | | | | | Case 1:
% 111.13/15.95 | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | (85) ~ (all_46_1 = e0)
% 111.13/15.95 | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | REDUCE: (74), (85) imply:
% 111.13/15.95 | | | | | | | | | | (86) $false
% 111.13/15.95 | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | CLOSE: (86) is inconsistent.
% 111.13/15.95 | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | Case 2:
% 111.13/15.95 | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | (87) ~ (all_46_0 = e3) & op(e0, e1) = all_46_0 &
% 111.13/15.95 | | | | | | | | | | $i(all_46_0)
% 111.13/15.95 | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | ALPHA: (87) implies:
% 111.13/15.95 | | | | | | | | | | (88) ~ (all_46_0 = e3)
% 111.13/15.95 | | | | | | | | | | (89) op(e0, e1) = all_46_0
% 111.13/15.95 | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | GROUND_INST: instantiating (23) with all_53_1, all_46_0, e1,
% 111.13/15.95 | | | | | | | | | | e0, simplifying with (16), (89) gives:
% 111.13/15.95 | | | | | | | | | | (90) all_53_1 = all_46_0
% 111.13/15.95 | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | GROUND_INST: instantiating (23) with all_53_9, e2, e1, e2,
% 111.13/15.95 | | | | | | | | | | simplifying with (17), (84) gives:
% 111.13/15.95 | | | | | | | | | | (91) all_53_9 = e2
% 111.13/15.95 | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | COMBINE_EQS: (30), (90) imply:
% 111.13/15.95 | | | | | | | | | | (92) all_55_1 = all_46_0
% 111.13/15.95 | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | REDUCE: (10), (90), (91) imply:
% 111.13/15.95 | | | | | | | | | | (93) ~ (all_46_0 = e2)
% 111.13/15.95 | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | BETA: splitting (33) gives:
% 111.13/15.95 | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | Case 1:
% 111.13/15.95 | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | | (94) all_55_1 = e3
% 111.13/15.95 | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | | COMBINE_EQS: (92), (94) imply:
% 111.13/15.95 | | | | | | | | | | | (95) all_46_0 = e3
% 111.13/15.95 | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | | REDUCE: (88), (95) imply:
% 111.13/15.95 | | | | | | | | | | | (96) $false
% 111.13/15.95 | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | | CLOSE: (96) is inconsistent.
% 111.13/15.95 | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | Case 2:
% 111.13/15.95 | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | | (97) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 111.13/15.95 | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | | BETA: splitting (97) gives:
% 111.13/15.95 | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | | Case 1:
% 111.13/15.95 | | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | | | (98) all_55_1 = e2
% 111.13/15.95 | | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | | | COMBINE_EQS: (92), (98) imply:
% 111.13/15.95 | | | | | | | | | | | | (99) all_46_0 = e2
% 111.13/15.95 | | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | | | REDUCE: (93), (99) imply:
% 111.13/15.95 | | | | | | | | | | | | (100) $false
% 111.13/15.95 | | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | | | CLOSE: (100) is inconsistent.
% 111.13/15.95 | | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | | Case 2:
% 111.13/15.95 | | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | | | (101) all_55_1 = e1 | all_55_1 = e0
% 111.13/15.95 | | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | | | REF_CLOSE: (20), (30), (36), (101) are inconsistent by
% 111.13/15.95 | | | | | | | | | | | | sub-proof #49.
% 111.13/15.95 | | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | | End of split
% 111.13/15.95 | | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | | End of split
% 111.13/15.95 | | | | | | | | | |
% 111.13/15.95 | | | | | | | | | End of split
% 111.13/15.95 | | | | | | | | |
% 111.13/15.95 | | | | | | | | Case 2:
% 111.13/15.95 | | | | | | | | |
% 111.13/15.95 | | | | | | | | | (102) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0) =
% 111.13/15.95 | | | | | | | | | all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 111.13/15.95 | | | | | | | | |
% 111.13/15.95 | | | | | | | | | ALPHA: (102) implies:
% 111.13/15.95 | | | | | | | | | (103) op(e0, e1) = e0
% 111.13/15.95 | | | | | | | | |
% 111.13/15.95 | | | | | | | | | REF_CLOSE: (16), (23), (36), (103) are inconsistent by
% 111.13/15.95 | | | | | | | | | sub-proof #230.
% 111.13/15.95 | | | | | | | | |
% 111.13/15.95 | | | | | | | | End of split
% 111.13/15.95 | | | | | | | |
% 111.13/15.95 | | | | | | | End of split
% 111.13/15.95 | | | | | | |
% 111.13/15.95 | | | | | | End of split
% 111.13/15.95 | | | | | |
% 111.13/15.95 | | | | | Case 2:
% 111.13/15.95 | | | | | |
% 111.13/15.95 | | | | | | (104) (all_57_74 = e1 & op(e2, e1) = e1) | (all_57_75 = e1 &
% 111.13/15.95 | | | | | | op(e2, e0) = e1)
% 111.13/15.95 | | | | | |
% 111.13/15.95 | | | | | | REF_CLOSE: (17), (21), (23), (58), (59), (104) are inconsistent by
% 111.13/15.95 | | | | | | sub-proof #47.
% 111.13/15.95 | | | | | |
% 111.13/15.95 | | | | | End of split
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | Case 2:
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | (105) all_57_45 = e1 & op(e2, e1) = e1
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | ALPHA: (105) implies:
% 111.13/15.95 | | | | | (106) op(e2, e1) = e1
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | REF_CLOSE: (17), (23), (59), (106) are inconsistent by sub-proof #48.
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | End of split
% 111.13/15.95 | | | |
% 111.13/15.95 | | | Case 2:
% 111.13/15.95 | | | |
% 111.13/15.95 | | | | (107) (all_57_46 = e1 & op(e1, e1) = e1) | (all_57_47 = e1 & op(e0,
% 111.13/15.95 | | | | e1) = e1)
% 111.13/15.95 | | | |
% 111.13/15.95 | | | | BETA: splitting (107) gives:
% 111.13/15.95 | | | |
% 111.13/15.95 | | | | Case 1:
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | (108) all_57_46 = e1 & op(e1, e1) = e1
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | ALPHA: (108) implies:
% 111.13/15.95 | | | | | (109) op(e1, e1) = e1
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | GROUND_INST: instantiating (23) with e0, all_46_1, e1, e1, simplifying
% 111.13/15.95 | | | | | with (37), (67) gives:
% 111.13/15.95 | | | | | (110) all_46_1 = e0
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | GROUND_INST: instantiating (23) with all_24_1, all_46_1, e1, e1,
% 111.13/15.95 | | | | | simplifying with (54), (67) gives:
% 111.13/15.95 | | | | | (111) all_46_1 = all_24_1
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | GROUND_INST: instantiating (23) with e1, all_46_1, e1, e1, simplifying
% 111.13/15.95 | | | | | with (67), (109) gives:
% 111.13/15.95 | | | | | (112) all_46_1 = e1
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | COMBINE_EQS: (111), (112) imply:
% 111.13/15.95 | | | | | (113) all_24_1 = e1
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | COMBINE_EQS: (110), (111) imply:
% 111.13/15.95 | | | | | (114) all_24_1 = e0
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | COMBINE_EQS: (113), (114) imply:
% 111.13/15.95 | | | | | (115) e1 = e0
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | SIMP: (115) implies:
% 111.13/15.95 | | | | | (116) e1 = e0
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | REDUCE: (63), (116) imply:
% 111.13/15.95 | | | | | (117) $false
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | CLOSE: (117) is inconsistent.
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | Case 2:
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | (118) all_57_47 = e1 & op(e0, e1) = e1
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | ALPHA: (118) implies:
% 111.13/15.95 | | | | | (119) op(e0, e1) = e1
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | | REF_CLOSE: (16), (20), (23), (119) are inconsistent by sub-proof #170.
% 111.13/15.95 | | | | |
% 111.13/15.95 | | | | End of split
% 111.13/15.95 | | | |
% 111.13/15.95 | | | End of split
% 111.13/15.95 | | |
% 111.13/15.95 | | End of split
% 111.13/15.95 | |
% 111.13/15.95 | End of split
% 111.13/15.95 |
% 111.13/15.95 End of proof
% 111.13/15.95
% 111.13/15.95 Sub-proof #47 shows that the following formulas are inconsistent:
% 111.13/15.95 ----------------------------------------------------------------
% 111.13/15.95 (1) ~ (all_53_9 = e1)
% 111.13/15.95 (2) ~ (all_53_8 = e1)
% 111.13/15.95 (3) op(e2, e1) = all_53_9
% 111.13/15.95 (4) op(e2, e0) = all_53_8
% 111.13/15.95 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/15.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/15.95 (6) (all_57_74 = e1 & op(e2, e1) = e1) | (all_57_75 = e1 & op(e2, e0) = e1)
% 111.13/15.95
% 111.13/15.95 Begin of proof
% 111.13/15.95 |
% 111.13/15.95 | BETA: splitting (6) gives:
% 111.13/15.95 |
% 111.13/15.95 | Case 1:
% 111.13/15.95 | |
% 111.13/15.95 | | (7) all_57_74 = e1 & op(e2, e1) = e1
% 111.13/15.95 | |
% 111.13/15.95 | | ALPHA: (7) implies:
% 111.13/15.97 | | (8) op(e2, e1) = e1
% 111.13/15.97 | |
% 111.13/15.97 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #48.
% 111.13/15.97 | |
% 111.13/15.97 | Case 2:
% 111.13/15.97 | |
% 111.13/15.97 | | (9) all_57_75 = e1 & op(e2, e0) = e1
% 111.13/15.97 | |
% 111.13/15.97 | | ALPHA: (9) implies:
% 111.13/15.97 | | (10) op(e2, e0) = e1
% 111.13/15.97 | |
% 111.13/15.97 | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #173.
% 111.13/15.97 | |
% 111.13/15.97 | End of split
% 111.13/15.97 |
% 111.13/15.97 End of proof
% 111.13/15.97
% 111.13/15.97 Sub-proof #48 shows that the following formulas are inconsistent:
% 111.13/15.97 ----------------------------------------------------------------
% 111.13/15.97 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/15.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/15.97 (2) op(e2, e1) = all_53_9
% 111.13/15.97 (3) op(e2, e1) = e1
% 111.13/15.97 (4) ~ (all_53_9 = e1)
% 111.13/15.97
% 111.13/15.97 Begin of proof
% 111.13/15.97 |
% 111.13/15.97 | GROUND_INST: instantiating (1) with all_53_9, e1, e1, e2, simplifying with
% 111.13/15.97 | (2), (3) gives:
% 111.13/15.97 | (5) all_53_9 = e1
% 111.13/15.97 |
% 111.13/15.97 | REDUCE: (4), (5) imply:
% 111.13/15.97 | (6) $false
% 111.13/15.97 |
% 111.13/15.97 | CLOSE: (6) is inconsistent.
% 111.13/15.97 |
% 111.13/15.97 End of proof
% 111.13/15.97
% 111.13/15.97 Sub-proof #49 shows that the following formulas are inconsistent:
% 111.13/15.97 ----------------------------------------------------------------
% 111.13/15.97 (1) all_55_1 = e1 | all_55_1 = e0
% 111.13/15.97 (2) all_55_1 = all_53_1
% 111.13/15.97 (3) ~ (all_53_1 = e1)
% 111.13/15.97 (4) ~ (all_53_1 = e0)
% 111.13/15.97
% 111.13/15.97 Begin of proof
% 111.13/15.97 |
% 111.13/15.97 | BETA: splitting (1) gives:
% 111.13/15.97 |
% 111.13/15.97 | Case 1:
% 111.13/15.97 | |
% 111.13/15.97 | | (5) all_55_1 = e1
% 111.13/15.97 | |
% 111.13/15.97 | | COMBINE_EQS: (2), (5) imply:
% 111.13/15.97 | | (6) all_53_1 = e1
% 111.13/15.97 | |
% 111.13/15.97 | | SIMP: (6) implies:
% 111.13/15.97 | | (7) all_53_1 = e1
% 111.13/15.97 | |
% 111.13/15.97 | | REDUCE: (3), (7) imply:
% 111.13/15.97 | | (8) $false
% 111.13/15.97 | |
% 111.13/15.97 | | CLOSE: (8) is inconsistent.
% 111.13/15.97 | |
% 111.13/15.97 | Case 2:
% 111.13/15.97 | |
% 111.13/15.97 | | (9) all_55_1 = e0
% 111.13/15.97 | |
% 111.13/15.97 | | COMBINE_EQS: (2), (9) imply:
% 111.13/15.97 | | (10) all_53_1 = e0
% 111.13/15.97 | |
% 111.13/15.97 | | SIMP: (10) implies:
% 111.13/15.97 | | (11) all_53_1 = e0
% 111.13/15.97 | |
% 111.13/15.97 | | REDUCE: (4), (11) imply:
% 111.13/15.97 | | (12) $false
% 111.13/15.97 | |
% 111.13/15.97 | | CLOSE: (12) is inconsistent.
% 111.13/15.97 | |
% 111.13/15.97 | End of split
% 111.13/15.97 |
% 111.13/15.97 End of proof
% 111.13/15.97
% 111.13/15.97 Sub-proof #50 shows that the following formulas are inconsistent:
% 111.13/15.97 ----------------------------------------------------------------
% 111.13/15.97 (1) all_57_72 = e1 & op(e2, e3) = e1
% 111.13/15.97 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/15.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/15.97 (3) op(e2, e3) = all_53_10
% 111.13/15.97 (4) ~ (all_53_10 = e1)
% 111.13/15.97
% 111.13/15.97 Begin of proof
% 111.13/15.97 |
% 111.13/15.97 | ALPHA: (1) implies:
% 111.13/15.97 | (5) op(e2, e3) = e1
% 111.13/15.97 |
% 111.13/15.97 | GROUND_INST: instantiating (2) with all_53_10, e1, e3, e2, simplifying with
% 111.13/15.97 | (3), (5) gives:
% 111.13/15.97 | (6) all_53_10 = e1
% 111.13/15.97 |
% 111.13/15.97 | REDUCE: (4), (6) imply:
% 111.13/15.97 | (7) $false
% 111.13/15.97 |
% 111.13/15.97 | CLOSE: (7) is inconsistent.
% 111.13/15.97 |
% 111.13/15.97 End of proof
% 111.13/15.97
% 111.13/15.97 Sub-proof #51 shows that the following formulas are inconsistent:
% 111.13/15.97 ----------------------------------------------------------------
% 111.13/15.97 (1) ~ (all_53_9 = e2)
% 111.13/15.97 (2) ~ (all_53_1 = e0)
% 111.13/15.97 (3) op(e3, e0) = all_53_12
% 111.13/15.97 (4) ~ (all_53_12 = all_53_13)
% 111.13/15.97 (5) op(e0, e1) = all_53_1
% 111.13/15.98 (6) op(e2, e1) = all_53_9
% 111.13/15.98 (7) op(e3, e0) = e3
% 111.13/15.98 (8) op(e3, e1) = all_53_13
% 111.13/15.98 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/15.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/15.98 (10) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.13/15.98 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 111.13/15.98 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 111.13/15.98 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.13/15.98 $i(all_52_10))
% 111.13/15.98
% 111.13/15.98 Begin of proof
% 111.13/15.98 |
% 111.13/15.98 | BETA: splitting (10) gives:
% 111.13/15.98 |
% 111.13/15.98 | Case 1:
% 111.13/15.98 | |
% 111.13/15.98 | | (11) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.13/15.98 | | all_52_6 & $i(all_52_6)
% 111.13/15.98 | |
% 111.13/15.98 | | ALPHA: (11) implies:
% 111.13/15.98 | | (12) op(e3, e1) = e3
% 111.13/15.98 | |
% 111.13/15.98 | | REF_CLOSE: (3), (4), (7), (8), (9), (12) are inconsistent by sub-proof #213.
% 111.13/15.98 | |
% 111.13/15.98 | Case 2:
% 111.13/15.98 | |
% 111.13/15.98 | | (13) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 111.13/15.98 | | all_52_8 & $i(all_52_8)) | (all_52_11 = e0 & ~ (all_52_10 = e1) &
% 111.13/15.98 | | op(e1, e0) = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 111.13/15.98 | |
% 111.13/15.98 | | REF_CLOSE: (1), (2), (5), (6), (9), (13) are inconsistent by sub-proof #229.
% 111.13/15.98 | |
% 111.13/15.98 | End of split
% 111.13/15.98 |
% 111.13/15.98 End of proof
% 111.13/15.98
% 111.13/15.98 Sub-proof #52 shows that the following formulas are inconsistent:
% 111.13/15.98 ----------------------------------------------------------------
% 111.13/15.98 (1) op(e2, e2) = all_44_1
% 111.13/15.98 (2) op(e2, e2) = all_14_1
% 111.13/15.98 (3) op(e2, e2) = e3
% 111.13/15.98 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/15.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/15.98 (5) op(e2, e2) = e2
% 111.13/15.98 (6) ~ (e3 = e2)
% 111.13/15.98
% 111.13/15.98 Begin of proof
% 111.13/15.98 |
% 111.13/15.98 | GROUND_INST: instantiating (4) with e3, all_44_1, e2, e2, simplifying with
% 111.13/15.98 | (1), (3) gives:
% 111.13/15.98 | (7) all_44_1 = e3
% 111.13/15.98 |
% 111.13/15.98 | GROUND_INST: instantiating (4) with all_14_1, all_44_1, e2, e2, simplifying
% 111.13/15.98 | with (1), (2) gives:
% 111.13/15.98 | (8) all_44_1 = all_14_1
% 111.13/15.98 |
% 111.13/15.98 | GROUND_INST: instantiating (4) with e2, all_44_1, e2, e2, simplifying with
% 111.13/15.98 | (1), (5) gives:
% 111.13/15.98 | (9) all_44_1 = e2
% 111.13/15.98 |
% 111.13/15.98 | COMBINE_EQS: (7), (8) imply:
% 111.13/15.98 | (10) all_14_1 = e3
% 111.13/15.98 |
% 111.13/15.98 | COMBINE_EQS: (8), (9) imply:
% 111.13/15.98 | (11) all_14_1 = e2
% 111.13/15.98 |
% 111.13/15.98 | COMBINE_EQS: (10), (11) imply:
% 111.13/15.98 | (12) e3 = e2
% 111.13/15.98 |
% 111.13/15.98 | REDUCE: (6), (12) imply:
% 111.13/15.98 | (13) $false
% 111.13/15.98 |
% 111.13/15.98 | CLOSE: (13) is inconsistent.
% 111.13/15.98 |
% 111.13/15.98 End of proof
% 111.13/15.98
% 111.13/15.98 Sub-proof #53 shows that the following formulas are inconsistent:
% 111.13/15.98 ----------------------------------------------------------------
% 111.13/15.98 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/15.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/15.98 (2) op(e2, e3) = e2
% 111.13/15.98 (3) op(e2, e3) = e1
% 111.13/15.98 (4) ~ (e2 = e1)
% 111.13/15.98
% 111.13/15.98 Begin of proof
% 111.13/15.98 |
% 111.13/15.98 | GROUND_INST: instantiating (1) with e2, e1, e3, e2, simplifying with (2), (3)
% 111.13/15.98 | gives:
% 111.13/15.98 | (5) e2 = e1
% 111.13/15.98 |
% 111.13/15.98 | REDUCE: (4), (5) imply:
% 111.13/15.98 | (6) $false
% 111.13/15.98 |
% 111.13/15.98 | CLOSE: (6) is inconsistent.
% 111.13/15.98 |
% 111.13/15.98 End of proof
% 111.13/15.98
% 111.13/15.98 Sub-proof #54 shows that the following formulas are inconsistent:
% 111.13/15.98 ----------------------------------------------------------------
% 111.13/15.98 (1) ~ (all_53_6 = all_53_10)
% 111.13/15.98 (2) ~ (all_53_10 = e3)
% 111.13/15.98 (3) op(e0, e3) = e3
% 111.13/15.98 (4) all_18_1 = e2
% 111.13/15.98 (5) op(e2, e3) = all_53_10
% 111.13/15.98 (6) all_55_11 = all_53_10
% 111.13/15.98 (7) ~ (e3 = e0)
% 111.13/15.98 (8) ~ (all_18_1 = e2) | ( ~ (all_18_0 = e0) & op(e2, e3) = all_18_0 &
% 111.13/15.98 $i(all_18_0))
% 111.13/15.98 (9) op(e1, e3) = all_53_6
% 111.13/15.98 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/15.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/15.98 (11) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 111.13/15.98 e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20 = e3) &
% 111.13/15.98 op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23
% 111.13/15.98 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0
% 111.13/15.98 & $i(all_52_22))
% 111.13/15.98 (12) all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 111.13/15.98 (13) ~ (all_53_10 = e2)
% 111.13/15.98
% 111.13/15.98 Begin of proof
% 111.13/15.98 |
% 111.13/15.98 | BETA: splitting (11) gives:
% 111.13/15.98 |
% 111.13/15.98 | Case 1:
% 111.13/15.98 | |
% 111.13/15.98 | | (14) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 &
% 111.13/15.98 | | op(e2, e3) = e2 & $i(all_52_18)
% 111.13/15.98 | |
% 111.13/15.98 | | REF_CLOSE: (5), (10), (13), (14) are inconsistent by sub-proof #215.
% 111.13/15.98 | |
% 111.13/15.98 | Case 2:
% 111.13/15.98 | |
% 111.13/15.98 | | (15) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 &
% 111.13/15.98 | | op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23 = e0 & ~ (all_52_22
% 111.13/15.98 | | = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0 &
% 111.13/15.98 | | $i(all_52_22))
% 111.13/15.98 | |
% 111.13/15.98 | | BETA: splitting (15) gives:
% 111.13/15.98 | |
% 111.13/15.98 | | Case 1:
% 111.13/15.98 | | |
% 111.13/15.99 | | | (16) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 &
% 111.13/15.99 | | | op(e1, e3) = e1 & $i(all_52_20)
% 111.13/15.99 | | |
% 111.13/15.99 | | | ALPHA: (16) implies:
% 111.13/15.99 | | | (17) op(e1, e3) = e1
% 111.13/15.99 | | |
% 111.13/15.99 | | | BETA: splitting (8) gives:
% 111.13/15.99 | | |
% 111.13/15.99 | | | Case 1:
% 111.13/15.99 | | | |
% 111.13/15.99 | | | | (18) ~ (all_18_1 = e2)
% 111.13/15.99 | | | |
% 111.13/15.99 | | | | REDUCE: (4), (18) imply:
% 111.13/15.99 | | | | (19) $false
% 111.13/15.99 | | | |
% 111.13/15.99 | | | | CLOSE: (19) is inconsistent.
% 111.13/15.99 | | | |
% 111.13/15.99 | | | Case 2:
% 111.13/15.99 | | | |
% 111.13/15.99 | | | | (20) ~ (all_18_0 = e0) & op(e2, e3) = all_18_0 & $i(all_18_0)
% 111.13/15.99 | | | |
% 111.13/15.99 | | | | ALPHA: (20) implies:
% 111.13/15.99 | | | | (21) ~ (all_18_0 = e0)
% 111.13/15.99 | | | | (22) op(e2, e3) = all_18_0
% 111.13/15.99 | | | |
% 111.13/15.99 | | | | GROUND_INST: instantiating (10) with all_53_6, e1, e3, e1, simplifying
% 111.13/15.99 | | | | with (9), (17) gives:
% 111.13/15.99 | | | | (23) all_53_6 = e1
% 111.13/15.99 | | | |
% 111.13/15.99 | | | | GROUND_INST: instantiating (10) with all_53_10, all_18_0, e3, e2,
% 111.13/15.99 | | | | simplifying with (5), (22) gives:
% 111.13/15.99 | | | | (24) all_53_10 = all_18_0
% 111.13/15.99 | | | |
% 111.13/15.99 | | | | COMBINE_EQS: (6), (24) imply:
% 111.13/15.99 | | | | (25) all_55_11 = all_18_0
% 111.13/15.99 | | | |
% 111.13/15.99 | | | | REDUCE: (1), (23), (24) imply:
% 111.13/15.99 | | | | (26) ~ (all_18_0 = e1)
% 111.13/15.99 | | | |
% 111.13/15.99 | | | | SIMP: (26) implies:
% 111.13/15.99 | | | | (27) ~ (all_18_0 = e1)
% 111.13/15.99 | | | |
% 111.13/15.99 | | | | REDUCE: (2), (24) imply:
% 111.13/15.99 | | | | (28) ~ (all_18_0 = e3)
% 111.13/15.99 | | | |
% 111.13/15.99 | | | | REDUCE: (13), (24) imply:
% 111.13/15.99 | | | | (29) ~ (all_18_0 = e2)
% 111.13/15.99 | | | |
% 111.13/15.99 | | | | BETA: splitting (12) gives:
% 111.13/15.99 | | | |
% 111.13/15.99 | | | | Case 1:
% 111.13/15.99 | | | | |
% 111.13/15.99 | | | | | (30) all_55_11 = e3
% 111.13/15.99 | | | | |
% 111.13/15.99 | | | | | COMBINE_EQS: (25), (30) imply:
% 111.13/15.99 | | | | | (31) all_18_0 = e3
% 111.13/15.99 | | | | |
% 111.13/15.99 | | | | | REDUCE: (28), (31) imply:
% 111.13/15.99 | | | | | (32) $false
% 111.13/15.99 | | | | |
% 111.13/15.99 | | | | | CLOSE: (32) is inconsistent.
% 111.13/15.99 | | | | |
% 111.13/15.99 | | | | Case 2:
% 111.13/15.99 | | | | |
% 111.13/15.99 | | | | | (33) all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 111.13/15.99 | | | | |
% 111.13/15.99 | | | | | REF_CLOSE: (21), (25), (27), (29), (33) are inconsistent by sub-proof
% 111.13/15.99 | | | | | #55.
% 111.13/15.99 | | | | |
% 111.13/15.99 | | | | End of split
% 111.13/15.99 | | | |
% 111.13/15.99 | | | End of split
% 111.13/15.99 | | |
% 111.13/15.99 | | Case 2:
% 111.13/15.99 | | |
% 111.13/15.99 | | | (34) all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 &
% 111.13/15.99 | | | op(e0, e3) = e0 & $i(all_52_22)
% 111.13/15.99 | | |
% 111.13/15.99 | | | ALPHA: (34) implies:
% 111.13/15.99 | | | (35) op(e0, e3) = e0
% 111.13/15.99 | | |
% 111.13/15.99 | | | REF_CLOSE: (3), (7), (10), (35) are inconsistent by sub-proof #122.
% 111.13/15.99 | | |
% 111.13/15.99 | | End of split
% 111.13/15.99 | |
% 111.13/15.99 | End of split
% 111.13/15.99 |
% 111.13/15.99 End of proof
% 111.13/15.99
% 111.13/15.99 Sub-proof #55 shows that the following formulas are inconsistent:
% 111.13/15.99 ----------------------------------------------------------------
% 111.13/15.99 (1) ~ (all_18_0 = e2)
% 111.13/15.99 (2) ~ (all_18_0 = e0)
% 111.13/15.99 (3) all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 111.13/15.99 (4) ~ (all_18_0 = e1)
% 111.13/15.99 (5) all_55_11 = all_18_0
% 111.13/15.99
% 111.13/15.99 Begin of proof
% 111.13/15.99 |
% 111.13/15.99 | BETA: splitting (3) gives:
% 111.13/15.99 |
% 111.13/15.99 | Case 1:
% 111.13/15.99 | |
% 111.13/15.99 | | (6) all_55_11 = e2
% 111.13/15.99 | |
% 111.13/15.99 | | COMBINE_EQS: (5), (6) imply:
% 111.13/15.99 | | (7) all_18_0 = e2
% 111.13/15.99 | |
% 111.13/15.99 | | REDUCE: (1), (7) imply:
% 111.13/15.99 | | (8) $false
% 111.13/15.99 | |
% 111.13/15.99 | | CLOSE: (8) is inconsistent.
% 111.13/15.99 | |
% 111.13/15.99 | Case 2:
% 111.13/15.99 | |
% 111.13/15.99 | | (9) all_55_11 = e1 | all_55_11 = e0
% 111.13/15.99 | |
% 111.13/15.99 | | BETA: splitting (9) gives:
% 111.13/15.99 | |
% 111.13/15.99 | | Case 1:
% 111.13/15.99 | | |
% 111.13/15.99 | | | (10) all_55_11 = e1
% 111.13/15.99 | | |
% 111.13/15.99 | | | COMBINE_EQS: (5), (10) imply:
% 111.13/15.99 | | | (11) all_18_0 = e1
% 111.13/15.99 | | |
% 111.13/15.99 | | | REDUCE: (4), (11) imply:
% 111.13/15.99 | | | (12) $false
% 111.13/15.99 | | |
% 111.13/15.99 | | | CLOSE: (12) is inconsistent.
% 111.13/15.99 | | |
% 111.13/15.99 | | Case 2:
% 111.13/15.99 | | |
% 111.13/15.99 | | | (13) all_55_11 = e0
% 111.13/15.99 | | |
% 111.13/15.99 | | | COMBINE_EQS: (5), (13) imply:
% 111.13/15.99 | | | (14) all_18_0 = e0
% 111.13/15.99 | | |
% 111.13/15.99 | | | REDUCE: (2), (14) imply:
% 111.13/15.99 | | | (15) $false
% 111.13/15.99 | | |
% 111.13/15.99 | | | CLOSE: (15) is inconsistent.
% 111.13/15.99 | | |
% 111.13/15.99 | | End of split
% 111.13/15.99 | |
% 111.13/15.99 | End of split
% 111.13/15.99 |
% 111.13/15.99 End of proof
% 111.13/15.99
% 111.13/15.99 Sub-proof #56 shows that the following formulas are inconsistent:
% 111.13/15.99 ----------------------------------------------------------------
% 111.13/15.99 (1) ~ (all_48_0 = e1)
% 111.13/15.99 (2) ~ (all_48_0 = e2)
% 111.13/15.99 (3) all_55_7 = all_48_0
% 111.13/15.99 (4) all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 111.13/15.99 (5) ~ (all_48_0 = e0)
% 111.13/15.99
% 111.13/15.99 Begin of proof
% 111.13/15.99 |
% 111.13/15.99 | BETA: splitting (4) gives:
% 111.13/15.99 |
% 111.13/15.99 | Case 1:
% 111.13/15.99 | |
% 111.13/15.99 | | (6) all_55_7 = e2
% 111.13/15.99 | |
% 111.13/15.99 | | COMBINE_EQS: (3), (6) imply:
% 111.13/15.99 | | (7) all_48_0 = e2
% 111.13/15.99 | |
% 111.13/15.99 | | REDUCE: (2), (7) imply:
% 111.13/15.99 | | (8) $false
% 111.13/15.99 | |
% 111.13/15.99 | | CLOSE: (8) is inconsistent.
% 111.13/15.99 | |
% 111.13/15.99 | Case 2:
% 111.13/15.99 | |
% 111.13/15.99 | | (9) all_55_7 = e1 | all_55_7 = e0
% 111.13/15.99 | |
% 111.13/15.99 | | BETA: splitting (9) gives:
% 111.13/15.99 | |
% 111.13/15.99 | | Case 1:
% 111.13/15.99 | | |
% 111.13/15.99 | | | (10) all_55_7 = e1
% 111.13/15.99 | | |
% 111.13/15.99 | | | COMBINE_EQS: (3), (10) imply:
% 111.13/15.99 | | | (11) all_48_0 = e1
% 111.13/15.99 | | |
% 111.13/15.99 | | | REDUCE: (1), (11) imply:
% 111.13/15.99 | | | (12) $false
% 111.13/15.99 | | |
% 111.13/15.99 | | | CLOSE: (12) is inconsistent.
% 111.13/15.99 | | |
% 111.13/15.99 | | Case 2:
% 111.13/15.99 | | |
% 111.13/15.99 | | | (13) all_55_7 = e0
% 111.13/15.99 | | |
% 111.13/15.99 | | | COMBINE_EQS: (3), (13) imply:
% 111.13/15.99 | | | (14) all_48_0 = e0
% 111.13/15.99 | | |
% 111.13/15.99 | | | REDUCE: (5), (14) imply:
% 111.13/15.99 | | | (15) $false
% 111.13/15.99 | | |
% 111.13/15.99 | | | CLOSE: (15) is inconsistent.
% 111.13/15.99 | | |
% 111.13/15.99 | | End of split
% 111.13/15.99 | |
% 111.13/15.99 | End of split
% 111.13/15.99 |
% 111.13/15.99 End of proof
% 111.13/15.99
% 111.13/15.99 Sub-proof #57 shows that the following formulas are inconsistent:
% 111.13/15.99 ----------------------------------------------------------------
% 111.13/15.99 (1) ~ (all_53_3 = all_53_7)
% 111.13/15.99 (2) all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 111.13/15.99 (3) ~ (all_53_15 = e3)
% 111.13/15.99 (4) ~ (all_53_3 = e3)
% 111.13/15.99 (5) all_55_14 = all_16_0
% 111.13/15.99 (6) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 111.13/15.99 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 111.13/15.99 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 111.13/15.99 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 111.13/15.99 $i(all_52_16))
% 111.13/15.99 (7) op(e3, e2) = all_53_15
% 111.13/15.99 (8) op(e1, e2) = all_53_7
% 111.13/15.99 (9) ~ (all_16_0 = e1)
% 111.13/15.99 (10) ~ (all_53_3 = e2)
% 111.13/15.99 (11) all_55_2 = all_53_3
% 111.13/15.99 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/15.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.00 (13) all_55_14 = e1 | all_55_14 = e0
% 111.13/16.00 (14) ~ (all_53_3 = all_16_0)
% 111.13/16.00 (15) op(e0, e2) = all_53_3
% 111.13/16.00
% 111.13/16.00 Begin of proof
% 111.13/16.00 |
% 111.13/16.00 | BETA: splitting (13) gives:
% 111.13/16.00 |
% 111.13/16.00 | Case 1:
% 111.13/16.00 | |
% 111.13/16.00 | | (16) all_55_14 = e1
% 111.13/16.00 | |
% 111.13/16.00 | | COMBINE_EQS: (5), (16) imply:
% 111.13/16.00 | | (17) all_16_0 = e1
% 111.13/16.00 | |
% 111.13/16.00 | | SIMP: (17) implies:
% 111.13/16.00 | | (18) all_16_0 = e1
% 111.13/16.00 | |
% 111.13/16.00 | | REDUCE: (9), (18) imply:
% 111.13/16.00 | | (19) $false
% 111.13/16.00 | |
% 111.13/16.00 | | CLOSE: (19) is inconsistent.
% 111.13/16.00 | |
% 111.13/16.00 | Case 2:
% 111.13/16.00 | |
% 111.13/16.00 | | (20) all_55_14 = e0
% 111.13/16.00 | |
% 111.13/16.00 | | COMBINE_EQS: (5), (20) imply:
% 111.13/16.00 | | (21) all_16_0 = e0
% 111.13/16.00 | |
% 111.13/16.00 | | SIMP: (21) implies:
% 111.13/16.00 | | (22) all_16_0 = e0
% 111.13/16.00 | |
% 111.13/16.00 | | REDUCE: (14), (22) imply:
% 111.13/16.00 | | (23) ~ (all_53_3 = e0)
% 111.13/16.00 | |
% 111.13/16.00 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (15), (23)
% 111.13/16.00 | | are inconsistent by sub-proof #66.
% 111.13/16.00 | |
% 111.13/16.00 | End of split
% 111.13/16.00 |
% 111.13/16.00 End of proof
% 111.13/16.00
% 111.13/16.00 Sub-proof #58 shows that the following formulas are inconsistent:
% 111.13/16.00 ----------------------------------------------------------------
% 111.13/16.00 (1) all_55_14 = all_16_0
% 111.13/16.00 (2) all_55_14 = e3
% 111.13/16.00 (3) ~ (all_16_0 = e3)
% 111.13/16.00
% 111.13/16.00 Begin of proof
% 111.13/16.00 |
% 111.13/16.00 | COMBINE_EQS: (1), (2) imply:
% 111.13/16.00 | (4) all_16_0 = e3
% 111.13/16.00 |
% 111.13/16.00 | SIMP: (4) implies:
% 111.13/16.00 | (5) all_16_0 = e3
% 111.13/16.00 |
% 111.13/16.00 | REDUCE: (3), (5) imply:
% 111.13/16.00 | (6) $false
% 111.13/16.00 |
% 111.13/16.00 | CLOSE: (6) is inconsistent.
% 111.13/16.00 |
% 111.13/16.00 End of proof
% 111.13/16.00
% 111.13/16.00 Sub-proof #59 shows that the following formulas are inconsistent:
% 111.13/16.00 ----------------------------------------------------------------
% 111.13/16.00 (1) all_55_15 = all_4_2
% 111.13/16.00 (2) op(e3, e0) = all_53_12
% 111.13/16.00 (3) op(e1, e0) = all_53_4
% 111.13/16.00 (4) all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 111.13/16.00 (5) op(e0, e0) = e2
% 111.13/16.00 (6) ~ (all_53_8 = e2)
% 111.13/16.00 (7) ~ (all_53_12 = all_4_2)
% 111.13/16.00 (8) (all_57_28 = e3 & op(e3, e0) = e3) | (all_57_29 = e3 & op(e2, e0) = e3) |
% 111.13/16.00 (all_57_30 = e3 & op(e1, e0) = e3) | (all_57_31 = e3 & op(e0, e0) = e3)
% 111.13/16.00 (9) ~ (all_4_2 = e1)
% 111.13/16.00 (10) ~ (all_4_2 = e0)
% 111.13/16.00 (11) ~ (all_4_2 = e2)
% 111.13/16.00 (12) op(e2, e0) = all_53_8
% 111.13/16.00 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.00 (14) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 111.13/16.00 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 111.13/16.00 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 111.13/16.00 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 111.13/16.00 $i(all_52_4))
% 111.13/16.00 (15) ~ (all_53_8 = e3)
% 111.13/16.00
% 111.13/16.00 Begin of proof
% 111.13/16.00 |
% 111.13/16.00 | BETA: splitting (4) gives:
% 111.13/16.00 |
% 111.13/16.00 | Case 1:
% 111.13/16.00 | |
% 111.13/16.00 | | (16) all_55_15 = e3
% 111.13/16.00 | |
% 111.13/16.00 | | COMBINE_EQS: (1), (16) imply:
% 111.13/16.00 | | (17) all_4_2 = e3
% 111.13/16.00 | |
% 111.13/16.00 | | SIMP: (17) implies:
% 111.13/16.00 | | (18) all_4_2 = e3
% 111.13/16.00 | |
% 111.13/16.00 | | REDUCE: (7), (18) imply:
% 111.13/16.00 | | (19) ~ (all_53_12 = e3)
% 111.13/16.00 | |
% 111.13/16.00 | | REDUCE: (11), (18) imply:
% 111.13/16.00 | | (20) ~ (e3 = e2)
% 111.13/16.00 | |
% 111.13/16.00 | | REDUCE: (9), (18) imply:
% 111.13/16.00 | | (21) ~ (e3 = e1)
% 111.13/16.00 | |
% 111.13/16.00 | | REF_CLOSE: (2), (3), (5), (6), (8), (12), (13), (14), (15), (19), (20), (21)
% 111.13/16.00 | | are inconsistent by sub-proof #60.
% 111.13/16.00 | |
% 111.13/16.00 | Case 2:
% 111.13/16.00 | |
% 111.13/16.00 | | (22) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 111.13/16.00 | |
% 111.13/16.00 | | REF_CLOSE: (1), (9), (10), (11), (22) are inconsistent by sub-proof #191.
% 111.13/16.00 | |
% 111.13/16.00 | End of split
% 111.13/16.00 |
% 111.13/16.00 End of proof
% 111.13/16.00
% 111.13/16.00 Sub-proof #60 shows that the following formulas are inconsistent:
% 111.13/16.00 ----------------------------------------------------------------
% 111.13/16.00 (1) op(e3, e0) = all_53_12
% 111.13/16.00 (2) op(e1, e0) = all_53_4
% 111.13/16.00 (3) op(e0, e0) = e2
% 111.13/16.00 (4) ~ (e3 = e1)
% 111.13/16.00 (5) ~ (all_53_8 = e2)
% 111.13/16.00 (6) ~ (all_53_12 = e3)
% 111.13/16.00 (7) (all_57_28 = e3 & op(e3, e0) = e3) | (all_57_29 = e3 & op(e2, e0) = e3) |
% 111.13/16.00 (all_57_30 = e3 & op(e1, e0) = e3) | (all_57_31 = e3 & op(e0, e0) = e3)
% 111.13/16.00 (8) op(e2, e0) = all_53_8
% 111.13/16.00 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.00 (10) ~ (e3 = e2)
% 111.13/16.00 (11) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 111.13/16.00 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 111.13/16.00 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 111.13/16.00 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 111.13/16.00 $i(all_52_4))
% 111.13/16.00 (12) ~ (all_53_8 = e3)
% 111.13/16.00
% 111.13/16.00 Begin of proof
% 111.13/16.00 |
% 111.13/16.00 | BETA: splitting (11) gives:
% 111.13/16.00 |
% 111.13/16.00 | Case 1:
% 111.13/16.00 | |
% 111.13/16.00 | | (13) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 111.13/16.00 | | all_52_0 & $i(all_52_0)
% 111.13/16.00 | |
% 111.13/16.00 | | ALPHA: (13) implies:
% 111.13/16.00 | | (14) op(e3, e0) = e3
% 111.13/16.00 | |
% 111.13/16.00 | | REF_CLOSE: (1), (6), (9), (14) are inconsistent by sub-proof #180.
% 111.13/16.00 | |
% 111.13/16.00 | Case 2:
% 111.13/16.00 | |
% 111.13/16.01 | | (15) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 111.13/16.01 | | all_52_2 & $i(all_52_2)) | (all_52_5 = e1 & ~ (all_52_4 = e0) &
% 111.13/16.01 | | op(e1, e0) = e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 111.13/16.01 | |
% 111.13/16.01 | | BETA: splitting (15) gives:
% 111.13/16.01 | |
% 111.13/16.01 | | Case 1:
% 111.13/16.01 | | |
% 111.13/16.01 | | | (16) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 111.13/16.01 | | | = all_52_2 & $i(all_52_2)
% 111.13/16.01 | | |
% 111.13/16.01 | | | ALPHA: (16) implies:
% 111.13/16.01 | | | (17) op(e2, e0) = e2
% 111.13/16.01 | | |
% 111.13/16.01 | | | REF_CLOSE: (5), (8), (9), (17) are inconsistent by sub-proof #227.
% 111.13/16.01 | | |
% 111.13/16.01 | | Case 2:
% 111.13/16.01 | | |
% 111.13/16.01 | | | (18) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 111.13/16.01 | | | = all_52_4 & $i(all_52_4)
% 111.13/16.01 | | |
% 111.13/16.01 | | | ALPHA: (18) implies:
% 111.13/16.01 | | | (19) op(e1, e0) = e1
% 111.13/16.01 | | |
% 111.13/16.01 | | | BETA: splitting (7) gives:
% 111.13/16.01 | | |
% 111.13/16.01 | | | Case 1:
% 111.13/16.01 | | | |
% 111.13/16.01 | | | | (20) (all_57_28 = e3 & op(e3, e0) = e3) | (all_57_29 = e3 & op(e2,
% 111.13/16.01 | | | | e0) = e3)
% 111.13/16.01 | | | |
% 111.13/16.01 | | | | BETA: splitting (20) gives:
% 111.13/16.01 | | | |
% 111.13/16.01 | | | | Case 1:
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | | (21) all_57_28 = e3 & op(e3, e0) = e3
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | | ALPHA: (21) implies:
% 111.13/16.01 | | | | | (22) op(e3, e0) = e3
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | | REF_CLOSE: (1), (6), (9), (22) are inconsistent by sub-proof #180.
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | Case 2:
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | | (23) all_57_29 = e3 & op(e2, e0) = e3
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | | ALPHA: (23) implies:
% 111.13/16.01 | | | | | (24) op(e2, e0) = e3
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | | REF_CLOSE: (8), (9), (12), (24) are inconsistent by sub-proof #194.
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | End of split
% 111.13/16.01 | | | |
% 111.13/16.01 | | | Case 2:
% 111.13/16.01 | | | |
% 111.13/16.01 | | | | (25) (all_57_30 = e3 & op(e1, e0) = e3) | (all_57_31 = e3 & op(e0,
% 111.13/16.01 | | | | e0) = e3)
% 111.13/16.01 | | | |
% 111.13/16.01 | | | | BETA: splitting (25) gives:
% 111.13/16.01 | | | |
% 111.13/16.01 | | | | Case 1:
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | | (26) all_57_30 = e3 & op(e1, e0) = e3
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | | ALPHA: (26) implies:
% 111.13/16.01 | | | | | (27) op(e1, e0) = e3
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | | REF_CLOSE: (2), (4), (9), (19), (27) are inconsistent by sub-proof
% 111.13/16.01 | | | | | #62.
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | Case 2:
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | | (28) all_57_31 = e3 & op(e0, e0) = e3
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | | ALPHA: (28) implies:
% 111.13/16.01 | | | | | (29) op(e0, e0) = e3
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | | REF_CLOSE: (3), (9), (10), (29) are inconsistent by sub-proof #61.
% 111.13/16.01 | | | | |
% 111.13/16.01 | | | | End of split
% 111.13/16.01 | | | |
% 111.13/16.01 | | | End of split
% 111.13/16.01 | | |
% 111.13/16.01 | | End of split
% 111.13/16.01 | |
% 111.13/16.01 | End of split
% 111.13/16.01 |
% 111.13/16.01 End of proof
% 111.13/16.01
% 111.13/16.01 Sub-proof #61 shows that the following formulas are inconsistent:
% 111.13/16.01 ----------------------------------------------------------------
% 111.13/16.01 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.01 (2) op(e0, e0) = e3
% 111.13/16.01 (3) op(e0, e0) = e2
% 111.13/16.01 (4) ~ (e3 = e2)
% 111.13/16.01
% 111.13/16.01 Begin of proof
% 111.13/16.01 |
% 111.13/16.01 | GROUND_INST: instantiating (1) with e2, e3, e0, e0, simplifying with (2), (3)
% 111.13/16.01 | gives:
% 111.13/16.01 | (5) e3 = e2
% 111.13/16.01 |
% 111.13/16.01 | REDUCE: (4), (5) imply:
% 111.13/16.01 | (6) $false
% 111.13/16.01 |
% 111.13/16.01 | CLOSE: (6) is inconsistent.
% 111.13/16.01 |
% 111.13/16.01 End of proof
% 111.13/16.01
% 111.13/16.01 Sub-proof #62 shows that the following formulas are inconsistent:
% 111.13/16.01 ----------------------------------------------------------------
% 111.13/16.01 (1) op(e1, e0) = all_53_4
% 111.13/16.01 (2) ~ (e3 = e1)
% 111.13/16.01 (3) op(e1, e0) = e1
% 111.13/16.01 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.01 (5) op(e1, e0) = e3
% 111.13/16.01
% 111.13/16.01 Begin of proof
% 111.13/16.01 |
% 111.13/16.01 | GROUND_INST: instantiating (4) with all_53_4, e1, e0, e1, simplifying with
% 111.13/16.01 | (1), (3) gives:
% 111.13/16.01 | (6) all_53_4 = e1
% 111.13/16.01 |
% 111.13/16.01 | GROUND_INST: instantiating (4) with all_53_4, e3, e0, e1, simplifying with
% 111.13/16.01 | (1), (5) gives:
% 111.13/16.01 | (7) all_53_4 = e3
% 111.13/16.01 |
% 111.13/16.01 | COMBINE_EQS: (6), (7) imply:
% 111.13/16.01 | (8) e3 = e1
% 111.13/16.01 |
% 111.13/16.01 | SIMP: (8) implies:
% 111.13/16.01 | (9) e3 = e1
% 111.13/16.01 |
% 111.13/16.01 | REDUCE: (2), (9) imply:
% 111.13/16.01 | (10) $false
% 111.13/16.01 |
% 111.13/16.01 | CLOSE: (10) is inconsistent.
% 111.13/16.01 |
% 111.13/16.01 End of proof
% 111.13/16.01
% 111.13/16.01 Sub-proof #63 shows that the following formulas are inconsistent:
% 111.13/16.01 ----------------------------------------------------------------
% 111.13/16.01 (1) ~ (all_53_8 = e0)
% 111.13/16.01 (2) ~ (all_53_8 = e2)
% 111.13/16.01 (3) ~ (all_53_8 = e1)
% 111.13/16.01 (4) all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 111.13/16.01 (5) all_55_8 = all_53_8
% 111.13/16.01
% 111.13/16.01 Begin of proof
% 111.13/16.01 |
% 111.13/16.01 | BETA: splitting (4) gives:
% 111.13/16.01 |
% 111.13/16.01 | Case 1:
% 111.13/16.01 | |
% 111.13/16.01 | | (6) all_55_8 = e2
% 111.13/16.01 | |
% 111.13/16.01 | | COMBINE_EQS: (5), (6) imply:
% 111.13/16.01 | | (7) all_53_8 = e2
% 111.13/16.01 | |
% 111.13/16.01 | | SIMP: (7) implies:
% 111.13/16.01 | | (8) all_53_8 = e2
% 111.13/16.01 | |
% 111.13/16.01 | | REDUCE: (2), (8) imply:
% 111.13/16.01 | | (9) $false
% 111.13/16.01 | |
% 111.13/16.01 | | CLOSE: (9) is inconsistent.
% 111.13/16.01 | |
% 111.13/16.01 | Case 2:
% 111.13/16.01 | |
% 111.13/16.01 | | (10) all_55_8 = e1 | all_55_8 = e0
% 111.13/16.01 | |
% 111.13/16.01 | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #182.
% 111.13/16.01 | |
% 111.13/16.01 | End of split
% 111.13/16.01 |
% 111.13/16.01 End of proof
% 111.13/16.01
% 111.13/16.01 Sub-proof #64 shows that the following formulas are inconsistent:
% 111.13/16.01 ----------------------------------------------------------------
% 111.13/16.01 (1) ~ (all_53_10 = e1)
% 111.13/16.01 (2) ~ (all_53_10 = e3)
% 111.13/16.01 (3) op(e2, e3) = all_53_10
% 111.13/16.01 (4) all_55_11 = all_53_10
% 111.13/16.01 (5) op(e2, e1) = e2
% 111.13/16.01 (6) all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 111.13/16.01 (7) all_55_3 = all_53_2
% 111.13/16.01 (8) ~ (all_53_2 = e2)
% 111.13/16.01 (9) op(e0, e3) = all_53_2
% 111.13/16.01 (10) op(e2, e1) = all_53_9
% 111.13/16.01 (11) ~ (all_53_6 = e1)
% 111.13/16.01 (12) op(e1, e3) = all_53_6
% 111.13/16.01 (13) ~ (all_53_9 = all_53_10)
% 111.13/16.01 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.02 (15) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 111.13/16.02 e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20 = e3) &
% 111.13/16.02 op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23
% 111.13/16.02 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0
% 111.13/16.02 & $i(all_52_22))
% 111.13/16.02 (16) ~ (all_53_2 = e1)
% 111.13/16.02 (17) all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 111.13/16.02 (18) ~ (all_53_2 = all_53_10)
% 111.13/16.02
% 111.13/16.02 Begin of proof
% 111.13/16.02 |
% 111.13/16.02 | GROUND_INST: instantiating (14) with all_53_9, e2, e1, e2, simplifying with
% 111.13/16.02 | (5), (10) gives:
% 111.13/16.02 | (19) all_53_9 = e2
% 111.13/16.02 |
% 111.13/16.02 | REDUCE: (13), (19) imply:
% 111.13/16.02 | (20) ~ (all_53_10 = e2)
% 111.13/16.02 |
% 111.13/16.02 | SIMP: (20) implies:
% 111.13/16.02 | (21) ~ (all_53_10 = e2)
% 111.13/16.02 |
% 111.13/16.02 | BETA: splitting (15) gives:
% 111.13/16.02 |
% 111.13/16.02 | Case 1:
% 111.13/16.02 | |
% 111.13/16.02 | | (22) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 &
% 111.13/16.02 | | op(e2, e3) = e2 & $i(all_52_18)
% 111.13/16.02 | |
% 111.13/16.02 | | REF_CLOSE: (3), (14), (21), (22) are inconsistent by sub-proof #215.
% 111.13/16.02 | |
% 111.13/16.02 | Case 2:
% 111.13/16.02 | |
% 111.13/16.02 | | (23) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 &
% 111.13/16.02 | | op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23 = e0 & ~ (all_52_22
% 111.13/16.02 | | = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0 &
% 111.13/16.02 | | $i(all_52_22))
% 111.13/16.02 | |
% 111.13/16.02 | | BETA: splitting (23) gives:
% 111.13/16.02 | |
% 111.13/16.02 | | Case 1:
% 111.13/16.02 | | |
% 111.13/16.02 | | | (24) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 &
% 111.13/16.02 | | | op(e1, e3) = e1 & $i(all_52_20)
% 111.13/16.02 | | |
% 111.13/16.02 | | | ALPHA: (24) implies:
% 111.13/16.02 | | | (25) op(e1, e3) = e1
% 111.13/16.02 | | |
% 111.13/16.02 | | | REF_CLOSE: (11), (12), (14), (25) are inconsistent by sub-proof #223.
% 111.13/16.02 | | |
% 111.13/16.02 | | Case 2:
% 111.13/16.02 | | |
% 111.13/16.02 | | | (26) all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 &
% 111.13/16.02 | | | op(e0, e3) = e0 & $i(all_52_22)
% 111.13/16.02 | | |
% 111.13/16.02 | | | ALPHA: (26) implies:
% 111.13/16.02 | | | (27) op(e0, e3) = e0
% 111.13/16.02 | | |
% 111.13/16.02 | | | BETA: splitting (17) gives:
% 111.13/16.02 | | |
% 111.13/16.02 | | | Case 1:
% 111.13/16.02 | | | |
% 111.13/16.02 | | | | (28) all_55_11 = e3
% 111.13/16.02 | | | |
% 111.13/16.02 | | | | REF_CLOSE: (2), (4), (28) are inconsistent by sub-proof #144.
% 111.13/16.02 | | | |
% 111.13/16.02 | | | Case 2:
% 111.13/16.02 | | | |
% 111.13/16.02 | | | | (29) all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 111.13/16.02 | | | |
% 111.13/16.02 | | | | BETA: splitting (29) gives:
% 111.13/16.02 | | | |
% 111.13/16.02 | | | | Case 1:
% 111.13/16.02 | | | | |
% 111.13/16.02 | | | | | (30) all_55_11 = e2
% 111.13/16.02 | | | | |
% 111.13/16.02 | | | | | COMBINE_EQS: (4), (30) imply:
% 111.13/16.02 | | | | | (31) all_53_10 = e2
% 111.13/16.02 | | | | |
% 111.13/16.02 | | | | | REDUCE: (21), (31) imply:
% 111.13/16.02 | | | | | (32) $false
% 111.13/16.02 | | | | |
% 111.13/16.02 | | | | | CLOSE: (32) is inconsistent.
% 111.13/16.02 | | | | |
% 111.13/16.02 | | | | Case 2:
% 111.13/16.02 | | | | |
% 111.13/16.02 | | | | | (33) all_55_11 = e1 | all_55_11 = e0
% 111.13/16.02 | | | | |
% 111.13/16.02 | | | | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (14), (16), (18), (27), (33)
% 111.13/16.02 | | | | | are inconsistent by sub-proof #120.
% 111.13/16.02 | | | | |
% 111.13/16.02 | | | | End of split
% 111.13/16.02 | | | |
% 111.13/16.02 | | | End of split
% 111.13/16.02 | | |
% 111.13/16.02 | | End of split
% 111.13/16.02 | |
% 111.13/16.02 | End of split
% 111.13/16.02 |
% 111.13/16.02 End of proof
% 111.13/16.02
% 111.13/16.02 Sub-proof #65 shows that the following formulas are inconsistent:
% 111.13/16.02 ----------------------------------------------------------------
% 111.13/16.02 (1) ~ (all_52_0 = e2)
% 111.13/16.02 (2) ~ (all_52_0 = e1)
% 111.13/16.02 (3) ~ (all_52_0 = e0)
% 111.13/16.02 (4) all_55_3 = all_52_0
% 111.13/16.02 (5) all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 111.13/16.02
% 111.13/16.02 Begin of proof
% 111.13/16.02 |
% 111.13/16.02 | BETA: splitting (5) gives:
% 111.13/16.02 |
% 111.13/16.02 | Case 1:
% 111.13/16.02 | |
% 111.13/16.02 | | (6) all_55_3 = e2
% 111.13/16.02 | |
% 111.13/16.02 | | COMBINE_EQS: (4), (6) imply:
% 111.13/16.02 | | (7) all_52_0 = e2
% 111.13/16.02 | |
% 111.13/16.02 | | REDUCE: (1), (7) imply:
% 111.13/16.02 | | (8) $false
% 111.13/16.02 | |
% 111.13/16.02 | | CLOSE: (8) is inconsistent.
