TSTP Solution File: SWV117+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV117+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 22:54:59 EDT 2023
% Result : Theorem 83.01s 11.50s
% Output : Proof 207.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV117+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.10/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.32 % Computer : n005.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue Aug 29 03:29:07 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.17/0.59 ________ _____
% 0.17/0.59 ___ __ \_________(_)________________________________
% 0.17/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.59
% 0.17/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.59 (2023-06-19)
% 0.17/0.59
% 0.17/0.59 (c) Philipp Rümmer, 2009-2023
% 0.17/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.59 Amanda Stjerna.
% 0.17/0.59 Free software under BSD-3-Clause.
% 0.17/0.59
% 0.17/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.59
% 0.17/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/0.60 Running up to 7 provers in parallel.
% 0.17/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.77/1.36 Prover 1: Preprocessing ...
% 4.77/1.37 Prover 4: Preprocessing ...
% 4.77/1.40 Prover 0: Preprocessing ...
% 4.77/1.40 Prover 3: Preprocessing ...
% 4.77/1.40 Prover 2: Preprocessing ...
% 4.77/1.40 Prover 6: Preprocessing ...
% 4.77/1.40 Prover 5: Preprocessing ...
% 11.93/2.30 Prover 1: Warning: ignoring some quantifiers
% 12.43/2.34 Prover 3: Warning: ignoring some quantifiers
% 12.78/2.38 Prover 3: Constructing countermodel ...
% 12.78/2.39 Prover 1: Constructing countermodel ...
% 12.78/2.39 Prover 6: Proving ...
% 13.61/2.48 Prover 4: Warning: ignoring some quantifiers
% 14.03/2.55 Prover 2: Proving ...
% 14.03/2.56 Prover 5: Proving ...
% 14.03/2.57 Prover 4: Constructing countermodel ...
% 14.03/2.60 Prover 0: Proving ...
% 73.27/10.28 Prover 2: stopped
% 73.85/10.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.78/10.42 Prover 7: Preprocessing ...
% 76.84/10.69 Prover 7: Warning: ignoring some quantifiers
% 76.84/10.71 Prover 7: Constructing countermodel ...
% 83.01/11.50 Prover 3: proved (10891ms)
% 83.01/11.50
% 83.01/11.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 83.01/11.50
% 83.01/11.50 Prover 5: stopped
% 83.01/11.50 Prover 0: stopped
% 83.23/11.51 Prover 6: stopped
% 83.23/11.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 83.23/11.52 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 83.23/11.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 83.36/11.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 83.36/11.61 Prover 8: Preprocessing ...
% 84.06/11.63 Prover 11: Preprocessing ...
% 84.06/11.64 Prover 13: Preprocessing ...
% 84.06/11.67 Prover 10: Preprocessing ...
% 85.35/11.78 Prover 10: Warning: ignoring some quantifiers
% 85.35/11.79 Prover 10: Constructing countermodel ...
% 85.56/11.82 Prover 8: Warning: ignoring some quantifiers
% 85.56/11.83 Prover 8: Constructing countermodel ...
% 85.56/11.84 Prover 13: Warning: ignoring some quantifiers
% 85.56/11.86 Prover 13: Constructing countermodel ...
% 86.32/11.94 Prover 11: Warning: ignoring some quantifiers
% 86.32/11.96 Prover 11: Constructing countermodel ...
% 115.28/15.67 Prover 13: stopped
% 115.28/15.68 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 115.91/15.76 Prover 16: Preprocessing ...
% 116.40/15.87 Prover 16: Warning: ignoring some quantifiers
% 116.40/15.87 Prover 16: Constructing countermodel ...
% 117.43/15.96 Prover 1: stopped
% 117.43/15.96 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 117.43/16.04 Prover 19: Preprocessing ...
% 119.61/16.22 Prover 19: Warning: ignoring some quantifiers
% 119.61/16.24 Prover 19: Constructing countermodel ...
% 145.45/19.69 Prover 19: stopped
% 151.99/20.71 Prover 16: stopped
% 189.66/27.94 Prover 4: stopped
% 200.12/30.30 Prover 7: stopped
% 204.43/31.48 Prover 10: Found proof (size 5933)
% 204.43/31.48 Prover 10: proved (19971ms)
% 204.43/31.48 Prover 11: stopped
% 204.43/31.48 Prover 8: stopped
% 204.43/31.48
% 204.43/31.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 204.43/31.48
% 204.43/31.57 % SZS output start Proof for theBenchmark
% 204.98/31.58 Assumptions after simplification:
% 204.98/31.58 ---------------------------------
% 204.98/31.58
% 204.98/31.58 (finite_domain_1)
% 204.98/31.59 $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0,
% 204.98/31.59 n1) | ~ leq(n0, v0))
% 204.98/31.59
% 204.98/31.59 (finite_domain_2)
% 204.98/31.59 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~
% 204.98/31.59 $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0))
% 204.98/31.59
% 204.98/31.59 (finite_domain_5)
% 204.98/31.59 $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n5 |
% 204.98/31.59 v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n5)
% 204.98/31.59 | ~ leq(n0, v0))
% 204.98/31.59
% 204.98/31.59 (irreflexivity_gt)
% 204.98/31.59 ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0))
% 204.98/31.59
% 204.98/31.59 (leq_gt2)
% 204.98/31.60 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1)
% 204.98/31.60 | gt(v1, v0))
% 204.98/31.60
% 204.98/31.60 (leq_gt_pred)
% 204.98/31.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~
% 204.98/31.62 $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 204.98/31.62 $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0,
% 204.98/31.62 v2))
% 204.98/31.62
% 204.98/31.62 (pred_minus_1)
% 204.98/31.62 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 204.98/31.62 (pred(v0) = v1 & $i(v1)))
% 204.98/31.62
% 204.98/31.62 (pred_succ)
% 204.98/31.62 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0)
% 204.98/31.62
% 204.98/31.62 (quaternion_ds1_symm_0010)
% 204.98/31.63 $i(id_ds1_filter) & $i(pminus_ds1_filter) & $i(r_ds1_filter) &
% 204.98/31.63 $i(q_ds1_filter) & $i(n6) & $i(n999) & $i(pv5) & $i(n3) & $i(n1) & $i(n0) & ?
% 204.98/31.63 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i]
% 204.98/31.63 : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ?
% 204.98/31.63 [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ?
% 204.98/31.63 [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] :
% 204.98/31.63 (minus(v3, n1) = v4 & minus(n6, n1) = v1 & minus(n999, n1) = v0 & minus(n3,
% 204.98/31.63 n1) = v2 & plus(n1, v1) = v3 & $i(v18) & $i(v17) & $i(v14) & $i(v13) &
% 204.98/31.63 $i(v10) & $i(v9) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 204.98/31.63 $i(v0) & leq(pv5, v0) & leq(n0, pv5) & ! [v21: $i] : ! [v22: $i] : !
% 204.98/31.63 [v23: $i] : ( ~ (a_select3(id_ds1_filter, v21, v22) = v23) | ~ $i(v22) | ~
% 204.98/31.63 $i(v21) | ~ leq(v22, v1) | ~ leq(v21, v4) | ~ leq(n0, v22) | ~ leq(n0,
% 204.98/31.63 v21) | (a_select3(id_ds1_filter, v22, v21) = v23 & $i(v23))) & ! [v21:
% 204.98/31.63 $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (a_select3(pminus_ds1_filter, v21,
% 204.98/31.63 v22) = v23) | ~ $i(v22) | ~ $i(v21) | ~ leq(v22, v1) | ~ leq(v21,
% 204.98/31.63 v1) | ~ leq(n0, v22) | ~ leq(n0, v21) | (a_select3(pminus_ds1_filter,
% 204.98/31.63 v22, v21) = v23 & $i(v23))) & ! [v21: $i] : ! [v22: $i] : ! [v23:
% 204.98/31.63 $i] : ( ~ (a_select3(r_ds1_filter, v21, v22) = v23) | ~ $i(v22) | ~
% 204.98/31.63 $i(v21) | ~ leq(v22, v2) | ~ leq(v21, v2) | ~ leq(n0, v22) | ~ leq(n0,
% 204.98/31.63 v21) | (a_select3(r_ds1_filter, v22, v21) = v23 & $i(v23))) & ! [v21:
% 204.98/31.63 $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (a_select3(q_ds1_filter, v21, v22)
% 204.98/31.63 = v23) | ~ $i(v22) | ~ $i(v21) | ~ leq(v22, v1) | ~ leq(v21, v1) |
% 204.98/31.63 ~ leq(n0, v22) | ~ leq(n0, v21) | (a_select3(q_ds1_filter, v22, v21) =
% 204.98/31.63 v23 & $i(v23))) & (( ~ (v20 = v19) & a_select3(q_ds1_filter, v18, v17) =
% 204.98/31.63 v20 & a_select3(q_ds1_filter, v17, v18) = v19 & $i(v20) & $i(v19) &
% 204.98/31.63 leq(v18, v1) & leq(v17, v1) & leq(n0, v18) & leq(n0, v17)) | ( ~ (v16 =
% 204.98/31.63 v15) & a_select3(r_ds1_filter, v14, v13) = v16 &
% 204.98/31.63 a_select3(r_ds1_filter, v13, v14) = v15 & $i(v16) & $i(v15) & leq(v14,
% 204.98/31.63 v2) & leq(v13, v2) & leq(n0, v14) & leq(n0, v13)) | ( ~ (v12 = v11) &
% 204.98/31.63 a_select3(pminus_ds1_filter, v10, v9) = v12 &
% 204.98/31.63 a_select3(pminus_ds1_filter, v9, v10) = v11 & $i(v12) & $i(v11) &
% 204.98/31.63 leq(v10, v1) & leq(v9, v1) & leq(n0, v10) & leq(n0, v9)) | ( ~ (v8 = v7)
% 204.98/31.63 & a_select3(id_ds1_filter, v6, v5) = v8 & a_select3(id_ds1_filter, v5,
% 204.98/31.63 v6) = v7 & $i(v8) & $i(v7) & leq(v6, v1) & leq(v5, v1) & leq(n0, v6) &
% 204.98/31.63 leq(n0, v5))))
% 204.98/31.63
% 204.98/31.63 (succ_plus_1_l)
% 204.98/31.63 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (plus(n1, v0) = v1) | ~ $i(v0) |
% 204.98/31.63 (succ(v0) = v1 & $i(v1)))
% 204.98/31.63
% 204.98/31.63 (successor_1)
% 204.98/31.63 succ(n0) = n1 & $i(n1) & $i(n0)
% 204.98/31.63
% 204.98/31.63 (successor_2)
% 204.98/31.63 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 204.98/31.63
% 204.98/31.63 (successor_3)
% 204.98/31.63 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 &
% 204.98/31.63 succ(n0) = v0 & $i(v1) & $i(v0))
% 204.98/31.64
% 204.98/31.64 (successor_4)
% 204.98/31.64 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 &
% 204.98/31.64 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 204.98/31.64
% 204.98/31.64 (successor_5)
% 204.98/31.64 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 204.98/31.64 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0
% 204.98/31.64 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 204.98/31.64
% 204.98/31.64 (successor_6)
% 204.98/31.64 $i(n6) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 204.98/31.64 [v4: $i] : (succ(v4) = n6 & succ(v3) = v4 & succ(v2) = v3 & succ(v1) = v2 &
% 204.98/31.64 succ(v0) = v1 & succ(n0) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 204.98/31.64
% 204.98/31.64 (function-axioms)
% 204.98/31.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 204.98/31.65 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 204.98/31.65 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 204.98/31.65 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 204.98/31.65 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 204.98/31.65 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 204.98/31.65 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 204.98/31.65 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 204.98/31.65 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 204.98/31.65 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 204.98/31.65 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 204.98/31.65 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 204.98/31.65 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 204.98/31.65 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 204.98/31.65 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 204.98/31.65 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 204.98/31.65 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 204.98/31.65 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 204.98/31.65 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 204.98/31.65 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 204.98/31.65 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 204.98/31.65 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 204.98/31.65 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 204.98/31.65 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 204.98/31.65 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 204.98/31.65 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 204.98/31.65 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~
% 204.98/31.65 (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 204.98/31.65 (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 204.98/31.65 [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] :
% 204.98/31.65 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) =
% 204.98/31.65 v0))
% 204.98/31.65
% 204.98/31.65 Further assumptions not needed in the proof:
% 204.98/31.65 --------------------------------------------
% 204.98/31.65 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 204.98/31.65 finite_domain_3, finite_domain_4, finite_domain_6, gt_0_tptp_minus_1, gt_1_0,
% 204.98/31.65 gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2,
% 204.98/31.65 gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0,
% 204.98/31.65 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_6_0, gt_6_1, gt_6_2,
% 204.98/31.65 gt_6_3, gt_6_4, gt_6_5, gt_6_tptp_minus_1, gt_999_0, gt_999_1, gt_999_2,
% 204.98/31.65 gt_999_3, gt_999_4, gt_999_5, gt_999_6, gt_999_tptp_minus_1, gt_succ, leq_geq,
% 204.98/31.65 leq_gt1, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ,
% 204.98/31.65 lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv,
% 204.98/31.65 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 204.98/31.65 matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2,
% 204.98/31.65 sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_r,
% 204.98/31.65 succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l,
% 204.98/31.65 succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1,
% 204.98/31.65 sum_plus_base, sum_plus_base_float, totality, transitivity_gt, transitivity_leq,
% 204.98/31.65 ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 204.98/31.65
% 204.98/31.65 Those formulas are unsatisfiable:
% 204.98/31.65 ---------------------------------
% 204.98/31.65
% 204.98/31.65 Begin of proof
% 204.98/31.65 |
% 204.98/31.65 | ALPHA: (leq_gt_pred) implies:
% 204.98/31.65 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 204.98/31.65 | $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 204.98/31.65 |
% 204.98/31.65 | ALPHA: (succ_plus_1_l) implies:
% 204.98/31.65 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (plus(n1, v0) = v1) | ~ $i(v0) |
% 204.98/31.65 | (succ(v0) = v1 & $i(v1)))
% 204.98/31.65 |
% 204.98/31.65 | ALPHA: (pred_minus_1) implies:
% 205.33/31.65 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 205.33/31.65 | (pred(v0) = v1 & $i(v1)))
% 205.33/31.65 |
% 205.33/31.65 | ALPHA: (finite_domain_5) implies:
% 205.33/31.66 | (4) ! [v0: $i] : (v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 =
% 205.33/31.66 | n0 | ~ $i(v0) | ~ leq(v0, n5) | ~ leq(n0, v0))
% 205.33/31.66 |
% 205.33/31.66 | ALPHA: (finite_domain_1) implies:
% 205.33/31.66 | (5) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 205.33/31.66 | leq(n0, v0))
% 205.33/31.66 |
% 205.33/31.66 | ALPHA: (finite_domain_2) implies:
% 205.33/31.66 | (6) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n2)
% 205.33/31.66 | | ~ leq(n0, v0))
% 205.33/31.66 |
% 205.33/31.66 | ALPHA: (successor_4) implies:
% 205.33/31.66 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) =
% 205.33/31.66 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 205.33/31.66 |
% 205.33/31.66 | ALPHA: (successor_5) implies:
% 205.33/31.66 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5
% 205.33/31.66 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 &
% 205.33/31.66 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 205.33/31.66 |
% 205.33/31.66 | ALPHA: (successor_6) implies:
% 205.33/31.66 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 205.33/31.66 | (succ(v4) = n6 & succ(v3) = v4 & succ(v2) = v3 & succ(v1) = v2 &
% 205.33/31.66 | succ(v0) = v1 & succ(n0) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 205.33/31.66 | $i(v0))
% 205.33/31.66 |
% 205.33/31.66 | ALPHA: (successor_1) implies:
% 205.33/31.66 | (10) succ(n0) = n1
% 205.33/31.66 |
% 205.33/31.66 | ALPHA: (successor_2) implies:
% 205.33/31.66 | (11) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 205.33/31.66 |
% 205.33/31.66 | ALPHA: (successor_3) implies:
% 205.33/31.66 | (12) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0)
% 205.33/31.66 | = v0 & $i(v1) & $i(v0))
% 205.33/31.66 |
% 205.33/31.66 | ALPHA: (quaternion_ds1_symm_0010) implies:
% 205.33/31.66 | (13) $i(n0)
% 205.33/31.66 | (14) $i(n6)
% 205.33/31.67 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 205.33/31.67 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 205.33/31.67 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 205.33/31.67 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ?
% 205.33/31.67 | [v19: $i] : ? [v20: $i] : (minus(v3, n1) = v4 & minus(n6, n1) = v1 &
% 205.33/31.67 | minus(n999, n1) = v0 & minus(n3, n1) = v2 & plus(n1, v1) = v3 &
% 205.33/31.67 | $i(v18) & $i(v17) & $i(v14) & $i(v13) & $i(v10) & $i(v9) & $i(v6) &
% 205.33/31.67 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & leq(pv5, v0) &
% 205.33/31.67 | leq(n0, pv5) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~
% 205.33/31.67 | (a_select3(id_ds1_filter, v21, v22) = v23) | ~ $i(v22) | ~
% 205.33/31.67 | $i(v21) | ~ leq(v22, v1) | ~ leq(v21, v4) | ~ leq(n0, v22) | ~
% 205.33/31.67 | leq(n0, v21) | (a_select3(id_ds1_filter, v22, v21) = v23 &
% 205.33/31.67 | $i(v23))) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~
% 205.33/31.67 | (a_select3(pminus_ds1_filter, v21, v22) = v23) | ~ $i(v22) | ~
% 205.33/31.67 | $i(v21) | ~ leq(v22, v1) | ~ leq(v21, v1) | ~ leq(n0, v22) | ~
% 205.33/31.67 | leq(n0, v21) | (a_select3(pminus_ds1_filter, v22, v21) = v23 &
% 205.33/31.67 | $i(v23))) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~
% 205.33/31.67 | (a_select3(r_ds1_filter, v21, v22) = v23) | ~ $i(v22) | ~
% 205.33/31.67 | $i(v21) | ~ leq(v22, v2) | ~ leq(v21, v2) | ~ leq(n0, v22) | ~
% 205.33/31.67 | leq(n0, v21) | (a_select3(r_ds1_filter, v22, v21) = v23 &
% 205.33/31.67 | $i(v23))) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~
% 205.33/31.67 | (a_select3(q_ds1_filter, v21, v22) = v23) | ~ $i(v22) | ~
% 205.33/31.67 | $i(v21) | ~ leq(v22, v1) | ~ leq(v21, v1) | ~ leq(n0, v22) | ~
% 205.33/31.67 | leq(n0, v21) | (a_select3(q_ds1_filter, v22, v21) = v23 &
% 205.33/31.67 | $i(v23))) & (( ~ (v20 = v19) & a_select3(q_ds1_filter, v18, v17)
% 205.33/31.67 | = v20 & a_select3(q_ds1_filter, v17, v18) = v19 & $i(v20) &
% 205.33/31.67 | $i(v19) & leq(v18, v1) & leq(v17, v1) & leq(n0, v18) & leq(n0,
% 205.33/31.67 | v17)) | ( ~ (v16 = v15) & a_select3(r_ds1_filter, v14, v13) =
% 205.33/31.67 | v16 & a_select3(r_ds1_filter, v13, v14) = v15 & $i(v16) &
% 205.33/31.67 | $i(v15) & leq(v14, v2) & leq(v13, v2) & leq(n0, v14) & leq(n0,
% 205.33/31.67 | v13)) | ( ~ (v12 = v11) & a_select3(pminus_ds1_filter, v10,
% 205.33/31.67 | v9) = v12 & a_select3(pminus_ds1_filter, v9, v10) = v11 &
% 205.33/31.67 | $i(v12) & $i(v11) & leq(v10, v1) & leq(v9, v1) & leq(n0, v10) &
% 205.33/31.67 | leq(n0, v9)) | ( ~ (v8 = v7) & a_select3(id_ds1_filter, v6, v5)
% 205.33/31.67 | = v8 & a_select3(id_ds1_filter, v5, v6) = v7 & $i(v8) & $i(v7) &
% 205.33/31.67 | leq(v6, v1) & leq(v5, v1) & leq(n0, v6) & leq(n0, v5))))
% 205.33/31.67 |
% 205.33/31.67 | ALPHA: (function-axioms) implies:
% 205.33/31.67 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) =
% 205.33/31.67 | v1) | ~ (pred(v2) = v0))
% 205.33/31.67 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) =
% 205.33/31.67 | v1) | ~ (succ(v2) = v0))
% 205.33/31.67 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 205.33/31.67 | (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0))
% 205.33/31.67 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 205.33/31.67 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2)
% 205.33/31.67 | = v0))
% 205.33/31.67 |
% 205.33/31.67 | DELTA: instantiating (11) with fresh symbol all_55_0 gives:
% 205.33/31.67 | (20) succ(all_55_0) = n2 & succ(n0) = all_55_0 & $i(all_55_0)
% 205.33/31.67 |
% 205.33/31.67 | ALPHA: (20) implies:
% 205.33/31.67 | (21) $i(all_55_0)
% 205.33/31.67 | (22) succ(n0) = all_55_0
% 205.33/31.67 | (23) succ(all_55_0) = n2
% 205.33/31.67 |
% 205.33/31.67 | DELTA: instantiating (12) with fresh symbols all_57_0, all_57_1 gives:
% 205.33/31.67 | (24) succ(all_57_0) = n3 & succ(all_57_1) = all_57_0 & succ(n0) = all_57_1
% 205.33/31.67 | & $i(all_57_0) & $i(all_57_1)
% 205.33/31.67 |
% 205.33/31.67 | ALPHA: (24) implies:
% 205.33/31.67 | (25) $i(all_57_0)
% 205.33/31.67 | (26) succ(n0) = all_57_1
% 205.33/31.67 | (27) succ(all_57_1) = all_57_0
% 205.33/31.67 | (28) succ(all_57_0) = n3
% 205.33/31.67 |
% 205.33/31.67 | DELTA: instantiating (7) with fresh symbols all_60_0, all_60_1, all_60_2
% 205.33/31.67 | gives:
% 205.33/31.68 | (29) succ(all_60_0) = n4 & succ(all_60_1) = all_60_0 & succ(all_60_2) =
% 205.33/31.68 | all_60_1 & succ(n0) = all_60_2 & $i(all_60_0) & $i(all_60_1) &
% 205.33/31.68 | $i(all_60_2)
% 205.33/31.68 |
% 205.33/31.68 | ALPHA: (29) implies:
% 205.33/31.68 | (30) $i(all_60_0)
% 205.33/31.68 | (31) succ(n0) = all_60_2
% 205.33/31.68 | (32) succ(all_60_2) = all_60_1
% 205.33/31.68 | (33) succ(all_60_1) = all_60_0
% 205.33/31.68 | (34) succ(all_60_0) = n4
% 205.33/31.68 |
% 205.33/31.68 | DELTA: instantiating (8) with fresh symbols all_62_0, all_62_1, all_62_2,
% 205.33/31.68 | all_62_3 gives:
% 205.33/31.68 | (35) succ(all_62_0) = n5 & succ(all_62_1) = all_62_0 & succ(all_62_2) =
% 205.33/31.68 | all_62_1 & succ(all_62_3) = all_62_2 & succ(n0) = all_62_3 &
% 205.33/31.68 | $i(all_62_0) & $i(all_62_1) & $i(all_62_2) & $i(all_62_3)
% 205.33/31.68 |
% 205.33/31.68 | ALPHA: (35) implies:
% 205.33/31.68 | (36) $i(all_62_0)
% 205.33/31.68 | (37) succ(n0) = all_62_3
% 205.33/31.68 | (38) succ(all_62_3) = all_62_2
% 205.33/31.68 | (39) succ(all_62_2) = all_62_1
% 205.33/31.68 | (40) succ(all_62_1) = all_62_0
% 205.33/31.68 | (41) succ(all_62_0) = n5
% 205.33/31.68 |
% 205.33/31.68 | DELTA: instantiating (9) with fresh symbols all_64_0, all_64_1, all_64_2,
% 205.33/31.68 | all_64_3, all_64_4 gives:
% 205.33/31.68 | (42) succ(all_64_0) = n6 & succ(all_64_1) = all_64_0 & succ(all_64_2) =
% 205.33/31.68 | all_64_1 & succ(all_64_3) = all_64_2 & succ(all_64_4) = all_64_3 &
% 205.33/31.68 | succ(n0) = all_64_4 & $i(all_64_0) & $i(all_64_1) & $i(all_64_2) &
% 205.33/31.68 | $i(all_64_3) & $i(all_64_4)
% 205.33/31.68 |
% 205.33/31.68 | ALPHA: (42) implies:
% 205.33/31.68 | (43) $i(all_64_0)
% 205.33/31.68 | (44) succ(n0) = all_64_4
% 205.33/31.68 | (45) succ(all_64_4) = all_64_3
% 205.33/31.68 | (46) succ(all_64_3) = all_64_2
% 205.33/31.68 | (47) succ(all_64_2) = all_64_1
% 205.33/31.68 | (48) succ(all_64_1) = all_64_0
% 205.33/31.68 | (49) succ(all_64_0) = n6
% 205.33/31.68 |
% 205.33/31.68 | DELTA: instantiating (15) with fresh symbols all_74_0, all_74_1, all_74_2,
% 205.33/31.68 | all_74_3, all_74_4, all_74_5, all_74_6, all_74_7, all_74_8, all_74_9,
% 205.33/31.68 | all_74_10, all_74_11, all_74_12, all_74_13, all_74_14, all_74_15,
% 205.33/31.68 | all_74_16, all_74_17, all_74_18, all_74_19, all_74_20 gives:
% 205.33/31.69 | (50) minus(all_74_17, n1) = all_74_16 & minus(n6, n1) = all_74_19 &
% 205.33/31.69 | minus(n999, n1) = all_74_20 & minus(n3, n1) = all_74_18 & plus(n1,
% 205.33/31.69 | all_74_19) = all_74_17 & $i(all_74_2) & $i(all_74_3) & $i(all_74_6)
% 205.33/31.69 | & $i(all_74_7) & $i(all_74_10) & $i(all_74_11) & $i(all_74_14) &
% 205.33/31.69 | $i(all_74_15) & $i(all_74_16) & $i(all_74_17) & $i(all_74_18) &
% 205.33/31.69 | $i(all_74_19) & $i(all_74_20) & leq(pv5, all_74_20) & leq(n0, pv5) &
% 205.33/31.69 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter,
% 205.33/31.69 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_19) |
% 205.33/31.69 | ~ leq(v0, all_74_16) | ~ leq(n0, v1) | ~ leq(n0, v0) |
% 205.33/31.69 | (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2))) & ! [v0: $i] : !
% 205.33/31.69 | [v1: $i] : ! [v2: $i] : ( ~ (a_select3(pminus_ds1_filter, v0, v1) =
% 205.33/31.69 | v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_19) | ~ leq(v0,
% 205.33/31.69 | all_74_19) | ~ leq(n0, v1) | ~ leq(n0, v0) |
% 205.33/31.69 | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) & ! [v0: $i]
% 205.33/31.69 | : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(r_ds1_filter, v0, v1) =
% 205.33/31.69 | v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_18) | ~ leq(v0,
% 205.33/31.69 | all_74_18) | ~ leq(n0, v1) | ~ leq(n0, v0) |
% 205.33/31.69 | (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2))) & ! [v0: $i] : !