% 111.13/16.02 | |
% 111.13/16.02 | Case 2:
% 111.13/16.02 | |
% 111.13/16.02 | | (9) all_55_3 = e1 | all_55_3 = e0
% 111.13/16.02 | |
% 111.13/16.02 | | BETA: splitting (9) gives:
% 111.13/16.02 | |
% 111.13/16.02 | | Case 1:
% 111.13/16.02 | | |
% 111.13/16.02 | | | (10) all_55_3 = e1
% 111.13/16.02 | | |
% 111.13/16.02 | | | COMBINE_EQS: (4), (10) imply:
% 111.13/16.02 | | | (11) all_52_0 = e1
% 111.13/16.02 | | |
% 111.13/16.02 | | | SIMP: (11) implies:
% 111.13/16.02 | | | (12) all_52_0 = e1
% 111.13/16.02 | | |
% 111.13/16.02 | | | REDUCE: (2), (12) imply:
% 111.13/16.02 | | | (13) $false
% 111.13/16.02 | | |
% 111.13/16.02 | | | CLOSE: (13) is inconsistent.
% 111.13/16.02 | | |
% 111.13/16.02 | | Case 2:
% 111.13/16.02 | | |
% 111.13/16.02 | | | (14) all_55_3 = e0
% 111.13/16.02 | | |
% 111.13/16.02 | | | COMBINE_EQS: (4), (14) imply:
% 111.13/16.02 | | | (15) all_52_0 = e0
% 111.13/16.02 | | |
% 111.13/16.02 | | | SIMP: (15) implies:
% 111.13/16.02 | | | (16) all_52_0 = e0
% 111.13/16.02 | | |
% 111.13/16.02 | | | REDUCE: (3), (16) imply:
% 111.13/16.02 | | | (17) $false
% 111.13/16.02 | | |
% 111.13/16.02 | | | CLOSE: (17) is inconsistent.
% 111.13/16.02 | | |
% 111.13/16.02 | | End of split
% 111.13/16.02 | |
% 111.13/16.02 | End of split
% 111.13/16.02 |
% 111.13/16.02 End of proof
% 111.13/16.02
% 111.13/16.02 Sub-proof #66 shows that the following formulas are inconsistent:
% 111.13/16.02 ----------------------------------------------------------------
% 111.13/16.02 (1) ~ (all_53_3 = all_53_7)
% 111.13/16.02 (2) all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 111.13/16.02 (3) ~ (all_53_15 = e3)
% 111.13/16.02 (4) ~ (all_53_3 = e3)
% 111.13/16.02 (5) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 111.13/16.02 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 111.13/16.02 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 111.13/16.02 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 111.13/16.02 $i(all_52_16))
% 111.13/16.02 (6) op(e3, e2) = all_53_15
% 111.13/16.02 (7) op(e1, e2) = all_53_7
% 111.13/16.02 (8) ~ (all_53_3 = e2)
% 111.13/16.02 (9) all_55_2 = all_53_3
% 111.13/16.02 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.02 (11) op(e0, e2) = all_53_3
% 111.13/16.02 (12) ~ (all_53_3 = e0)
% 111.13/16.02
% 111.13/16.02 Begin of proof
% 111.13/16.02 |
% 111.13/16.02 | BETA: splitting (5) gives:
% 111.13/16.02 |
% 111.13/16.02 | Case 1:
% 111.13/16.02 | |
% 111.13/16.02 | | (13) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3)
% 111.13/16.02 | | = all_52_12 & $i(all_52_12)
% 111.13/16.02 | |
% 111.13/16.02 | | ALPHA: (13) implies:
% 111.13/16.02 | | (14) op(e3, e2) = e3
% 111.13/16.02 | |
% 111.13/16.02 | | REF_CLOSE: (3), (6), (10), (14) are inconsistent by sub-proof #214.
% 111.13/16.02 | |
% 111.13/16.02 | Case 2:
% 111.13/16.02 | |
% 111.13/16.03 | | (15) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 111.13/16.03 | | op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~ (all_52_16
% 111.13/16.03 | | = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 111.13/16.03 | | $i(all_52_16))
% 111.13/16.03 | |
% 111.13/16.03 | | BETA: splitting (15) gives:
% 111.13/16.03 | |
% 111.13/16.03 | | Case 1:
% 111.13/16.03 | | |
% 111.13/16.03 | | | (16) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 111.13/16.03 | | | op(e1, e2) = e1 & $i(all_52_14)
% 111.13/16.03 | | |
% 111.13/16.03 | | | ALPHA: (16) implies:
% 111.13/16.03 | | | (17) op(e1, e2) = e1
% 111.13/16.03 | | |
% 111.13/16.03 | | | BETA: splitting (2) gives:
% 111.13/16.03 | | |
% 111.13/16.03 | | | Case 1:
% 111.13/16.03 | | | |
% 111.13/16.03 | | | | (18) all_55_2 = e3
% 111.13/16.03 | | | |
% 111.13/16.03 | | | | REF_CLOSE: (4), (9), (18) are inconsistent by sub-proof #111.
% 111.13/16.03 | | | |
% 111.13/16.03 | | | Case 2:
% 111.13/16.03 | | | |
% 111.13/16.03 | | | | (19) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 111.13/16.03 | | | |
% 111.13/16.03 | | | | REF_CLOSE: (1), (7), (8), (9), (10), (12), (17), (19) are inconsistent
% 111.13/16.03 | | | | by sub-proof #67.
% 111.13/16.03 | | | |
% 111.13/16.03 | | | End of split
% 111.13/16.03 | | |
% 111.13/16.03 | | Case 2:
% 111.13/16.03 | | |
% 111.13/16.03 | | | (20) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 &
% 111.13/16.03 | | | op(e0, e2) = e0 & $i(all_52_16)
% 111.13/16.03 | | |
% 111.13/16.03 | | | ALPHA: (20) implies:
% 111.13/16.03 | | | (21) op(e0, e2) = e0
% 111.13/16.03 | | |
% 111.13/16.03 | | | REF_CLOSE: (10), (11), (12), (21) are inconsistent by sub-proof #219.
% 111.13/16.03 | | |
% 111.13/16.03 | | End of split
% 111.13/16.03 | |
% 111.13/16.03 | End of split
% 111.13/16.03 |
% 111.13/16.03 End of proof
% 111.13/16.03
% 111.13/16.03 Sub-proof #67 shows that the following formulas are inconsistent:
% 111.13/16.03 ----------------------------------------------------------------
% 111.13/16.03 (1) ~ (all_53_3 = all_53_7)
% 111.13/16.03 (2) op(e1, e2) = e1
% 111.13/16.03 (3) op(e1, e2) = all_53_7
% 111.13/16.03 (4) ~ (all_53_3 = e2)
% 111.13/16.03 (5) all_55_2 = all_53_3
% 111.13/16.03 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.03 (7) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 111.13/16.03 (8) ~ (all_53_3 = e0)
% 111.13/16.03
% 111.13/16.03 Begin of proof
% 111.13/16.03 |
% 111.13/16.03 | BETA: splitting (7) gives:
% 111.13/16.03 |
% 111.13/16.03 | Case 1:
% 111.13/16.03 | |
% 111.13/16.03 | | (9) all_55_2 = e2
% 111.13/16.03 | |
% 111.13/16.03 | | COMBINE_EQS: (5), (9) imply:
% 111.13/16.03 | | (10) all_53_3 = e2
% 111.13/16.03 | |
% 111.13/16.03 | | REDUCE: (4), (10) imply:
% 111.13/16.03 | | (11) $false
% 111.13/16.03 | |
% 111.13/16.03 | | CLOSE: (11) is inconsistent.
% 111.13/16.03 | |
% 111.13/16.03 | Case 2:
% 111.13/16.03 | |
% 111.13/16.03 | | (12) all_55_2 = e1 | all_55_2 = e0
% 111.13/16.03 | |
% 111.13/16.03 | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (12) are inconsistent by sub-proof
% 111.13/16.03 | | #119.
% 111.13/16.03 | |
% 111.13/16.03 | End of split
% 111.13/16.03 |
% 111.13/16.03 End of proof
% 111.13/16.03
% 111.13/16.03 Sub-proof #68 shows that the following formulas are inconsistent:
% 111.13/16.03 ----------------------------------------------------------------
% 111.13/16.03 (1) op(e2, e2) = e0
% 111.13/16.03 (2) ~ (all_53_10 = e3)
% 111.13/16.03 (3) ~ (all_53_9 = e3)
% 111.13/16.03 (4) op(e2, e3) = all_53_10
% 111.13/16.03 (5) (all_57_88 = e3 & op(e2, e3) = e3) | (all_57_89 = e3 & op(e2, e2) = e3) |
% 111.13/16.03 (all_57_90 = e3 & op(e2, e1) = e3) | (all_57_91 = e3 & op(e2, e0) = e3)
% 111.13/16.03 (6) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 111.13/16.03 all_52_2 & $i(all_52_2)
% 111.13/16.03 (7) ~ (e3 = e0)
% 111.13/16.03 (8) op(e2, e1) = all_53_9
% 111.13/16.03 (9) op(e2, e0) = all_53_8
% 111.13/16.03 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.03 (11) ~ (e3 = e2)
% 111.13/16.03
% 111.13/16.03 Begin of proof
% 111.13/16.03 |
% 111.13/16.03 | ALPHA: (6) implies:
% 111.13/16.03 | (12) op(e2, e0) = e2
% 111.13/16.03 |
% 111.13/16.03 | BETA: splitting (5) gives:
% 111.13/16.03 |
% 111.13/16.03 | Case 1:
% 111.13/16.03 | |
% 111.13/16.03 | | (13) (all_57_88 = e3 & op(e2, e3) = e3) | (all_57_89 = e3 & op(e2, e2) =
% 111.13/16.03 | | e3)
% 111.13/16.03 | |
% 111.13/16.03 | | BETA: splitting (13) gives:
% 111.13/16.03 | |
% 111.13/16.03 | | Case 1:
% 111.13/16.03 | | |
% 111.13/16.03 | | | (14) all_57_88 = e3 & op(e2, e3) = e3
% 111.13/16.03 | | |
% 111.13/16.03 | | | ALPHA: (14) implies:
% 111.13/16.03 | | | (15) op(e2, e3) = e3
% 111.13/16.03 | | |
% 111.13/16.03 | | | REF_CLOSE: (2), (4), (10), (15) are inconsistent by sub-proof #198.
% 111.13/16.03 | | |
% 111.13/16.03 | | Case 2:
% 111.13/16.03 | | |
% 111.13/16.03 | | | (16) all_57_89 = e3 & op(e2, e2) = e3
% 111.13/16.03 | | |
% 111.13/16.03 | | | ALPHA: (16) implies:
% 111.13/16.03 | | | (17) op(e2, e2) = e3
% 111.13/16.03 | | |
% 111.13/16.03 | | | REF_CLOSE: (1), (7), (10), (17) are inconsistent by sub-proof #139.
% 111.13/16.03 | | |
% 111.13/16.03 | | End of split
% 111.13/16.03 | |
% 111.13/16.03 | Case 2:
% 111.13/16.03 | |
% 111.13/16.03 | | (18) (all_57_90 = e3 & op(e2, e1) = e3) | (all_57_91 = e3 & op(e2, e0) =
% 111.13/16.03 | | e3)
% 111.13/16.03 | |
% 111.13/16.03 | | BETA: splitting (18) gives:
% 111.13/16.03 | |
% 111.13/16.03 | | Case 1:
% 111.13/16.03 | | |
% 111.13/16.03 | | | (19) all_57_90 = e3 & op(e2, e1) = e3
% 111.13/16.03 | | |
% 111.13/16.03 | | | ALPHA: (19) implies:
% 111.13/16.03 | | | (20) op(e2, e1) = e3
% 111.13/16.03 | | |
% 111.13/16.03 | | | REF_CLOSE: (3), (8), (10), (20) are inconsistent by sub-proof #138.
% 111.13/16.03 | | |
% 111.13/16.03 | | Case 2:
% 111.13/16.03 | | |
% 111.13/16.03 | | | (21) all_57_91 = e3 & op(e2, e0) = e3
% 111.13/16.03 | | |
% 111.13/16.03 | | | ALPHA: (21) implies:
% 111.13/16.03 | | | (22) op(e2, e0) = e3
% 111.13/16.03 | | |
% 111.13/16.03 | | | REF_CLOSE: (9), (10), (11), (12), (22) are inconsistent by sub-proof #69.
% 111.13/16.03 | | |
% 111.13/16.03 | | End of split
% 111.13/16.03 | |
% 111.13/16.03 | End of split
% 111.13/16.03 |
% 111.13/16.03 End of proof
% 111.13/16.03
% 111.13/16.03 Sub-proof #69 shows that the following formulas are inconsistent:
% 111.13/16.03 ----------------------------------------------------------------
% 111.13/16.03 (1) op(e2, e0) = e2
% 111.13/16.03 (2) op(e2, e0) = all_53_8
% 111.13/16.03 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.03 (4) ~ (e3 = e2)
% 111.13/16.03 (5) op(e2, e0) = e3
% 111.13/16.03
% 111.13/16.03 Begin of proof
% 111.13/16.03 |
% 111.13/16.03 | GROUND_INST: instantiating (3) with all_53_8, e2, e0, e2, simplifying with
% 111.13/16.03 | (1), (2) gives:
% 111.13/16.03 | (6) all_53_8 = e2
% 111.13/16.03 |
% 111.13/16.03 | GROUND_INST: instantiating (3) with all_53_8, e3, e0, e2, simplifying with
% 111.13/16.03 | (2), (5) gives:
% 111.13/16.03 | (7) all_53_8 = e3
% 111.13/16.03 |
% 111.13/16.03 | COMBINE_EQS: (6), (7) imply:
% 111.13/16.03 | (8) e3 = e2
% 111.13/16.03 |
% 111.13/16.03 | SIMP: (8) implies:
% 111.13/16.03 | (9) e3 = e2
% 111.13/16.03 |
% 111.13/16.03 | REDUCE: (4), (9) imply:
% 111.13/16.03 | (10) $false
% 111.13/16.03 |
% 111.13/16.03 | CLOSE: (10) is inconsistent.
% 111.13/16.03 |
% 111.13/16.03 End of proof
% 111.13/16.03
% 111.13/16.03 Sub-proof #70 shows that the following formulas are inconsistent:
% 111.13/16.03 ----------------------------------------------------------------
% 111.13/16.04 (1) ~ (all_53_7 = e2)
% 111.13/16.04 (2) op(e1, e2) = all_53_7
% 111.13/16.04 (3) (all_57_86 = e2 & op(e1, e2) = e2) | (all_57_87 = e2 & op(e0, e2) = e2)
% 111.13/16.04 (4) ~ (all_53_3 = e2)
% 111.13/16.04 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.04 (6) op(e0, e2) = all_53_3
% 111.13/16.04
% 111.13/16.04 Begin of proof
% 111.13/16.04 |
% 111.13/16.04 | BETA: splitting (3) gives:
% 111.13/16.04 |
% 111.13/16.04 | Case 1:
% 111.13/16.04 | |
% 111.13/16.04 | | (7) all_57_86 = e2 & op(e1, e2) = e2
% 111.13/16.04 | |
% 111.13/16.04 | | ALPHA: (7) implies:
% 111.13/16.04 | | (8) op(e1, e2) = e2
% 111.13/16.04 | |
% 111.13/16.04 | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #80.
% 111.13/16.04 | |
% 111.13/16.04 | Case 2:
% 111.13/16.04 | |
% 111.13/16.04 | | (9) all_57_87 = e2 & op(e0, e2) = e2
% 111.13/16.04 | |
% 111.13/16.04 | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #71.
% 111.13/16.04 | |
% 111.13/16.04 | End of split
% 111.13/16.04 |
% 111.13/16.04 End of proof
% 111.13/16.04
% 111.13/16.04 Sub-proof #71 shows that the following formulas are inconsistent:
% 111.13/16.04 ----------------------------------------------------------------
% 111.13/16.04 (1) all_57_87 = e2 & op(e0, e2) = e2
% 111.13/16.04 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.04 (3) op(e0, e2) = all_53_3
% 111.13/16.04 (4) ~ (all_53_3 = e2)
% 111.13/16.04
% 111.13/16.04 Begin of proof
% 111.13/16.04 |
% 111.13/16.04 | ALPHA: (1) implies:
% 111.13/16.04 | (5) op(e0, e2) = e2
% 111.13/16.04 |
% 111.13/16.04 | GROUND_INST: instantiating (2) with all_53_3, e2, e2, e0, simplifying with
% 111.13/16.04 | (3), (5) gives:
% 111.13/16.04 | (6) all_53_3 = e2
% 111.13/16.04 |
% 111.13/16.04 | REDUCE: (4), (6) imply:
% 111.13/16.04 | (7) $false
% 111.13/16.04 |
% 111.13/16.04 | CLOSE: (7) is inconsistent.
% 111.13/16.04 |
% 111.13/16.04 End of proof
% 111.13/16.04
% 111.13/16.04 Sub-proof #72 shows that the following formulas are inconsistent:
% 111.13/16.04 ----------------------------------------------------------------
% 111.13/16.04 (1) all_55_6 = all_8_0
% 111.13/16.04 (2) all_55_6 = e1
% 111.13/16.04 (3) ~ (all_8_0 = e1)
% 111.13/16.04
% 111.13/16.04 Begin of proof
% 111.13/16.04 |
% 111.13/16.04 | COMBINE_EQS: (1), (2) imply:
% 111.13/16.04 | (4) all_8_0 = e1
% 111.13/16.04 |
% 111.13/16.04 | SIMP: (4) implies:
% 111.13/16.04 | (5) all_8_0 = e1
% 111.13/16.04 |
% 111.13/16.04 | REDUCE: (3), (5) imply:
% 111.13/16.04 | (6) $false
% 111.13/16.04 |
% 111.13/16.04 | CLOSE: (6) is inconsistent.
% 111.13/16.04 |
% 111.13/16.04 End of proof
% 111.13/16.04
% 111.13/16.04 Sub-proof #73 shows that the following formulas are inconsistent:
% 111.13/16.04 ----------------------------------------------------------------
% 111.13/16.04 (1) all_55_6 = all_8_0
% 111.13/16.04 (2) all_55_6 = e2
% 111.13/16.04 (3) ~ (all_8_0 = e2)
% 111.13/16.04
% 111.13/16.04 Begin of proof
% 111.13/16.04 |
% 111.13/16.04 | COMBINE_EQS: (1), (2) imply:
% 111.13/16.04 | (4) all_8_0 = e2
% 111.13/16.04 |
% 111.13/16.04 | SIMP: (4) implies:
% 111.13/16.04 | (5) all_8_0 = e2
% 111.13/16.04 |
% 111.13/16.04 | REDUCE: (3), (5) imply:
% 111.13/16.04 | (6) $false
% 111.13/16.04 |
% 111.13/16.04 | CLOSE: (6) is inconsistent.
% 111.13/16.04 |
% 111.13/16.04 End of proof
% 111.13/16.04
% 111.13/16.04 Sub-proof #74 shows that the following formulas are inconsistent:
% 111.13/16.04 ----------------------------------------------------------------
% 111.13/16.04 (1) all_55_6 = all_8_0
% 111.13/16.04 (2) all_55_6 = e3
% 111.13/16.04 (3) ~ (all_8_0 = e3)
% 111.13/16.04
% 111.13/16.04 Begin of proof
% 111.13/16.04 |
% 111.13/16.04 | COMBINE_EQS: (1), (2) imply:
% 111.13/16.04 | (4) all_8_0 = e3
% 111.13/16.04 |
% 111.13/16.04 | SIMP: (4) implies:
% 111.13/16.04 | (5) all_8_0 = e3
% 111.13/16.04 |
% 111.13/16.04 | REDUCE: (3), (5) imply:
% 111.13/16.04 | (6) $false
% 111.13/16.04 |
% 111.13/16.04 | CLOSE: (6) is inconsistent.
% 111.13/16.04 |
% 111.13/16.04 End of proof
% 111.13/16.04
% 111.13/16.04 Sub-proof #75 shows that the following formulas are inconsistent:
% 111.13/16.04 ----------------------------------------------------------------
% 111.13/16.04 (1) op(e3, e0) = all_53_12
% 111.13/16.04 (2) op(e2, e3) = all_53_10
% 111.13/16.04 (3) op(e1, e0) = all_53_4
% 111.13/16.04 (4) ~ (all_53_12 = all_53_15)
% 111.13/16.04 (5) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 111.13/16.04 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 111.13/16.04 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 111.13/16.04 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 111.13/16.04 $i(all_52_16))
% 111.13/16.04 (6) op(e3, e2) = all_53_15
% 111.13/16.04 (7) ~ (all_8_1 = e1)
% 111.13/16.04 (8) op(e1, e2) = all_53_7
% 111.13/16.04 (9) ~ (all_53_12 = all_53_13)
% 111.13/16.04 (10) all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 111.13/16.04 (11) op(e0, e3) = all_53_2
% 111.13/16.04 (12) ~ (all_8_1 = e0)
% 111.13/16.04 (13) op(e0, e1) = all_53_1
% 111.13/16.04 (14) op(e2, e1) = all_53_9
% 111.13/16.04 (15) ~ (all_53_8 = all_8_1)
% 111.13/16.04 (16) ~ (all_53_2 = all_53_3)
% 111.13/16.04 (17) ~ (all_53_6 = all_53_7)
% 111.13/16.04 (18) ~ (all_53_4 = all_53_6)
% 111.13/16.04 (19) op(e1, e3) = all_53_6
% 111.13/16.04 (20) all_55_10 = all_8_1
% 111.13/16.04 (21) op(e2, e0) = all_53_8
% 111.13/16.04 (22) op(e3, e1) = all_53_13
% 111.13/16.04 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.04 (24) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 111.13/16.04 e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20 = e3) &
% 111.13/16.04 op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23
% 111.13/16.04 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0
% 111.13/16.04 & $i(all_52_22))
% 111.13/16.04 (25) ~ (all_53_13 = all_53_15)
% 111.13/16.04 (26) ~ (all_53_10 = all_8_1)
% 111.13/16.04 (27) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 111.13/16.04 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 111.13/16.04 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 111.13/16.04 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 111.13/16.04 $i(all_52_4))
% 111.13/16.04 (28) ~ (all_53_4 = all_53_7)
% 111.13/16.04 (29) ~ (all_53_9 = all_8_1)
% 111.13/16.04 (30) ~ (all_53_1 = all_53_3)
% 111.13/16.04 (31) ~ (all_8_1 = e3)
% 111.13/16.04 (32) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.13/16.04 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 111.13/16.04 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 111.13/16.04 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.13/16.04 $i(all_52_10))
% 111.13/16.04 (33) op(e0, e2) = all_53_3
% 111.13/16.04 (34) ~ (all_53_1 = all_53_2)
% 111.13/16.04
% 111.13/16.04 Begin of proof
% 111.13/16.04 |
% 111.13/16.04 | BETA: splitting (10) gives:
% 111.13/16.04 |
% 111.13/16.04 | Case 1:
% 111.13/16.04 | |
% 111.13/16.04 | | (35) all_55_10 = e3
% 111.13/16.04 | |
% 111.13/16.04 | | COMBINE_EQS: (20), (35) imply:
% 111.13/16.04 | | (36) all_8_1 = e3
% 111.13/16.04 | |
% 111.13/16.04 | | REDUCE: (31), (36) imply:
% 111.13/16.04 | | (37) $false
% 111.13/16.04 | |
% 111.13/16.04 | | CLOSE: (37) is inconsistent.
% 111.13/16.04 | |
% 111.13/16.04 | Case 2:
% 111.13/16.04 | |
% 111.13/16.04 | | (38) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 111.13/16.04 | |
% 111.13/16.04 | | BETA: splitting (38) gives:
% 111.13/16.04 | |
% 111.13/16.04 | | Case 1:
% 111.13/16.04 | | |
% 111.13/16.04 | | | (39) all_55_10 = e2
% 111.13/16.04 | | |
% 111.13/16.04 | | | COMBINE_EQS: (20), (39) imply:
% 111.13/16.04 | | | (40) all_8_1 = e2
% 111.13/16.04 | | |
% 111.13/16.04 | | | REDUCE: (15), (40) imply:
% 111.13/16.04 | | | (41) ~ (all_53_8 = e2)
% 111.13/16.04 | | |
% 111.13/16.04 | | | REDUCE: (29), (40) imply:
% 111.13/16.04 | | | (42) ~ (all_53_9 = e2)
% 111.13/16.04 | | |
% 111.13/16.04 | | | REDUCE: (26), (40) imply:
% 111.13/16.05 | | | (43) ~ (all_53_10 = e2)
% 111.13/16.05 | | |
% 111.13/16.05 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (13), (14), (16),
% 111.13/16.05 | | | (17), (18), (19), (21), (22), (23), (24), (25), (27), (28),
% 111.13/16.05 | | | (30), (32), (33), (34), (41), (42), (43) are inconsistent by
% 111.13/16.05 | | | sub-proof #209.
% 111.13/16.05 | | |
% 111.13/16.05 | | Case 2:
% 111.13/16.05 | | |
% 111.13/16.05 | | | (44) all_55_10 = e1 | all_55_10 = e0
% 111.13/16.05 | | |
% 111.13/16.05 | | | REF_CLOSE: (7), (12), (20), (44) are inconsistent by sub-proof #84.
% 111.13/16.05 | | |
% 111.13/16.05 | | End of split
% 111.13/16.05 | |
% 111.13/16.05 | End of split
% 111.13/16.05 |
% 111.13/16.05 End of proof
% 111.13/16.05
% 111.13/16.05 Sub-proof #76 shows that the following formulas are inconsistent:
% 111.13/16.05 ----------------------------------------------------------------
% 111.13/16.05 (1) op(e3, e2) = e3
% 111.13/16.05 (2) ~ (all_53_3 = all_53_15)
% 111.13/16.05 (3) all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 111.13/16.05 (4) op(e3, e2) = all_53_15
% 111.13/16.05 (5) ~ (all_53_3 = e2)
% 111.13/16.05 (6) ~ (all_53_3 = e1)
% 111.13/16.05 (7) all_55_2 = all_53_3
% 111.13/16.05 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.05 (9) ~ (all_53_3 = e0)
% 111.13/16.05
% 111.13/16.05 Begin of proof
% 111.13/16.05 |
% 111.13/16.05 | BETA: splitting (3) gives:
% 111.13/16.05 |
% 111.13/16.05 | Case 1:
% 111.13/16.05 | |
% 111.13/16.05 | | (10) all_55_2 = e3
% 111.13/16.05 | |
% 111.13/16.05 | | COMBINE_EQS: (7), (10) imply:
% 111.13/16.05 | | (11) all_53_3 = e3
% 111.13/16.05 | |
% 111.13/16.05 | | SIMP: (11) implies:
% 111.13/16.05 | | (12) all_53_3 = e3
% 111.13/16.05 | |
% 111.13/16.05 | | REDUCE: (2), (12) imply:
% 111.13/16.05 | | (13) ~ (all_53_15 = e3)
% 111.13/16.05 | |
% 111.13/16.05 | | SIMP: (13) implies:
% 111.13/16.05 | | (14) ~ (all_53_15 = e3)
% 111.13/16.05 | |
% 111.13/16.05 | | REF_CLOSE: (1), (4), (8), (14) are inconsistent by sub-proof #214.
% 111.13/16.05 | |
% 111.13/16.05 | Case 2:
% 111.13/16.05 | |
% 111.13/16.05 | | (15) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 111.13/16.05 | |
% 111.13/16.05 | | BETA: splitting (15) gives:
% 111.13/16.05 | |
% 111.13/16.05 | | Case 1:
% 111.13/16.05 | | |
% 111.13/16.05 | | | (16) all_55_2 = e2
% 111.13/16.05 | | |
% 111.13/16.05 | | | COMBINE_EQS: (7), (16) imply:
% 111.13/16.05 | | | (17) all_53_3 = e2
% 111.13/16.05 | | |
% 111.13/16.05 | | | SIMP: (17) implies:
% 111.13/16.05 | | | (18) all_53_3 = e2
% 111.13/16.05 | | |
% 111.13/16.05 | | | REDUCE: (5), (18) imply:
% 111.13/16.05 | | | (19) $false
% 111.13/16.05 | | |
% 111.13/16.05 | | | CLOSE: (19) is inconsistent.
% 111.13/16.05 | | |
% 111.13/16.05 | | Case 2:
% 111.13/16.05 | | |
% 111.13/16.05 | | | (20) all_55_2 = e1 | all_55_2 = e0
% 111.13/16.05 | | |
% 111.13/16.05 | | | BETA: splitting (20) gives:
% 111.13/16.05 | | |
% 111.13/16.05 | | | Case 1:
% 111.13/16.05 | | | |
% 111.13/16.05 | | | | (21) all_55_2 = e1
% 111.13/16.05 | | | |
% 111.13/16.05 | | | | COMBINE_EQS: (7), (21) imply:
% 111.13/16.05 | | | | (22) all_53_3 = e1
% 111.13/16.05 | | | |
% 111.13/16.05 | | | | SIMP: (22) implies:
% 111.13/16.05 | | | | (23) all_53_3 = e1
% 111.13/16.05 | | | |
% 111.13/16.05 | | | | REDUCE: (6), (23) imply:
% 111.13/16.05 | | | | (24) $false
% 111.13/16.05 | | | |
% 111.13/16.05 | | | | CLOSE: (24) is inconsistent.
% 111.13/16.05 | | | |
% 111.13/16.05 | | | Case 2:
% 111.13/16.05 | | | |
% 111.13/16.05 | | | | (25) all_55_2 = e0
% 111.13/16.05 | | | |
% 111.13/16.05 | | | | COMBINE_EQS: (7), (25) imply:
% 111.13/16.05 | | | | (26) all_53_3 = e0
% 111.13/16.05 | | | |
% 111.13/16.05 | | | | SIMP: (26) implies:
% 111.13/16.05 | | | | (27) all_53_3 = e0
% 111.13/16.05 | | | |
% 111.13/16.05 | | | | REDUCE: (9), (27) imply:
% 111.13/16.05 | | | | (28) $false
% 111.13/16.05 | | | |
% 111.13/16.05 | | | | CLOSE: (28) is inconsistent.
% 111.13/16.05 | | | |
% 111.13/16.05 | | | End of split
% 111.13/16.05 | | |
% 111.13/16.05 | | End of split
% 111.13/16.05 | |
% 111.13/16.05 | End of split
% 111.13/16.05 |
% 111.13/16.05 End of proof
% 111.13/16.05
% 111.13/16.05 Sub-proof #77 shows that the following formulas are inconsistent:
% 111.13/16.05 ----------------------------------------------------------------
% 111.13/16.05 (1) all_55_1 = all_53_1
% 111.13/16.05 (2) all_55_1 = e2
% 111.13/16.05 (3) ~ (all_53_1 = e2)
% 111.13/16.05
% 111.13/16.05 Begin of proof
% 111.13/16.05 |
% 111.13/16.05 | COMBINE_EQS: (1), (2) imply:
% 111.13/16.05 | (4) all_53_1 = e2
% 111.13/16.05 |
% 111.13/16.05 | SIMP: (4) implies:
% 111.13/16.05 | (5) all_53_1 = e2
% 111.13/16.05 |
% 111.13/16.05 | REDUCE: (3), (5) imply:
% 111.13/16.05 | (6) $false
% 111.13/16.05 |
% 111.13/16.05 | CLOSE: (6) is inconsistent.
% 111.13/16.05 |
% 111.13/16.05 End of proof
% 111.13/16.05
% 111.13/16.05 Sub-proof #78 shows that the following formulas are inconsistent:
% 111.13/16.05 ----------------------------------------------------------------
% 111.13/16.05 (1) all_55_1 = all_53_1
% 111.13/16.05 (2) all_55_1 = e3
% 111.13/16.05 (3) ~ (all_53_1 = e3)
% 111.13/16.05
% 111.13/16.05 Begin of proof
% 111.13/16.05 |
% 111.13/16.05 | COMBINE_EQS: (1), (2) imply:
% 111.13/16.05 | (4) all_53_1 = e3
% 111.13/16.05 |
% 111.13/16.05 | SIMP: (4) implies:
% 111.13/16.05 | (5) all_53_1 = e3
% 111.13/16.05 |
% 111.13/16.05 | REDUCE: (3), (5) imply:
% 111.13/16.05 | (6) $false
% 111.13/16.05 |
% 111.13/16.05 | CLOSE: (6) is inconsistent.
% 111.13/16.05 |
% 111.13/16.05 End of proof
% 111.13/16.05
% 111.13/16.05 Sub-proof #79 shows that the following formulas are inconsistent:
% 111.13/16.05 ----------------------------------------------------------------
% 111.13/16.05 (1) ~ (all_53_13 = e3)
% 111.13/16.05 (2) op(e1, e1) = e2
% 111.13/16.05 (3) ~ (all_53_9 = e3)
% 111.13/16.05 (4) (all_57_60 = e3 & op(e3, e1) = e3) | (all_57_61 = e3 & op(e2, e1) = e3) |
% 111.13/16.05 (all_57_62 = e3 & op(e1, e1) = e3) | (all_57_63 = e3 & op(e0, e1) = e3)
% 111.13/16.05 (5) ~ (e3 = e0)
% 111.13/16.05 (6) op(e0, e1) = all_53_1
% 111.13/16.05 (7) op(e2, e1) = all_53_9
% 111.13/16.05 (8) op(e0, e1) = e0
% 111.13/16.05 (9) op(e3, e1) = all_53_13
% 111.13/16.05 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.05 (11) ~ (e3 = e2)
% 111.13/16.05
% 111.13/16.05 Begin of proof
% 111.13/16.05 |
% 111.13/16.05 | BETA: splitting (4) gives:
% 111.13/16.05 |
% 111.13/16.05 | Case 1:
% 111.13/16.05 | |
% 111.13/16.05 | | (12) (all_57_60 = e3 & op(e3, e1) = e3) | (all_57_61 = e3 & op(e2, e1) =
% 111.13/16.05 | | e3)
% 111.13/16.05 | |
% 111.13/16.05 | | BETA: splitting (12) gives:
% 111.13/16.05 | |
% 111.13/16.05 | | Case 1:
% 111.13/16.05 | | |
% 111.13/16.05 | | | (13) all_57_60 = e3 & op(e3, e1) = e3
% 111.13/16.05 | | |
% 111.13/16.05 | | | ALPHA: (13) implies:
% 111.13/16.05 | | | (14) op(e3, e1) = e3
% 111.13/16.05 | | |
% 111.13/16.05 | | | REF_CLOSE: (1), (9), (10), (14) are inconsistent by sub-proof #232.
% 111.13/16.05 | | |
% 111.13/16.05 | | Case 2:
% 111.13/16.05 | | |
% 111.13/16.05 | | | (15) all_57_61 = e3 & op(e2, e1) = e3
% 111.13/16.05 | | |
% 111.13/16.05 | | | ALPHA: (15) implies:
% 111.13/16.05 | | | (16) op(e2, e1) = e3
% 111.13/16.05 | | |
% 111.13/16.05 | | | REF_CLOSE: (3), (7), (10), (16) are inconsistent by sub-proof #138.
% 111.13/16.05 | | |
% 111.13/16.05 | | End of split
% 111.13/16.05 | |
% 111.13/16.05 | Case 2:
% 111.13/16.05 | |
% 111.13/16.05 | | (17) (all_57_62 = e3 & op(e1, e1) = e3) | (all_57_63 = e3 & op(e0, e1) =
% 111.13/16.05 | | e3)
% 111.13/16.05 | |
% 111.13/16.05 | | BETA: splitting (17) gives:
% 111.13/16.05 | |
% 111.13/16.05 | | Case 1:
% 111.13/16.05 | | |
% 111.13/16.05 | | | (18) all_57_62 = e3 & op(e1, e1) = e3
% 111.13/16.05 | | |
% 111.13/16.05 | | | ALPHA: (18) implies:
% 111.13/16.05 | | | (19) op(e1, e1) = e3
% 111.13/16.05 | | |
% 111.13/16.05 | | | REF_CLOSE: (2), (10), (11), (19) are inconsistent by sub-proof #131.
% 111.13/16.05 | | |
% 111.13/16.05 | | Case 2:
% 111.13/16.05 | | |
% 111.13/16.05 | | | (20) all_57_63 = e3 & op(e0, e1) = e3
% 111.13/16.05 | | |
% 111.13/16.05 | | | ALPHA: (20) implies:
% 111.13/16.05 | | | (21) op(e0, e1) = e3
% 111.13/16.05 | | |
% 111.13/16.05 | | | GROUND_INST: instantiating (10) with all_53_1, e0, e1, e0, simplifying
% 111.13/16.05 | | | with (6), (8) gives:
% 111.13/16.05 | | | (22) all_53_1 = e0
% 111.13/16.05 | | |
% 111.13/16.05 | | | GROUND_INST: instantiating (10) with all_53_1, e3, e1, e0, simplifying
% 111.13/16.05 | | | with (6), (21) gives:
% 111.13/16.05 | | | (23) all_53_1 = e3
% 111.13/16.05 | | |
% 111.13/16.05 | | | COMBINE_EQS: (22), (23) imply:
% 111.13/16.05 | | | (24) e3 = e0
% 111.13/16.05 | | |
% 111.13/16.05 | | | SIMP: (24) implies:
% 111.13/16.05 | | | (25) e3 = e0
% 111.13/16.05 | | |
% 111.13/16.05 | | | REDUCE: (5), (25) imply:
% 111.13/16.05 | | | (26) $false
% 111.13/16.05 | | |
% 111.13/16.05 | | | CLOSE: (26) is inconsistent.
% 111.13/16.05 | | |
% 111.13/16.05 | | End of split
% 111.13/16.05 | |
% 111.13/16.05 | End of split
% 111.13/16.05 |
% 111.13/16.05 End of proof
% 111.13/16.05
% 111.13/16.05 Sub-proof #80 shows that the following formulas are inconsistent:
% 111.13/16.05 ----------------------------------------------------------------
% 111.13/16.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.05 (2) op(e1, e2) = all_53_7
% 111.13/16.05 (3) op(e1, e2) = e2
% 111.13/16.05 (4) ~ (all_53_7 = e2)
% 111.13/16.05
% 111.13/16.05 Begin of proof
% 111.13/16.05 |
% 111.13/16.05 | GROUND_INST: instantiating (1) with all_53_7, e2, e2, e1, simplifying with
% 111.13/16.05 | (2), (3) gives:
% 111.13/16.05 | (5) all_53_7 = e2
% 111.13/16.05 |
% 111.13/16.05 | REDUCE: (4), (5) imply:
% 111.13/16.05 | (6) $false
% 111.13/16.05 |
% 111.13/16.05 | CLOSE: (6) is inconsistent.
% 111.13/16.05 |
% 111.13/16.05 End of proof
% 111.13/16.05
% 111.13/16.05 Sub-proof #81 shows that the following formulas are inconsistent:
% 111.13/16.05 ----------------------------------------------------------------
% 111.13/16.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.05 (2) op(e1, e0) = e1
% 111.13/16.05 (3) op(e1, e0) = e0
% 111.13/16.05 (4) ~ (e1 = e0)
% 111.13/16.05
% 111.13/16.05 Begin of proof
% 111.13/16.05 |
% 111.13/16.05 | GROUND_INST: instantiating (1) with e0, e1, e0, e1, simplifying with (2), (3)
% 111.13/16.05 | gives:
% 111.13/16.05 | (5) e1 = e0
% 111.13/16.05 |
% 111.13/16.05 | REDUCE: (4), (5) imply:
% 111.13/16.05 | (6) $false
% 111.13/16.05 |
% 111.13/16.05 | CLOSE: (6) is inconsistent.
% 111.13/16.05 |
% 111.13/16.05 End of proof
% 111.13/16.05
% 111.13/16.05 Sub-proof #82 shows that the following formulas are inconsistent:
% 111.13/16.05 ----------------------------------------------------------------
% 111.13/16.05 (1) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 & op(e1,
% 111.13/16.05 e3) = e1 & $i(all_52_20)
% 111.13/16.05 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.05 (3) op(e1, e3) = e2
% 111.13/16.05 (4) ~ (e2 = e1)
% 111.13/16.05
% 111.13/16.05 Begin of proof
% 111.13/16.05 |
% 111.13/16.05 | ALPHA: (1) implies:
% 111.13/16.05 | (5) op(e1, e3) = e1
% 111.13/16.05 |
% 111.13/16.05 | GROUND_INST: instantiating (2) with e1, e2, e3, e1, simplifying with (3), (5)
% 111.13/16.05 | gives:
% 111.13/16.05 | (6) e2 = e1
% 111.13/16.05 |
% 111.13/16.05 | REDUCE: (4), (6) imply:
% 111.13/16.05 | (7) $false
% 111.13/16.05 |
% 111.13/16.05 | CLOSE: (7) is inconsistent.
% 111.13/16.05 |
% 111.13/16.05 End of proof
% 111.13/16.05
% 111.13/16.05 Sub-proof #83 shows that the following formulas are inconsistent:
% 111.13/16.05 ----------------------------------------------------------------
% 111.13/16.05 (1) ~ (all_53_1 = e0)
% 111.13/16.05 (2) ~ (all_53_1 = e2)
% 111.13/16.05 (3) ~ (all_8_1 = e1)
% 111.13/16.05 (4) all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 111.13/16.05 (5) ~ (all_8_1 = e0)
% 111.13/16.05 (6) op(e0, e1) = all_53_1
% 111.13/16.05 (7) (all_57_52 = e2 & op(e3, e1) = e2) | (all_57_53 = e2 & op(e2, e1) = e2) |
% 111.13/16.05 (all_57_54 = e2 & op(e1, e1) = e2) | (all_57_55 = e2 & op(e0, e1) = e2)
% 111.13/16.05 (8) op(e2, e1) = all_53_9
% 111.13/16.05 (9) all_55_10 = all_8_1
% 111.13/16.05 (10) op(e3, e1) = all_53_13
% 111.13/16.05 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.06 (12) op(e1, e1) = e0
% 111.13/16.06 (13) ~ (all_53_9 = all_8_1)
% 111.13/16.06 (14) ~ (all_8_1 = e3)
% 111.13/16.06 (15) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.13/16.06 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 111.13/16.06 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 111.13/16.06 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.13/16.06 $i(all_52_10))
% 111.13/16.06
% 111.13/16.06 Begin of proof
% 111.13/16.06 |
% 111.13/16.06 | BETA: splitting (4) gives:
% 111.13/16.06 |
% 111.13/16.06 | Case 1:
% 111.13/16.06 | |
% 111.13/16.06 | | (16) all_55_10 = e3
% 111.13/16.06 | |
% 111.13/16.06 | | COMBINE_EQS: (9), (16) imply:
% 111.13/16.06 | | (17) all_8_1 = e3
% 111.13/16.06 | |
% 111.13/16.06 | | REDUCE: (14), (17) imply:
% 111.13/16.06 | | (18) $false
% 111.13/16.06 | |
% 111.13/16.06 | | CLOSE: (18) is inconsistent.
% 111.13/16.06 | |
% 111.13/16.06 | Case 2:
% 111.13/16.06 | |
% 111.13/16.06 | | (19) ~ (all_55_10 = e3)
% 111.13/16.06 | | (20) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 111.13/16.06 | |
% 111.13/16.06 | | BETA: splitting (20) gives:
% 111.13/16.06 | |
% 111.13/16.06 | | Case 1:
% 111.13/16.06 | | |
% 111.13/16.06 | | | (21) all_55_10 = e2
% 111.13/16.06 | | |
% 111.13/16.06 | | | COMBINE_EQS: (9), (21) imply:
% 111.13/16.06 | | | (22) all_8_1 = e2
% 111.13/16.06 | | |
% 111.13/16.06 | | | REDUCE: (13), (22) imply:
% 111.13/16.06 | | | (23) ~ (all_53_9 = e2)
% 111.13/16.06 | | |
% 111.13/16.06 | | | REDUCE: (14), (22) imply:
% 111.13/16.06 | | | (24) ~ (e3 = e2)
% 111.13/16.06 | | |
% 111.13/16.06 | | | SIMP: (24) implies:
% 111.13/16.06 | | | (25) ~ (e3 = e2)
% 111.13/16.06 | | |
% 111.13/16.06 | | | REDUCE: (5), (22) imply:
% 111.13/16.06 | | | (26) ~ (e2 = e0)
% 111.13/16.06 | | |
% 111.13/16.06 | | | BETA: splitting (15) gives:
% 111.13/16.06 | | |
% 111.13/16.06 | | | Case 1:
% 111.13/16.06 | | | |
% 111.13/16.06 | | | | (27) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1,
% 111.13/16.06 | | | | e3) = all_52_6 & $i(all_52_6)
% 111.13/16.06 | | | |
% 111.13/16.06 | | | | ALPHA: (27) implies:
% 111.13/16.06 | | | | (28) op(e3, e1) = e3
% 111.13/16.06 | | | |
% 111.13/16.06 | | | | REF_CLOSE: (2), (6), (7), (8), (10), (11), (12), (23), (25), (26), (28)
% 111.13/16.06 | | | | are inconsistent by sub-proof #85.
% 111.13/16.06 | | | |
% 111.13/16.06 | | | Case 2:
% 111.13/16.06 | | | |
% 111.13/16.06 | | | | (29) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1,
% 111.13/16.06 | | | | e2) = all_52_8 & $i(all_52_8)) | (all_52_11 = e0 & ~
% 111.13/16.06 | | | | (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.13/16.06 | | | | $i(all_52_10))
% 111.13/16.06 | | | |
% 111.13/16.06 | | | | REF_CLOSE: (1), (6), (8), (11), (23), (29) are inconsistent by sub-proof
% 111.13/16.06 | | | | #229.
% 111.13/16.06 | | | |
% 111.13/16.06 | | | End of split
% 111.13/16.06 | | |
% 111.13/16.06 | | Case 2:
% 111.13/16.06 | | |
% 111.13/16.06 | | | (30) all_55_10 = e1 | all_55_10 = e0
% 111.13/16.06 | | |
% 111.13/16.06 | | | REF_CLOSE: (3), (5), (9), (30) are inconsistent by sub-proof #84.
% 111.13/16.06 | | |
% 111.13/16.06 | | End of split
% 111.13/16.06 | |
% 111.13/16.06 | End of split
% 111.13/16.06 |
% 111.13/16.06 End of proof
% 111.13/16.06
% 111.13/16.06 Sub-proof #84 shows that the following formulas are inconsistent:
% 111.13/16.06 ----------------------------------------------------------------
% 111.13/16.06 (1) all_55_10 = e1 | all_55_10 = e0
% 111.13/16.06 (2) all_55_10 = all_8_1
% 111.13/16.06 (3) ~ (all_8_1 = e1)
% 111.13/16.06 (4) ~ (all_8_1 = e0)
% 111.13/16.06
% 111.13/16.06 Begin of proof
% 111.13/16.06 |
% 111.13/16.06 | BETA: splitting (1) gives:
% 111.13/16.06 |
% 111.13/16.06 | Case 1:
% 111.13/16.06 | |
% 111.13/16.06 | | (5) all_55_10 = e1
% 111.13/16.06 | |
% 111.13/16.06 | | COMBINE_EQS: (2), (5) imply:
% 111.13/16.06 | | (6) all_8_1 = e1
% 111.13/16.06 | |
% 111.13/16.06 | | REDUCE: (3), (6) imply:
% 111.13/16.06 | | (7) $false
% 111.13/16.06 | |
% 111.13/16.06 | | CLOSE: (7) is inconsistent.
% 111.13/16.06 | |
% 111.13/16.06 | Case 2:
% 111.13/16.06 | |
% 111.13/16.06 | | (8) all_55_10 = e0
% 111.13/16.06 | |
% 111.13/16.06 | | COMBINE_EQS: (2), (8) imply:
% 111.13/16.06 | | (9) all_8_1 = e0
% 111.13/16.06 | |
% 111.13/16.06 | | REDUCE: (4), (9) imply:
% 111.13/16.06 | | (10) $false
% 111.13/16.06 | |
% 111.13/16.06 | | CLOSE: (10) is inconsistent.
% 111.13/16.06 | |
% 111.13/16.06 | End of split
% 111.13/16.06 |
% 111.13/16.06 End of proof
% 111.13/16.06
% 111.13/16.06 Sub-proof #85 shows that the following formulas are inconsistent:
% 111.13/16.06 ----------------------------------------------------------------
% 111.13/16.06 (1) ~ (all_53_9 = e2)
% 111.13/16.06 (2) ~ (all_53_1 = e2)
% 111.13/16.06 (3) ~ (e2 = e0)
% 111.13/16.06 (4) op(e0, e1) = all_53_1
% 111.13/16.06 (5) (all_57_52 = e2 & op(e3, e1) = e2) | (all_57_53 = e2 & op(e2, e1) = e2) |
% 111.13/16.06 (all_57_54 = e2 & op(e1, e1) = e2) | (all_57_55 = e2 & op(e0, e1) = e2)
% 111.13/16.06 (6) op(e2, e1) = all_53_9
% 111.13/16.06 (7) op(e3, e1) = all_53_13
% 111.13/16.06 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.06 (9) ~ (e3 = e2)
% 111.13/16.06 (10) op(e1, e1) = e0
% 111.13/16.06 (11) op(e3, e1) = e3
% 111.13/16.06
% 111.13/16.06 Begin of proof
% 111.13/16.06 |
% 111.13/16.06 | BETA: splitting (5) gives:
% 111.13/16.06 |
% 111.13/16.06 | Case 1:
% 111.13/16.06 | |
% 111.13/16.06 | | (12) (all_57_52 = e2 & op(e3, e1) = e2) | (all_57_53 = e2 & op(e2, e1) =
% 111.13/16.06 | | e2)
% 111.13/16.06 | |
% 111.13/16.06 | | BETA: splitting (12) gives:
% 111.13/16.06 | |
% 111.13/16.06 | | Case 1:
% 111.13/16.06 | | |
% 111.13/16.06 | | | (13) all_57_52 = e2 & op(e3, e1) = e2
% 111.13/16.06 | | |
% 111.13/16.06 | | | ALPHA: (13) implies:
% 111.13/16.06 | | | (14) op(e3, e1) = e2
% 111.13/16.06 | | |
% 111.13/16.06 | | | REF_CLOSE: (7), (8), (9), (11), (14) are inconsistent by sub-proof #177.
% 111.13/16.06 | | |
% 111.13/16.06 | | Case 2:
% 111.13/16.06 | | |
% 111.13/16.06 | | | (15) all_57_53 = e2 & op(e2, e1) = e2
% 111.13/16.06 | | |
% 111.13/16.06 | | | ALPHA: (15) implies:
% 111.13/16.06 | | | (16) op(e2, e1) = e2
% 111.13/16.06 | | |
% 111.13/16.06 | | | REF_CLOSE: (1), (6), (8), (16) are inconsistent by sub-proof #231.
% 111.13/16.06 | | |
% 111.13/16.06 | | End of split
% 111.13/16.06 | |
% 111.13/16.06 | Case 2:
% 111.13/16.06 | |
% 111.13/16.06 | | (17) (all_57_54 = e2 & op(e1, e1) = e2) | (all_57_55 = e2 & op(e0, e1) =
% 111.13/16.06 | | e2)
% 111.13/16.06 | |
% 111.13/16.06 | | REF_CLOSE: (2), (3), (4), (8), (10), (17) are inconsistent by sub-proof
% 111.13/16.06 | | #108.
% 111.13/16.06 | |
% 111.13/16.06 | End of split
% 111.13/16.06 |
% 111.13/16.06 End of proof
% 111.13/16.06
% 111.13/16.06 Sub-proof #86 shows that the following formulas are inconsistent:
% 111.13/16.06 ----------------------------------------------------------------
% 111.13/16.06 (1) all_55_14 = all_14_0
% 111.13/16.06 (2) all_55_14 = e0
% 111.13/16.06 (3) ~ (all_14_0 = e0)
% 111.13/16.06
% 111.13/16.06 Begin of proof
% 111.13/16.06 |
% 111.13/16.06 | COMBINE_EQS: (1), (2) imply:
% 111.13/16.06 | (4) all_14_0 = e0
% 111.13/16.06 |
% 111.13/16.06 | SIMP: (4) implies:
% 111.13/16.06 | (5) all_14_0 = e0
% 111.13/16.06 |
% 111.13/16.06 | REDUCE: (3), (5) imply:
% 111.13/16.06 | (6) $false
% 111.13/16.06 |
% 111.13/16.06 | CLOSE: (6) is inconsistent.
% 111.13/16.06 |
% 111.13/16.06 End of proof
% 111.13/16.06
% 111.13/16.06 Sub-proof #87 shows that the following formulas are inconsistent:
% 111.13/16.06 ----------------------------------------------------------------
% 111.13/16.06 (1) op(e3, e2) = e3
% 111.13/16.06 (2) op(e3, e2) = e1
% 111.13/16.06 (3) op(e3, e2) = all_53_15
% 111.13/16.06 (4) ~ (e3 = e1)
% 111.13/16.06 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.06
% 111.13/16.06 Begin of proof
% 111.13/16.06 |
% 111.13/16.06 | GROUND_INST: instantiating (5) with all_53_15, e1, e2, e3, simplifying with
% 111.13/16.06 | (2), (3) gives:
% 111.13/16.06 | (6) all_53_15 = e1
% 111.13/16.06 |
% 111.13/16.06 | GROUND_INST: instantiating (5) with all_53_15, e3, e2, e3, simplifying with
% 111.13/16.06 | (1), (3) gives:
% 111.13/16.06 | (7) all_53_15 = e3
% 111.13/16.06 |
% 111.13/16.06 | COMBINE_EQS: (6), (7) imply:
% 111.13/16.06 | (8) e3 = e1
% 111.13/16.06 |
% 111.13/16.06 | REDUCE: (4), (8) imply:
% 111.13/16.06 | (9) $false
% 111.13/16.06 |
% 111.13/16.06 | CLOSE: (9) is inconsistent.
% 111.13/16.06 |
% 111.13/16.06 End of proof
% 111.13/16.06
% 111.13/16.06 Sub-proof #88 shows that the following formulas are inconsistent:
% 111.13/16.06 ----------------------------------------------------------------
% 111.13/16.06 (1) all_55_14 = all_14_0
% 111.13/16.06 (2) all_55_14 = e2
% 111.13/16.06 (3) ~ (all_14_0 = e2)
% 111.13/16.06
% 111.13/16.06 Begin of proof
% 111.13/16.06 |
% 111.13/16.06 | COMBINE_EQS: (1), (2) imply:
% 111.13/16.06 | (4) all_14_0 = e2
% 111.13/16.06 |
% 111.13/16.06 | SIMP: (4) implies:
% 111.13/16.06 | (5) all_14_0 = e2
% 111.13/16.06 |
% 111.13/16.06 | REDUCE: (3), (5) imply:
% 111.13/16.06 | (6) $false
% 111.13/16.06 |
% 111.13/16.06 | CLOSE: (6) is inconsistent.
% 111.13/16.06 |
% 111.13/16.06 End of proof
% 111.13/16.06
% 111.13/16.06 Sub-proof #89 shows that the following formulas are inconsistent:
% 111.13/16.06 ----------------------------------------------------------------
% 111.13/16.06 (1) (all_57_62 = e3 & op(e1, e1) = e3) | (all_57_63 = e3 & op(e0, e1) = e3)
% 111.13/16.06 (2) op(e1, e1) = e2
% 111.13/16.06 (3) op(e0, e1) = all_53_1
% 111.13/16.06 (4) ~ (all_53_1 = e3)
% 111.13/16.06 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.06 (6) ~ (e3 = e2)
% 111.13/16.06
% 111.13/16.06 Begin of proof
% 111.13/16.06 |
% 111.13/16.06 | BETA: splitting (1) gives:
% 111.13/16.06 |
% 111.13/16.06 | Case 1:
% 111.13/16.06 | |
% 111.13/16.06 | | (7) all_57_62 = e3 & op(e1, e1) = e3
% 111.13/16.06 | |
% 111.13/16.06 | | ALPHA: (7) implies:
% 111.13/16.06 | | (8) op(e1, e1) = e3
% 111.13/16.06 | |
% 111.13/16.06 | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #131.
% 111.13/16.06 | |
% 111.13/16.06 | Case 2:
% 111.13/16.06 | |
% 111.13/16.06 | | (9) all_57_63 = e3 & op(e0, e1) = e3
% 111.13/16.06 | |
% 111.13/16.06 | | ALPHA: (9) implies:
% 111.13/16.06 | | (10) op(e0, e1) = e3
% 111.13/16.06 | |
% 111.13/16.06 | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #145.