% 205.33/31.69 | [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, v0, v1) = v2) |
% 205.33/31.69 | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_19) | ~ leq(v0, all_74_19)
% 205.33/31.69 | | ~ leq(n0, v1) | ~ leq(n0, v0) | (a_select3(q_ds1_filter, v1, v0)
% 205.33/31.69 | = v2 & $i(v2))) & (( ~ (all_74_0 = all_74_1) &
% 205.33/31.69 | a_select3(q_ds1_filter, all_74_2, all_74_3) = all_74_0 &
% 205.33/31.69 | a_select3(q_ds1_filter, all_74_3, all_74_2) = all_74_1 &
% 205.33/31.69 | $i(all_74_0) & $i(all_74_1) & leq(all_74_2, all_74_19) &
% 205.33/31.69 | leq(all_74_3, all_74_19) & leq(n0, all_74_2) & leq(n0, all_74_3))
% 205.33/31.69 | | ( ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6,
% 205.33/31.69 | all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7,
% 205.33/31.69 | all_74_6) = all_74_5 & $i(all_74_4) & $i(all_74_5) &
% 205.33/31.69 | leq(all_74_6, all_74_18) & leq(all_74_7, all_74_18) & leq(n0,
% 205.33/31.69 | all_74_6) & leq(n0, all_74_7)) | ( ~ (all_74_8 = all_74_9) &
% 205.33/31.69 | a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8 &
% 205.33/31.69 | a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 &
% 205.33/31.69 | $i(all_74_8) & $i(all_74_9) & leq(all_74_10, all_74_19) &
% 205.33/31.69 | leq(all_74_11, all_74_19) & leq(n0, all_74_10) & leq(n0,
% 205.33/31.69 | all_74_11)) | ( ~ (all_74_12 = all_74_13) &
% 205.33/31.69 | a_select3(id_ds1_filter, all_74_14, all_74_15) = all_74_12 &
% 205.33/31.69 | a_select3(id_ds1_filter, all_74_15, all_74_14) = all_74_13 &
% 205.33/31.69 | $i(all_74_12) & $i(all_74_13) & leq(all_74_14, all_74_19) &
% 205.33/31.69 | leq(all_74_15, all_74_19) & leq(n0, all_74_14) & leq(n0,
% 205.33/31.69 | all_74_15)))
% 205.33/31.69 |
% 205.33/31.69 | ALPHA: (50) implies:
% 205.33/31.69 | (51) $i(all_74_19)
% 205.33/31.69 | (52) $i(all_74_15)
% 205.33/31.69 | (53) $i(all_74_14)
% 205.33/31.69 | (54) $i(all_74_11)
% 205.33/31.69 | (55) $i(all_74_10)
% 205.33/31.69 | (56) $i(all_74_7)
% 205.33/31.69 | (57) $i(all_74_6)
% 205.33/31.69 | (58) $i(all_74_3)
% 205.33/31.69 | (59) $i(all_74_2)
% 205.33/31.69 | (60) plus(n1, all_74_19) = all_74_17
% 205.33/31.69 | (61) minus(n3, n1) = all_74_18
% 205.33/31.69 | (62) minus(n6, n1) = all_74_19
% 205.33/31.69 | (63) minus(all_74_17, n1) = all_74_16
% 205.33/31.69 | (64) ( ~ (all_74_0 = all_74_1) & a_select3(q_ds1_filter, all_74_2,
% 205.33/31.69 | all_74_3) = all_74_0 & a_select3(q_ds1_filter, all_74_3, all_74_2)
% 205.33/31.69 | = all_74_1 & $i(all_74_0) & $i(all_74_1) & leq(all_74_2, all_74_19)
% 205.33/31.69 | & leq(all_74_3, all_74_19) & leq(n0, all_74_2) & leq(n0, all_74_3))
% 205.33/31.69 | | ( ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6,
% 205.33/31.69 | all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7, all_74_6)
% 205.33/31.69 | = all_74_5 & $i(all_74_4) & $i(all_74_5) & leq(all_74_6, all_74_18)
% 205.33/31.69 | & leq(all_74_7, all_74_18) & leq(n0, all_74_6) & leq(n0, all_74_7))
% 205.33/31.69 | | ( ~ (all_74_8 = all_74_9) & a_select3(pminus_ds1_filter, all_74_10,
% 205.33/31.69 | all_74_11) = all_74_8 & a_select3(pminus_ds1_filter, all_74_11,
% 205.33/31.69 | all_74_10) = all_74_9 & $i(all_74_8) & $i(all_74_9) &
% 205.33/31.69 | leq(all_74_10, all_74_19) & leq(all_74_11, all_74_19) & leq(n0,
% 205.33/31.69 | all_74_10) & leq(n0, all_74_11)) | ( ~ (all_74_12 = all_74_13) &
% 205.33/31.69 | a_select3(id_ds1_filter, all_74_14, all_74_15) = all_74_12 &
% 205.33/31.69 | a_select3(id_ds1_filter, all_74_15, all_74_14) = all_74_13 &
% 205.33/31.69 | $i(all_74_12) & $i(all_74_13) & leq(all_74_14, all_74_19) &
% 205.33/31.69 | leq(all_74_15, all_74_19) & leq(n0, all_74_14) & leq(n0, all_74_15))
% 205.33/31.69 | (65) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter,
% 205.33/31.69 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_19) |
% 205.33/31.69 | ~ leq(v0, all_74_19) | ~ leq(n0, v1) | ~ leq(n0, v0) |
% 205.33/31.69 | (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2)))
% 205.33/31.69 | (66) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(r_ds1_filter,
% 205.33/31.69 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_18) |
% 205.33/31.69 | ~ leq(v0, all_74_18) | ~ leq(n0, v1) | ~ leq(n0, v0) |
% 205.33/31.69 | (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2)))
% 205.33/31.69 | (67) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 205.33/31.69 | (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 205.33/31.69 | | ~ leq(v1, all_74_19) | ~ leq(v0, all_74_19) | ~ leq(n0, v1) |
% 205.33/31.69 | ~ leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 &
% 205.33/31.69 | $i(v2)))
% 205.54/31.70 | (68) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 205.54/31.70 | (a_select3(id_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 205.54/31.70 | leq(v1, all_74_19) | ~ leq(v0, all_74_16) | ~ leq(n0, v1) | ~
% 205.54/31.70 | leq(n0, v0) | (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2)))
% 205.54/31.70 |
% 205.54/31.70 | GROUND_INST: instantiating (17) with all_60_2, all_62_3, n0, simplifying with
% 205.54/31.70 | (31), (37) gives:
% 205.54/31.70 | (69) all_62_3 = all_60_2
% 205.54/31.70 |
% 205.54/31.70 | GROUND_INST: instantiating (17) with all_57_1, all_62_3, n0, simplifying with
% 205.54/31.70 | (26), (37) gives:
% 205.54/31.70 | (70) all_62_3 = all_57_1
% 205.54/31.70 |
% 205.54/31.70 | GROUND_INST: instantiating (17) with all_55_0, all_62_3, n0, simplifying with
% 205.54/31.70 | (22), (37) gives:
% 205.54/31.70 | (71) all_62_3 = all_55_0
% 205.54/31.70 |
% 205.54/31.70 | GROUND_INST: instantiating (17) with all_57_1, all_64_4, n0, simplifying with
% 205.54/31.70 | (26), (44) gives:
% 205.54/31.70 | (72) all_64_4 = all_57_1
% 205.54/31.70 |
% 205.54/31.70 | GROUND_INST: instantiating (17) with n1, all_64_4, n0, simplifying with (10),
% 205.54/31.70 | (44) gives:
% 205.54/31.70 | (73) all_64_4 = n1
% 205.54/31.70 |
% 205.54/31.70 | COMBINE_EQS: (72), (73) imply:
% 205.54/31.70 | (74) all_57_1 = n1
% 205.54/31.70 |
% 205.54/31.70 | SIMP: (74) implies:
% 205.54/31.70 | (75) all_57_1 = n1
% 205.54/31.70 |
% 205.54/31.70 | COMBINE_EQS: (69), (71) imply:
% 205.54/31.70 | (76) all_60_2 = all_55_0
% 205.54/31.70 |
% 205.54/31.70 | COMBINE_EQS: (69), (70) imply:
% 205.54/31.70 | (77) all_60_2 = all_57_1
% 205.54/31.70 |
% 205.54/31.70 | COMBINE_EQS: (76), (77) imply:
% 205.54/31.70 | (78) all_57_1 = all_55_0
% 205.54/31.70 |
% 205.54/31.70 | SIMP: (78) implies:
% 205.54/31.70 | (79) all_57_1 = all_55_0
% 205.54/31.70 |
% 205.54/31.70 | COMBINE_EQS: (75), (79) imply:
% 205.54/31.70 | (80) all_55_0 = n1
% 205.54/31.70 |
% 205.54/31.70 | COMBINE_EQS: (76), (80) imply:
% 205.54/31.70 | (81) all_60_2 = n1
% 205.54/31.70 |
% 205.54/31.70 | COMBINE_EQS: (69), (81) imply:
% 205.54/31.70 | (82) all_62_3 = n1
% 205.54/31.70 |
% 205.54/31.70 | REDUCE: (45), (73) imply:
% 205.54/31.70 | (83) succ(n1) = all_64_3
% 205.54/31.70 |
% 205.54/31.70 | REDUCE: (38), (82) imply:
% 205.54/31.70 | (84) succ(n1) = all_62_2
% 205.54/31.70 |
% 205.54/31.70 | REDUCE: (32), (81) imply:
% 205.54/31.70 | (85) succ(n1) = all_60_1
% 205.54/31.70 |
% 205.54/31.70 | REDUCE: (27), (75) imply:
% 205.54/31.70 | (86) succ(n1) = all_57_0
% 205.54/31.70 |
% 205.54/31.70 | REDUCE: (23), (80) imply:
% 205.54/31.70 | (87) succ(n1) = n2
% 205.54/31.70 |
% 205.54/31.70 | REDUCE: (21), (80) imply:
% 205.54/31.70 | (88) $i(n1)
% 205.54/31.70 |
% 205.54/31.70 | GROUND_INST: instantiating (17) with all_60_1, all_62_2, n1, simplifying with
% 205.54/31.70 | (84), (85) gives:
% 205.54/31.70 | (89) all_62_2 = all_60_1
% 205.54/31.70 |
% 205.54/31.70 | GROUND_INST: instantiating (17) with all_57_0, all_62_2, n1, simplifying with
% 205.54/31.70 | (84), (86) gives:
% 205.54/31.70 | (90) all_62_2 = all_57_0
% 205.54/31.70 |
% 205.54/31.70 | GROUND_INST: instantiating (17) with all_60_1, all_64_3, n1, simplifying with
% 205.54/31.70 | (83), (85) gives:
% 205.54/31.70 | (91) all_64_3 = all_60_1
% 205.54/31.70 |
% 205.54/31.70 | GROUND_INST: instantiating (17) with n2, all_64_3, n1, simplifying with (83),
% 205.54/31.70 | (87) gives:
% 205.54/31.70 | (92) all_64_3 = n2
% 205.54/31.70 |
% 205.54/31.70 | COMBINE_EQS: (91), (92) imply:
% 205.54/31.70 | (93) all_60_1 = n2
% 205.54/31.70 |
% 205.54/31.70 | SIMP: (93) implies:
% 205.54/31.70 | (94) all_60_1 = n2
% 205.54/31.70 |
% 205.54/31.70 | COMBINE_EQS: (89), (90) imply:
% 205.54/31.70 | (95) all_60_1 = all_57_0
% 205.54/31.70 |
% 205.54/31.70 | SIMP: (95) implies:
% 205.54/31.70 | (96) all_60_1 = all_57_0
% 205.54/31.70 |
% 205.54/31.70 | COMBINE_EQS: (94), (96) imply:
% 205.54/31.70 | (97) all_57_0 = n2
% 205.54/31.70 |
% 205.54/31.70 | SIMP: (97) implies:
% 205.54/31.70 | (98) all_57_0 = n2
% 205.54/31.70 |
% 205.54/31.70 | COMBINE_EQS: (90), (98) imply:
% 205.54/31.70 | (99) all_62_2 = n2
% 205.54/31.70 |
% 205.54/31.70 | REDUCE: (46), (92) imply:
% 205.54/31.70 | (100) succ(n2) = all_64_2
% 205.54/31.70 |
% 205.54/31.70 | REDUCE: (39), (99) imply:
% 205.54/31.70 | (101) succ(n2) = all_62_1
% 205.54/31.70 |
% 205.54/31.70 | REDUCE: (33), (94) imply:
% 205.54/31.70 | (102) succ(n2) = all_60_0
% 205.54/31.70 |
% 205.54/31.70 | REDUCE: (28), (98) imply:
% 205.54/31.70 | (103) succ(n2) = n3
% 205.54/31.71 |
% 205.54/31.71 | REDUCE: (25), (98) imply:
% 205.54/31.71 | (104) $i(n2)
% 205.54/31.71 |
% 205.54/31.71 | GROUND_INST: instantiating (17) with all_60_0, all_62_1, n2, simplifying with
% 205.54/31.71 | (101), (102) gives:
% 205.54/31.71 | (105) all_62_1 = all_60_0
% 205.54/31.71 |
% 205.54/31.71 | GROUND_INST: instantiating (17) with all_62_1, all_64_2, n2, simplifying with
% 205.54/31.71 | (100), (101) gives:
% 205.54/31.71 | (106) all_64_2 = all_62_1
% 205.54/31.71 |
% 205.54/31.71 | GROUND_INST: instantiating (17) with n3, all_64_2, n2, simplifying with (100),
% 205.54/31.71 | (103) gives:
% 205.54/31.71 | (107) all_64_2 = n3
% 205.54/31.71 |
% 205.54/31.71 | COMBINE_EQS: (106), (107) imply:
% 205.54/31.71 | (108) all_62_1 = n3
% 205.54/31.71 |
% 205.54/31.71 | SIMP: (108) implies:
% 205.54/31.71 | (109) all_62_1 = n3
% 205.54/31.71 |
% 205.54/31.71 | COMBINE_EQS: (105), (109) imply:
% 205.54/31.71 | (110) all_60_0 = n3
% 205.54/31.71 |
% 205.54/31.71 | SIMP: (110) implies:
% 205.54/31.71 | (111) all_60_0 = n3
% 205.54/31.71 |
% 205.54/31.71 | REDUCE: (47), (107) imply:
% 205.54/31.71 | (112) succ(n3) = all_64_1
% 205.54/31.71 |
% 205.54/31.71 | REDUCE: (40), (109) imply:
% 205.54/31.71 | (113) succ(n3) = all_62_0
% 205.54/31.71 |
% 205.54/31.71 | REDUCE: (34), (111) imply:
% 205.54/31.71 | (114) succ(n3) = n4
% 205.54/31.71 |
% 205.54/31.71 | REDUCE: (30), (111) imply:
% 205.54/31.71 | (115) $i(n3)
% 205.54/31.71 |
% 205.54/31.71 | GROUND_INST: instantiating (17) with all_62_0, all_64_1, n3, simplifying with
% 205.54/31.71 | (112), (113) gives:
% 205.54/31.71 | (116) all_64_1 = all_62_0
% 205.54/31.71 |
% 205.54/31.71 | GROUND_INST: instantiating (17) with n4, all_64_1, n3, simplifying with (112),
% 205.54/31.71 | (114) gives:
% 205.54/31.71 | (117) all_64_1 = n4
% 205.54/31.71 |
% 205.54/31.71 | COMBINE_EQS: (116), (117) imply:
% 205.54/31.71 | (118) all_62_0 = n4
% 205.54/31.71 |
% 205.54/31.71 | SIMP: (118) implies:
% 205.54/31.71 | (119) all_62_0 = n4
% 205.54/31.71 |
% 205.54/31.71 | REDUCE: (48), (117) imply:
% 205.54/31.71 | (120) succ(n4) = all_64_0
% 205.54/31.71 |
% 205.54/31.71 | REDUCE: (41), (119) imply:
% 205.54/31.71 | (121) succ(n4) = n5
% 205.54/31.71 |
% 205.54/31.71 | REDUCE: (36), (119) imply:
% 205.54/31.71 | (122) $i(n4)
% 205.54/31.71 |
% 205.54/31.71 | GROUND_INST: instantiating (17) with n5, all_64_0, n4, simplifying with (120),
% 205.54/31.71 | (121) gives:
% 205.54/31.71 | (123) all_64_0 = n5
% 205.54/31.71 |
% 205.54/31.71 | REDUCE: (49), (123) imply:
% 205.54/31.71 | (124) succ(n5) = n6
% 205.54/31.71 |
% 205.54/31.71 | REDUCE: (43), (123) imply:
% 205.54/31.71 | (125) $i(n5)
% 205.54/31.71 |
% 205.54/31.71 | GROUND_INST: instantiating (pred_succ) with n1, n2, simplifying with (87),
% 205.54/31.71 | (88) gives:
% 205.54/31.71 | (126) pred(n2) = n1
% 205.54/31.71 |
% 205.54/31.71 | GROUND_INST: instantiating (pred_succ) with n2, n3, simplifying with (103),
% 205.54/31.71 | (104) gives:
% 205.54/31.71 | (127) pred(n3) = n2
% 205.54/31.71 |
% 205.54/31.71 | GROUND_INST: instantiating (pred_succ) with n3, n4, simplifying with (114),
% 205.54/31.71 | (115) gives:
% 205.54/31.71 | (128) pred(n4) = n3
% 205.54/31.71 |
% 205.54/31.71 | GROUND_INST: instantiating (pred_succ) with n4, n5, simplifying with (121),
% 205.54/31.71 | (122) gives:
% 205.54/31.71 | (129) pred(n5) = n4
% 205.54/31.71 |
% 205.54/31.71 | GROUND_INST: instantiating (pred_succ) with n5, n6, simplifying with (124),
% 205.54/31.71 | (125) gives:
% 205.54/31.71 | (130) pred(n6) = n5
% 205.54/31.71 |
% 205.54/31.71 | GROUND_INST: instantiating (2) with all_74_19, all_74_17, simplifying with
% 205.54/31.71 | (51), (60) gives:
% 205.54/31.71 | (131) succ(all_74_19) = all_74_17 & $i(all_74_17)
% 205.54/31.71 |
% 205.54/31.71 | ALPHA: (131) implies:
% 205.54/31.71 | (132) $i(all_74_17)
% 205.54/31.71 | (133) succ(all_74_19) = all_74_17
% 205.54/31.71 |
% 205.54/31.71 | GROUND_INST: instantiating (3) with n3, all_74_18, simplifying with (61),
% 205.54/31.71 | (115) gives:
% 205.54/31.71 | (134) pred(n3) = all_74_18 & $i(all_74_18)
% 205.54/31.71 |
% 205.54/31.71 | ALPHA: (134) implies:
% 205.54/31.71 | (135) $i(all_74_18)
% 205.54/31.71 | (136) pred(n3) = all_74_18
% 205.54/31.71 |
% 205.54/31.71 | GROUND_INST: instantiating (3) with n6, all_74_19, simplifying with (14), (62)
% 205.54/31.71 | gives:
% 205.54/31.71 | (137) pred(n6) = all_74_19 & $i(all_74_19)
% 205.54/31.71 |
% 205.54/31.71 | ALPHA: (137) implies:
% 205.54/31.71 | (138) pred(n6) = all_74_19
% 205.54/31.71 |
% 205.54/31.71 | GROUND_INST: instantiating (3) with all_74_17, all_74_16, simplifying with
% 205.54/31.71 | (63), (132) gives:
% 205.54/31.71 | (139) pred(all_74_17) = all_74_16 & $i(all_74_16)
% 205.54/31.71 |
% 205.54/31.71 | ALPHA: (139) implies:
% 205.54/31.71 | (140) $i(all_74_16)
% 205.54/31.72 |
% 205.54/31.72 | GROUND_INST: instantiating (16) with n2, all_74_18, n3, simplifying with
% 205.54/31.72 | (127), (136) gives:
% 205.54/31.72 | (141) all_74_18 = n2
% 205.54/31.72 |
% 205.54/31.72 | GROUND_INST: instantiating (16) with n5, all_74_19, n6, simplifying with
% 205.54/31.72 | (130), (138) gives:
% 205.54/31.72 | (142) all_74_19 = n5
% 205.54/31.72 |
% 205.54/31.72 | REDUCE: (62), (142) imply:
% 205.54/31.72 | (143) minus(n6, n1) = n5
% 205.54/31.72 |
% 205.54/31.72 | REDUCE: (133), (142) imply:
% 205.54/31.72 | (144) succ(n5) = all_74_17
% 205.54/31.72 |
% 205.54/31.72 | GROUND_INST: instantiating (17) with n6, all_74_17, n5, simplifying with
% 205.54/31.72 | (124), (144) gives:
% 205.54/31.72 | (145) all_74_17 = n6
% 205.54/31.72 |
% 205.54/31.72 | REDUCE: (63), (145) imply:
% 205.54/31.72 | (146) minus(n6, n1) = all_74_16
% 205.54/31.72 |
% 205.54/31.72 | GROUND_INST: instantiating (18) with n5, all_74_16, n1, n6, simplifying with
% 205.54/31.72 | (143), (146) gives:
% 205.54/31.72 | (147) all_74_16 = n5
% 205.54/31.72 |
% 205.54/31.72 | BETA: splitting (64) gives:
% 205.54/31.72 |
% 205.54/31.72 | Case 1:
% 205.54/31.72 | |
% 205.54/31.72 | | (148) ( ~ (all_74_0 = all_74_1) & a_select3(q_ds1_filter, all_74_2,
% 205.54/31.72 | | all_74_3) = all_74_0 & a_select3(q_ds1_filter, all_74_3,
% 205.54/31.72 | | all_74_2) = all_74_1 & $i(all_74_0) & $i(all_74_1) &
% 205.54/31.72 | | leq(all_74_2, all_74_19) & leq(all_74_3, all_74_19) & leq(n0,
% 205.54/31.72 | | all_74_2) & leq(n0, all_74_3)) | ( ~ (all_74_4 = all_74_5) &
% 205.54/31.72 | | a_select3(r_ds1_filter, all_74_6, all_74_7) = all_74_4 &
% 205.54/31.72 | | a_select3(r_ds1_filter, all_74_7, all_74_6) = all_74_5 &
% 205.54/31.72 | | $i(all_74_4) & $i(all_74_5) & leq(all_74_6, all_74_18) &
% 205.54/31.72 | | leq(all_74_7, all_74_18) & leq(n0, all_74_6) & leq(n0, all_74_7))
% 205.54/31.72 | |
% 205.54/31.72 | | BETA: splitting (148) gives:
% 205.54/31.72 | |
% 205.54/31.72 | | Case 1:
% 205.54/31.72 | | |
% 205.54/31.72 | | | (149) ~ (all_74_0 = all_74_1) & a_select3(q_ds1_filter, all_74_2,
% 205.54/31.72 | | | all_74_3) = all_74_0 & a_select3(q_ds1_filter, all_74_3,
% 205.54/31.72 | | | all_74_2) = all_74_1 & $i(all_74_0) & $i(all_74_1) &
% 205.54/31.72 | | | leq(all_74_2, all_74_19) & leq(all_74_3, all_74_19) & leq(n0,
% 205.54/31.72 | | | all_74_2) & leq(n0, all_74_3)
% 205.54/31.72 | | |
% 205.54/31.72 | | | ALPHA: (149) implies:
% 205.54/31.72 | | | (150) ~ (all_74_0 = all_74_1)
% 205.54/31.72 | | | (151) leq(n0, all_74_3)
% 205.54/31.72 | | | (152) leq(n0, all_74_2)
% 205.54/31.72 | | | (153) leq(all_74_3, all_74_19)
% 205.54/31.72 | | | (154) leq(all_74_2, all_74_19)
% 205.54/31.72 | | | (155) a_select3(q_ds1_filter, all_74_3, all_74_2) = all_74_1
% 205.54/31.72 | | | (156) a_select3(q_ds1_filter, all_74_2, all_74_3) = all_74_0
% 205.54/31.72 | | |
% 205.54/31.72 | | | REDUCE: (142), (154) imply:
% 205.54/31.72 | | | (157) leq(all_74_2, n5)
% 205.54/31.72 | | |
% 205.54/31.72 | | | REDUCE: (142), (153) imply:
% 205.54/31.72 | | | (158) leq(all_74_3, n5)
% 205.54/31.72 | | |
% 205.54/31.72 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_3, simplifying with
% 205.54/31.72 | | | (13), (58), (151) gives:
% 205.54/31.72 | | | (159) all_74_3 = n0 | gt(all_74_3, n0)
% 205.54/31.72 | | |
% 205.54/31.72 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_2, simplifying with
% 205.54/31.72 | | | (13), (59), (152) gives:
% 205.54/31.72 | | | (160) all_74_2 = n0 | gt(all_74_2, n0)
% 205.54/31.72 | | |
% 205.54/31.72 | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with (58),
% 205.54/31.72 | | | (151), (158) gives:
% 205.54/31.72 | | | (161) all_74_3 = n5 | all_74_3 = n4 | all_74_3 = n3 | all_74_3 = n2 |
% 205.54/31.72 | | | all_74_3 = n1 | all_74_3 = n0
% 205.54/31.72 | | |
% 205.54/31.72 | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n5, simplifying with
% 205.54/31.72 | | | (58), (125), (158) gives:
% 205.54/31.72 | | | (162) all_74_3 = n5 | gt(n5, all_74_3)
% 205.54/31.72 | | |
% 205.54/31.72 | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with (59),
% 205.54/31.72 | | | (152), (157) gives:
% 205.54/31.72 | | | (163) all_74_2 = n5 | all_74_2 = n4 | all_74_2 = n3 | all_74_2 = n2 |
% 205.54/31.72 | | | all_74_2 = n1 | all_74_2 = n0
% 205.54/31.72 | | |
% 205.54/31.72 | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n5, simplifying with
% 205.54/31.72 | | | (59), (125), (157) gives:
% 205.54/31.72 | | | (164) all_74_2 = n5 | gt(n5, all_74_2)
% 205.54/31.72 | | |
% 205.54/31.72 | | | BETA: splitting (160) gives:
% 205.54/31.72 | | |
% 205.54/31.72 | | | Case 1:
% 205.54/31.72 | | | |
% 205.54/31.72 | | | | (165) gt(all_74_2, n0)
% 205.54/31.72 | | | |
% 205.54/31.72 | | | | BETA: splitting (159) gives:
% 205.54/31.72 | | | |
% 205.54/31.72 | | | | Case 1:
% 205.54/31.72 | | | | |
% 205.54/31.73 | | | | | (166) gt(all_74_3, n0)
% 205.54/31.73 | | | | |
% 205.54/31.73 | | | | | BETA: splitting (162) gives:
% 205.54/31.73 | | | | |
% 205.54/31.73 | | | | | Case 1:
% 205.54/31.73 | | | | | |
% 205.54/31.73 | | | | | | (167) gt(n5, all_74_3)
% 205.54/31.73 | | | | | |
% 205.54/31.73 | | | | | | GROUND_INST: instantiating (1) with all_74_3, n5, n4, simplifying
% 205.54/31.73 | | | | | | with (58), (125), (129), (167) gives:
% 205.54/31.73 | | | | | | (168) leq(all_74_3, n4)
% 205.54/31.73 | | | | | |
% 205.54/31.73 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n4, simplifying
% 205.54/31.73 | | | | | | with (58), (122), (168) gives:
% 205.54/31.73 | | | | | | (169) all_74_3 = n4 | gt(n4, all_74_3)
% 205.54/31.73 | | | | | |
% 205.54/31.73 | | | | | | BETA: splitting (164) gives:
% 205.54/31.73 | | | | | |
% 205.54/31.73 | | | | | | Case 1:
% 205.54/31.73 | | | | | | |
% 205.54/31.73 | | | | | | | (170) gt(n5, all_74_2)
% 205.54/31.73 | | | | | | |
% 205.54/31.73 | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, simplifying
% 205.54/31.73 | | | | | | | with (59), (125), (129), (170) gives:
% 205.54/31.73 | | | | | | | (171) leq(all_74_2, n4)
% 205.54/31.73 | | | | | | |
% 205.54/31.73 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n4,
% 205.54/31.73 | | | | | | | simplifying with (59), (122), (171) gives:
% 205.54/31.73 | | | | | | | (172) all_74_2 = n4 | gt(n4, all_74_2)
% 205.54/31.73 | | | | | | |
% 205.54/31.73 | | | | | | | BETA: splitting (163) gives:
% 205.54/31.73 | | | | | | |
% 205.54/31.73 | | | | | | | Case 1:
% 205.54/31.73 | | | | | | | |
% 205.54/31.73 | | | | | | | | (173) all_74_2 = n0
% 205.54/31.73 | | | | | | | |
% 205.54/31.73 | | | | | | | | REDUCE: (165), (173) imply:
% 205.54/31.73 | | | | | | | | (174) gt(n0, n0)
% 205.54/31.73 | | | | | | | |
% 205.54/31.73 | | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n0,
% 205.54/31.73 | | | | | | | | simplifying with (13), (174) gives:
% 205.54/31.73 | | | | | | | | (175) $false
% 205.54/31.73 | | | | | | | |
% 205.54/31.73 | | | | | | | | CLOSE: (175) is inconsistent.
% 205.54/31.73 | | | | | | | |
% 205.54/31.73 | | | | | | | Case 2:
% 205.54/31.73 | | | | | | | |
% 205.54/31.73 | | | | | | | | (176) ~ (all_74_2 = n0)
% 205.54/31.73 | | | | | | | |
% 205.54/31.73 | | | | | | | | BETA: splitting (161) gives:
% 205.54/31.73 | | | | | | | |
% 205.54/31.73 | | | | | | | | Case 1:
% 205.54/31.73 | | | | | | | | |
% 205.54/31.73 | | | | | | | | | (177) all_74_3 = n0
% 205.54/31.73 | | | | | | | | |
% 205.54/31.73 | | | | | | | | | REF_CLOSE: (58), (166), (177), (irreflexivity_gt) are
% 205.54/31.73 | | | | | | | | | inconsistent by sub-proof #45.
% 205.54/31.73 | | | | | | | | |
% 205.54/31.73 | | | | | | | | Case 2:
% 205.54/31.73 | | | | | | | | |
% 205.54/31.73 | | | | | | | | | (178) ~ (all_74_3 = n0)
% 205.54/31.73 | | | | | | | | |
% 205.54/31.73 | | | | | | | | | BETA: splitting (169) gives:
% 205.54/31.73 | | | | | | | | |
% 205.54/31.73 | | | | | | | | | Case 1:
% 205.54/31.73 | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | (179) gt(n4, all_74_3)
% 205.54/31.73 | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n4, n3,
% 205.54/31.73 | | | | | | | | | | simplifying with (58), (122), (128), (179) gives:
% 205.54/31.73 | | | | | | | | | | (180) leq(all_74_3, n3)
% 205.54/31.73 | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n3,
% 205.54/31.73 | | | | | | | | | | simplifying with (58), (115), (180) gives:
% 205.54/31.73 | | | | | | | | | | (181) all_74_3 = n3 | gt(n3, all_74_3)
% 205.54/31.73 | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | BETA: splitting (172) gives:
% 205.54/31.73 | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | Case 1:
% 205.54/31.73 | | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | | (182) gt(n4, all_74_2)
% 205.54/31.73 | | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n4, n3,
% 205.54/31.73 | | | | | | | | | | | simplifying with (59), (122), (128), (182) gives:
% 205.54/31.73 | | | | | | | | | | | (183) leq(all_74_2, n3)
% 205.54/31.73 | | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n3,
% 205.54/31.73 | | | | | | | | | | | simplifying with (59), (115), (183) gives:
% 205.54/31.73 | | | | | | | | | | | (184) all_74_2 = n3 | gt(n3, all_74_2)
% 205.54/31.73 | | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | | BETA: splitting (181) gives:
% 205.54/31.73 | | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | | Case 1:
% 205.54/31.73 | | | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | | | (185) gt(n3, all_74_3)
% 205.54/31.73 | | | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2,
% 205.54/31.73 | | | | | | | | | | | | simplifying with (58), (115), (127), (185) gives:
% 205.54/31.73 | | | | | | | | | | | | (186) leq(all_74_3, n2)
% 205.54/31.73 | | | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n2,
% 205.54/31.73 | | | | | | | | | | | | simplifying with (58), (104), (186) gives:
% 205.54/31.73 | | | | | | | | | | | | (187) all_74_3 = n2 | gt(n2, all_74_3)
% 205.54/31.73 | | | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | | | BETA: splitting (184) gives:
% 205.54/31.73 | | | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | | | Case 1:
% 205.54/31.73 | | | | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | | | | (188) gt(n3, all_74_2)
% 205.54/31.73 | | | | | | | | | | | | |
% 205.54/31.73 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2,
% 205.54/31.73 | | | | | | | | | | | | | simplifying with (59), (115), (127), (188) gives:
% 205.54/31.74 | | | | | | | | | | | | | (189) leq(all_74_2, n2)
% 205.54/31.74 | | | | | | | | | | | | |
% 205.54/31.74 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n2,
% 205.54/31.74 | | | | | | | | | | | | | simplifying with (59), (104), (189) gives:
% 205.54/31.74 | | | | | | | | | | | | | (190) all_74_2 = n2 | gt(n2, all_74_2)
% 205.54/31.74 | | | | | | | | | | | | |
% 205.54/31.74 | | | | | | | | | | | | | BETA: splitting (187) gives:
% 205.54/31.74 | | | | | | | | | | | | |
% 205.54/31.74 | | | | | | | | | | | | | Case 1:
% 205.54/31.74 | | | | | | | | | | | | | |
% 205.54/31.74 | | | | | | | | | | | | | | (191) gt(n2, all_74_3)
% 205.54/31.74 | | | | | | | | | | | | | |
% 205.54/31.74 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1,
% 205.54/31.74 | | | | | | | | | | | | | | simplifying with (58), (104), (126), (191) gives:
% 205.54/31.74 | | | | | | | | | | | | | | (192) leq(all_74_3, n1)
% 205.54/31.74 | | | | | | | | | | | | | |
% 205.54/31.74 | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_74_3, simplifying with
% 205.54/31.74 | | | | | | | | | | | | | | (58), (151), (192) gives:
% 205.54/31.74 | | | | | | | | | | | | | | (193) all_74_3 = n1 | all_74_3 = n0
% 205.54/31.74 | | | | | | | | | | | | | |
% 205.54/31.74 | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 205.54/31.74 | | | | | | | | | | | | | |
% 205.54/31.74 | | | | | | | | | | | | | | Case 1:
% 205.54/31.74 | | | | | | | | | | | | | | |
% 205.54/31.74 | | | | | | | | | | | | | | | (194) all_74_3 = n0
% 205.54/31.74 | | | | | | | | | | | | | | |
% 205.54/31.74 | | | | | | | | | | | | | | | REDUCE: (178), (194) imply:
% 205.54/31.74 | | | | | | | | | | | | | | | (195) $false
% 205.54/31.74 | | | | | | | | | | | | | | |
% 205.54/31.74 | | | | | | | | | | | | | | | CLOSE: (195) is inconsistent.
% 205.54/31.74 | | | | | | | | | | | | | | |
% 205.54/31.74 | | | | | | | | | | | | | | Case 2:
% 205.54/31.74 | | | | | | | | | | | | | | |
% 205.54/31.74 | | | | | | | | | | | | | | | (196) all_74_3 = n1
% 205.54/31.74 | | | | | | | | | | | | | | |
% 205.54/31.74 | | | | | | | | | | | | | | | REDUCE: (156), (196) imply:
% 205.54/31.74 | | | | | | | | | | | | | | | (197) a_select3(q_ds1_filter, all_74_2, n1) = all_74_0
% 205.54/31.74 | | | | | | | | | | | | | | |
% 205.54/31.74 | | | | | | | | | | | | | | | REDUCE: (155), (196) imply:
% 205.75/31.74 | | | | | | | | | | | | | | | (198) a_select3(q_ds1_filter, n1, all_74_2) = all_74_1
% 205.75/31.74 | | | | | | | | | | | | | | |
% 205.75/31.74 | | | | | | | | | | | | | | | REDUCE: (158), (196) imply:
% 205.75/31.74 | | | | | | | | | | | | | | | (199) leq(n1, n5)
% 205.75/31.74 | | | | | | | | | | | | | | |
% 205.75/31.74 | | | | | | | | | | | | | | | REDUCE: (151), (196) imply:
% 205.75/31.74 | | | | | | | | | | | | | | | (200) leq(n0, n1)
% 205.75/31.74 | | | | | | | | | | | | | | |
% 205.75/31.74 | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 205.75/31.74 | | | | | | | | | | | | | | |
% 205.75/31.74 | | | | | | | | | | | | | | | Case 1:
% 205.75/31.74 | | | | | | | | | | | | | | | |
% 205.75/31.74 | | | | | | | | | | | | | | | | (201) gt(n2, all_74_2)
% 205.75/31.74 | | | | | | | | | | | | | | | |
% 205.75/31.74 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1,
% 205.75/31.74 | | | | | | | | | | | | | | | | simplifying with (59), (104), (126), (201) gives:
% 205.75/31.74 | | | | | | | | | | | | | | | | (202) leq(all_74_2, n1)
% 205.75/31.74 | | | | | | | | | | | | | | | |
% 205.75/31.74 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_74_2, simplifying with
% 205.75/31.74 | | | | | | | | | | | | | | | | (59), (152), (202) gives:
% 205.75/31.74 | | | | | | | | | | | | | | | | (203) all_74_2 = n1 | all_74_2 = n0
% 205.75/31.74 | | | | | | | | | | | | | | | |
% 205.75/31.74 | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 205.75/31.74 | | | | | | | | | | | | | | | |
% 205.75/31.74 | | | | | | | | | | | | | | | | Case 1:
% 205.75/31.74 | | | | | | | | | | | | | | | | |
% 205.75/31.74 | | | | | | | | | | | | | | | | | (204) all_74_2 = n0
% 205.75/31.74 | | | | | | | | | | | | | | | | |
% 205.75/31.74 | | | | | | | | | | | | | | | | | REDUCE: (176), (204) imply:
% 205.75/31.74 | | | | | | | | | | | | | | | | | (205) $false
% 205.75/31.74 | | | | | | | | | | | | | | | | |
% 205.75/31.74 | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent.
% 205.75/31.74 | | | | | | | | | | | | | | | | |
% 205.75/31.74 | | | | | | | | | | | | | | | | Case 2:
% 205.75/31.74 | | | | | | | | | | | | | | | | |
% 205.75/31.74 | | | | | | | | | | | | | | | | | (206) all_74_2 = n1
% 205.75/31.74 | | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | | REDUCE: (197), (206) imply:
% 205.77/31.74 | | | | | | | | | | | | | | | | | (207) a_select3(q_ds1_filter, n1, n1) = all_74_0
% 205.77/31.74 | | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | | REDUCE: (198), (206) imply:
% 205.77/31.74 | | | | | | | | | | | | | | | | | (208) a_select3(q_ds1_filter, n1, n1) = all_74_1
% 205.77/31.74 | | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_74_1, all_74_0, n1,
% 205.77/31.74 | | | | | | | | | | | | | | | | | n1, q_ds1_filter, simplifying with (207), (208)
% 205.77/31.74 | | | | | | | | | | | | | | | | | gives:
% 205.77/31.74 | | | | | | | | | | | | | | | | | (209) all_74_0 = all_74_1
% 205.77/31.74 | | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | | REDUCE: (150), (209) imply:
% 205.77/31.74 | | | | | | | | | | | | | | | | | (210) $false
% 205.77/31.74 | | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | | CLOSE: (210) is inconsistent.
% 205.77/31.74 | | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | End of split
% 205.77/31.74 | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | Case 2:
% 205.77/31.74 | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | (211) all_74_2 = n2
% 205.77/31.74 | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | REDUCE: (197), (211) imply:
% 205.77/31.74 | | | | | | | | | | | | | | | | (212) a_select3(q_ds1_filter, n2, n1) = all_74_0
% 205.77/31.74 | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | REDUCE: (198), (211) imply:
% 205.77/31.74 | | | | | | | | | | | | | | | | (213) a_select3(q_ds1_filter, n1, n2) = all_74_1
% 205.77/31.74 | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | REDUCE: (157), (211) imply:
% 205.77/31.74 | | | | | | | | | | | | | | | | (214) leq(n2, n5)
% 205.77/31.74 | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | REDUCE: (152), (211) imply:
% 205.77/31.74 | | | | | | | | | | | | | | | | (215) leq(n0, n2)
% 205.77/31.74 | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, n2, all_74_1,
% 205.77/31.74 | | | | | | | | | | | | | | | | simplifying with (88), (104), (200), (213), (215)
% 205.77/31.74 | | | | | | | | | | | | | | | | gives:
% 205.77/31.74 | | | | | | | | | | | | | | | | (216) ~ leq(n2, all_74_19) | ~ leq(n1, all_74_19) |
% 205.77/31.74 | | | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n2, n1) = all_74_1 &
% 205.77/31.74 | | | | | | | | | | | | | | | | $i(all_74_1))
% 205.77/31.74 | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 205.77/31.74 | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | Case 1:
% 205.77/31.74 | | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | | (217) ~ leq(n2, all_74_19)
% 205.77/31.74 | | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | | REDUCE: (142), (217) imply:
% 205.77/31.74 | | | | | | | | | | | | | | | | | (218) ~ leq(n2, n5)
% 205.77/31.74 | | | | | | | | | | | | | | | | |
% 205.77/31.74 | | | | | | | | | | | | | | | | | PRED_UNIFY: (214), (218) imply:
% 205.77/31.75 | | | | | | | | | | | | | | | | | (219) $false
% 205.77/31.75 | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent.
% 205.77/31.75 | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | Case 2:
% 205.77/31.75 | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | (220) ~ leq(n1, all_74_19) | (a_select3(q_ds1_filter,
% 205.77/31.75 | | | | | | | | | | | | | | | | | n2, n1) = all_74_1 & $i(all_74_1))
% 205.77/31.75 | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 205.77/31.75 | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | Case 1:
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | | (221) ~ leq(n1, all_74_19)
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | | REDUCE: (142), (221) imply:
% 205.77/31.75 | | | | | | | | | | | | | | | | | | (222) ~ leq(n1, n5)
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (199), (222) imply:
% 205.77/31.75 | | | | | | | | | | | | | | | | | | (223) $false
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | | CLOSE: (223) is inconsistent.
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | Case 2:
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | | (224) a_select3(q_ds1_filter, n2, n1) = all_74_1 &
% 205.77/31.75 | | | | | | | | | | | | | | | | | | $i(all_74_1)
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | | ALPHA: (224) implies:
% 205.77/31.75 | | | | | | | | | | | | | | | | | | (225) a_select3(q_ds1_filter, n2, n1) = all_74_1
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (150), (212), (225) are inconsistent by
% 205.77/31.75 | | | | | | | | | | | | | | | | | | sub-proof #44.
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | End of split
% 205.77/31.75 | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | End of split
% 205.77/31.75 | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | End of split
% 205.77/31.75 | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | End of split
% 205.77/31.75 | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | Case 2:
% 205.77/31.75 | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | (226) all_74_3 = n2
% 205.77/31.75 | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | REDUCE: (156), (226) imply:
% 205.77/31.75 | | | | | | | | | | | | | | (227) a_select3(q_ds1_filter, all_74_2, n2) = all_74_0
% 205.77/31.75 | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | REDUCE: (155), (226) imply:
% 205.77/31.75 | | | | | | | | | | | | | | (228) a_select3(q_ds1_filter, n2, all_74_2) = all_74_1
% 205.77/31.75 | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | REDUCE: (158), (226) imply:
% 205.77/31.75 | | | | | | | | | | | | | | (229) leq(n2, n5)
% 205.77/31.75 | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | REDUCE: (151), (226) imply:
% 205.77/31.75 | | | | | | | | | | | | | | (230) leq(n0, n2)
% 205.77/31.75 | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 205.77/31.75 | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | Case 1:
% 205.77/31.75 | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | (231) gt(n2, all_74_2)
% 205.77/31.75 | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1,
% 205.77/31.75 | | | | | | | | | | | | | | | simplifying with (59), (104), (126), (231) gives:
% 205.77/31.75 | | | | | | | | | | | | | | | (232) leq(all_74_2, n1)
% 205.77/31.75 | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_74_2, simplifying with
% 205.77/31.75 | | | | | | | | | | | | | | | (59), (152), (232) gives:
% 205.77/31.75 | | | | | | | | | | | | | | | (233) all_74_2 = n1 | all_74_2 = n0
% 205.77/31.75 | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 205.77/31.75 | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | Case 1:
% 205.77/31.75 | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | (234) all_74_2 = n0
% 205.77/31.75 | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | REDUCE: (176), (234) imply:
% 205.77/31.75 | | | | | | | | | | | | | | | | (235) $false
% 205.77/31.75 | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | CLOSE: (235) is inconsistent.
% 205.77/31.75 | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | Case 2:
% 205.77/31.75 | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | (236) all_74_2 = n1
% 205.77/31.75 | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | REDUCE: (227), (236) imply:
% 205.77/31.75 | | | | | | | | | | | | | | | | (237) a_select3(q_ds1_filter, n1, n2) = all_74_0
% 205.77/31.75 | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | REDUCE: (228), (236) imply:
% 205.77/31.75 | | | | | | | | | | | | | | | | (238) a_select3(q_ds1_filter, n2, n1) = all_74_1
% 205.77/31.75 | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | REDUCE: (157), (236) imply:
% 205.77/31.75 | | | | | | | | | | | | | | | | (239) leq(n1, n5)
% 205.77/31.75 | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | REDUCE: (152), (236) imply:
% 205.77/31.75 | | | | | | | | | | | | | | | | (240) leq(n0, n1)
% 205.77/31.75 | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, n2, all_74_0,
% 205.77/31.75 | | | | | | | | | | | | | | | | simplifying with (88), (104), (230), (237), (240)
% 205.77/31.75 | | | | | | | | | | | | | | | | gives:
% 205.77/31.75 | | | | | | | | | | | | | | | | (241) ~ leq(n2, all_74_19) | ~ leq(n1, all_74_19) |
% 205.77/31.75 | | | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n2, n1) = all_74_0 &
% 205.77/31.75 | | | | | | | | | | | | | | | | $i(all_74_0))
% 205.77/31.75 | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 205.77/31.75 | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | Case 1:
% 205.77/31.75 | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | (242) ~ leq(n2, all_74_19)
% 205.77/31.75 | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | REDUCE: (142), (242) imply:
% 205.77/31.75 | | | | | | | | | | | | | | | | | (243) ~ leq(n2, n5)
% 205.77/31.75 | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | PRED_UNIFY: (229), (243) imply:
% 205.77/31.75 | | | | | | | | | | | | | | | | | (244) $false
% 205.77/31.75 | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | CLOSE: (244) is inconsistent.
% 205.77/31.75 | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | Case 2:
% 205.77/31.75 | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | (245) ~ leq(n1, all_74_19) | (a_select3(q_ds1_filter,
% 205.77/31.75 | | | | | | | | | | | | | | | | | n2, n1) = all_74_0 & $i(all_74_0))
% 205.77/31.75 | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 205.77/31.75 | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | Case 1:
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | | (246) ~ leq(n1, all_74_19)
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | | REDUCE: (142), (246) imply:
% 205.77/31.75 | | | | | | | | | | | | | | | | | | (247) ~ leq(n1, n5)
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (239), (247) imply:
% 205.77/31.75 | | | | | | | | | | | | | | | | | | (248) $false
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | | CLOSE: (248) is inconsistent.
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | Case 2:
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | | (249) a_select3(q_ds1_filter, n2, n1) = all_74_0 &
% 205.77/31.75 | | | | | | | | | | | | | | | | | | $i(all_74_0)
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | | ALPHA: (249) implies:
% 205.77/31.75 | | | | | | | | | | | | | | | | | | (250) a_select3(q_ds1_filter, n2, n1) = all_74_0
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (150), (238), (250) are inconsistent by
% 205.77/31.75 | | | | | | | | | | | | | | | | | | sub-proof #44.
% 205.77/31.75 | | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | | End of split
% 205.77/31.75 | | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | | End of split
% 205.77/31.75 | | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | End of split
% 205.77/31.75 | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | Case 2:
% 205.77/31.75 | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | (251) all_74_2 = n2
% 205.77/31.75 | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | REDUCE: (227), (251) imply:
% 205.77/31.75 | | | | | | | | | | | | | | | (252) a_select3(q_ds1_filter, n2, n2) = all_74_0
% 205.77/31.75 | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | REDUCE: (228), (251) imply:
% 205.77/31.75 | | | | | | | | | | | | | | | (253) a_select3(q_ds1_filter, n2, n2) = all_74_1
% 205.77/31.75 | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_74_1, all_74_0, n2,
% 205.77/31.75 | | | | | | | | | | | | | | | n2, q_ds1_filter, simplifying with (252), (253)
% 205.77/31.75 | | | | | | | | | | | | | | | gives:
% 205.77/31.75 | | | | | | | | | | | | | | | (254) all_74_0 = all_74_1
% 205.77/31.75 | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | REDUCE: (150), (254) imply:
% 205.77/31.75 | | | | | | | | | | | | | | | (255) $false
% 205.77/31.75 | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | | CLOSE: (255) is inconsistent.
% 205.77/31.75 | | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | | End of split
% 205.77/31.75 | | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | End of split
% 205.77/31.75 | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | Case 2:
% 205.77/31.75 | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | (256) all_74_2 = n3
% 205.77/31.75 | | | | | | | | | | | | |
% 205.77/31.75 | | | | | | | | | | | | | REDUCE: (156), (256) imply:
% 205.77/31.76 | | | | | | | | | | | | | (257) a_select3(q_ds1_filter, n3, all_74_3) = all_74_0
% 205.77/31.76 | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | REDUCE: (155), (256) imply:
% 205.77/31.76 | | | | | | | | | | | | | (258) a_select3(q_ds1_filter, all_74_3, n3) = all_74_1
% 205.77/31.76 | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | REDUCE: (157), (256) imply:
% 205.77/31.76 | | | | | | | | | | | | | (259) leq(n3, n5)
% 205.77/31.76 | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | REDUCE: (152), (256) imply:
% 205.77/31.76 | | | | | | | | | | | | | (260) leq(n0, n3)
% 205.77/31.76 | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | BETA: splitting (187) gives:
% 205.77/31.76 | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | Case 1:
% 205.77/31.76 | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | (261) gt(n2, all_74_3)
% 205.77/31.76 | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1,
% 205.77/31.76 | | | | | | | | | | | | | | simplifying with (58), (104), (126), (261) gives:
% 205.77/31.76 | | | | | | | | | | | | | | (262) leq(all_74_3, n1)
% 205.77/31.76 | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_74_3, simplifying with
% 205.77/31.76 | | | | | | | | | | | | | | (58), (151), (262) gives:
% 205.77/31.76 | | | | | | | | | | | | | | (263) all_74_3 = n1 | all_74_3 = n0
% 205.77/31.76 | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 205.77/31.76 | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | Case 1:
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | (264) all_74_3 = n0
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | REDUCE: (178), (264) imply:
% 205.77/31.76 | | | | | | | | | | | | | | | (265) $false
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | CLOSE: (265) is inconsistent.
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | Case 2:
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | (266) all_74_3 = n1
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | REDUCE: (258), (266) imply:
% 205.77/31.76 | | | | | | | | | | | | | | | (267) a_select3(q_ds1_filter, n1, n3) = all_74_1
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | REDUCE: (257), (266) imply:
% 205.77/31.76 | | | | | | | | | | | | | | | (268) a_select3(q_ds1_filter, n3, n1) = all_74_0
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | REDUCE: (158), (266) imply:
% 205.77/31.76 | | | | | | | | | | | | | | | (269) leq(n1, n5)
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | REDUCE: (151), (266) imply:
% 205.77/31.76 | | | | | | | | | | | | | | | (270) leq(n0, n1)
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, n3, all_74_1,
% 205.77/31.76 | | | | | | | | | | | | | | | simplifying with (88), (115), (260), (267), (270)
% 205.77/31.76 | | | | | | | | | | | | | | | gives:
% 205.77/31.76 | | | | | | | | | | | | | | | (271) ~ leq(n3, all_74_19) | ~ leq(n1, all_74_19) |
% 205.77/31.76 | | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n3, n1) = all_74_1 &
% 205.77/31.76 | | | | | | | | | | | | | | | $i(all_74_1))
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | Case 1:
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | (272) ~ leq(n3, all_74_19)
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | REDUCE: (142), (272) imply:
% 205.77/31.76 | | | | | | | | | | | | | | | | (273) ~ leq(n3, n5)
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | PRED_UNIFY: (259), (273) imply:
% 205.77/31.76 | | | | | | | | | | | | | | | | (274) $false
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | CLOSE: (274) is inconsistent.
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | Case 2:
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | (275) ~ leq(n1, all_74_19) | (a_select3(q_ds1_filter,
% 205.77/31.76 | | | | | | | | | | | | | | | | n3, n1) = all_74_1 & $i(all_74_1))
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | Case 1:
% 205.77/31.76 | | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | | (276) ~ leq(n1, all_74_19)
% 205.77/31.76 | | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | | REDUCE: (142), (276) imply:
% 205.77/31.76 | | | | | | | | | | | | | | | | | (277) ~ leq(n1, n5)
% 205.77/31.76 | | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | | PRED_UNIFY: (269), (277) imply:
% 205.77/31.76 | | | | | | | | | | | | | | | | | (278) $false
% 205.77/31.76 | | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | | CLOSE: (278) is inconsistent.
% 205.77/31.76 | | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | Case 2:
% 205.77/31.76 | | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | | (279) a_select3(q_ds1_filter, n3, n1) = all_74_1 &
% 205.77/31.76 | | | | | | | | | | | | | | | | | $i(all_74_1)
% 205.77/31.76 | | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | | ALPHA: (279) implies:
% 205.77/31.76 | | | | | | | | | | | | | | | | | (280) a_select3(q_ds1_filter, n3, n1) = all_74_1
% 205.77/31.76 | | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (150), (268), (280) are inconsistent by
% 205.77/31.76 | | | | | | | | | | | | | | | | | sub-proof #43.
% 205.77/31.76 | | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | End of split
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | End of split
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | End of split
% 205.77/31.76 | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | Case 2:
% 205.77/31.76 | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | (281) all_74_3 = n2
% 205.77/31.76 | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | REDUCE: (258), (281) imply:
% 205.77/31.76 | | | | | | | | | | | | | | (282) a_select3(q_ds1_filter, n2, n3) = all_74_1
% 205.77/31.76 | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | REDUCE: (257), (281) imply:
% 205.77/31.76 | | | | | | | | | | | | | | (283) a_select3(q_ds1_filter, n3, n2) = all_74_0
% 205.77/31.76 | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | REDUCE: (158), (281) imply:
% 205.77/31.76 | | | | | | | | | | | | | | (284) leq(n2, n5)
% 205.77/31.76 | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | REDUCE: (151), (281) imply:
% 205.77/31.76 | | | | | | | | | | | | | | (285) leq(n0, n2)
% 205.77/31.76 | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n2, n3, all_74_1,
% 205.77/31.76 | | | | | | | | | | | | | | simplifying with (104), (115), (260), (282), (285)
% 205.77/31.76 | | | | | | | | | | | | | | gives:
% 205.77/31.76 | | | | | | | | | | | | | | (286) ~ leq(n3, all_74_19) | ~ leq(n2, all_74_19) |
% 205.77/31.76 | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n3, n2) = all_74_1 &
% 205.77/31.76 | | | | | | | | | | | | | | $i(all_74_1))
% 205.77/31.76 | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 205.77/31.76 | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | Case 1:
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | (287) ~ leq(n3, all_74_19)
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | REDUCE: (142), (287) imply:
% 205.77/31.76 | | | | | | | | | | | | | | | (288) ~ leq(n3, n5)
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | PRED_UNIFY: (259), (288) imply:
% 205.77/31.76 | | | | | | | | | | | | | | | (289) $false
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | CLOSE: (289) is inconsistent.