% 111.13/16.06 | |
% 111.13/16.06 | End of split
% 111.13/16.06 |
% 111.13/16.06 End of proof
% 111.13/16.06
% 111.13/16.06 Sub-proof #90 shows that the following formulas are inconsistent:
% 111.13/16.06 ----------------------------------------------------------------
% 111.13/16.06 (1) all_55_14 = e1 | all_55_14 = e0
% 111.13/16.06 (2) all_55_14 = all_14_0
% 111.13/16.06 (3) ~ (all_14_0 = e1)
% 111.13/16.06 (4) ~ (all_14_0 = e0)
% 111.13/16.06
% 111.13/16.06 Begin of proof
% 111.13/16.06 |
% 111.13/16.06 | BETA: splitting (1) gives:
% 111.13/16.06 |
% 111.13/16.06 | Case 1:
% 111.13/16.06 | |
% 111.13/16.06 | | (5) all_55_14 = e1
% 111.13/16.06 | |
% 111.13/16.06 | | COMBINE_EQS: (2), (5) imply:
% 111.13/16.06 | | (6) all_14_0 = e1
% 111.13/16.06 | |
% 111.13/16.06 | | REDUCE: (3), (6) imply:
% 111.13/16.06 | | (7) $false
% 111.13/16.06 | |
% 111.13/16.06 | | CLOSE: (7) is inconsistent.
% 111.13/16.06 | |
% 111.13/16.06 | Case 2:
% 111.13/16.06 | |
% 111.13/16.06 | | (8) all_55_14 = e0
% 111.13/16.06 | |
% 111.13/16.06 | | COMBINE_EQS: (2), (8) imply:
% 111.13/16.06 | | (9) all_14_0 = e0
% 111.13/16.06 | |
% 111.13/16.06 | | REDUCE: (4), (9) imply:
% 111.13/16.06 | | (10) $false
% 111.13/16.06 | |
% 111.13/16.06 | | CLOSE: (10) is inconsistent.
% 111.13/16.06 | |
% 111.13/16.06 | End of split
% 111.13/16.06 |
% 111.13/16.06 End of proof
% 111.13/16.06
% 111.13/16.06 Sub-proof #91 shows that the following formulas are inconsistent:
% 111.13/16.06 ----------------------------------------------------------------
% 111.13/16.06 (1) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 111.13/16.06 all_52_12 & $i(all_52_12)
% 111.13/16.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.06 (3) op(e3, e2) = e2
% 111.13/16.06 (4) ~ (e3 = e2)
% 111.13/16.06
% 111.13/16.06 Begin of proof
% 111.13/16.06 |
% 111.13/16.06 | ALPHA: (1) implies:
% 111.13/16.06 | (5) op(e3, e2) = e3
% 111.13/16.06 |
% 111.13/16.06 | GROUND_INST: instantiating (2) with e2, e3, e2, e3, simplifying with (3), (5)
% 111.13/16.06 | gives:
% 111.13/16.06 | (6) e3 = e2
% 111.13/16.06 |
% 111.13/16.06 | REDUCE: (4), (6) imply:
% 111.13/16.06 | (7) $false
% 111.13/16.06 |
% 111.13/16.06 | CLOSE: (7) is inconsistent.
% 111.13/16.06 |
% 111.13/16.06 End of proof
% 111.13/16.06
% 111.13/16.06 Sub-proof #92 shows that the following formulas are inconsistent:
% 111.13/16.06 ----------------------------------------------------------------
% 111.13/16.06 (1) all_55_12 = all_53_12
% 111.13/16.06 (2) all_55_12 = e1
% 111.13/16.06 (3) ~ (all_53_12 = e1)
% 111.13/16.06
% 111.13/16.06 Begin of proof
% 111.13/16.06 |
% 111.13/16.06 | COMBINE_EQS: (1), (2) imply:
% 111.13/16.06 | (4) all_53_12 = e1
% 111.13/16.06 |
% 111.13/16.06 | SIMP: (4) implies:
% 111.13/16.06 | (5) all_53_12 = e1
% 111.13/16.06 |
% 111.13/16.06 | REDUCE: (3), (5) imply:
% 111.13/16.06 | (6) $false
% 111.13/16.06 |
% 111.13/16.06 | CLOSE: (6) is inconsistent.
% 111.13/16.06 |
% 111.13/16.06 End of proof
% 111.13/16.06
% 111.13/16.06 Sub-proof #93 shows that the following formulas are inconsistent:
% 111.13/16.06 ----------------------------------------------------------------
% 111.13/16.06 (1) all_55_12 = all_53_12
% 111.13/16.06 (2) all_55_12 = e2
% 111.13/16.06 (3) ~ (all_53_12 = e2)
% 111.13/16.06
% 111.13/16.06 Begin of proof
% 111.13/16.06 |
% 111.13/16.06 | COMBINE_EQS: (1), (2) imply:
% 111.13/16.06 | (4) all_53_12 = e2
% 111.13/16.06 |
% 111.13/16.06 | SIMP: (4) implies:
% 111.13/16.06 | (5) all_53_12 = e2
% 111.13/16.06 |
% 111.13/16.06 | REDUCE: (3), (5) imply:
% 111.13/16.06 | (6) $false
% 111.13/16.06 |
% 111.13/16.06 | CLOSE: (6) is inconsistent.
% 111.13/16.06 |
% 111.13/16.06 End of proof
% 111.13/16.06
% 111.13/16.06 Sub-proof #94 shows that the following formulas are inconsistent:
% 111.13/16.06 ----------------------------------------------------------------
% 111.13/16.06 (1) all_55_12 = all_53_12
% 111.13/16.06 (2) all_55_12 = e3
% 111.13/16.06 (3) ~ (all_53_12 = e3)
% 111.13/16.06
% 111.13/16.06 Begin of proof
% 111.13/16.06 |
% 111.13/16.06 | COMBINE_EQS: (1), (2) imply:
% 111.13/16.06 | (4) all_53_12 = e3
% 111.13/16.06 |
% 111.13/16.06 | SIMP: (4) implies:
% 111.13/16.06 | (5) all_53_12 = e3
% 111.13/16.06 |
% 111.13/16.06 | REDUCE: (3), (5) imply:
% 111.13/16.06 | (6) $false
% 111.13/16.06 |
% 111.13/16.06 | CLOSE: (6) is inconsistent.
% 111.13/16.06 |
% 111.13/16.06 End of proof
% 111.13/16.06
% 111.13/16.06 Sub-proof #95 shows that the following formulas are inconsistent:
% 111.13/16.06 ----------------------------------------------------------------
% 111.13/16.06 (1) all_55_14 = all_14_0
% 111.13/16.06 (2) all_55_14 = e3
% 111.13/16.06 (3) ~ (all_14_0 = e3)
% 111.13/16.06
% 111.13/16.06 Begin of proof
% 111.13/16.06 |
% 111.13/16.06 | COMBINE_EQS: (1), (2) imply:
% 111.13/16.06 | (4) all_14_0 = e3
% 111.13/16.06 |
% 111.13/16.06 | SIMP: (4) implies:
% 111.13/16.06 | (5) all_14_0 = e3
% 111.13/16.06 |
% 111.13/16.06 | REDUCE: (3), (5) imply:
% 111.13/16.06 | (6) $false
% 111.13/16.06 |
% 111.13/16.06 | CLOSE: (6) is inconsistent.
% 111.13/16.06 |
% 111.13/16.06 End of proof
% 111.13/16.06
% 111.13/16.06 Sub-proof #96 shows that the following formulas are inconsistent:
% 111.13/16.06 ----------------------------------------------------------------
% 111.13/16.06 (1) ~ (all_53_13 = e3)
% 111.13/16.07 (2) op(e3, e0) = all_53_12
% 111.13/16.07 (3) (all_57_122 = e3 & op(e3, e1) = e3) | (all_57_123 = e3 & op(e3, e0) = e3)
% 111.13/16.07 (4) ~ (all_53_12 = e3)
% 111.13/16.07 (5) op(e3, e1) = all_53_13
% 111.13/16.07 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.07
% 111.13/16.07 Begin of proof
% 111.13/16.07 |
% 111.13/16.07 | BETA: splitting (3) gives:
% 111.13/16.07 |
% 111.13/16.07 | Case 1:
% 111.13/16.07 | |
% 111.13/16.07 | | (7) all_57_122 = e3 & op(e3, e1) = e3
% 111.13/16.07 | |
% 111.13/16.07 | | ALPHA: (7) implies:
% 111.13/16.07 | | (8) op(e3, e1) = e3
% 111.13/16.07 | |
% 111.13/16.07 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #232.
% 111.13/16.07 | |
% 111.13/16.07 | Case 2:
% 111.13/16.07 | |
% 111.13/16.07 | | (9) all_57_123 = e3 & op(e3, e0) = e3
% 111.13/16.07 | |
% 111.13/16.07 | | ALPHA: (9) implies:
% 111.13/16.07 | | (10) op(e3, e0) = e3
% 111.13/16.07 | |
% 111.13/16.07 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #180.
% 111.13/16.07 | |
% 111.13/16.07 | End of split
% 111.13/16.07 |
% 111.13/16.07 End of proof
% 111.13/16.07
% 111.13/16.07 Sub-proof #97 shows that the following formulas are inconsistent:
% 111.13/16.07 ----------------------------------------------------------------
% 111.13/16.07 (1) op(e3, e0) = all_53_12
% 111.13/16.07 (2) op(e2, e3) = all_53_10
% 111.13/16.07 (3) op(e1, e0) = all_53_4
% 111.13/16.07 (4) op(e3, e3) = all_36_1
% 111.13/16.07 (5) op(e3, e3) = all_28_1
% 111.13/16.07 (6) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 111.13/16.07 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 111.13/16.07 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 111.13/16.07 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 111.13/16.07 $i(all_52_16))
% 111.13/16.07 (7) op(e3, e2) = all_53_15
% 111.13/16.07 (8) op(e1, e2) = all_53_7
% 111.13/16.07 (9) ~ (all_53_12 = all_4_2)
% 111.13/16.07 (10) op(e0, e3) = all_53_2
% 111.13/16.07 (11) op(e0, e1) = all_53_1
% 111.13/16.07 (12) op(e2, e1) = all_53_9
% 111.13/16.07 (13) ~ (all_53_2 = all_53_3)
% 111.13/16.07 (14) op(e3, e3) = e3
% 111.13/16.07 (15) ~ (all_53_6 = all_53_7)
% 111.13/16.07 (16) ~ (all_53_8 = all_53_10)
% 111.13/16.07 (17) ~ (all_53_4 = all_53_6)
% 111.13/16.07 (18) op(e1, e3) = all_53_6
% 111.13/16.07 (19) op(e2, e0) = all_53_8
% 111.13/16.07 (20) op(e3, e1) = all_53_13
% 111.13/16.07 (21) ~ (all_53_9 = all_53_10)
% 111.13/16.07 (22) ~ (all_53_13 = all_4_2)
% 111.13/16.07 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.07 (24) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 111.13/16.07 e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20 = e3) &
% 111.13/16.07 op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23
% 111.13/16.07 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0
% 111.13/16.07 & $i(all_52_22))
% 111.13/16.07 (25) ~ (all_53_15 = all_4_2)
% 111.13/16.07 (26) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 111.13/16.07 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 111.13/16.07 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 111.13/16.07 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 111.13/16.07 $i(all_52_4))
% 111.13/16.07 (27) ~ (all_53_4 = all_53_7)
% 111.13/16.07 (28) ~ (all_53_1 = all_53_3)
% 111.13/16.07 (29) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.13/16.07 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 111.13/16.07 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 111.13/16.07 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.13/16.07 $i(all_52_10))
% 111.13/16.07 (30) op(e3, e3) = all_4_2
% 111.13/16.07 (31) ~ (all_53_8 = all_53_9)
% 111.13/16.07 (32) op(e0, e2) = all_53_3
% 111.13/16.07 (33) ~ (all_53_1 = all_53_2)
% 111.13/16.07
% 111.13/16.07 Begin of proof
% 111.13/16.07 |
% 111.13/16.07 | GROUND_INST: instantiating (23) with all_4_2, all_28_1, e3, e3, simplifying
% 111.13/16.07 | with (5), (30) gives:
% 111.13/16.07 | (34) all_28_1 = all_4_2
% 111.13/16.07 |
% 111.13/16.07 | GROUND_INST: instantiating (23) with all_28_1, all_36_1, e3, e3, simplifying
% 111.13/16.07 | with (4), (5) gives:
% 111.13/16.07 | (35) all_36_1 = all_28_1
% 111.13/16.07 |
% 111.13/16.07 | GROUND_INST: instantiating (23) with e3, all_36_1, e3, e3, simplifying with
% 111.13/16.07 | (4), (14) gives:
% 111.13/16.07 | (36) all_36_1 = e3
% 111.13/16.07 |
% 111.13/16.07 | COMBINE_EQS: (35), (36) imply:
% 111.13/16.07 | (37) all_28_1 = e3
% 111.13/16.07 |
% 111.13/16.07 | SIMP: (37) implies:
% 111.13/16.07 | (38) all_28_1 = e3
% 111.13/16.07 |
% 111.13/16.07 | COMBINE_EQS: (34), (38) imply:
% 111.13/16.07 | (39) all_4_2 = e3
% 111.13/16.07 |
% 111.13/16.07 | SIMP: (39) implies:
% 111.13/16.07 | (40) all_4_2 = e3
% 111.13/16.07 |
% 111.13/16.07 | REDUCE: (9), (40) imply:
% 111.13/16.07 | (41) ~ (all_53_12 = e3)
% 111.13/16.07 |
% 111.13/16.07 | REDUCE: (22), (40) imply:
% 111.13/16.07 | (42) ~ (all_53_13 = e3)
% 111.13/16.07 |
% 111.13/16.07 | REDUCE: (25), (40) imply:
% 111.13/16.07 | (43) ~ (all_53_15 = e3)
% 111.13/16.07 |
% 111.13/16.07 | BETA: splitting (29) gives:
% 111.13/16.07 |
% 111.13/16.07 | Case 1:
% 111.13/16.07 | |
% 111.13/16.07 | | (44) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.13/16.07 | | all_52_6 & $i(all_52_6)
% 111.13/16.07 | |
% 111.13/16.07 | | ALPHA: (44) implies:
% 111.13/16.07 | | (45) op(e3, e1) = e3
% 111.13/16.07 | |
% 111.13/16.07 | | REF_CLOSE: (20), (23), (42), (45) are inconsistent by sub-proof #232.
% 111.13/16.07 | |
% 111.13/16.07 | Case 2:
% 111.13/16.07 | |
% 111.13/16.07 | | (46) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 111.13/16.07 | | all_52_8 & $i(all_52_8)) | (all_52_11 = e0 & ~ (all_52_10 = e1) &
% 111.13/16.07 | | op(e1, e0) = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 111.13/16.07 | |
% 111.13/16.07 | | BETA: splitting (46) gives:
% 111.13/16.07 | |
% 111.13/16.07 | | Case 1:
% 111.13/16.07 | | |
% 111.13/16.07 | | | (47) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 111.13/16.07 | | | = all_52_8 & $i(all_52_8)
% 111.13/16.07 | | |
% 111.13/16.07 | | | ALPHA: (47) implies:
% 111.13/16.07 | | | (48) op(e2, e1) = e2
% 111.13/16.07 | | |
% 111.13/16.07 | | | GROUND_INST: instantiating (23) with all_53_9, e2, e1, e2, simplifying
% 111.13/16.07 | | | with (12), (48) gives:
% 111.13/16.07 | | | (49) all_53_9 = e2
% 111.13/16.07 | | |
% 111.13/16.07 | | | REDUCE: (31), (49) imply:
% 111.13/16.07 | | | (50) ~ (all_53_8 = e2)
% 111.13/16.07 | | |
% 111.13/16.07 | | | REDUCE: (21), (49) imply:
% 111.13/16.07 | | | (51) ~ (all_53_10 = e2)
% 111.13/16.07 | | |
% 111.13/16.07 | | | SIMP: (51) implies:
% 111.13/16.07 | | | (52) ~ (all_53_10 = e2)
% 111.13/16.07 | | |
% 111.13/16.07 | | | BETA: splitting (6) gives:
% 111.13/16.07 | | |
% 111.13/16.07 | | | Case 1:
% 111.13/16.07 | | | |
% 111.13/16.07 | | | | (53) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2,
% 111.13/16.07 | | | | e3) = all_52_12 & $i(all_52_12)
% 111.13/16.07 | | | |
% 111.13/16.07 | | | | ALPHA: (53) implies:
% 111.13/16.07 | | | | (54) op(e3, e2) = e3
% 111.13/16.07 | | | |
% 111.13/16.07 | | | | REF_CLOSE: (7), (23), (43), (54) are inconsistent by sub-proof #214.
% 111.13/16.07 | | | |
% 111.13/16.07 | | | Case 2:
% 111.13/16.07 | | | |
% 111.13/16.07 | | | | (55) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 111.13/16.07 | | | | op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~
% 111.13/16.07 | | | | (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 111.13/16.07 | | | | $i(all_52_16))
% 111.13/16.07 | | | |
% 111.13/16.07 | | | | BETA: splitting (55) gives:
% 111.13/16.07 | | | |
% 111.13/16.07 | | | | Case 1:
% 111.13/16.07 | | | | |
% 111.13/16.07 | | | | | (56) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14
% 111.13/16.07 | | | | | & op(e1, e2) = e1 & $i(all_52_14)
% 111.13/16.07 | | | | |
% 111.13/16.07 | | | | | ALPHA: (56) implies:
% 111.13/16.07 | | | | | (57) ~ (all_52_14 = e2)
% 111.13/16.07 | | | | | (58) op(e2, e1) = all_52_14
% 111.13/16.07 | | | | |
% 111.13/16.07 | | | | | REF_CLOSE: (12), (23), (48), (57), (58) are inconsistent by sub-proof
% 111.13/16.07 | | | | | #110.
% 111.13/16.07 | | | | |
% 111.13/16.07 | | | | Case 2:
% 111.13/16.07 | | | | |
% 111.13/16.07 | | | | | (59) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16
% 111.13/16.07 | | | | | & op(e0, e2) = e0 & $i(all_52_16)
% 111.13/16.07 | | | | |
% 111.13/16.07 | | | | | ALPHA: (59) implies:
% 111.13/16.07 | | | | | (60) op(e0, e2) = e0
% 111.13/16.07 | | | | |
% 111.13/16.07 | | | | | BETA: splitting (26) gives:
% 111.13/16.07 | | | | |
% 111.13/16.07 | | | | | Case 1:
% 111.13/16.07 | | | | | |
% 111.13/16.07 | | | | | | (61) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 &
% 111.13/16.07 | | | | | | op(e0, e3) = all_52_0 & $i(all_52_0)
% 111.13/16.07 | | | | | |
% 111.13/16.07 | | | | | | ALPHA: (61) implies:
% 111.13/16.07 | | | | | | (62) op(e3, e0) = e3
% 111.13/16.07 | | | | | |
% 111.13/16.07 | | | | | | REF_CLOSE: (1), (23), (41), (62) are inconsistent by sub-proof #180.
% 111.13/16.07 | | | | | |
% 111.13/16.07 | | | | | Case 2:
% 111.13/16.07 | | | | | |
% 111.13/16.07 | | | | | | (63) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 &
% 111.13/16.07 | | | | | | op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 = e1 &
% 111.13/16.07 | | | | | | ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) =
% 111.13/16.07 | | | | | | all_52_4 & $i(all_52_4))
% 111.13/16.07 | | | | | |
% 111.13/16.07 | | | | | | BETA: splitting (63) gives:
% 111.13/16.07 | | | | | |
% 111.13/16.07 | | | | | | Case 1:
% 111.13/16.07 | | | | | | |
% 111.13/16.07 | | | | | | | (64) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 &
% 111.13/16.07 | | | | | | | op(e0, e2) = all_52_2 & $i(all_52_2)
% 111.13/16.07 | | | | | | |
% 111.13/16.07 | | | | | | | ALPHA: (64) implies:
% 111.13/16.07 | | | | | | | (65) op(e2, e0) = e2
% 111.13/16.07 | | | | | | |
% 111.13/16.07 | | | | | | | REF_CLOSE: (19), (23), (50), (65) are inconsistent by sub-proof
% 111.13/16.07 | | | | | | | #227.
% 111.13/16.07 | | | | | | |
% 111.13/16.07 | | | | | | Case 2:
% 111.13/16.07 | | | | | | |
% 111.13/16.07 | | | | | | | (66) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 &
% 111.13/16.07 | | | | | | | op(e0, e1) = all_52_4 & $i(all_52_4)
% 111.13/16.07 | | | | | | |
% 111.13/16.07 | | | | | | | ALPHA: (66) implies:
% 111.13/16.07 | | | | | | | (67) op(e1, e0) = e1
% 111.13/16.07 | | | | | | |
% 111.13/16.07 | | | | | | | GROUND_INST: instantiating (23) with all_53_3, e0, e2, e0,
% 111.13/16.07 | | | | | | | simplifying with (32), (60) gives:
% 111.13/16.07 | | | | | | | (68) all_53_3 = e0
% 111.13/16.07 | | | | | | |
% 111.13/16.07 | | | | | | | GROUND_INST: instantiating (23) with all_53_4, e1, e0, e1,
% 111.13/16.07 | | | | | | | simplifying with (3), (67) gives:
% 111.13/16.07 | | | | | | | (69) all_53_4 = e1
% 111.13/16.07 | | | | | | |
% 111.13/16.07 | | | | | | | REDUCE: (13), (68) imply:
% 111.13/16.07 | | | | | | | (70) ~ (all_53_2 = e0)
% 111.13/16.07 | | | | | | |
% 111.13/16.07 | | | | | | | REDUCE: (17), (69) imply:
% 111.13/16.07 | | | | | | | (71) ~ (all_53_6 = e1)
% 111.13/16.07 | | | | | | |
% 111.13/16.07 | | | | | | | SIMP: (71) implies:
% 111.13/16.07 | | | | | | | (72) ~ (all_53_6 = e1)
% 111.13/16.07 | | | | | | |
% 111.13/16.07 | | | | | | | BETA: splitting (24) gives:
% 111.13/16.07 | | | | | | |
% 111.13/16.07 | | | | | | | Case 1:
% 111.13/16.07 | | | | | | | |
% 111.13/16.07 | | | | | | | | (73) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) =
% 111.13/16.07 | | | | | | | | all_52_18 & op(e2, e3) = e2 & $i(all_52_18)
% 111.13/16.07 | | | | | | | |
% 111.13/16.07 | | | | | | | | REF_CLOSE: (2), (23), (52), (73) are inconsistent by sub-proof
% 111.13/16.07 | | | | | | | | #215.
% 111.13/16.07 | | | | | | | |
% 111.13/16.07 | | | | | | | Case 2:
% 111.13/16.07 | | | | | | | |
% 111.13/16.07 | | | | | | | | (74) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) =
% 111.13/16.08 | | | | | | | | all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) |
% 111.13/16.08 | | | | | | | | (all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0) =
% 111.13/16.08 | | | | | | | | all_52_22 & op(e0, e3) = e0 & $i(all_52_22))
% 111.13/16.08 | | | | | | | |
% 111.13/16.08 | | | | | | | | REF_CLOSE: (10), (18), (23), (70), (72), (74) are inconsistent
% 111.13/16.08 | | | | | | | | by sub-proof #102.
% 111.13/16.08 | | | | | | | |
% 111.13/16.08 | | | | | | | End of split
% 111.13/16.08 | | | | | | |
% 111.13/16.08 | | | | | | End of split
% 111.13/16.08 | | | | | |
% 111.13/16.08 | | | | | End of split
% 111.13/16.08 | | | | |
% 111.13/16.08 | | | | End of split
% 111.13/16.08 | | | |
% 111.13/16.08 | | | End of split
% 111.13/16.08 | | |
% 111.13/16.08 | | Case 2:
% 111.13/16.08 | | |
% 111.13/16.08 | | | (75) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 &
% 111.13/16.08 | | | op(e0, e1) = e0 & $i(all_52_10)
% 111.13/16.08 | | |
% 111.13/16.08 | | | ALPHA: (75) implies:
% 111.13/16.08 | | | (76) op(e0, e1) = e0
% 111.13/16.08 | | |
% 111.13/16.08 | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (10), (11), (15), (16), (18),
% 111.13/16.08 | | | (19), (23), (24), (26), (27), (28), (32), (33), (41), (43),
% 111.13/16.08 | | | (76) are inconsistent by sub-proof #98.
% 111.13/16.08 | | |
% 111.13/16.08 | | End of split
% 111.13/16.08 | |
% 111.13/16.08 | End of split
% 111.13/16.08 |
% 111.13/16.08 End of proof
% 111.13/16.08
% 111.13/16.08 Sub-proof #98 shows that the following formulas are inconsistent:
% 111.13/16.08 ----------------------------------------------------------------
% 111.13/16.08 (1) op(e3, e0) = all_53_12
% 111.13/16.08 (2) ~ (all_53_15 = e3)
% 111.13/16.08 (3) op(e2, e3) = all_53_10
% 111.13/16.08 (4) op(e1, e0) = all_53_4
% 111.13/16.08 (5) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 111.13/16.08 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 111.13/16.08 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 111.13/16.08 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 111.13/16.08 $i(all_52_16))
% 111.13/16.08 (6) op(e3, e2) = all_53_15
% 111.13/16.08 (7) op(e1, e2) = all_53_7
% 111.13/16.08 (8) op(e0, e3) = all_53_2
% 111.13/16.08 (9) ~ (all_53_12 = e3)
% 111.13/16.08 (10) op(e0, e1) = all_53_1
% 111.13/16.08 (11) op(e0, e1) = e0
% 111.13/16.08 (12) ~ (all_53_6 = all_53_7)
% 111.13/16.08 (13) ~ (all_53_8 = all_53_10)
% 111.13/16.08 (14) op(e1, e3) = all_53_6
% 111.13/16.08 (15) op(e2, e0) = all_53_8
% 111.13/16.08 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.08 (17) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 111.13/16.08 e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20 = e3) &
% 111.13/16.08 op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23
% 111.13/16.08 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0
% 111.13/16.08 & $i(all_52_22))
% 111.13/16.08 (18) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 111.13/16.08 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 111.13/16.08 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 111.13/16.08 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 111.13/16.08 $i(all_52_4))
% 111.13/16.08 (19) ~ (all_53_4 = all_53_7)
% 111.13/16.08 (20) ~ (all_53_1 = all_53_3)
% 111.13/16.08 (21) op(e0, e2) = all_53_3
% 111.13/16.08 (22) ~ (all_53_1 = all_53_2)
% 111.13/16.08
% 111.13/16.08 Begin of proof
% 111.13/16.08 |
% 111.13/16.08 | GROUND_INST: instantiating (16) with all_53_1, e0, e1, e0, simplifying with
% 111.13/16.08 | (10), (11) gives:
% 111.13/16.08 | (23) all_53_1 = e0
% 111.13/16.08 |
% 111.13/16.08 | REDUCE: (22), (23) imply:
% 111.13/16.08 | (24) ~ (all_53_2 = e0)
% 111.13/16.08 |
% 111.13/16.08 | SIMP: (24) implies:
% 111.13/16.08 | (25) ~ (all_53_2 = e0)
% 111.13/16.08 |
% 111.13/16.08 | BETA: splitting (5) gives:
% 111.13/16.08 |
% 111.13/16.08 | Case 1:
% 111.13/16.08 | |
% 111.13/16.08 | | (26) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3)
% 111.13/16.08 | | = all_52_12 & $i(all_52_12)
% 111.13/16.08 | |
% 111.13/16.08 | | ALPHA: (26) implies:
% 111.13/16.08 | | (27) op(e3, e2) = e3
% 111.13/16.08 | |
% 111.13/16.08 | | REF_CLOSE: (2), (6), (16), (27) are inconsistent by sub-proof #214.
% 111.13/16.08 | |
% 111.13/16.08 | Case 2:
% 111.13/16.08 | |
% 111.13/16.08 | | (28) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 111.13/16.08 | | op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~ (all_52_16
% 111.13/16.08 | | = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 111.13/16.08 | | $i(all_52_16))
% 111.13/16.08 | |
% 111.13/16.08 | | BETA: splitting (28) gives:
% 111.13/16.08 | |
% 111.13/16.08 | | Case 1:
% 111.13/16.08 | | |
% 111.13/16.08 | | | (29) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 111.13/16.08 | | | op(e1, e2) = e1 & $i(all_52_14)
% 111.13/16.08 | | |
% 111.13/16.08 | | | ALPHA: (29) implies:
% 111.13/16.08 | | | (30) op(e1, e2) = e1
% 111.13/16.08 | | |
% 111.13/16.08 | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (12), (13), (14), (15), (16),
% 111.13/16.08 | | | (17), (18), (19), (25), (30) are inconsistent by sub-proof #99.
% 111.13/16.08 | | |
% 111.13/16.08 | | Case 2:
% 111.13/16.08 | | |
% 111.13/16.08 | | | (31) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 &
% 111.13/16.08 | | | op(e0, e2) = e0 & $i(all_52_16)
% 111.13/16.08 | | |
% 111.13/16.08 | | | ALPHA: (31) implies:
% 111.13/16.08 | | | (32) op(e0, e2) = e0
% 111.13/16.08 | | |
% 111.13/16.08 | | | REF_CLOSE: (10), (11), (16), (20), (21), (32) are inconsistent by
% 111.13/16.08 | | | sub-proof #167.
% 111.13/16.08 | | |
% 111.13/16.08 | | End of split
% 111.13/16.08 | |
% 111.13/16.08 | End of split
% 111.13/16.08 |
% 111.13/16.08 End of proof
% 111.13/16.08
% 111.13/16.08 Sub-proof #99 shows that the following formulas are inconsistent:
% 111.13/16.08 ----------------------------------------------------------------
% 111.13/16.08 (1) op(e3, e0) = all_53_12
% 111.13/16.08 (2) op(e2, e3) = all_53_10
% 111.13/16.08 (3) op(e1, e0) = all_53_4
% 111.13/16.08 (4) op(e1, e2) = e1
% 111.13/16.08 (5) op(e1, e2) = all_53_7
% 111.13/16.08 (6) op(e0, e3) = all_53_2
% 111.13/16.08 (7) ~ (all_53_12 = e3)
% 111.13/16.08 (8) ~ (all_53_6 = all_53_7)
% 111.13/16.08 (9) ~ (all_53_8 = all_53_10)
% 111.13/16.08 (10) op(e1, e3) = all_53_6
% 111.13/16.08 (11) op(e2, e0) = all_53_8
% 111.13/16.08 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.08 (13) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 111.13/16.08 e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20 = e3) &
% 111.13/16.08 op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23
% 111.13/16.08 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0
% 111.13/16.08 & $i(all_52_22))
% 111.13/16.08 (14) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 111.13/16.08 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 111.13/16.08 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 111.13/16.08 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 111.13/16.08 $i(all_52_4))
% 111.13/16.08 (15) ~ (all_53_4 = all_53_7)
% 111.13/16.08 (16) ~ (all_53_2 = e0)
% 111.13/16.08
% 111.13/16.08 Begin of proof
% 111.13/16.08 |
% 111.13/16.08 | BETA: splitting (14) gives:
% 111.13/16.08 |
% 111.13/16.08 | Case 1:
% 111.13/16.08 | |
% 111.13/16.08 | | (17) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 111.13/16.08 | | all_52_0 & $i(all_52_0)
% 111.13/16.08 | |
% 111.13/16.08 | | ALPHA: (17) implies:
% 111.13/16.08 | | (18) op(e3, e0) = e3
% 111.13/16.08 | |
% 111.13/16.08 | | REF_CLOSE: (1), (7), (12), (18) are inconsistent by sub-proof #180.
% 111.13/16.08 | |
% 111.13/16.08 | Case 2:
% 111.13/16.08 | |
% 111.13/16.08 | | (19) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 111.13/16.08 | | all_52_2 & $i(all_52_2)) | (all_52_5 = e1 & ~ (all_52_4 = e0) &
% 111.13/16.08 | | op(e1, e0) = e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 111.13/16.08 | |
% 111.13/16.08 | | BETA: splitting (19) gives:
% 111.13/16.08 | |
% 111.13/16.08 | | Case 1:
% 111.13/16.08 | | |
% 111.13/16.08 | | | (20) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 111.13/16.08 | | | = all_52_2 & $i(all_52_2)
% 111.13/16.08 | | |
% 111.13/16.08 | | | ALPHA: (20) implies:
% 111.13/16.08 | | | (21) op(e2, e0) = e2
% 111.13/16.08 | | |
% 111.13/16.08 | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (16),
% 111.13/16.08 | | | (21) are inconsistent by sub-proof #101.
% 111.13/16.08 | | |
% 111.13/16.08 | | Case 2:
% 111.13/16.08 | | |
% 111.13/16.08 | | | (22) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 111.13/16.08 | | | = all_52_4 & $i(all_52_4)
% 111.13/16.08 | | |
% 111.13/16.08 | | | REF_CLOSE: (3), (4), (5), (12), (15), (22) are inconsistent by sub-proof
% 111.13/16.08 | | | #100.
% 111.13/16.08 | | |
% 111.13/16.08 | | End of split
% 111.13/16.08 | |
% 111.13/16.08 | End of split
% 111.13/16.08 |
% 111.13/16.08 End of proof
% 111.13/16.08
% 111.13/16.08 Sub-proof #100 shows that the following formulas are inconsistent:
% 111.13/16.08 ----------------------------------------------------------------
% 111.13/16.08 (1) op(e1, e0) = all_53_4
% 111.13/16.08 (2) op(e1, e2) = e1
% 111.13/16.08 (3) op(e1, e2) = all_53_7
% 111.13/16.08 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.08 (5) ~ (all_53_4 = all_53_7)
% 111.13/16.08 (6) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) =
% 111.13/16.08 all_52_4 & $i(all_52_4)
% 111.13/16.08
% 111.13/16.08 Begin of proof
% 111.13/16.08 |
% 111.13/16.08 | ALPHA: (6) implies:
% 111.13/16.08 | (7) op(e1, e0) = e1
% 111.13/16.08 |
% 111.13/16.08 | GROUND_INST: instantiating (4) with all_53_4, e1, e0, e1, simplifying with
% 111.13/16.08 | (1), (7) gives:
% 111.13/16.08 | (8) all_53_4 = e1
% 111.13/16.08 |
% 111.13/16.08 | GROUND_INST: instantiating (4) with all_53_7, e1, e2, e1, simplifying with
% 111.13/16.08 | (2), (3) gives:
% 111.13/16.08 | (9) all_53_7 = e1
% 111.13/16.08 |
% 111.13/16.08 | REDUCE: (5), (8), (9) imply:
% 111.13/16.08 | (10) $false
% 111.13/16.08 |
% 111.13/16.08 | CLOSE: (10) is inconsistent.
% 111.13/16.08 |
% 111.13/16.08 End of proof
% 111.13/16.08
% 111.13/16.08 Sub-proof #101 shows that the following formulas are inconsistent:
% 111.13/16.08 ----------------------------------------------------------------
% 111.13/16.08 (1) op(e2, e3) = all_53_10
% 111.13/16.08 (2) op(e1, e2) = e1
% 111.13/16.08 (3) op(e1, e2) = all_53_7
% 111.13/16.08 (4) op(e2, e0) = e2
% 111.13/16.08 (5) op(e0, e3) = all_53_2
% 111.13/16.08 (6) ~ (all_53_6 = all_53_7)
% 111.13/16.08 (7) ~ (all_53_8 = all_53_10)
% 111.13/16.08 (8) op(e1, e3) = all_53_6
% 111.13/16.08 (9) op(e2, e0) = all_53_8
% 111.13/16.08 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.08 (11) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 111.13/16.08 e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20 = e3) &
% 111.13/16.08 op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23
% 111.13/16.08 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0
% 111.13/16.08 & $i(all_52_22))
% 111.13/16.08 (12) ~ (all_53_2 = e0)
% 111.13/16.08
% 111.13/16.08 Begin of proof
% 111.13/16.08 |
% 111.13/16.09 | GROUND_INST: instantiating (10) with all_53_7, e1, e2, e1, simplifying with
% 111.13/16.09 | (2), (3) gives:
% 111.13/16.09 | (13) all_53_7 = e1
% 111.13/16.09 |
% 111.13/16.09 | GROUND_INST: instantiating (10) with all_53_8, e2, e0, e2, simplifying with
% 111.13/16.09 | (4), (9) gives:
% 111.13/16.09 | (14) all_53_8 = e2
% 111.13/16.09 |
% 111.13/16.09 | REDUCE: (6), (13) imply:
% 111.13/16.09 | (15) ~ (all_53_6 = e1)
% 111.13/16.09 |
% 111.13/16.09 | REDUCE: (7), (14) imply:
% 111.13/16.09 | (16) ~ (all_53_10 = e2)
% 111.13/16.09 |
% 111.13/16.09 | SIMP: (16) implies:
% 111.13/16.09 | (17) ~ (all_53_10 = e2)
% 111.13/16.09 |
% 111.13/16.09 | BETA: splitting (11) gives:
% 111.13/16.09 |
% 111.13/16.09 | Case 1:
% 111.13/16.09 | |
% 111.13/16.09 | | (18) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 &
% 111.13/16.09 | | op(e2, e3) = e2 & $i(all_52_18)
% 111.13/16.09 | |
% 111.13/16.09 | | REF_CLOSE: (1), (10), (17), (18) are inconsistent by sub-proof #215.
% 111.13/16.09 | |
% 111.13/16.09 | Case 2:
% 111.13/16.09 | |
% 111.13/16.09 | | (19) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 &
% 111.13/16.09 | | op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23 = e0 & ~ (all_52_22
% 111.13/16.09 | | = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0 &
% 111.13/16.09 | | $i(all_52_22))
% 111.13/16.09 | |
% 111.13/16.09 | | REF_CLOSE: (5), (8), (10), (12), (15), (19) are inconsistent by sub-proof
% 111.13/16.09 | | #102.
% 111.13/16.09 | |
% 111.13/16.09 | End of split
% 111.13/16.09 |
% 111.13/16.09 End of proof
% 111.13/16.09
% 111.13/16.09 Sub-proof #102 shows that the following formulas are inconsistent:
% 111.13/16.09 ----------------------------------------------------------------
% 111.13/16.09 (1) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 & op(e1,
% 111.13/16.09 e3) = e1 & $i(all_52_20)) | (all_52_23 = e0 & ~ (all_52_22 = e3) &
% 111.13/16.09 op(e3, e0) = all_52_22 & op(e0, e3) = e0 & $i(all_52_22))
% 111.13/16.09 (2) op(e0, e3) = all_53_2
% 111.13/16.09 (3) ~ (all_53_6 = e1)
% 111.13/16.09 (4) op(e1, e3) = all_53_6
% 111.13/16.09 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.09 (6) ~ (all_53_2 = e0)
% 111.13/16.09
% 111.13/16.09 Begin of proof
% 111.13/16.09 |
% 111.13/16.09 | BETA: splitting (1) gives:
% 111.13/16.09 |
% 111.13/16.09 | Case 1:
% 111.13/16.09 | |
% 111.13/16.09 | | (7) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 &
% 111.13/16.09 | | op(e1, e3) = e1 & $i(all_52_20)
% 111.13/16.09 | |
% 111.13/16.09 | | ALPHA: (7) implies:
% 111.13/16.09 | | (8) op(e1, e3) = e1
% 111.13/16.09 | |
% 111.13/16.09 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #223.
% 111.13/16.09 | |
% 111.13/16.09 | Case 2:
% 111.13/16.09 | |
% 111.13/16.09 | | (9) all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 &
% 111.13/16.09 | | op(e0, e3) = e0 & $i(all_52_22)
% 111.13/16.09 | |
% 111.13/16.09 | | ALPHA: (9) implies:
% 111.13/16.09 | | (10) op(e0, e3) = e0
% 111.13/16.09 | |
% 111.13/16.09 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #149.
% 111.13/16.09 | |
% 111.13/16.09 | End of split
% 111.13/16.09 |
% 111.13/16.09 End of proof
% 111.13/16.09
% 111.13/16.09 Sub-proof #103 shows that the following formulas are inconsistent:
% 111.13/16.09 ----------------------------------------------------------------
% 111.13/16.09 (1) all_55_14 = e1 | all_55_14 = e0
% 111.13/16.09 (2) all_55_14 = all_53_15
% 111.13/16.09 (3) ~ (all_53_15 = e1)
% 111.13/16.09 (4) ~ (all_53_15 = e0)
% 111.13/16.09
% 111.13/16.09 Begin of proof
% 111.13/16.09 |
% 111.13/16.09 | BETA: splitting (1) gives:
% 111.13/16.09 |
% 111.13/16.09 | Case 1:
% 111.13/16.09 | |
% 111.13/16.09 | | (5) all_55_14 = e1
% 111.13/16.09 | |
% 111.13/16.09 | | COMBINE_EQS: (2), (5) imply:
% 111.13/16.09 | | (6) all_53_15 = e1
% 111.13/16.09 | |
% 111.13/16.09 | | SIMP: (6) implies:
% 111.13/16.09 | | (7) all_53_15 = e1
% 111.13/16.09 | |
% 111.13/16.09 | | REDUCE: (3), (7) imply:
% 111.13/16.09 | | (8) $false
% 111.13/16.09 | |
% 111.13/16.09 | | CLOSE: (8) is inconsistent.
% 111.13/16.09 | |
% 111.13/16.09 | Case 2:
% 111.13/16.09 | |
% 111.13/16.09 | | (9) all_55_14 = e0
% 111.13/16.09 | |
% 111.13/16.09 | | COMBINE_EQS: (2), (9) imply:
% 111.13/16.09 | | (10) all_53_15 = e0
% 111.13/16.09 | |
% 111.13/16.09 | | SIMP: (10) implies:
% 111.13/16.09 | | (11) all_53_15 = e0
% 111.13/16.09 | |
% 111.13/16.09 | | REDUCE: (4), (11) imply:
% 111.13/16.09 | | (12) $false
% 111.13/16.09 | |
% 111.13/16.09 | | CLOSE: (12) is inconsistent.
% 111.13/16.09 | |
% 111.13/16.09 | End of split
% 111.13/16.09 |
% 111.13/16.09 End of proof
% 111.13/16.09
% 111.13/16.09 Sub-proof #104 shows that the following formulas are inconsistent:
% 111.13/16.09 ----------------------------------------------------------------
% 111.13/16.09 (1) all_55_4 = e1 | all_55_4 = e0
% 111.13/16.09 (2) all_55_4 = all_53_4
% 111.13/16.09 (3) ~ (all_53_4 = e1)
% 111.13/16.09 (4) ~ (all_53_4 = e0)
% 111.13/16.09
% 111.13/16.09 Begin of proof
% 111.13/16.09 |
% 111.13/16.09 | BETA: splitting (1) gives:
% 111.13/16.09 |
% 111.13/16.09 | Case 1:
% 111.13/16.09 | |
% 111.13/16.09 | | (5) all_55_4 = e1
% 111.13/16.09 | |
% 111.13/16.09 | | COMBINE_EQS: (2), (5) imply:
% 111.13/16.09 | | (6) all_53_4 = e1
% 111.13/16.09 | |
% 111.13/16.09 | | SIMP: (6) implies:
% 111.13/16.09 | | (7) all_53_4 = e1
% 111.13/16.09 | |
% 111.13/16.09 | | REDUCE: (3), (7) imply:
% 111.13/16.09 | | (8) $false
% 111.13/16.09 | |
% 111.13/16.09 | | CLOSE: (8) is inconsistent.
% 111.13/16.09 | |
% 111.13/16.09 | Case 2:
% 111.13/16.09 | |
% 111.13/16.09 | | (9) all_55_4 = e0
% 111.13/16.09 | |
% 111.13/16.09 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #113.
% 111.13/16.09 | |
% 111.13/16.09 | End of split
% 111.13/16.09 |
% 111.13/16.09 End of proof
% 111.13/16.09
% 111.13/16.09 Sub-proof #105 shows that the following formulas are inconsistent:
% 111.13/16.09 ----------------------------------------------------------------
% 111.13/16.09 (1) ~ (all_6_2 = e2)
% 111.13/16.09 (2) ~ (all_53_1 = all_6_2)
% 111.13/16.09 (3) ~ (all_53_3 = all_53_7)
% 111.13/16.09 (4) ~ (all_53_3 = all_53_15)
% 111.13/16.09 (5) all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 111.13/16.09 (6) ~ (all_53_15 = e3)
% 111.13/16.09 (7) ~ (all_53_3 = e3)
% 111.13/16.09 (8) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 111.13/16.09 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 111.13/16.09 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 111.13/16.09 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 111.13/16.09 $i(all_52_16))
% 111.13/16.09 (9) op(e3, e2) = all_53_15
% 111.13/16.09 (10) op(e1, e2) = all_53_7
% 111.13/16.09 (11) op(e0, e1) = all_53_1
% 111.13/16.09 (12) (all_57_52 = e2 & op(e3, e1) = e2) | (all_57_53 = e2 & op(e2, e1) = e2)
% 111.13/16.09 | (all_57_54 = e2 & op(e1, e1) = e2) | (all_57_55 = e2 & op(e0, e1) =
% 111.13/16.09 e2)
% 111.13/16.09 (13) op(e2, e1) = all_53_9
% 111.13/16.09 (14) ~ (all_6_2 = e3)
% 111.13/16.09 (15) (all_57_68 = e0 & op(e3, e2) = e0) | (all_57_69 = e0 & op(e2, e2) = e0)
% 111.13/16.09 | (all_57_70 = e0 & op(e1, e2) = e0) | (all_57_71 = e0 & op(e0, e2) =
% 111.13/16.09 e0)
% 111.13/16.09 (16) ~ (all_53_3 = all_6_2)
% 111.13/16.09 (17) ~ (all_53_7 = e0)
% 111.13/16.09 (18) all_55_0 = all_6_2
% 111.13/16.09 (19) all_55_2 = all_53_3
% 111.13/16.09 (20) op(e3, e1) = all_53_13
% 111.13/16.09 (21) op(e2, e2) = e3
% 111.13/16.09 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.09 (23) op(e1, e1) = e0
% 111.13/16.09 (24) ~ (all_53_1 = all_53_3)
% 111.13/16.09 (25) all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 111.13/16.09 (26) ~ (all_6_2 = e1)
% 111.13/16.09 (27) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.13/16.09 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 111.13/16.09 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 111.13/16.09 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.13/16.09 $i(all_52_10))
% 111.13/16.09 (28) op(e0, e2) = all_53_3
% 111.13/16.09
% 111.13/16.09 Begin of proof
% 111.13/16.09 |
% 111.13/16.09 | BETA: splitting (25) gives:
% 111.13/16.09 |
% 111.13/16.09 | Case 1:
% 111.13/16.09 | |
% 111.13/16.09 | | (29) all_55_0 = e3
% 111.13/16.09 | |
% 111.13/16.09 | | COMBINE_EQS: (18), (29) imply:
% 111.13/16.09 | | (30) all_6_2 = e3
% 111.13/16.09 | |
% 111.13/16.09 | | REDUCE: (14), (30) imply:
% 111.13/16.09 | | (31) $false
% 111.13/16.09 | |
% 111.13/16.09 | | CLOSE: (31) is inconsistent.
% 111.13/16.09 | |
% 111.13/16.09 | Case 2:
% 111.13/16.09 | |
% 111.13/16.09 | | (32) ~ (all_55_0 = e3)
% 111.13/16.09 | | (33) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 111.13/16.09 | |
% 111.13/16.09 | | BETA: splitting (33) gives:
% 111.13/16.09 | |
% 111.13/16.09 | | Case 1:
% 111.13/16.09 | | |
% 111.13/16.09 | | | (34) all_55_0 = e2
% 111.13/16.09 | | |
% 111.13/16.09 | | | COMBINE_EQS: (18), (34) imply:
% 111.13/16.09 | | | (35) all_6_2 = e2
% 111.13/16.09 | | |
% 111.13/16.09 | | | REDUCE: (1), (35) imply:
% 111.13/16.09 | | | (36) $false
% 111.13/16.09 | | |
% 111.13/16.09 | | | CLOSE: (36) is inconsistent.
% 111.13/16.09 | | |
% 111.13/16.09 | | Case 2:
% 111.13/16.09 | | |
% 111.13/16.09 | | | (37) all_55_0 = e1 | all_55_0 = e0
% 111.13/16.09 | | |
% 111.13/16.09 | | | BETA: splitting (37) gives:
% 111.13/16.09 | | |
% 111.13/16.09 | | | Case 1:
% 111.13/16.09 | | | |
% 111.13/16.09 | | | | (38) all_55_0 = e1
% 111.13/16.09 | | | |
% 111.13/16.09 | | | | COMBINE_EQS: (18), (38) imply:
% 111.13/16.09 | | | | (39) all_6_2 = e1
% 111.13/16.09 | | | |
% 111.13/16.09 | | | | REDUCE: (26), (39) imply:
% 111.13/16.09 | | | | (40) $false
% 111.13/16.09 | | | |
% 111.13/16.09 | | | | CLOSE: (40) is inconsistent.
% 111.13/16.09 | | | |
% 111.13/16.09 | | | Case 2:
% 111.13/16.09 | | | |
% 111.13/16.09 | | | | (41) all_55_0 = e0
% 111.13/16.09 | | | |
% 111.13/16.09 | | | | COMBINE_EQS: (18), (41) imply:
% 111.13/16.09 | | | | (42) all_6_2 = e0
% 111.13/16.09 | | | |
% 111.13/16.09 | | | | REDUCE: (2), (42) imply:
% 111.13/16.09 | | | | (43) ~ (all_53_1 = e0)
% 111.13/16.09 | | | |
% 111.13/16.09 | | | | REDUCE: (16), (42) imply:
% 111.13/16.09 | | | | (44) ~ (all_53_3 = e0)
% 111.13/16.09 | | | |
% 111.13/16.09 | | | | REDUCE: (14), (42) imply:
% 111.13/16.09 | | | | (45) ~ (e3 = e0)
% 111.13/16.09 | | | |
% 111.13/16.09 | | | | SIMP: (45) implies:
% 111.13/16.09 | | | | (46) ~ (e3 = e0)
% 111.13/16.09 | | | |
% 111.13/16.09 | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 111.13/16.09 | | | | (15), (17), (19), (20), (21), (22), (23), (24), (27), (28),
% 111.13/16.09 | | | | (43), (44), (46) are inconsistent by sub-proof #106.
% 111.13/16.09 | | | |
% 111.13/16.09 | | | End of split
% 111.13/16.09 | | |
% 111.13/16.09 | | End of split
% 111.13/16.09 | |
% 111.13/16.09 | End of split
% 111.13/16.09 |
% 111.13/16.09 End of proof
% 111.13/16.09
% 111.13/16.09 Sub-proof #106 shows that the following formulas are inconsistent:
% 111.13/16.09 ----------------------------------------------------------------
% 111.13/16.09 (1) ~ (all_53_3 = all_53_7)
% 111.13/16.09 (2) ~ (all_53_1 = e0)
% 111.13/16.09 (3) ~ (all_53_3 = all_53_15)
% 111.13/16.09 (4) all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 111.13/16.09 (5) ~ (all_53_15 = e3)
% 111.13/16.09 (6) ~ (all_53_3 = e3)
% 111.13/16.09 (7) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 111.13/16.09 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 111.13/16.09 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 111.13/16.09 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 111.13/16.09 $i(all_52_16))
% 111.13/16.09 (8) op(e3, e2) = all_53_15
% 111.13/16.09 (9) op(e1, e2) = all_53_7
% 111.13/16.09 (10) ~ (e3 = e0)
% 111.13/16.09 (11) op(e0, e1) = all_53_1
% 111.13/16.09 (12) (all_57_52 = e2 & op(e3, e1) = e2) | (all_57_53 = e2 & op(e2, e1) = e2)
% 111.13/16.09 | (all_57_54 = e2 & op(e1, e1) = e2) | (all_57_55 = e2 & op(e0, e1) =
% 111.13/16.09 e2)
% 111.13/16.09 (13) op(e2, e1) = all_53_9
% 111.13/16.09 (14) (all_57_68 = e0 & op(e3, e2) = e0) | (all_57_69 = e0 & op(e2, e2) = e0)
% 111.13/16.09 | (all_57_70 = e0 & op(e1, e2) = e0) | (all_57_71 = e0 & op(e0, e2) =
% 111.13/16.09 e0)
% 111.13/16.09 (15) ~ (all_53_7 = e0)
% 111.13/16.09 (16) all_55_2 = all_53_3
% 111.13/16.09 (17) op(e3, e1) = all_53_13
% 111.13/16.09 (18) op(e2, e2) = e3
% 111.13/16.09 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.09 (20) op(e1, e1) = e0
% 111.13/16.10 (21) ~ (all_53_1 = all_53_3)
% 111.13/16.10 (22) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.13/16.10 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 111.13/16.10 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 111.13/16.10 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.13/16.10 $i(all_52_10))
% 111.13/16.10 (23) op(e0, e2) = all_53_3
% 111.13/16.10 (24) ~ (all_53_3 = e0)
% 111.13/16.10
% 111.13/16.10 Begin of proof
% 111.13/16.10 |
% 111.13/16.10 | BETA: splitting (7) gives:
% 111.13/16.10 |
% 111.13/16.10 | Case 1:
% 111.13/16.10 | |
% 111.13/16.10 | | (25) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3)
% 111.13/16.10 | | = all_52_12 & $i(all_52_12)
% 111.13/16.10 | |
% 111.13/16.10 | | ALPHA: (25) implies:
% 111.13/16.10 | | (26) op(e3, e2) = e3
% 111.13/16.10 | |
% 111.13/16.10 | | REF_CLOSE: (5), (8), (19), (26) are inconsistent by sub-proof #214.
% 111.13/16.10 | |
% 111.13/16.10 | Case 2:
% 111.13/16.10 | |
% 111.13/16.10 | | (27) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 111.13/16.10 | | op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~ (all_52_16
% 111.13/16.10 | | = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 111.13/16.10 | | $i(all_52_16))
% 111.13/16.10 | |
% 111.13/16.10 | | BETA: splitting (27) gives:
% 111.13/16.10 | |
% 111.13/16.10 | | Case 1:
% 111.13/16.10 | | |
% 111.13/16.10 | | | (28) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 111.13/16.10 | | | op(e1, e2) = e1 & $i(all_52_14)
% 111.13/16.10 | | |
% 111.13/16.10 | | | ALPHA: (28) implies:
% 111.13/16.10 | | | (29) ~ (all_52_14 = e2)
% 111.13/16.10 | | | (30) op(e1, e2) = e1
% 111.13/16.10 | | | (31) op(e2, e1) = all_52_14
% 111.13/16.10 | | |
% 111.13/16.10 | | | BETA: splitting (14) gives:
% 111.13/16.10 | | |
% 111.13/16.10 | | | Case 1:
% 111.13/16.10 | | | |
% 111.13/16.10 | | | | (32) (all_57_68 = e0 & op(e3, e2) = e0) | (all_57_69 = e0 & op(e2,
% 111.13/16.10 | | | | e2) = e0)
% 111.13/16.10 | | | |
% 111.13/16.10 | | | | BETA: splitting (32) gives:
% 111.13/16.10 | | | |
% 111.13/16.10 | | | | Case 1:
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | (33) all_57_68 = e0 & op(e3, e2) = e0
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | ALPHA: (33) implies:
% 111.13/16.10 | | | | | (34) op(e3, e2) = e0
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | GROUND_INST: instantiating (19) with all_53_7, e1, e2, e1, simplifying
% 111.13/16.10 | | | | | with (9), (30) gives:
% 111.13/16.10 | | | | | (35) all_53_7 = e1
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | GROUND_INST: instantiating (19) with all_53_9, all_52_14, e1, e2,
% 111.13/16.10 | | | | | simplifying with (13), (31) gives:
% 111.13/16.10 | | | | | (36) all_53_9 = all_52_14
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | GROUND_INST: instantiating (19) with all_53_15, e0, e2, e3,
% 111.13/16.10 | | | | | simplifying with (8), (34) gives:
% 111.13/16.10 | | | | | (37) all_53_15 = e0
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | BETA: splitting (22) gives:
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | Case 1:
% 111.13/16.10 | | | | | |
% 111.13/16.10 | | | | | | (38) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 &
% 111.13/16.10 | | | | | | op(e1, e3) = all_52_6 & $i(all_52_6)
% 111.13/16.10 | | | | | |
% 111.13/16.10 | | | | | | ALPHA: (38) implies:
% 111.13/16.10 | | | | | | (39) op(e3, e1) = e3
% 111.13/16.10 | | | | | |
% 111.13/16.10 | | | | | | BETA: splitting (4) gives:
% 111.13/16.10 | | | | | |
% 111.13/16.10 | | | | | | Case 1:
% 111.13/16.10 | | | | | | |
% 111.13/16.10 | | | | | | | (40) all_55_2 = e3
% 111.13/16.10 | | | | | | |
% 111.13/16.10 | | | | | | | REF_CLOSE: (6), (16), (40) are inconsistent by sub-proof #111.
% 111.13/16.10 | | | | | | |
% 111.13/16.10 | | | | | | Case 2:
% 111.13/16.10 | | | | | | |
% 111.13/16.10 | | | | | | | (41) ~ (all_55_2 = e3)
% 111.13/16.10 | | | | | | | (42) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 111.13/16.10 | | | | | | |
% 111.13/16.10 | | | | | | | BETA: splitting (42) gives:
% 111.13/16.10 | | | | | | |
% 111.13/16.10 | | | | | | | Case 1:
% 111.13/16.10 | | | | | | | |
% 111.13/16.10 | | | | | | | | (43) all_55_2 = e2
% 111.13/16.10 | | | | | | | |
% 111.13/16.10 | | | | | | | | COMBINE_EQS: (16), (43) imply:
% 111.13/16.10 | | | | | | | | (44) all_53_3 = e2
% 111.13/16.10 | | | | | | | |
% 111.13/16.10 | | | | | | | | SIMP: (44) implies:
% 111.13/16.10 | | | | | | | | (45) all_53_3 = e2
% 111.13/16.10 | | | | | | | |
% 111.13/16.10 | | | | | | | | REDUCE: (21), (45) imply:
% 111.13/16.10 | | | | | | | | (46) ~ (all_53_1 = e2)
% 111.13/16.10 | | | | | | | |
% 111.13/16.10 | | | | | | | | REDUCE: (6), (45) imply:
% 111.13/16.10 | | | | | | | | (47) ~ (e3 = e2)
% 111.13/16.10 | | | | | | | |
% 111.13/16.10 | | | | | | | | SIMP: (47) implies:
% 111.13/16.10 | | | | | | | | (48) ~ (e3 = e2)
% 111.13/16.10 | | | | | | | |
% 111.13/16.10 | | | | | | | | REDUCE: (24), (45) imply:
% 111.13/16.10 | | | | | | | | (49) ~ (e2 = e0)
% 111.13/16.10 | | | | | | | |
% 111.13/16.10 | | | | | | | | BETA: splitting (12) gives:
% 111.13/16.10 | | | | | | | |
% 111.13/16.10 | | | | | | | | Case 1:
% 111.13/16.10 | | | | | | | | |
% 111.13/16.10 | | | | | | | | | (50) (all_57_52 = e2 & op(e3, e1) = e2) | (all_57_53 = e2 &
% 111.13/16.10 | | | | | | | | | op(e2, e1) = e2)
% 111.13/16.10 | | | | | | | | |
% 111.13/16.10 | | | | | | | | | BETA: splitting (50) gives:
% 111.13/16.10 | | | | | | | | |
% 111.13/16.10 | | | | | | | | | Case 1:
% 111.13/16.10 | | | | | | | | | |
% 111.13/16.10 | | | | | | | | | | (51) all_57_52 = e2 & op(e3, e1) = e2
% 111.13/16.10 | | | | | | | | | |
% 111.13/16.10 | | | | | | | | | | ALPHA: (51) implies:
% 111.13/16.10 | | | | | | | | | | (52) op(e3, e1) = e2
% 111.13/16.10 | | | | | | | | | |
% 111.13/16.10 | | | | | | | | | | REF_CLOSE: (17), (19), (39), (48), (52) are inconsistent by
% 111.13/16.10 | | | | | | | | | | sub-proof #177.
% 111.13/16.10 | | | | | | | | | |
% 111.13/16.10 | | | | | | | | | Case 2:
% 111.13/16.10 | | | | | | | | | |
% 111.13/16.10 | | | | | | | | | | (53) all_57_53 = e2 & op(e2, e1) = e2
% 111.13/16.10 | | | | | | | | | |
% 111.13/16.10 | | | | | | | | | | ALPHA: (53) implies:
% 111.13/16.10 | | | | | | | | | | (54) op(e2, e1) = e2
% 111.13/16.10 | | | | | | | | | |
% 111.13/16.10 | | | | | | | | | | REF_CLOSE: (13), (19), (29), (31), (54) are inconsistent by
% 111.13/16.10 | | | | | | | | | | sub-proof #110.
% 111.13/16.10 | | | | | | | | | |
% 111.13/16.10 | | | | | | | | | End of split
% 111.13/16.10 | | | | | | | | |
% 111.13/16.10 | | | | | | | | Case 2:
% 111.13/16.10 | | | | | | | | |
% 111.13/16.10 | | | | | | | | | (55) (all_57_54 = e2 & op(e1, e1) = e2) | (all_57_55 = e2 &
% 111.13/16.10 | | | | | | | | | op(e0, e1) = e2)
% 111.13/16.10 | | | | | | | | |
% 111.13/16.10 | | | | | | | | | REF_CLOSE: (11), (19), (20), (46), (49), (55) are inconsistent
% 111.13/16.10 | | | | | | | | | by sub-proof #108.
% 111.13/16.10 | | | | | | | | |
% 111.13/16.10 | | | | | | | | End of split
% 111.13/16.10 | | | | | | | |
% 111.13/16.10 | | | | | | | Case 2:
% 111.13/16.10 | | | | | | | |
% 111.13/16.10 | | | | | | | | (56) all_55_2 = e1 | all_55_2 = e0
% 111.13/16.10 | | | | | | | |
% 111.13/16.10 | | | | | | | | REF_CLOSE: (1), (9), (16), (19), (24), (30), (56) are
% 111.13/16.10 | | | | | | | | inconsistent by sub-proof #119.
% 111.13/16.10 | | | | | | | |
% 111.13/16.10 | | | | | | | End of split
% 111.13/16.10 | | | | | | |
% 111.13/16.10 | | | | | | End of split
% 111.13/16.10 | | | | | |
% 111.13/16.10 | | | | | Case 2:
% 111.13/16.10 | | | | | |
% 111.13/16.10 | | | | | | (57) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 &
% 111.13/16.10 | | | | | | op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 = e0 &
% 111.13/16.10 | | | | | | ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) =
% 111.13/16.10 | | | | | | e0 & $i(all_52_10))
% 111.13/16.10 | | | | | |
% 111.13/16.10 | | | | | | REF_CLOSE: (2), (11), (13), (19), (29), (31), (57) are inconsistent
% 111.13/16.10 | | | | | | by sub-proof #107.
% 111.13/16.10 | | | | | |
% 111.13/16.10 | | | | | End of split
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | Case 2:
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | (58) all_57_69 = e0 & op(e2, e2) = e0
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | ALPHA: (58) implies:
% 111.13/16.10 | | | | | (59) op(e2, e2) = e0
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | REF_CLOSE: (10), (18), (19), (59) are inconsistent by sub-proof #139.
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | End of split
% 111.13/16.10 | | | |
% 111.13/16.10 | | | Case 2:
% 111.13/16.10 | | | |
% 111.13/16.10 | | | | (60) (all_57_70 = e0 & op(e1, e2) = e0) | (all_57_71 = e0 & op(e0,
% 111.13/16.10 | | | | e2) = e0)
% 111.13/16.10 | | | |
% 111.13/16.10 | | | | BETA: splitting (60) gives:
% 111.13/16.10 | | | |
% 111.13/16.10 | | | | Case 1:
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | (61) all_57_70 = e0 & op(e1, e2) = e0
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | ALPHA: (61) implies:
% 111.13/16.10 | | | | | (62) op(e1, e2) = e0
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | REF_CLOSE: (9), (15), (19), (62) are inconsistent by sub-proof #153.
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | Case 2:
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | (63) all_57_71 = e0 & op(e0, e2) = e0
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | ALPHA: (63) implies:
% 111.13/16.10 | | | | | (64) op(e0, e2) = e0
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | | REF_CLOSE: (19), (23), (24), (64) are inconsistent by sub-proof #219.
% 111.13/16.10 | | | | |
% 111.13/16.10 | | | | End of split
% 111.13/16.10 | | | |
% 111.13/16.10 | | | End of split
% 111.13/16.10 | | |
% 111.13/16.10 | | Case 2:
% 111.13/16.10 | | |
% 111.13/16.10 | | | (65) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 &
% 111.13/16.10 | | | op(e0, e2) = e0 & $i(all_52_16)
% 111.13/16.10 | | |
% 111.13/16.10 | | | ALPHA: (65) implies:
% 111.13/16.10 | | | (66) op(e0, e2) = e0
% 111.13/16.10 | | |
% 111.13/16.10 | | | REF_CLOSE: (19), (23), (24), (66) are inconsistent by sub-proof #219.
% 111.13/16.10 | | |
% 111.13/16.10 | | End of split
% 111.13/16.10 | |
% 111.13/16.10 | End of split
% 111.13/16.10 |
% 111.13/16.10 End of proof
% 111.13/16.10
% 111.13/16.10 Sub-proof #107 shows that the following formulas are inconsistent:
% 111.13/16.10 ----------------------------------------------------------------
% 111.13/16.10 (1) ~ (all_53_1 = e0)
% 111.13/16.10 (2) op(e0, e1) = all_53_1
% 111.13/16.10 (3) op(e2, e1) = all_53_9
% 111.13/16.10 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.10 (5) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 111.13/16.10 all_52_8 & $i(all_52_8)) | (all_52_11 = e0 & ~ (all_52_10 = e1) &
% 111.13/16.10 op(e1, e0) = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 111.13/16.10 (6) op(e2, e1) = all_52_14
% 111.13/16.10 (7) ~ (all_52_14 = e2)
% 111.13/16.10
% 111.13/16.10 Begin of proof
% 111.13/16.10 |
% 111.13/16.10 | BETA: splitting (5) gives:
% 111.13/16.10 |
% 111.13/16.10 | Case 1:
% 111.13/16.10 | |
% 111.13/16.10 | | (8) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 111.13/16.10 | | all_52_8 & $i(all_52_8)
% 111.13/16.10 | |
% 111.13/16.10 | | ALPHA: (8) implies:
% 111.13/16.10 | | (9) op(e2, e1) = e2
% 111.13/16.10 | |
% 111.13/16.10 | | REF_CLOSE: (3), (4), (6), (7), (9) are inconsistent by sub-proof #110.
% 111.13/16.10 | |
% 111.13/16.10 | Case 2:
% 111.13/16.10 | |
% 111.13/16.10 | | (10) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 &
% 111.13/16.10 | | op(e0, e1) = e0 & $i(all_52_10)
% 111.13/16.10 | |
% 111.13/16.10 | | ALPHA: (10) implies:
% 111.13/16.10 | | (11) op(e0, e1) = e0
% 111.13/16.10 | |
% 111.13/16.10 | | REF_CLOSE: (1), (2), (4), (11) are inconsistent by sub-proof #230.
% 111.13/16.10 | |
% 111.13/16.10 | End of split
% 111.13/16.10 |
% 111.13/16.10 End of proof
% 111.13/16.10
% 111.13/16.10 Sub-proof #108 shows that the following formulas are inconsistent:
% 111.13/16.10 ----------------------------------------------------------------
% 111.13/16.10 (1) ~ (all_53_1 = e2)
% 111.13/16.10 (2) ~ (e2 = e0)
% 111.13/16.10 (3) op(e0, e1) = all_53_1
% 111.13/16.10 (4) (all_57_54 = e2 & op(e1, e1) = e2) | (all_57_55 = e2 & op(e0, e1) = e2)
% 111.13/16.10 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.10 (6) op(e1, e1) = e0
% 111.13/16.10
% 111.13/16.10 Begin of proof
% 111.13/16.10 |
% 111.13/16.10 | BETA: splitting (4) gives:
% 111.13/16.10 |
% 111.13/16.10 | Case 1:
% 111.13/16.10 | |
% 111.13/16.10 | | (7) all_57_54 = e2 & op(e1, e1) = e2
% 111.13/16.10 | |
% 111.13/16.10 | | ALPHA: (7) implies:
% 111.13/16.10 | | (8) op(e1, e1) = e2
% 111.13/16.10 | |
% 111.13/16.10 | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #109.
% 111.13/16.10 | |
% 111.13/16.10 | Case 2:
% 111.13/16.10 | |
% 111.13/16.10 | | (9) all_57_55 = e2 & op(e0, e1) = e2
% 111.13/16.10 | |
% 111.13/16.10 | | ALPHA: (9) implies:
% 111.13/16.10 | | (10) op(e0, e1) = e2
% 111.13/16.10 | |
% 111.13/16.10 | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #161.
% 111.13/16.10 | |
% 111.13/16.10 | End of split
% 111.13/16.10 |
% 111.13/16.10 End of proof
% 111.13/16.10
% 111.13/16.10 Sub-proof #109 shows that the following formulas are inconsistent:
% 111.13/16.10 ----------------------------------------------------------------
% 111.13/16.10 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.10 (2) op(e1, e1) = e2
% 111.13/16.10 (3) op(e1, e1) = e0
% 111.13/16.10 (4) ~ (e2 = e0)
% 111.13/16.10
% 111.13/16.10 Begin of proof
% 111.13/16.10 |
% 111.13/16.10 | GROUND_INST: instantiating (1) with e0, e2, e1, e1, simplifying with (2), (3)
% 111.13/16.10 | gives:
% 111.13/16.10 | (5) e2 = e0
% 111.13/16.10 |
% 111.13/16.10 | REDUCE: (4), (5) imply:
% 111.13/16.10 | (6) $false
% 111.13/16.10 |
% 111.13/16.10 | CLOSE: (6) is inconsistent.
% 111.13/16.10 |
% 111.13/16.10 End of proof
% 111.13/16.10
% 111.13/16.10 Sub-proof #110 shows that the following formulas are inconsistent:
% 111.13/16.10 ----------------------------------------------------------------
% 111.13/16.10 (1) op(e2, e1) = e2
% 111.13/16.10 (2) op(e2, e1) = all_53_9
% 111.13/16.10 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.13/16.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.13/16.10 (4) op(e2, e1) = all_52_14
% 111.64/16.10 (5) ~ (all_52_14 = e2)
% 111.64/16.10
% 111.64/16.10 Begin of proof
% 111.64/16.10 |
% 111.64/16.10 | GROUND_INST: instantiating (3) with all_53_9, e2, e1, e2, simplifying with
% 111.64/16.10 | (1), (2) gives:
% 111.64/16.10 | (6) all_53_9 = e2
% 111.64/16.10 |
% 111.64/16.10 | GROUND_INST: instantiating (3) with all_53_9, all_52_14, e1, e2, simplifying
% 111.64/16.10 | with (2), (4) gives:
% 111.64/16.10 | (7) all_53_9 = all_52_14
% 111.64/16.10 |
% 111.64/16.10 | COMBINE_EQS: (6), (7) imply:
% 111.64/16.10 | (8) all_52_14 = e2
% 111.64/16.10 |
% 111.64/16.10 | SIMP: (8) implies:
% 111.64/16.10 | (9) all_52_14 = e2
% 111.64/16.10 |
% 111.64/16.10 | REDUCE: (5), (9) imply:
% 111.64/16.10 | (10) $false
% 111.64/16.10 |
% 111.64/16.10 | CLOSE: (10) is inconsistent.
% 111.64/16.10 |
% 111.64/16.10 End of proof
% 111.64/16.10
% 111.64/16.10 Sub-proof #111 shows that the following formulas are inconsistent:
% 111.64/16.10 ----------------------------------------------------------------
% 111.64/16.10 (1) all_55_2 = all_53_3
% 111.64/16.10 (2) all_55_2 = e3
% 111.64/16.10 (3) ~ (all_53_3 = e3)
% 111.64/16.10
% 111.64/16.10 Begin of proof
% 111.64/16.10 |
% 111.64/16.10 | COMBINE_EQS: (1), (2) imply:
% 111.64/16.10 | (4) all_53_3 = e3
% 111.64/16.10 |
% 111.64/16.11 | SIMP: (4) implies:
% 111.64/16.11 | (5) all_53_3 = e3
% 111.64/16.11 |
% 111.64/16.11 | REDUCE: (3), (5) imply:
% 111.64/16.11 | (6) $false
% 111.64/16.11 |
% 111.64/16.11 | CLOSE: (6) is inconsistent.
% 111.64/16.11 |
% 111.64/16.11 End of proof
% 111.64/16.11
% 111.64/16.11 Sub-proof #112 shows that the following formulas are inconsistent:
% 111.64/16.11 ----------------------------------------------------------------
% 111.64/16.11 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.11 (2) op(e1, e0) = all_53_4
% 111.64/16.11 (3) op(e1, e0) = e2
% 111.64/16.11 (4) ~ (all_53_4 = e2)
% 111.64/16.11
% 111.64/16.11 Begin of proof
% 111.64/16.11 |
% 111.64/16.11 | GROUND_INST: instantiating (1) with all_53_4, e2, e0, e1, simplifying with
% 111.64/16.11 | (2), (3) gives:
% 111.64/16.11 | (5) all_53_4 = e2
% 111.64/16.11 |
% 111.64/16.11 | REDUCE: (4), (5) imply:
% 111.64/16.11 | (6) $false
% 111.64/16.11 |
% 111.64/16.11 | CLOSE: (6) is inconsistent.
% 111.64/16.11 |
% 111.64/16.11 End of proof
% 111.64/16.11
% 111.64/16.11 Sub-proof #113 shows that the following formulas are inconsistent:
% 111.64/16.11 ----------------------------------------------------------------
% 111.64/16.11 (1) all_55_4 = all_53_4
% 111.64/16.11 (2) all_55_4 = e0
% 111.64/16.11 (3) ~ (all_53_4 = e0)
% 111.64/16.11
% 111.64/16.11 Begin of proof
% 111.64/16.11 |
% 111.64/16.11 | COMBINE_EQS: (1), (2) imply:
% 111.64/16.11 | (4) all_53_4 = e0
% 111.64/16.11 |
% 111.64/16.11 | SIMP: (4) implies:
% 111.64/16.11 | (5) all_53_4 = e0
% 111.64/16.11 |
% 111.64/16.11 | REDUCE: (3), (5) imply:
% 111.64/16.11 | (6) $false
% 111.64/16.11 |
% 111.64/16.11 | CLOSE: (6) is inconsistent.
% 111.64/16.11 |
% 111.64/16.11 End of proof
% 111.64/16.11
% 111.64/16.11 Sub-proof #114 shows that the following formulas are inconsistent:
% 111.64/16.11 ----------------------------------------------------------------
% 111.64/16.11 (1) all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 111.64/16.11 (2) ~ (all_53_7 = e2)
% 111.64/16.11 (3) ~ (all_53_7 = e0)
% 111.64/16.11 (4) all_55_6 = all_53_7
% 111.64/16.11 (5) ~ (all_53_7 = e1)
% 111.64/16.11
% 111.64/16.11 Begin of proof
% 111.64/16.11 |
% 111.64/16.11 | BETA: splitting (1) gives:
% 111.64/16.11 |
% 111.64/16.11 | Case 1:
% 111.64/16.11 | |
% 111.64/16.11 | | (6) all_55_6 = e2
% 111.64/16.11 | |
% 111.64/16.11 | | COMBINE_EQS: (4), (6) imply:
% 111.64/16.11 | | (7) all_53_7 = e2
% 111.64/16.11 | |
% 111.64/16.11 | | REDUCE: (2), (7) imply:
% 111.64/16.11 | | (8) $false
% 111.64/16.11 | |
% 111.64/16.11 | | CLOSE: (8) is inconsistent.
% 111.64/16.11 | |
% 111.64/16.11 | Case 2:
% 111.64/16.11 | |
% 111.64/16.11 | | (9) all_55_6 = e1 | all_55_6 = e0
% 111.64/16.11 | |
% 111.64/16.11 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #115.
% 111.64/16.11 | |
% 111.64/16.11 | End of split
% 111.64/16.11 |
% 111.64/16.11 End of proof
% 111.64/16.11
% 111.64/16.11 Sub-proof #115 shows that the following formulas are inconsistent:
% 111.64/16.11 ----------------------------------------------------------------
% 111.64/16.11 (1) all_55_6 = e1 | all_55_6 = e0
% 111.64/16.11 (2) all_55_6 = all_53_7
% 111.64/16.11 (3) ~ (all_53_7 = e1)
% 111.64/16.11 (4) ~ (all_53_7 = e0)
% 111.64/16.11
% 111.64/16.11 Begin of proof
% 111.64/16.11 |
% 111.64/16.11 | BETA: splitting (1) gives:
% 111.64/16.11 |
% 111.64/16.11 | Case 1:
% 111.64/16.11 | |
% 111.64/16.11 | | (5) all_55_6 = e1
% 111.64/16.11 | |
% 111.64/16.11 | | COMBINE_EQS: (2), (5) imply:
% 111.64/16.11 | | (6) all_53_7 = e1
% 111.64/16.11 | |
% 111.64/16.11 | | SIMP: (6) implies:
% 111.64/16.11 | | (7) all_53_7 = e1
% 111.64/16.11 | |
% 111.64/16.11 | | REDUCE: (3), (7) imply:
% 111.64/16.11 | | (8) $false
% 111.64/16.11 | |
% 111.64/16.11 | | CLOSE: (8) is inconsistent.
% 111.64/16.11 | |
% 111.64/16.11 | Case 2:
% 111.64/16.11 | |
% 111.64/16.11 | | (9) all_55_6 = e0
% 111.64/16.11 | |
% 111.64/16.11 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #132.
% 111.64/16.11 | |
% 111.64/16.11 | End of split
% 111.64/16.11 |
% 111.64/16.11 End of proof
% 111.64/16.11
% 111.64/16.11 Sub-proof #116 shows that the following formulas are inconsistent:
% 111.64/16.11 ----------------------------------------------------------------
% 111.64/16.11 (1) all_55_4 = all_53_4
% 111.64/16.11 (2) all_55_4 = e2
% 111.64/16.11 (3) ~ (all_53_4 = e2)
% 111.64/16.11
% 111.64/16.11 Begin of proof
% 111.64/16.11 |
% 111.64/16.11 | COMBINE_EQS: (1), (2) imply:
% 111.64/16.11 | (4) all_53_4 = e2
% 111.64/16.11 |
% 111.64/16.11 | SIMP: (4) implies:
% 111.64/16.11 | (5) all_53_4 = e2
% 111.64/16.11 |
% 111.64/16.11 | REDUCE: (3), (5) imply:
% 111.64/16.11 | (6) $false
% 111.64/16.11 |
% 111.64/16.11 | CLOSE: (6) is inconsistent.
% 111.64/16.11 |
% 111.64/16.11 End of proof
% 111.64/16.11
% 111.64/16.11 Sub-proof #117 shows that the following formulas are inconsistent:
% 111.64/16.11 ----------------------------------------------------------------
% 111.64/16.11 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.11 (2) op(e3, e0) = all_53_12
% 111.64/16.11 (3) op(e3, e0) = e2
% 111.64/16.11 (4) ~ (all_53_12 = e2)
% 111.64/16.11
% 111.64/16.11 Begin of proof
% 111.64/16.11 |
% 111.64/16.11 | GROUND_INST: instantiating (1) with all_53_12, e2, e0, e3, simplifying with
% 111.64/16.11 | (2), (3) gives:
% 111.64/16.11 | (5) all_53_12 = e2
% 111.64/16.11 |
% 111.64/16.11 | REDUCE: (4), (5) imply:
% 111.64/16.11 | (6) $false
% 111.64/16.11 |
% 111.64/16.11 | CLOSE: (6) is inconsistent.
% 111.64/16.11 |
% 111.64/16.11 End of proof
% 111.64/16.11
% 111.64/16.11 Sub-proof #118 shows that the following formulas are inconsistent:
% 111.64/16.11 ----------------------------------------------------------------
% 111.64/16.11 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.11 (2) op(e3, e1) = all_53_13
% 111.64/16.11 (3) op(e3, e1) = e1
% 111.64/16.11 (4) ~ (all_53_13 = e1)
% 111.64/16.11
% 111.64/16.11 Begin of proof
% 111.64/16.11 |
% 111.64/16.11 | GROUND_INST: instantiating (1) with all_53_13, e1, e1, e3, simplifying with
% 111.64/16.11 | (2), (3) gives:
% 111.64/16.11 | (5) all_53_13 = e1
% 111.64/16.11 |
% 111.64/16.11 | REDUCE: (4), (5) imply:
% 111.64/16.11 | (6) $false
% 111.64/16.11 |
% 111.64/16.11 | CLOSE: (6) is inconsistent.
% 111.64/16.11 |
% 111.64/16.11 End of proof
% 111.64/16.11
% 111.64/16.11 Sub-proof #119 shows that the following formulas are inconsistent:
% 111.64/16.11 ----------------------------------------------------------------
% 111.64/16.11 (1) ~ (all_53_3 = all_53_7)
% 111.64/16.11 (2) op(e1, e2) = e1
% 111.64/16.11 (3) op(e1, e2) = all_53_7
% 111.64/16.11 (4) all_55_2 = all_53_3
% 111.64/16.11 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.11 (6) all_55_2 = e1 | all_55_2 = e0
% 111.64/16.11 (7) ~ (all_53_3 = e0)
% 111.64/16.11
% 111.64/16.11 Begin of proof
% 111.64/16.11 |
% 111.64/16.11 | BETA: splitting (6) gives:
% 111.64/16.11 |
% 111.64/16.11 | Case 1:
% 111.64/16.11 | |
% 111.64/16.11 | | (8) all_55_2 = e1
% 111.64/16.11 | |
% 111.64/16.11 | | COMBINE_EQS: (4), (8) imply:
% 111.64/16.11 | | (9) all_53_3 = e1
% 111.64/16.11 | |
% 111.64/16.11 | | REDUCE: (1), (9) imply:
% 111.64/16.11 | | (10) ~ (all_53_7 = e1)
% 111.64/16.11 | |
% 111.64/16.11 | | SIMP: (10) implies:
% 111.64/16.11 | | (11) ~ (all_53_7 = e1)
% 111.64/16.11 | |
% 111.64/16.11 | | REF_CLOSE: (2), (3), (5), (11) are inconsistent by sub-proof #233.
% 111.64/16.11 | |
% 111.64/16.11 | Case 2:
% 111.64/16.11 | |
% 111.64/16.11 | | (12) all_55_2 = e0
% 111.64/16.11 | |
% 111.64/16.11 | | COMBINE_EQS: (4), (12) imply:
% 111.64/16.11 | | (13) all_53_3 = e0
% 111.64/16.11 | |
% 111.64/16.11 | | REDUCE: (7), (13) imply:
% 111.64/16.11 | | (14) $false
% 111.64/16.11 | |
% 111.64/16.11 | | CLOSE: (14) is inconsistent.
% 111.64/16.11 | |
% 111.64/16.11 | End of split
% 111.64/16.11 |
% 111.64/16.11 End of proof
% 111.64/16.11
% 111.64/16.11 Sub-proof #120 shows that the following formulas are inconsistent:
% 111.64/16.11 ----------------------------------------------------------------
% 111.64/16.11 (1) ~ (all_53_10 = e1)
% 111.64/16.11 (2) all_55_11 = e1 | all_55_11 = e0
% 111.64/16.11 (3) all_55_11 = all_53_10
% 111.64/16.11 (4) all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 111.64/16.11 (5) all_55_3 = all_53_2
% 111.64/16.11 (6) op(e0, e3) = e0
% 111.64/16.11 (7) ~ (all_53_2 = e2)
% 111.64/16.11 (8) op(e0, e3) = all_53_2
% 111.64/16.11 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.11 (10) ~ (all_53_2 = e1)
% 111.64/16.11 (11) ~ (all_53_2 = all_53_10)
% 111.64/16.11
% 111.64/16.11 Begin of proof
% 111.64/16.11 |
% 111.64/16.11 | BETA: splitting (2) gives:
% 111.64/16.11 |
% 111.64/16.11 | Case 1:
% 111.64/16.11 | |
% 111.64/16.11 | | (12) all_55_11 = e1
% 111.64/16.11 | |
% 111.64/16.11 | | COMBINE_EQS: (3), (12) imply:
% 111.64/16.11 | | (13) all_53_10 = e1
% 111.64/16.11 | |
% 111.64/16.11 | | REDUCE: (1), (13) imply:
% 111.64/16.11 | | (14) $false
% 111.64/16.11 | |
% 111.64/16.11 | | CLOSE: (14) is inconsistent.
% 111.64/16.11 | |
% 111.64/16.11 | Case 2:
% 111.64/16.11 | |
% 111.64/16.11 | | (15) all_55_11 = e0
% 111.64/16.11 | |
% 111.64/16.11 | | COMBINE_EQS: (3), (15) imply:
% 111.64/16.11 | | (16) all_53_10 = e0
% 111.64/16.11 | |
% 111.64/16.11 | | REDUCE: (11), (16) imply:
% 111.64/16.11 | | (17) ~ (all_53_2 = e0)
% 111.64/16.11 | |
% 111.64/16.11 | | BETA: splitting (4) gives:
% 111.64/16.11 | |
% 111.64/16.11 | | Case 1:
% 111.64/16.11 | | |
% 111.64/16.11 | | | (18) all_55_3 = e3
% 111.64/16.11 | | |
% 111.64/16.11 | | | COMBINE_EQS: (5), (18) imply:
% 111.64/16.11 | | | (19) all_53_2 = e3
% 111.64/16.11 | | |
% 111.64/16.11 | | | REDUCE: (17), (19) imply:
% 111.64/16.11 | | | (20) ~ (e3 = e0)
% 111.64/16.11 | | |
% 111.64/16.11 | | | REDUCE: (8), (19) imply:
% 111.64/16.11 | | | (21) op(e0, e3) = e3
% 111.64/16.11 | | |
% 111.64/16.11 | | | REF_CLOSE: (6), (9), (20), (21) are inconsistent by sub-proof #122.
% 111.64/16.11 | | |
% 111.64/16.11 | | Case 2:
% 111.64/16.11 | | |
% 111.64/16.11 | | | (22) all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 111.64/16.11 | | |
% 111.64/16.11 | | | BETA: splitting (22) gives:
% 111.64/16.11 | | |
% 111.64/16.11 | | | Case 1:
% 111.64/16.11 | | | |
% 111.64/16.11 | | | | (23) all_55_3 = e2
% 111.64/16.11 | | | |
% 111.64/16.11 | | | | COMBINE_EQS: (5), (23) imply:
% 111.64/16.11 | | | | (24) all_53_2 = e2
% 111.64/16.11 | | | |
% 111.64/16.11 | | | | SIMP: (24) implies:
% 111.64/16.11 | | | | (25) all_53_2 = e2
% 111.64/16.11 | | | |
% 111.64/16.11 | | | | REDUCE: (7), (25) imply:
% 111.64/16.11 | | | | (26) $false
% 111.64/16.11 | | | |
% 111.64/16.11 | | | | CLOSE: (26) is inconsistent.
% 111.64/16.11 | | | |
% 111.64/16.11 | | | Case 2:
% 111.64/16.11 | | | |
% 111.64/16.11 | | | | (27) all_55_3 = e1 | all_55_3 = e0
% 111.64/16.11 | | | |
% 111.64/16.11 | | | | BETA: splitting (27) gives:
% 111.64/16.11 | | | |
% 111.64/16.11 | | | | Case 1:
% 111.64/16.11 | | | | |
% 111.64/16.11 | | | | | (28) all_55_3 = e1
% 111.64/16.11 | | | | |
% 111.64/16.11 | | | | | REF_CLOSE: (5), (10), (28) are inconsistent by sub-proof #121.
% 111.64/16.11 | | | | |
% 111.64/16.11 | | | | Case 2:
% 111.64/16.11 | | | | |
% 111.64/16.11 | | | | | (29) all_55_3 = e0
% 111.64/16.11 | | | | |
% 111.64/16.11 | | | | | COMBINE_EQS: (5), (29) imply:
% 111.64/16.11 | | | | | (30) all_53_2 = e0
% 111.64/16.11 | | | | |
% 111.64/16.11 | | | | | SIMP: (30) implies:
% 111.64/16.11 | | | | | (31) all_53_2 = e0
% 111.64/16.11 | | | | |
% 111.64/16.11 | | | | | REDUCE: (17), (31) imply:
% 111.64/16.11 | | | | | (32) $false
% 111.64/16.11 | | | | |
% 111.64/16.11 | | | | | CLOSE: (32) is inconsistent.
% 111.64/16.11 | | | | |
% 111.64/16.11 | | | | End of split
% 111.64/16.11 | | | |
% 111.64/16.11 | | | End of split
% 111.64/16.11 | | |
% 111.64/16.11 | | End of split
% 111.64/16.11 | |
% 111.64/16.11 | End of split
% 111.64/16.11 |
% 111.64/16.11 End of proof
% 111.64/16.11
% 111.64/16.11 Sub-proof #121 shows that the following formulas are inconsistent:
% 111.64/16.11 ----------------------------------------------------------------
% 111.64/16.11 (1) all_55_3 = all_53_2
% 111.64/16.11 (2) all_55_3 = e1
% 111.64/16.11 (3) ~ (all_53_2 = e1)
% 111.64/16.11
% 111.64/16.11 Begin of proof
% 111.64/16.11 |
% 111.64/16.11 | COMBINE_EQS: (1), (2) imply:
% 111.64/16.11 | (4) all_53_2 = e1
% 111.64/16.11 |
% 111.64/16.11 | SIMP: (4) implies:
% 111.64/16.11 | (5) all_53_2 = e1
% 111.64/16.11 |
% 111.64/16.11 | REDUCE: (3), (5) imply:
% 111.64/16.11 | (6) $false
% 111.64/16.11 |
% 111.64/16.11 | CLOSE: (6) is inconsistent.
% 111.64/16.11 |
% 111.64/16.11 End of proof
% 111.64/16.11
% 111.64/16.11 Sub-proof #122 shows that the following formulas are inconsistent:
% 111.64/16.11 ----------------------------------------------------------------
% 111.64/16.11 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.11 (2) op(e0, e3) = e3
% 111.64/16.11 (3) op(e0, e3) = e0
% 111.64/16.11 (4) ~ (e3 = e0)
% 111.64/16.11
% 111.64/16.11 Begin of proof
% 111.64/16.11 |
% 111.64/16.11 | GROUND_INST: instantiating (1) with e3, e0, e3, e0, simplifying with (2), (3)
% 111.64/16.11 | gives:
% 111.64/16.11 | (5) e3 = e0
% 111.64/16.11 |
% 111.64/16.11 | REDUCE: (4), (5) imply:
% 111.64/16.11 | (6) $false
% 111.64/16.11 |
% 111.64/16.11 | CLOSE: (6) is inconsistent.
% 111.64/16.11 |
% 111.64/16.11 End of proof
% 111.64/16.11
% 111.64/16.11 Sub-proof #123 shows that the following formulas are inconsistent:
% 111.64/16.11 ----------------------------------------------------------------
% 111.64/16.11 (1) all_55_4 = all_53_4
% 111.64/16.11 (2) all_55_4 = e3
% 111.64/16.11 (3) ~ (all_53_4 = e3)
% 111.64/16.11
% 111.64/16.11 Begin of proof
% 111.64/16.11 |
% 111.64/16.11 | COMBINE_EQS: (1), (2) imply:
% 111.64/16.11 | (4) all_53_4 = e3
% 111.64/16.11 |
% 111.64/16.11 | SIMP: (4) implies:
% 111.64/16.11 | (5) all_53_4 = e3
% 111.64/16.11 |
% 111.64/16.11 | REDUCE: (3), (5) imply:
% 111.64/16.11 | (6) $false
% 111.64/16.11 |
% 111.64/16.11 | CLOSE: (6) is inconsistent.
% 111.64/16.11 |
% 111.64/16.11 End of proof
% 111.64/16.11
% 111.64/16.11 Sub-proof #124 shows that the following formulas are inconsistent:
% 111.64/16.11 ----------------------------------------------------------------
% 111.64/16.11 (1) op(e0, e1) = all_53_1
% 111.64/16.11 (2) all_55_13 = all_53_13
% 111.64/16.11 (3) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 111.64/16.11 (4) op(e0, e1) = e0
% 111.64/16.11 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.11 (6) ~ (all_53_1 = all_53_13)
% 111.64/16.11 (7) ~ (all_53_13 = e1)
% 111.64/16.11 (8) ~ (all_53_13 = e2)
% 111.64/16.11
% 111.64/16.11 Begin of proof
% 111.64/16.11 |
% 111.64/16.11 | BETA: splitting (3) gives:
% 111.64/16.11 |
% 111.64/16.11 | Case 1:
% 111.64/16.11 | |
% 111.64/16.11 | | (9) all_55_13 = e2
% 111.64/16.11 | |
% 111.64/16.11 | | COMBINE_EQS: (2), (9) imply:
% 111.64/16.11 | | (10) all_53_13 = e2
% 111.64/16.11 | |
% 111.64/16.11 | | SIMP: (10) implies:
% 111.64/16.11 | | (11) all_53_13 = e2
% 111.64/16.11 | |
% 111.64/16.11 | | REDUCE: (8), (11) imply:
% 111.64/16.11 | | (12) $false
% 111.64/16.11 | |
% 111.64/16.11 | | CLOSE: (12) is inconsistent.
% 111.64/16.11 | |
% 111.64/16.11 | Case 2:
% 111.64/16.11 | |
% 111.64/16.11 | | (13) all_55_13 = e1 | all_55_13 = e0
% 111.64/16.11 | |
% 111.64/16.11 | | BETA: splitting (13) gives:
% 111.64/16.11 | |
% 111.64/16.11 | | Case 1:
% 111.64/16.11 | | |
% 111.64/16.11 | | | (14) all_55_13 = e1
% 111.64/16.11 | | |
% 111.64/16.11 | | | COMBINE_EQS: (2), (14) imply:
% 111.64/16.11 | | | (15) all_53_13 = e1
% 111.64/16.11 | | |
% 111.64/16.11 | | | SIMP: (15) implies:
% 111.64/16.11 | | | (16) all_53_13 = e1
% 111.64/16.11 | | |
% 111.64/16.11 | | | REDUCE: (7), (16) imply:
% 111.64/16.11 | | | (17) $false
% 111.64/16.11 | | |
% 111.64/16.11 | | | CLOSE: (17) is inconsistent.
% 111.64/16.11 | | |
% 111.64/16.11 | | Case 2:
% 111.64/16.11 | | |
% 111.64/16.11 | | | (18) all_55_13 = e0
% 111.64/16.11 | | |
% 111.64/16.11 | | | COMBINE_EQS: (2), (18) imply:
% 111.64/16.11 | | | (19) all_53_13 = e0
% 111.64/16.11 | | |
% 111.64/16.11 | | | SIMP: (19) implies:
% 111.64/16.11 | | | (20) all_53_13 = e0
% 111.64/16.11 | | |
% 111.64/16.11 | | | REDUCE: (6), (20) imply:
% 111.64/16.11 | | | (21) ~ (all_53_1 = e0)
% 111.64/16.11 | | |
% 111.64/16.11 | | | REF_CLOSE: (1), (4), (5), (21) are inconsistent by sub-proof #230.
% 111.64/16.11 | | |
% 111.64/16.11 | | End of split
% 111.64/16.11 | |
% 111.64/16.11 | End of split
% 111.64/16.11 |
% 111.64/16.11 End of proof
% 111.64/16.11
% 111.64/16.11 Sub-proof #125 shows that the following formulas are inconsistent:
% 111.64/16.11 ----------------------------------------------------------------
% 111.64/16.11 (1) (all_57_58 = e3 & op(e1, e1) = e3) | (all_57_59 = e3 & op(e1, e0) = e3)
% 111.64/16.11 (2) op(e1, e1) = e2
% 111.64/16.11 (3) op(e1, e0) = all_53_4
% 111.64/16.11 (4) ~ (all_53_4 = e3)
% 111.64/16.12 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.12 (6) ~ (e3 = e2)
% 111.64/16.12
% 111.64/16.12 Begin of proof
% 111.64/16.12 |
% 111.64/16.12 | BETA: splitting (1) gives:
% 111.64/16.12 |
% 111.64/16.12 | Case 1:
% 111.64/16.12 | |
% 111.64/16.12 | | (7) all_57_58 = e3 & op(e1, e1) = e3
% 111.64/16.12 | |
% 111.64/16.12 | | ALPHA: (7) implies:
% 111.64/16.12 | | (8) op(e1, e1) = e3
% 111.64/16.12 | |
% 111.64/16.12 | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #131.
% 111.64/16.12 | |
% 111.64/16.12 | Case 2:
% 111.64/16.12 | |
% 111.64/16.12 | | (9) all_57_59 = e3 & op(e1, e0) = e3
% 111.64/16.12 | |
% 111.64/16.12 | | ALPHA: (9) implies:
% 111.64/16.12 | | (10) op(e1, e0) = e3
% 111.64/16.12 | |
% 111.64/16.12 | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #126.
% 111.64/16.12 | |
% 111.64/16.12 | End of split
% 111.64/16.12 |
% 111.64/16.12 End of proof
% 111.64/16.12
% 111.64/16.12 Sub-proof #126 shows that the following formulas are inconsistent:
% 111.64/16.12 ----------------------------------------------------------------
% 111.64/16.12 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.12 (2) op(e1, e0) = all_53_4
% 111.64/16.12 (3) op(e1, e0) = e3
% 111.64/16.12 (4) ~ (all_53_4 = e3)
% 111.64/16.12
% 111.64/16.12 Begin of proof
% 111.64/16.12 |
% 111.64/16.12 | GROUND_INST: instantiating (1) with all_53_4, e3, e0, e1, simplifying with
% 111.64/16.12 | (2), (3) gives:
% 111.64/16.12 | (5) all_53_4 = e3
% 111.64/16.12 |
% 111.64/16.12 | REDUCE: (4), (5) imply:
% 111.64/16.12 | (6) $false
% 111.64/16.12 |
% 111.64/16.12 | CLOSE: (6) is inconsistent.
% 111.64/16.12 |
% 111.64/16.12 End of proof
% 111.64/16.12
% 111.64/16.12 Sub-proof #127 shows that the following formulas are inconsistent:
% 111.64/16.12 ----------------------------------------------------------------
% 111.64/16.12 (1) all_57_56 = e3 & op(e1, e3) = e3
% 111.64/16.12 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.12 (3) op(e1, e3) = all_53_6
% 111.64/16.12 (4) ~ (all_53_6 = e3)
% 111.64/16.12
% 111.64/16.12 Begin of proof
% 111.64/16.12 |
% 111.64/16.12 | ALPHA: (1) implies:
% 111.64/16.12 | (5) op(e1, e3) = e3
% 111.64/16.12 |
% 111.64/16.12 | GROUND_INST: instantiating (2) with all_53_6, e3, e3, e1, simplifying with
% 111.64/16.12 | (3), (5) gives:
% 111.64/16.12 | (6) all_53_6 = e3
% 111.64/16.12 |
% 111.64/16.12 | REDUCE: (4), (6) imply:
% 111.64/16.12 | (7) $false
% 111.64/16.12 |
% 111.64/16.12 | CLOSE: (7) is inconsistent.
% 111.64/16.12 |
% 111.64/16.12 End of proof
% 111.64/16.12
% 111.64/16.12 Sub-proof #128 shows that the following formulas are inconsistent:
% 111.64/16.12 ----------------------------------------------------------------
% 111.64/16.12 (1) (all_57_96 = e0 & op(e3, e3) = e0) | (all_57_97 = e0 & op(e3, e2) = e0) |
% 111.64/16.12 (all_57_98 = e0 & op(e3, e1) = e0) | (all_57_99 = e0 & op(e3, e0) = e0)
% 111.64/16.12 (2) ~ (all_53_9 = e2)
% 111.64/16.12 (3) ~ (all_53_15 = e0)
% 111.64/16.12 (4) ~ (all_6_2 = e2)
% 111.64/16.12 (5) ~ (all_53_1 = all_6_2)
% 111.64/16.12 (6) op(e3, e0) = all_53_12
% 111.64/16.12 (7) op(e3, e2) = all_53_15
% 111.64/16.12 (8) ~ (all_53_12 = all_6_2)
% 111.64/16.12 (9) op(e0, e1) = all_53_1
% 111.64/16.12 (10) op(e2, e1) = all_53_9
% 111.64/16.12 (11) ~ (all_6_2 = e3)
% 111.64/16.12 (12) ~ (all_4_2 = e0)
% 111.64/16.12 (13) all_55_0 = all_6_2
% 111.64/16.12 (14) op(e3, e1) = all_53_13
% 111.64/16.12 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.12 (16) all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 111.64/16.12 (17) ~ (all_6_2 = e1)
% 111.64/16.12 (18) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.64/16.12 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 111.64/16.12 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 111.64/16.12 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.64/16.12 $i(all_52_10))
% 111.64/16.12 (19) op(e3, e3) = all_4_2
% 111.64/16.12
% 111.64/16.12 Begin of proof
% 111.64/16.12 |
% 111.64/16.12 | BETA: splitting (16) gives:
% 111.64/16.12 |
% 111.64/16.12 | Case 1:
% 111.64/16.12 | |
% 111.64/16.12 | | (20) all_55_0 = e3
% 111.64/16.12 | |
% 111.64/16.12 | | COMBINE_EQS: (13), (20) imply:
% 111.64/16.12 | | (21) all_6_2 = e3
% 111.64/16.12 | |
% 111.64/16.12 | | REDUCE: (11), (21) imply:
% 111.64/16.12 | | (22) $false
% 111.64/16.12 | |
% 111.64/16.12 | | CLOSE: (22) is inconsistent.
% 111.64/16.12 | |
% 111.64/16.12 | Case 2:
% 111.64/16.12 | |
% 111.64/16.12 | | (23) ~ (all_55_0 = e3)
% 111.64/16.12 | | (24) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 111.64/16.12 | |
% 111.64/16.12 | | BETA: splitting (24) gives:
% 111.64/16.12 | |
% 111.64/16.12 | | Case 1:
% 111.64/16.12 | | |
% 111.64/16.12 | | | (25) all_55_0 = e2
% 111.64/16.12 | | |
% 111.64/16.12 | | | COMBINE_EQS: (13), (25) imply:
% 111.64/16.12 | | | (26) all_6_2 = e2
% 111.64/16.12 | | |
% 111.64/16.12 | | | REDUCE: (4), (26) imply:
% 111.64/16.12 | | | (27) $false
% 111.64/16.12 | | |
% 111.64/16.12 | | | CLOSE: (27) is inconsistent.
% 111.64/16.12 | | |
% 111.64/16.12 | | Case 2:
% 111.64/16.12 | | |
% 111.64/16.12 | | | (28) all_55_0 = e1 | all_55_0 = e0
% 111.64/16.12 | | |
% 111.64/16.12 | | | BETA: splitting (28) gives:
% 111.64/16.12 | | |
% 111.64/16.12 | | | Case 1:
% 111.64/16.12 | | | |
% 111.64/16.12 | | | | (29) all_55_0 = e1
% 111.64/16.12 | | | |
% 111.64/16.12 | | | | COMBINE_EQS: (13), (29) imply:
% 111.64/16.12 | | | | (30) all_6_2 = e1
% 111.64/16.12 | | | |
% 111.64/16.12 | | | | REDUCE: (17), (30) imply:
% 111.64/16.12 | | | | (31) $false
% 111.64/16.12 | | | |
% 111.64/16.12 | | | | CLOSE: (31) is inconsistent.
% 111.64/16.12 | | | |
% 111.64/16.12 | | | Case 2:
% 111.64/16.12 | | | |
% 111.64/16.12 | | | | (32) all_55_0 = e0
% 111.64/16.12 | | | |
% 111.64/16.12 | | | | COMBINE_EQS: (13), (32) imply:
% 111.64/16.12 | | | | (33) all_6_2 = e0
% 111.64/16.12 | | | |
% 111.64/16.12 | | | | REDUCE: (5), (33) imply:
% 111.64/16.12 | | | | (34) ~ (all_53_1 = e0)
% 111.64/16.12 | | | |
% 111.64/16.12 | | | | REDUCE: (8), (33) imply:
% 111.64/16.12 | | | | (35) ~ (all_53_12 = e0)
% 111.64/16.12 | | | |
% 111.64/16.12 | | | | REDUCE: (11), (33) imply:
% 111.64/16.12 | | | | (36) ~ (e3 = e0)
% 111.64/16.12 | | | |
% 111.64/16.12 | | | | SIMP: (36) implies:
% 111.64/16.12 | | | | (37) ~ (e3 = e0)
% 111.64/16.12 | | | |
% 111.64/16.12 | | | | BETA: splitting (18) gives:
% 111.64/16.12 | | | |
% 111.64/16.12 | | | | Case 1:
% 111.64/16.12 | | | | |
% 111.64/16.12 | | | | | (38) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1,
% 111.64/16.12 | | | | | e3) = all_52_6 & $i(all_52_6)
% 111.64/16.12 | | | | |
% 111.64/16.12 | | | | | ALPHA: (38) implies:
% 111.64/16.12 | | | | | (39) op(e3, e1) = e3
% 111.64/16.12 | | | | |
% 111.64/16.12 | | | | | BETA: splitting (1) gives:
% 111.64/16.12 | | | | |
% 111.64/16.12 | | | | | Case 1:
% 111.64/16.12 | | | | | |
% 111.64/16.12 | | | | | | (40) (all_57_96 = e0 & op(e3, e3) = e0) | (all_57_97 = e0 &
% 111.64/16.12 | | | | | | op(e3, e2) = e0)
% 111.64/16.12 | | | | | |
% 111.64/16.12 | | | | | | REF_CLOSE: (3), (7), (12), (15), (19), (40) are inconsistent by
% 111.64/16.12 | | | | | | sub-proof #155.
% 111.64/16.12 | | | | | |
% 111.64/16.12 | | | | | Case 2:
% 111.64/16.12 | | | | | |
% 111.64/16.12 | | | | | | (41) (all_57_98 = e0 & op(e3, e1) = e0) | (all_57_99 = e0 &
% 111.64/16.12 | | | | | | op(e3, e0) = e0)
% 111.64/16.12 | | | | | |
% 111.64/16.12 | | | | | | REF_CLOSE: (6), (14), (15), (35), (37), (39), (41) are inconsistent
% 111.64/16.12 | | | | | | by sub-proof #129.
% 111.64/16.12 | | | | | |
% 111.64/16.12 | | | | | End of split
% 111.64/16.12 | | | | |
% 111.64/16.12 | | | | Case 2:
% 111.64/16.12 | | | | |
% 111.64/16.12 | | | | | (42) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1,
% 111.64/16.12 | | | | | e2) = all_52_8 & $i(all_52_8)) | (all_52_11 = e0 & ~
% 111.64/16.12 | | | | | (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0
% 111.64/16.12 | | | | | & $i(all_52_10))
% 111.64/16.12 | | | | |
% 111.64/16.12 | | | | | REF_CLOSE: (2), (9), (10), (15), (34), (42) are inconsistent by
% 111.64/16.12 | | | | | sub-proof #229.
% 111.64/16.12 | | | | |
% 111.64/16.12 | | | | End of split
% 111.64/16.12 | | | |
% 111.64/16.12 | | | End of split
% 111.64/16.12 | | |
% 111.64/16.12 | | End of split
% 111.64/16.12 | |
% 111.64/16.12 | End of split
% 111.64/16.12 |
% 111.64/16.12 End of proof
% 111.64/16.12
% 111.64/16.12 Sub-proof #129 shows that the following formulas are inconsistent:
% 111.64/16.12 ----------------------------------------------------------------
% 111.64/16.12 (1) op(e3, e0) = all_53_12
% 111.64/16.12 (2) (all_57_98 = e0 & op(e3, e1) = e0) | (all_57_99 = e0 & op(e3, e0) = e0)
% 111.64/16.12 (3) ~ (e3 = e0)
% 111.64/16.12 (4) ~ (all_53_12 = e0)
% 111.64/16.12 (5) op(e3, e1) = all_53_13
% 111.64/16.12 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.12 (7) op(e3, e1) = e3
% 111.64/16.12
% 111.64/16.12 Begin of proof
% 111.64/16.12 |
% 111.64/16.12 | BETA: splitting (2) gives:
% 111.64/16.12 |
% 111.64/16.12 | Case 1:
% 111.64/16.12 | |
% 111.64/16.12 | | (8) all_57_98 = e0 & op(e3, e1) = e0
% 111.64/16.12 | |
% 111.64/16.12 | | ALPHA: (8) implies:
% 111.64/16.12 | | (9) op(e3, e1) = e0
% 111.64/16.12 | |
% 111.64/16.12 | | REF_CLOSE: (3), (5), (6), (7), (9) are inconsistent by sub-proof #154.
% 111.64/16.12 | |
% 111.64/16.12 | Case 2:
% 111.64/16.12 | |
% 111.64/16.12 | | (10) all_57_99 = e0 & op(e3, e0) = e0
% 111.64/16.12 | |
% 111.64/16.12 | | ALPHA: (10) implies:
% 111.64/16.12 | | (11) op(e3, e0) = e0
% 111.64/16.12 | |
% 111.64/16.12 | | REF_CLOSE: (1), (4), (6), (11) are inconsistent by sub-proof #201.
% 111.64/16.12 | |
% 111.64/16.12 | End of split
% 111.64/16.12 |
% 111.64/16.12 End of proof
% 111.64/16.12
% 111.64/16.12 Sub-proof #130 shows that the following formulas are inconsistent:
% 111.64/16.12 ----------------------------------------------------------------
% 111.64/16.12 (1) all_55_2 = e1 | all_55_2 = e0
% 111.64/16.12 (2) all_55_2 = all_26_0
% 111.64/16.12 (3) ~ (all_26_0 = e1)
% 111.64/16.12 (4) ~ (all_26_0 = e0)
% 111.64/16.12
% 111.64/16.12 Begin of proof
% 111.64/16.12 |
% 111.64/16.12 | BETA: splitting (1) gives:
% 111.64/16.12 |
% 111.64/16.12 | Case 1:
% 111.64/16.12 | |
% 111.64/16.12 | | (5) all_55_2 = e1
% 111.64/16.12 | |
% 111.64/16.12 | | COMBINE_EQS: (2), (5) imply:
% 111.64/16.12 | | (6) all_26_0 = e1
% 111.64/16.12 | |
% 111.64/16.12 | | REDUCE: (3), (6) imply:
% 111.64/16.12 | | (7) $false
% 111.64/16.12 | |
% 111.64/16.12 | | CLOSE: (7) is inconsistent.
% 111.64/16.12 | |
% 111.64/16.12 | Case 2:
% 111.64/16.12 | |
% 111.64/16.12 | | (8) all_55_2 = e0
% 111.64/16.12 | |
% 111.64/16.12 | | COMBINE_EQS: (2), (8) imply:
% 111.64/16.12 | | (9) all_26_0 = e0
% 111.64/16.12 | |
% 111.64/16.12 | | REDUCE: (4), (9) imply:
% 111.64/16.12 | | (10) $false
% 111.64/16.12 | |
% 111.64/16.12 | | CLOSE: (10) is inconsistent.
% 111.64/16.12 | |
% 111.64/16.12 | End of split
% 111.64/16.12 |
% 111.64/16.12 End of proof
% 111.64/16.12
% 111.64/16.12 Sub-proof #131 shows that the following formulas are inconsistent:
% 111.64/16.12 ----------------------------------------------------------------
% 111.64/16.12 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.12 (2) op(e1, e1) = e3
% 111.64/16.12 (3) op(e1, e1) = e2
% 111.64/16.12 (4) ~ (e3 = e2)
% 111.64/16.12
% 111.64/16.12 Begin of proof
% 111.64/16.12 |
% 111.64/16.12 | GROUND_INST: instantiating (1) with e2, e3, e1, e1, simplifying with (2), (3)
% 111.64/16.12 | gives:
% 111.64/16.12 | (5) e3 = e2
% 111.64/16.12 |
% 111.64/16.12 | REDUCE: (4), (5) imply:
% 111.64/16.12 | (6) $false
% 111.64/16.12 |
% 111.64/16.12 | CLOSE: (6) is inconsistent.
% 111.64/16.12 |
% 111.64/16.12 End of proof
% 111.64/16.12
% 111.64/16.12 Sub-proof #132 shows that the following formulas are inconsistent:
% 111.64/16.12 ----------------------------------------------------------------
% 111.64/16.12 (1) all_55_6 = all_53_7
% 111.64/16.12 (2) all_55_6 = e0
% 111.64/16.12 (3) ~ (all_53_7 = e0)
% 111.64/16.12
% 111.64/16.12 Begin of proof
% 111.64/16.12 |
% 111.64/16.12 | COMBINE_EQS: (1), (2) imply:
% 111.64/16.12 | (4) all_53_7 = e0
% 111.64/16.12 |
% 111.64/16.12 | SIMP: (4) implies:
% 111.64/16.12 | (5) all_53_7 = e0
% 111.64/16.12 |
% 111.64/16.12 | REDUCE: (3), (5) imply:
% 111.64/16.12 | (6) $false
% 111.64/16.12 |
% 111.64/16.12 | CLOSE: (6) is inconsistent.
% 111.64/16.12 |
% 111.64/16.12 End of proof
% 111.64/16.12
% 111.64/16.12 Sub-proof #133 shows that the following formulas are inconsistent:
% 111.64/16.12 ----------------------------------------------------------------
% 111.64/16.12 (1) op(e3, e0) = all_53_12
% 111.64/16.12 (2) op(e1, e0) = all_53_4
% 111.64/16.12 (3) op(e2, e1) = e2
% 111.64/16.12 (4) ~ (all_53_4 = e1)
% 111.64/16.12 (5) ~ (all_53_12 = e3)
% 111.64/16.12 (6) op(e2, e1) = all_53_9
% 111.64/16.12 (7) op(e2, e0) = all_53_8
% 111.64/16.12 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.12 (9) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 111.64/16.12 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2,
% 111.64/16.12 e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 = e1 &
% 111.64/16.12 ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 111.64/16.12 $i(all_52_4))
% 111.64/16.12 (10) ~ (all_53_8 = all_53_9)
% 111.64/16.12
% 111.64/16.12 Begin of proof
% 111.64/16.12 |
% 111.64/16.12 | BETA: splitting (9) gives:
% 111.64/16.12 |
% 111.64/16.12 | Case 1:
% 111.64/16.12 | |
% 111.64/16.12 | | (11) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 111.64/16.12 | | all_52_0 & $i(all_52_0)
% 111.64/16.12 | |
% 111.64/16.12 | | ALPHA: (11) implies:
% 111.64/16.12 | | (12) op(e3, e0) = e3
% 111.64/16.12 | |
% 111.64/16.12 | | REF_CLOSE: (1), (5), (8), (12) are inconsistent by sub-proof #180.