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | Case 2:
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | (290) ~ leq(n2, all_74_19) | (a_select3(q_ds1_filter,
% 205.77/31.76 | | | | | | | | | | | | | | | n3, n2) = all_74_1 & $i(all_74_1))
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | Case 1:
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | (291) ~ leq(n2, all_74_19)
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | REDUCE: (142), (291) imply:
% 205.77/31.76 | | | | | | | | | | | | | | | | (292) ~ leq(n2, n5)
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | PRED_UNIFY: (284), (292) imply:
% 205.77/31.76 | | | | | | | | | | | | | | | | (293) $false
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | CLOSE: (293) is inconsistent.
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | Case 2:
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | (294) a_select3(q_ds1_filter, n3, n2) = all_74_1 &
% 205.77/31.76 | | | | | | | | | | | | | | | | $i(all_74_1)
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | ALPHA: (294) implies:
% 205.77/31.76 | | | | | | | | | | | | | | | | (295) a_select3(q_ds1_filter, n3, n2) = all_74_1
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | | REF_CLOSE: (19), (150), (283), (295) are inconsistent by
% 205.77/31.76 | | | | | | | | | | | | | | | | sub-proof #42.
% 205.77/31.76 | | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | | End of split
% 205.77/31.76 | | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | | End of split
% 205.77/31.76 | | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | End of split
% 205.77/31.76 | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | End of split
% 205.77/31.76 | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | Case 2:
% 205.77/31.76 | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | (296) all_74_3 = n3
% 205.77/31.76 | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | REDUCE: (156), (296) imply:
% 205.77/31.76 | | | | | | | | | | | | (297) a_select3(q_ds1_filter, all_74_2, n3) = all_74_0
% 205.77/31.76 | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | REDUCE: (155), (296) imply:
% 205.77/31.76 | | | | | | | | | | | | (298) a_select3(q_ds1_filter, n3, all_74_2) = all_74_1
% 205.77/31.76 | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | REDUCE: (158), (296) imply:
% 205.77/31.76 | | | | | | | | | | | | (299) leq(n3, n5)
% 205.77/31.76 | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | REDUCE: (151), (296) imply:
% 205.77/31.76 | | | | | | | | | | | | (300) leq(n0, n3)
% 205.77/31.76 | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | BETA: splitting (184) gives:
% 205.77/31.76 | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | Case 1:
% 205.77/31.76 | | | | | | | | | | | | |
% 205.77/31.76 | | | | | | | | | | | | | (301) gt(n3, all_74_2)
% 205.77/31.77 | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2,
% 205.77/31.77 | | | | | | | | | | | | | simplifying with (59), (115), (127), (301) gives:
% 205.77/31.77 | | | | | | | | | | | | | (302) leq(all_74_2, n2)
% 205.77/31.77 | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n2,
% 205.77/31.77 | | | | | | | | | | | | | simplifying with (59), (104), (302) gives:
% 205.77/31.77 | | | | | | | | | | | | | (303) all_74_2 = n2 | gt(n2, all_74_2)
% 205.77/31.77 | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | BETA: splitting (303) gives:
% 205.77/31.77 | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | Case 1:
% 205.77/31.77 | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | (304) gt(n2, all_74_2)
% 205.77/31.77 | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1,
% 205.77/31.77 | | | | | | | | | | | | | | simplifying with (59), (104), (126), (304) gives:
% 205.77/31.77 | | | | | | | | | | | | | | (305) leq(all_74_2, n1)
% 205.77/31.77 | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_74_2, simplifying with
% 205.77/31.77 | | | | | | | | | | | | | | (59), (152), (305) gives:
% 205.77/31.77 | | | | | | | | | | | | | | (306) all_74_2 = n1 | all_74_2 = n0
% 205.77/31.77 | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 205.77/31.77 | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | Case 1:
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | (307) all_74_2 = n0
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | REDUCE: (176), (307) imply:
% 205.77/31.77 | | | | | | | | | | | | | | | (308) $false
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | CLOSE: (308) is inconsistent.
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | Case 2:
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | (309) all_74_2 = n1
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | REDUCE: (297), (309) imply:
% 205.77/31.77 | | | | | | | | | | | | | | | (310) a_select3(q_ds1_filter, n1, n3) = all_74_0
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | REDUCE: (298), (309) imply:
% 205.77/31.77 | | | | | | | | | | | | | | | (311) a_select3(q_ds1_filter, n3, n1) = all_74_1
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | REDUCE: (157), (309) imply:
% 205.77/31.77 | | | | | | | | | | | | | | | (312) leq(n1, n5)
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | REDUCE: (152), (309) imply:
% 205.77/31.77 | | | | | | | | | | | | | | | (313) leq(n0, n1)
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, n3, all_74_0,
% 205.77/31.77 | | | | | | | | | | | | | | | simplifying with (88), (115), (300), (310), (313)
% 205.77/31.77 | | | | | | | | | | | | | | | gives:
% 205.77/31.77 | | | | | | | | | | | | | | | (314) ~ leq(n3, all_74_19) | ~ leq(n1, all_74_19) |
% 205.77/31.77 | | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n3, n1) = all_74_0 &
% 205.77/31.77 | | | | | | | | | | | | | | | $i(all_74_0))
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | Case 1:
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | (315) ~ leq(n3, all_74_19)
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | REDUCE: (142), (315) imply:
% 205.77/31.77 | | | | | | | | | | | | | | | | (316) ~ leq(n3, n5)
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | PRED_UNIFY: (299), (316) imply:
% 205.77/31.77 | | | | | | | | | | | | | | | | (317) $false
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | CLOSE: (317) is inconsistent.
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | Case 2:
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | (318) ~ leq(n1, all_74_19) | (a_select3(q_ds1_filter,
% 205.77/31.77 | | | | | | | | | | | | | | | | n3, n1) = all_74_0 & $i(all_74_0))
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | Case 1:
% 205.77/31.77 | | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | | (319) ~ leq(n1, all_74_19)
% 205.77/31.77 | | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | | REDUCE: (142), (319) imply:
% 205.77/31.77 | | | | | | | | | | | | | | | | | (320) ~ leq(n1, n5)
% 205.77/31.77 | | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | | PRED_UNIFY: (312), (320) imply:
% 205.77/31.77 | | | | | | | | | | | | | | | | | (321) $false
% 205.77/31.77 | | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | | CLOSE: (321) is inconsistent.
% 205.77/31.77 | | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | Case 2:
% 205.77/31.77 | | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | | (322) a_select3(q_ds1_filter, n3, n1) = all_74_0 &
% 205.77/31.77 | | | | | | | | | | | | | | | | | $i(all_74_0)
% 205.77/31.77 | | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | | ALPHA: (322) implies:
% 205.77/31.77 | | | | | | | | | | | | | | | | | (323) a_select3(q_ds1_filter, n3, n1) = all_74_0
% 205.77/31.77 | | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (150), (311), (323) are inconsistent by
% 205.77/31.77 | | | | | | | | | | | | | | | | | sub-proof #43.
% 205.77/31.77 | | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | End of split
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | End of split
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | End of split
% 205.77/31.77 | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | Case 2:
% 205.77/31.77 | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | (324) all_74_2 = n2
% 205.77/31.77 | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | REDUCE: (297), (324) imply:
% 205.77/31.77 | | | | | | | | | | | | | | (325) a_select3(q_ds1_filter, n2, n3) = all_74_0
% 205.77/31.77 | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | REDUCE: (298), (324) imply:
% 205.77/31.77 | | | | | | | | | | | | | | (326) a_select3(q_ds1_filter, n3, n2) = all_74_1
% 205.77/31.77 | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | REDUCE: (157), (324) imply:
% 205.77/31.77 | | | | | | | | | | | | | | (327) leq(n2, n5)
% 205.77/31.77 | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | REDUCE: (152), (324) imply:
% 205.77/31.77 | | | | | | | | | | | | | | (328) leq(n0, n2)
% 205.77/31.77 | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n2, n3, all_74_0,
% 205.77/31.77 | | | | | | | | | | | | | | simplifying with (104), (115), (300), (325), (328)
% 205.77/31.77 | | | | | | | | | | | | | | gives:
% 205.77/31.77 | | | | | | | | | | | | | | (329) ~ leq(n3, all_74_19) | ~ leq(n2, all_74_19) |
% 205.77/31.77 | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n3, n2) = all_74_0 &
% 205.77/31.77 | | | | | | | | | | | | | | $i(all_74_0))
% 205.77/31.77 | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | BETA: splitting (329) gives:
% 205.77/31.77 | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | Case 1:
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | (330) ~ leq(n3, all_74_19)
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | REDUCE: (142), (330) imply:
% 205.77/31.77 | | | | | | | | | | | | | | | (331) ~ leq(n3, n5)
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | PRED_UNIFY: (299), (331) imply:
% 205.77/31.77 | | | | | | | | | | | | | | | (332) $false
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | CLOSE: (332) is inconsistent.
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | Case 2:
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | (333) ~ leq(n2, all_74_19) | (a_select3(q_ds1_filter,
% 205.77/31.77 | | | | | | | | | | | | | | | n3, n2) = all_74_0 & $i(all_74_0))
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | Case 1:
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | (334) ~ leq(n2, all_74_19)
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | REDUCE: (142), (334) imply:
% 205.77/31.77 | | | | | | | | | | | | | | | | (335) ~ leq(n2, n5)
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | PRED_UNIFY: (327), (335) imply:
% 205.77/31.77 | | | | | | | | | | | | | | | | (336) $false
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | CLOSE: (336) is inconsistent.
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | Case 2:
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | (337) a_select3(q_ds1_filter, n3, n2) = all_74_0 &
% 205.77/31.77 | | | | | | | | | | | | | | | | $i(all_74_0)
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | ALPHA: (337) implies:
% 205.77/31.77 | | | | | | | | | | | | | | | | (338) a_select3(q_ds1_filter, n3, n2) = all_74_0
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | | REF_CLOSE: (19), (150), (326), (338) are inconsistent by
% 205.77/31.77 | | | | | | | | | | | | | | | | sub-proof #42.
% 205.77/31.77 | | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | | End of split
% 205.77/31.77 | | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | | End of split
% 205.77/31.77 | | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | End of split
% 205.77/31.77 | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | Case 2:
% 205.77/31.77 | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | (339) all_74_2 = n3
% 205.77/31.77 | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | REDUCE: (297), (339) imply:
% 205.77/31.77 | | | | | | | | | | | | | (340) a_select3(q_ds1_filter, n3, n3) = all_74_0
% 205.77/31.77 | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | REDUCE: (298), (339) imply:
% 205.77/31.77 | | | | | | | | | | | | | (341) a_select3(q_ds1_filter, n3, n3) = all_74_1
% 205.77/31.77 | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_74_1, all_74_0, n3,
% 205.77/31.77 | | | | | | | | | | | | | n3, q_ds1_filter, simplifying with (340), (341)
% 205.77/31.77 | | | | | | | | | | | | | gives:
% 205.77/31.77 | | | | | | | | | | | | | (342) all_74_0 = all_74_1
% 205.77/31.77 | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | REDUCE: (150), (342) imply:
% 205.77/31.77 | | | | | | | | | | | | | (343) $false
% 205.77/31.77 | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | | CLOSE: (343) is inconsistent.
% 205.77/31.77 | | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | | End of split
% 205.77/31.77 | | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | End of split
% 205.77/31.77 | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | Case 2:
% 205.77/31.77 | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | (344) all_74_2 = n4
% 205.77/31.77 | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | REDUCE: (156), (344) imply:
% 205.77/31.77 | | | | | | | | | | | (345) a_select3(q_ds1_filter, n4, all_74_3) = all_74_0
% 205.77/31.77 | | | | | | | | | | |
% 205.77/31.77 | | | | | | | | | | | REDUCE: (155), (344) imply:
% 205.77/31.78 | | | | | | | | | | | (346) a_select3(q_ds1_filter, all_74_3, n4) = all_74_1
% 205.77/31.78 | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | REDUCE: (157), (344) imply:
% 205.77/31.78 | | | | | | | | | | | (347) leq(n4, n5)
% 205.77/31.78 | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | REDUCE: (152), (344) imply:
% 205.77/31.78 | | | | | | | | | | | (348) leq(n0, n4)
% 205.77/31.78 | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | BETA: splitting (181) gives:
% 205.77/31.78 | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | Case 1:
% 205.77/31.78 | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | (349) gt(n3, all_74_3)
% 205.77/31.78 | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2,
% 205.77/31.78 | | | | | | | | | | | | simplifying with (58), (115), (127), (349) gives:
% 205.77/31.78 | | | | | | | | | | | | (350) leq(all_74_3, n2)
% 205.77/31.78 | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n2,
% 205.77/31.78 | | | | | | | | | | | | simplifying with (58), (104), (350) gives:
% 205.77/31.78 | | | | | | | | | | | | (351) all_74_3 = n2 | gt(n2, all_74_3)
% 205.77/31.78 | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | BETA: splitting (351) gives:
% 205.77/31.78 | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | Case 1:
% 205.77/31.78 | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | (352) gt(n2, all_74_3)
% 205.77/31.78 | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1,
% 205.77/31.78 | | | | | | | | | | | | | simplifying with (58), (104), (126), (352) gives:
% 205.77/31.78 | | | | | | | | | | | | | (353) leq(all_74_3, n1)
% 205.77/31.78 | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_74_3, simplifying with
% 205.77/31.78 | | | | | | | | | | | | | (58), (151), (353) gives:
% 205.77/31.78 | | | | | | | | | | | | | (354) all_74_3 = n1 | all_74_3 = n0
% 205.77/31.78 | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | BETA: splitting (354) gives:
% 205.77/31.78 | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | Case 1:
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | (355) all_74_3 = n0
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | REDUCE: (178), (355) imply:
% 205.77/31.78 | | | | | | | | | | | | | | (356) $false
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | CLOSE: (356) is inconsistent.
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | Case 2:
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | (357) all_74_3 = n1
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | REDUCE: (346), (357) imply:
% 205.77/31.78 | | | | | | | | | | | | | | (358) a_select3(q_ds1_filter, n1, n4) = all_74_1
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | REDUCE: (345), (357) imply:
% 205.77/31.78 | | | | | | | | | | | | | | (359) a_select3(q_ds1_filter, n4, n1) = all_74_0
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | REDUCE: (158), (357) imply:
% 205.77/31.78 | | | | | | | | | | | | | | (360) leq(n1, n5)
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | REDUCE: (151), (357) imply:
% 205.77/31.78 | | | | | | | | | | | | | | (361) leq(n0, n1)
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, n4, all_74_1,
% 205.77/31.78 | | | | | | | | | | | | | | simplifying with (88), (122), (348), (358), (361)
% 205.77/31.78 | | | | | | | | | | | | | | gives:
% 205.77/31.78 | | | | | | | | | | | | | | (362) ~ leq(n4, all_74_19) | ~ leq(n1, all_74_19) |
% 205.77/31.78 | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n4, n1) = all_74_1 &
% 205.77/31.78 | | | | | | | | | | | | | | $i(all_74_1))
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | BETA: splitting (362) gives:
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | Case 1:
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | (363) ~ leq(n4, all_74_19)
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | REDUCE: (142), (363) imply:
% 205.77/31.78 | | | | | | | | | | | | | | | (364) ~ leq(n4, n5)
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | PRED_UNIFY: (347), (364) imply:
% 205.77/31.78 | | | | | | | | | | | | | | | (365) $false
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | CLOSE: (365) is inconsistent.
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | Case 2:
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | (366) ~ leq(n1, all_74_19) | (a_select3(q_ds1_filter,
% 205.77/31.78 | | | | | | | | | | | | | | | n4, n1) = all_74_1 & $i(all_74_1))
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | BETA: splitting (366) gives:
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | Case 1:
% 205.77/31.78 | | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | | (367) ~ leq(n1, all_74_19)
% 205.77/31.78 | | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | | REDUCE: (142), (367) imply:
% 205.77/31.78 | | | | | | | | | | | | | | | | (368) ~ leq(n1, n5)
% 205.77/31.78 | | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | | PRED_UNIFY: (360), (368) imply:
% 205.77/31.78 | | | | | | | | | | | | | | | | (369) $false
% 205.77/31.78 | | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | | CLOSE: (369) is inconsistent.
% 205.77/31.78 | | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | Case 2:
% 205.77/31.78 | | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | | (370) a_select3(q_ds1_filter, n4, n1) = all_74_1 &
% 205.77/31.78 | | | | | | | | | | | | | | | | $i(all_74_1)
% 205.77/31.78 | | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | | ALPHA: (370) implies:
% 205.77/31.78 | | | | | | | | | | | | | | | | (371) a_select3(q_ds1_filter, n4, n1) = all_74_1
% 205.77/31.78 | | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_74_0, all_74_1, n1,
% 205.77/31.78 | | | | | | | | | | | | | | | | n4, q_ds1_filter, simplifying with (359), (371)
% 205.77/31.78 | | | | | | | | | | | | | | | | gives:
% 205.77/31.78 | | | | | | | | | | | | | | | | (372) all_74_0 = all_74_1
% 205.77/31.78 | | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | | REDUCE: (150), (372) imply:
% 205.77/31.78 | | | | | | | | | | | | | | | | (373) $false
% 205.77/31.78 | | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | | CLOSE: (373) is inconsistent.
% 205.77/31.78 | | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | End of split
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | End of split
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | End of split
% 205.77/31.78 | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | Case 2:
% 205.77/31.78 | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | (374) all_74_3 = n2
% 205.77/31.78 | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | REDUCE: (346), (374) imply:
% 205.77/31.78 | | | | | | | | | | | | | (375) a_select3(q_ds1_filter, n2, n4) = all_74_1
% 205.77/31.78 | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | REDUCE: (345), (374) imply:
% 205.77/31.78 | | | | | | | | | | | | | (376) a_select3(q_ds1_filter, n4, n2) = all_74_0
% 205.77/31.78 | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | REDUCE: (158), (374) imply:
% 205.77/31.78 | | | | | | | | | | | | | (377) leq(n2, n5)
% 205.77/31.78 | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | REDUCE: (151), (374) imply:
% 205.77/31.78 | | | | | | | | | | | | | (378) leq(n0, n2)
% 205.77/31.78 | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n2, n4, all_74_1,
% 205.77/31.78 | | | | | | | | | | | | | simplifying with (104), (122), (348), (375), (378)
% 205.77/31.78 | | | | | | | | | | | | | gives:
% 205.77/31.78 | | | | | | | | | | | | | (379) ~ leq(n4, all_74_19) | ~ leq(n2, all_74_19) |
% 205.77/31.78 | | | | | | | | | | | | | (a_select3(q_ds1_filter, n4, n2) = all_74_1 &
% 205.77/31.78 | | | | | | | | | | | | | $i(all_74_1))
% 205.77/31.78 | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | BETA: splitting (379) gives:
% 205.77/31.78 | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | Case 1:
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | (380) ~ leq(n4, all_74_19)
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | REDUCE: (142), (380) imply:
% 205.77/31.78 | | | | | | | | | | | | | | (381) ~ leq(n4, n5)
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | PRED_UNIFY: (347), (381) imply:
% 205.77/31.78 | | | | | | | | | | | | | | (382) $false
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | CLOSE: (382) is inconsistent.
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | Case 2:
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | (383) ~ leq(n2, all_74_19) | (a_select3(q_ds1_filter,
% 205.77/31.78 | | | | | | | | | | | | | | n4, n2) = all_74_1 & $i(all_74_1))
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | BETA: splitting (383) gives:
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | Case 1:
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | (384) ~ leq(n2, all_74_19)
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | REDUCE: (142), (384) imply:
% 205.77/31.78 | | | | | | | | | | | | | | | (385) ~ leq(n2, n5)
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | PRED_UNIFY: (377), (385) imply:
% 205.77/31.78 | | | | | | | | | | | | | | | (386) $false
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | CLOSE: (386) is inconsistent.
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | Case 2:
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | (387) a_select3(q_ds1_filter, n4, n2) = all_74_1 &
% 205.77/31.78 | | | | | | | | | | | | | | | $i(all_74_1)
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | ALPHA: (387) implies:
% 205.77/31.78 | | | | | | | | | | | | | | | (388) a_select3(q_ds1_filter, n4, n2) = all_74_1
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_74_0, all_74_1, n2,
% 205.77/31.78 | | | | | | | | | | | | | | | n4, q_ds1_filter, simplifying with (376), (388)
% 205.77/31.78 | | | | | | | | | | | | | | | gives:
% 205.77/31.78 | | | | | | | | | | | | | | | (389) all_74_0 = all_74_1
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | REDUCE: (150), (389) imply:
% 205.77/31.78 | | | | | | | | | | | | | | | (390) $false
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | | CLOSE: (390) is inconsistent.
% 205.77/31.78 | | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | | End of split
% 205.77/31.78 | | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | | End of split
% 205.77/31.78 | | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | End of split
% 205.77/31.78 | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | Case 2:
% 205.77/31.78 | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | (391) all_74_3 = n3
% 205.77/31.78 | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | REDUCE: (346), (391) imply:
% 205.77/31.78 | | | | | | | | | | | | (392) a_select3(q_ds1_filter, n3, n4) = all_74_1
% 205.77/31.78 | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | REDUCE: (345), (391) imply:
% 205.77/31.78 | | | | | | | | | | | | (393) a_select3(q_ds1_filter, n4, n3) = all_74_0
% 205.77/31.78 | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | REDUCE: (158), (391) imply:
% 205.77/31.78 | | | | | | | | | | | | (394) leq(n3, n5)
% 205.77/31.78 | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | REDUCE: (151), (391) imply:
% 205.77/31.78 | | | | | | | | | | | | (395) leq(n0, n3)
% 205.77/31.78 | | | | | | | | | | | |
% 205.77/31.78 | | | | | | | | | | | | GROUND_INST: instantiating (65) with n3, n4, all_74_1,
% 205.77/31.78 | | | | | | | | | | | | simplifying with (115), (122), (348), (392), (395)
% 205.77/31.78 | | | | | | | | | | | | gives:
% 205.77/31.79 | | | | | | | | | | | | (396) ~ leq(n4, all_74_19) | ~ leq(n3, all_74_19) |
% 205.77/31.79 | | | | | | | | | | | | (a_select3(q_ds1_filter, n4, n3) = all_74_1 &
% 205.77/31.79 | | | | | | | | | | | | $i(all_74_1))
% 205.77/31.79 | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | BETA: splitting (396) gives:
% 205.77/31.79 | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | Case 1:
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | (397) ~ leq(n4, all_74_19)
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | REDUCE: (142), (397) imply:
% 205.77/31.79 | | | | | | | | | | | | | (398) ~ leq(n4, n5)
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | PRED_UNIFY: (347), (398) imply:
% 205.77/31.79 | | | | | | | | | | | | | (399) $false
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | CLOSE: (399) is inconsistent.
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | Case 2:
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | (400) ~ leq(n3, all_74_19) | (a_select3(q_ds1_filter,
% 205.77/31.79 | | | | | | | | | | | | | n4, n3) = all_74_1 & $i(all_74_1))
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | BETA: splitting (400) gives:
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | Case 1:
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | (401) ~ leq(n3, all_74_19)
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | REDUCE: (142), (401) imply:
% 205.77/31.79 | | | | | | | | | | | | | | (402) ~ leq(n3, n5)
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | PRED_UNIFY: (394), (402) imply:
% 205.77/31.79 | | | | | | | | | | | | | | (403) $false
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | CLOSE: (403) is inconsistent.
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | Case 2:
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | (404) a_select3(q_ds1_filter, n4, n3) = all_74_1 &
% 205.77/31.79 | | | | | | | | | | | | | | $i(all_74_1)
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | ALPHA: (404) implies:
% 205.77/31.79 | | | | | | | | | | | | | | (405) a_select3(q_ds1_filter, n4, n3) = all_74_1
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | REF_CLOSE: (19), (150), (393), (405) are inconsistent by
% 205.77/31.79 | | | | | | | | | | | | | | sub-proof #41.
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | End of split
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | End of split
% 205.77/31.79 | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | End of split
% 205.77/31.79 | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | End of split
% 205.77/31.79 | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | Case 2:
% 205.77/31.79 | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | (406) all_74_3 = n4
% 205.77/31.79 | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | REDUCE: (156), (406) imply:
% 205.77/31.79 | | | | | | | | | | (407) a_select3(q_ds1_filter, all_74_2, n4) = all_74_0
% 205.77/31.79 | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | REDUCE: (155), (406) imply:
% 205.77/31.79 | | | | | | | | | | (408) a_select3(q_ds1_filter, n4, all_74_2) = all_74_1
% 205.77/31.79 | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | REDUCE: (158), (406) imply:
% 205.77/31.79 | | | | | | | | | | (409) leq(n4, n5)
% 205.77/31.79 | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | REDUCE: (151), (406) imply:
% 205.77/31.79 | | | | | | | | | | (410) leq(n0, n4)
% 205.77/31.79 | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | BETA: splitting (172) gives:
% 205.77/31.79 | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | Case 1:
% 205.77/31.79 | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | (411) gt(n4, all_74_2)
% 205.77/31.79 | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n4, n3,
% 205.77/31.79 | | | | | | | | | | | simplifying with (59), (122), (128), (411) gives:
% 205.77/31.79 | | | | | | | | | | | (412) leq(all_74_2, n3)
% 205.77/31.79 | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n3,
% 205.77/31.79 | | | | | | | | | | | simplifying with (59), (115), (412) gives:
% 205.77/31.79 | | | | | | | | | | | (413) all_74_2 = n3 | gt(n3, all_74_2)
% 205.77/31.79 | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | BETA: splitting (413) gives:
% 205.77/31.79 | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | Case 1:
% 205.77/31.79 | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | (414) gt(n3, all_74_2)
% 205.77/31.79 | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2,
% 205.77/31.79 | | | | | | | | | | | | simplifying with (59), (115), (127), (414) gives:
% 205.77/31.79 | | | | | | | | | | | | (415) leq(all_74_2, n2)
% 205.77/31.79 | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n2,
% 205.77/31.79 | | | | | | | | | | | | simplifying with (59), (104), (415) gives:
% 205.77/31.79 | | | | | | | | | | | | (416) all_74_2 = n2 | gt(n2, all_74_2)
% 205.77/31.79 | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | BETA: splitting (416) gives:
% 205.77/31.79 | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | Case 1:
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | (417) gt(n2, all_74_2)
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1,
% 205.77/31.79 | | | | | | | | | | | | | simplifying with (59), (104), (126), (417) gives:
% 205.77/31.79 | | | | | | | | | | | | | (418) leq(all_74_2, n1)
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_74_2, simplifying with
% 205.77/31.79 | | | | | | | | | | | | | (59), (152), (418) gives:
% 205.77/31.79 | | | | | | | | | | | | | (419) all_74_2 = n1 | all_74_2 = n0
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | BETA: splitting (419) gives:
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | Case 1:
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | (420) all_74_2 = n0
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | REDUCE: (176), (420) imply:
% 205.77/31.79 | | | | | | | | | | | | | | (421) $false
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | CLOSE: (421) is inconsistent.