% 111.64/16.12 | |
% 111.64/16.12 | Case 2:
% 111.64/16.12 | |
% 111.64/16.12 | | (13) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 111.64/16.12 | | all_52_2 & $i(all_52_2)) | (all_52_5 = e1 & ~ (all_52_4 = e0) &
% 111.64/16.12 | | op(e1, e0) = e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 111.64/16.12 | |
% 111.64/16.12 | | BETA: splitting (13) gives:
% 111.64/16.12 | |
% 111.64/16.12 | | Case 1:
% 111.64/16.12 | | |
% 111.64/16.13 | | | (14) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 111.64/16.13 | | | = all_52_2 & $i(all_52_2)
% 111.64/16.13 | | |
% 111.64/16.13 | | | ALPHA: (14) implies:
% 111.64/16.13 | | | (15) op(e2, e0) = e2
% 111.64/16.13 | | |
% 111.64/16.13 | | | REF_CLOSE: (3), (6), (7), (8), (10), (15) are inconsistent by sub-proof
% 111.64/16.13 | | | #186.
% 111.64/16.13 | | |
% 111.64/16.13 | | Case 2:
% 111.64/16.13 | | |
% 111.64/16.13 | | | (16) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 111.64/16.13 | | | = all_52_4 & $i(all_52_4)
% 111.64/16.13 | | |
% 111.64/16.13 | | | ALPHA: (16) implies:
% 111.64/16.13 | | | (17) op(e1, e0) = e1
% 111.64/16.13 | | |
% 111.64/16.13 | | | REF_CLOSE: (2), (4), (8), (17) are inconsistent by sub-proof #226.
% 111.64/16.13 | | |
% 111.64/16.13 | | End of split
% 111.64/16.13 | |
% 111.64/16.13 | End of split
% 111.64/16.13 |
% 111.64/16.13 End of proof
% 111.64/16.13
% 111.64/16.13 Sub-proof #134 shows that the following formulas are inconsistent:
% 111.64/16.13 ----------------------------------------------------------------
% 111.64/16.13 (1) all_55_6 = all_53_7
% 111.64/16.13 (2) all_55_6 = e2
% 111.64/16.13 (3) ~ (all_53_7 = e2)
% 111.64/16.13
% 111.64/16.13 Begin of proof
% 111.64/16.13 |
% 111.64/16.13 | COMBINE_EQS: (1), (2) imply:
% 111.64/16.13 | (4) all_53_7 = e2
% 111.64/16.13 |
% 111.64/16.13 | SIMP: (4) implies:
% 111.64/16.13 | (5) all_53_7 = e2
% 111.64/16.13 |
% 111.64/16.13 | REDUCE: (3), (5) imply:
% 111.64/16.13 | (6) $false
% 111.64/16.13 |
% 111.64/16.13 | CLOSE: (6) is inconsistent.
% 111.64/16.13 |
% 111.64/16.13 End of proof
% 111.64/16.13
% 111.64/16.13 Sub-proof #135 shows that the following formulas are inconsistent:
% 111.64/16.13 ----------------------------------------------------------------
% 111.64/16.13 (1) all_55_6 = all_53_7
% 111.64/16.13 (2) all_55_6 = e3
% 111.64/16.13 (3) ~ (all_53_7 = e3)
% 111.64/16.13
% 111.64/16.13 Begin of proof
% 111.64/16.13 |
% 111.64/16.13 | COMBINE_EQS: (1), (2) imply:
% 111.64/16.13 | (4) all_53_7 = e3
% 111.64/16.13 |
% 111.64/16.13 | SIMP: (4) implies:
% 111.64/16.13 | (5) all_53_7 = e3
% 111.64/16.13 |
% 111.64/16.13 | REDUCE: (3), (5) imply:
% 111.64/16.13 | (6) $false
% 111.64/16.13 |
% 111.64/16.13 | CLOSE: (6) is inconsistent.
% 111.64/16.13 |
% 111.64/16.13 End of proof
% 111.64/16.13
% 111.64/16.13 Sub-proof #136 shows that the following formulas are inconsistent:
% 111.64/16.13 ----------------------------------------------------------------
% 111.64/16.13 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.13 (2) op(e3, e1) = all_53_13
% 111.64/16.13 (3) op(e3, e1) = e2
% 111.64/16.13 (4) ~ (all_53_13 = e2)
% 111.64/16.13
% 111.64/16.13 Begin of proof
% 111.64/16.13 |
% 111.64/16.13 | GROUND_INST: instantiating (1) with all_53_13, e2, e1, e3, simplifying with
% 111.64/16.13 | (2), (3) gives:
% 111.64/16.13 | (5) all_53_13 = e2
% 111.64/16.13 |
% 111.64/16.13 | REDUCE: (4), (5) imply:
% 111.64/16.13 | (6) $false
% 111.64/16.13 |
% 111.64/16.13 | CLOSE: (6) is inconsistent.
% 111.64/16.13 |
% 111.64/16.13 End of proof
% 111.64/16.13
% 111.64/16.13 Sub-proof #137 shows that the following formulas are inconsistent:
% 111.64/16.13 ----------------------------------------------------------------
% 111.64/16.13 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.13 (2) op(e0, e2) = all_53_3
% 111.64/16.13 (3) op(e0, e2) = e3
% 111.64/16.13 (4) ~ (all_53_3 = e3)
% 111.64/16.13
% 111.64/16.13 Begin of proof
% 111.64/16.13 |
% 111.64/16.13 | GROUND_INST: instantiating (1) with all_53_3, e3, e2, e0, simplifying with
% 111.64/16.13 | (2), (3) gives:
% 111.64/16.13 | (5) all_53_3 = e3
% 111.64/16.13 |
% 111.64/16.13 | REDUCE: (4), (5) imply:
% 111.64/16.13 | (6) $false
% 111.64/16.13 |
% 111.64/16.13 | CLOSE: (6) is inconsistent.
% 111.64/16.13 |
% 111.64/16.13 End of proof
% 111.64/16.13
% 111.64/16.13 Sub-proof #138 shows that the following formulas are inconsistent:
% 111.64/16.13 ----------------------------------------------------------------
% 111.64/16.13 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.13 (2) op(e2, e1) = all_53_9
% 111.64/16.13 (3) op(e2, e1) = e3
% 111.64/16.13 (4) ~ (all_53_9 = e3)
% 111.64/16.13
% 111.64/16.13 Begin of proof
% 111.64/16.13 |
% 111.64/16.13 | GROUND_INST: instantiating (1) with all_53_9, e3, e1, e2, simplifying with
% 111.64/16.13 | (2), (3) gives:
% 111.64/16.13 | (5) all_53_9 = e3
% 111.64/16.13 |
% 111.64/16.13 | REDUCE: (4), (5) imply:
% 111.64/16.13 | (6) $false
% 111.64/16.13 |
% 111.64/16.13 | CLOSE: (6) is inconsistent.
% 111.64/16.13 |
% 111.64/16.13 End of proof
% 111.64/16.13
% 111.64/16.13 Sub-proof #139 shows that the following formulas are inconsistent:
% 111.64/16.13 ----------------------------------------------------------------
% 111.64/16.13 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.13 (2) op(e2, e2) = e3
% 111.64/16.13 (3) op(e2, e2) = e0
% 111.64/16.13 (4) ~ (e3 = e0)
% 111.64/16.13
% 111.64/16.13 Begin of proof
% 111.64/16.13 |
% 111.64/16.13 | GROUND_INST: instantiating (1) with e0, e3, e2, e2, simplifying with (2), (3)
% 111.64/16.13 | gives:
% 111.64/16.13 | (5) e3 = e0
% 111.64/16.13 |
% 111.64/16.13 | REDUCE: (4), (5) imply:
% 111.64/16.13 | (6) $false
% 111.64/16.13 |
% 111.64/16.13 | CLOSE: (6) is inconsistent.
% 111.64/16.13 |
% 111.64/16.13 End of proof
% 111.64/16.13
% 111.64/16.13 Sub-proof #140 shows that the following formulas are inconsistent:
% 111.64/16.13 ----------------------------------------------------------------
% 111.64/16.13 (1) all_55_15 = all_4_2
% 111.64/16.13 (2) all_55_15 = e3
% 111.64/16.13 (3) ~ (all_4_2 = e3)
% 111.64/16.13
% 111.64/16.13 Begin of proof
% 111.64/16.13 |
% 111.64/16.13 | COMBINE_EQS: (1), (2) imply:
% 111.64/16.13 | (4) all_4_2 = e3
% 111.64/16.13 |
% 111.64/16.13 | SIMP: (4) implies:
% 111.64/16.13 | (5) all_4_2 = e3
% 111.64/16.13 |
% 111.64/16.13 | REDUCE: (3), (5) imply:
% 111.64/16.13 | (6) $false
% 111.64/16.13 |
% 111.64/16.13 | CLOSE: (6) is inconsistent.
% 111.64/16.13 |
% 111.64/16.13 End of proof
% 111.64/16.13
% 111.64/16.13 Sub-proof #141 shows that the following formulas are inconsistent:
% 111.64/16.13 ----------------------------------------------------------------
% 111.64/16.13 (1) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 111.64/16.13 all_52_0 & $i(all_52_0)
% 111.64/16.13 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.13 (3) op(e3, e0) = e0
% 111.64/16.13 (4) ~ (e3 = e0)
% 111.64/16.13
% 111.64/16.13 Begin of proof
% 111.64/16.13 |
% 111.64/16.13 | ALPHA: (1) implies:
% 111.64/16.13 | (5) op(e3, e0) = e3
% 111.64/16.13 |
% 111.64/16.13 | GROUND_INST: instantiating (2) with e0, e3, e0, e3, simplifying with (3), (5)
% 111.64/16.13 | gives:
% 111.64/16.13 | (6) e3 = e0
% 111.64/16.13 |
% 111.64/16.13 | REDUCE: (4), (6) imply:
% 111.64/16.13 | (7) $false
% 111.64/16.13 |
% 111.64/16.13 | CLOSE: (7) is inconsistent.
% 111.64/16.13 |
% 111.64/16.13 End of proof
% 111.64/16.13
% 111.64/16.13 Sub-proof #142 shows that the following formulas are inconsistent:
% 111.64/16.13 ----------------------------------------------------------------
% 111.64/16.13 (1) ~ (all_28_0 = e0)
% 111.64/16.13 (2) all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 111.64/16.13 (3) ~ (all_28_0 = e2)
% 111.64/16.13 (4) all_55_7 = all_28_0
% 111.64/16.13 (5) ~ (all_28_0 = e1)
% 111.64/16.13
% 111.64/16.13 Begin of proof
% 111.64/16.13 |
% 111.64/16.13 | BETA: splitting (2) gives:
% 111.64/16.13 |
% 111.64/16.13 | Case 1:
% 111.64/16.13 | |
% 111.64/16.13 | | (6) all_55_7 = e2
% 111.64/16.13 | |
% 111.64/16.13 | | COMBINE_EQS: (4), (6) imply:
% 111.64/16.13 | | (7) all_28_0 = e2
% 111.64/16.13 | |
% 111.64/16.13 | | SIMP: (7) implies:
% 111.64/16.13 | | (8) all_28_0 = e2
% 111.64/16.13 | |
% 111.64/16.13 | | REDUCE: (3), (8) imply:
% 111.64/16.13 | | (9) $false
% 111.64/16.13 | |
% 111.64/16.13 | | CLOSE: (9) is inconsistent.
% 111.64/16.13 | |
% 111.64/16.13 | Case 2:
% 111.64/16.13 | |
% 111.64/16.13 | | (10) all_55_7 = e1 | all_55_7 = e0
% 111.64/16.13 | |
% 111.64/16.13 | | BETA: splitting (10) gives:
% 111.64/16.13 | |
% 111.64/16.13 | | Case 1:
% 111.64/16.13 | | |
% 111.64/16.13 | | | (11) all_55_7 = e1
% 111.64/16.13 | | |
% 111.64/16.13 | | | COMBINE_EQS: (4), (11) imply:
% 111.64/16.13 | | | (12) all_28_0 = e1
% 111.64/16.13 | | |
% 111.64/16.13 | | | SIMP: (12) implies:
% 111.64/16.13 | | | (13) all_28_0 = e1
% 111.64/16.13 | | |
% 111.64/16.13 | | | REDUCE: (5), (13) imply:
% 111.64/16.13 | | | (14) $false
% 111.64/16.13 | | |
% 111.64/16.13 | | | CLOSE: (14) is inconsistent.
% 111.64/16.13 | | |
% 111.64/16.13 | | Case 2:
% 111.64/16.13 | | |
% 111.64/16.13 | | | (15) all_55_7 = e0
% 111.64/16.13 | | |
% 111.64/16.13 | | | COMBINE_EQS: (4), (15) imply:
% 111.64/16.13 | | | (16) all_28_0 = e0
% 111.64/16.13 | | |
% 111.64/16.13 | | | SIMP: (16) implies:
% 111.64/16.13 | | | (17) all_28_0 = e0
% 111.64/16.13 | | |
% 111.64/16.13 | | | REDUCE: (1), (17) imply:
% 111.64/16.13 | | | (18) $false
% 111.64/16.13 | | |
% 111.64/16.13 | | | CLOSE: (18) is inconsistent.
% 111.64/16.13 | | |
% 111.64/16.13 | | End of split
% 111.64/16.13 | |
% 111.64/16.13 | End of split
% 111.64/16.13 |
% 111.64/16.13 End of proof
% 111.64/16.13
% 111.64/16.13 Sub-proof #143 shows that the following formulas are inconsistent:
% 111.64/16.13 ----------------------------------------------------------------
% 111.64/16.13 (1) all_55_11 = all_53_10
% 111.64/16.13 (2) all_55_11 = e0
% 111.64/16.13 (3) ~ (all_53_10 = e0)
% 111.64/16.13
% 111.64/16.13 Begin of proof
% 111.64/16.13 |
% 111.64/16.13 | COMBINE_EQS: (1), (2) imply:
% 111.64/16.13 | (4) all_53_10 = e0
% 111.64/16.13 |
% 111.64/16.13 | SIMP: (4) implies:
% 111.64/16.13 | (5) all_53_10 = e0
% 111.64/16.13 |
% 111.64/16.13 | REDUCE: (3), (5) imply:
% 111.64/16.13 | (6) $false
% 111.64/16.13 |
% 111.64/16.13 | CLOSE: (6) is inconsistent.
% 111.64/16.13 |
% 111.64/16.13 End of proof
% 111.64/16.13
% 111.64/16.13 Sub-proof #144 shows that the following formulas are inconsistent:
% 111.64/16.13 ----------------------------------------------------------------
% 111.64/16.13 (1) all_55_11 = all_53_10
% 111.64/16.13 (2) all_55_11 = e3
% 111.64/16.13 (3) ~ (all_53_10 = e3)
% 111.64/16.13
% 111.64/16.13 Begin of proof
% 111.64/16.13 |
% 111.64/16.13 | COMBINE_EQS: (1), (2) imply:
% 111.64/16.13 | (4) all_53_10 = e3
% 111.64/16.13 |
% 111.64/16.13 | SIMP: (4) implies:
% 111.64/16.13 | (5) all_53_10 = e3
% 111.64/16.13 |
% 111.64/16.13 | REDUCE: (3), (5) imply:
% 111.64/16.13 | (6) $false
% 111.64/16.13 |
% 111.64/16.13 | CLOSE: (6) is inconsistent.
% 111.64/16.13 |
% 111.64/16.13 End of proof
% 111.64/16.13
% 111.64/16.13 Sub-proof #145 shows that the following formulas are inconsistent:
% 111.64/16.13 ----------------------------------------------------------------
% 111.64/16.13 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.13 (2) op(e0, e1) = all_53_1
% 111.64/16.13 (3) op(e0, e1) = e3
% 111.64/16.13 (4) ~ (all_53_1 = e3)
% 111.64/16.13
% 111.64/16.13 Begin of proof
% 111.64/16.13 |
% 111.64/16.13 | GROUND_INST: instantiating (1) with all_53_1, e3, e1, e0, simplifying with
% 111.64/16.13 | (2), (3) gives:
% 111.64/16.13 | (5) all_53_1 = e3
% 111.64/16.13 |
% 111.64/16.13 | REDUCE: (4), (5) imply:
% 111.64/16.13 | (6) $false
% 111.64/16.13 |
% 111.64/16.13 | CLOSE: (6) is inconsistent.
% 111.64/16.13 |
% 111.64/16.13 End of proof
% 111.64/16.13
% 111.64/16.13 Sub-proof #146 shows that the following formulas are inconsistent:
% 111.64/16.13 ----------------------------------------------------------------
% 111.64/16.13 (1) ~ (all_53_2 = all_53_6)
% 111.64/16.13 (2) ~ (all_53_13 = e3)
% 111.64/16.13 (3) op(e1, e1) = e3
% 111.64/16.13 (4) ~ (all_53_1 = e0)
% 111.64/16.13 (5) op(e2, e3) = all_53_10
% 111.64/16.13 (6) op(e1, e0) = all_53_4
% 111.64/16.13 (7) (all_57_36 = e0 & op(e3, e1) = e0) | (all_57_37 = e0 & op(e2, e1) = e0) |
% 111.64/16.13 (all_57_38 = e0 & op(e1, e1) = e0) | (all_57_39 = e0 & op(e0, e1) = e0)
% 111.64/16.13 (8) op(e1, e2) = all_53_7
% 111.64/16.13 (9) ~ (e1 = e0)
% 111.64/16.13 (10) (all_57_32 = e0 & op(e1, e3) = e0) | (all_57_33 = e0 & op(e1, e2) = e0)
% 111.64/16.13 | (all_57_34 = e0 & op(e1, e1) = e0) | (all_57_35 = e0 & op(e1, e0) =
% 111.64/16.13 e0)
% 111.64/16.13 (11) ~ (e3 = e0)
% 111.64/16.13 (12) op(e0, e3) = all_53_2
% 111.64/16.13 (13) op(e0, e1) = all_53_1
% 111.64/16.13 (14) op(e2, e1) = all_53_9
% 111.64/16.13 (15) ~ (all_53_7 = e0)
% 111.64/16.13 (16) ~ (all_53_4 = all_53_6)
% 111.64/16.13 (17) op(e1, e3) = all_53_6
% 111.64/16.13 (18) op(e3, e1) = all_53_13
% 111.64/16.13 (19) ~ (all_53_9 = all_53_10)
% 111.64/16.13 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.13 (21) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 111.64/16.13 e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20 = e3) &
% 111.64/16.13 op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23
% 111.64/16.13 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0
% 111.64/16.13 & $i(all_52_22))
% 111.64/16.13 (22) ~ (all_53_4 = e0)
% 111.64/16.13 (23) ~ (all_53_9 = e0)
% 111.64/16.13 (24) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.64/16.13 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 111.64/16.13 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 111.64/16.13 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.64/16.13 $i(all_52_10))
% 111.64/16.13
% 111.64/16.13 Begin of proof
% 111.64/16.13 |
% 111.64/16.13 | BETA: splitting (7) gives:
% 111.64/16.13 |
% 111.64/16.13 | Case 1:
% 111.64/16.13 | |
% 111.64/16.13 | | (25) (all_57_36 = e0 & op(e3, e1) = e0) | (all_57_37 = e0 & op(e2, e1) =
% 111.64/16.13 | | e0)
% 111.64/16.13 | |
% 111.64/16.13 | | BETA: splitting (25) gives:
% 111.64/16.13 | |
% 111.64/16.13 | | Case 1:
% 111.64/16.13 | | |
% 111.64/16.13 | | | (26) all_57_36 = e0 & op(e3, e1) = e0
% 111.64/16.13 | | |
% 111.64/16.13 | | | ALPHA: (26) implies:
% 111.64/16.13 | | | (27) op(e3, e1) = e0
% 111.64/16.13 | | |
% 111.64/16.13 | | | BETA: splitting (24) gives:
% 111.64/16.13 | | |
% 111.64/16.13 | | | Case 1:
% 111.64/16.13 | | | |
% 111.64/16.14 | | | | (28) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1,
% 111.64/16.14 | | | | e3) = all_52_6 & $i(all_52_6)
% 111.64/16.14 | | | |
% 111.64/16.14 | | | | ALPHA: (28) implies:
% 111.64/16.14 | | | | (29) op(e3, e1) = e3
% 111.64/16.14 | | | |
% 111.64/16.14 | | | | REF_CLOSE: (11), (18), (20), (27), (29) are inconsistent by sub-proof
% 111.64/16.14 | | | | #154.
% 111.64/16.14 | | | |
% 111.64/16.14 | | | Case 2:
% 111.64/16.14 | | | |
% 111.64/16.14 | | | | (30) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1,
% 111.64/16.14 | | | | e2) = all_52_8 & $i(all_52_8)) | (all_52_11 = e0 & ~
% 111.64/16.14 | | | | (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.64/16.14 | | | | $i(all_52_10))
% 111.64/16.14 | | | |
% 111.64/16.14 | | | | BETA: splitting (30) gives:
% 111.64/16.14 | | | |
% 111.64/16.14 | | | | Case 1:
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | (31) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1,
% 111.64/16.14 | | | | | e2) = all_52_8 & $i(all_52_8)
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | ALPHA: (31) implies:
% 111.64/16.14 | | | | | (32) op(e2, e1) = e2
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | BETA: splitting (10) gives:
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | Case 1:
% 111.64/16.14 | | | | | |
% 111.64/16.14 | | | | | | (33) (all_57_32 = e0 & op(e1, e3) = e0) | (all_57_33 = e0 &
% 111.64/16.14 | | | | | | op(e1, e2) = e0)
% 111.64/16.14 | | | | | |
% 111.64/16.14 | | | | | | BETA: splitting (33) gives:
% 111.64/16.14 | | | | | |
% 111.64/16.14 | | | | | | Case 1:
% 111.64/16.14 | | | | | | |
% 111.64/16.14 | | | | | | | (34) all_57_32 = e0 & op(e1, e3) = e0
% 111.64/16.14 | | | | | | |
% 111.64/16.14 | | | | | | | ALPHA: (34) implies:
% 111.64/16.14 | | | | | | | (35) op(e1, e3) = e0
% 111.64/16.14 | | | | | | |
% 111.64/16.14 | | | | | | | GROUND_INST: instantiating (20) with all_53_6, e0, e3, e1,
% 111.64/16.14 | | | | | | | simplifying with (17), (35) gives:
% 111.64/16.14 | | | | | | | (36) all_53_6 = e0
% 111.64/16.14 | | | | | | |
% 111.64/16.14 | | | | | | | GROUND_INST: instantiating (20) with all_53_9, e2, e1, e2,
% 111.64/16.14 | | | | | | | simplifying with (14), (32) gives:
% 111.64/16.14 | | | | | | | (37) all_53_9 = e2
% 111.64/16.14 | | | | | | |
% 111.64/16.14 | | | | | | | GROUND_INST: instantiating (20) with all_53_13, e0, e1, e3,
% 111.64/16.14 | | | | | | | simplifying with (18), (27) gives:
% 111.64/16.14 | | | | | | | (38) all_53_13 = e0
% 111.64/16.14 | | | | | | |
% 111.64/16.14 | | | | | | | REDUCE: (1), (36) imply:
% 111.64/16.14 | | | | | | | (39) ~ (all_53_2 = e0)
% 111.64/16.14 | | | | | | |
% 111.64/16.14 | | | | | | | REDUCE: (19), (37) imply:
% 111.64/16.14 | | | | | | | (40) ~ (all_53_10 = e2)
% 111.64/16.14 | | | | | | |
% 111.64/16.14 | | | | | | | SIMP: (40) implies:
% 111.64/16.14 | | | | | | | (41) ~ (all_53_10 = e2)
% 111.64/16.14 | | | | | | |
% 111.64/16.14 | | | | | | | REDUCE: (2), (38) imply:
% 111.64/16.14 | | | | | | | (42) ~ (e3 = e0)
% 111.64/16.14 | | | | | | |
% 111.64/16.14 | | | | | | | REF_CLOSE: (3), (5), (6), (8), (9), (10), (11), (12), (15), (17),
% 111.64/16.14 | | | | | | | (20), (21), (22), (39), (41) are inconsistent by
% 111.64/16.14 | | | | | | | sub-proof #148.
% 111.64/16.14 | | | | | | |
% 111.64/16.14 | | | | | | Case 2:
% 111.64/16.14 | | | | | | |
% 111.64/16.14 | | | | | | | (43) all_57_33 = e0 & op(e1, e2) = e0
% 111.64/16.14 | | | | | | |
% 111.64/16.14 | | | | | | | ALPHA: (43) implies:
% 111.64/16.14 | | | | | | | (44) op(e1, e2) = e0
% 111.64/16.14 | | | | | | |
% 111.64/16.14 | | | | | | | REF_CLOSE: (8), (15), (20), (44) are inconsistent by sub-proof
% 111.64/16.14 | | | | | | | #153.
% 111.64/16.14 | | | | | | |
% 111.64/16.14 | | | | | | End of split
% 111.64/16.14 | | | | | |
% 111.64/16.14 | | | | | Case 2:
% 111.64/16.14 | | | | | |
% 111.64/16.14 | | | | | | (45) (all_57_34 = e0 & op(e1, e1) = e0) | (all_57_35 = e0 &
% 111.64/16.14 | | | | | | op(e1, e0) = e0)
% 111.64/16.14 | | | | | |
% 111.64/16.14 | | | | | | REF_CLOSE: (3), (6), (11), (20), (22), (45) are inconsistent by
% 111.64/16.14 | | | | | | sub-proof #150.
% 111.64/16.14 | | | | | |
% 111.64/16.14 | | | | | End of split
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | Case 2:
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | (46) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10
% 111.64/16.14 | | | | | & op(e0, e1) = e0 & $i(all_52_10)
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | ALPHA: (46) implies:
% 111.64/16.14 | | | | | (47) op(e0, e1) = e0
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | REF_CLOSE: (4), (13), (20), (47) are inconsistent by sub-proof #230.
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | End of split
% 111.64/16.14 | | | |
% 111.64/16.14 | | | End of split
% 111.64/16.14 | | |
% 111.64/16.14 | | Case 2:
% 111.64/16.14 | | |
% 111.64/16.14 | | | (48) all_57_37 = e0 & op(e2, e1) = e0
% 111.64/16.14 | | |
% 111.64/16.14 | | | ALPHA: (48) implies:
% 111.64/16.14 | | | (49) op(e2, e1) = e0
% 111.64/16.14 | | |
% 111.64/16.14 | | | REF_CLOSE: (14), (20), (23), (49) are inconsistent by sub-proof #147.
% 111.64/16.14 | | |
% 111.64/16.14 | | End of split
% 111.64/16.14 | |
% 111.64/16.14 | Case 2:
% 111.64/16.14 | |
% 111.64/16.14 | | (50) (all_57_38 = e0 & op(e1, e1) = e0) | (all_57_39 = e0 & op(e0, e1) =
% 111.64/16.14 | | e0)
% 111.64/16.14 | |
% 111.64/16.14 | | BETA: splitting (50) gives:
% 111.64/16.14 | |
% 111.64/16.14 | | Case 1:
% 111.64/16.14 | | |
% 111.64/16.14 | | | (51) all_57_38 = e0 & op(e1, e1) = e0
% 111.64/16.14 | | |
% 111.64/16.14 | | | ALPHA: (51) implies:
% 111.64/16.14 | | | (52) op(e1, e1) = e0
% 111.64/16.14 | | |
% 111.64/16.14 | | | REF_CLOSE: (3), (11), (20), (52) are inconsistent by sub-proof #152.
% 111.64/16.14 | | |
% 111.64/16.14 | | Case 2:
% 111.64/16.14 | | |
% 111.64/16.14 | | | (53) all_57_39 = e0 & op(e0, e1) = e0
% 111.64/16.14 | | |
% 111.64/16.14 | | | ALPHA: (53) implies:
% 111.64/16.14 | | | (54) op(e0, e1) = e0
% 111.64/16.14 | | |
% 111.64/16.14 | | | REF_CLOSE: (4), (13), (20), (54) are inconsistent by sub-proof #230.
% 111.64/16.14 | | |
% 111.64/16.14 | | End of split
% 111.64/16.14 | |
% 111.64/16.14 | End of split
% 111.64/16.14 |
% 111.64/16.14 End of proof
% 111.64/16.14
% 111.64/16.14 Sub-proof #147 shows that the following formulas are inconsistent:
% 111.64/16.14 ----------------------------------------------------------------
% 111.64/16.14 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.14 (2) op(e2, e1) = all_53_9
% 111.64/16.14 (3) op(e2, e1) = e0
% 111.64/16.14 (4) ~ (all_53_9 = e0)
% 111.64/16.14
% 111.64/16.14 Begin of proof
% 111.64/16.14 |
% 111.64/16.14 | GROUND_INST: instantiating (1) with all_53_9, e0, e1, e2, simplifying with
% 111.64/16.14 | (2), (3) gives:
% 111.64/16.14 | (5) all_53_9 = e0
% 111.64/16.14 |
% 111.64/16.14 | REDUCE: (4), (5) imply:
% 111.64/16.14 | (6) $false
% 111.64/16.14 |
% 111.64/16.14 | CLOSE: (6) is inconsistent.
% 111.64/16.14 |
% 111.64/16.14 End of proof
% 111.64/16.14
% 111.64/16.14 Sub-proof #148 shows that the following formulas are inconsistent:
% 111.64/16.14 ----------------------------------------------------------------
% 111.64/16.14 (1) op(e1, e1) = e3
% 111.64/16.14 (2) op(e2, e3) = all_53_10
% 111.64/16.14 (3) op(e1, e0) = all_53_4
% 111.64/16.14 (4) op(e1, e2) = all_53_7
% 111.64/16.14 (5) ~ (e1 = e0)
% 111.64/16.14 (6) (all_57_32 = e0 & op(e1, e3) = e0) | (all_57_33 = e0 & op(e1, e2) = e0) |
% 111.64/16.14 (all_57_34 = e0 & op(e1, e1) = e0) | (all_57_35 = e0 & op(e1, e0) = e0)
% 111.64/16.14 (7) ~ (e3 = e0)
% 111.64/16.14 (8) op(e0, e3) = all_53_2
% 111.64/16.14 (9) ~ (all_53_7 = e0)
% 111.64/16.14 (10) op(e1, e3) = all_53_6
% 111.64/16.14 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.14 (12) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 111.64/16.14 e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20 = e3) &
% 111.64/16.14 op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23
% 111.64/16.14 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0
% 111.64/16.14 & $i(all_52_22))
% 111.64/16.14 (13) ~ (all_53_4 = e0)
% 111.64/16.14 (14) ~ (all_53_10 = e2)
% 111.64/16.14 (15) ~ (all_53_2 = e0)
% 111.64/16.14
% 111.64/16.14 Begin of proof
% 111.64/16.14 |
% 111.64/16.14 | BETA: splitting (12) gives:
% 111.64/16.14 |
% 111.64/16.14 | Case 1:
% 111.64/16.14 | |
% 111.64/16.14 | | (16) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 &
% 111.64/16.14 | | op(e2, e3) = e2 & $i(all_52_18)
% 111.64/16.14 | |
% 111.64/16.14 | | REF_CLOSE: (2), (11), (14), (16) are inconsistent by sub-proof #215.
% 111.64/16.14 | |
% 111.64/16.14 | Case 2:
% 111.64/16.14 | |
% 111.64/16.14 | | (17) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 &
% 111.64/16.14 | | op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23 = e0 & ~ (all_52_22
% 111.64/16.14 | | = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0 &
% 111.64/16.14 | | $i(all_52_22))
% 111.64/16.14 | |
% 111.64/16.14 | | BETA: splitting (17) gives:
% 111.64/16.14 | |
% 111.64/16.14 | | Case 1:
% 111.64/16.14 | | |
% 111.64/16.14 | | | (18) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 &
% 111.64/16.14 | | | op(e1, e3) = e1 & $i(all_52_20)
% 111.64/16.14 | | |
% 111.64/16.14 | | | ALPHA: (18) implies:
% 111.64/16.14 | | | (19) op(e1, e3) = e1
% 111.64/16.14 | | |
% 111.64/16.14 | | | BETA: splitting (6) gives:
% 111.64/16.14 | | |
% 111.64/16.14 | | | Case 1:
% 111.64/16.14 | | | |
% 111.64/16.14 | | | | (20) (all_57_32 = e0 & op(e1, e3) = e0) | (all_57_33 = e0 & op(e1,
% 111.64/16.14 | | | | e2) = e0)
% 111.64/16.14 | | | |
% 111.64/16.14 | | | | BETA: splitting (20) gives:
% 111.64/16.14 | | | |
% 111.64/16.14 | | | | Case 1:
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | (21) all_57_32 = e0 & op(e1, e3) = e0
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | ALPHA: (21) implies:
% 111.64/16.14 | | | | | (22) op(e1, e3) = e0
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | GROUND_INST: instantiating (11) with all_53_6, e0, e3, e1, simplifying
% 111.64/16.14 | | | | | with (10), (22) gives:
% 111.64/16.14 | | | | | (23) all_53_6 = e0
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | GROUND_INST: instantiating (11) with all_53_6, e1, e3, e1, simplifying
% 111.64/16.14 | | | | | with (10), (19) gives:
% 111.64/16.14 | | | | | (24) all_53_6 = e1
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | COMBINE_EQS: (23), (24) imply:
% 111.64/16.14 | | | | | (25) e1 = e0
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | SIMP: (25) implies:
% 111.64/16.14 | | | | | (26) e1 = e0
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | REDUCE: (5), (26) imply:
% 111.64/16.14 | | | | | (27) $false
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | CLOSE: (27) is inconsistent.
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | Case 2:
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | (28) all_57_33 = e0 & op(e1, e2) = e0
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | ALPHA: (28) implies:
% 111.64/16.14 | | | | | (29) op(e1, e2) = e0
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | | REF_CLOSE: (4), (9), (11), (29) are inconsistent by sub-proof #153.
% 111.64/16.14 | | | | |
% 111.64/16.14 | | | | End of split
% 111.64/16.14 | | | |
% 111.64/16.14 | | | Case 2:
% 111.64/16.14 | | | |
% 111.64/16.14 | | | | (30) (all_57_34 = e0 & op(e1, e1) = e0) | (all_57_35 = e0 & op(e1,
% 111.64/16.14 | | | | e0) = e0)
% 111.64/16.14 | | | |
% 111.64/16.14 | | | | REF_CLOSE: (1), (3), (7), (11), (13), (30) are inconsistent by sub-proof
% 111.64/16.14 | | | | #150.
% 111.64/16.14 | | | |
% 111.64/16.14 | | | End of split
% 111.64/16.14 | | |
% 111.64/16.14 | | Case 2:
% 111.64/16.14 | | |
% 111.64/16.14 | | | (31) all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 &
% 111.64/16.14 | | | op(e0, e3) = e0 & $i(all_52_22)
% 111.64/16.14 | | |
% 111.64/16.14 | | | ALPHA: (31) implies:
% 111.64/16.14 | | | (32) op(e0, e3) = e0
% 111.64/16.14 | | |
% 111.64/16.14 | | | REF_CLOSE: (8), (11), (15), (32) are inconsistent by sub-proof #149.
% 111.64/16.14 | | |
% 111.64/16.14 | | End of split
% 111.64/16.14 | |
% 111.64/16.14 | End of split
% 111.64/16.14 |
% 111.64/16.14 End of proof
% 111.64/16.14
% 111.64/16.14 Sub-proof #149 shows that the following formulas are inconsistent:
% 111.64/16.14 ----------------------------------------------------------------
% 111.64/16.14 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.14 (2) op(e0, e3) = all_53_2
% 111.64/16.14 (3) op(e0, e3) = e0
% 111.64/16.14 (4) ~ (all_53_2 = e0)
% 111.64/16.14
% 111.64/16.14 Begin of proof
% 111.64/16.14 |
% 111.64/16.14 | GROUND_INST: instantiating (1) with all_53_2, e0, e3, e0, simplifying with
% 111.64/16.14 | (2), (3) gives:
% 111.64/16.14 | (5) all_53_2 = e0
% 111.64/16.14 |
% 111.64/16.14 | REDUCE: (4), (5) imply:
% 111.64/16.14 | (6) $false
% 111.64/16.14 |
% 111.64/16.14 | CLOSE: (6) is inconsistent.
% 111.64/16.14 |
% 111.64/16.14 End of proof
% 111.64/16.14
% 111.64/16.14 Sub-proof #150 shows that the following formulas are inconsistent:
% 111.64/16.14 ----------------------------------------------------------------
% 111.64/16.14 (1) op(e1, e1) = e3
% 111.64/16.14 (2) op(e1, e0) = all_53_4
% 111.64/16.14 (3) ~ (e3 = e0)
% 111.64/16.14 (4) (all_57_34 = e0 & op(e1, e1) = e0) | (all_57_35 = e0 & op(e1, e0) = e0)
% 111.64/16.14 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.14 (6) ~ (all_53_4 = e0)
% 111.64/16.14
% 111.64/16.14 Begin of proof
% 111.64/16.14 |
% 111.64/16.14 | BETA: splitting (4) gives:
% 111.64/16.14 |
% 111.64/16.14 | Case 1:
% 111.64/16.14 | |
% 111.64/16.14 | | (7) all_57_34 = e0 & op(e1, e1) = e0
% 111.64/16.14 | |
% 111.64/16.14 | | ALPHA: (7) implies:
% 111.64/16.14 | | (8) op(e1, e1) = e0
% 111.64/16.14 | |
% 111.64/16.14 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #152.
% 111.64/16.14 | |
% 111.64/16.14 | Case 2:
% 111.64/16.14 | |
% 111.64/16.14 | | (9) all_57_35 = e0 & op(e1, e0) = e0
% 111.64/16.14 | |
% 111.64/16.14 | | ALPHA: (9) implies:
% 111.64/16.14 | | (10) op(e1, e0) = e0
% 111.64/16.14 | |
% 111.64/16.14 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #151.
% 111.64/16.14 | |
% 111.64/16.14 | End of split
% 111.64/16.14 |
% 111.64/16.14 End of proof
% 111.64/16.14
% 111.64/16.14 Sub-proof #151 shows that the following formulas are inconsistent:
% 111.64/16.14 ----------------------------------------------------------------
% 111.64/16.14 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.14 (2) op(e1, e0) = all_53_4
% 111.64/16.14 (3) op(e1, e0) = e0
% 111.64/16.14 (4) ~ (all_53_4 = e0)
% 111.64/16.14
% 111.64/16.14 Begin of proof
% 111.64/16.14 |
% 111.64/16.14 | GROUND_INST: instantiating (1) with all_53_4, e0, e0, e1, simplifying with
% 111.64/16.14 | (2), (3) gives:
% 111.64/16.15 | (5) all_53_4 = e0
% 111.64/16.15 |
% 111.64/16.15 | REDUCE: (4), (5) imply:
% 111.64/16.15 | (6) $false
% 111.64/16.15 |
% 111.64/16.15 | CLOSE: (6) is inconsistent.
% 111.64/16.15 |
% 111.64/16.15 End of proof
% 111.64/16.15
% 111.64/16.15 Sub-proof #152 shows that the following formulas are inconsistent:
% 111.64/16.15 ----------------------------------------------------------------
% 111.64/16.15 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.15 (2) op(e1, e1) = e3
% 111.64/16.15 (3) op(e1, e1) = e0
% 111.64/16.15 (4) ~ (e3 = e0)
% 111.64/16.15
% 111.64/16.15 Begin of proof
% 111.64/16.15 |
% 111.64/16.15 | GROUND_INST: instantiating (1) with e0, e3, e1, e1, simplifying with (2), (3)
% 111.64/16.15 | gives:
% 111.64/16.15 | (5) e3 = e0
% 111.64/16.15 |
% 111.64/16.15 | REDUCE: (4), (5) imply:
% 111.64/16.15 | (6) $false
% 111.64/16.15 |
% 111.64/16.15 | CLOSE: (6) is inconsistent.
% 111.64/16.15 |
% 111.64/16.15 End of proof
% 111.64/16.15
% 111.64/16.15 Sub-proof #153 shows that the following formulas are inconsistent:
% 111.64/16.15 ----------------------------------------------------------------
% 111.64/16.15 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.15 (2) op(e1, e2) = all_53_7
% 111.64/16.15 (3) op(e1, e2) = e0
% 111.64/16.15 (4) ~ (all_53_7 = e0)
% 111.64/16.15
% 111.64/16.15 Begin of proof
% 111.64/16.15 |
% 111.64/16.15 | GROUND_INST: instantiating (1) with all_53_7, e0, e2, e1, simplifying with
% 111.64/16.15 | (2), (3) gives:
% 111.64/16.15 | (5) all_53_7 = e0
% 111.64/16.15 |
% 111.64/16.15 | REDUCE: (4), (5) imply:
% 111.64/16.15 | (6) $false
% 111.64/16.15 |
% 111.64/16.15 | CLOSE: (6) is inconsistent.
% 111.64/16.15 |
% 111.64/16.15 End of proof
% 111.64/16.15
% 111.64/16.15 Sub-proof #154 shows that the following formulas are inconsistent:
% 111.64/16.15 ----------------------------------------------------------------
% 111.64/16.15 (1) op(e3, e1) = e0
% 111.64/16.15 (2) ~ (e3 = e0)
% 111.64/16.15 (3) op(e3, e1) = all_53_13
% 111.64/16.15 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.15 (5) op(e3, e1) = e3
% 111.64/16.15
% 111.64/16.15 Begin of proof
% 111.64/16.15 |
% 111.64/16.15 | GROUND_INST: instantiating (4) with all_53_13, e0, e1, e3, simplifying with
% 111.64/16.15 | (1), (3) gives:
% 111.64/16.15 | (6) all_53_13 = e0
% 111.64/16.15 |
% 111.64/16.15 | GROUND_INST: instantiating (4) with all_53_13, e3, e1, e3, simplifying with
% 111.64/16.15 | (3), (5) gives:
% 111.64/16.15 | (7) all_53_13 = e3
% 111.64/16.15 |
% 111.64/16.15 | COMBINE_EQS: (6), (7) imply:
% 111.64/16.15 | (8) e3 = e0
% 111.64/16.15 |
% 111.64/16.15 | REDUCE: (2), (8) imply:
% 111.64/16.15 | (9) $false
% 111.64/16.15 |
% 111.64/16.15 | CLOSE: (9) is inconsistent.
% 111.64/16.15 |
% 111.64/16.15 End of proof
% 111.64/16.15
% 111.64/16.15 Sub-proof #155 shows that the following formulas are inconsistent:
% 111.64/16.15 ----------------------------------------------------------------
% 111.64/16.15 (1) ~ (all_53_15 = e0)
% 111.64/16.15 (2) op(e3, e2) = all_53_15
% 111.64/16.15 (3) ~ (all_4_2 = e0)
% 111.64/16.15 (4) (all_57_96 = e0 & op(e3, e3) = e0) | (all_57_97 = e0 & op(e3, e2) = e0)
% 111.64/16.15 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.15 (6) op(e3, e3) = all_4_2
% 111.64/16.15
% 111.64/16.15 Begin of proof
% 111.64/16.15 |
% 111.64/16.15 | BETA: splitting (4) gives:
% 111.64/16.15 |
% 111.64/16.15 | Case 1:
% 111.64/16.15 | |
% 111.64/16.15 | | (7) all_57_96 = e0 & op(e3, e3) = e0
% 111.64/16.15 | |
% 111.64/16.15 | | ALPHA: (7) implies:
% 111.64/16.15 | | (8) op(e3, e3) = e0
% 111.64/16.15 | |
% 111.64/16.15 | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #206.
% 111.64/16.15 | |
% 111.64/16.15 | Case 2:
% 111.64/16.15 | |
% 111.64/16.15 | | (9) all_57_97 = e0 & op(e3, e2) = e0
% 111.64/16.15 | |
% 111.64/16.15 | | ALPHA: (9) implies:
% 111.64/16.15 | | (10) op(e3, e2) = e0
% 111.64/16.15 | |
% 111.64/16.15 | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #156.
% 111.64/16.15 | |
% 111.64/16.15 | End of split
% 111.64/16.15 |
% 111.64/16.15 End of proof
% 111.64/16.15
% 111.64/16.15 Sub-proof #156 shows that the following formulas are inconsistent:
% 111.64/16.15 ----------------------------------------------------------------
% 111.64/16.15 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.15 (2) op(e3, e2) = all_53_15
% 111.64/16.15 (3) op(e3, e2) = e0
% 111.64/16.15 (4) ~ (all_53_15 = e0)
% 111.64/16.15
% 111.64/16.15 Begin of proof
% 111.64/16.15 |
% 111.64/16.15 | GROUND_INST: instantiating (1) with all_53_15, e0, e2, e3, simplifying with
% 111.64/16.15 | (2), (3) gives:
% 111.64/16.15 | (5) all_53_15 = e0
% 111.64/16.15 |
% 111.64/16.15 | REDUCE: (4), (5) imply:
% 111.64/16.15 | (6) $false
% 111.64/16.15 |
% 111.64/16.15 | CLOSE: (6) is inconsistent.
% 111.64/16.15 |
% 111.64/16.15 End of proof
% 111.64/16.15
% 111.64/16.15 Sub-proof #157 shows that the following formulas are inconsistent:
% 111.64/16.15 ----------------------------------------------------------------
% 111.64/16.15 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.15 (2) op(e1, e3) = all_53_6
% 111.64/16.15 (3) op(e1, e3) = e0
% 111.64/16.15 (4) ~ (all_53_6 = e0)
% 111.64/16.15
% 111.64/16.15 Begin of proof
% 111.64/16.15 |
% 111.64/16.15 | GROUND_INST: instantiating (1) with all_53_6, e0, e3, e1, simplifying with
% 111.64/16.15 | (2), (3) gives:
% 111.64/16.15 | (5) all_53_6 = e0
% 111.64/16.15 |
% 111.64/16.15 | REDUCE: (4), (5) imply:
% 111.64/16.15 | (6) $false
% 111.64/16.15 |
% 111.64/16.15 | CLOSE: (6) is inconsistent.
% 111.64/16.15 |
% 111.64/16.15 End of proof
% 111.64/16.15
% 111.64/16.15 Sub-proof #158 shows that the following formulas are inconsistent:
% 111.64/16.15 ----------------------------------------------------------------
% 111.64/16.15 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.15 (2) op(e2, e3) = all_53_10
% 111.64/16.15 (3) op(e2, e3) = e0
% 111.64/16.15 (4) ~ (all_53_10 = e0)
% 111.64/16.15
% 111.64/16.15 Begin of proof
% 111.64/16.15 |
% 111.64/16.15 | GROUND_INST: instantiating (1) with all_53_10, e0, e3, e2, simplifying with
% 111.64/16.15 | (2), (3) gives:
% 111.64/16.15 | (5) all_53_10 = e0
% 111.64/16.15 |
% 111.64/16.15 | REDUCE: (4), (5) imply:
% 111.64/16.15 | (6) $false
% 111.64/16.15 |
% 111.64/16.15 | CLOSE: (6) is inconsistent.
% 111.64/16.15 |
% 111.64/16.15 End of proof
% 111.64/16.15
% 111.64/16.15 Sub-proof #159 shows that the following formulas are inconsistent:
% 111.64/16.15 ----------------------------------------------------------------
% 111.64/16.15 (1) ~ (all_6_2 = e2)
% 111.64/16.15 (2) ~ (all_53_1 = e2)
% 111.64/16.15 (3) op(e0, e1) = all_53_1
% 111.64/16.15 (4) op(e0, e0) = all_6_2
% 111.64/16.15 (5) (all_57_18 = e2 & op(e0, e1) = e2) | (all_57_19 = e2 & op(e0, e0) = e2)
% 111.64/16.15 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.15
% 111.64/16.15 Begin of proof
% 111.64/16.15 |
% 111.64/16.15 | BETA: splitting (5) gives:
% 111.64/16.15 |
% 111.64/16.15 | Case 1:
% 111.64/16.15 | |
% 111.64/16.15 | | (7) all_57_18 = e2 & op(e0, e1) = e2
% 111.64/16.15 | |
% 111.64/16.15 | | ALPHA: (7) implies:
% 111.64/16.15 | | (8) op(e0, e1) = e2
% 111.64/16.15 | |
% 111.64/16.15 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #161.
% 111.64/16.15 | |
% 111.64/16.15 | Case 2:
% 111.64/16.15 | |
% 111.64/16.15 | | (9) all_57_19 = e2 & op(e0, e0) = e2
% 111.64/16.15 | |
% 111.64/16.15 | | ALPHA: (9) implies:
% 111.64/16.15 | | (10) op(e0, e0) = e2
% 111.64/16.15 | |
% 111.64/16.15 | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #160.
% 111.64/16.15 | |
% 111.64/16.15 | End of split
% 111.64/16.15 |
% 111.64/16.15 End of proof
% 111.64/16.15
% 111.64/16.15 Sub-proof #160 shows that the following formulas are inconsistent:
% 111.64/16.15 ----------------------------------------------------------------
% 111.64/16.15 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.15 (2) op(e0, e0) = all_6_2
% 111.64/16.15 (3) op(e0, e0) = e2
% 111.64/16.15 (4) ~ (all_6_2 = e2)
% 111.64/16.15
% 111.64/16.15 Begin of proof
% 111.64/16.15 |
% 111.64/16.15 | GROUND_INST: instantiating (1) with all_6_2, e2, e0, e0, simplifying with (2),
% 111.64/16.15 | (3) gives:
% 111.64/16.15 | (5) all_6_2 = e2
% 111.64/16.15 |
% 111.64/16.15 | REDUCE: (4), (5) imply:
% 111.64/16.15 | (6) $false
% 111.64/16.15 |
% 111.64/16.15 | CLOSE: (6) is inconsistent.
% 111.64/16.15 |
% 111.64/16.15 End of proof
% 111.64/16.15
% 111.64/16.15 Sub-proof #161 shows that the following formulas are inconsistent:
% 111.64/16.15 ----------------------------------------------------------------
% 111.64/16.15 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.15 (2) op(e0, e1) = all_53_1
% 111.64/16.15 (3) op(e0, e1) = e2
% 111.64/16.15 (4) ~ (all_53_1 = e2)
% 111.64/16.15
% 111.64/16.15 Begin of proof
% 111.64/16.15 |
% 111.64/16.15 | GROUND_INST: instantiating (1) with all_53_1, e2, e1, e0, simplifying with
% 111.64/16.15 | (2), (3) gives:
% 111.64/16.15 | (5) all_53_1 = e2
% 111.64/16.15 |
% 111.64/16.15 | REDUCE: (4), (5) imply:
% 111.64/16.15 | (6) $false
% 111.64/16.15 |
% 111.64/16.15 | CLOSE: (6) is inconsistent.
% 111.64/16.15 |
% 111.64/16.15 End of proof
% 111.64/16.15
% 111.64/16.15 Sub-proof #162 shows that the following formulas are inconsistent:
% 111.64/16.15 ----------------------------------------------------------------
% 111.64/16.15 (1) ~ (e2 = e0)
% 111.64/16.15 (2) op(e0, e2) = e2
% 111.64/16.15 (3) op(e1, e2) = all_53_7
% 111.64/16.15 (4) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 & op(e1,
% 111.64/16.15 e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~ (all_52_16 = e2) &
% 111.64/16.15 op(e2, e0) = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 111.64/16.15 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.15 (6) ~ (all_53_7 = e1)
% 111.64/16.15
% 111.64/16.15 Begin of proof
% 111.64/16.15 |
% 111.64/16.15 | BETA: splitting (4) gives:
% 111.64/16.15 |
% 111.64/16.15 | Case 1:
% 111.64/16.15 | |
% 111.64/16.15 | | (7) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 111.64/16.15 | | op(e1, e2) = e1 & $i(all_52_14)
% 111.64/16.15 | |
% 111.64/16.15 | | ALPHA: (7) implies:
% 111.64/16.15 | | (8) op(e1, e2) = e1
% 111.64/16.15 | |
% 111.64/16.15 | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #233.
% 111.64/16.15 | |
% 111.64/16.15 | Case 2:
% 111.64/16.15 | |
% 111.64/16.15 | | (9) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 &
% 111.64/16.15 | | op(e0, e2) = e0 & $i(all_52_16)
% 111.64/16.15 | |
% 111.64/16.15 | | ALPHA: (9) implies:
% 111.64/16.15 | | (10) op(e0, e2) = e0
% 111.64/16.15 | |
% 111.64/16.15 | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #163.
% 111.64/16.15 | |
% 111.64/16.15 | End of split
% 111.64/16.15 |
% 111.64/16.15 End of proof
% 111.64/16.15
% 111.64/16.15 Sub-proof #163 shows that the following formulas are inconsistent:
% 111.64/16.15 ----------------------------------------------------------------
% 111.64/16.15 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.15 (2) op(e0, e2) = e2
% 111.64/16.15 (3) op(e0, e2) = e0
% 111.64/16.15 (4) ~ (e2 = e0)
% 111.64/16.15
% 111.64/16.15 Begin of proof
% 111.64/16.15 |
% 111.64/16.15 | GROUND_INST: instantiating (1) with e2, e0, e2, e0, simplifying with (2), (3)
% 111.64/16.15 | gives:
% 111.64/16.15 | (5) e2 = e0
% 111.64/16.15 |
% 111.64/16.15 | REDUCE: (4), (5) imply:
% 111.64/16.15 | (6) $false
% 111.64/16.15 |
% 111.64/16.15 | CLOSE: (6) is inconsistent.
% 111.64/16.15 |
% 111.64/16.15 End of proof
% 111.64/16.15
% 111.64/16.15 Sub-proof #164 shows that the following formulas are inconsistent:
% 111.64/16.15 ----------------------------------------------------------------
% 111.64/16.15 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.15 (2) op(e0, e3) = all_53_2
% 111.64/16.15 (3) op(e0, e3) = e2
% 111.64/16.15 (4) ~ (all_53_2 = e2)
% 111.64/16.15
% 111.64/16.15 Begin of proof
% 111.64/16.15 |
% 111.64/16.15 | GROUND_INST: instantiating (1) with all_53_2, e2, e3, e0, simplifying with
% 111.64/16.15 | (2), (3) gives:
% 111.64/16.15 | (5) all_53_2 = e2
% 111.64/16.15 |
% 111.64/16.15 | REDUCE: (4), (5) imply:
% 111.64/16.15 | (6) $false
% 111.64/16.15 |
% 111.64/16.15 | CLOSE: (6) is inconsistent.
% 111.64/16.15 |
% 111.64/16.15 End of proof
% 111.64/16.15
% 111.64/16.15 Sub-proof #165 shows that the following formulas are inconsistent:
% 111.64/16.15 ----------------------------------------------------------------
% 111.64/16.15 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.15 (2) op(e0, e0) = e3
% 111.64/16.15 (3) op(e0, e0) = e1
% 111.64/16.15 (4) ~ (e3 = e1)
% 111.64/16.15
% 111.64/16.15 Begin of proof
% 111.64/16.15 |
% 111.64/16.15 | GROUND_INST: instantiating (1) with e1, e3, e0, e0, simplifying with (2), (3)
% 111.64/16.15 | gives:
% 111.64/16.15 | (5) e3 = e1
% 111.64/16.15 |
% 111.64/16.15 | REDUCE: (4), (5) imply:
% 111.64/16.15 | (6) $false
% 111.64/16.15 |
% 111.64/16.15 | CLOSE: (6) is inconsistent.
% 111.64/16.15 |
% 111.64/16.15 End of proof
% 111.64/16.15
% 111.64/16.15 Sub-proof #166 shows that the following formulas are inconsistent:
% 111.64/16.15 ----------------------------------------------------------------
% 111.64/16.15 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.15 (2) op(e0, e3) = all_53_2
% 111.64/16.15 (3) op(e0, e3) = e1
% 111.64/16.16 (4) ~ (all_53_2 = e1)
% 111.64/16.16
% 111.64/16.16 Begin of proof
% 111.64/16.16 |
% 111.64/16.16 | GROUND_INST: instantiating (1) with all_53_2, e1, e3, e0, simplifying with
% 111.64/16.16 | (2), (3) gives:
% 111.64/16.16 | (5) all_53_2 = e1
% 111.64/16.16 |
% 111.64/16.16 | REDUCE: (4), (5) imply:
% 111.64/16.16 | (6) $false
% 111.64/16.16 |
% 111.64/16.16 | CLOSE: (6) is inconsistent.