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | Case 2:
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | (422) all_74_2 = n1
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | REDUCE: (407), (422) imply:
% 205.77/31.79 | | | | | | | | | | | | | | (423) a_select3(q_ds1_filter, n1, n4) = all_74_0
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | REDUCE: (408), (422) imply:
% 205.77/31.79 | | | | | | | | | | | | | | (424) a_select3(q_ds1_filter, n4, n1) = all_74_1
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | REDUCE: (157), (422) imply:
% 205.77/31.79 | | | | | | | | | | | | | | (425) leq(n1, n5)
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | REDUCE: (152), (422) imply:
% 205.77/31.79 | | | | | | | | | | | | | | (426) leq(n0, n1)
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, n4, all_74_0,
% 205.77/31.79 | | | | | | | | | | | | | | simplifying with (88), (122), (410), (423), (426)
% 205.77/31.79 | | | | | | | | | | | | | | gives:
% 205.77/31.79 | | | | | | | | | | | | | | (427) ~ leq(n4, all_74_19) | ~ leq(n1, all_74_19) |
% 205.77/31.79 | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n4, n1) = all_74_0 &
% 205.77/31.79 | | | | | | | | | | | | | | $i(all_74_0))
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | BETA: splitting (427) gives:
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | Case 1:
% 205.77/31.79 | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | (428) ~ leq(n4, all_74_19)
% 205.77/31.79 | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | REDUCE: (142), (428) imply:
% 205.77/31.79 | | | | | | | | | | | | | | | (429) ~ leq(n4, n5)
% 205.77/31.79 | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | PRED_UNIFY: (409), (429) imply:
% 205.77/31.79 | | | | | | | | | | | | | | | (430) $false
% 205.77/31.79 | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | CLOSE: (430) is inconsistent.
% 205.77/31.79 | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | Case 2:
% 205.77/31.79 | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | (431) ~ leq(n1, all_74_19) | (a_select3(q_ds1_filter,
% 205.77/31.79 | | | | | | | | | | | | | | | n4, n1) = all_74_0 & $i(all_74_0))
% 205.77/31.79 | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | BETA: splitting (431) gives:
% 205.77/31.79 | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | Case 1:
% 205.77/31.79 | | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | | (432) ~ leq(n1, all_74_19)
% 205.77/31.79 | | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | | REDUCE: (142), (432) imply:
% 205.77/31.79 | | | | | | | | | | | | | | | | (433) ~ leq(n1, n5)
% 205.77/31.79 | | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | | PRED_UNIFY: (425), (433) imply:
% 205.77/31.79 | | | | | | | | | | | | | | | | (434) $false
% 205.77/31.79 | | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | | CLOSE: (434) is inconsistent.
% 205.77/31.79 | | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | Case 2:
% 205.77/31.79 | | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | | (435) a_select3(q_ds1_filter, n4, n1) = all_74_0 &
% 205.77/31.79 | | | | | | | | | | | | | | | | $i(all_74_0)
% 205.77/31.79 | | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | | ALPHA: (435) implies:
% 205.77/31.79 | | | | | | | | | | | | | | | | (436) a_select3(q_ds1_filter, n4, n1) = all_74_0
% 205.77/31.79 | | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_74_0, all_74_1, n1,
% 205.77/31.79 | | | | | | | | | | | | | | | | n4, q_ds1_filter, simplifying with (424), (436)
% 205.77/31.79 | | | | | | | | | | | | | | | | gives:
% 205.77/31.79 | | | | | | | | | | | | | | | | (437) all_74_0 = all_74_1
% 205.77/31.79 | | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | | REDUCE: (150), (437) imply:
% 205.77/31.79 | | | | | | | | | | | | | | | | (438) $false
% 205.77/31.79 | | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | | CLOSE: (438) is inconsistent.
% 205.77/31.79 | | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | End of split
% 205.77/31.79 | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | End of split
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | End of split
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | Case 2:
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | (439) all_74_2 = n2
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | REDUCE: (407), (439) imply:
% 205.77/31.79 | | | | | | | | | | | | | (440) a_select3(q_ds1_filter, n2, n4) = all_74_0
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | REDUCE: (408), (439) imply:
% 205.77/31.79 | | | | | | | | | | | | | (441) a_select3(q_ds1_filter, n4, n2) = all_74_1
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | REDUCE: (157), (439) imply:
% 205.77/31.79 | | | | | | | | | | | | | (442) leq(n2, n5)
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | REDUCE: (152), (439) imply:
% 205.77/31.79 | | | | | | | | | | | | | (443) leq(n0, n2)
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n2, n4, all_74_0,
% 205.77/31.79 | | | | | | | | | | | | | simplifying with (104), (122), (410), (440), (443)
% 205.77/31.79 | | | | | | | | | | | | | gives:
% 205.77/31.79 | | | | | | | | | | | | | (444) ~ leq(n4, all_74_19) | ~ leq(n2, all_74_19) |
% 205.77/31.79 | | | | | | | | | | | | | (a_select3(q_ds1_filter, n4, n2) = all_74_0 &
% 205.77/31.79 | | | | | | | | | | | | | $i(all_74_0))
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | BETA: splitting (444) gives:
% 205.77/31.79 | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | Case 1:
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | (445) ~ leq(n4, all_74_19)
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | REDUCE: (142), (445) imply:
% 205.77/31.79 | | | | | | | | | | | | | | (446) ~ leq(n4, n5)
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | PRED_UNIFY: (409), (446) imply:
% 205.77/31.79 | | | | | | | | | | | | | | (447) $false
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | CLOSE: (447) is inconsistent.
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | Case 2:
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | (448) ~ leq(n2, all_74_19) | (a_select3(q_ds1_filter,
% 205.77/31.79 | | | | | | | | | | | | | | n4, n2) = all_74_0 & $i(all_74_0))
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | BETA: splitting (448) gives:
% 205.77/31.79 | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | Case 1:
% 205.77/31.79 | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | (449) ~ leq(n2, all_74_19)
% 205.77/31.79 | | | | | | | | | | | | | | |
% 205.77/31.79 | | | | | | | | | | | | | | | REDUCE: (142), (449) imply:
% 205.77/31.80 | | | | | | | | | | | | | | | (450) ~ leq(n2, n5)
% 205.77/31.80 | | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | | PRED_UNIFY: (442), (450) imply:
% 205.77/31.80 | | | | | | | | | | | | | | | (451) $false
% 205.77/31.80 | | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | | CLOSE: (451) is inconsistent.
% 205.77/31.80 | | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | Case 2:
% 205.77/31.80 | | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | | (452) a_select3(q_ds1_filter, n4, n2) = all_74_0 &
% 205.77/31.80 | | | | | | | | | | | | | | | $i(all_74_0)
% 205.77/31.80 | | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | | ALPHA: (452) implies:
% 205.77/31.80 | | | | | | | | | | | | | | | (453) a_select3(q_ds1_filter, n4, n2) = all_74_0
% 205.77/31.80 | | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_74_0, all_74_1, n2,
% 205.77/31.80 | | | | | | | | | | | | | | | n4, q_ds1_filter, simplifying with (441), (453)
% 205.77/31.80 | | | | | | | | | | | | | | | gives:
% 205.77/31.80 | | | | | | | | | | | | | | | (454) all_74_0 = all_74_1
% 205.77/31.80 | | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | | REDUCE: (150), (454) imply:
% 205.77/31.80 | | | | | | | | | | | | | | | (455) $false
% 205.77/31.80 | | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | | CLOSE: (455) is inconsistent.
% 205.77/31.80 | | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | End of split
% 205.77/31.80 | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | End of split
% 205.77/31.80 | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | End of split
% 205.77/31.80 | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | Case 2:
% 205.77/31.80 | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | (456) all_74_2 = n3
% 205.77/31.80 | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | REDUCE: (407), (456) imply:
% 205.77/31.80 | | | | | | | | | | | | (457) a_select3(q_ds1_filter, n3, n4) = all_74_0
% 205.77/31.80 | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | REDUCE: (408), (456) imply:
% 205.77/31.80 | | | | | | | | | | | | (458) a_select3(q_ds1_filter, n4, n3) = all_74_1
% 205.77/31.80 | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | REDUCE: (157), (456) imply:
% 205.77/31.80 | | | | | | | | | | | | (459) leq(n3, n5)
% 205.77/31.80 | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | REDUCE: (152), (456) imply:
% 205.77/31.80 | | | | | | | | | | | | (460) leq(n0, n3)
% 205.77/31.80 | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | GROUND_INST: instantiating (65) with n3, n4, all_74_0,
% 205.77/31.80 | | | | | | | | | | | | simplifying with (115), (122), (410), (457), (460)
% 205.77/31.80 | | | | | | | | | | | | gives:
% 205.77/31.80 | | | | | | | | | | | | (461) ~ leq(n4, all_74_19) | ~ leq(n3, all_74_19) |
% 205.77/31.80 | | | | | | | | | | | | (a_select3(q_ds1_filter, n4, n3) = all_74_0 &
% 205.77/31.80 | | | | | | | | | | | | $i(all_74_0))
% 205.77/31.80 | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | BETA: splitting (461) gives:
% 205.77/31.80 | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | Case 1:
% 205.77/31.80 | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | (462) ~ leq(n4, all_74_19)
% 205.77/31.80 | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | REDUCE: (142), (462) imply:
% 205.77/31.80 | | | | | | | | | | | | | (463) ~ leq(n4, n5)
% 205.77/31.80 | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | PRED_UNIFY: (409), (463) imply:
% 205.77/31.80 | | | | | | | | | | | | | (464) $false
% 205.77/31.80 | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | CLOSE: (464) is inconsistent.
% 205.77/31.80 | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | Case 2:
% 205.77/31.80 | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | (465) ~ leq(n3, all_74_19) | (a_select3(q_ds1_filter,
% 205.77/31.80 | | | | | | | | | | | | | n4, n3) = all_74_0 & $i(all_74_0))
% 205.77/31.80 | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | BETA: splitting (465) gives:
% 205.77/31.80 | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | Case 1:
% 205.77/31.80 | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | (466) ~ leq(n3, all_74_19)
% 205.77/31.80 | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | REDUCE: (142), (466) imply:
% 205.77/31.80 | | | | | | | | | | | | | | (467) ~ leq(n3, n5)
% 205.77/31.80 | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | PRED_UNIFY: (459), (467) imply:
% 205.77/31.80 | | | | | | | | | | | | | | (468) $false
% 205.77/31.80 | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | CLOSE: (468) is inconsistent.
% 205.77/31.80 | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | Case 2:
% 205.77/31.80 | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | (469) a_select3(q_ds1_filter, n4, n3) = all_74_0 &
% 205.77/31.80 | | | | | | | | | | | | | | $i(all_74_0)
% 205.77/31.80 | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | ALPHA: (469) implies:
% 205.77/31.80 | | | | | | | | | | | | | | (470) a_select3(q_ds1_filter, n4, n3) = all_74_0
% 205.77/31.80 | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | | REF_CLOSE: (19), (150), (458), (470) are inconsistent by
% 205.77/31.80 | | | | | | | | | | | | | | sub-proof #41.
% 205.77/31.80 | | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | | End of split
% 205.77/31.80 | | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | | End of split
% 205.77/31.80 | | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | End of split
% 205.77/31.80 | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | Case 2:
% 205.77/31.80 | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | (471) all_74_2 = n4
% 205.77/31.80 | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | REDUCE: (407), (471) imply:
% 205.77/31.80 | | | | | | | | | | | (472) a_select3(q_ds1_filter, n4, n4) = all_74_0
% 205.77/31.80 | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | REDUCE: (408), (471) imply:
% 205.77/31.80 | | | | | | | | | | | (473) a_select3(q_ds1_filter, n4, n4) = all_74_1
% 205.77/31.80 | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | GROUND_INST: instantiating (19) with all_74_1, all_74_0, n4,
% 205.77/31.80 | | | | | | | | | | | n4, q_ds1_filter, simplifying with (472), (473)
% 205.77/31.80 | | | | | | | | | | | gives:
% 205.77/31.80 | | | | | | | | | | | (474) all_74_0 = all_74_1
% 205.77/31.80 | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | REDUCE: (150), (474) imply:
% 205.77/31.80 | | | | | | | | | | | (475) $false
% 205.77/31.80 | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | | CLOSE: (475) is inconsistent.
% 205.77/31.80 | | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | | End of split
% 205.77/31.80 | | | | | | | | | |
% 205.77/31.80 | | | | | | | | | End of split
% 205.77/31.80 | | | | | | | | |
% 205.77/31.80 | | | | | | | | End of split
% 205.77/31.80 | | | | | | | |
% 205.77/31.80 | | | | | | | End of split
% 205.77/31.80 | | | | | | |
% 206.06/31.80 | | | | | | Case 2:
% 206.06/31.80 | | | | | | |
% 206.06/31.80 | | | | | | | (476) all_74_2 = n5
% 206.06/31.80 | | | | | | |
% 206.06/31.80 | | | | | | | REDUCE: (156), (476) imply:
% 206.06/31.80 | | | | | | | (477) a_select3(q_ds1_filter, n5, all_74_3) = all_74_0
% 206.06/31.80 | | | | | | |
% 206.06/31.80 | | | | | | | REDUCE: (155), (476) imply:
% 206.06/31.80 | | | | | | | (478) a_select3(q_ds1_filter, all_74_3, n5) = all_74_1
% 206.06/31.80 | | | | | | |
% 206.06/31.80 | | | | | | | REDUCE: (157), (476) imply:
% 206.06/31.80 | | | | | | | (479) leq(n5, n5)
% 206.06/31.80 | | | | | | |
% 206.06/31.80 | | | | | | | REDUCE: (152), (476) imply:
% 206.06/31.80 | | | | | | | (480) leq(n0, n5)
% 206.06/31.80 | | | | | | |
% 206.06/31.80 | | | | | | | BETA: splitting (161) gives:
% 206.06/31.80 | | | | | | |
% 206.06/31.80 | | | | | | | Case 1:
% 206.06/31.80 | | | | | | | |
% 206.06/31.80 | | | | | | | | (481) all_74_3 = n0
% 206.06/31.80 | | | | | | | |
% 206.06/31.80 | | | | | | | | REF_CLOSE: (58), (166), (481), (irreflexivity_gt) are
% 206.06/31.80 | | | | | | | | inconsistent by sub-proof #45.
% 206.06/31.80 | | | | | | | |
% 206.06/31.80 | | | | | | | Case 2:
% 206.06/31.80 | | | | | | | |
% 206.06/31.80 | | | | | | | | (482) ~ (all_74_3 = n0)
% 206.06/31.80 | | | | | | | |
% 206.06/31.80 | | | | | | | | BETA: splitting (169) gives:
% 206.06/31.80 | | | | | | | |
% 206.06/31.80 | | | | | | | | Case 1:
% 206.06/31.80 | | | | | | | | |
% 206.06/31.80 | | | | | | | | | (483) gt(n4, all_74_3)
% 206.06/31.80 | | | | | | | | |
% 206.06/31.80 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n4, n3,
% 206.06/31.80 | | | | | | | | | simplifying with (58), (122), (128), (483) gives:
% 206.06/31.80 | | | | | | | | | (484) leq(all_74_3, n3)
% 206.06/31.80 | | | | | | | | |
% 206.06/31.80 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n3,
% 206.06/31.80 | | | | | | | | | simplifying with (58), (115), (484) gives:
% 206.06/31.80 | | | | | | | | | (485) all_74_3 = n3 | gt(n3, all_74_3)
% 206.06/31.80 | | | | | | | | |
% 206.06/31.80 | | | | | | | | | BETA: splitting (485) gives:
% 206.06/31.80 | | | | | | | | |
% 206.06/31.80 | | | | | | | | | Case 1:
% 206.06/31.80 | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | (486) gt(n3, all_74_3)
% 206.06/31.80 | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2,
% 206.06/31.80 | | | | | | | | | | simplifying with (58), (115), (127), (486) gives:
% 206.06/31.80 | | | | | | | | | | (487) leq(all_74_3, n2)
% 206.06/31.80 | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n2,
% 206.06/31.80 | | | | | | | | | | simplifying with (58), (104), (487) gives:
% 206.06/31.80 | | | | | | | | | | (488) all_74_3 = n2 | gt(n2, all_74_3)
% 206.06/31.80 | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | BETA: splitting (488) gives:
% 206.06/31.80 | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | Case 1:
% 206.06/31.80 | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | (489) gt(n2, all_74_3)
% 206.06/31.80 | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1,
% 206.06/31.80 | | | | | | | | | | | simplifying with (58), (104), (126), (489) gives:
% 206.06/31.80 | | | | | | | | | | | (490) leq(all_74_3, n1)
% 206.06/31.80 | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | GROUND_INST: instantiating (5) with all_74_3, simplifying with
% 206.06/31.80 | | | | | | | | | | | (58), (151), (490) gives:
% 206.06/31.80 | | | | | | | | | | | (491) all_74_3 = n1 | all_74_3 = n0
% 206.06/31.80 | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | BETA: splitting (491) gives:
% 206.06/31.80 | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | Case 1:
% 206.06/31.80 | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | (492) all_74_3 = n0
% 206.06/31.80 | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | REDUCE: (482), (492) imply:
% 206.06/31.80 | | | | | | | | | | | | (493) $false
% 206.06/31.80 | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | CLOSE: (493) is inconsistent.
% 206.06/31.80 | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | Case 2:
% 206.06/31.80 | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | (494) all_74_3 = n1
% 206.06/31.80 | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | REDUCE: (478), (494) imply:
% 206.06/31.80 | | | | | | | | | | | | (495) a_select3(q_ds1_filter, n1, n5) = all_74_1
% 206.06/31.80 | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | REDUCE: (477), (494) imply:
% 206.06/31.80 | | | | | | | | | | | | (496) a_select3(q_ds1_filter, n5, n1) = all_74_0
% 206.06/31.80 | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | REDUCE: (158), (494) imply:
% 206.06/31.80 | | | | | | | | | | | | (497) leq(n1, n5)
% 206.06/31.80 | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | REDUCE: (151), (494) imply:
% 206.06/31.80 | | | | | | | | | | | | (498) leq(n0, n1)
% 206.06/31.80 | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, n5, all_74_1,
% 206.06/31.80 | | | | | | | | | | | | simplifying with (88), (125), (480), (495), (498)
% 206.06/31.80 | | | | | | | | | | | | gives:
% 206.06/31.80 | | | | | | | | | | | | (499) ~ leq(n5, all_74_19) | ~ leq(n1, all_74_19) |
% 206.06/31.80 | | | | | | | | | | | | (a_select3(q_ds1_filter, n5, n1) = all_74_1 &
% 206.06/31.80 | | | | | | | | | | | | $i(all_74_1))
% 206.06/31.80 | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | BETA: splitting (499) gives:
% 206.06/31.80 | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | Case 1:
% 206.06/31.80 | | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | | (500) ~ leq(n5, all_74_19)
% 206.06/31.80 | | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | | REDUCE: (142), (500) imply:
% 206.06/31.80 | | | | | | | | | | | | | (501) ~ leq(n5, n5)
% 206.06/31.80 | | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | | PRED_UNIFY: (479), (501) imply:
% 206.06/31.80 | | | | | | | | | | | | | (502) $false
% 206.06/31.80 | | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | | CLOSE: (502) is inconsistent.
% 206.06/31.80 | | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | Case 2:
% 206.06/31.80 | | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | | (503) ~ leq(n1, all_74_19) | (a_select3(q_ds1_filter,
% 206.06/31.80 | | | | | | | | | | | | | n5, n1) = all_74_1 & $i(all_74_1))
% 206.06/31.80 | | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | | BETA: splitting (503) gives:
% 206.06/31.80 | | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | | Case 1:
% 206.06/31.80 | | | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | | | (504) ~ leq(n1, all_74_19)
% 206.06/31.80 | | | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | | | REDUCE: (142), (504) imply:
% 206.06/31.80 | | | | | | | | | | | | | | (505) ~ leq(n1, n5)
% 206.06/31.80 | | | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | | | PRED_UNIFY: (497), (505) imply:
% 206.06/31.80 | | | | | | | | | | | | | | (506) $false
% 206.06/31.80 | | | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | | | CLOSE: (506) is inconsistent.
% 206.06/31.80 | | | | | | | | | | | | | |
% 206.06/31.80 | | | | | | | | | | | | | Case 2:
% 206.06/31.80 | | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | | | (507) a_select3(q_ds1_filter, n5, n1) = all_74_1 &
% 206.06/31.81 | | | | | | | | | | | | | | $i(all_74_1)
% 206.06/31.81 | | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | | | ALPHA: (507) implies:
% 206.06/31.81 | | | | | | | | | | | | | | (508) a_select3(q_ds1_filter, n5, n1) = all_74_1
% 206.06/31.81 | | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | | | REF_CLOSE: (19), (150), (496), (508) are inconsistent by
% 206.06/31.81 | | | | | | | | | | | | | | sub-proof #40.
% 206.06/31.81 | | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | | End of split
% 206.06/31.81 | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | End of split
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | End of split
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | Case 2:
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | (509) all_74_3 = n2
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | REDUCE: (478), (509) imply:
% 206.06/31.81 | | | | | | | | | | | (510) a_select3(q_ds1_filter, n2, n5) = all_74_1
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | REDUCE: (477), (509) imply:
% 206.06/31.81 | | | | | | | | | | | (511) a_select3(q_ds1_filter, n5, n2) = all_74_0
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | REDUCE: (158), (509) imply:
% 206.06/31.81 | | | | | | | | | | | (512) leq(n2, n5)
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | REDUCE: (151), (509) imply:
% 206.06/31.81 | | | | | | | | | | | (513) leq(n0, n2)
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | GROUND_INST: instantiating (65) with n2, n5, all_74_1,
% 206.06/31.81 | | | | | | | | | | | simplifying with (104), (125), (480), (510), (513)
% 206.06/31.81 | | | | | | | | | | | gives:
% 206.06/31.81 | | | | | | | | | | | (514) ~ leq(n5, all_74_19) | ~ leq(n2, all_74_19) |
% 206.06/31.81 | | | | | | | | | | | (a_select3(q_ds1_filter, n5, n2) = all_74_1 &
% 206.06/31.81 | | | | | | | | | | | $i(all_74_1))
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | BETA: splitting (514) gives:
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | Case 1:
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | (515) ~ leq(n5, all_74_19)
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | REDUCE: (142), (515) imply:
% 206.06/31.81 | | | | | | | | | | | | (516) ~ leq(n5, n5)
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | PRED_UNIFY: (479), (516) imply:
% 206.06/31.81 | | | | | | | | | | | | (517) $false
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | CLOSE: (517) is inconsistent.
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | Case 2:
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | (518) ~ leq(n2, all_74_19) | (a_select3(q_ds1_filter,
% 206.06/31.81 | | | | | | | | | | | | n5, n2) = all_74_1 & $i(all_74_1))
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | BETA: splitting (518) gives:
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | Case 1:
% 206.06/31.81 | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | | (519) ~ leq(n2, all_74_19)
% 206.06/31.81 | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | | REDUCE: (142), (519) imply:
% 206.06/31.81 | | | | | | | | | | | | | (520) ~ leq(n2, n5)
% 206.06/31.81 | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | | PRED_UNIFY: (512), (520) imply:
% 206.06/31.81 | | | | | | | | | | | | | (521) $false
% 206.06/31.81 | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | | CLOSE: (521) is inconsistent.
% 206.06/31.81 | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | Case 2:
% 206.06/31.81 | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | | (522) a_select3(q_ds1_filter, n5, n2) = all_74_1 &
% 206.06/31.81 | | | | | | | | | | | | | $i(all_74_1)
% 206.06/31.81 | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | | ALPHA: (522) implies:
% 206.06/31.81 | | | | | | | | | | | | | (523) a_select3(q_ds1_filter, n5, n2) = all_74_1
% 206.06/31.81 | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_74_1, all_74_0, n2,
% 206.06/31.81 | | | | | | | | | | | | | n5, q_ds1_filter, simplifying with (511), (523)
% 206.06/31.81 | | | | | | | | | | | | | gives:
% 206.06/31.81 | | | | | | | | | | | | | (524) all_74_0 = all_74_1
% 206.06/31.81 | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | | REDUCE: (150), (524) imply:
% 206.06/31.81 | | | | | | | | | | | | | (525) $false
% 206.06/31.81 | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | | CLOSE: (525) is inconsistent.
% 206.06/31.81 | | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | End of split
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | End of split
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | End of split
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | Case 2:
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | (526) all_74_3 = n3
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | REDUCE: (478), (526) imply:
% 206.06/31.81 | | | | | | | | | | (527) a_select3(q_ds1_filter, n3, n5) = all_74_1
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | REDUCE: (477), (526) imply:
% 206.06/31.81 | | | | | | | | | | (528) a_select3(q_ds1_filter, n5, n3) = all_74_0
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | REDUCE: (158), (526) imply:
% 206.06/31.81 | | | | | | | | | | (529) leq(n3, n5)
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | REDUCE: (151), (526) imply:
% 206.06/31.81 | | | | | | | | | | (530) leq(n0, n3)
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | GROUND_INST: instantiating (65) with n3, n5, all_74_1,
% 206.06/31.81 | | | | | | | | | | simplifying with (115), (125), (480), (527), (530)
% 206.06/31.81 | | | | | | | | | | gives:
% 206.06/31.81 | | | | | | | | | | (531) ~ leq(n5, all_74_19) | ~ leq(n3, all_74_19) |
% 206.06/31.81 | | | | | | | | | | (a_select3(q_ds1_filter, n5, n3) = all_74_1 &
% 206.06/31.81 | | | | | | | | | | $i(all_74_1))
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | BETA: splitting (531) gives:
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | Case 1:
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | (532) ~ leq(n5, all_74_19)
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | REDUCE: (142), (532) imply:
% 206.06/31.81 | | | | | | | | | | | (533) ~ leq(n5, n5)
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | PRED_UNIFY: (479), (533) imply:
% 206.06/31.81 | | | | | | | | | | | (534) $false
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | CLOSE: (534) is inconsistent.
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | Case 2:
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | (535) ~ leq(n3, all_74_19) | (a_select3(q_ds1_filter,
% 206.06/31.81 | | | | | | | | | | | n5, n3) = all_74_1 & $i(all_74_1))
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | BETA: splitting (535) gives:
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | Case 1:
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | (536) ~ leq(n3, all_74_19)
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | REDUCE: (142), (536) imply:
% 206.06/31.81 | | | | | | | | | | | | (537) ~ leq(n3, n5)
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | PRED_UNIFY: (529), (537) imply:
% 206.06/31.81 | | | | | | | | | | | | (538) $false
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | CLOSE: (538) is inconsistent.
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | Case 2:
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | (539) a_select3(q_ds1_filter, n5, n3) = all_74_1 &
% 206.06/31.81 | | | | | | | | | | | | $i(all_74_1)
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | ALPHA: (539) implies:
% 206.06/31.81 | | | | | | | | | | | | (540) a_select3(q_ds1_filter, n5, n3) = all_74_1
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | | REF_CLOSE: (19), (150), (528), (540) are inconsistent by
% 206.06/31.81 | | | | | | | | | | | | sub-proof #39.