% 111.64/16.16 |
% 111.64/16.16 End of proof
% 111.64/16.16
% 111.64/16.16 Sub-proof #167 shows that the following formulas are inconsistent:
% 111.64/16.16 ----------------------------------------------------------------
% 111.64/16.16 (1) op(e0, e1) = all_53_1
% 111.64/16.16 (2) op(e0, e1) = e0
% 111.64/16.16 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.16 (4) op(e0, e2) = e0
% 111.64/16.16 (5) ~ (all_53_1 = all_53_3)
% 111.64/16.16 (6) op(e0, e2) = all_53_3
% 111.64/16.16
% 111.64/16.16 Begin of proof
% 111.64/16.16 |
% 111.64/16.16 | GROUND_INST: instantiating (3) with all_53_1, e0, e1, e0, simplifying with
% 111.64/16.16 | (1), (2) gives:
% 111.64/16.16 | (7) all_53_1 = e0
% 111.64/16.16 |
% 111.64/16.16 | GROUND_INST: instantiating (3) with all_53_3, e0, e2, e0, simplifying with
% 111.64/16.16 | (4), (6) gives:
% 111.64/16.16 | (8) all_53_3 = e0
% 111.64/16.16 |
% 111.64/16.16 | REDUCE: (5), (7), (8) imply:
% 111.64/16.16 | (9) $false
% 111.64/16.16 |
% 111.64/16.16 | CLOSE: (9) is inconsistent.
% 111.64/16.16 |
% 111.64/16.16 End of proof
% 111.64/16.16
% 111.64/16.16 Sub-proof #168 shows that the following formulas are inconsistent:
% 111.64/16.16 ----------------------------------------------------------------
% 111.64/16.16 (1) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 111.64/16.16 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 111.64/16.16 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 111.64/16.16 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 111.64/16.16 $i(all_52_16))
% 111.64/16.16 (2) op(e3, e2) = all_53_15
% 111.64/16.16 (3) op(e1, e2) = all_53_7
% 111.64/16.16 (4) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.64/16.16 all_52_6 & $i(all_52_6)
% 111.64/16.16 (5) op(e3, e1) = all_53_13
% 111.64/16.16 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.16 (7) ~ (all_53_13 = all_53_15)
% 111.64/16.16 (8) ~ (all_53_7 = e1)
% 111.64/16.16 (9) op(e0, e2) = all_53_3
% 111.64/16.16 (10) ~ (all_53_3 = e0)
% 111.64/16.16
% 111.64/16.16 Begin of proof
% 111.64/16.16 |
% 111.64/16.16 | ALPHA: (4) implies:
% 111.64/16.16 | (11) op(e3, e1) = e3
% 111.64/16.16 |
% 111.64/16.16 | BETA: splitting (1) gives:
% 111.64/16.16 |
% 111.64/16.16 | Case 1:
% 111.64/16.16 | |
% 111.64/16.16 | | (12) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3)
% 111.64/16.16 | | = all_52_12 & $i(all_52_12)
% 111.64/16.16 | |
% 111.64/16.16 | | ALPHA: (12) implies:
% 111.64/16.16 | | (13) op(e3, e2) = e3
% 111.64/16.16 | |
% 111.64/16.16 | | REF_CLOSE: (2), (5), (6), (7), (11), (13) are inconsistent by sub-proof
% 111.64/16.16 | | #169.
% 111.64/16.16 | |
% 111.64/16.16 | Case 2:
% 111.64/16.16 | |
% 111.64/16.16 | | (14) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 111.64/16.16 | | op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~ (all_52_16
% 111.64/16.16 | | = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 111.64/16.16 | | $i(all_52_16))
% 111.64/16.16 | |
% 111.64/16.16 | | REF_CLOSE: (3), (6), (8), (9), (10), (14) are inconsistent by sub-proof
% 111.64/16.16 | | #218.
% 111.64/16.16 | |
% 111.64/16.16 | End of split
% 111.64/16.16 |
% 111.64/16.16 End of proof
% 111.64/16.16
% 111.64/16.16 Sub-proof #169 shows that the following formulas are inconsistent:
% 111.64/16.16 ----------------------------------------------------------------
% 111.64/16.16 (1) op(e3, e2) = e3
% 111.64/16.16 (2) op(e3, e2) = all_53_15
% 111.64/16.16 (3) op(e3, e1) = all_53_13
% 111.64/16.16 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.16 (5) ~ (all_53_13 = all_53_15)
% 111.64/16.16 (6) op(e3, e1) = e3
% 111.64/16.16
% 111.64/16.16 Begin of proof
% 111.64/16.16 |
% 111.64/16.16 | GROUND_INST: instantiating (4) with all_53_13, e3, e1, e3, simplifying with
% 111.64/16.16 | (3), (6) gives:
% 111.64/16.16 | (7) all_53_13 = e3
% 111.64/16.16 |
% 111.64/16.16 | GROUND_INST: instantiating (4) with all_53_15, e3, e2, e3, simplifying with
% 111.64/16.16 | (1), (2) gives:
% 111.64/16.16 | (8) all_53_15 = e3
% 111.64/16.16 |
% 111.64/16.16 | REDUCE: (5), (7), (8) imply:
% 111.64/16.16 | (9) $false
% 111.64/16.16 |
% 111.64/16.16 | CLOSE: (9) is inconsistent.
% 111.64/16.16 |
% 111.64/16.16 End of proof
% 111.64/16.16
% 111.64/16.16 Sub-proof #170 shows that the following formulas are inconsistent:
% 111.64/16.16 ----------------------------------------------------------------
% 111.64/16.16 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.16 (2) op(e0, e1) = all_53_1
% 111.64/16.16 (3) op(e0, e1) = e1
% 111.64/16.16 (4) ~ (all_53_1 = e1)
% 111.64/16.16
% 111.64/16.16 Begin of proof
% 111.64/16.16 |
% 111.64/16.16 | GROUND_INST: instantiating (1) with all_53_1, e1, e1, e0, simplifying with
% 111.64/16.16 | (2), (3) gives:
% 111.64/16.16 | (5) all_53_1 = e1
% 111.64/16.16 |
% 111.64/16.16 | REDUCE: (4), (5) imply:
% 111.64/16.16 | (6) $false
% 111.64/16.16 |
% 111.64/16.16 | CLOSE: (6) is inconsistent.
% 111.64/16.16 |
% 111.64/16.16 End of proof
% 111.64/16.16
% 111.64/16.16 Sub-proof #171 shows that the following formulas are inconsistent:
% 111.64/16.16 ----------------------------------------------------------------
% 111.64/16.16 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.16 (2) op(e0, e0) = all_6_2
% 111.64/16.16 (3) op(e0, e0) = e1
% 111.64/16.16 (4) ~ (all_6_2 = e1)
% 111.64/16.16
% 111.64/16.16 Begin of proof
% 111.64/16.16 |
% 111.64/16.16 | GROUND_INST: instantiating (1) with all_6_2, e1, e0, e0, simplifying with (2),
% 111.64/16.16 | (3) gives:
% 111.64/16.16 | (5) all_6_2 = e1
% 111.64/16.16 |
% 111.64/16.16 | REDUCE: (4), (5) imply:
% 111.64/16.16 | (6) $false
% 111.64/16.16 |
% 111.64/16.16 | CLOSE: (6) is inconsistent.
% 111.64/16.16 |
% 111.64/16.16 End of proof
% 111.64/16.16
% 111.64/16.16 Sub-proof #172 shows that the following formulas are inconsistent:
% 111.64/16.16 ----------------------------------------------------------------
% 111.64/16.16 (1) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 & op(e1,
% 111.64/16.16 e3) = e1 & $i(all_52_20)) | (all_52_23 = e0 & ~ (all_52_22 = e3) &
% 111.64/16.16 op(e3, e0) = all_52_22 & op(e0, e3) = e0 & $i(all_52_22))
% 111.64/16.16 (2) op(e0, e3) = e1
% 111.64/16.16 (3) ~ (e1 = e0)
% 111.64/16.16 (4) ~ (all_53_6 = e1)
% 111.64/16.16 (5) op(e1, e3) = all_53_6
% 111.64/16.16 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.16
% 111.64/16.16 Begin of proof
% 111.64/16.16 |
% 111.64/16.16 | BETA: splitting (1) gives:
% 111.64/16.16 |
% 111.64/16.16 | Case 1:
% 111.64/16.16 | |
% 111.64/16.16 | | (7) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 &
% 111.64/16.16 | | op(e1, e3) = e1 & $i(all_52_20)
% 111.64/16.16 | |
% 111.64/16.16 | | ALPHA: (7) implies:
% 111.64/16.16 | | (8) op(e1, e3) = e1
% 111.64/16.16 | |
% 111.64/16.16 | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #223.
% 111.64/16.16 | |
% 111.64/16.16 | Case 2:
% 111.64/16.16 | |
% 111.64/16.16 | | (9) all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 &
% 111.64/16.16 | | op(e0, e3) = e0 & $i(all_52_22)
% 111.64/16.16 | |
% 111.64/16.16 | | ALPHA: (9) implies:
% 111.64/16.16 | | (10) op(e0, e3) = e0
% 111.64/16.16 | |
% 111.64/16.16 | | GROUND_INST: instantiating (6) with e1, e0, e3, e0, simplifying with (2),
% 111.64/16.16 | | (10) gives:
% 111.64/16.16 | | (11) e1 = e0
% 111.64/16.16 | |
% 111.64/16.16 | | REDUCE: (3), (11) imply:
% 111.64/16.16 | | (12) $false
% 111.64/16.16 | |
% 111.64/16.16 | | CLOSE: (12) is inconsistent.
% 111.64/16.16 | |
% 111.64/16.16 | End of split
% 111.64/16.16 |
% 111.64/16.16 End of proof
% 111.64/16.16
% 111.64/16.16 Sub-proof #173 shows that the following formulas are inconsistent:
% 111.64/16.16 ----------------------------------------------------------------
% 111.64/16.16 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.16 (2) op(e2, e0) = all_53_8
% 111.64/16.16 (3) op(e2, e0) = e1
% 111.64/16.16 (4) ~ (all_53_8 = e1)
% 111.64/16.16
% 111.64/16.16 Begin of proof
% 111.64/16.16 |
% 111.64/16.16 | GROUND_INST: instantiating (1) with all_53_8, e1, e0, e2, simplifying with
% 111.64/16.16 | (2), (3) gives:
% 111.64/16.16 | (5) all_53_8 = e1
% 111.64/16.16 |
% 111.64/16.16 | REDUCE: (4), (5) imply:
% 111.64/16.16 | (6) $false
% 111.64/16.16 |
% 111.64/16.16 | CLOSE: (6) is inconsistent.
% 111.64/16.16 |
% 111.64/16.16 End of proof
% 111.64/16.16
% 111.64/16.16 Sub-proof #174 shows that the following formulas are inconsistent:
% 111.64/16.16 ----------------------------------------------------------------
% 111.64/16.16 (1) ~ (all_24_0 = e3)
% 111.64/16.16 (2) all_55_15 = all_4_2
% 111.64/16.16 (3) ~ (all_53_9 = all_24_0)
% 111.64/16.16 (4) ~ (all_53_9 = e1)
% 111.64/16.16 (5) ~ (all_24_0 = e0)
% 111.64/16.16 (6) ~ (all_53_9 = e3)
% 111.64/16.16 (7) ~ (all_53_7 = e3)
% 111.64/16.16 (8) all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 111.64/16.16 (9) all_55_13 = all_24_0
% 111.64/16.16 (10) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 111.64/16.16 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 111.64/16.16 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 111.64/16.16 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0
% 111.64/16.16 & $i(all_52_16))
% 111.64/16.16 (11) op(e3, e2) = all_53_15
% 111.64/16.16 (12) ~ (all_53_1 = all_53_9)
% 111.64/16.16 (13) op(e1, e2) = all_53_7
% 111.64/16.16 (14) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 111.64/16.16 (15) ~ (all_24_0 = all_4_2)
% 111.64/16.16 (16) (all_57_92 = e3 & op(e3, e2) = e3) | (all_57_93 = e3 & op(e2, e2) = e3)
% 111.64/16.16 | (all_57_94 = e3 & op(e1, e2) = e3) | (all_57_95 = e3 & op(e0, e2) =
% 111.64/16.16 e3)
% 111.64/16.16 (17) op(e0, e1) = all_53_1
% 111.64/16.16 (18) op(e2, e1) = all_53_9
% 111.64/16.16 (19) ~ (all_4_2 = e0)
% 111.64/16.16 (20) op(e3, e1) = all_24_0
% 111.64/16.16 (21) ~ (all_4_2 = e2)
% 111.64/16.16 (22) op(e3, e1) = all_53_13
% 111.64/16.16 (23) all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 111.64/16.16 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.16 (25) ~ (all_53_15 = all_4_2)
% 111.64/16.16 (26) ~ (all_53_7 = e1)
% 111.64/16.16 (27) all_34_2 = all_4_2
% 111.64/16.16 (28) all_55_9 = all_53_9
% 111.64/16.16 (29) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.64/16.16 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 111.64/16.16 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 111.64/16.16 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.64/16.16 $i(all_52_10))
% 111.64/16.16 (30) op(e2, e2) = e1
% 111.64/16.16 (31) ~ (all_34_2 = e1) | (op(e1, e1) = all_34_1 & $i(all_34_1) & ( ~
% 111.64/16.16 (all_34_1 = e2) | ( ~ (all_34_0 = e0) & op(e2, e1) = all_34_0 &
% 111.64/16.16 $i(all_34_0))))
% 111.64/16.16 (32) op(e0, e2) = all_53_3
% 111.64/16.16
% 111.64/16.16 Begin of proof
% 111.64/16.16 |
% 111.64/16.16 | BETA: splitting (31) gives:
% 111.64/16.16 |
% 111.64/16.17 | Case 1:
% 111.64/16.17 | |
% 111.64/16.17 | | (33) ~ (all_34_2 = e1)
% 111.64/16.17 | |
% 111.64/16.17 | | REDUCE: (27), (33) imply:
% 111.64/16.17 | | (34) ~ (all_4_2 = e1)
% 111.64/16.17 | |
% 111.64/16.17 | | BETA: splitting (8) gives:
% 111.64/16.17 | |
% 111.64/16.17 | | Case 1:
% 111.64/16.17 | | |
% 111.64/16.17 | | | (35) all_55_15 = e3
% 111.64/16.17 | | |
% 111.64/16.17 | | | COMBINE_EQS: (2), (35) imply:
% 111.64/16.17 | | | (36) all_4_2 = e3
% 111.64/16.17 | | |
% 111.64/16.17 | | | REDUCE: (25), (36) imply:
% 111.64/16.17 | | | (37) ~ (all_53_15 = e3)
% 111.64/16.17 | | |
% 111.64/16.17 | | | REDUCE: (34), (36) imply:
% 111.64/16.17 | | | (38) ~ (e3 = e1)
% 111.64/16.17 | | |
% 111.64/16.17 | | | REDUCE: (19), (36) imply:
% 111.64/16.17 | | | (39) ~ (e3 = e0)
% 111.64/16.17 | | |
% 111.64/16.17 | | | REF_CLOSE: (7), (10), (11), (13), (16), (24), (26), (30), (32), (37),
% 111.64/16.17 | | | (38), (39) are inconsistent by sub-proof #178.
% 111.64/16.17 | | |
% 111.64/16.17 | | Case 2:
% 111.64/16.17 | | |
% 111.64/16.17 | | | (40) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 111.64/16.17 | | |
% 111.64/16.17 | | | REF_CLOSE: (2), (19), (21), (34), (40) are inconsistent by sub-proof #191.
% 111.64/16.17 | | |
% 111.64/16.17 | | End of split
% 111.64/16.17 | |
% 111.64/16.17 | Case 2:
% 111.64/16.17 | |
% 111.64/16.17 | | (41) all_34_2 = e1
% 111.64/16.17 | |
% 111.64/16.17 | | COMBINE_EQS: (27), (41) imply:
% 111.64/16.17 | | (42) all_4_2 = e1
% 111.64/16.17 | |
% 111.64/16.17 | | REDUCE: (15), (42) imply:
% 111.64/16.17 | | (43) ~ (all_24_0 = e1)
% 111.64/16.17 | |
% 111.64/16.17 | | BETA: splitting (23) gives:
% 111.64/16.17 | |
% 111.64/16.17 | | Case 1:
% 111.64/16.17 | | |
% 111.64/16.17 | | | (44) all_55_13 = e3
% 111.64/16.17 | | |
% 111.64/16.17 | | | COMBINE_EQS: (9), (44) imply:
% 111.64/16.17 | | | (45) all_24_0 = e3
% 111.64/16.17 | | |
% 111.64/16.17 | | | REDUCE: (1), (45) imply:
% 111.64/16.17 | | | (46) $false
% 111.64/16.17 | | |
% 111.64/16.17 | | | CLOSE: (46) is inconsistent.
% 111.64/16.17 | | |
% 111.64/16.17 | | Case 2:
% 111.64/16.17 | | |
% 111.64/16.17 | | | (47) ~ (all_55_13 = e3)
% 111.64/16.17 | | | (48) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 111.64/16.17 | | |
% 111.64/16.17 | | | BETA: splitting (48) gives:
% 111.64/16.17 | | |
% 111.64/16.17 | | | Case 1:
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | (49) all_55_13 = e2
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | COMBINE_EQS: (9), (49) imply:
% 111.64/16.17 | | | | (50) all_24_0 = e2
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | REDUCE: (3), (50) imply:
% 111.64/16.17 | | | | (51) ~ (all_53_9 = e2)
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | REDUCE: (1), (50) imply:
% 111.64/16.17 | | | | (52) ~ (e3 = e2)
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | SIMP: (52) implies:
% 111.64/16.17 | | | | (53) ~ (e3 = e2)
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | REDUCE: (20), (50) imply:
% 111.64/16.17 | | | | (54) op(e3, e1) = e2
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | BETA: splitting (29) gives:
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | Case 1:
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | (55) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1,
% 111.64/16.17 | | | | | e3) = all_52_6 & $i(all_52_6)
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | ALPHA: (55) implies:
% 111.64/16.17 | | | | | (56) op(e3, e1) = e3
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | REF_CLOSE: (22), (24), (53), (54), (56) are inconsistent by sub-proof
% 111.64/16.17 | | | | | #177.
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | Case 2:
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | (57) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1,
% 111.64/16.17 | | | | | e2) = all_52_8 & $i(all_52_8)) | (all_52_11 = e0 & ~
% 111.64/16.17 | | | | | (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0
% 111.64/16.17 | | | | | & $i(all_52_10))
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | BETA: splitting (57) gives:
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | Case 1:
% 111.64/16.17 | | | | | |
% 111.64/16.17 | | | | | | (58) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 &
% 111.64/16.17 | | | | | | op(e1, e2) = all_52_8 & $i(all_52_8)
% 111.64/16.17 | | | | | |
% 111.64/16.17 | | | | | | ALPHA: (58) implies:
% 111.64/16.17 | | | | | | (59) op(e2, e1) = e2
% 111.64/16.17 | | | | | |
% 111.64/16.17 | | | | | | REF_CLOSE: (18), (24), (51), (59) are inconsistent by sub-proof
% 111.64/16.17 | | | | | | #231.
% 111.64/16.17 | | | | | |
% 111.64/16.17 | | | | | Case 2:
% 111.64/16.17 | | | | | |
% 111.64/16.17 | | | | | | (60) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0) =
% 111.64/16.17 | | | | | | all_52_10 & op(e0, e1) = e0 & $i(all_52_10)
% 111.64/16.17 | | | | | |
% 111.64/16.17 | | | | | | ALPHA: (60) implies:
% 111.64/16.17 | | | | | | (61) op(e0, e1) = e0
% 111.64/16.17 | | | | | |
% 111.64/16.17 | | | | | | BETA: splitting (14) gives:
% 111.64/16.17 | | | | | |
% 111.64/16.17 | | | | | | Case 1:
% 111.64/16.17 | | | | | | |
% 111.64/16.17 | | | | | | | (62) all_55_9 = e3
% 111.64/16.17 | | | | | | |
% 111.64/16.17 | | | | | | | REF_CLOSE: (6), (28), (62) are inconsistent by sub-proof #176.
% 111.64/16.17 | | | | | | |
% 111.64/16.17 | | | | | | Case 2:
% 111.64/16.17 | | | | | | |
% 111.64/16.17 | | | | | | | (63) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 111.64/16.17 | | | | | | |
% 111.64/16.17 | | | | | | | BETA: splitting (63) gives:
% 111.64/16.17 | | | | | | |
% 111.64/16.17 | | | | | | | Case 1:
% 111.64/16.17 | | | | | | | |
% 111.64/16.17 | | | | | | | | (64) all_55_9 = e2
% 111.64/16.17 | | | | | | | |
% 111.64/16.17 | | | | | | | | REF_CLOSE: (28), (51), (64) are inconsistent by sub-proof #175.
% 111.64/16.17 | | | | | | | |
% 111.64/16.17 | | | | | | | Case 2:
% 111.64/16.17 | | | | | | | |
% 111.64/16.17 | | | | | | | | (65) all_55_9 = e1 | all_55_9 = e0
% 111.64/16.17 | | | | | | | |
% 111.64/16.17 | | | | | | | | BETA: splitting (65) gives:
% 111.64/16.17 | | | | | | | |
% 111.64/16.17 | | | | | | | | Case 1:
% 111.64/16.17 | | | | | | | | |
% 111.64/16.17 | | | | | | | | | (66) all_55_9 = e1
% 111.64/16.17 | | | | | | | | |
% 111.64/16.17 | | | | | | | | | COMBINE_EQS: (28), (66) imply:
% 111.64/16.17 | | | | | | | | | (67) all_53_9 = e1
% 111.64/16.17 | | | | | | | | |
% 111.64/16.17 | | | | | | | | | SIMP: (67) implies:
% 111.64/16.17 | | | | | | | | | (68) all_53_9 = e1
% 111.64/16.17 | | | | | | | | |
% 111.64/16.17 | | | | | | | | | REDUCE: (4), (68) imply:
% 111.64/16.17 | | | | | | | | | (69) $false
% 111.64/16.17 | | | | | | | | |
% 111.64/16.17 | | | | | | | | | CLOSE: (69) is inconsistent.
% 111.64/16.17 | | | | | | | | |
% 111.64/16.17 | | | | | | | | Case 2:
% 111.64/16.17 | | | | | | | | |
% 111.64/16.17 | | | | | | | | | (70) all_55_9 = e0
% 111.64/16.17 | | | | | | | | |
% 111.64/16.17 | | | | | | | | | COMBINE_EQS: (28), (70) imply:
% 111.64/16.17 | | | | | | | | | (71) all_53_9 = e0
% 111.64/16.17 | | | | | | | | |
% 111.64/16.17 | | | | | | | | | SIMP: (71) implies:
% 111.64/16.17 | | | | | | | | | (72) all_53_9 = e0
% 111.64/16.17 | | | | | | | | |
% 111.64/16.17 | | | | | | | | | REDUCE: (12), (72) imply:
% 111.64/16.17 | | | | | | | | | (73) ~ (all_53_1 = e0)
% 111.64/16.17 | | | | | | | | |
% 111.64/16.17 | | | | | | | | | REF_CLOSE: (17), (24), (61), (73) are inconsistent by
% 111.64/16.17 | | | | | | | | | sub-proof #230.
% 111.64/16.17 | | | | | | | | |
% 111.64/16.17 | | | | | | | | End of split
% 111.64/16.17 | | | | | | | |
% 111.64/16.17 | | | | | | | End of split
% 111.64/16.17 | | | | | | |
% 111.64/16.17 | | | | | | End of split
% 111.64/16.17 | | | | | |
% 111.64/16.17 | | | | | End of split
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | End of split
% 111.64/16.17 | | | |
% 111.64/16.17 | | | Case 2:
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | (74) all_55_13 = e1 | all_55_13 = e0
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | BETA: splitting (74) gives:
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | Case 1:
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | (75) all_55_13 = e1
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | COMBINE_EQS: (9), (75) imply:
% 111.64/16.17 | | | | | (76) all_24_0 = e1
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | REDUCE: (43), (76) imply:
% 111.64/16.17 | | | | | (77) $false
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | CLOSE: (77) is inconsistent.
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | Case 2:
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | (78) all_55_13 = e0
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | COMBINE_EQS: (9), (78) imply:
% 111.64/16.17 | | | | | (79) all_24_0 = e0
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | REDUCE: (5), (79) imply:
% 111.64/16.17 | | | | | (80) $false
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | CLOSE: (80) is inconsistent.
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | End of split
% 111.64/16.17 | | | |
% 111.64/16.17 | | | End of split
% 111.64/16.17 | | |
% 111.64/16.17 | | End of split
% 111.64/16.17 | |
% 111.64/16.17 | End of split
% 111.64/16.17 |
% 111.64/16.17 End of proof
% 111.64/16.17
% 111.64/16.17 Sub-proof #175 shows that the following formulas are inconsistent:
% 111.64/16.17 ----------------------------------------------------------------
% 111.64/16.17 (1) all_55_9 = all_53_9
% 111.64/16.17 (2) all_55_9 = e2
% 111.64/16.17 (3) ~ (all_53_9 = e2)
% 111.64/16.17
% 111.64/16.17 Begin of proof
% 111.64/16.17 |
% 111.64/16.17 | COMBINE_EQS: (1), (2) imply:
% 111.64/16.17 | (4) all_53_9 = e2
% 111.64/16.17 |
% 111.64/16.17 | SIMP: (4) implies:
% 111.64/16.17 | (5) all_53_9 = e2
% 111.64/16.17 |
% 111.64/16.17 | REDUCE: (3), (5) imply:
% 111.64/16.17 | (6) $false
% 111.64/16.17 |
% 111.64/16.17 | CLOSE: (6) is inconsistent.
% 111.64/16.17 |
% 111.64/16.17 End of proof
% 111.64/16.17
% 111.64/16.17 Sub-proof #176 shows that the following formulas are inconsistent:
% 111.64/16.17 ----------------------------------------------------------------
% 111.64/16.17 (1) all_55_9 = all_53_9
% 111.64/16.17 (2) all_55_9 = e3
% 111.64/16.17 (3) ~ (all_53_9 = e3)
% 111.64/16.17
% 111.64/16.17 Begin of proof
% 111.64/16.17 |
% 111.64/16.17 | COMBINE_EQS: (1), (2) imply:
% 111.64/16.17 | (4) all_53_9 = e3
% 111.64/16.17 |
% 111.64/16.17 | SIMP: (4) implies:
% 111.64/16.17 | (5) all_53_9 = e3
% 111.64/16.17 |
% 111.64/16.17 | REDUCE: (3), (5) imply:
% 111.64/16.17 | (6) $false
% 111.64/16.17 |
% 111.64/16.17 | CLOSE: (6) is inconsistent.
% 111.64/16.17 |
% 111.64/16.17 End of proof
% 111.64/16.17
% 111.64/16.17 Sub-proof #177 shows that the following formulas are inconsistent:
% 111.64/16.17 ----------------------------------------------------------------
% 111.64/16.17 (1) op(e3, e1) = all_53_13
% 111.64/16.17 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.17 (3) ~ (e3 = e2)
% 111.64/16.17 (4) op(e3, e1) = e3
% 111.64/16.17 (5) op(e3, e1) = e2
% 111.64/16.17
% 111.64/16.17 Begin of proof
% 111.64/16.17 |
% 111.64/16.17 | GROUND_INST: instantiating (2) with all_53_13, e2, e1, e3, simplifying with
% 111.64/16.17 | (1), (5) gives:
% 111.64/16.17 | (6) all_53_13 = e2
% 111.64/16.17 |
% 111.64/16.17 | GROUND_INST: instantiating (2) with all_53_13, e3, e1, e3, simplifying with
% 111.64/16.17 | (1), (4) gives:
% 111.64/16.17 | (7) all_53_13 = e3
% 111.64/16.17 |
% 111.64/16.17 | COMBINE_EQS: (6), (7) imply:
% 111.64/16.17 | (8) e3 = e2
% 111.64/16.17 |
% 111.64/16.17 | REDUCE: (3), (8) imply:
% 111.64/16.17 | (9) $false
% 111.64/16.17 |
% 111.64/16.17 | CLOSE: (9) is inconsistent.
% 111.64/16.17 |
% 111.64/16.17 End of proof
% 111.64/16.17
% 111.64/16.17 Sub-proof #178 shows that the following formulas are inconsistent:
% 111.64/16.17 ----------------------------------------------------------------
% 111.64/16.17 (1) ~ (all_53_15 = e3)
% 111.64/16.17 (2) ~ (all_53_7 = e3)
% 111.64/16.17 (3) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 111.64/16.17 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 111.64/16.17 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 111.64/16.17 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 111.64/16.17 $i(all_52_16))
% 111.64/16.17 (4) op(e3, e2) = all_53_15
% 111.64/16.17 (5) op(e1, e2) = all_53_7
% 111.64/16.17 (6) ~ (e3 = e1)
% 111.64/16.17 (7) ~ (e3 = e0)
% 111.64/16.17 (8) (all_57_92 = e3 & op(e3, e2) = e3) | (all_57_93 = e3 & op(e2, e2) = e3) |
% 111.64/16.17 (all_57_94 = e3 & op(e1, e2) = e3) | (all_57_95 = e3 & op(e0, e2) = e3)
% 111.64/16.17 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.17 (10) ~ (all_53_7 = e1)
% 111.64/16.17 (11) op(e2, e2) = e1
% 111.64/16.17 (12) op(e0, e2) = all_53_3
% 111.64/16.17
% 111.64/16.17 Begin of proof
% 111.64/16.17 |
% 111.64/16.17 | BETA: splitting (3) gives:
% 111.64/16.17 |
% 111.64/16.17 | Case 1:
% 111.64/16.17 | |
% 111.64/16.17 | | (13) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3)
% 111.64/16.17 | | = all_52_12 & $i(all_52_12)
% 111.64/16.17 | |
% 111.64/16.17 | | ALPHA: (13) implies:
% 111.64/16.17 | | (14) op(e3, e2) = e3
% 111.64/16.17 | |
% 111.64/16.17 | | REF_CLOSE: (1), (4), (9), (14) are inconsistent by sub-proof #214.
% 111.64/16.17 | |
% 111.64/16.17 | Case 2:
% 111.64/16.17 | |
% 111.64/16.17 | | (15) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 111.64/16.17 | | op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~ (all_52_16
% 111.64/16.17 | | = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 111.64/16.17 | | $i(all_52_16))
% 111.64/16.17 | |
% 111.64/16.17 | | BETA: splitting (15) gives:
% 111.64/16.17 | |
% 111.64/16.17 | | Case 1:
% 111.64/16.17 | | |
% 111.64/16.17 | | | (16) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 111.64/16.17 | | | op(e1, e2) = e1 & $i(all_52_14)
% 111.64/16.17 | | |
% 111.64/16.17 | | | ALPHA: (16) implies:
% 111.64/16.17 | | | (17) op(e1, e2) = e1
% 111.64/16.17 | | |
% 111.64/16.17 | | | REF_CLOSE: (5), (9), (10), (17) are inconsistent by sub-proof #233.
% 111.64/16.17 | | |
% 111.64/16.17 | | Case 2:
% 111.64/16.17 | | |
% 111.64/16.17 | | | (18) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 &
% 111.64/16.17 | | | op(e0, e2) = e0 & $i(all_52_16)
% 111.64/16.17 | | |
% 111.64/16.17 | | | ALPHA: (18) implies:
% 111.64/16.17 | | | (19) op(e0, e2) = e0
% 111.64/16.17 | | |
% 111.64/16.17 | | | BETA: splitting (8) gives:
% 111.64/16.17 | | |
% 111.64/16.17 | | | Case 1:
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | (20) (all_57_92 = e3 & op(e3, e2) = e3) | (all_57_93 = e3 & op(e2,
% 111.64/16.17 | | | | e2) = e3)
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | BETA: splitting (20) gives:
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | Case 1:
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | (21) all_57_92 = e3 & op(e3, e2) = e3
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | ALPHA: (21) implies:
% 111.64/16.17 | | | | | (22) op(e3, e2) = e3
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | REF_CLOSE: (1), (4), (9), (22) are inconsistent by sub-proof #214.
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | Case 2:
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | (23) all_57_93 = e3 & op(e2, e2) = e3
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | ALPHA: (23) implies:
% 111.64/16.17 | | | | | (24) op(e2, e2) = e3
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | REF_CLOSE: (6), (9), (11), (24) are inconsistent by sub-proof #197.
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | End of split
% 111.64/16.17 | | | |
% 111.64/16.17 | | | Case 2:
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | (25) (all_57_94 = e3 & op(e1, e2) = e3) | (all_57_95 = e3 & op(e0,
% 111.64/16.17 | | | | e2) = e3)
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | BETA: splitting (25) gives:
% 111.64/16.17 | | | |
% 111.64/16.17 | | | | Case 1:
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | (26) all_57_94 = e3 & op(e1, e2) = e3
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | ALPHA: (26) implies:
% 111.64/16.17 | | | | | (27) op(e1, e2) = e3
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | REF_CLOSE: (2), (5), (9), (27) are inconsistent by sub-proof #179.
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | Case 2:
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | (28) all_57_95 = e3 & op(e0, e2) = e3
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | ALPHA: (28) implies:
% 111.64/16.17 | | | | | (29) op(e0, e2) = e3
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | GROUND_INST: instantiating (9) with all_53_3, e0, e2, e0, simplifying
% 111.64/16.17 | | | | | with (12), (19) gives:
% 111.64/16.17 | | | | | (30) all_53_3 = e0
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | GROUND_INST: instantiating (9) with all_53_3, e3, e2, e0, simplifying
% 111.64/16.17 | | | | | with (12), (29) gives:
% 111.64/16.17 | | | | | (31) all_53_3 = e3
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | COMBINE_EQS: (30), (31) imply:
% 111.64/16.17 | | | | | (32) e3 = e0
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | REDUCE: (7), (32) imply:
% 111.64/16.17 | | | | | (33) $false
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | | CLOSE: (33) is inconsistent.
% 111.64/16.17 | | | | |
% 111.64/16.17 | | | | End of split
% 111.64/16.17 | | | |
% 111.64/16.17 | | | End of split
% 111.64/16.17 | | |
% 111.64/16.17 | | End of split
% 111.64/16.17 | |
% 111.64/16.17 | End of split
% 111.64/16.17 |
% 111.64/16.17 End of proof
% 111.64/16.17
% 111.64/16.17 Sub-proof #179 shows that the following formulas are inconsistent:
% 111.64/16.17 ----------------------------------------------------------------
% 111.64/16.18 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.18 (2) op(e1, e2) = all_53_7
% 111.64/16.18 (3) op(e1, e2) = e3
% 111.64/16.18 (4) ~ (all_53_7 = e3)
% 111.64/16.18
% 111.64/16.18 Begin of proof
% 111.64/16.18 |
% 111.64/16.18 | GROUND_INST: instantiating (1) with all_53_7, e3, e2, e1, simplifying with
% 111.64/16.18 | (2), (3) gives:
% 111.64/16.18 | (5) all_53_7 = e3
% 111.64/16.18 |
% 111.64/16.18 | REDUCE: (4), (5) imply:
% 111.64/16.18 | (6) $false
% 111.64/16.18 |
% 111.64/16.18 | CLOSE: (6) is inconsistent.
% 111.64/16.18 |
% 111.64/16.18 End of proof
% 111.64/16.18
% 111.64/16.18 Sub-proof #180 shows that the following formulas are inconsistent:
% 111.64/16.18 ----------------------------------------------------------------
% 111.64/16.18 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.18 (2) op(e3, e0) = all_53_12
% 111.64/16.18 (3) op(e3, e0) = e3
% 111.64/16.18 (4) ~ (all_53_12 = e3)
% 111.64/16.18
% 111.64/16.18 Begin of proof
% 111.64/16.18 |
% 111.64/16.18 | GROUND_INST: instantiating (1) with all_53_12, e3, e0, e3, simplifying with
% 111.64/16.18 | (2), (3) gives:
% 111.64/16.18 | (5) all_53_12 = e3
% 111.64/16.18 |
% 111.64/16.18 | REDUCE: (4), (5) imply:
% 111.64/16.18 | (6) $false
% 111.64/16.18 |
% 111.64/16.18 | CLOSE: (6) is inconsistent.
% 111.64/16.18 |
% 111.64/16.18 End of proof
% 111.64/16.18
% 111.64/16.18 Sub-proof #181 shows that the following formulas are inconsistent:
% 111.64/16.18 ----------------------------------------------------------------
% 111.64/16.18 (1) ~ (all_53_9 = e1)
% 111.64/16.18 (2) ~ (all_53_1 = e0)
% 111.64/16.18 (3) ~ (all_32_0 = e2)
% 111.64/16.18 (4) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 111.64/16.18 (5) ~ (all_32_0 = e1)
% 111.64/16.18 (6) ~ (all_53_9 = all_53_13)
% 111.64/16.18 (7) ~ (all_53_8 = e1)
% 111.64/16.18 (8) all_55_12 = all_32_0
% 111.64/16.18 (9) op(e0, e1) = all_53_1
% 111.64/16.18 (10) op(e2, e1) = all_53_9
% 111.64/16.18 (11) ~ (all_32_0 = e3)
% 111.64/16.18 (12) all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 111.64/16.18 (13) op(e2, e0) = all_53_8
% 111.64/16.18 (14) op(e3, e1) = all_53_13
% 111.64/16.18 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.18 (16) ~ (all_53_8 = all_32_0)
% 111.64/16.18 (17) all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 111.64/16.18 (18) ~ (all_53_8 = e3)
% 111.64/16.18 (19) ~ (all_53_9 = e0)
% 111.64/16.18 (20) all_55_8 = all_53_8
% 111.64/16.18 (21) all_55_9 = all_53_9
% 111.64/16.18 (22) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.64/16.18 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 111.64/16.18 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 111.64/16.18 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.64/16.18 $i(all_52_10))
% 111.64/16.18 (23) ~ (all_53_8 = all_53_9)
% 111.64/16.18
% 111.64/16.18 Begin of proof
% 111.64/16.18 |
% 111.64/16.18 | BETA: splitting (12) gives:
% 111.64/16.18 |
% 111.64/16.18 | Case 1:
% 111.64/16.18 | |
% 111.64/16.18 | | (24) all_55_12 = e3
% 111.64/16.18 | |
% 111.64/16.18 | | REF_CLOSE: (8), (11), (24) are inconsistent by sub-proof #190.
% 111.64/16.18 | |
% 111.64/16.18 | Case 2:
% 111.64/16.18 | |
% 111.64/16.18 | | (25) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 111.64/16.18 | |
% 111.64/16.18 | | BETA: splitting (25) gives:
% 111.64/16.18 | |
% 111.64/16.18 | | Case 1:
% 111.64/16.18 | | |
% 111.64/16.18 | | | (26) all_55_12 = e2
% 111.64/16.18 | | |
% 111.64/16.18 | | | REF_CLOSE: (3), (8), (26) are inconsistent by sub-proof #189.
% 111.64/16.18 | | |
% 111.64/16.18 | | Case 2:
% 111.64/16.18 | | |
% 111.64/16.18 | | | (27) all_55_12 = e1 | all_55_12 = e0
% 111.64/16.18 | | |
% 111.64/16.18 | | | BETA: splitting (27) gives:
% 111.64/16.18 | | |
% 111.64/16.18 | | | Case 1:
% 111.64/16.18 | | | |
% 111.64/16.18 | | | | (28) all_55_12 = e1
% 111.64/16.18 | | | |
% 111.64/16.18 | | | | REF_CLOSE: (5), (8), (28) are inconsistent by sub-proof #188.
% 111.64/16.18 | | | |
% 111.64/16.18 | | | Case 2:
% 111.64/16.18 | | | |
% 111.64/16.18 | | | | (29) all_55_12 = e0
% 111.64/16.18 | | | |
% 111.64/16.18 | | | | COMBINE_EQS: (8), (29) imply:
% 111.64/16.18 | | | | (30) all_32_0 = e0
% 111.64/16.18 | | | |
% 111.64/16.18 | | | | SIMP: (30) implies:
% 111.64/16.18 | | | | (31) all_32_0 = e0
% 111.64/16.18 | | | |
% 111.64/16.18 | | | | REDUCE: (16), (31) imply:
% 111.64/16.18 | | | | (32) ~ (all_53_8 = e0)
% 111.64/16.18 | | | |
% 111.64/16.18 | | | | BETA: splitting (17) gives:
% 111.64/16.18 | | | |
% 111.64/16.18 | | | | Case 1:
% 111.64/16.18 | | | | |
% 111.64/16.18 | | | | | (33) all_55_8 = e3
% 111.64/16.18 | | | | |
% 111.64/16.18 | | | | | REF_CLOSE: (18), (20), (33) are inconsistent by sub-proof #187.
% 111.64/16.18 | | | | |
% 111.64/16.18 | | | | Case 2:
% 111.64/16.18 | | | | |
% 111.64/16.18 | | | | | (34) all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 111.64/16.18 | | | | |
% 111.64/16.18 | | | | | BETA: splitting (34) gives:
% 111.64/16.18 | | | | |
% 111.64/16.18 | | | | | Case 1:
% 111.64/16.18 | | | | | |
% 111.64/16.18 | | | | | | (35) all_55_8 = e2
% 111.64/16.18 | | | | | |
% 111.64/16.18 | | | | | | COMBINE_EQS: (20), (35) imply:
% 111.64/16.18 | | | | | | (36) all_53_8 = e2
% 111.64/16.18 | | | | | |
% 111.64/16.18 | | | | | | SIMP: (36) implies:
% 111.64/16.18 | | | | | | (37) all_53_8 = e2
% 111.64/16.18 | | | | | |
% 111.64/16.18 | | | | | | REF_CLOSE: (1), (2), (4), (6), (9), (10), (13), (14), (15), (19),
% 111.64/16.18 | | | | | | (21), (22), (23), (37) are inconsistent by sub-proof
% 111.64/16.18 | | | | | | #183.
% 111.64/16.18 | | | | | |
% 111.64/16.18 | | | | | Case 2:
% 111.64/16.18 | | | | | |
% 111.64/16.18 | | | | | | (38) all_55_8 = e1 | all_55_8 = e0
% 111.64/16.18 | | | | | |
% 111.64/16.18 | | | | | | REF_CLOSE: (7), (20), (32), (38) are inconsistent by sub-proof #182.
% 111.64/16.18 | | | | | |
% 111.64/16.18 | | | | | End of split
% 111.64/16.18 | | | | |
% 111.64/16.18 | | | | End of split
% 111.64/16.18 | | | |
% 111.64/16.18 | | | End of split
% 111.64/16.18 | | |
% 111.64/16.18 | | End of split
% 111.64/16.18 | |
% 111.64/16.18 | End of split
% 111.64/16.18 |
% 111.64/16.18 End of proof
% 111.64/16.18
% 111.64/16.18 Sub-proof #182 shows that the following formulas are inconsistent:
% 111.64/16.18 ----------------------------------------------------------------
% 111.64/16.18 (1) all_55_8 = e1 | all_55_8 = e0
% 111.64/16.18 (2) all_55_8 = all_53_8
% 111.64/16.18 (3) ~ (all_53_8 = e1)
% 111.64/16.18 (4) ~ (all_53_8 = e0)
% 111.64/16.18
% 111.64/16.18 Begin of proof
% 111.64/16.18 |
% 111.64/16.18 | BETA: splitting (1) gives:
% 111.64/16.18 |
% 111.64/16.18 | Case 1:
% 111.64/16.18 | |
% 111.64/16.18 | | (5) all_55_8 = e1
% 111.64/16.18 | |
% 111.64/16.18 | | COMBINE_EQS: (2), (5) imply:
% 111.64/16.18 | | (6) all_53_8 = e1
% 111.64/16.18 | |
% 111.64/16.18 | | SIMP: (6) implies:
% 111.64/16.18 | | (7) all_53_8 = e1
% 111.64/16.18 | |
% 111.64/16.18 | | REDUCE: (3), (7) imply:
% 111.64/16.18 | | (8) $false
% 111.64/16.18 | |
% 111.64/16.18 | | CLOSE: (8) is inconsistent.
% 111.64/16.18 | |
% 111.64/16.18 | Case 2:
% 111.64/16.18 | |
% 111.64/16.18 | | (9) all_55_8 = e0
% 111.64/16.18 | |
% 111.64/16.18 | | COMBINE_EQS: (2), (9) imply:
% 111.64/16.18 | | (10) all_53_8 = e0
% 111.64/16.18 | |
% 111.64/16.18 | | SIMP: (10) implies:
% 111.64/16.18 | | (11) all_53_8 = e0
% 111.64/16.18 | |
% 111.64/16.18 | | REDUCE: (4), (11) imply:
% 111.64/16.18 | | (12) $false
% 111.64/16.18 | |
% 111.64/16.18 | | CLOSE: (12) is inconsistent.
% 111.64/16.18 | |
% 111.64/16.18 | End of split
% 111.64/16.18 |
% 111.64/16.18 End of proof
% 111.64/16.18
% 111.64/16.18 Sub-proof #183 shows that the following formulas are inconsistent:
% 111.64/16.18 ----------------------------------------------------------------
% 111.64/16.18 (1) ~ (all_53_9 = e1)
% 111.64/16.18 (2) ~ (all_53_1 = e0)
% 111.64/16.18 (3) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 111.64/16.18 (4) all_53_8 = e2
% 111.64/16.18 (5) ~ (all_53_9 = all_53_13)
% 111.64/16.18 (6) op(e0, e1) = all_53_1
% 111.64/16.18 (7) op(e2, e1) = all_53_9
% 111.64/16.18 (8) op(e2, e0) = all_53_8
% 111.64/16.18 (9) op(e3, e1) = all_53_13
% 111.64/16.18 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.64/16.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.64/16.18 (11) ~ (all_53_9 = e0)
% 111.64/16.18 (12) all_55_9 = all_53_9
% 111.64/16.18 (13) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.64/16.18 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 111.64/16.18 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 111.64/16.18 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 111.64/16.18 $i(all_52_10))
% 111.64/16.18 (14) ~ (all_53_8 = all_53_9)
% 111.64/16.18
% 111.64/16.18 Begin of proof
% 111.64/16.18 |
% 111.64/16.18 | REDUCE: (4), (14) imply:
% 111.64/16.18 | (15) ~ (all_53_9 = e2)
% 111.64/16.18 |
% 111.64/16.18 | SIMP: (15) implies:
% 111.64/16.18 | (16) ~ (all_53_9 = e2)
% 111.64/16.18 |
% 111.64/16.18 | REDUCE: (4), (8) imply:
% 111.64/16.18 | (17) op(e2, e0) = e2
% 111.64/16.18 |
% 111.64/16.18 | BETA: splitting (13) gives:
% 111.64/16.18 |
% 111.64/16.18 | Case 1:
% 111.64/16.18 | |
% 111.64/16.18 | | (18) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 111.64/16.18 | | all_52_6 & $i(all_52_6)
% 111.64/16.18 | |
% 112.17/16.18 | | ALPHA: (18) implies:
% 112.17/16.18 | | (19) op(e3, e1) = e3
% 112.17/16.18 | |
% 112.17/16.18 | | BETA: splitting (3) gives:
% 112.17/16.18 | |
% 112.17/16.18 | | Case 1:
% 112.17/16.18 | | |
% 112.17/16.18 | | | (20) all_55_9 = e3
% 112.17/16.18 | | |
% 112.17/16.18 | | | COMBINE_EQS: (12), (20) imply:
% 112.17/16.18 | | | (21) all_53_9 = e3
% 112.17/16.18 | | |
% 112.17/16.18 | | | SIMP: (21) implies:
% 112.17/16.18 | | | (22) all_53_9 = e3
% 112.17/16.18 | | |
% 112.17/16.18 | | | REDUCE: (5), (22) imply:
% 112.17/16.18 | | | (23) ~ (all_53_13 = e3)
% 112.17/16.18 | | |
% 112.17/16.18 | | | SIMP: (23) implies:
% 112.17/16.18 | | | (24) ~ (all_53_13 = e3)
% 112.17/16.18 | | |
% 112.17/16.18 | | | REF_CLOSE: (9), (10), (19), (24) are inconsistent by sub-proof #232.
% 112.17/16.18 | | |
% 112.17/16.18 | | Case 2:
% 112.17/16.18 | | |
% 112.17/16.18 | | | (25) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 112.17/16.18 | | |
% 112.17/16.18 | | | REF_CLOSE: (1), (7), (8), (10), (11), (12), (14), (17), (25) are
% 112.17/16.18 | | | inconsistent by sub-proof #184.
% 112.17/16.18 | | |
% 112.17/16.18 | | End of split
% 112.17/16.18 | |
% 112.17/16.18 | Case 2:
% 112.17/16.18 | |
% 112.17/16.18 | | (26) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 112.17/16.18 | | all_52_8 & $i(all_52_8)) | (all_52_11 = e0 & ~ (all_52_10 = e1) &
% 112.17/16.18 | | op(e1, e0) = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 112.17/16.18 | |
% 112.17/16.18 | | REF_CLOSE: (2), (6), (7), (10), (16), (26) are inconsistent by sub-proof
% 112.17/16.18 | | #229.
% 112.17/16.18 | |
% 112.17/16.18 | End of split
% 112.17/16.18 |
% 112.17/16.18 End of proof
% 112.17/16.18
% 112.17/16.18 Sub-proof #184 shows that the following formulas are inconsistent:
% 112.17/16.18 ----------------------------------------------------------------
% 112.17/16.18 (1) ~ (all_53_9 = e1)
% 112.17/16.18 (2) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 112.17/16.18 (3) op(e2, e0) = e2
% 112.17/16.18 (4) op(e2, e1) = all_53_9
% 112.17/16.18 (5) op(e2, e0) = all_53_8
% 112.17/16.18 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.17/16.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.17/16.18 (7) ~ (all_53_9 = e0)
% 112.17/16.18 (8) all_55_9 = all_53_9
% 112.17/16.18 (9) ~ (all_53_8 = all_53_9)
% 112.17/16.18
% 112.17/16.18 Begin of proof
% 112.17/16.18 |
% 112.17/16.18 | BETA: splitting (2) gives:
% 112.17/16.18 |
% 112.17/16.18 | Case 1:
% 112.17/16.18 | |
% 112.17/16.18 | | (10) all_55_9 = e2
% 112.17/16.18 | |
% 112.17/16.18 | | COMBINE_EQS: (8), (10) imply:
% 112.17/16.18 | | (11) all_53_9 = e2
% 112.17/16.18 | |
% 112.17/16.18 | | REDUCE: (4), (11) imply:
% 112.17/16.18 | | (12) op(e2, e1) = e2
% 112.17/16.18 | |
% 112.17/16.18 | | REF_CLOSE: (3), (4), (5), (6), (9), (12) are inconsistent by sub-proof #186.
% 112.17/16.18 | |
% 112.17/16.18 | Case 2:
% 112.17/16.18 | |
% 112.17/16.18 | | (13) all_55_9 = e1 | all_55_9 = e0
% 112.17/16.18 | |
% 112.17/16.18 | | REF_CLOSE: (1), (7), (8), (13) are inconsistent by sub-proof #185.
% 112.17/16.18 | |
% 112.17/16.18 | End of split
% 112.17/16.18 |
% 112.17/16.18 End of proof
% 112.17/16.18
% 112.17/16.18 Sub-proof #185 shows that the following formulas are inconsistent:
% 112.17/16.18 ----------------------------------------------------------------
% 112.17/16.18 (1) all_55_9 = e1 | all_55_9 = e0
% 112.17/16.18 (2) all_55_9 = all_53_9
% 112.17/16.18 (3) ~ (all_53_9 = e1)
% 112.17/16.18 (4) ~ (all_53_9 = e0)
% 112.17/16.18
% 112.17/16.18 Begin of proof
% 112.17/16.18 |
% 112.17/16.18 | BETA: splitting (1) gives:
% 112.17/16.18 |
% 112.17/16.18 | Case 1:
% 112.17/16.18 | |
% 112.17/16.18 | | (5) all_55_9 = e1
% 112.17/16.18 | |
% 112.17/16.18 | | COMBINE_EQS: (2), (5) imply:
% 112.17/16.18 | | (6) all_53_9 = e1
% 112.17/16.18 | |
% 112.17/16.18 | | REDUCE: (3), (6) imply:
% 112.17/16.18 | | (7) $false
% 112.17/16.18 | |
% 112.17/16.18 | | CLOSE: (7) is inconsistent.
% 112.17/16.18 | |
% 112.17/16.18 | Case 2:
% 112.17/16.18 | |
% 112.17/16.18 | | (8) all_55_9 = e0
% 112.17/16.18 | |
% 112.17/16.18 | | COMBINE_EQS: (2), (8) imply:
% 112.17/16.18 | | (9) all_53_9 = e0
% 112.17/16.18 | |
% 112.17/16.18 | | REDUCE: (4), (9) imply:
% 112.17/16.18 | | (10) $false
% 112.17/16.18 | |
% 112.17/16.18 | | CLOSE: (10) is inconsistent.
% 112.17/16.18 | |
% 112.17/16.18 | End of split
% 112.17/16.18 |
% 112.17/16.18 End of proof
% 112.17/16.18
% 112.17/16.18 Sub-proof #186 shows that the following formulas are inconsistent:
% 112.17/16.18 ----------------------------------------------------------------
% 112.17/16.18 (1) op(e2, e1) = e2
% 112.17/16.18 (2) op(e2, e0) = e2
% 112.17/16.18 (3) op(e2, e1) = all_53_9
% 112.17/16.18 (4) op(e2, e0) = all_53_8
% 112.17/16.18 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.17/16.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.17/16.18 (6) ~ (all_53_8 = all_53_9)
% 112.17/16.18
% 112.17/16.18 Begin of proof
% 112.17/16.18 |
% 112.17/16.18 | GROUND_INST: instantiating (5) with all_53_8, e2, e0, e2, simplifying with
% 112.17/16.18 | (2), (4) gives:
% 112.17/16.18 | (7) all_53_8 = e2
% 112.17/16.18 |
% 112.17/16.18 | GROUND_INST: instantiating (5) with all_53_9, e2, e1, e2, simplifying with
% 112.17/16.18 | (1), (3) gives:
% 112.17/16.18 | (8) all_53_9 = e2
% 112.17/16.18 |
% 112.17/16.18 | REDUCE: (6), (7), (8) imply:
% 112.17/16.18 | (9) $false
% 112.17/16.18 |
% 112.17/16.18 | CLOSE: (9) is inconsistent.
% 112.17/16.18 |
% 112.17/16.18 End of proof
% 112.17/16.18
% 112.17/16.18 Sub-proof #187 shows that the following formulas are inconsistent:
% 112.17/16.18 ----------------------------------------------------------------
% 112.17/16.18 (1) all_55_8 = all_53_8
% 112.17/16.18 (2) all_55_8 = e3
% 112.17/16.18 (3) ~ (all_53_8 = e3)
% 112.17/16.18
% 112.17/16.18 Begin of proof
% 112.17/16.18 |
% 112.17/16.18 | COMBINE_EQS: (1), (2) imply:
% 112.17/16.18 | (4) all_53_8 = e3
% 112.17/16.18 |
% 112.17/16.18 | SIMP: (4) implies:
% 112.17/16.19 | (5) all_53_8 = e3
% 112.17/16.19 |
% 112.17/16.19 | REDUCE: (3), (5) imply:
% 112.17/16.19 | (6) $false
% 112.17/16.19 |
% 112.17/16.19 | CLOSE: (6) is inconsistent.
% 112.17/16.19 |
% 112.17/16.19 End of proof
% 112.17/16.19
% 112.17/16.19 Sub-proof #188 shows that the following formulas are inconsistent:
% 112.17/16.19 ----------------------------------------------------------------
% 112.17/16.19 (1) all_55_12 = all_32_0
% 112.17/16.19 (2) all_55_12 = e1
% 112.17/16.19 (3) ~ (all_32_0 = e1)
% 112.17/16.19
% 112.17/16.19 Begin of proof
% 112.17/16.19 |
% 112.17/16.19 | COMBINE_EQS: (1), (2) imply:
% 112.17/16.19 | (4) all_32_0 = e1
% 112.17/16.19 |
% 112.17/16.19 | SIMP: (4) implies:
% 112.17/16.19 | (5) all_32_0 = e1
% 112.17/16.19 |
% 112.17/16.19 | REDUCE: (3), (5) imply:
% 112.17/16.19 | (6) $false
% 112.17/16.19 |
% 112.17/16.19 | CLOSE: (6) is inconsistent.
% 112.17/16.19 |
% 112.17/16.19 End of proof
% 112.17/16.19
% 112.17/16.19 Sub-proof #189 shows that the following formulas are inconsistent:
% 112.17/16.19 ----------------------------------------------------------------
% 112.17/16.19 (1) all_55_12 = all_32_0
% 112.17/16.19 (2) all_55_12 = e2
% 112.17/16.19 (3) ~ (all_32_0 = e2)
% 112.17/16.19
% 112.17/16.19 Begin of proof
% 112.17/16.19 |
% 112.17/16.19 | COMBINE_EQS: (1), (2) imply:
% 112.17/16.19 | (4) all_32_0 = e2
% 112.17/16.19 |
% 112.17/16.19 | SIMP: (4) implies:
% 112.17/16.19 | (5) all_32_0 = e2
% 112.17/16.19 |
% 112.17/16.19 | REDUCE: (3), (5) imply:
% 112.17/16.19 | (6) $false
% 112.17/16.19 |
% 112.17/16.19 | CLOSE: (6) is inconsistent.
% 112.17/16.19 |
% 112.17/16.19 End of proof
% 112.17/16.19
% 112.17/16.19 Sub-proof #190 shows that the following formulas are inconsistent:
% 112.17/16.19 ----------------------------------------------------------------
% 112.17/16.19 (1) all_55_12 = all_32_0
% 112.17/16.19 (2) all_55_12 = e3
% 112.17/16.19 (3) ~ (all_32_0 = e3)
% 112.17/16.19
% 112.17/16.19 Begin of proof
% 112.17/16.19 |
% 112.17/16.19 | COMBINE_EQS: (1), (2) imply:
% 112.17/16.19 | (4) all_32_0 = e3
% 112.17/16.19 |
% 112.17/16.19 | SIMP: (4) implies:
% 112.17/16.19 | (5) all_32_0 = e3
% 112.17/16.19 |
% 112.17/16.19 | REDUCE: (3), (5) imply:
% 112.17/16.19 | (6) $false
% 112.17/16.19 |
% 112.17/16.19 | CLOSE: (6) is inconsistent.
% 112.17/16.19 |
% 112.17/16.19 End of proof
% 112.17/16.19
% 112.17/16.19 Sub-proof #191 shows that the following formulas are inconsistent:
% 112.17/16.19 ----------------------------------------------------------------
% 112.17/16.19 (1) all_55_15 = all_4_2
% 112.17/16.19 (2) ~ (all_4_2 = e1)
% 112.17/16.19 (3) ~ (all_4_2 = e0)
% 112.17/16.19 (4) ~ (all_4_2 = e2)
% 112.17/16.19 (5) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 112.17/16.19
% 112.17/16.19 Begin of proof
% 112.17/16.19 |
% 112.17/16.19 | BETA: splitting (5) gives:
% 112.17/16.19 |
% 112.17/16.19 | Case 1:
% 112.17/16.19 | |
% 112.17/16.19 | | (6) all_55_15 = e2
% 112.17/16.19 | |
% 112.17/16.19 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #193.
% 112.17/16.19 | |
% 112.17/16.19 | Case 2:
% 112.17/16.19 | |
% 112.17/16.19 | | (7) all_55_15 = e1 | all_55_15 = e0
% 112.17/16.19 | |
% 112.17/16.19 | | BETA: splitting (7) gives:
% 112.17/16.19 | |
% 112.17/16.19 | | Case 1:
% 112.17/16.19 | | |
% 112.17/16.19 | | | (8) all_55_15 = e1
% 112.17/16.19 | | |
% 112.17/16.19 | | | COMBINE_EQS: (1), (8) imply:
% 112.17/16.19 | | | (9) all_4_2 = e1
% 112.17/16.19 | | |
% 112.17/16.19 | | | SIMP: (9) implies:
% 112.17/16.19 | | | (10) all_4_2 = e1
% 112.17/16.19 | | |
% 112.17/16.19 | | | REDUCE: (2), (10) imply:
% 112.17/16.19 | | | (11) $false
% 112.17/16.19 | | |
% 112.17/16.19 | | | CLOSE: (11) is inconsistent.
% 112.17/16.19 | | |
% 112.17/16.19 | | Case 2:
% 112.17/16.19 | | |
% 112.17/16.19 | | | (12) all_55_15 = e0
% 112.17/16.19 | | |
% 112.17/16.19 | | | REF_CLOSE: (1), (3), (12) are inconsistent by sub-proof #192.
% 112.17/16.19 | | |
% 112.17/16.19 | | End of split
% 112.17/16.19 | |
% 112.17/16.19 | End of split
% 112.17/16.19 |
% 112.17/16.19 End of proof
% 112.17/16.19
% 112.17/16.19 Sub-proof #192 shows that the following formulas are inconsistent:
% 112.17/16.19 ----------------------------------------------------------------
% 112.17/16.19 (1) all_55_15 = all_4_2
% 112.17/16.19 (2) all_55_15 = e0
% 112.17/16.19 (3) ~ (all_4_2 = e0)
% 112.17/16.19
% 112.17/16.19 Begin of proof
% 112.17/16.19 |
% 112.17/16.19 | COMBINE_EQS: (1), (2) imply:
% 112.17/16.19 | (4) all_4_2 = e0
% 112.17/16.19 |
% 112.17/16.19 | SIMP: (4) implies:
% 112.17/16.19 | (5) all_4_2 = e0
% 112.17/16.19 |
% 112.17/16.19 | REDUCE: (3), (5) imply:
% 112.17/16.19 | (6) $false
% 112.17/16.19 |
% 112.17/16.19 | CLOSE: (6) is inconsistent.
% 112.17/16.19 |
% 112.17/16.19 End of proof
% 112.17/16.19
% 112.17/16.19 Sub-proof #193 shows that the following formulas are inconsistent:
% 112.17/16.19 ----------------------------------------------------------------
% 112.17/16.19 (1) all_55_15 = all_4_2
% 112.17/16.19 (2) all_55_15 = e2
% 112.17/16.19 (3) ~ (all_4_2 = e2)
% 112.17/16.19
% 112.17/16.19 Begin of proof
% 112.17/16.19 |
% 112.17/16.19 | COMBINE_EQS: (1), (2) imply:
% 112.17/16.19 | (4) all_4_2 = e2
% 112.17/16.19 |
% 112.17/16.19 | SIMP: (4) implies:
% 112.17/16.19 | (5) all_4_2 = e2
% 112.17/16.19 |
% 112.17/16.19 | REDUCE: (3), (5) imply:
% 112.17/16.19 | (6) $false
% 112.17/16.19 |
% 112.17/16.19 | CLOSE: (6) is inconsistent.
% 112.17/16.19 |
% 112.17/16.19 End of proof
% 112.17/16.19
% 112.17/16.19 Sub-proof #194 shows that the following formulas are inconsistent:
% 112.17/16.19 ----------------------------------------------------------------
% 112.17/16.19 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.17/16.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.17/16.19 (2) op(e2, e0) = all_53_8
% 112.17/16.19 (3) op(e2, e0) = e3
% 112.17/16.19 (4) ~ (all_53_8 = e3)
% 112.17/16.19
% 112.17/16.19 Begin of proof
% 112.17/16.19 |
% 112.17/16.19 | GROUND_INST: instantiating (1) with all_53_8, e3, e0, e2, simplifying with
% 112.17/16.19 | (2), (3) gives:
% 112.17/16.19 | (5) all_53_8 = e3
% 112.17/16.19 |
% 112.17/16.19 | REDUCE: (4), (5) imply:
% 112.17/16.19 | (6) $false
% 112.17/16.19 |
% 112.17/16.19 | CLOSE: (6) is inconsistent.
% 112.17/16.19 |
% 112.17/16.19 End of proof
% 112.17/16.19
% 112.17/16.19 Sub-proof #195 shows that the following formulas are inconsistent:
% 112.17/16.19 ----------------------------------------------------------------
% 112.17/16.19 (1) op(e2, e1) = e2
% 112.17/16.19 (2) op(e2, e1) = all_53_9
% 112.17/16.19 (3) op(e2, e1) = e3
% 112.17/16.19 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.17/16.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.17/16.19 (5) ~ (e3 = e2)
% 112.17/16.19
% 112.17/16.19 Begin of proof
% 112.17/16.19 |
% 112.17/16.19 | GROUND_INST: instantiating (4) with all_53_9, e2, e1, e2, simplifying with
% 112.17/16.19 | (1), (2) gives:
% 112.17/16.19 | (6) all_53_9 = e2
% 112.17/16.19 |
% 112.17/16.19 | GROUND_INST: instantiating (4) with all_53_9, e3, e1, e2, simplifying with
% 112.17/16.19 | (2), (3) gives:
% 112.17/16.19 | (7) all_53_9 = e3
% 112.17/16.19 |
% 112.17/16.19 | COMBINE_EQS: (6), (7) imply:
% 112.17/16.19 | (8) e3 = e2
% 112.17/16.19 |
% 112.17/16.19 | SIMP: (8) implies:
% 112.17/16.19 | (9) e3 = e2
% 112.17/16.19 |
% 112.17/16.19 | REDUCE: (5), (9) imply:
% 112.17/16.19 | (10) $false
% 112.17/16.19 |
% 112.17/16.19 | CLOSE: (10) is inconsistent.
% 112.17/16.19 |
% 112.17/16.19 End of proof
% 112.17/16.19
% 112.17/16.19 Sub-proof #196 shows that the following formulas are inconsistent:
% 112.17/16.19 ----------------------------------------------------------------
% 112.17/16.19 (1) ~ (all_53_10 = e3)
% 112.17/16.19 (2) op(e2, e3) = all_53_10
% 112.17/16.19 (3) ~ (e3 = e1)
% 112.17/16.19 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.17/16.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.17/16.19 (5) (all_57_88 = e3 & op(e2, e3) = e3) | (all_57_89 = e3 & op(e2, e2) = e3)
% 112.17/16.19 (6) op(e2, e2) = e1
% 112.17/16.19
% 112.17/16.19 Begin of proof
% 112.17/16.19 |
% 112.17/16.19 | BETA: splitting (5) gives:
% 112.17/16.19 |
% 112.17/16.19 | Case 1:
% 112.17/16.19 | |
% 112.17/16.19 | | (7) all_57_88 = e3 & op(e2, e3) = e3
% 112.17/16.19 | |
% 112.17/16.19 | | ALPHA: (7) implies:
% 112.17/16.19 | | (8) op(e2, e3) = e3
% 112.17/16.19 | |
% 112.17/16.19 | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #198.
% 112.17/16.19 | |
% 112.17/16.19 | Case 2:
% 112.17/16.19 | |
% 112.17/16.19 | | (9) all_57_89 = e3 & op(e2, e2) = e3
% 112.17/16.19 | |
% 112.17/16.19 | | ALPHA: (9) implies:
% 112.17/16.19 | | (10) op(e2, e2) = e3
% 112.17/16.19 | |
% 112.17/16.19 | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #197.
% 112.17/16.19 | |
% 112.17/16.19 | End of split
% 112.17/16.19 |
% 112.17/16.19 End of proof
% 112.17/16.19
% 112.17/16.19 Sub-proof #197 shows that the following formulas are inconsistent:
% 112.17/16.19 ----------------------------------------------------------------
% 112.17/16.19 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.17/16.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.17/16.19 (2) op(e2, e2) = e3
% 112.17/16.19 (3) op(e2, e2) = e1
% 112.17/16.19 (4) ~ (e3 = e1)
% 112.17/16.19
% 112.17/16.19 Begin of proof
% 112.17/16.19 |
% 112.17/16.19 | GROUND_INST: instantiating (1) with e3, e1, e2, e2, simplifying with (2), (3)
% 112.17/16.19 | gives:
% 112.17/16.19 | (5) e3 = e1
% 112.17/16.19 |
% 112.17/16.19 | REDUCE: (4), (5) imply:
% 112.17/16.19 | (6) $false
% 112.17/16.19 |
% 112.17/16.19 | CLOSE: (6) is inconsistent.
% 112.17/16.19 |
% 112.17/16.19 End of proof
% 112.17/16.19
% 112.17/16.19 Sub-proof #198 shows that the following formulas are inconsistent:
% 112.17/16.19 ----------------------------------------------------------------
% 112.17/16.19 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.17/16.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.17/16.19 (2) op(e2, e3) = all_53_10
% 112.17/16.19 (3) op(e2, e3) = e3
% 112.17/16.19 (4) ~ (all_53_10 = e3)
% 112.17/16.19
% 112.17/16.19 Begin of proof
% 112.17/16.19 |
% 112.17/16.19 | GROUND_INST: instantiating (1) with all_53_10, e3, e3, e2, simplifying with
% 112.17/16.19 | (2), (3) gives:
% 112.17/16.19 | (5) all_53_10 = e3
% 112.17/16.19 |
% 112.17/16.19 | REDUCE: (4), (5) imply:
% 112.17/16.19 | (6) $false
% 112.17/16.19 |
% 112.17/16.19 | CLOSE: (6) is inconsistent.
% 112.17/16.19 |
% 112.17/16.19 End of proof
% 112.17/16.19
% 112.17/16.19 Sub-proof #199 shows that the following formulas are inconsistent:
% 112.17/16.19 ----------------------------------------------------------------
% 112.17/16.19 (1) (all_57_96 = e0 & op(e3, e3) = e0) | (all_57_97 = e0 & op(e3, e2) = e0) |
% 112.17/16.19 (all_57_98 = e0 & op(e3, e1) = e0) | (all_57_99 = e0 & op(e3, e0) = e0)
% 112.17/16.19 (2) ~ (all_6_2 = e2)
% 112.17/16.19 (3) ~ (all_53_15 = e1)
% 112.17/16.19 (4) ~ (all_53_3 = all_53_15)
% 112.17/16.19 (5) op(e3, e0) = all_53_12
% 112.17/16.19 (6) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 112.17/16.19 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 112.17/16.19 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 112.17/16.19 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 112.17/16.19 $i(all_52_16))
% 112.17/16.19 (7) op(e3, e2) = all_53_15
% 112.17/16.19 (8) ~ (all_53_12 = all_6_2)
% 112.17/16.19 (9) op(e1, e2) = all_53_7
% 112.17/16.19 (10) ~ (all_6_2 = e3)
% 112.17/16.19 (11) ~ (all_4_2 = e0)
% 112.17/16.19 (12) ~ (all_53_3 = e1)
% 112.17/16.19 (13) (all_57_76 = e1 & op(e3, e2) = e1) | (all_57_77 = e1 & op(e2, e2) = e1)
% 112.17/16.19 | (all_57_78 = e1 & op(e1, e2) = e1) | (all_57_79 = e1 & op(e0, e2) =
% 112.17/16.19 e1)
% 112.17/16.19 (14) all_55_0 = all_6_2
% 112.17/16.19 (15) op(e3, e1) = all_53_13
% 112.17/16.19 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.17/16.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.17/16.19 (17) ~ (all_53_13 = e0)
% 112.17/16.19 (18) ~ (all_53_7 = e1)
% 112.17/16.19 (19) all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 112.17/16.19 (20) ~ (all_6_2 = e1)
% 112.17/16.19 (21) op(e3, e3) = all_4_2
% 112.17/16.19 (22) op(e0, e2) = all_53_3
% 112.17/16.19
% 112.17/16.19 Begin of proof
% 112.17/16.19 |
% 112.17/16.19 | BETA: splitting (19) gives:
% 112.17/16.19 |
% 112.17/16.19 | Case 1:
% 112.17/16.19 | |
% 112.17/16.19 | | (23) all_55_0 = e3
% 112.17/16.19 | |
% 112.17/16.19 | | COMBINE_EQS: (14), (23) imply:
% 112.17/16.19 | | (24) all_6_2 = e3
% 112.17/16.19 | |
% 112.17/16.19 | | REDUCE: (10), (24) imply:
% 112.17/16.19 | | (25) $false
% 112.17/16.19 | |
% 112.17/16.19 | | CLOSE: (25) is inconsistent.
% 112.17/16.19 | |
% 112.17/16.19 | Case 2:
% 112.17/16.19 | |
% 112.17/16.19 | | (26) ~ (all_55_0 = e3)
% 112.17/16.19 | | (27) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 112.17/16.19 | |
% 112.17/16.19 | | BETA: splitting (27) gives:
% 112.17/16.19 | |
% 112.17/16.19 | | Case 1:
% 112.17/16.19 | | |
% 112.17/16.19 | | | (28) all_55_0 = e2
% 112.17/16.19 | | |
% 112.17/16.19 | | | COMBINE_EQS: (14), (28) imply:
% 112.17/16.19 | | | (29) all_6_2 = e2
% 112.17/16.19 | | |
% 112.17/16.19 | | | REDUCE: (2), (29) imply:
% 112.17/16.19 | | | (30) $false
% 112.17/16.19 | | |
% 112.17/16.19 | | | CLOSE: (30) is inconsistent.
% 112.17/16.19 | | |
% 112.17/16.19 | | Case 2:
% 112.17/16.19 | | |
% 112.17/16.19 | | | (31) all_55_0 = e1 | all_55_0 = e0
% 112.17/16.19 | | |
% 112.17/16.19 | | | BETA: splitting (31) gives:
% 112.17/16.19 | | |
% 112.17/16.19 | | | Case 1:
% 112.17/16.19 | | | |
% 112.17/16.19 | | | | (32) all_55_0 = e1
% 112.17/16.19 | | | |
% 112.17/16.19 | | | | COMBINE_EQS: (14), (32) imply:
% 112.17/16.19 | | | | (33) all_6_2 = e1
% 112.17/16.19 | | | |
% 112.17/16.19 | | | | REDUCE: (20), (33) imply:
% 112.17/16.19 | | | | (34) $false
% 112.17/16.19 | | | |
% 112.17/16.19 | | | | CLOSE: (34) is inconsistent.
% 112.17/16.19 | | | |
% 112.17/16.19 | | | Case 2:
% 112.17/16.19 | | | |
% 112.17/16.19 | | | | (35) all_55_0 = e0
% 112.17/16.19 | | | |
% 112.17/16.19 | | | | COMBINE_EQS: (14), (35) imply:
% 112.17/16.19 | | | | (36) all_6_2 = e0
% 112.17/16.19 | | | |
% 112.17/16.19 | | | | REDUCE: (8), (36) imply:
% 112.17/16.19 | | | | (37) ~ (all_53_12 = e0)
% 112.17/16.19 | | | |
% 112.17/16.19 | | | | REDUCE: (10), (36) imply:
% 112.17/16.19 | | | | (38) ~ (e3 = e0)
% 112.17/16.19 | | | |
% 112.17/16.19 | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (11), (12), (13), (15),
% 112.17/16.19 | | | | (16), (17), (18), (21), (22), (37), (38) are inconsistent by
% 112.17/16.19 | | | | sub-proof #200.
% 112.17/16.19 | | | |
% 112.17/16.19 | | | End of split
% 112.17/16.19 | | |
% 112.17/16.19 | | End of split
% 112.17/16.19 | |
% 112.17/16.19 | End of split
% 112.17/16.19 |
% 112.17/16.19 End of proof
% 112.17/16.19
% 112.17/16.19 Sub-proof #200 shows that the following formulas are inconsistent:
% 112.17/16.19 ----------------------------------------------------------------
% 112.17/16.19 (1) (all_57_96 = e0 & op(e3, e3) = e0) | (all_57_97 = e0 & op(e3, e2) = e0) |
% 112.17/16.19 (all_57_98 = e0 & op(e3, e1) = e0) | (all_57_99 = e0 & op(e3, e0) = e0)
% 112.17/16.19 (2) ~ (all_53_15 = e1)
% 112.17/16.19 (3) ~ (all_53_3 = all_53_15)
% 112.17/16.19 (4) op(e3, e0) = all_53_12
% 112.17/16.20 (5) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 112.17/16.20 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 112.17/16.20 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 112.17/16.20 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 112.17/16.20 $i(all_52_16))
% 112.17/16.20 (6) op(e3, e2) = all_53_15
% 112.17/16.20 (7) op(e1, e2) = all_53_7
% 112.17/16.20 (8) ~ (e3 = e0)
% 112.17/16.20 (9) ~ (all_53_12 = e0)
% 112.17/16.20 (10) ~ (all_4_2 = e0)
% 112.17/16.20 (11) ~ (all_53_3 = e1)
% 112.17/16.20 (12) (all_57_76 = e1 & op(e3, e2) = e1) | (all_57_77 = e1 & op(e2, e2) = e1)
% 112.17/16.20 | (all_57_78 = e1 & op(e1, e2) = e1) | (all_57_79 = e1 & op(e0, e2) =
% 112.17/16.20 e1)
% 112.17/16.20 (13) op(e3, e1) = all_53_13
% 112.17/16.20 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.17/16.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.17/16.20 (15) ~ (all_53_13 = e0)
% 112.17/16.20 (16) ~ (all_53_7 = e1)
% 112.17/16.20 (17) op(e3, e3) = all_4_2
% 112.17/16.20 (18) op(e0, e2) = all_53_3
% 112.17/16.20
% 112.17/16.20 Begin of proof
% 112.17/16.20 |
% 112.17/16.20 | SIMP: (8) implies:
% 112.17/16.20 | (19) ~ (e3 = e0)
% 112.17/16.20 |
% 112.17/16.20 | BETA: splitting (1) gives:
% 112.17/16.20 |
% 112.17/16.20 | Case 1:
% 112.17/16.20 | |
% 112.17/16.20 | | (20) (all_57_96 = e0 & op(e3, e3) = e0) | (all_57_97 = e0 & op(e3, e2) =
% 112.17/16.20 | | e0)
% 112.17/16.20 | |
% 112.17/16.20 | | BETA: splitting (20) gives:
% 112.17/16.20 | |
% 112.17/16.20 | | Case 1:
% 112.17/16.20 | | |
% 112.17/16.20 | | | (21) all_57_96 = e0 & op(e3, e3) = e0
% 112.17/16.20 | | |
% 112.17/16.20 | | | ALPHA: (21) implies:
% 112.17/16.20 | | | (22) op(e3, e3) = e0
% 112.17/16.20 | | |
% 112.22/16.20 | | | REF_CLOSE: (10), (14), (17), (22) are inconsistent by sub-proof #206.
% 112.22/16.20 | | |
% 112.22/16.20 | | Case 2:
% 112.22/16.20 | | |
% 112.22/16.20 | | | (23) all_57_97 = e0 & op(e3, e2) = e0
% 112.22/16.20 | | |
% 112.22/16.20 | | | ALPHA: (23) implies:
% 112.22/16.20 | | | (24) op(e3, e2) = e0
% 112.22/16.20 | | |
% 112.22/16.20 | | | BETA: splitting (12) gives:
% 112.22/16.20 | | |
% 112.22/16.20 | | | Case 1:
% 112.22/16.20 | | | |
% 112.22/16.20 | | | | (25) (all_57_76 = e1 & op(e3, e2) = e1) | (all_57_77 = e1 & op(e2,
% 112.22/16.20 | | | | e2) = e1)
% 112.22/16.20 | | | |
% 112.22/16.20 | | | | BETA: splitting (25) gives:
% 112.22/16.20 | | | |
% 112.22/16.20 | | | | Case 1:
% 112.22/16.20 | | | | |
% 112.22/16.20 | | | | | (26) all_57_76 = e1 & op(e3, e2) = e1
% 112.22/16.20 | | | | |
% 112.22/16.20 | | | | | ALPHA: (26) implies:
% 112.22/16.20 | | | | | (27) op(e3, e2) = e1
% 112.22/16.20 | | | | |
% 112.22/16.20 | | | | | REF_CLOSE: (2), (6), (14), (27) are inconsistent by sub-proof #205.
% 112.22/16.20 | | | | |
% 112.22/16.20 | | | | Case 2:
% 112.22/16.20 | | | | |
% 112.22/16.20 | | | | |
% 112.22/16.20 | | | | | GROUND_INST: instantiating (14) with all_53_15, e0, e2, e3,
% 112.22/16.20 | | | | | simplifying with (6), (24) gives:
% 112.22/16.20 | | | | | (28) all_53_15 = e0
% 112.22/16.20 | | | | |
% 112.22/16.20 | | | | | REDUCE: (3), (28) imply:
% 112.22/16.20 | | | | | (29) ~ (all_53_3 = e0)
% 112.22/16.20 | | | | |
% 112.22/16.20 | | | | | BETA: splitting (5) gives:
% 112.22/16.20 | | | | |
% 112.22/16.20 | | | | | Case 1:
% 112.22/16.20 | | | | | |
% 112.22/16.20 | | | | | | (30) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 &
% 112.22/16.20 | | | | | | op(e2, e3) = all_52_12 & $i(all_52_12)
% 112.22/16.20 | | | | | |
% 112.22/16.20 | | | | | | ALPHA: (30) implies:
% 112.22/16.20 | | | | | | (31) op(e3, e2) = e3
% 112.22/16.20 | | | | | |
% 112.22/16.20 | | | | | | GROUND_INST: instantiating (14) with e0, e3, e2, e3, simplifying
% 112.22/16.20 | | | | | | with (24), (31) gives:
% 112.22/16.20 | | | | | | (32) e3 = e0
% 112.22/16.20 | | | | | |
% 112.22/16.20 | | | | | | REDUCE: (19), (32) imply:
% 112.22/16.20 | | | | | | (33) $false
% 112.22/16.20 | | | | | |
% 112.22/16.20 | | | | | | CLOSE: (33) is inconsistent.
% 112.22/16.20 | | | | | |
% 112.22/16.20 | | | | | Case 2:
% 112.22/16.20 | | | | | |
% 112.22/16.20 | | | | | | (34) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) =
% 112.22/16.20 | | | | | | all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 112.22/16.20 | | | | | | = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 &
% 112.22/16.20 | | | | | | op(e0, e2) = e0 & $i(all_52_16))
% 112.22/16.20 | | | | | |
% 112.22/16.20 | | | | | | REF_CLOSE: (7), (14), (16), (18), (29), (34) are inconsistent by
% 112.22/16.20 | | | | | | sub-proof #218.
% 112.22/16.20 | | | | | |
% 112.22/16.20 | | | | | End of split
% 112.22/16.20 | | | | |
% 112.22/16.20 | | | | End of split
% 112.22/16.20 | | | |
% 112.22/16.20 | | | Case 2:
% 112.22/16.20 | | | |
% 112.22/16.20 | | | | (35) (all_57_78 = e1 & op(e1, e2) = e1) | (all_57_79 = e1 & op(e0,
% 112.22/16.20 | | | | e2) = e1)
% 112.22/16.20 | | | |
% 112.22/16.20 | | | | REF_CLOSE: (7), (11), (14), (16), (18), (35) are inconsistent by
% 112.22/16.20 | | | | sub-proof #203.
% 112.22/16.20 | | | |
% 112.22/16.20 | | | End of split
% 112.22/16.20 | | |
% 112.22/16.20 | | End of split
% 112.22/16.20 | |
% 112.22/16.20 | Case 2:
% 112.22/16.20 | |
% 112.22/16.20 | | (36) (all_57_98 = e0 & op(e3, e1) = e0) | (all_57_99 = e0 & op(e3, e0) =
% 112.22/16.20 | | e0)
% 112.22/16.20 | |
% 112.22/16.20 | | BETA: splitting (36) gives:
% 112.22/16.20 | |
% 112.22/16.20 | | Case 1:
% 112.22/16.20 | | |
% 112.22/16.20 | | | (37) all_57_98 = e0 & op(e3, e1) = e0
% 112.22/16.20 | | |
% 112.22/16.20 | | | ALPHA: (37) implies:
% 112.22/16.20 | | | (38) op(e3, e1) = e0
% 112.22/16.20 | | |
% 112.22/16.20 | | | REF_CLOSE: (13), (14), (15), (38) are inconsistent by sub-proof #202.
% 112.22/16.20 | | |
% 112.22/16.20 | | Case 2:
% 112.22/16.20 | | |
% 112.22/16.20 | | | (39) all_57_99 = e0 & op(e3, e0) = e0
% 112.22/16.20 | | |
% 112.22/16.20 | | | ALPHA: (39) implies:
% 112.22/16.20 | | | (40) op(e3, e0) = e0
% 112.22/16.20 | | |
% 112.22/16.20 | | | REF_CLOSE: (4), (9), (14), (40) are inconsistent by sub-proof #201.
% 112.22/16.20 | | |
% 112.22/16.20 | | End of split
% 112.22/16.20 | |
% 112.22/16.20 | End of split
% 112.22/16.20 |
% 112.22/16.20 End of proof
% 112.22/16.20
% 112.22/16.20 Sub-proof #201 shows that the following formulas are inconsistent:
% 112.22/16.20 ----------------------------------------------------------------
% 112.22/16.20 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.22/16.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.22/16.20 (2) op(e3, e0) = all_53_12
% 112.22/16.20 (3) op(e3, e0) = e0
% 112.22/16.20 (4) ~ (all_53_12 = e0)
% 112.22/16.20
% 112.22/16.20 Begin of proof
% 112.22/16.20 |
% 112.22/16.20 | GROUND_INST: instantiating (1) with all_53_12, e0, e0, e3, simplifying with
% 112.22/16.20 | (2), (3) gives:
% 112.22/16.20 | (5) all_53_12 = e0
% 112.22/16.20 |
% 112.22/16.20 | REDUCE: (4), (5) imply:
% 112.22/16.20 | (6) $false
% 112.22/16.20 |
% 112.22/16.20 | CLOSE: (6) is inconsistent.
% 112.22/16.20 |
% 112.22/16.20 End of proof
% 112.22/16.20
% 112.22/16.20 Sub-proof #202 shows that the following formulas are inconsistent:
% 112.22/16.20 ----------------------------------------------------------------
% 112.22/16.20 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.22/16.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.22/16.20 (2) op(e3, e1) = all_53_13
% 112.22/16.20 (3) op(e3, e1) = e0
% 112.22/16.20 (4) ~ (all_53_13 = e0)
% 112.22/16.20
% 112.22/16.20 Begin of proof
% 112.22/16.20 |
% 112.22/16.20 | GROUND_INST: instantiating (1) with all_53_13, e0, e1, e3, simplifying with
% 112.22/16.20 | (2), (3) gives:
% 112.22/16.20 | (5) all_53_13 = e0
% 112.22/16.20 |
% 112.22/16.20 | REDUCE: (4), (5) imply:
% 112.22/16.20 | (6) $false
% 112.22/16.20 |
% 112.22/16.20 | CLOSE: (6) is inconsistent.
% 112.22/16.20 |
% 112.22/16.20 End of proof
% 112.22/16.20
% 112.22/16.20 Sub-proof #203 shows that the following formulas are inconsistent:
% 112.22/16.20 ----------------------------------------------------------------
% 112.22/16.20 (1) op(e1, e2) = all_53_7
% 112.22/16.20 (2) (all_57_78 = e1 & op(e1, e2) = e1) | (all_57_79 = e1 & op(e0, e2) = e1)
% 112.22/16.20 (3) ~ (all_53_3 = e1)
% 112.22/16.20 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.22/16.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.22/16.20 (5) ~ (all_53_7 = e1)
% 112.22/16.20 (6) op(e0, e2) = all_53_3
% 112.22/16.20
% 112.22/16.20 Begin of proof
% 112.22/16.20 |
% 112.22/16.20 | BETA: splitting (2) gives:
% 112.22/16.20 |
% 112.22/16.20 | Case 1:
% 112.22/16.20 | |
% 112.22/16.20 | | (7) all_57_78 = e1 & op(e1, e2) = e1
% 112.22/16.20 | |
% 112.22/16.20 | | ALPHA: (7) implies:
% 112.22/16.20 | | (8) op(e1, e2) = e1
% 112.22/16.20 | |
% 112.22/16.20 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #233.
% 112.22/16.20 | |
% 112.22/16.20 | Case 2:
% 112.22/16.20 | |
% 112.22/16.20 | | (9) all_57_79 = e1 & op(e0, e2) = e1
% 112.22/16.20 | |
% 112.22/16.20 | | ALPHA: (9) implies:
% 112.22/16.20 | | (10) op(e0, e2) = e1
% 112.22/16.20 | |
% 112.22/16.20 | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #204.
% 112.22/16.20 | |
% 112.22/16.20 | End of split
% 112.22/16.20 |
% 112.22/16.20 End of proof
% 112.22/16.20
% 112.22/16.20 Sub-proof #204 shows that the following formulas are inconsistent:
% 112.22/16.20 ----------------------------------------------------------------
% 112.22/16.20 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.22/16.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.22/16.20 (2) op(e0, e2) = all_53_3
% 112.22/16.20 (3) op(e0, e2) = e1
% 112.22/16.20 (4) ~ (all_53_3 = e1)
% 112.22/16.20
% 112.22/16.20 Begin of proof
% 112.22/16.20 |
% 112.22/16.20 | GROUND_INST: instantiating (1) with all_53_3, e1, e2, e0, simplifying with
% 112.22/16.20 | (2), (3) gives:
% 112.22/16.20 | (5) all_53_3 = e1
% 112.22/16.20 |
% 112.22/16.20 | REDUCE: (4), (5) imply:
% 112.22/16.20 | (6) $false
% 112.22/16.20 |
% 112.22/16.20 | CLOSE: (6) is inconsistent.
% 112.22/16.20 |
% 112.22/16.20 End of proof
% 112.22/16.20
% 112.22/16.20 Sub-proof #205 shows that the following formulas are inconsistent:
% 112.22/16.20 ----------------------------------------------------------------
% 112.22/16.20 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.22/16.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.22/16.20 (2) op(e3, e2) = all_53_15
% 112.22/16.20 (3) op(e3, e2) = e1
% 112.22/16.20 (4) ~ (all_53_15 = e1)
% 112.22/16.20
% 112.22/16.20 Begin of proof
% 112.22/16.20 |
% 112.22/16.20 | GROUND_INST: instantiating (1) with all_53_15, e1, e2, e3, simplifying with
% 112.22/16.20 | (2), (3) gives:
% 112.22/16.20 | (5) all_53_15 = e1
% 112.22/16.20 |
% 112.22/16.20 | REDUCE: (4), (5) imply:
% 112.22/16.20 | (6) $false
% 112.22/16.20 |
% 112.22/16.20 | CLOSE: (6) is inconsistent.
% 112.22/16.20 |
% 112.22/16.20 End of proof
% 112.22/16.20
% 112.22/16.20 Sub-proof #206 shows that the following formulas are inconsistent:
% 112.22/16.20 ----------------------------------------------------------------
% 112.22/16.20 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.22/16.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.22/16.20 (2) op(e3, e3) = all_4_2
% 112.22/16.20 (3) op(e3, e3) = e0
% 112.22/16.20 (4) ~ (all_4_2 = e0)
% 112.22/16.20
% 112.22/16.20 Begin of proof
% 112.22/16.20 |
% 112.22/16.20 | GROUND_INST: instantiating (1) with all_4_2, e0, e3, e3, simplifying with (2),
% 112.22/16.20 | (3) gives:
% 112.22/16.20 | (5) all_4_2 = e0
% 112.22/16.20 |
% 112.22/16.20 | REDUCE: (4), (5) imply:
% 112.22/16.20 | (6) $false
% 112.22/16.20 |
% 112.22/16.20 | CLOSE: (6) is inconsistent.
% 112.22/16.20 |
% 112.22/16.20 End of proof
% 112.22/16.20
% 112.22/16.20 Sub-proof #207 shows that the following formulas are inconsistent:
% 112.22/16.20 ----------------------------------------------------------------
% 112.22/16.20 (1) op(e3, e0) = all_53_12
% 112.22/16.20 (2) ~ (all_10_2 = e3)
% 112.22/16.20 (3) op(e2, e3) = all_53_10
% 112.22/16.20 (4) op(e1, e0) = all_53_4
% 112.22/16.20 (5) all_55_10 = all_10_2
% 112.22/16.20 (6) ~ (all_53_12 = all_53_15)
% 112.22/16.20 (7) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 112.22/16.20 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 112.22/16.20 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 112.22/16.20 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 112.22/16.20 $i(all_52_16))
% 112.22/16.20 (8) op(e3, e2) = all_53_15
% 112.22/16.20 (9) op(e1, e2) = all_53_7
% 112.22/16.20 (10) ~ (all_53_12 = all_53_13)
% 112.22/16.20 (11) ~ (all_53_8 = all_10_2)
% 112.22/16.20 (12) all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 112.22/16.20 (13) op(e0, e3) = all_53_2
% 112.22/16.20 (14) ~ (all_10_2 = e0)
% 112.22/16.20 (15) op(e0, e1) = all_53_1
% 112.22/16.20 (16) op(e2, e1) = all_53_9
% 112.22/16.20 (17) ~ (all_53_2 = all_53_3)
% 112.22/16.20 (18) ~ (all_53_6 = all_53_7)
% 112.22/16.20 (19) ~ (all_53_4 = all_53_6)
% 112.22/16.20 (20) ~ (all_53_9 = all_10_2)
% 112.22/16.20 (21) op(e1, e3) = all_53_6
% 112.22/16.20 (22) op(e2, e0) = all_53_8
% 112.22/16.20 (23) op(e3, e1) = all_53_13
% 112.22/16.20 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.22/16.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.22/16.20 (25) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 112.22/16.20 e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20 = e3) &
% 112.22/16.20 op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23
% 112.22/16.20 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0
% 112.22/16.20 & $i(all_52_22))
% 112.22/16.20 (26) ~ (all_53_13 = all_53_15)
% 112.22/16.20 (27) ~ (all_10_2 = e1)
% 112.22/16.21 (28) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 112.22/16.21 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 112.22/16.21 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 112.22/16.21 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 112.22/16.21 $i(all_52_4))
% 112.22/16.21 (29) ~ (all_53_4 = all_53_7)
% 112.22/16.21 (30) ~ (all_53_10 = all_10_2)
% 112.22/16.21 (31) ~ (all_53_1 = all_53_3)
% 112.22/16.21 (32) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 112.22/16.21 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 112.22/16.21 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 112.22/16.21 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 112.22/16.21 $i(all_52_10))
% 112.22/16.21 (33) op(e0, e2) = all_53_3
% 112.22/16.21 (34) ~ (all_53_1 = all_53_2)
% 112.22/16.21
% 112.22/16.21 Begin of proof
% 112.22/16.21 |
% 112.22/16.21 | BETA: splitting (12) gives:
% 112.22/16.21 |
% 112.22/16.21 | Case 1:
% 112.22/16.21 | |
% 112.22/16.21 | | (35) all_55_10 = e3
% 112.22/16.21 | |
% 112.22/16.21 | | COMBINE_EQS: (5), (35) imply:
% 112.22/16.21 | | (36) all_10_2 = e3
% 112.22/16.21 | |
% 112.22/16.21 | | REDUCE: (2), (36) imply:
% 112.22/16.21 | | (37) $false
% 112.22/16.21 | |
% 112.22/16.21 | | CLOSE: (37) is inconsistent.
% 112.22/16.21 | |
% 112.22/16.21 | Case 2:
% 112.22/16.21 | |
% 112.22/16.21 | | (38) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 112.22/16.21 | |
% 112.22/16.21 | | BETA: splitting (38) gives:
% 112.22/16.21 | |
% 112.22/16.21 | | Case 1:
% 112.22/16.21 | | |
% 112.22/16.21 | | | (39) all_55_10 = e2
% 112.22/16.21 | | |
% 112.22/16.21 | | | COMBINE_EQS: (5), (39) imply:
% 112.22/16.21 | | | (40) all_10_2 = e2
% 112.22/16.21 | | |
% 112.22/16.21 | | | REDUCE: (11), (40) imply:
% 112.22/16.21 | | | (41) ~ (all_53_8 = e2)
% 112.22/16.21 | | |
% 112.22/16.21 | | | REDUCE: (20), (40) imply:
% 112.22/16.21 | | | (42) ~ (all_53_9 = e2)
% 112.22/16.21 | | |
% 112.22/16.21 | | | REDUCE: (30), (40) imply:
% 112.22/16.21 | | | (43) ~ (all_53_10 = e2)
% 112.22/16.21 | | |
% 112.22/16.21 | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (13), (15), (16),
% 112.22/16.21 | | | (17), (18), (19), (21), (22), (23), (24), (25), (26), (28),
% 112.22/16.21 | | | (29), (31), (32), (33), (34), (41), (42), (43) are inconsistent
% 112.22/16.21 | | | by sub-proof #209.
% 112.22/16.21 | | |
% 112.22/16.21 | | Case 2:
% 112.22/16.21 | | |
% 112.22/16.21 | | | (44) all_55_10 = e1 | all_55_10 = e0
% 112.22/16.21 | | |
% 112.22/16.21 | | | REF_CLOSE: (5), (14), (27), (44) are inconsistent by sub-proof #208.
% 112.22/16.21 | | |
% 112.22/16.21 | | End of split
% 112.22/16.21 | |
% 112.22/16.21 | End of split
% 112.22/16.21 |
% 112.22/16.21 End of proof
% 112.22/16.21
% 112.22/16.21 Sub-proof #208 shows that the following formulas are inconsistent:
% 112.22/16.21 ----------------------------------------------------------------
% 112.22/16.21 (1) all_55_10 = e1 | all_55_10 = e0
% 112.22/16.21 (2) all_55_10 = all_10_2
% 112.22/16.21 (3) ~ (all_10_2 = e1)
% 112.22/16.21 (4) ~ (all_10_2 = e0)
% 112.22/16.21
% 112.22/16.21 Begin of proof
% 112.22/16.21 |
% 112.22/16.21 | BETA: splitting (1) gives:
% 112.22/16.21 |
% 112.22/16.21 | Case 1:
% 112.22/16.21 | |
% 112.22/16.21 | | (5) all_55_10 = e1
% 112.22/16.21 | |
% 112.22/16.21 | | COMBINE_EQS: (2), (5) imply:
% 112.22/16.21 | | (6) all_10_2 = e1
% 112.22/16.21 | |
% 112.22/16.21 | | REDUCE: (3), (6) imply:
% 112.22/16.21 | | (7) $false
% 112.22/16.21 | |
% 112.22/16.21 | | CLOSE: (7) is inconsistent.
% 112.22/16.21 | |
% 112.22/16.21 | Case 2:
% 112.22/16.21 | |
% 112.22/16.21 | | (8) all_55_10 = e0
% 112.22/16.21 | |
% 112.22/16.21 | | COMBINE_EQS: (2), (8) imply:
% 112.22/16.21 | | (9) all_10_2 = e0
% 112.22/16.21 | |
% 112.22/16.21 | | REDUCE: (4), (9) imply:
% 112.22/16.21 | | (10) $false
% 112.22/16.21 | |
% 112.22/16.21 | | CLOSE: (10) is inconsistent.
% 112.22/16.21 | |
% 112.22/16.21 | End of split
% 112.22/16.21 |
% 112.22/16.21 End of proof
% 112.22/16.21
% 112.22/16.21 Sub-proof #209 shows that the following formulas are inconsistent:
% 112.22/16.21 ----------------------------------------------------------------
% 112.22/16.21 (1) ~ (all_53_9 = e2)
% 112.22/16.21 (2) op(e3, e0) = all_53_12
% 112.22/16.21 (3) op(e2, e3) = all_53_10
% 112.22/16.21 (4) op(e1, e0) = all_53_4
% 112.22/16.21 (5) ~ (all_53_12 = all_53_15)
% 112.22/16.21 (6) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 112.22/16.21 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 112.22/16.21 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 112.22/16.21 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 112.22/16.21 $i(all_52_16))
% 112.22/16.21 (7) op(e3, e2) = all_53_15
% 112.22/16.21 (8) op(e1, e2) = all_53_7
% 112.22/16.21 (9) ~ (all_53_12 = all_53_13)
% 112.22/16.21 (10) ~ (all_53_8 = e2)
% 112.22/16.21 (11) op(e0, e3) = all_53_2
% 112.22/16.21 (12) op(e0, e1) = all_53_1
% 112.22/16.21 (13) op(e2, e1) = all_53_9
% 112.22/16.21 (14) ~ (all_53_2 = all_53_3)
% 112.22/16.21 (15) ~ (all_53_6 = all_53_7)
% 112.22/16.21 (16) ~ (all_53_4 = all_53_6)
% 112.22/16.21 (17) op(e1, e3) = all_53_6
% 112.22/16.21 (18) op(e2, e0) = all_53_8
% 112.22/16.21 (19) op(e3, e1) = all_53_13
% 112.22/16.21 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.22/16.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.22/16.21 (21) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 112.22/16.21 e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20 = e3) &
% 112.22/16.21 op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23
% 112.22/16.21 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0
% 112.22/16.21 & $i(all_52_22))
% 112.22/16.21 (22) ~ (all_53_13 = all_53_15)
% 112.22/16.21 (23) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 112.22/16.21 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 112.22/16.21 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 112.22/16.21 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 112.22/16.21 $i(all_52_4))
% 112.22/16.21 (24) ~ (all_53_10 = e2)
% 112.22/16.21 (25) ~ (all_53_4 = all_53_7)
% 112.22/16.21 (26) ~ (all_53_1 = all_53_3)
% 112.22/16.21 (27) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 112.22/16.21 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 112.22/16.21 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 112.22/16.21 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 112.22/16.21 $i(all_52_10))
% 112.22/16.21 (28) op(e0, e2) = all_53_3
% 112.22/16.21 (29) ~ (all_53_1 = all_53_2)
% 112.22/16.21
% 112.22/16.21 Begin of proof
% 112.22/16.21 |
% 112.22/16.21 | BETA: splitting (21) gives:
% 112.22/16.21 |
% 112.22/16.21 | Case 1:
% 112.22/16.21 | |
% 112.22/16.21 | | (30) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 &
% 112.22/16.21 | | op(e2, e3) = e2 & $i(all_52_18)
% 112.22/16.21 | |
% 112.22/16.21 | | REF_CLOSE: (3), (20), (24), (30) are inconsistent by sub-proof #215.
% 112.22/16.21 | |
% 112.22/16.21 | Case 2:
% 112.22/16.21 | |
% 112.22/16.21 | | (31) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 &
% 112.22/16.21 | | op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23 = e0 & ~ (all_52_22
% 112.22/16.21 | | = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0 &
% 112.22/16.21 | | $i(all_52_22))
% 112.22/16.21 | |
% 112.22/16.21 | | BETA: splitting (31) gives:
% 112.22/16.21 | |
% 112.22/16.21 | | Case 1:
% 112.22/16.21 | | |
% 112.22/16.21 | | | (32) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 &
% 112.22/16.21 | | | op(e1, e3) = e1 & $i(all_52_20)
% 112.22/16.21 | | |
% 112.22/16.21 | | | ALPHA: (32) implies:
% 112.22/16.21 | | | (33) op(e1, e3) = e1
% 112.22/16.21 | | |
% 112.22/16.21 | | | GROUND_INST: instantiating (20) with all_53_6, e1, e3, e1, simplifying
% 112.22/16.21 | | | with (17), (33) gives:
% 112.22/16.21 | | | (34) all_53_6 = e1
% 112.22/16.21 | | |
% 112.22/16.21 | | | REDUCE: (16), (34) imply:
% 112.22/16.21 | | | (35) ~ (all_53_4 = e1)
% 112.22/16.21 | | |
% 112.22/16.21 | | | REDUCE: (15), (34) imply:
% 112.22/16.21 | | | (36) ~ (all_53_7 = e1)
% 112.22/16.21 | | |
% 112.22/16.21 | | | SIMP: (36) implies:
% 112.22/16.21 | | | (37) ~ (all_53_7 = e1)
% 112.22/16.21 | | |
% 112.22/16.21 | | | BETA: splitting (23) gives:
% 112.22/16.21 | | |
% 112.22/16.21 | | | Case 1:
% 112.22/16.21 | | | |
% 112.22/16.21 | | | | (38) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0,
% 112.22/16.21 | | | | e3) = all_52_0 & $i(all_52_0)
% 112.22/16.21 | | | |
% 112.22/16.21 | | | | ALPHA: (38) implies:
% 112.22/16.21 | | | | (39) op(e3, e0) = e3
% 112.22/16.21 | | | |
% 112.22/16.21 | | | | GROUND_INST: instantiating (20) with all_53_12, e3, e0, e3, simplifying
% 112.22/16.21 | | | | with (2), (39) gives:
% 112.22/16.21 | | | | (40) all_53_12 = e3
% 112.22/16.21 | | | |
% 112.22/16.21 | | | | REDUCE: (5), (40) imply:
% 112.22/16.21 | | | | (41) ~ (all_53_15 = e3)
% 112.22/16.21 | | | |
% 112.22/16.21 | | | | SIMP: (41) implies:
% 112.22/16.21 | | | | (42) ~ (all_53_15 = e3)
% 112.22/16.21 | | | |
% 112.22/16.21 | | | | BETA: splitting (6) gives:
% 112.22/16.21 | | | |
% 112.22/16.21 | | | | Case 1:
% 112.22/16.21 | | | | |
% 112.22/16.21 | | | | | (43) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 &
% 112.22/16.21 | | | | | op(e2, e3) = all_52_12 & $i(all_52_12)
% 112.22/16.21 | | | | |
% 112.22/16.21 | | | | | ALPHA: (43) implies:
% 112.22/16.21 | | | | | (44) op(e3, e2) = e3
% 112.22/16.21 | | | | |
% 112.22/16.21 | | | | | REF_CLOSE: (7), (20), (42), (44) are inconsistent by sub-proof #214.
% 112.22/16.21 | | | | |
% 112.22/16.21 | | | | Case 2:
% 112.22/16.21 | | | | |
% 112.28/16.21 | | | | | (45) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14
% 112.28/16.21 | | | | | & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~
% 112.28/16.21 | | | | | (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0
% 112.28/16.21 | | | | | & $i(all_52_16))
% 112.28/16.21 | | | | |
% 112.28/16.21 | | | | | BETA: splitting (45) gives:
% 112.28/16.21 | | | | |
% 112.28/16.21 | | | | | Case 1:
% 112.28/16.21 | | | | | |
% 112.28/16.21 | | | | | | (46) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) =
% 112.28/16.21 | | | | | | all_52_14 & op(e1, e2) = e1 & $i(all_52_14)
% 112.28/16.21 | | | | | |
% 112.28/16.21 | | | | | | ALPHA: (46) implies:
% 112.28/16.21 | | | | | | (47) op(e1, e2) = e1
% 112.28/16.21 | | | | | |
% 112.28/16.21 | | | | | | REF_CLOSE: (8), (20), (37), (47) are inconsistent by sub-proof #233.
% 112.28/16.21 | | | | | |
% 112.28/16.21 | | | | | Case 2:
% 112.28/16.21 | | | | | |
% 112.28/16.21 | | | | | | (48) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0) =
% 112.28/16.21 | | | | | | all_52_16 & op(e0, e2) = e0 & $i(all_52_16)
% 112.28/16.21 | | | | | |
% 112.28/16.21 | | | | | | ALPHA: (48) implies:
% 112.28/16.21 | | | | | | (49) op(e0, e2) = e0
% 112.28/16.21 | | | | | |
% 112.28/16.21 | | | | | | REF_CLOSE: (1), (2), (4), (9), (10), (12), (13), (18), (19), (20),
% 112.28/16.21 | | | | | | (23), (26), (27), (28), (35), (49) are inconsistent by
% 112.28/16.21 | | | | | | sub-proof #224.
% 112.28/16.21 | | | | | |
% 112.28/16.21 | | | | | End of split
% 112.28/16.21 | | | | |
% 112.28/16.21 | | | | End of split
% 112.28/16.21 | | | |
% 112.28/16.21 | | | Case 2:
% 112.28/16.21 | | | |
% 112.28/16.21 | | | | (50) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0,
% 112.28/16.21 | | | | e2) = all_52_2 & $i(all_52_2)) | (all_52_5 = e1 & ~
% 112.28/16.21 | | | | (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 112.28/16.21 | | | | $i(all_52_4))
% 112.28/16.21 | | | |
% 112.28/16.21 | | | | REF_CLOSE: (4), (10), (18), (20), (35), (50) are inconsistent by
% 112.28/16.21 | | | | sub-proof #225.
% 112.28/16.21 | | | |
% 112.28/16.21 | | | End of split
% 112.28/16.21 | | |
% 112.28/16.21 | | Case 2:
% 112.28/16.21 | | |
% 112.28/16.21 | | | (51) all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 &
% 112.28/16.21 | | | op(e0, e3) = e0 & $i(all_52_22)
% 112.28/16.21 | | |
% 112.28/16.21 | | | ALPHA: (51) implies:
% 112.28/16.21 | | | (52) op(e0, e3) = e0
% 112.28/16.21 | | |
% 112.28/16.21 | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 112.28/16.21 | | | (14), (18), (19), (20), (22), (23), (25), (27), (28), (29),
% 112.28/16.21 | | | (52) are inconsistent by sub-proof #210.
% 112.28/16.21 | | |
% 112.28/16.21 | | End of split
% 112.28/16.21 | |
% 112.28/16.21 | End of split
% 112.28/16.21 |
% 112.28/16.21 End of proof
% 112.28/16.21
% 112.28/16.21 Sub-proof #210 shows that the following formulas are inconsistent:
% 112.28/16.21 ----------------------------------------------------------------
% 112.28/16.21 (1) ~ (all_53_9 = e2)
% 112.28/16.21 (2) op(e3, e0) = all_53_12
% 112.28/16.21 (3) op(e1, e0) = all_53_4
% 112.28/16.21 (4) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 112.28/16.21 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 112.28/16.21 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 112.28/16.21 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 112.28/16.21 $i(all_52_16))
% 112.28/16.21 (5) op(e3, e2) = all_53_15
% 112.28/16.21 (6) op(e0, e3) = e0
% 112.28/16.21 (7) op(e1, e2) = all_53_7
% 112.28/16.21 (8) ~ (all_53_12 = all_53_13)
% 112.28/16.21 (9) ~ (all_53_8 = e2)
% 112.28/16.21 (10) op(e0, e3) = all_53_2
% 112.28/16.21 (11) op(e0, e1) = all_53_1
% 112.28/16.21 (12) op(e2, e1) = all_53_9
% 112.28/16.22 (13) ~ (all_53_2 = all_53_3)
% 112.28/16.22 (14) op(e2, e0) = all_53_8
% 112.28/16.22 (15) op(e3, e1) = all_53_13
% 112.28/16.22 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.22 (17) ~ (all_53_13 = all_53_15)
% 112.28/16.22 (18) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 112.28/16.22 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 112.28/16.22 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 112.28/16.22 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 112.28/16.22 $i(all_52_4))
% 112.28/16.22 (19) ~ (all_53_4 = all_53_7)
% 112.28/16.22 (20) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 112.28/16.22 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 112.28/16.22 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 112.28/16.22 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 112.28/16.22 $i(all_52_10))
% 112.28/16.22 (21) op(e0, e2) = all_53_3
% 112.28/16.22 (22) ~ (all_53_1 = all_53_2)
% 112.28/16.22
% 112.28/16.22 Begin of proof
% 112.28/16.22 |
% 112.28/16.22 | GROUND_INST: instantiating (16) with all_53_2, e0, e3, e0, simplifying with
% 112.28/16.22 | (6), (10) gives:
% 112.28/16.22 | (23) all_53_2 = e0
% 112.28/16.22 |
% 112.28/16.22 | REDUCE: (22), (23) imply:
% 112.28/16.22 | (24) ~ (all_53_1 = e0)
% 112.28/16.22 |
% 112.28/16.22 | REDUCE: (13), (23) imply:
% 112.28/16.22 | (25) ~ (all_53_3 = e0)
% 112.28/16.22 |
% 112.28/16.22 | SIMP: (25) implies:
% 112.28/16.22 | (26) ~ (all_53_3 = e0)
% 112.28/16.22 |
% 112.28/16.22 | BETA: splitting (20) gives:
% 112.28/16.22 |
% 112.28/16.22 | Case 1:
% 112.28/16.22 | |
% 112.28/16.22 | | (27) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 112.28/16.22 | | all_52_6 & $i(all_52_6)
% 112.28/16.22 | |
% 112.28/16.22 | | ALPHA: (27) implies:
% 112.28/16.22 | | (28) op(e3, e1) = e3
% 112.28/16.22 | |
% 112.28/16.22 | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (14), (15), (16), (17), (18),
% 112.28/16.22 | | (19), (21), (26), (28) are inconsistent by sub-proof #211.
% 112.28/16.22 | |
% 112.28/16.22 | Case 2:
% 112.28/16.22 | |
% 112.28/16.22 | | (29) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 112.28/16.22 | | all_52_8 & $i(all_52_8)) | (all_52_11 = e0 & ~ (all_52_10 = e1) &
% 112.28/16.22 | | op(e1, e0) = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 112.28/16.22 | |
% 112.28/16.22 | | REF_CLOSE: (1), (11), (12), (16), (24), (29) are inconsistent by sub-proof
% 112.28/16.22 | | #229.