% 206.06/31.81 | | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | End of split
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | End of split
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | End of split
% 206.06/31.81 | | | | | | | | |
% 206.06/31.81 | | | | | | | | Case 2:
% 206.06/31.81 | | | | | | | | |
% 206.06/31.81 | | | | | | | | | (541) all_74_3 = n4
% 206.06/31.81 | | | | | | | | |
% 206.06/31.81 | | | | | | | | | REDUCE: (478), (541) imply:
% 206.06/31.81 | | | | | | | | | (542) a_select3(q_ds1_filter, n4, n5) = all_74_1
% 206.06/31.81 | | | | | | | | |
% 206.06/31.81 | | | | | | | | | REDUCE: (477), (541) imply:
% 206.06/31.81 | | | | | | | | | (543) a_select3(q_ds1_filter, n5, n4) = all_74_0
% 206.06/31.81 | | | | | | | | |
% 206.06/31.81 | | | | | | | | | REDUCE: (158), (541) imply:
% 206.06/31.81 | | | | | | | | | (544) leq(n4, n5)
% 206.06/31.81 | | | | | | | | |
% 206.06/31.81 | | | | | | | | | REDUCE: (151), (541) imply:
% 206.06/31.81 | | | | | | | | | (545) leq(n0, n4)
% 206.06/31.81 | | | | | | | | |
% 206.06/31.81 | | | | | | | | | GROUND_INST: instantiating (65) with n4, n5, all_74_1,
% 206.06/31.81 | | | | | | | | | simplifying with (122), (125), (480), (542), (545)
% 206.06/31.81 | | | | | | | | | gives:
% 206.06/31.81 | | | | | | | | | (546) ~ leq(n5, all_74_19) | ~ leq(n4, all_74_19) |
% 206.06/31.81 | | | | | | | | | (a_select3(q_ds1_filter, n5, n4) = all_74_1 &
% 206.06/31.81 | | | | | | | | | $i(all_74_1))
% 206.06/31.81 | | | | | | | | |
% 206.06/31.81 | | | | | | | | | BETA: splitting (546) gives:
% 206.06/31.81 | | | | | | | | |
% 206.06/31.81 | | | | | | | | | Case 1:
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | (547) ~ leq(n5, all_74_19)
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | REDUCE: (142), (547) imply:
% 206.06/31.81 | | | | | | | | | | (548) ~ leq(n5, n5)
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | PRED_UNIFY: (479), (548) imply:
% 206.06/31.81 | | | | | | | | | | (549) $false
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | CLOSE: (549) is inconsistent.
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | Case 2:
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | (550) ~ leq(n4, all_74_19) | (a_select3(q_ds1_filter,
% 206.06/31.81 | | | | | | | | | | n5, n4) = all_74_1 & $i(all_74_1))
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | BETA: splitting (550) gives:
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | Case 1:
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | (551) ~ leq(n4, all_74_19)
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | REDUCE: (142), (551) imply:
% 206.06/31.81 | | | | | | | | | | | (552) ~ leq(n4, n5)
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | PRED_UNIFY: (544), (552) imply:
% 206.06/31.81 | | | | | | | | | | | (553) $false
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | CLOSE: (553) is inconsistent.
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | Case 2:
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | (554) a_select3(q_ds1_filter, n5, n4) = all_74_1 &
% 206.06/31.81 | | | | | | | | | | | $i(all_74_1)
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | ALPHA: (554) implies:
% 206.06/31.81 | | | | | | | | | | | (555) a_select3(q_ds1_filter, n5, n4) = all_74_1
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | | REF_CLOSE: (19), (150), (543), (555) are inconsistent by
% 206.06/31.81 | | | | | | | | | | | sub-proof #38.
% 206.06/31.81 | | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | | End of split
% 206.06/31.81 | | | | | | | | | |
% 206.06/31.81 | | | | | | | | | End of split
% 206.06/31.81 | | | | | | | | |
% 206.06/31.81 | | | | | | | | End of split
% 206.06/31.81 | | | | | | | |
% 206.06/31.81 | | | | | | | End of split
% 206.06/31.81 | | | | | | |
% 206.06/31.81 | | | | | | End of split
% 206.06/31.81 | | | | | |
% 206.06/31.81 | | | | | Case 2:
% 206.06/31.81 | | | | | |
% 206.06/31.81 | | | | | | (556) all_74_3 = n5
% 206.06/31.81 | | | | | |
% 206.06/31.81 | | | | | | REDUCE: (156), (556) imply:
% 206.06/31.81 | | | | | | (557) a_select3(q_ds1_filter, all_74_2, n5) = all_74_0
% 206.06/31.81 | | | | | |
% 206.06/31.81 | | | | | | REDUCE: (155), (556) imply:
% 206.06/31.81 | | | | | | (558) a_select3(q_ds1_filter, n5, all_74_2) = all_74_1
% 206.06/31.81 | | | | | |
% 206.06/31.81 | | | | | | REDUCE: (158), (556) imply:
% 206.06/31.81 | | | | | | (559) leq(n5, n5)
% 206.06/31.81 | | | | | |
% 206.06/31.81 | | | | | | REDUCE: (151), (556) imply:
% 206.06/31.81 | | | | | | (560) leq(n0, n5)
% 206.06/31.81 | | | | | |
% 206.06/31.81 | | | | | | BETA: splitting (164) gives:
% 206.06/31.81 | | | | | |
% 206.06/31.81 | | | | | | Case 1:
% 206.06/31.81 | | | | | | |
% 206.06/31.81 | | | | | | | (561) gt(n5, all_74_2)
% 206.06/31.81 | | | | | | |
% 206.06/31.81 | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, simplifying
% 206.06/31.81 | | | | | | | with (59), (125), (129), (561) gives:
% 206.06/31.81 | | | | | | | (562) leq(all_74_2, n4)
% 206.06/31.81 | | | | | | |
% 206.06/31.81 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n4,
% 206.06/31.81 | | | | | | | simplifying with (59), (122), (562) gives:
% 206.06/31.81 | | | | | | | (563) all_74_2 = n4 | gt(n4, all_74_2)
% 206.06/31.81 | | | | | | |
% 206.06/31.81 | | | | | | | BETA: splitting (163) gives:
% 206.06/31.81 | | | | | | |
% 206.06/31.81 | | | | | | | Case 1:
% 206.06/31.81 | | | | | | | |
% 206.06/31.81 | | | | | | | | (564) all_74_2 = n0
% 206.06/31.81 | | | | | | | |
% 206.06/31.81 | | | | | | | | REDUCE: (165), (564) imply:
% 206.06/31.81 | | | | | | | | (565) gt(n0, n0)
% 206.06/31.81 | | | | | | | |
% 206.06/31.81 | | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n0,
% 206.06/31.82 | | | | | | | | simplifying with (13), (565) gives:
% 206.06/31.82 | | | | | | | | (566) $false
% 206.06/31.82 | | | | | | | |
% 206.06/31.82 | | | | | | | | CLOSE: (566) is inconsistent.
% 206.06/31.82 | | | | | | | |
% 206.06/31.82 | | | | | | | Case 2:
% 206.06/31.82 | | | | | | | |
% 206.06/31.82 | | | | | | | | (567) ~ (all_74_2 = n0)
% 206.06/31.82 | | | | | | | |
% 206.06/31.82 | | | | | | | | BETA: splitting (563) gives:
% 206.06/31.82 | | | | | | | |
% 206.06/31.82 | | | | | | | | Case 1:
% 206.06/31.82 | | | | | | | | |
% 206.06/31.82 | | | | | | | | | (568) gt(n4, all_74_2)
% 206.06/31.82 | | | | | | | | |
% 206.06/31.82 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n4, n3,
% 206.06/31.82 | | | | | | | | | simplifying with (59), (122), (128), (568) gives:
% 206.06/31.82 | | | | | | | | | (569) leq(all_74_2, n3)
% 206.06/31.82 | | | | | | | | |
% 206.06/31.82 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n3,
% 206.06/31.82 | | | | | | | | | simplifying with (59), (115), (569) gives:
% 206.06/31.82 | | | | | | | | | (570) all_74_2 = n3 | gt(n3, all_74_2)
% 206.06/31.82 | | | | | | | | |
% 206.06/31.82 | | | | | | | | | BETA: splitting (570) gives:
% 206.06/31.82 | | | | | | | | |
% 206.06/31.82 | | | | | | | | | Case 1:
% 206.06/31.82 | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | (571) gt(n3, all_74_2)
% 206.06/31.82 | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2,
% 206.06/31.82 | | | | | | | | | | simplifying with (59), (115), (127), (571) gives:
% 206.06/31.82 | | | | | | | | | | (572) leq(all_74_2, n2)
% 206.06/31.82 | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n2,
% 206.06/31.82 | | | | | | | | | | simplifying with (59), (104), (572) gives:
% 206.06/31.82 | | | | | | | | | | (573) all_74_2 = n2 | gt(n2, all_74_2)
% 206.06/31.82 | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | BETA: splitting (573) gives:
% 206.06/31.82 | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | Case 1:
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | (574) gt(n2, all_74_2)
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1,
% 206.06/31.82 | | | | | | | | | | | simplifying with (59), (104), (126), (574) gives:
% 206.06/31.82 | | | | | | | | | | | (575) leq(all_74_2, n1)
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | GROUND_INST: instantiating (5) with all_74_2, simplifying with
% 206.06/31.82 | | | | | | | | | | | (59), (152), (575) gives:
% 206.06/31.82 | | | | | | | | | | | (576) all_74_2 = n1 | all_74_2 = n0
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | BETA: splitting (576) gives:
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | Case 1:
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | (577) all_74_2 = n0
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | REDUCE: (567), (577) imply:
% 206.06/31.82 | | | | | | | | | | | | (578) $false
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | CLOSE: (578) is inconsistent.
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | Case 2:
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | (579) all_74_2 = n1
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | REDUCE: (557), (579) imply:
% 206.06/31.82 | | | | | | | | | | | | (580) a_select3(q_ds1_filter, n1, n5) = all_74_0
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | REDUCE: (558), (579) imply:
% 206.06/31.82 | | | | | | | | | | | | (581) a_select3(q_ds1_filter, n5, n1) = all_74_1
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | REDUCE: (157), (579) imply:
% 206.06/31.82 | | | | | | | | | | | | (582) leq(n1, n5)
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | REDUCE: (152), (579) imply:
% 206.06/31.82 | | | | | | | | | | | | (583) leq(n0, n1)
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, n5, all_74_0,
% 206.06/31.82 | | | | | | | | | | | | simplifying with (88), (125), (560), (580), (583)
% 206.06/31.82 | | | | | | | | | | | | gives:
% 206.06/31.82 | | | | | | | | | | | | (584) ~ leq(n5, all_74_19) | ~ leq(n1, all_74_19) |
% 206.06/31.82 | | | | | | | | | | | | (a_select3(q_ds1_filter, n5, n1) = all_74_0 &
% 206.06/31.82 | | | | | | | | | | | | $i(all_74_0))
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | BETA: splitting (584) gives:
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | Case 1:
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | (585) ~ leq(n5, all_74_19)
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | REDUCE: (142), (585) imply:
% 206.06/31.82 | | | | | | | | | | | | | (586) ~ leq(n5, n5)
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | PRED_UNIFY: (559), (586) imply:
% 206.06/31.82 | | | | | | | | | | | | | (587) $false
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | CLOSE: (587) is inconsistent.
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | Case 2:
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | (588) ~ leq(n1, all_74_19) | (a_select3(q_ds1_filter,
% 206.06/31.82 | | | | | | | | | | | | | n5, n1) = all_74_0 & $i(all_74_0))
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | BETA: splitting (588) gives:
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | Case 1:
% 206.06/31.82 | | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | | (589) ~ leq(n1, all_74_19)
% 206.06/31.82 | | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | | REDUCE: (142), (589) imply:
% 206.06/31.82 | | | | | | | | | | | | | | (590) ~ leq(n1, n5)
% 206.06/31.82 | | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | | PRED_UNIFY: (582), (590) imply:
% 206.06/31.82 | | | | | | | | | | | | | | (591) $false
% 206.06/31.82 | | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | | CLOSE: (591) is inconsistent.
% 206.06/31.82 | | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | Case 2:
% 206.06/31.82 | | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | | (592) a_select3(q_ds1_filter, n5, n1) = all_74_0 &
% 206.06/31.82 | | | | | | | | | | | | | | $i(all_74_0)
% 206.06/31.82 | | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | | ALPHA: (592) implies:
% 206.06/31.82 | | | | | | | | | | | | | | (593) a_select3(q_ds1_filter, n5, n1) = all_74_0
% 206.06/31.82 | | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | | REF_CLOSE: (19), (150), (581), (593) are inconsistent by
% 206.06/31.82 | | | | | | | | | | | | | | sub-proof #40.
% 206.06/31.82 | | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | End of split
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | End of split
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | End of split
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | Case 2:
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | (594) all_74_2 = n2
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | REDUCE: (557), (594) imply:
% 206.06/31.82 | | | | | | | | | | | (595) a_select3(q_ds1_filter, n2, n5) = all_74_0
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | REDUCE: (558), (594) imply:
% 206.06/31.82 | | | | | | | | | | | (596) a_select3(q_ds1_filter, n5, n2) = all_74_1
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | REDUCE: (157), (594) imply:
% 206.06/31.82 | | | | | | | | | | | (597) leq(n2, n5)
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | REDUCE: (152), (594) imply:
% 206.06/31.82 | | | | | | | | | | | (598) leq(n0, n2)
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | GROUND_INST: instantiating (65) with n2, n5, all_74_0,
% 206.06/31.82 | | | | | | | | | | | simplifying with (104), (125), (560), (595), (598)
% 206.06/31.82 | | | | | | | | | | | gives:
% 206.06/31.82 | | | | | | | | | | | (599) ~ leq(n5, all_74_19) | ~ leq(n2, all_74_19) |
% 206.06/31.82 | | | | | | | | | | | (a_select3(q_ds1_filter, n5, n2) = all_74_0 &
% 206.06/31.82 | | | | | | | | | | | $i(all_74_0))
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | BETA: splitting (599) gives:
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | Case 1:
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | (600) ~ leq(n5, all_74_19)
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | REDUCE: (142), (600) imply:
% 206.06/31.82 | | | | | | | | | | | | (601) ~ leq(n5, n5)
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | PRED_UNIFY: (559), (601) imply:
% 206.06/31.82 | | | | | | | | | | | | (602) $false
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | CLOSE: (602) is inconsistent.
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | Case 2:
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | (603) ~ leq(n2, all_74_19) | (a_select3(q_ds1_filter,
% 206.06/31.82 | | | | | | | | | | | | n5, n2) = all_74_0 & $i(all_74_0))
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | BETA: splitting (603) gives:
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | Case 1:
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | (604) ~ leq(n2, all_74_19)
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | REDUCE: (142), (604) imply:
% 206.06/31.82 | | | | | | | | | | | | | (605) ~ leq(n2, n5)
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | PRED_UNIFY: (597), (605) imply:
% 206.06/31.82 | | | | | | | | | | | | | (606) $false
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | CLOSE: (606) is inconsistent.
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | Case 2:
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | (607) a_select3(q_ds1_filter, n5, n2) = all_74_0 &
% 206.06/31.82 | | | | | | | | | | | | | $i(all_74_0)
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | ALPHA: (607) implies:
% 206.06/31.82 | | | | | | | | | | | | | (608) a_select3(q_ds1_filter, n5, n2) = all_74_0
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_74_1, all_74_0, n2,
% 206.06/31.82 | | | | | | | | | | | | | n5, q_ds1_filter, simplifying with (596), (608)
% 206.06/31.82 | | | | | | | | | | | | | gives:
% 206.06/31.82 | | | | | | | | | | | | | (609) all_74_0 = all_74_1
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | REDUCE: (150), (609) imply:
% 206.06/31.82 | | | | | | | | | | | | | (610) $false
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | | CLOSE: (610) is inconsistent.
% 206.06/31.82 | | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | End of split
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | End of split
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | End of split
% 206.06/31.82 | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | Case 2:
% 206.06/31.82 | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | (611) all_74_2 = n3
% 206.06/31.82 | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | REDUCE: (557), (611) imply:
% 206.06/31.82 | | | | | | | | | | (612) a_select3(q_ds1_filter, n3, n5) = all_74_0
% 206.06/31.82 | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | REDUCE: (558), (611) imply:
% 206.06/31.82 | | | | | | | | | | (613) a_select3(q_ds1_filter, n5, n3) = all_74_1
% 206.06/31.82 | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | REDUCE: (157), (611) imply:
% 206.06/31.82 | | | | | | | | | | (614) leq(n3, n5)
% 206.06/31.82 | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | REDUCE: (152), (611) imply:
% 206.06/31.82 | | | | | | | | | | (615) leq(n0, n3)
% 206.06/31.82 | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | GROUND_INST: instantiating (65) with n3, n5, all_74_0,
% 206.06/31.82 | | | | | | | | | | simplifying with (115), (125), (560), (612), (615)
% 206.06/31.82 | | | | | | | | | | gives:
% 206.06/31.82 | | | | | | | | | | (616) ~ leq(n5, all_74_19) | ~ leq(n3, all_74_19) |
% 206.06/31.82 | | | | | | | | | | (a_select3(q_ds1_filter, n5, n3) = all_74_0 &
% 206.06/31.82 | | | | | | | | | | $i(all_74_0))
% 206.06/31.82 | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | BETA: splitting (616) gives:
% 206.06/31.82 | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | Case 1:
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | (617) ~ leq(n5, all_74_19)
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | REDUCE: (142), (617) imply:
% 206.06/31.82 | | | | | | | | | | | (618) ~ leq(n5, n5)
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | PRED_UNIFY: (559), (618) imply:
% 206.06/31.82 | | | | | | | | | | | (619) $false
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | CLOSE: (619) is inconsistent.
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | Case 2:
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | (620) ~ leq(n3, all_74_19) | (a_select3(q_ds1_filter,
% 206.06/31.82 | | | | | | | | | | | n5, n3) = all_74_0 & $i(all_74_0))
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | BETA: splitting (620) gives:
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | Case 1:
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | (621) ~ leq(n3, all_74_19)
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | REDUCE: (142), (621) imply:
% 206.06/31.82 | | | | | | | | | | | | (622) ~ leq(n3, n5)
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | PRED_UNIFY: (614), (622) imply:
% 206.06/31.82 | | | | | | | | | | | | (623) $false
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | CLOSE: (623) is inconsistent.
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | Case 2:
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | (624) a_select3(q_ds1_filter, n5, n3) = all_74_0 &
% 206.06/31.82 | | | | | | | | | | | | $i(all_74_0)
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | ALPHA: (624) implies:
% 206.06/31.82 | | | | | | | | | | | | (625) a_select3(q_ds1_filter, n5, n3) = all_74_0
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | | REF_CLOSE: (19), (150), (613), (625) are inconsistent by
% 206.06/31.82 | | | | | | | | | | | | sub-proof #39.
% 206.06/31.82 | | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | | End of split
% 206.06/31.82 | | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | | End of split
% 206.06/31.82 | | | | | | | | | |
% 206.06/31.82 | | | | | | | | | End of split
% 206.06/31.82 | | | | | | | | |
% 206.06/31.82 | | | | | | | | Case 2:
% 206.06/31.82 | | | | | | | | |
% 206.06/31.82 | | | | | | | | | (626) all_74_2 = n4
% 206.06/31.82 | | | | | | | | |
% 206.06/31.82 | | | | | | | | | REDUCE: (557), (626) imply:
% 206.06/31.82 | | | | | | | | | (627) a_select3(q_ds1_filter, n4, n5) = all_74_0
% 206.06/31.82 | | | | | | | | |
% 206.06/31.82 | | | | | | | | | REDUCE: (558), (626) imply:
% 206.06/31.82 | | | | | | | | | (628) a_select3(q_ds1_filter, n5, n4) = all_74_1
% 206.06/31.82 | | | | | | | | |
% 206.06/31.82 | | | | | | | | | REDUCE: (157), (626) imply:
% 206.06/31.82 | | | | | | | | | (629) leq(n4, n5)
% 206.06/31.82 | | | | | | | | |
% 206.06/31.82 | | | | | | | | | REDUCE: (152), (626) imply:
% 206.06/31.82 | | | | | | | | | (630) leq(n0, n4)
% 206.06/31.82 | | | | | | | | |
% 206.06/31.82 | | | | | | | | | GROUND_INST: instantiating (65) with n4, n5, all_74_0,
% 206.06/31.82 | | | | | | | | | simplifying with (122), (125), (560), (627), (630)
% 206.06/31.82 | | | | | | | | | gives:
% 206.06/31.83 | | | | | | | | | (631) ~ leq(n5, all_74_19) | ~ leq(n4, all_74_19) |
% 206.06/31.83 | | | | | | | | | (a_select3(q_ds1_filter, n5, n4) = all_74_0 &
% 206.06/31.83 | | | | | | | | | $i(all_74_0))
% 206.06/31.83 | | | | | | | | |
% 206.06/31.83 | | | | | | | | | BETA: splitting (631) gives:
% 206.06/31.83 | | | | | | | | |
% 206.06/31.83 | | | | | | | | | Case 1:
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | (632) ~ leq(n5, all_74_19)
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | REDUCE: (142), (632) imply:
% 206.06/31.83 | | | | | | | | | | (633) ~ leq(n5, n5)
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | PRED_UNIFY: (559), (633) imply:
% 206.06/31.83 | | | | | | | | | | (634) $false
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | CLOSE: (634) is inconsistent.
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | Case 2:
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | (635) ~ leq(n4, all_74_19) | (a_select3(q_ds1_filter,
% 206.06/31.83 | | | | | | | | | | n5, n4) = all_74_0 & $i(all_74_0))
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | BETA: splitting (635) gives:
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | Case 1:
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | (636) ~ leq(n4, all_74_19)
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | REDUCE: (142), (636) imply:
% 206.06/31.83 | | | | | | | | | | | (637) ~ leq(n4, n5)
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | PRED_UNIFY: (629), (637) imply:
% 206.06/31.83 | | | | | | | | | | | (638) $false
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | CLOSE: (638) is inconsistent.
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | Case 2:
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | (639) a_select3(q_ds1_filter, n5, n4) = all_74_0 &
% 206.06/31.83 | | | | | | | | | | | $i(all_74_0)
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | ALPHA: (639) implies:
% 206.06/31.83 | | | | | | | | | | | (640) a_select3(q_ds1_filter, n5, n4) = all_74_0
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | REF_CLOSE: (19), (150), (628), (640) are inconsistent by
% 206.06/31.83 | | | | | | | | | | | sub-proof #38.
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | End of split
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | End of split
% 206.06/31.83 | | | | | | | | |
% 206.06/31.83 | | | | | | | | End of split
% 206.06/31.83 | | | | | | | |
% 206.06/31.83 | | | | | | | End of split
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | Case 2:
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | | (641) all_74_2 = n5
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | | REDUCE: (557), (641) imply:
% 206.06/31.83 | | | | | | | (642) a_select3(q_ds1_filter, n5, n5) = all_74_0
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | | REDUCE: (558), (641) imply:
% 206.06/31.83 | | | | | | | (643) a_select3(q_ds1_filter, n5, n5) = all_74_1
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | | GROUND_INST: instantiating (19) with all_74_1, all_74_0, n5, n5,
% 206.06/31.83 | | | | | | | q_ds1_filter, simplifying with (642), (643) gives:
% 206.06/31.83 | | | | | | | (644) all_74_0 = all_74_1
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | | REDUCE: (150), (644) imply:
% 206.06/31.83 | | | | | | | (645) $false
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | | CLOSE: (645) is inconsistent.
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | End of split
% 206.06/31.83 | | | | | |
% 206.06/31.83 | | | | | End of split
% 206.06/31.83 | | | | |
% 206.06/31.83 | | | | Case 2:
% 206.06/31.83 | | | | |
% 206.06/31.83 | | | | | (646) all_74_3 = n0
% 206.06/31.83 | | | | | (647) ~ gt(all_74_3, n0)
% 206.06/31.83 | | | | |
% 206.06/31.83 | | | | | REDUCE: (156), (646) imply:
% 206.06/31.83 | | | | | (648) a_select3(q_ds1_filter, all_74_2, n0) = all_74_0
% 206.06/31.83 | | | | |
% 206.06/31.83 | | | | | REDUCE: (155), (646) imply:
% 206.06/31.83 | | | | | (649) a_select3(q_ds1_filter, n0, all_74_2) = all_74_1
% 206.06/31.83 | | | | |
% 206.06/31.83 | | | | | REDUCE: (158), (646) imply:
% 206.06/31.83 | | | | | (650) leq(n0, n5)
% 206.06/31.83 | | | | |
% 206.06/31.83 | | | | | REDUCE: (151), (646) imply:
% 206.06/31.83 | | | | | (651) leq(n0, n0)
% 206.06/31.83 | | | | |
% 206.06/31.83 | | | | | REDUCE: (646), (647) imply:
% 206.06/31.83 | | | | | (652) ~ gt(n0, n0)
% 206.06/31.83 | | | | |
% 206.06/31.83 | | | | | BETA: splitting (164) gives:
% 206.06/31.83 | | | | |
% 206.06/31.83 | | | | | Case 1:
% 206.06/31.83 | | | | | |
% 206.06/31.83 | | | | | | (653) gt(n5, all_74_2)
% 206.06/31.83 | | | | | |
% 206.06/31.83 | | | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, simplifying
% 206.06/31.83 | | | | | | with (59), (125), (129), (653) gives:
% 206.06/31.83 | | | | | | (654) leq(all_74_2, n4)
% 206.06/31.83 | | | | | |
% 206.06/31.83 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n4, simplifying
% 206.06/31.83 | | | | | | with (59), (122), (654) gives:
% 206.06/31.83 | | | | | | (655) all_74_2 = n4 | gt(n4, all_74_2)
% 206.06/31.83 | | | | | |
% 206.06/31.83 | | | | | | BETA: splitting (163) gives:
% 206.06/31.83 | | | | | |
% 206.06/31.83 | | | | | | Case 1:
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | | (656) all_74_2 = n0
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | | REDUCE: (165), (656) imply:
% 206.06/31.83 | | | | | | | (657) gt(n0, n0)
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | | PRED_UNIFY: (652), (657) imply:
% 206.06/31.83 | | | | | | | (658) $false
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | | CLOSE: (658) is inconsistent.
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | Case 2:
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | | (659) ~ (all_74_2 = n0)
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | | BETA: splitting (655) gives:
% 206.06/31.83 | | | | | | |
% 206.06/31.83 | | | | | | | Case 1:
% 206.06/31.83 | | | | | | | |
% 206.06/31.83 | | | | | | | | (660) gt(n4, all_74_2)
% 206.06/31.83 | | | | | | | |
% 206.06/31.83 | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n4, n3,
% 206.06/31.83 | | | | | | | | simplifying with (59), (122), (128), (660) gives:
% 206.06/31.83 | | | | | | | | (661) leq(all_74_2, n3)
% 206.06/31.83 | | | | | | | |
% 206.06/31.83 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n3,
% 206.06/31.83 | | | | | | | | simplifying with (59), (115), (661) gives:
% 206.06/31.83 | | | | | | | | (662) all_74_2 = n3 | gt(n3, all_74_2)
% 206.06/31.83 | | | | | | | |
% 206.06/31.83 | | | | | | | | BETA: splitting (662) gives:
% 206.06/31.83 | | | | | | | |
% 206.06/31.83 | | | | | | | | Case 1:
% 206.06/31.83 | | | | | | | | |
% 206.06/31.83 | | | | | | | | | (663) gt(n3, all_74_2)
% 206.06/31.83 | | | | | | | | |
% 206.06/31.83 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2,
% 206.06/31.83 | | | | | | | | | simplifying with (59), (115), (127), (663) gives:
% 206.06/31.83 | | | | | | | | | (664) leq(all_74_2, n2)
% 206.06/31.83 | | | | | | | | |
% 206.06/31.83 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n2,
% 206.06/31.83 | | | | | | | | | simplifying with (59), (104), (664) gives:
% 206.06/31.83 | | | | | | | | | (665) all_74_2 = n2 | gt(n2, all_74_2)
% 206.06/31.83 | | | | | | | | |
% 206.06/31.83 | | | | | | | | | BETA: splitting (665) gives:
% 206.06/31.83 | | | | | | | | |
% 206.06/31.83 | | | | | | | | | Case 1:
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | (666) gt(n2, all_74_2)
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1,
% 206.06/31.83 | | | | | | | | | | simplifying with (59), (104), (126), (666) gives:
% 206.06/31.83 | | | | | | | | | | (667) leq(all_74_2, n1)
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | GROUND_INST: instantiating (5) with all_74_2, simplifying with
% 206.06/31.83 | | | | | | | | | | (59), (152), (667) gives:
% 206.06/31.83 | | | | | | | | | | (668) all_74_2 = n1 | all_74_2 = n0
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | BETA: splitting (668) gives:
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | Case 1:
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | (669) all_74_2 = n0
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | REDUCE: (659), (669) imply:
% 206.06/31.83 | | | | | | | | | | | (670) $false
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | CLOSE: (670) is inconsistent.