% 112.28/16.22 | |
% 112.28/16.22 | End of split
% 112.28/16.22 |
% 112.28/16.22 End of proof
% 112.28/16.22
% 112.28/16.22 Sub-proof #211 shows that the following formulas are inconsistent:
% 112.28/16.22 ----------------------------------------------------------------
% 112.28/16.22 (1) op(e3, e0) = all_53_12
% 112.28/16.22 (2) op(e1, e0) = all_53_4
% 112.28/16.22 (3) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 112.28/16.22 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 112.28/16.22 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 112.28/16.22 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 112.28/16.22 $i(all_52_16))
% 112.28/16.22 (4) op(e3, e2) = all_53_15
% 112.28/16.22 (5) op(e1, e2) = all_53_7
% 112.28/16.22 (6) ~ (all_53_12 = all_53_13)
% 112.28/16.22 (7) ~ (all_53_8 = e2)
% 112.28/16.22 (8) op(e2, e0) = all_53_8
% 112.28/16.22 (9) op(e3, e1) = all_53_13
% 112.28/16.22 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.22 (11) ~ (all_53_13 = all_53_15)
% 112.28/16.22 (12) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 112.28/16.22 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 112.28/16.22 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 112.28/16.22 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 112.28/16.22 $i(all_52_4))
% 112.28/16.22 (13) ~ (all_53_4 = all_53_7)
% 112.28/16.22 (14) op(e3, e1) = e3
% 112.28/16.22 (15) op(e0, e2) = all_53_3
% 112.28/16.22 (16) ~ (all_53_3 = e0)
% 112.28/16.22
% 112.28/16.22 Begin of proof
% 112.28/16.22 |
% 112.28/16.22 | BETA: splitting (12) gives:
% 112.28/16.22 |
% 112.28/16.22 | Case 1:
% 112.28/16.22 | |
% 112.28/16.22 | | (17) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 112.28/16.22 | | all_52_0 & $i(all_52_0)
% 112.28/16.22 | |
% 112.28/16.22 | | ALPHA: (17) implies:
% 112.28/16.22 | | (18) op(e3, e0) = e3
% 112.28/16.22 | |
% 112.28/16.22 | | REF_CLOSE: (1), (6), (9), (10), (14), (18) are inconsistent by sub-proof
% 112.28/16.22 | | #213.
% 112.28/16.22 | |
% 112.28/16.22 | Case 2:
% 112.28/16.22 | |
% 112.28/16.22 | | (19) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 112.28/16.22 | | all_52_2 & $i(all_52_2)) | (all_52_5 = e1 & ~ (all_52_4 = e0) &
% 112.28/16.22 | | op(e1, e0) = e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 112.28/16.22 | |
% 112.28/16.22 | | BETA: splitting (19) gives:
% 112.28/16.22 | |
% 112.28/16.22 | | Case 1:
% 112.28/16.22 | | |
% 112.28/16.22 | | | (20) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 112.28/16.22 | | | = all_52_2 & $i(all_52_2)
% 112.28/16.22 | | |
% 112.28/16.22 | | | ALPHA: (20) implies:
% 112.28/16.22 | | | (21) op(e2, e0) = e2
% 112.28/16.22 | | |
% 112.28/16.22 | | | REF_CLOSE: (7), (8), (10), (21) are inconsistent by sub-proof #227.
% 112.28/16.22 | | |
% 112.28/16.22 | | Case 2:
% 112.28/16.22 | | |
% 112.28/16.22 | | | (22) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 112.28/16.22 | | | = all_52_4 & $i(all_52_4)
% 112.28/16.22 | | |
% 112.28/16.22 | | | ALPHA: (22) implies:
% 112.28/16.22 | | | (23) op(e1, e0) = e1
% 112.28/16.22 | | |
% 112.28/16.22 | | | REF_CLOSE: (2), (3), (4), (5), (9), (10), (11), (13), (14), (15), (16),
% 112.28/16.22 | | | (23) are inconsistent by sub-proof #212.
% 112.28/16.22 | | |
% 112.28/16.22 | | End of split
% 112.28/16.22 | |
% 112.28/16.22 | End of split
% 112.28/16.22 |
% 112.28/16.22 End of proof
% 112.28/16.22
% 112.28/16.22 Sub-proof #212 shows that the following formulas are inconsistent:
% 112.28/16.22 ----------------------------------------------------------------
% 112.28/16.22 (1) op(e1, e0) = all_53_4
% 112.28/16.22 (2) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 112.28/16.22 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 112.28/16.22 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 112.28/16.22 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 112.28/16.22 $i(all_52_16))
% 112.28/16.22 (3) op(e3, e2) = all_53_15
% 112.28/16.22 (4) op(e1, e2) = all_53_7
% 112.28/16.22 (5) op(e1, e0) = e1
% 112.28/16.22 (6) op(e3, e1) = all_53_13
% 112.28/16.22 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.22 (8) ~ (all_53_13 = all_53_15)
% 112.28/16.22 (9) ~ (all_53_4 = all_53_7)
% 112.28/16.22 (10) op(e3, e1) = e3
% 112.28/16.22 (11) op(e0, e2) = all_53_3
% 112.28/16.22 (12) ~ (all_53_3 = e0)
% 112.28/16.22
% 112.28/16.22 Begin of proof
% 112.28/16.22 |
% 112.28/16.22 | GROUND_INST: instantiating (7) with all_53_4, e1, e0, e1, simplifying with
% 112.28/16.22 | (1), (5) gives:
% 112.28/16.22 | (13) all_53_4 = e1
% 112.28/16.22 |
% 112.28/16.22 | GROUND_INST: instantiating (7) with all_53_13, e3, e1, e3, simplifying with
% 112.28/16.22 | (6), (10) gives:
% 112.28/16.22 | (14) all_53_13 = e3
% 112.28/16.22 |
% 112.28/16.22 | REDUCE: (9), (13) imply:
% 112.28/16.22 | (15) ~ (all_53_7 = e1)
% 112.28/16.22 |
% 112.28/16.22 | SIMP: (15) implies:
% 112.28/16.22 | (16) ~ (all_53_7 = e1)
% 112.28/16.22 |
% 112.28/16.22 | REDUCE: (8), (14) imply:
% 112.28/16.22 | (17) ~ (all_53_15 = e3)
% 112.28/16.22 |
% 112.28/16.22 | SIMP: (17) implies:
% 112.28/16.22 | (18) ~ (all_53_15 = e3)
% 112.28/16.22 |
% 112.28/16.22 | BETA: splitting (2) gives:
% 112.28/16.22 |
% 112.28/16.22 | Case 1:
% 112.28/16.22 | |
% 112.28/16.22 | | (19) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3)
% 112.28/16.22 | | = all_52_12 & $i(all_52_12)
% 112.28/16.22 | |
% 112.28/16.22 | | ALPHA: (19) implies:
% 112.28/16.22 | | (20) op(e3, e2) = e3
% 112.28/16.22 | |
% 112.28/16.22 | | REF_CLOSE: (3), (7), (18), (20) are inconsistent by sub-proof #214.
% 112.28/16.22 | |
% 112.28/16.22 | Case 2:
% 112.28/16.22 | |
% 112.28/16.22 | | (21) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 112.28/16.22 | | op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~ (all_52_16
% 112.28/16.22 | | = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 112.28/16.22 | | $i(all_52_16))
% 112.28/16.22 | |
% 112.28/16.22 | | REF_CLOSE: (4), (7), (11), (12), (16), (21) are inconsistent by sub-proof
% 112.28/16.22 | | #218.
% 112.28/16.22 | |
% 112.28/16.22 | End of split
% 112.28/16.22 |
% 112.28/16.22 End of proof
% 112.28/16.22
% 112.28/16.22 Sub-proof #213 shows that the following formulas are inconsistent:
% 112.28/16.22 ----------------------------------------------------------------
% 112.28/16.22 (1) op(e3, e0) = all_53_12
% 112.28/16.22 (2) ~ (all_53_12 = all_53_13)
% 112.28/16.22 (3) op(e3, e0) = e3
% 112.28/16.22 (4) op(e3, e1) = all_53_13
% 112.28/16.22 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.22 (6) op(e3, e1) = e3
% 112.28/16.22
% 112.28/16.22 Begin of proof
% 112.28/16.22 |
% 112.28/16.22 | GROUND_INST: instantiating (5) with all_53_12, e3, e0, e3, simplifying with
% 112.28/16.22 | (1), (3) gives:
% 112.28/16.22 | (7) all_53_12 = e3
% 112.28/16.22 |
% 112.28/16.22 | GROUND_INST: instantiating (5) with all_53_13, e3, e1, e3, simplifying with
% 112.28/16.22 | (4), (6) gives:
% 112.28/16.22 | (8) all_53_13 = e3
% 112.28/16.22 |
% 112.28/16.22 | REDUCE: (2), (7), (8) imply:
% 112.28/16.22 | (9) $false
% 112.28/16.22 |
% 112.28/16.22 | CLOSE: (9) is inconsistent.
% 112.28/16.22 |
% 112.28/16.22 End of proof
% 112.28/16.22
% 112.28/16.22 Sub-proof #214 shows that the following formulas are inconsistent:
% 112.28/16.22 ----------------------------------------------------------------
% 112.28/16.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.22 (2) op(e3, e2) = all_53_15
% 112.28/16.22 (3) op(e3, e2) = e3
% 112.28/16.22 (4) ~ (all_53_15 = e3)
% 112.28/16.22
% 112.28/16.22 Begin of proof
% 112.28/16.22 |
% 112.28/16.22 | GROUND_INST: instantiating (1) with all_53_15, e3, e2, e3, simplifying with
% 112.28/16.22 | (2), (3) gives:
% 112.28/16.22 | (5) all_53_15 = e3
% 112.28/16.22 |
% 112.28/16.22 | REDUCE: (4), (5) imply:
% 112.28/16.22 | (6) $false
% 112.28/16.22 |
% 112.28/16.22 | CLOSE: (6) is inconsistent.
% 112.28/16.22 |
% 112.28/16.22 End of proof
% 112.28/16.22
% 112.28/16.22 Sub-proof #215 shows that the following formulas are inconsistent:
% 112.28/16.22 ----------------------------------------------------------------
% 112.28/16.22 (1) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 112.28/16.22 e3) = e2 & $i(all_52_18)
% 112.28/16.22 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.22 (3) op(e2, e3) = all_53_10
% 112.28/16.22 (4) ~ (all_53_10 = e2)
% 112.28/16.22
% 112.28/16.22 Begin of proof
% 112.28/16.22 |
% 112.28/16.22 | ALPHA: (1) implies:
% 112.28/16.22 | (5) op(e2, e3) = e2
% 112.28/16.22 |
% 112.28/16.22 | GROUND_INST: instantiating (2) with all_53_10, e2, e3, e2, simplifying with
% 112.28/16.22 | (3), (5) gives:
% 112.28/16.22 | (6) all_53_10 = e2
% 112.28/16.22 |
% 112.28/16.22 | REDUCE: (4), (6) imply:
% 112.28/16.22 | (7) $false
% 112.28/16.22 |
% 112.28/16.22 | CLOSE: (7) is inconsistent.
% 112.28/16.22 |
% 112.28/16.22 End of proof
% 112.28/16.22
% 112.28/16.22 Sub-proof #216 shows that the following formulas are inconsistent:
% 112.28/16.22 ----------------------------------------------------------------
% 112.28/16.22 (1) all_55_5 = all_14_2
% 112.28/16.22 (2) op(e3, e0) = all_53_12
% 112.28/16.22 (3) op(e2, e3) = all_53_10
% 112.28/16.22 (4) op(e1, e0) = all_53_4
% 112.28/16.22 (5) ~ (all_14_2 = e0)
% 112.28/16.22 (6) ~ (all_53_7 = all_14_2)
% 112.28/16.23 (7) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 112.28/16.23 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 112.28/16.23 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 112.28/16.23 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 112.28/16.23 $i(all_52_16))
% 112.28/16.23 (8) op(e3, e2) = all_53_15
% 112.28/16.23 (9) op(e1, e2) = all_53_7
% 112.28/16.23 (10) ~ (all_14_2 = e3)
% 112.28/16.23 (11) ~ (all_53_12 = all_53_13)
% 112.28/16.23 (12) op(e0, e3) = all_53_2
% 112.28/16.23 (13) op(e0, e1) = all_53_1
% 112.28/16.23 (14) op(e2, e1) = all_53_9
% 112.28/16.23 (15) ~ (all_14_2 = e2)
% 112.28/16.23 (16) ~ (all_53_2 = all_53_3)
% 112.28/16.23 (17) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 112.28/16.23 (18) ~ (all_53_4 = all_14_2)
% 112.28/16.23 (19) ~ (all_53_8 = all_53_10)
% 112.28/16.23 (20) op(e1, e3) = all_53_6
% 112.28/16.23 (21) op(e2, e0) = all_53_8
% 112.28/16.23 (22) op(e3, e1) = all_53_13
% 112.28/16.23 (23) ~ (all_53_9 = all_53_10)
% 112.28/16.23 (24) ~ (all_53_6 = all_14_2)
% 112.28/16.23 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.23 (26) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 112.28/16.23 e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20 = e3) &
% 112.28/16.23 op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23
% 112.28/16.23 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0
% 112.28/16.23 & $i(all_52_22))
% 112.28/16.23 (27) ~ (all_53_13 = all_53_15)
% 112.28/16.23 (28) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 112.28/16.23 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 112.28/16.23 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 112.28/16.23 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 112.28/16.23 $i(all_52_4))
% 112.28/16.23 (29) ~ (all_53_1 = all_53_3)
% 112.28/16.23 (30) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 112.28/16.23 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 112.28/16.23 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 112.28/16.23 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 112.28/16.23 $i(all_52_10))
% 112.28/16.23 (31) ~ (all_53_8 = all_53_9)
% 112.28/16.23 (32) op(e0, e2) = all_53_3
% 112.28/16.23 (33) ~ (all_53_1 = all_53_2)
% 112.28/16.23
% 112.28/16.23 Begin of proof
% 112.28/16.23 |
% 112.28/16.23 | BETA: splitting (17) gives:
% 112.28/16.23 |
% 112.28/16.23 | Case 1:
% 112.28/16.23 | |
% 112.28/16.23 | | (34) all_55_5 = e3
% 112.28/16.23 | |
% 112.28/16.23 | | COMBINE_EQS: (1), (34) imply:
% 112.28/16.23 | | (35) all_14_2 = e3
% 112.28/16.23 | |
% 112.28/16.23 | | REDUCE: (10), (35) imply:
% 112.28/16.23 | | (36) $false
% 112.28/16.23 | |
% 112.28/16.23 | | CLOSE: (36) is inconsistent.
% 112.28/16.23 | |
% 112.28/16.23 | Case 2:
% 112.28/16.23 | |
% 112.28/16.23 | | (37) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 112.28/16.23 | |
% 112.28/16.23 | | BETA: splitting (37) gives:
% 112.28/16.23 | |
% 112.28/16.23 | | Case 1:
% 112.28/16.23 | | |
% 112.28/16.23 | | | (38) all_55_5 = e2
% 112.28/16.23 | | |
% 112.28/16.23 | | | COMBINE_EQS: (1), (38) imply:
% 112.28/16.23 | | | (39) all_14_2 = e2
% 112.28/16.23 | | |
% 112.28/16.23 | | | REDUCE: (15), (39) imply:
% 112.28/16.23 | | | (40) $false
% 112.28/16.23 | | |
% 112.28/16.23 | | | CLOSE: (40) is inconsistent.
% 112.28/16.23 | | |
% 112.28/16.23 | | Case 2:
% 112.28/16.23 | | |
% 112.28/16.23 | | | (41) all_55_5 = e1 | all_55_5 = e0
% 112.28/16.23 | | |
% 112.28/16.23 | | | BETA: splitting (41) gives:
% 112.28/16.23 | | |
% 112.28/16.23 | | | Case 1:
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | (42) all_55_5 = e1
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | COMBINE_EQS: (1), (42) imply:
% 112.28/16.23 | | | | (43) all_14_2 = e1
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | REDUCE: (18), (43) imply:
% 112.28/16.23 | | | | (44) ~ (all_53_4 = e1)
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | REDUCE: (24), (43) imply:
% 112.28/16.23 | | | | (45) ~ (all_53_6 = e1)
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | REDUCE: (6), (43) imply:
% 112.28/16.23 | | | | (46) ~ (all_53_7 = e1)
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (11), (12), (13), (14), (16),
% 112.28/16.23 | | | | (19), (20), (21), (22), (23), (25), (26), (27), (28), (29),
% 112.28/16.23 | | | | (30), (31), (32), (33), (44), (45), (46) are inconsistent by
% 112.28/16.23 | | | | sub-proof #217.
% 112.28/16.23 | | | |
% 112.28/16.23 | | | Case 2:
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | (47) all_55_5 = e0
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | COMBINE_EQS: (1), (47) imply:
% 112.28/16.23 | | | | (48) all_14_2 = e0
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | REDUCE: (5), (48) imply:
% 112.28/16.23 | | | | (49) $false
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | CLOSE: (49) is inconsistent.
% 112.28/16.23 | | | |
% 112.28/16.23 | | | End of split
% 112.28/16.23 | | |
% 112.28/16.23 | | End of split
% 112.28/16.23 | |
% 112.28/16.23 | End of split
% 112.28/16.23 |
% 112.28/16.23 End of proof
% 112.28/16.23
% 112.28/16.23 Sub-proof #217 shows that the following formulas are inconsistent:
% 112.28/16.23 ----------------------------------------------------------------
% 112.28/16.23 (1) op(e3, e0) = all_53_12
% 112.28/16.23 (2) op(e2, e3) = all_53_10
% 112.28/16.23 (3) op(e1, e0) = all_53_4
% 112.28/16.23 (4) (all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 112.28/16.23 all_52_12 & $i(all_52_12)) | (all_52_15 = e1 & ~ (all_52_14 = e2) &
% 112.28/16.23 op(e2, e1) = all_52_14 & op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17
% 112.28/16.23 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 112.28/16.23 $i(all_52_16))
% 112.28/16.23 (5) op(e3, e2) = all_53_15
% 112.28/16.23 (6) ~ (all_53_4 = e1)
% 112.28/16.23 (7) op(e1, e2) = all_53_7
% 112.28/16.23 (8) ~ (all_53_12 = all_53_13)
% 112.28/16.23 (9) op(e0, e3) = all_53_2
% 112.28/16.23 (10) op(e0, e1) = all_53_1
% 112.28/16.23 (11) op(e2, e1) = all_53_9
% 112.28/16.23 (12) ~ (all_53_2 = all_53_3)
% 112.28/16.23 (13) ~ (all_53_8 = all_53_10)
% 112.28/16.23 (14) ~ (all_53_6 = e1)
% 112.28/16.23 (15) op(e1, e3) = all_53_6
% 112.28/16.23 (16) op(e2, e0) = all_53_8
% 112.28/16.23 (17) op(e3, e1) = all_53_13
% 112.28/16.23 (18) ~ (all_53_9 = all_53_10)
% 112.28/16.23 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.23 (20) (all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 & op(e2,
% 112.28/16.23 e3) = e2 & $i(all_52_18)) | (all_52_21 = e1 & ~ (all_52_20 = e3) &
% 112.28/16.23 op(e3, e1) = all_52_20 & op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23
% 112.28/16.23 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0
% 112.28/16.23 & $i(all_52_22))
% 112.28/16.23 (21) ~ (all_53_13 = all_53_15)
% 112.28/16.23 (22) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 112.28/16.23 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 112.28/16.23 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 112.28/16.23 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 112.28/16.23 $i(all_52_4))
% 112.28/16.23 (23) ~ (all_53_7 = e1)
% 112.28/16.23 (24) ~ (all_53_1 = all_53_3)
% 112.28/16.23 (25) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 112.28/16.23 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 112.28/16.23 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 112.28/16.23 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 112.28/16.23 $i(all_52_10))
% 112.28/16.23 (26) ~ (all_53_8 = all_53_9)
% 112.28/16.23 (27) op(e0, e2) = all_53_3
% 112.28/16.23 (28) ~ (all_53_1 = all_53_2)
% 112.28/16.23
% 112.28/16.23 Begin of proof
% 112.28/16.23 |
% 112.28/16.23 | BETA: splitting (20) gives:
% 112.28/16.23 |
% 112.28/16.23 | Case 1:
% 112.28/16.23 | |
% 112.28/16.23 | | (29) all_52_19 = e2 & ~ (all_52_18 = e3) & op(e3, e2) = all_52_18 &
% 112.28/16.23 | | op(e2, e3) = e2 & $i(all_52_18)
% 112.28/16.23 | |
% 112.28/16.23 | | ALPHA: (29) implies:
% 112.28/16.23 | | (30) ~ (all_52_18 = e3)
% 112.28/16.23 | | (31) op(e2, e3) = e2
% 112.28/16.23 | | (32) op(e3, e2) = all_52_18
% 112.28/16.23 | |
% 112.28/16.23 | | GROUND_INST: instantiating (19) with all_53_10, e2, e3, e2, simplifying with
% 112.28/16.23 | | (2), (31) gives:
% 112.28/16.23 | | (33) all_53_10 = e2
% 112.28/16.23 | |
% 112.28/16.23 | | GROUND_INST: instantiating (19) with all_53_15, all_52_18, e2, e3,
% 112.28/16.23 | | simplifying with (5), (32) gives:
% 112.28/16.23 | | (34) all_53_15 = all_52_18
% 112.28/16.23 | |
% 112.28/16.23 | | REDUCE: (13), (33) imply:
% 112.28/16.23 | | (35) ~ (all_53_8 = e2)
% 112.28/16.23 | |
% 112.28/16.23 | | REDUCE: (18), (33) imply:
% 112.28/16.23 | | (36) ~ (all_53_9 = e2)
% 112.28/16.23 | |
% 112.28/16.23 | | BETA: splitting (4) gives:
% 112.28/16.23 | |
% 112.28/16.23 | | Case 1:
% 112.28/16.23 | | |
% 112.28/16.23 | | | (37) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2,
% 112.28/16.23 | | | e3) = all_52_12 & $i(all_52_12)
% 112.28/16.23 | | |
% 112.28/16.23 | | | ALPHA: (37) implies:
% 112.28/16.23 | | | (38) op(e3, e2) = e3
% 112.28/16.23 | | |
% 112.28/16.23 | | | REF_CLOSE: (19), (30), (32), (38) are inconsistent by sub-proof #234.
% 112.28/16.23 | | |
% 112.28/16.23 | | Case 2:
% 112.28/16.23 | | |
% 112.28/16.23 | | | (39) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 112.28/16.23 | | | op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~
% 112.28/16.23 | | | (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 112.28/16.23 | | | $i(all_52_16))
% 112.28/16.23 | | |
% 112.28/16.23 | | | BETA: splitting (39) gives:
% 112.28/16.23 | | |
% 112.28/16.23 | | | Case 1:
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | (40) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 112.28/16.23 | | | | op(e1, e2) = e1 & $i(all_52_14)
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | ALPHA: (40) implies:
% 112.28/16.23 | | | | (41) op(e1, e2) = e1
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | REF_CLOSE: (7), (19), (23), (41) are inconsistent by sub-proof #233.
% 112.28/16.23 | | | |
% 112.28/16.23 | | | Case 2:
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | (42) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 &
% 112.28/16.23 | | | | op(e0, e2) = e0 & $i(all_52_16)
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | ALPHA: (42) implies:
% 112.28/16.23 | | | | (43) op(e0, e2) = e0
% 112.28/16.23 | | | |
% 112.28/16.23 | | | | REF_CLOSE: (1), (3), (6), (8), (10), (11), (16), (17), (19), (22), (24),
% 112.28/16.23 | | | | (25), (27), (35), (36), (43) are inconsistent by sub-proof
% 112.28/16.23 | | | | #224.
% 112.28/16.23 | | | |
% 112.28/16.23 | | | End of split
% 112.28/16.23 | | |
% 112.28/16.23 | | End of split
% 112.28/16.23 | |
% 112.28/16.23 | Case 2:
% 112.28/16.23 | |
% 112.28/16.23 | | (44) (all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 &
% 112.28/16.23 | | op(e1, e3) = e1 & $i(all_52_20)) | (all_52_23 = e0 & ~ (all_52_22
% 112.28/16.23 | | = e3) & op(e3, e0) = all_52_22 & op(e0, e3) = e0 &
% 112.28/16.23 | | $i(all_52_22))
% 112.28/16.23 | |
% 112.28/16.23 | | BETA: splitting (44) gives:
% 112.28/16.23 | |
% 112.28/16.23 | | Case 1:
% 112.28/16.23 | | |
% 112.28/16.23 | | | (45) all_52_21 = e1 & ~ (all_52_20 = e3) & op(e3, e1) = all_52_20 &
% 112.28/16.23 | | | op(e1, e3) = e1 & $i(all_52_20)
% 112.28/16.23 | | |
% 112.28/16.23 | | | ALPHA: (45) implies:
% 112.28/16.23 | | | (46) op(e1, e3) = e1
% 112.28/16.23 | | |
% 112.28/16.23 | | | REF_CLOSE: (14), (15), (19), (46) are inconsistent by sub-proof #223.
% 112.28/16.23 | | |
% 112.28/16.23 | | Case 2:
% 112.28/16.23 | | |
% 112.28/16.23 | | | (47) all_52_23 = e0 & ~ (all_52_22 = e3) & op(e3, e0) = all_52_22 &
% 112.28/16.23 | | | op(e0, e3) = e0 & $i(all_52_22)
% 112.28/16.23 | | |
% 112.28/16.23 | | | ALPHA: (47) implies:
% 112.28/16.23 | | | (48) ~ (all_52_22 = e3)
% 112.28/16.23 | | | (49) op(e0, e3) = e0
% 112.28/16.23 | | | (50) op(e3, e0) = all_52_22
% 112.28/16.23 | | |
% 112.28/16.23 | | | GROUND_INST: instantiating (19) with all_53_2, e0, e3, e0, simplifying
% 112.28/16.23 | | | with (9), (49) gives:
% 112.28/16.23 | | | (51) all_53_2 = e0
% 112.28/16.23 | | |
% 112.28/16.24 | | | GROUND_INST: instantiating (19) with all_53_12, all_52_22, e0, e3,
% 112.28/16.24 | | | simplifying with (1), (50) gives:
% 112.28/16.24 | | | (52) all_53_12 = all_52_22
% 112.28/16.24 | | |
% 112.28/16.24 | | | REDUCE: (28), (51) imply:
% 112.28/16.24 | | | (53) ~ (all_53_1 = e0)
% 112.28/16.24 | | |
% 112.28/16.24 | | | REDUCE: (12), (51) imply:
% 112.28/16.24 | | | (54) ~ (all_53_3 = e0)
% 112.28/16.24 | | |
% 112.28/16.24 | | | SIMP: (54) implies:
% 112.28/16.24 | | | (55) ~ (all_53_3 = e0)
% 112.28/16.24 | | |
% 112.28/16.24 | | | BETA: splitting (4) gives:
% 112.28/16.24 | | |
% 112.28/16.24 | | | Case 1:
% 112.28/16.24 | | | |
% 112.28/16.24 | | | | (56) all_52_13 = e3 & ~ (all_52_12 = e2) & op(e3, e2) = e3 & op(e2,
% 112.28/16.24 | | | | e3) = all_52_12 & $i(all_52_12)
% 112.28/16.24 | | | |
% 112.28/16.24 | | | | ALPHA: (56) implies:
% 112.28/16.24 | | | | (57) op(e3, e2) = e3
% 112.28/16.24 | | | |
% 112.28/16.24 | | | | BETA: splitting (22) gives:
% 112.28/16.24 | | | |
% 112.28/16.24 | | | | Case 1:
% 112.28/16.24 | | | | |
% 112.28/16.24 | | | | | (58) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0,
% 112.28/16.24 | | | | | e3) = all_52_0 & $i(all_52_0)
% 112.28/16.24 | | | | |
% 112.28/16.24 | | | | | ALPHA: (58) implies:
% 112.28/16.24 | | | | | (59) op(e3, e0) = e3
% 112.28/16.24 | | | | |
% 112.28/16.24 | | | | | REF_CLOSE: (1), (19), (48), (50), (59) are inconsistent by sub-proof
% 112.28/16.24 | | | | | #222.
% 112.28/16.24 | | | | |
% 112.28/16.24 | | | | Case 2:
% 112.28/16.24 | | | | |
% 112.28/16.24 | | | | | (60) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0,
% 112.28/16.24 | | | | | e2) = all_52_2 & $i(all_52_2)) | (all_52_5 = e1 & ~
% 112.28/16.24 | | | | | (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 112.28/16.24 | | | | | $i(all_52_4))
% 112.28/16.24 | | | | |
% 112.28/16.24 | | | | | REF_CLOSE: (3), (5), (6), (10), (11), (16), (17), (19), (21), (25),
% 112.28/16.24 | | | | | (26), (53), (57), (60) are inconsistent by sub-proof #220.
% 112.28/16.24 | | | | |
% 112.28/16.24 | | | | End of split
% 112.28/16.24 | | | |
% 112.28/16.24 | | | Case 2:
% 112.28/16.24 | | | |
% 112.28/16.24 | | | | (61) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 112.28/16.24 | | | | op(e1, e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~
% 112.28/16.24 | | | | (all_52_16 = e2) & op(e2, e0) = all_52_16 & op(e0, e2) = e0 &
% 112.28/16.24 | | | | $i(all_52_16))
% 112.28/16.24 | | | |
% 112.28/16.24 | | | | REF_CLOSE: (7), (19), (23), (27), (55), (61) are inconsistent by
% 112.28/16.24 | | | | sub-proof #218.
% 112.28/16.24 | | | |
% 112.28/16.24 | | | End of split
% 112.28/16.24 | | |
% 112.28/16.24 | | End of split
% 112.28/16.24 | |
% 112.28/16.24 | End of split
% 112.28/16.24 |
% 112.28/16.24 End of proof
% 112.28/16.24
% 112.28/16.24 Sub-proof #218 shows that the following formulas are inconsistent:
% 112.28/16.24 ----------------------------------------------------------------
% 112.28/16.24 (1) op(e1, e2) = all_53_7
% 112.28/16.24 (2) (all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 & op(e1,
% 112.28/16.24 e2) = e1 & $i(all_52_14)) | (all_52_17 = e0 & ~ (all_52_16 = e2) &
% 112.28/16.24 op(e2, e0) = all_52_16 & op(e0, e2) = e0 & $i(all_52_16))
% 112.28/16.24 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.24 (4) ~ (all_53_7 = e1)
% 112.28/16.24 (5) op(e0, e2) = all_53_3
% 112.28/16.24 (6) ~ (all_53_3 = e0)
% 112.28/16.24
% 112.28/16.24 Begin of proof
% 112.28/16.24 |
% 112.28/16.24 | BETA: splitting (2) gives:
% 112.28/16.24 |
% 112.28/16.24 | Case 1:
% 112.28/16.24 | |
% 112.28/16.24 | | (7) all_52_15 = e1 & ~ (all_52_14 = e2) & op(e2, e1) = all_52_14 &
% 112.28/16.24 | | op(e1, e2) = e1 & $i(all_52_14)
% 112.28/16.24 | |
% 112.28/16.24 | | ALPHA: (7) implies:
% 112.28/16.24 | | (8) op(e1, e2) = e1
% 112.28/16.24 | |
% 112.28/16.24 | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #233.
% 112.28/16.24 | |
% 112.28/16.24 | Case 2:
% 112.28/16.24 | |
% 112.28/16.24 | | (9) all_52_17 = e0 & ~ (all_52_16 = e2) & op(e2, e0) = all_52_16 &
% 112.28/16.24 | | op(e0, e2) = e0 & $i(all_52_16)
% 112.28/16.24 | |
% 112.28/16.24 | | ALPHA: (9) implies:
% 112.28/16.24 | | (10) op(e0, e2) = e0
% 112.28/16.24 | |
% 112.28/16.24 | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #219.
% 112.28/16.24 | |
% 112.28/16.24 | End of split
% 112.28/16.24 |
% 112.28/16.24 End of proof
% 112.28/16.24
% 112.28/16.24 Sub-proof #219 shows that the following formulas are inconsistent:
% 112.28/16.24 ----------------------------------------------------------------
% 112.28/16.24 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.24 (2) op(e0, e2) = all_53_3
% 112.28/16.24 (3) op(e0, e2) = e0
% 112.28/16.24 (4) ~ (all_53_3 = e0)
% 112.28/16.24
% 112.28/16.24 Begin of proof
% 112.28/16.24 |
% 112.28/16.24 | GROUND_INST: instantiating (1) with all_53_3, e0, e2, e0, simplifying with
% 112.28/16.24 | (2), (3) gives:
% 112.28/16.24 | (5) all_53_3 = e0
% 112.28/16.24 |
% 112.28/16.24 | REDUCE: (4), (5) imply:
% 112.28/16.24 | (6) $false
% 112.28/16.24 |
% 112.28/16.24 | CLOSE: (6) is inconsistent.
% 112.28/16.24 |
% 112.28/16.24 End of proof
% 112.28/16.24
% 112.28/16.24 Sub-proof #220 shows that the following formulas are inconsistent:
% 112.28/16.24 ----------------------------------------------------------------
% 112.28/16.24 (1) op(e3, e2) = e3
% 112.28/16.24 (2) ~ (all_53_1 = e0)
% 112.28/16.24 (3) op(e1, e0) = all_53_4
% 112.28/16.24 (4) op(e3, e2) = all_53_15
% 112.28/16.24 (5) ~ (all_53_4 = e1)
% 112.28/16.24 (6) op(e0, e1) = all_53_1
% 112.28/16.24 (7) op(e2, e1) = all_53_9
% 112.28/16.24 (8) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 112.28/16.24 all_52_2 & $i(all_52_2)) | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1,
% 112.28/16.24 e0) = e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 112.28/16.24 (9) op(e2, e0) = all_53_8
% 112.28/16.24 (10) op(e3, e1) = all_53_13
% 112.28/16.24 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.24 (12) ~ (all_53_13 = all_53_15)
% 112.28/16.24 (13) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 112.28/16.24 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 112.28/16.24 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 112.28/16.24 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 112.28/16.24 $i(all_52_10))
% 112.28/16.24 (14) ~ (all_53_8 = all_53_9)
% 112.28/16.24
% 112.28/16.24 Begin of proof
% 112.28/16.24 |
% 112.28/16.24 | BETA: splitting (8) gives:
% 112.28/16.24 |
% 112.28/16.24 | Case 1:
% 112.28/16.24 | |
% 112.28/16.24 | | (15) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 112.28/16.24 | | all_52_2 & $i(all_52_2)
% 112.28/16.24 | |
% 112.28/16.24 | | REF_CLOSE: (1), (2), (4), (6), (7), (9), (10), (11), (12), (13), (14), (15)
% 112.28/16.24 | | are inconsistent by sub-proof #221.
% 112.28/16.24 | |
% 112.28/16.24 | Case 2:
% 112.28/16.24 | |
% 112.28/16.24 | | (16) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) =
% 112.28/16.24 | | all_52_4 & $i(all_52_4)
% 112.28/16.24 | |
% 112.28/16.24 | | ALPHA: (16) implies:
% 112.28/16.24 | | (17) op(e1, e0) = e1
% 112.28/16.24 | |
% 112.28/16.24 | | REF_CLOSE: (3), (5), (11), (17) are inconsistent by sub-proof #226.
% 112.28/16.24 | |
% 112.28/16.24 | End of split
% 112.28/16.24 |
% 112.28/16.24 End of proof
% 112.28/16.24
% 112.28/16.24 Sub-proof #221 shows that the following formulas are inconsistent:
% 112.28/16.24 ----------------------------------------------------------------
% 112.28/16.24 (1) op(e3, e2) = e3
% 112.28/16.24 (2) ~ (all_53_1 = e0)
% 112.28/16.24 (3) op(e3, e2) = all_53_15
% 112.28/16.24 (4) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 112.28/16.24 all_52_2 & $i(all_52_2)
% 112.28/16.24 (5) op(e0, e1) = all_53_1
% 112.28/16.24 (6) op(e2, e1) = all_53_9
% 112.28/16.24 (7) op(e2, e0) = all_53_8
% 112.28/16.24 (8) op(e3, e1) = all_53_13
% 112.28/16.24 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.24 (10) ~ (all_53_13 = all_53_15)
% 112.28/16.24 (11) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 112.28/16.24 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 112.28/16.24 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 112.28/16.24 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 112.28/16.24 $i(all_52_10))
% 112.28/16.24 (12) ~ (all_53_8 = all_53_9)
% 112.28/16.24
% 112.28/16.24 Begin of proof
% 112.28/16.24 |
% 112.28/16.24 | ALPHA: (4) implies:
% 112.28/16.24 | (13) op(e2, e0) = e2
% 112.28/16.24 |
% 112.28/16.24 | GROUND_INST: instantiating (9) with all_53_8, e2, e0, e2, simplifying with
% 112.28/16.24 | (7), (13) gives:
% 112.28/16.24 | (14) all_53_8 = e2
% 112.28/16.24 |
% 112.28/16.24 | GROUND_INST: instantiating (9) with all_53_15, e3, e2, e3, simplifying with
% 112.28/16.24 | (1), (3) gives:
% 112.28/16.24 | (15) all_53_15 = e3
% 112.28/16.24 |
% 112.28/16.24 | REDUCE: (12), (14) imply:
% 112.28/16.24 | (16) ~ (all_53_9 = e2)
% 112.28/16.24 |
% 112.28/16.24 | SIMP: (16) implies:
% 112.28/16.24 | (17) ~ (all_53_9 = e2)
% 112.28/16.24 |
% 112.28/16.24 | REDUCE: (10), (15) imply:
% 112.28/16.24 | (18) ~ (all_53_13 = e3)
% 112.28/16.24 |
% 112.28/16.24 | REF_CLOSE: (2), (5), (6), (8), (9), (11), (17), (18) are inconsistent by
% 112.28/16.24 | sub-proof #228.
% 112.28/16.24 |
% 112.28/16.24 End of proof
% 112.28/16.24
% 112.28/16.24 Sub-proof #222 shows that the following formulas are inconsistent:
% 112.28/16.24 ----------------------------------------------------------------
% 112.28/16.24 (1) ~ (all_52_22 = e3)
% 112.28/16.24 (2) op(e3, e0) = all_53_12
% 112.28/16.24 (3) op(e3, e0) = e3
% 112.28/16.24 (4) op(e3, e0) = all_52_22
% 112.28/16.24 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.24
% 112.28/16.24 Begin of proof
% 112.28/16.24 |
% 112.28/16.24 | GROUND_INST: instantiating (5) with all_53_12, e3, e0, e3, simplifying with
% 112.28/16.24 | (2), (3) gives:
% 112.28/16.24 | (6) all_53_12 = e3
% 112.28/16.24 |
% 112.28/16.24 | GROUND_INST: instantiating (5) with all_53_12, all_52_22, e0, e3, simplifying
% 112.28/16.24 | with (2), (4) gives:
% 112.28/16.24 | (7) all_53_12 = all_52_22
% 112.28/16.24 |
% 112.28/16.24 | COMBINE_EQS: (6), (7) imply:
% 112.28/16.24 | (8) all_52_22 = e3
% 112.28/16.24 |
% 112.28/16.24 | REDUCE: (1), (8) imply:
% 112.28/16.24 | (9) $false
% 112.28/16.24 |
% 112.28/16.24 | CLOSE: (9) is inconsistent.
% 112.28/16.24 |
% 112.28/16.24 End of proof
% 112.28/16.24
% 112.28/16.24 Sub-proof #223 shows that the following formulas are inconsistent:
% 112.28/16.24 ----------------------------------------------------------------
% 112.28/16.24 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.24 (2) op(e1, e3) = all_53_6
% 112.28/16.24 (3) op(e1, e3) = e1
% 112.28/16.24 (4) ~ (all_53_6 = e1)
% 112.28/16.24
% 112.28/16.24 Begin of proof
% 112.28/16.24 |
% 112.28/16.24 | GROUND_INST: instantiating (1) with all_53_6, e1, e3, e1, simplifying with
% 112.28/16.24 | (2), (3) gives:
% 112.28/16.24 | (5) all_53_6 = e1
% 112.28/16.24 |
% 112.28/16.24 | REDUCE: (4), (5) imply:
% 112.28/16.24 | (6) $false
% 112.28/16.24 |
% 112.28/16.24 | CLOSE: (6) is inconsistent.
% 112.28/16.24 |
% 112.28/16.24 End of proof
% 112.28/16.24
% 112.28/16.24 Sub-proof #224 shows that the following formulas are inconsistent:
% 112.28/16.24 ----------------------------------------------------------------
% 112.28/16.24 (1) ~ (all_53_9 = e2)
% 112.28/16.24 (2) op(e3, e0) = all_53_12
% 112.28/16.24 (3) op(e1, e0) = all_53_4
% 112.28/16.24 (4) ~ (all_53_4 = e1)
% 112.28/16.24 (5) ~ (all_53_12 = all_53_13)
% 112.28/16.24 (6) ~ (all_53_8 = e2)
% 112.28/16.24 (7) op(e0, e1) = all_53_1
% 112.28/16.24 (8) op(e2, e1) = all_53_9
% 112.28/16.24 (9) op(e2, e0) = all_53_8
% 112.28/16.24 (10) op(e3, e1) = all_53_13
% 112.28/16.24 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.24 (12) op(e0, e2) = e0
% 112.28/16.24 (13) (all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 112.28/16.24 all_52_0 & $i(all_52_0)) | (all_52_3 = e2 & ~ (all_52_2 = e0) &
% 112.28/16.24 op(e2, e0) = e2 & op(e0, e2) = all_52_2 & $i(all_52_2)) | (all_52_5 =
% 112.28/16.24 e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) = all_52_4 &
% 112.28/16.24 $i(all_52_4))
% 112.28/16.24 (14) ~ (all_53_1 = all_53_3)
% 112.28/16.24 (15) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 112.28/16.24 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) &
% 112.28/16.24 op(e2, e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 =
% 112.28/16.24 e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 112.28/16.24 $i(all_52_10))
% 112.28/16.24 (16) op(e0, e2) = all_53_3
% 112.28/16.24
% 112.28/16.24 Begin of proof
% 112.28/16.24 |
% 112.28/16.25 | BETA: splitting (13) gives:
% 112.28/16.25 |
% 112.28/16.25 | Case 1:
% 112.28/16.25 | |
% 112.28/16.25 | | (17) all_52_1 = e3 & ~ (all_52_0 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 112.28/16.25 | | all_52_0 & $i(all_52_0)
% 112.28/16.25 | |
% 112.28/16.25 | | ALPHA: (17) implies:
% 112.28/16.25 | | (18) op(e3, e0) = e3
% 112.28/16.25 | |
% 112.28/16.25 | | GROUND_INST: instantiating (11) with all_53_3, e0, e2, e0, simplifying with
% 112.28/16.25 | | (12), (16) gives:
% 112.28/16.25 | | (19) all_53_3 = e0
% 112.28/16.25 | |
% 112.28/16.25 | | GROUND_INST: instantiating (11) with all_53_12, e3, e0, e3, simplifying with
% 112.28/16.25 | | (2), (18) gives:
% 112.28/16.25 | | (20) all_53_12 = e3
% 112.28/16.25 | |
% 112.28/16.25 | | REDUCE: (14), (19) imply:
% 112.28/16.25 | | (21) ~ (all_53_1 = e0)
% 112.28/16.25 | |
% 112.28/16.25 | | REDUCE: (5), (20) imply:
% 112.28/16.25 | | (22) ~ (all_53_13 = e3)
% 112.28/16.25 | |
% 112.28/16.25 | | SIMP: (22) implies:
% 112.28/16.25 | | (23) ~ (all_53_13 = e3)
% 112.28/16.25 | |
% 112.28/16.25 | | REF_CLOSE: (1), (7), (8), (10), (11), (15), (21), (23) are inconsistent by
% 112.28/16.25 | | sub-proof #228.
% 112.28/16.25 | |
% 112.28/16.25 | Case 2:
% 112.28/16.25 | |
% 112.28/16.25 | | (24) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 112.28/16.25 | | all_52_2 & $i(all_52_2)) | (all_52_5 = e1 & ~ (all_52_4 = e0) &
% 112.28/16.25 | | op(e1, e0) = e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 112.28/16.25 | |
% 112.28/16.25 | | REF_CLOSE: (3), (4), (6), (9), (11), (24) are inconsistent by sub-proof
% 112.28/16.25 | | #225.
% 112.28/16.25 | |
% 112.28/16.25 | End of split
% 112.28/16.25 |
% 112.28/16.25 End of proof
% 112.28/16.25
% 112.28/16.25 Sub-proof #225 shows that the following formulas are inconsistent:
% 112.28/16.25 ----------------------------------------------------------------
% 112.28/16.25 (1) op(e1, e0) = all_53_4
% 112.28/16.25 (2) ~ (all_53_4 = e1)
% 112.28/16.25 (3) ~ (all_53_8 = e2)
% 112.28/16.25 (4) (all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 112.28/16.25 all_52_2 & $i(all_52_2)) | (all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1,
% 112.28/16.25 e0) = e1 & op(e0, e1) = all_52_4 & $i(all_52_4))
% 112.28/16.25 (5) op(e2, e0) = all_53_8
% 112.28/16.25 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.25
% 112.28/16.25 Begin of proof
% 112.28/16.25 |
% 112.28/16.25 | BETA: splitting (4) gives:
% 112.28/16.25 |
% 112.28/16.25 | Case 1:
% 112.28/16.25 | |
% 112.28/16.25 | | (7) all_52_3 = e2 & ~ (all_52_2 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 112.28/16.25 | | all_52_2 & $i(all_52_2)
% 112.28/16.25 | |
% 112.28/16.25 | | ALPHA: (7) implies:
% 112.28/16.25 | | (8) op(e2, e0) = e2
% 112.28/16.25 | |
% 112.28/16.25 | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #227.
% 112.28/16.25 | |
% 112.28/16.25 | Case 2:
% 112.28/16.25 | |
% 112.28/16.25 | | (9) all_52_5 = e1 & ~ (all_52_4 = e0) & op(e1, e0) = e1 & op(e0, e1) =
% 112.28/16.25 | | all_52_4 & $i(all_52_4)
% 112.28/16.25 | |
% 112.28/16.25 | | ALPHA: (9) implies:
% 112.28/16.25 | | (10) op(e1, e0) = e1
% 112.28/16.25 | |
% 112.28/16.25 | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #226.
% 112.28/16.25 | |
% 112.28/16.25 | End of split
% 112.28/16.25 |
% 112.28/16.25 End of proof
% 112.28/16.25
% 112.28/16.25 Sub-proof #226 shows that the following formulas are inconsistent:
% 112.28/16.25 ----------------------------------------------------------------
% 112.28/16.25 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.25 (2) op(e1, e0) = all_53_4
% 112.28/16.25 (3) op(e1, e0) = e1
% 112.28/16.25 (4) ~ (all_53_4 = e1)
% 112.28/16.25
% 112.28/16.25 Begin of proof
% 112.28/16.25 |
% 112.28/16.25 | GROUND_INST: instantiating (1) with all_53_4, e1, e0, e1, simplifying with
% 112.28/16.25 | (2), (3) gives:
% 112.28/16.25 | (5) all_53_4 = e1
% 112.28/16.25 |
% 112.28/16.25 | REDUCE: (4), (5) imply:
% 112.28/16.25 | (6) $false
% 112.28/16.25 |
% 112.28/16.25 | CLOSE: (6) is inconsistent.
% 112.28/16.25 |
% 112.28/16.25 End of proof
% 112.28/16.25
% 112.28/16.25 Sub-proof #227 shows that the following formulas are inconsistent:
% 112.28/16.25 ----------------------------------------------------------------
% 112.28/16.25 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.25 (2) op(e2, e0) = all_53_8
% 112.28/16.25 (3) op(e2, e0) = e2
% 112.28/16.25 (4) ~ (all_53_8 = e2)
% 112.28/16.25
% 112.28/16.25 Begin of proof
% 112.28/16.25 |
% 112.28/16.25 | GROUND_INST: instantiating (1) with all_53_8, e2, e0, e2, simplifying with
% 112.28/16.25 | (2), (3) gives:
% 112.28/16.25 | (5) all_53_8 = e2
% 112.28/16.25 |
% 112.28/16.25 | REDUCE: (4), (5) imply:
% 112.28/16.25 | (6) $false
% 112.28/16.25 |
% 112.28/16.25 | CLOSE: (6) is inconsistent.
% 112.28/16.25 |
% 112.28/16.25 End of proof
% 112.28/16.25
% 112.28/16.25 Sub-proof #228 shows that the following formulas are inconsistent:
% 112.28/16.25 ----------------------------------------------------------------
% 112.28/16.25 (1) ~ (all_53_9 = e2)
% 112.28/16.25 (2) ~ (all_53_13 = e3)
% 112.28/16.25 (3) ~ (all_53_1 = e0)
% 112.28/16.25 (4) op(e0, e1) = all_53_1
% 112.28/16.25 (5) op(e2, e1) = all_53_9
% 112.28/16.25 (6) op(e3, e1) = all_53_13
% 112.28/16.25 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.25 (8) (all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 112.28/16.25 all_52_6 & $i(all_52_6)) | (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2,
% 112.28/16.25 e1) = e2 & op(e1, e2) = all_52_8 & $i(all_52_8)) | (all_52_11 = e0 &
% 112.28/16.25 ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 & op(e0, e1) = e0 &
% 112.28/16.25 $i(all_52_10))
% 112.28/16.25
% 112.28/16.25 Begin of proof
% 112.28/16.25 |
% 112.28/16.25 | BETA: splitting (8) gives:
% 112.28/16.25 |
% 112.28/16.25 | Case 1:
% 112.28/16.25 | |
% 112.28/16.25 | | (9) all_52_7 = e3 & ~ (all_52_6 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 112.28/16.25 | | all_52_6 & $i(all_52_6)
% 112.28/16.25 | |
% 112.28/16.25 | | ALPHA: (9) implies:
% 112.28/16.25 | | (10) op(e3, e1) = e3
% 112.28/16.25 | |
% 112.28/16.25 | | REF_CLOSE: (2), (6), (7), (10) are inconsistent by sub-proof #232.
% 112.28/16.25 | |
% 112.28/16.25 | Case 2:
% 112.28/16.25 | |
% 112.28/16.25 | | (11) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 112.28/16.25 | | all_52_8 & $i(all_52_8)) | (all_52_11 = e0 & ~ (all_52_10 = e1) &
% 112.28/16.25 | | op(e1, e0) = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 112.28/16.25 | |
% 112.28/16.25 | | REF_CLOSE: (1), (3), (4), (5), (7), (11) are inconsistent by sub-proof #229.
% 112.28/16.25 | |
% 112.28/16.25 | End of split
% 112.28/16.25 |
% 112.28/16.25 End of proof
% 112.28/16.25
% 112.28/16.25 Sub-proof #229 shows that the following formulas are inconsistent:
% 112.28/16.25 ----------------------------------------------------------------
% 112.28/16.25 (1) ~ (all_53_9 = e2)
% 112.28/16.25 (2) ~ (all_53_1 = e0)
% 112.28/16.25 (3) op(e0, e1) = all_53_1
% 112.28/16.25 (4) op(e2, e1) = all_53_9
% 112.28/16.25 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.25 (6) (all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 112.28/16.25 all_52_8 & $i(all_52_8)) | (all_52_11 = e0 & ~ (all_52_10 = e1) &
% 112.28/16.25 op(e1, e0) = all_52_10 & op(e0, e1) = e0 & $i(all_52_10))
% 112.28/16.25
% 112.28/16.25 Begin of proof
% 112.28/16.25 |
% 112.28/16.25 | BETA: splitting (6) gives:
% 112.28/16.25 |
% 112.28/16.25 | Case 1:
% 112.28/16.25 | |
% 112.28/16.25 | | (7) all_52_9 = e2 & ~ (all_52_8 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 112.28/16.25 | | all_52_8 & $i(all_52_8)
% 112.28/16.25 | |
% 112.28/16.25 | | ALPHA: (7) implies:
% 112.28/16.25 | | (8) op(e2, e1) = e2
% 112.28/16.25 | |
% 112.28/16.25 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #231.
% 112.28/16.25 | |
% 112.28/16.25 | Case 2:
% 112.28/16.25 | |
% 112.28/16.25 | | (9) all_52_11 = e0 & ~ (all_52_10 = e1) & op(e1, e0) = all_52_10 &
% 112.28/16.25 | | op(e0, e1) = e0 & $i(all_52_10)
% 112.28/16.25 | |
% 112.28/16.25 | | ALPHA: (9) implies:
% 112.28/16.25 | | (10) op(e0, e1) = e0
% 112.28/16.25 | |
% 112.28/16.25 | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #230.
% 112.28/16.25 | |
% 112.28/16.25 | End of split
% 112.28/16.25 |
% 112.28/16.25 End of proof
% 112.28/16.25
% 112.28/16.25 Sub-proof #230 shows that the following formulas are inconsistent:
% 112.28/16.25 ----------------------------------------------------------------
% 112.28/16.25 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.25 (2) op(e0, e1) = all_53_1
% 112.28/16.25 (3) op(e0, e1) = e0
% 112.28/16.25 (4) ~ (all_53_1 = e0)
% 112.28/16.25
% 112.28/16.25 Begin of proof
% 112.28/16.25 |
% 112.28/16.25 | GROUND_INST: instantiating (1) with all_53_1, e0, e1, e0, simplifying with
% 112.28/16.25 | (2), (3) gives:
% 112.28/16.25 | (5) all_53_1 = e0
% 112.28/16.25 |
% 112.28/16.25 | REDUCE: (4), (5) imply:
% 112.28/16.25 | (6) $false
% 112.28/16.25 |
% 112.28/16.25 | CLOSE: (6) is inconsistent.
% 112.28/16.25 |
% 112.28/16.25 End of proof
% 112.28/16.25
% 112.28/16.25 Sub-proof #231 shows that the following formulas are inconsistent:
% 112.28/16.25 ----------------------------------------------------------------
% 112.28/16.25 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.25 (2) op(e2, e1) = all_53_9
% 112.28/16.25 (3) op(e2, e1) = e2
% 112.28/16.25 (4) ~ (all_53_9 = e2)
% 112.28/16.25
% 112.28/16.25 Begin of proof
% 112.28/16.25 |
% 112.28/16.25 | GROUND_INST: instantiating (1) with all_53_9, e2, e1, e2, simplifying with
% 112.28/16.25 | (2), (3) gives:
% 112.28/16.25 | (5) all_53_9 = e2
% 112.28/16.25 |
% 112.28/16.25 | REDUCE: (4), (5) imply:
% 112.28/16.25 | (6) $false
% 112.28/16.25 |
% 112.28/16.25 | CLOSE: (6) is inconsistent.
% 112.28/16.25 |
% 112.28/16.25 End of proof
% 112.28/16.25
% 112.28/16.25 Sub-proof #232 shows that the following formulas are inconsistent:
% 112.28/16.25 ----------------------------------------------------------------
% 112.28/16.25 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.25 (2) op(e3, e1) = all_53_13
% 112.28/16.25 (3) op(e3, e1) = e3
% 112.28/16.25 (4) ~ (all_53_13 = e3)
% 112.28/16.25
% 112.28/16.25 Begin of proof
% 112.28/16.25 |
% 112.28/16.25 | GROUND_INST: instantiating (1) with all_53_13, e3, e1, e3, simplifying with
% 112.28/16.25 | (2), (3) gives:
% 112.28/16.25 | (5) all_53_13 = e3
% 112.28/16.25 |
% 112.28/16.25 | REDUCE: (4), (5) imply:
% 112.28/16.25 | (6) $false
% 112.28/16.25 |
% 112.28/16.25 | CLOSE: (6) is inconsistent.
% 112.28/16.25 |
% 112.28/16.25 End of proof
% 112.28/16.25
% 112.28/16.25 Sub-proof #233 shows that the following formulas are inconsistent:
% 112.28/16.25 ----------------------------------------------------------------
% 112.28/16.25 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.25 (2) op(e1, e2) = all_53_7
% 112.28/16.25 (3) op(e1, e2) = e1
% 112.28/16.25 (4) ~ (all_53_7 = e1)
% 112.28/16.25
% 112.28/16.25 Begin of proof
% 112.28/16.25 |
% 112.28/16.25 | GROUND_INST: instantiating (1) with all_53_7, e1, e2, e1, simplifying with
% 112.28/16.25 | (2), (3) gives:
% 112.28/16.25 | (5) all_53_7 = e1
% 112.28/16.25 |
% 112.28/16.25 | REDUCE: (4), (5) imply:
% 112.28/16.25 | (6) $false
% 112.28/16.25 |
% 112.28/16.25 | CLOSE: (6) is inconsistent.
% 112.28/16.25 |
% 112.28/16.25 End of proof
% 112.28/16.25
% 112.28/16.25 Sub-proof #234 shows that the following formulas are inconsistent:
% 112.28/16.25 ----------------------------------------------------------------
% 112.28/16.25 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.28/16.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.28/16.25 (2) op(e3, e2) = all_52_18
% 112.28/16.25 (3) op(e3, e2) = e3
% 112.28/16.25 (4) ~ (all_52_18 = e3)
% 112.28/16.25
% 112.28/16.25 Begin of proof
% 112.28/16.25 |
% 112.28/16.25 | GROUND_INST: instantiating (1) with all_52_18, e3, e2, e3, simplifying with
% 112.28/16.25 | (2), (3) gives:
% 112.28/16.25 | (5) all_52_18 = e3
% 112.28/16.25 |
% 112.28/16.25 | REDUCE: (4), (5) imply:
% 112.28/16.25 | (6) $false
% 112.28/16.25 |
% 112.28/16.25 | CLOSE: (6) is inconsistent.
% 112.28/16.25 |
% 112.28/16.25 End of proof
% 112.28/16.25 % SZS output end Proof for theBenchmark
% 112.28/16.25
% 112.28/16.25 15658ms
%------------------------------------------------------------------------------