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | Case 2:
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | (671) all_74_2 = n1
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | REDUCE: (648), (671) imply:
% 206.06/31.83 | | | | | | | | | | | (672) a_select3(q_ds1_filter, n1, n0) = all_74_0
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | REDUCE: (649), (671) imply:
% 206.06/31.83 | | | | | | | | | | | (673) a_select3(q_ds1_filter, n0, n1) = all_74_1
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | REDUCE: (157), (671) imply:
% 206.06/31.83 | | | | | | | | | | | (674) leq(n1, n5)
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | REDUCE: (152), (671) imply:
% 206.06/31.83 | | | | | | | | | | | (675) leq(n0, n1)
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, n1, all_74_1,
% 206.06/31.83 | | | | | | | | | | | simplifying with (13), (88), (651), (673), (675)
% 206.06/31.83 | | | | | | | | | | | gives:
% 206.06/31.83 | | | | | | | | | | | (676) ~ leq(n1, all_74_19) | ~ leq(n0, all_74_19) |
% 206.06/31.83 | | | | | | | | | | | (a_select3(q_ds1_filter, n1, n0) = all_74_1 &
% 206.06/31.83 | | | | | | | | | | | $i(all_74_1))
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | BETA: splitting (676) gives:
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | Case 1:
% 206.06/31.83 | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | (677) ~ leq(n0, all_74_19)
% 206.06/31.83 | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | REDUCE: (142), (677) imply:
% 206.06/31.83 | | | | | | | | | | | | (678) ~ leq(n0, n5)
% 206.06/31.83 | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | PRED_UNIFY: (650), (678) imply:
% 206.06/31.83 | | | | | | | | | | | | (679) $false
% 206.06/31.83 | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | CLOSE: (679) is inconsistent.
% 206.06/31.83 | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | Case 2:
% 206.06/31.83 | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | (680) ~ leq(n1, all_74_19) | (a_select3(q_ds1_filter,
% 206.06/31.83 | | | | | | | | | | | | n1, n0) = all_74_1 & $i(all_74_1))
% 206.06/31.83 | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | BETA: splitting (680) gives:
% 206.06/31.83 | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | Case 1:
% 206.06/31.83 | | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | | (681) ~ leq(n1, all_74_19)
% 206.06/31.83 | | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | | REDUCE: (142), (681) imply:
% 206.06/31.83 | | | | | | | | | | | | | (682) ~ leq(n1, n5)
% 206.06/31.83 | | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | | PRED_UNIFY: (674), (682) imply:
% 206.06/31.83 | | | | | | | | | | | | | (683) $false
% 206.06/31.83 | | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | | CLOSE: (683) is inconsistent.
% 206.06/31.83 | | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | Case 2:
% 206.06/31.83 | | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | | (684) a_select3(q_ds1_filter, n1, n0) = all_74_1 &
% 206.06/31.83 | | | | | | | | | | | | | $i(all_74_1)
% 206.06/31.83 | | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | | ALPHA: (684) implies:
% 206.06/31.83 | | | | | | | | | | | | | (685) a_select3(q_ds1_filter, n1, n0) = all_74_1
% 206.06/31.83 | | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | | REF_CLOSE: (19), (150), (672), (685) are inconsistent by
% 206.06/31.83 | | | | | | | | | | | | | sub-proof #37.
% 206.06/31.83 | | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | End of split
% 206.06/31.83 | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | End of split
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | End of split
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | Case 2:
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | (686) all_74_2 = n2
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | REDUCE: (648), (686) imply:
% 206.06/31.83 | | | | | | | | | | (687) a_select3(q_ds1_filter, n2, n0) = all_74_0
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | REDUCE: (649), (686) imply:
% 206.06/31.83 | | | | | | | | | | (688) a_select3(q_ds1_filter, n0, n2) = all_74_1
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | REDUCE: (157), (686) imply:
% 206.06/31.83 | | | | | | | | | | (689) leq(n2, n5)
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | REDUCE: (152), (686) imply:
% 206.06/31.83 | | | | | | | | | | (690) leq(n0, n2)
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | GROUND_INST: instantiating (65) with n0, n2, all_74_1,
% 206.06/31.83 | | | | | | | | | | simplifying with (13), (104), (651), (688), (690)
% 206.06/31.83 | | | | | | | | | | gives:
% 206.06/31.83 | | | | | | | | | | (691) ~ leq(n2, all_74_19) | ~ leq(n0, all_74_19) |
% 206.06/31.83 | | | | | | | | | | (a_select3(q_ds1_filter, n2, n0) = all_74_1 &
% 206.06/31.83 | | | | | | | | | | $i(all_74_1))
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | BETA: splitting (691) gives:
% 206.06/31.83 | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | Case 1:
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | (692) ~ leq(n0, all_74_19)
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | REDUCE: (142), (692) imply:
% 206.06/31.83 | | | | | | | | | | | (693) ~ leq(n0, n5)
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | PRED_UNIFY: (650), (693) imply:
% 206.06/31.83 | | | | | | | | | | | (694) $false
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | CLOSE: (694) is inconsistent.
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | Case 2:
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | (695) ~ leq(n2, all_74_19) | (a_select3(q_ds1_filter,
% 206.06/31.83 | | | | | | | | | | | n2, n0) = all_74_1 & $i(all_74_1))
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | BETA: splitting (695) gives:
% 206.06/31.83 | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | Case 1:
% 206.06/31.83 | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | (696) ~ leq(n2, all_74_19)
% 206.06/31.83 | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | REDUCE: (142), (696) imply:
% 206.06/31.83 | | | | | | | | | | | | (697) ~ leq(n2, n5)
% 206.06/31.83 | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | PRED_UNIFY: (689), (697) imply:
% 206.06/31.83 | | | | | | | | | | | | (698) $false
% 206.06/31.83 | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | CLOSE: (698) is inconsistent.
% 206.06/31.83 | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | Case 2:
% 206.06/31.83 | | | | | | | | | | | |
% 206.06/31.83 | | | | | | | | | | | | (699) a_select3(q_ds1_filter, n2, n0) = all_74_1 &
% 206.06/31.83 | | | | | | | | | | | | $i(all_74_1)
% 206.06/31.84 | | | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | | | ALPHA: (699) implies:
% 206.06/31.84 | | | | | | | | | | | | (700) a_select3(q_ds1_filter, n2, n0) = all_74_1
% 206.06/31.84 | | | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_74_1, all_74_0, n0,
% 206.06/31.84 | | | | | | | | | | | | n2, q_ds1_filter, simplifying with (687), (700)
% 206.06/31.84 | | | | | | | | | | | | gives:
% 206.06/31.84 | | | | | | | | | | | | (701) all_74_0 = all_74_1
% 206.06/31.84 | | | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | | | REDUCE: (150), (701) imply:
% 206.06/31.84 | | | | | | | | | | | | (702) $false
% 206.06/31.84 | | | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | | | CLOSE: (702) is inconsistent.
% 206.06/31.84 | | | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | | End of split
% 206.06/31.84 | | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | End of split
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | End of split
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | Case 2:
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | (703) all_74_2 = n3
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | REDUCE: (648), (703) imply:
% 206.06/31.84 | | | | | | | | | (704) a_select3(q_ds1_filter, n3, n0) = all_74_0
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | REDUCE: (649), (703) imply:
% 206.06/31.84 | | | | | | | | | (705) a_select3(q_ds1_filter, n0, n3) = all_74_1
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | REDUCE: (157), (703) imply:
% 206.06/31.84 | | | | | | | | | (706) leq(n3, n5)
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | REDUCE: (152), (703) imply:
% 206.06/31.84 | | | | | | | | | (707) leq(n0, n3)
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | GROUND_INST: instantiating (65) with n0, n3, all_74_1,
% 206.06/31.84 | | | | | | | | | simplifying with (13), (115), (651), (705), (707)
% 206.06/31.84 | | | | | | | | | gives:
% 206.06/31.84 | | | | | | | | | (708) ~ leq(n3, all_74_19) | ~ leq(n0, all_74_19) |
% 206.06/31.84 | | | | | | | | | (a_select3(q_ds1_filter, n3, n0) = all_74_1 &
% 206.06/31.84 | | | | | | | | | $i(all_74_1))
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | BETA: splitting (708) gives:
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | Case 1:
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | (709) ~ leq(n0, all_74_19)
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | REDUCE: (142), (709) imply:
% 206.06/31.84 | | | | | | | | | | (710) ~ leq(n0, n5)
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | PRED_UNIFY: (650), (710) imply:
% 206.06/31.84 | | | | | | | | | | (711) $false
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | CLOSE: (711) is inconsistent.
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | Case 2:
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | (712) ~ leq(n3, all_74_19) | (a_select3(q_ds1_filter,
% 206.06/31.84 | | | | | | | | | | n3, n0) = all_74_1 & $i(all_74_1))
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | BETA: splitting (712) gives:
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | Case 1:
% 206.06/31.84 | | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | | (713) ~ leq(n3, all_74_19)
% 206.06/31.84 | | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | | REDUCE: (142), (713) imply:
% 206.06/31.84 | | | | | | | | | | | (714) ~ leq(n3, n5)
% 206.06/31.84 | | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | | PRED_UNIFY: (706), (714) imply:
% 206.06/31.84 | | | | | | | | | | | (715) $false
% 206.06/31.84 | | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | | CLOSE: (715) is inconsistent.
% 206.06/31.84 | | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | Case 2:
% 206.06/31.84 | | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | | (716) a_select3(q_ds1_filter, n3, n0) = all_74_1 &
% 206.06/31.84 | | | | | | | | | | | $i(all_74_1)
% 206.06/31.84 | | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | | ALPHA: (716) implies:
% 206.06/31.84 | | | | | | | | | | | (717) a_select3(q_ds1_filter, n3, n0) = all_74_1
% 206.06/31.84 | | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | | REF_CLOSE: (19), (150), (704), (717) are inconsistent by
% 206.06/31.84 | | | | | | | | | | | sub-proof #36.
% 206.06/31.84 | | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | End of split
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | End of split
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | End of split
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | Case 2:
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | (718) all_74_2 = n4
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | REDUCE: (648), (718) imply:
% 206.06/31.84 | | | | | | | | (719) a_select3(q_ds1_filter, n4, n0) = all_74_0
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | REDUCE: (649), (718) imply:
% 206.06/31.84 | | | | | | | | (720) a_select3(q_ds1_filter, n0, n4) = all_74_1
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | REDUCE: (157), (718) imply:
% 206.06/31.84 | | | | | | | | (721) leq(n4, n5)
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | REDUCE: (152), (718) imply:
% 206.06/31.84 | | | | | | | | (722) leq(n0, n4)
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | GROUND_INST: instantiating (65) with n0, n4, all_74_1,
% 206.06/31.84 | | | | | | | | simplifying with (13), (122), (651), (720), (722)
% 206.06/31.84 | | | | | | | | gives:
% 206.06/31.84 | | | | | | | | (723) ~ leq(n4, all_74_19) | ~ leq(n0, all_74_19) |
% 206.06/31.84 | | | | | | | | (a_select3(q_ds1_filter, n4, n0) = all_74_1 &
% 206.06/31.84 | | | | | | | | $i(all_74_1))
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | BETA: splitting (723) gives:
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | Case 1:
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | (724) ~ leq(n0, all_74_19)
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | REDUCE: (142), (724) imply:
% 206.06/31.84 | | | | | | | | | (725) ~ leq(n0, n5)
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | PRED_UNIFY: (650), (725) imply:
% 206.06/31.84 | | | | | | | | | (726) $false
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | CLOSE: (726) is inconsistent.
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | Case 2:
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | (727) ~ leq(n4, all_74_19) | (a_select3(q_ds1_filter, n4,
% 206.06/31.84 | | | | | | | | | n0) = all_74_1 & $i(all_74_1))
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | BETA: splitting (727) gives:
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | Case 1:
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | (728) ~ leq(n4, all_74_19)
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | REDUCE: (142), (728) imply:
% 206.06/31.84 | | | | | | | | | | (729) ~ leq(n4, n5)
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | PRED_UNIFY: (721), (729) imply:
% 206.06/31.84 | | | | | | | | | | (730) $false
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | CLOSE: (730) is inconsistent.
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | Case 2:
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | (731) a_select3(q_ds1_filter, n4, n0) = all_74_1 &
% 206.06/31.84 | | | | | | | | | | $i(all_74_1)
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | ALPHA: (731) implies:
% 206.06/31.84 | | | | | | | | | | (732) a_select3(q_ds1_filter, n4, n0) = all_74_1
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | | REF_CLOSE: (19), (150), (719), (732) are inconsistent by
% 206.06/31.84 | | | | | | | | | | sub-proof #35.
% 206.06/31.84 | | | | | | | | | |
% 206.06/31.84 | | | | | | | | | End of split
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | End of split
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | End of split
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | End of split
% 206.06/31.84 | | | | | |
% 206.06/31.84 | | | | | Case 2:
% 206.06/31.84 | | | | | |
% 206.06/31.84 | | | | | | (733) all_74_2 = n5
% 206.06/31.84 | | | | | |
% 206.06/31.84 | | | | | | REDUCE: (648), (733) imply:
% 206.06/31.84 | | | | | | (734) a_select3(q_ds1_filter, n5, n0) = all_74_0
% 206.06/31.84 | | | | | |
% 206.06/31.84 | | | | | | REDUCE: (649), (733) imply:
% 206.06/31.84 | | | | | | (735) a_select3(q_ds1_filter, n0, n5) = all_74_1
% 206.06/31.84 | | | | | |
% 206.06/31.84 | | | | | | REDUCE: (157), (733) imply:
% 206.06/31.84 | | | | | | (736) leq(n5, n5)
% 206.06/31.84 | | | | | |
% 206.06/31.84 | | | | | | GROUND_INST: instantiating (65) with n0, n5, all_74_1, simplifying
% 206.06/31.84 | | | | | | with (13), (125), (650), (651), (735) gives:
% 206.06/31.84 | | | | | | (737) ~ leq(n5, all_74_19) | ~ leq(n0, all_74_19) |
% 206.06/31.84 | | | | | | (a_select3(q_ds1_filter, n5, n0) = all_74_1 & $i(all_74_1))
% 206.06/31.84 | | | | | |
% 206.06/31.84 | | | | | | BETA: splitting (737) gives:
% 206.06/31.84 | | | | | |
% 206.06/31.84 | | | | | | Case 1:
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | | (738) ~ leq(n0, all_74_19)
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | | REDUCE: (142), (738) imply:
% 206.06/31.84 | | | | | | | (739) ~ leq(n0, n5)
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | | PRED_UNIFY: (650), (739) imply:
% 206.06/31.84 | | | | | | | (740) $false
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | | CLOSE: (740) is inconsistent.
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | Case 2:
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | | (741) ~ leq(n5, all_74_19) | (a_select3(q_ds1_filter, n5, n0)
% 206.06/31.84 | | | | | | | = all_74_1 & $i(all_74_1))
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | | BETA: splitting (741) gives:
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | | Case 1:
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | (742) ~ leq(n5, all_74_19)
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | REDUCE: (142), (742) imply:
% 206.06/31.84 | | | | | | | | (743) ~ leq(n5, n5)
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | PRED_UNIFY: (736), (743) imply:
% 206.06/31.84 | | | | | | | | (744) $false
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | CLOSE: (744) is inconsistent.
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | Case 2:
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | (745) a_select3(q_ds1_filter, n5, n0) = all_74_1 &
% 206.06/31.84 | | | | | | | | $i(all_74_1)
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | ALPHA: (745) implies:
% 206.06/31.84 | | | | | | | | (746) a_select3(q_ds1_filter, n5, n0) = all_74_1
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | GROUND_INST: instantiating (19) with all_74_1, all_74_0, n0, n5,
% 206.06/31.84 | | | | | | | | q_ds1_filter, simplifying with (734), (746) gives:
% 206.06/31.84 | | | | | | | | (747) all_74_0 = all_74_1
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | REDUCE: (150), (747) imply:
% 206.06/31.84 | | | | | | | | (748) $false
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | CLOSE: (748) is inconsistent.
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | End of split
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | End of split
% 206.06/31.84 | | | | | |
% 206.06/31.84 | | | | | End of split
% 206.06/31.84 | | | | |
% 206.06/31.84 | | | | End of split
% 206.06/31.84 | | | |
% 206.06/31.84 | | | Case 2:
% 206.06/31.84 | | | |
% 206.06/31.84 | | | | (749) all_74_2 = n0
% 206.06/31.84 | | | | (750) ~ gt(all_74_2, n0)
% 206.06/31.84 | | | |
% 206.06/31.84 | | | | REDUCE: (156), (749) imply:
% 206.06/31.84 | | | | (751) a_select3(q_ds1_filter, n0, all_74_3) = all_74_0
% 206.06/31.84 | | | |
% 206.06/31.84 | | | | REDUCE: (155), (749) imply:
% 206.06/31.84 | | | | (752) a_select3(q_ds1_filter, all_74_3, n0) = all_74_1
% 206.06/31.84 | | | |
% 206.06/31.84 | | | | REDUCE: (157), (749) imply:
% 206.06/31.84 | | | | (753) leq(n0, n5)
% 206.06/31.84 | | | |
% 206.06/31.84 | | | | REDUCE: (152), (749) imply:
% 206.06/31.84 | | | | (754) leq(n0, n0)
% 206.06/31.84 | | | |
% 206.06/31.84 | | | | REDUCE: (749), (750) imply:
% 206.06/31.84 | | | | (755) ~ gt(n0, n0)
% 206.06/31.84 | | | |
% 206.06/31.84 | | | | BETA: splitting (159) gives:
% 206.06/31.84 | | | |
% 206.06/31.84 | | | | Case 1:
% 206.06/31.84 | | | | |
% 206.06/31.84 | | | | | (756) gt(all_74_3, n0)
% 206.06/31.84 | | | | |
% 206.06/31.84 | | | | | BETA: splitting (162) gives:
% 206.06/31.84 | | | | |
% 206.06/31.84 | | | | | Case 1:
% 206.06/31.84 | | | | | |
% 206.06/31.84 | | | | | | (757) gt(n5, all_74_3)
% 206.06/31.84 | | | | | |
% 206.06/31.84 | | | | | | GROUND_INST: instantiating (1) with all_74_3, n5, n4, simplifying
% 206.06/31.84 | | | | | | with (58), (125), (129), (757) gives:
% 206.06/31.84 | | | | | | (758) leq(all_74_3, n4)
% 206.06/31.84 | | | | | |
% 206.06/31.84 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n4, simplifying
% 206.06/31.84 | | | | | | with (58), (122), (758) gives:
% 206.06/31.84 | | | | | | (759) all_74_3 = n4 | gt(n4, all_74_3)
% 206.06/31.84 | | | | | |
% 206.06/31.84 | | | | | | BETA: splitting (161) gives:
% 206.06/31.84 | | | | | |
% 206.06/31.84 | | | | | | Case 1:
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | | (760) all_74_3 = n0
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | | REDUCE: (756), (760) imply:
% 206.06/31.84 | | | | | | | (761) gt(n0, n0)
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | | PRED_UNIFY: (755), (761) imply:
% 206.06/31.84 | | | | | | | (762) $false
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | | CLOSE: (762) is inconsistent.
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | Case 2:
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | | (763) ~ (all_74_3 = n0)
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | | BETA: splitting (759) gives:
% 206.06/31.84 | | | | | | |
% 206.06/31.84 | | | | | | | Case 1:
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | (764) gt(n4, all_74_3)
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n4, n3,
% 206.06/31.84 | | | | | | | | simplifying with (58), (122), (128), (764) gives:
% 206.06/31.84 | | | | | | | | (765) leq(all_74_3, n3)
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n3,
% 206.06/31.84 | | | | | | | | simplifying with (58), (115), (765) gives:
% 206.06/31.84 | | | | | | | | (766) all_74_3 = n3 | gt(n3, all_74_3)
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | BETA: splitting (766) gives:
% 206.06/31.84 | | | | | | | |
% 206.06/31.84 | | | | | | | | Case 1:
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | (767) gt(n3, all_74_3)
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2,
% 206.06/31.84 | | | | | | | | | simplifying with (58), (115), (127), (767) gives:
% 206.06/31.84 | | | | | | | | | (768) leq(all_74_3, n2)
% 206.06/31.84 | | | | | | | | |
% 206.06/31.84 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n2,
% 206.06/31.84 | | | | | | | | | simplifying with (58), (104), (768) gives:
% 206.06/31.85 | | | | | | | | | (769) all_74_3 = n2 | gt(n2, all_74_3)
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | BETA: splitting (769) gives:
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | Case 1:
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | (770) gt(n2, all_74_3)
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1,
% 206.06/31.85 | | | | | | | | | | simplifying with (58), (104), (126), (770) gives:
% 206.06/31.85 | | | | | | | | | | (771) leq(all_74_3, n1)
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | GROUND_INST: instantiating (5) with all_74_3, simplifying with
% 206.06/31.85 | | | | | | | | | | (58), (151), (771) gives:
% 206.06/31.85 | | | | | | | | | | (772) all_74_3 = n1 | all_74_3 = n0
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | BETA: splitting (772) gives:
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | Case 1:
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | (773) all_74_3 = n0
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | REDUCE: (763), (773) imply:
% 206.06/31.85 | | | | | | | | | | | (774) $false
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | CLOSE: (774) is inconsistent.
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | Case 2:
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | (775) all_74_3 = n1
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | REDUCE: (752), (775) imply:
% 206.06/31.85 | | | | | | | | | | | (776) a_select3(q_ds1_filter, n1, n0) = all_74_1
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | REDUCE: (751), (775) imply:
% 206.06/31.85 | | | | | | | | | | | (777) a_select3(q_ds1_filter, n0, n1) = all_74_0
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | REDUCE: (158), (775) imply:
% 206.06/31.85 | | | | | | | | | | | (778) leq(n1, n5)
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | REDUCE: (151), (775) imply:
% 206.06/31.85 | | | | | | | | | | | (779) leq(n0, n1)
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, n1, all_74_0,
% 206.06/31.85 | | | | | | | | | | | simplifying with (13), (88), (754), (777), (779)
% 206.06/31.85 | | | | | | | | | | | gives:
% 206.06/31.85 | | | | | | | | | | | (780) ~ leq(n1, all_74_19) | ~ leq(n0, all_74_19) |
% 206.06/31.85 | | | | | | | | | | | (a_select3(q_ds1_filter, n1, n0) = all_74_0 &
% 206.06/31.85 | | | | | | | | | | | $i(all_74_0))
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | BETA: splitting (780) gives:
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | Case 1:
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | (781) ~ leq(n0, all_74_19)
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | REDUCE: (142), (781) imply:
% 206.06/31.85 | | | | | | | | | | | | (782) ~ leq(n0, n5)
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | PRED_UNIFY: (753), (782) imply:
% 206.06/31.85 | | | | | | | | | | | | (783) $false
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | CLOSE: (783) is inconsistent.
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | Case 2:
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | (784) ~ leq(n1, all_74_19) | (a_select3(q_ds1_filter,
% 206.06/31.85 | | | | | | | | | | | | n1, n0) = all_74_0 & $i(all_74_0))
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | BETA: splitting (784) gives:
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | Case 1:
% 206.06/31.85 | | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | | (785) ~ leq(n1, all_74_19)
% 206.06/31.85 | | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | | REDUCE: (142), (785) imply:
% 206.06/31.85 | | | | | | | | | | | | | (786) ~ leq(n1, n5)
% 206.06/31.85 | | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | | PRED_UNIFY: (778), (786) imply:
% 206.06/31.85 | | | | | | | | | | | | | (787) $false
% 206.06/31.85 | | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | | CLOSE: (787) is inconsistent.
% 206.06/31.85 | | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | Case 2:
% 206.06/31.85 | | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | | (788) a_select3(q_ds1_filter, n1, n0) = all_74_0 &
% 206.06/31.85 | | | | | | | | | | | | | $i(all_74_0)
% 206.06/31.85 | | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | | ALPHA: (788) implies:
% 206.06/31.85 | | | | | | | | | | | | | (789) a_select3(q_ds1_filter, n1, n0) = all_74_0
% 206.06/31.85 | | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | | REF_CLOSE: (19), (150), (776), (789) are inconsistent by
% 206.06/31.85 | | | | | | | | | | | | | sub-proof #37.
% 206.06/31.85 | | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | End of split
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | End of split
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | End of split
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | Case 2:
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | (790) all_74_3 = n2
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | REDUCE: (752), (790) imply:
% 206.06/31.85 | | | | | | | | | | (791) a_select3(q_ds1_filter, n2, n0) = all_74_1
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | REDUCE: (751), (790) imply:
% 206.06/31.85 | | | | | | | | | | (792) a_select3(q_ds1_filter, n0, n2) = all_74_0
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | REDUCE: (158), (790) imply:
% 206.06/31.85 | | | | | | | | | | (793) leq(n2, n5)
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | REDUCE: (151), (790) imply:
% 206.06/31.85 | | | | | | | | | | (794) leq(n0, n2)
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | GROUND_INST: instantiating (65) with n0, n2, all_74_0,
% 206.06/31.85 | | | | | | | | | | simplifying with (13), (104), (754), (792), (794)
% 206.06/31.85 | | | | | | | | | | gives:
% 206.06/31.85 | | | | | | | | | | (795) ~ leq(n2, all_74_19) | ~ leq(n0, all_74_19) |
% 206.06/31.85 | | | | | | | | | | (a_select3(q_ds1_filter, n2, n0) = all_74_0 &
% 206.06/31.85 | | | | | | | | | | $i(all_74_0))
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | BETA: splitting (795) gives:
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | Case 1:
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | (796) ~ leq(n0, all_74_19)
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | REDUCE: (142), (796) imply:
% 206.06/31.85 | | | | | | | | | | | (797) ~ leq(n0, n5)
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | PRED_UNIFY: (753), (797) imply:
% 206.06/31.85 | | | | | | | | | | | (798) $false
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | CLOSE: (798) is inconsistent.
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | Case 2:
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | (799) ~ leq(n2, all_74_19) | (a_select3(q_ds1_filter,
% 206.06/31.85 | | | | | | | | | | | n2, n0) = all_74_0 & $i(all_74_0))
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | BETA: splitting (799) gives:
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | Case 1:
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | (800) ~ leq(n2, all_74_19)
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | REDUCE: (142), (800) imply:
% 206.06/31.85 | | | | | | | | | | | | (801) ~ leq(n2, n5)
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | PRED_UNIFY: (793), (801) imply:
% 206.06/31.85 | | | | | | | | | | | | (802) $false
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | CLOSE: (802) is inconsistent.
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | Case 2:
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | (803) a_select3(q_ds1_filter, n2, n0) = all_74_0 &
% 206.06/31.85 | | | | | | | | | | | | $i(all_74_0)
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | ALPHA: (803) implies:
% 206.06/31.85 | | | | | | | | | | | | (804) a_select3(q_ds1_filter, n2, n0) = all_74_0
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_74_1, all_74_0, n0,
% 206.06/31.85 | | | | | | | | | | | | n2, q_ds1_filter, simplifying with (791), (804)
% 206.06/31.85 | | | | | | | | | | | | gives:
% 206.06/31.85 | | | | | | | | | | | | (805) all_74_0 = all_74_1
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | REDUCE: (150), (805) imply:
% 206.06/31.85 | | | | | | | | | | | | (806) $false
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | | CLOSE: (806) is inconsistent.
% 206.06/31.85 | | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | End of split
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | End of split
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | End of split
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | Case 2:
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | (807) all_74_3 = n3
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | REDUCE: (752), (807) imply:
% 206.06/31.85 | | | | | | | | | (808) a_select3(q_ds1_filter, n3, n0) = all_74_1
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | REDUCE: (751), (807) imply:
% 206.06/31.85 | | | | | | | | | (809) a_select3(q_ds1_filter, n0, n3) = all_74_0
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | REDUCE: (158), (807) imply:
% 206.06/31.85 | | | | | | | | | (810) leq(n3, n5)
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | REDUCE: (151), (807) imply:
% 206.06/31.85 | | | | | | | | | (811) leq(n0, n3)
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | GROUND_INST: instantiating (65) with n0, n3, all_74_0,
% 206.06/31.85 | | | | | | | | | simplifying with (13), (115), (754), (809), (811)
% 206.06/31.85 | | | | | | | | | gives:
% 206.06/31.85 | | | | | | | | | (812) ~ leq(n3, all_74_19) | ~ leq(n0, all_74_19) |
% 206.06/31.85 | | | | | | | | | (a_select3(q_ds1_filter, n3, n0) = all_74_0 &
% 206.06/31.85 | | | | | | | | | $i(all_74_0))
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | BETA: splitting (812) gives:
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | Case 1:
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | (813) ~ leq(n0, all_74_19)
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | REDUCE: (142), (813) imply:
% 206.06/31.85 | | | | | | | | | | (814) ~ leq(n0, n5)
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | PRED_UNIFY: (753), (814) imply:
% 206.06/31.85 | | | | | | | | | | (815) $false
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | CLOSE: (815) is inconsistent.
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | Case 2:
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | (816) ~ leq(n3, all_74_19) | (a_select3(q_ds1_filter,
% 206.06/31.85 | | | | | | | | | | n3, n0) = all_74_0 & $i(all_74_0))
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | BETA: splitting (816) gives:
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | Case 1:
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | (817) ~ leq(n3, all_74_19)
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | REDUCE: (142), (817) imply:
% 206.06/31.85 | | | | | | | | | | | (818) ~ leq(n3, n5)
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | PRED_UNIFY: (810), (818) imply:
% 206.06/31.85 | | | | | | | | | | | (819) $false
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | CLOSE: (819) is inconsistent.
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | Case 2:
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | (820) a_select3(q_ds1_filter, n3, n0) = all_74_0 &
% 206.06/31.85 | | | | | | | | | | | $i(all_74_0)
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | ALPHA: (820) implies:
% 206.06/31.85 | | | | | | | | | | | (821) a_select3(q_ds1_filter, n3, n0) = all_74_0
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | | REF_CLOSE: (19), (150), (808), (821) are inconsistent by
% 206.06/31.85 | | | | | | | | | | | sub-proof #36.
% 206.06/31.85 | | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | End of split
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | End of split
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | End of split
% 206.06/31.85 | | | | | | | |
% 206.06/31.85 | | | | | | | Case 2:
% 206.06/31.85 | | | | | | | |
% 206.06/31.85 | | | | | | | | (822) all_74_3 = n4
% 206.06/31.85 | | | | | | | |
% 206.06/31.85 | | | | | | | | REDUCE: (752), (822) imply:
% 206.06/31.85 | | | | | | | | (823) a_select3(q_ds1_filter, n4, n0) = all_74_1
% 206.06/31.85 | | | | | | | |
% 206.06/31.85 | | | | | | | | REDUCE: (751), (822) imply:
% 206.06/31.85 | | | | | | | | (824) a_select3(q_ds1_filter, n0, n4) = all_74_0
% 206.06/31.85 | | | | | | | |
% 206.06/31.85 | | | | | | | | REDUCE: (158), (822) imply:
% 206.06/31.85 | | | | | | | | (825) leq(n4, n5)
% 206.06/31.85 | | | | | | | |
% 206.06/31.85 | | | | | | | | REDUCE: (151), (822) imply:
% 206.06/31.85 | | | | | | | | (826) leq(n0, n4)
% 206.06/31.85 | | | | | | | |
% 206.06/31.85 | | | | | | | | GROUND_INST: instantiating (65) with n0, n4, all_74_0,
% 206.06/31.85 | | | | | | | | simplifying with (13), (122), (754), (824), (826)
% 206.06/31.85 | | | | | | | | gives:
% 206.06/31.85 | | | | | | | | (827) ~ leq(n4, all_74_19) | ~ leq(n0, all_74_19) |
% 206.06/31.85 | | | | | | | | (a_select3(q_ds1_filter, n4, n0) = all_74_0 &
% 206.06/31.85 | | | | | | | | $i(all_74_0))
% 206.06/31.85 | | | | | | | |
% 206.06/31.85 | | | | | | | | BETA: splitting (827) gives:
% 206.06/31.85 | | | | | | | |
% 206.06/31.85 | | | | | | | | Case 1:
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | (828) ~ leq(n0, all_74_19)
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | REDUCE: (142), (828) imply:
% 206.06/31.85 | | | | | | | | | (829) ~ leq(n0, n5)
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | PRED_UNIFY: (753), (829) imply:
% 206.06/31.85 | | | | | | | | | (830) $false
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | CLOSE: (830) is inconsistent.
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | Case 2:
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | (831) ~ leq(n4, all_74_19) | (a_select3(q_ds1_filter, n4,
% 206.06/31.85 | | | | | | | | | n0) = all_74_0 & $i(all_74_0))
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | BETA: splitting (831) gives:
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | | Case 1:
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | (832) ~ leq(n4, all_74_19)
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | REDUCE: (142), (832) imply:
% 206.06/31.85 | | | | | | | | | | (833) ~ leq(n4, n5)
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | PRED_UNIFY: (825), (833) imply:
% 206.06/31.85 | | | | | | | | | | (834) $false
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | CLOSE: (834) is inconsistent.
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | Case 2:
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | (835) a_select3(q_ds1_filter, n4, n0) = all_74_0 &
% 206.06/31.85 | | | | | | | | | | $i(all_74_0)
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | ALPHA: (835) implies:
% 206.06/31.85 | | | | | | | | | | (836) a_select3(q_ds1_filter, n4, n0) = all_74_0
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | | REF_CLOSE: (19), (150), (823), (836) are inconsistent by
% 206.06/31.85 | | | | | | | | | | sub-proof #35.
% 206.06/31.85 | | | | | | | | | |
% 206.06/31.85 | | | | | | | | | End of split
% 206.06/31.85 | | | | | | | | |
% 206.06/31.85 | | | | | | | | End of split
% 206.06/31.85 | | | | | | | |
% 206.06/31.85 | | | | | | | End of split
% 206.06/31.85 | | | | | | |
% 206.06/31.85 | | | | | | End of split
% 206.06/31.85 | | | | | |
% 206.06/31.85 | | | | | Case 2:
% 206.06/31.85 | | | | | |
% 206.06/31.85 | | | | | | (837) all_74_3 = n5
% 206.06/31.85 | | | | | |
% 206.06/31.85 | | | | | | REDUCE: (752), (837) imply:
% 206.06/31.85 | | | | | | (838) a_select3(q_ds1_filter, n5, n0) = all_74_1
% 206.06/31.85 | | | | | |
% 206.06/31.85 | | | | | | REDUCE: (751), (837) imply:
% 206.06/31.85 | | | | | | (839) a_select3(q_ds1_filter, n0, n5) = all_74_0
% 206.06/31.85 | | | | | |
% 206.06/31.86 | | | | | | REDUCE: (158), (837) imply:
% 206.06/31.86 | | | | | | (840) leq(n5, n5)
% 206.06/31.86 | | | | | |
% 206.06/31.86 | | | | | | GROUND_INST: instantiating (65) with n0, n5, all_74_0, simplifying
% 206.06/31.86 | | | | | | with (13), (125), (753), (754), (839) gives:
% 206.06/31.86 | | | | | | (841) ~ leq(n5, all_74_19) | ~ leq(n0, all_74_19) |
% 206.06/31.86 | | | | | | (a_select3(q_ds1_filter, n5, n0) = all_74_0 & $i(all_74_0))
% 206.06/31.86 | | | | | |
% 206.06/31.86 | | | | | | BETA: splitting (841) gives:
% 206.06/31.86 | | | | | |
% 206.06/31.86 | | | | | | Case 1:
% 206.06/31.86 | | | | | | |
% 206.06/31.86 | | | | | | | (842) ~ leq(n0, all_74_19)
% 206.06/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | REDUCE: (142), (842) imply:
% 206.31/31.86 | | | | | | | (843) ~ leq(n0, n5)
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | PRED_UNIFY: (753), (843) imply:
% 206.31/31.86 | | | | | | | (844) $false
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | CLOSE: (844) is inconsistent.
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | Case 2:
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | (845) ~ leq(n5, all_74_19) | (a_select3(q_ds1_filter, n5, n0)
% 206.31/31.86 | | | | | | | = all_74_0 & $i(all_74_0))
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | BETA: splitting (845) gives:
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | Case 1:
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | (846) ~ leq(n5, all_74_19)
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | REDUCE: (142), (846) imply:
% 206.31/31.86 | | | | | | | | (847) ~ leq(n5, n5)
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | PRED_UNIFY: (840), (847) imply:
% 206.31/31.86 | | | | | | | | (848) $false
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | CLOSE: (848) is inconsistent.
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | Case 2:
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | (849) a_select3(q_ds1_filter, n5, n0) = all_74_0 &
% 206.31/31.86 | | | | | | | | $i(all_74_0)
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | ALPHA: (849) implies:
% 206.31/31.86 | | | | | | | | (850) a_select3(q_ds1_filter, n5, n0) = all_74_0
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | GROUND_INST: instantiating (19) with all_74_1, all_74_0, n0, n5,
% 206.31/31.86 | | | | | | | | q_ds1_filter, simplifying with (838), (850) gives:
% 206.31/31.86 | | | | | | | | (851) all_74_0 = all_74_1
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | REDUCE: (150), (851) imply:
% 206.31/31.86 | | | | | | | | (852) $false
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | CLOSE: (852) is inconsistent.
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | End of split
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | End of split
% 206.31/31.86 | | | | | |
% 206.31/31.86 | | | | | End of split
% 206.31/31.86 | | | | |
% 206.31/31.86 | | | | Case 2:
% 206.31/31.86 | | | | |
% 206.31/31.86 | | | | | (853) all_74_3 = n0
% 206.31/31.86 | | | | |
% 206.31/31.86 | | | | | REDUCE: (752), (853) imply:
% 206.31/31.86 | | | | | (854) a_select3(q_ds1_filter, n0, n0) = all_74_1
% 206.31/31.86 | | | | |
% 206.31/31.86 | | | | | REDUCE: (751), (853) imply:
% 206.31/31.86 | | | | | (855) a_select3(q_ds1_filter, n0, n0) = all_74_0
% 206.31/31.86 | | | | |
% 206.31/31.86 | | | | | GROUND_INST: instantiating (19) with all_74_1, all_74_0, n0, n0,
% 206.31/31.86 | | | | | q_ds1_filter, simplifying with (854), (855) gives:
% 206.31/31.86 | | | | | (856) all_74_0 = all_74_1
% 206.31/31.86 | | | | |
% 206.31/31.86 | | | | | REDUCE: (150), (856) imply:
% 206.31/31.86 | | | | | (857) $false
% 206.31/31.86 | | | | |
% 206.31/31.86 | | | | | CLOSE: (857) is inconsistent.
% 206.31/31.86 | | | | |
% 206.31/31.86 | | | | End of split
% 206.31/31.86 | | | |
% 206.31/31.86 | | | End of split
% 206.31/31.86 | | |
% 206.31/31.86 | | Case 2:
% 206.31/31.86 | | |
% 206.31/31.86 | | | (858) ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6,
% 206.31/31.86 | | | all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7,
% 206.31/31.86 | | | all_74_6) = all_74_5 & $i(all_74_4) & $i(all_74_5) &
% 206.31/31.86 | | | leq(all_74_6, all_74_18) & leq(all_74_7, all_74_18) & leq(n0,
% 206.31/31.86 | | | all_74_6) & leq(n0, all_74_7)
% 206.31/31.86 | | |
% 206.31/31.86 | | | ALPHA: (858) implies:
% 206.31/31.86 | | | (859) ~ (all_74_4 = all_74_5)
% 206.31/31.86 | | | (860) leq(n0, all_74_7)
% 206.31/31.86 | | | (861) leq(n0, all_74_6)
% 206.31/31.86 | | | (862) leq(all_74_7, all_74_18)
% 206.31/31.86 | | | (863) leq(all_74_6, all_74_18)
% 206.31/31.86 | | | (864) a_select3(r_ds1_filter, all_74_7, all_74_6) = all_74_5
% 206.31/31.86 | | | (865) a_select3(r_ds1_filter, all_74_6, all_74_7) = all_74_4
% 206.31/31.86 | | |
% 206.31/31.86 | | | REDUCE: (141), (863) imply:
% 206.31/31.86 | | | (866) leq(all_74_6, n2)
% 206.31/31.86 | | |
% 206.31/31.86 | | | REDUCE: (141), (862) imply:
% 206.31/31.86 | | | (867) leq(all_74_7, n2)
% 206.31/31.86 | | |
% 206.31/31.86 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_7, simplifying with
% 206.31/31.86 | | | (13), (56), (860) gives:
% 206.31/31.86 | | | (868) all_74_7 = n0 | gt(all_74_7, n0)
% 206.31/31.86 | | |
% 206.31/31.86 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_6, simplifying with
% 206.31/31.86 | | | (13), (57), (861) gives:
% 206.31/31.86 | | | (869) all_74_6 = n0 | gt(all_74_6, n0)
% 206.31/31.86 | | |
% 206.31/31.86 | | | GROUND_INST: instantiating (6) with all_74_7, simplifying with (56),
% 206.31/31.86 | | | (860), (867) gives:
% 206.31/31.86 | | | (870) all_74_7 = n2 | all_74_7 = n1 | all_74_7 = n0
% 206.31/31.86 | | |
% 206.31/31.86 | | | GROUND_INST: instantiating (leq_gt2) with all_74_7, n2, simplifying with
% 206.31/31.86 | | | (56), (104), (867) gives:
% 206.31/31.86 | | | (871) all_74_7 = n2 | gt(n2, all_74_7)
% 206.31/31.86 | | |
% 206.31/31.86 | | | GROUND_INST: instantiating (6) with all_74_6, simplifying with (57),
% 206.31/31.86 | | | (861), (866) gives:
% 206.31/31.86 | | | (872) all_74_6 = n2 | all_74_6 = n1 | all_74_6 = n0
% 206.31/31.86 | | |
% 206.31/31.86 | | | GROUND_INST: instantiating (leq_gt2) with all_74_6, n2, simplifying with
% 206.31/31.86 | | | (57), (104), (866) gives:
% 206.31/31.86 | | | (873) all_74_6 = n2 | gt(n2, all_74_6)
% 206.31/31.86 | | |
% 206.31/31.86 | | | BETA: splitting (868) gives:
% 206.31/31.86 | | |
% 206.31/31.86 | | | Case 1:
% 206.31/31.86 | | | |
% 206.31/31.86 | | | | (874) gt(all_74_7, n0)
% 206.31/31.86 | | | |
% 206.31/31.86 | | | | BETA: splitting (869) gives:
% 206.31/31.86 | | | |
% 206.31/31.86 | | | | Case 1:
% 206.31/31.86 | | | | |
% 206.31/31.86 | | | | | (875) gt(all_74_6, n0)
% 206.31/31.86 | | | | |
% 206.31/31.86 | | | | | BETA: splitting (873) gives:
% 206.31/31.86 | | | | |
% 206.31/31.86 | | | | | Case 1:
% 206.31/31.86 | | | | | |
% 206.31/31.86 | | | | | | (876) gt(n2, all_74_6)
% 206.31/31.86 | | | | | |
% 206.31/31.86 | | | | | | GROUND_INST: instantiating (1) with all_74_6, n2, n1, simplifying
% 206.31/31.86 | | | | | | with (57), (104), (126), (876) gives:
% 206.31/31.86 | | | | | | (877) leq(all_74_6, n1)
% 206.31/31.86 | | | | | |
% 206.31/31.86 | | | | | | GROUND_INST: instantiating (5) with all_74_6, simplifying with (57),
% 206.31/31.86 | | | | | | (861), (877) gives:
% 206.31/31.86 | | | | | | (878) all_74_6 = n1 | all_74_6 = n0
% 206.31/31.86 | | | | | |
% 206.31/31.86 | | | | | | BETA: splitting (871) gives:
% 206.31/31.86 | | | | | |
% 206.31/31.86 | | | | | | Case 1:
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | (879) gt(n2, all_74_7)
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | GROUND_INST: instantiating (1) with all_74_7, n2, n1, simplifying
% 206.31/31.86 | | | | | | | with (56), (104), (126), (879) gives:
% 206.31/31.86 | | | | | | | (880) leq(all_74_7, n1)
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | BETA: splitting (870) gives:
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | Case 1:
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | (881) all_74_7 = n0
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | REF_CLOSE: (56), (874), (881), (irreflexivity_gt) are
% 206.31/31.86 | | | | | | | | inconsistent by sub-proof #34.
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | Case 2:
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | (882) ~ (all_74_7 = n0)
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | BETA: splitting (872) gives:
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | Case 1:
% 206.31/31.86 | | | | | | | | |
% 206.31/31.86 | | | | | | | | | (883) all_74_6 = n0
% 206.31/31.86 | | | | | | | | |
% 206.31/31.86 | | | | | | | | | REF_CLOSE: (57), (875), (883), (irreflexivity_gt) are
% 206.31/31.86 | | | | | | | | | inconsistent by sub-proof #33.
% 206.31/31.86 | | | | | | | | |
% 206.31/31.86 | | | | | | | | Case 2:
% 206.31/31.86 | | | | | | | | |
% 206.31/31.86 | | | | | | | | | (884) ~ (all_74_6 = n0)
% 206.31/31.86 | | | | | | | | |
% 206.31/31.86 | | | | | | | | | BETA: splitting (878) gives:
% 206.31/31.86 | | | | | | | | |
% 206.31/31.86 | | | | | | | | | Case 1:
% 206.31/31.86 | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | (885) all_74_6 = n0
% 206.31/31.86 | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | REDUCE: (884), (885) imply:
% 206.31/31.86 | | | | | | | | | | (886) $false
% 206.31/31.86 | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | CLOSE: (886) is inconsistent.
% 206.31/31.86 | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | Case 2:
% 206.31/31.86 | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | (887) all_74_6 = n1
% 206.31/31.86 | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | REDUCE: (865), (887) imply:
% 206.31/31.86 | | | | | | | | | | (888) a_select3(r_ds1_filter, n1, all_74_7) = all_74_4
% 206.31/31.86 | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | REDUCE: (864), (887) imply:
% 206.31/31.86 | | | | | | | | | | (889) a_select3(r_ds1_filter, all_74_7, n1) = all_74_5
% 206.31/31.86 | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | GROUND_INST: instantiating (5) with all_74_7, simplifying with
% 206.31/31.86 | | | | | | | | | | (56), (860), (880) gives:
% 206.31/31.86 | | | | | | | | | | (890) all_74_7 = n1 | all_74_7 = n0
% 206.31/31.86 | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | BETA: splitting (890) gives:
% 206.31/31.86 | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | Case 1:
% 206.31/31.86 | | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | | (891) all_74_7 = n0
% 206.31/31.86 | | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | | REDUCE: (882), (891) imply:
% 206.31/31.86 | | | | | | | | | | | (892) $false
% 206.31/31.86 | | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | | CLOSE: (892) is inconsistent.
% 206.31/31.86 | | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | Case 2:
% 206.31/31.86 | | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | | (893) all_74_7 = n1
% 206.31/31.86 | | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | | REDUCE: (889), (893) imply:
% 206.31/31.86 | | | | | | | | | | | (894) a_select3(r_ds1_filter, n1, n1) = all_74_5
% 206.31/31.86 | | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | | REDUCE: (888), (893) imply:
% 206.31/31.86 | | | | | | | | | | | (895) a_select3(r_ds1_filter, n1, n1) = all_74_4
% 206.31/31.86 | | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | | GROUND_INST: instantiating (19) with all_74_5, all_74_4, n1,
% 206.31/31.86 | | | | | | | | | | | n1, r_ds1_filter, simplifying with (894), (895)
% 206.31/31.86 | | | | | | | | | | | gives:
% 206.31/31.86 | | | | | | | | | | | (896) all_74_4 = all_74_5
% 206.31/31.86 | | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | | REDUCE: (859), (896) imply:
% 206.31/31.86 | | | | | | | | | | | (897) $false
% 206.31/31.86 | | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | | CLOSE: (897) is inconsistent.
% 206.31/31.86 | | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | | End of split
% 206.31/31.86 | | | | | | | | | |
% 206.31/31.86 | | | | | | | | | End of split
% 206.31/31.86 | | | | | | | | |
% 206.31/31.86 | | | | | | | | End of split
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | End of split
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | Case 2:
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | (898) all_74_7 = n2
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | REDUCE: (865), (898) imply:
% 206.31/31.86 | | | | | | | (899) a_select3(r_ds1_filter, all_74_6, n2) = all_74_4
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | REDUCE: (864), (898) imply:
% 206.31/31.86 | | | | | | | (900) a_select3(r_ds1_filter, n2, all_74_6) = all_74_5
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | REDUCE: (867), (898) imply:
% 206.31/31.86 | | | | | | | (901) leq(n2, n2)
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | REDUCE: (860), (898) imply:
% 206.31/31.86 | | | | | | | (902) leq(n0, n2)
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | BETA: splitting (872) gives:
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | Case 1:
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | (903) all_74_6 = n0
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | REF_CLOSE: (57), (875), (903), (irreflexivity_gt) are
% 206.31/31.86 | | | | | | | | inconsistent by sub-proof #33.
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | Case 2:
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | (904) ~ (all_74_6 = n0)
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | | REF_CLOSE: (19), (57), (66), (104), (141), (859), (861), (866),
% 206.31/31.86 | | | | | | | | (878), (899), (900), (901), (902), (904) are
% 206.31/31.86 | | | | | | | | inconsistent by sub-proof #32.
% 206.31/31.86 | | | | | | | |
% 206.31/31.86 | | | | | | | End of split
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | End of split
% 206.31/31.86 | | | | | |
% 206.31/31.86 | | | | | Case 2:
% 206.31/31.86 | | | | | |
% 206.31/31.86 | | | | | | (905) all_74_6 = n2
% 206.31/31.86 | | | | | |
% 206.31/31.86 | | | | | | REDUCE: (865), (905) imply:
% 206.31/31.86 | | | | | | (906) a_select3(r_ds1_filter, n2, all_74_7) = all_74_4
% 206.31/31.86 | | | | | |
% 206.31/31.86 | | | | | | REDUCE: (864), (905) imply:
% 206.31/31.86 | | | | | | (907) a_select3(r_ds1_filter, all_74_7, n2) = all_74_5
% 206.31/31.86 | | | | | |
% 206.31/31.86 | | | | | | REDUCE: (866), (905) imply:
% 206.31/31.86 | | | | | | (908) leq(n2, n2)
% 206.31/31.86 | | | | | |
% 206.31/31.86 | | | | | | REDUCE: (861), (905) imply:
% 206.31/31.86 | | | | | | (909) leq(n0, n2)
% 206.31/31.86 | | | | | |
% 206.31/31.86 | | | | | | BETA: splitting (871) gives:
% 206.31/31.86 | | | | | |
% 206.31/31.86 | | | | | | Case 1:
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | (910) gt(n2, all_74_7)
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | GROUND_INST: instantiating (1) with all_74_7, n2, n1, simplifying
% 206.31/31.86 | | | | | | | with (56), (104), (126), (910) gives:
% 206.31/31.86 | | | | | | | (911) leq(all_74_7, n1)
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | GROUND_INST: instantiating (5) with all_74_7, simplifying with
% 206.31/31.86 | | | | | | | (56), (860), (911) gives:
% 206.31/31.86 | | | | | | | (912) all_74_7 = n1 | all_74_7 = n0
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | BETA: splitting (870) gives:
% 206.31/31.86 | | | | | | |
% 206.31/31.86 | | | | | | | Case 1:
% 206.31/31.86 | | | | | | | |
% 206.31/31.87 | | | | | | | | (913) all_74_7 = n0
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | REF_CLOSE: (56), (874), (913), (irreflexivity_gt) are
% 206.31/31.87 | | | | | | | | inconsistent by sub-proof #34.
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | Case 2:
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | (914) ~ (all_74_7 = n0)
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | REF_CLOSE: (19), (56), (66), (104), (141), (859), (860), (867),
% 206.31/31.87 | | | | | | | | (906), (907), (908), (909), (912), (914) are
% 206.31/31.87 | | | | | | | | inconsistent by sub-proof #31.
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | End of split
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | Case 2:
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | (915) all_74_7 = n2
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | REDUCE: (907), (915) imply:
% 206.31/31.87 | | | | | | | (916) a_select3(r_ds1_filter, n2, n2) = all_74_5
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | REDUCE: (906), (915) imply:
% 206.31/31.87 | | | | | | | (917) a_select3(r_ds1_filter, n2, n2) = all_74_4
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | GROUND_INST: instantiating (19) with all_74_5, all_74_4, n2, n2,
% 206.31/31.87 | | | | | | | r_ds1_filter, simplifying with (916), (917) gives:
% 206.31/31.87 | | | | | | | (918) all_74_4 = all_74_5
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | REDUCE: (859), (918) imply:
% 206.31/31.87 | | | | | | | (919) $false
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | CLOSE: (919) is inconsistent.
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | End of split
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | End of split
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | Case 2:
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | | (920) all_74_6 = n0
% 206.31/31.87 | | | | | (921) ~ gt(all_74_6, n0)
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | | REDUCE: (920), (921) imply:
% 206.31/31.87 | | | | | (922) ~ gt(n0, n0)
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | | REF_CLOSE: (1), (5), (19), (56), (57), (66), (104), (126), (141),
% 206.31/31.87 | | | | | (859), (860), (861), (864), (865), (866), (867), (869),
% 206.31/31.87 | | | | | (870), (871), (872), (873), (874), (922) are inconsistent
% 206.31/31.87 | | | | | by sub-proof #29.
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | End of split
% 206.31/31.87 | | | |
% 206.31/31.87 | | | Case 2:
% 206.31/31.87 | | | |
% 206.31/31.87 | | | | (923) all_74_7 = n0
% 206.31/31.87 | | | | (924) ~ gt(all_74_7, n0)
% 206.31/31.87 | | | |
% 206.31/31.87 | | | | REDUCE: (923), (924) imply:
% 206.31/31.87 | | | | (925) ~ gt(n0, n0)
% 206.31/31.87 | | | |
% 206.31/31.87 | | | | BETA: splitting (868) gives:
% 206.31/31.87 | | | |
% 206.31/31.87 | | | | Case 1:
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | | (926) gt(all_74_7, n0)
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | | REF_CLOSE: (1), (5), (19), (56), (57), (66), (104), (126), (141),
% 206.31/31.87 | | | | | (859), (860), (861), (864), (865), (866), (867), (869),
% 206.31/31.87 | | | | | (870), (871), (872), (873), (925), (926) are inconsistent
% 206.31/31.87 | | | | | by sub-proof #29.
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | Case 2:
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | | REDUCE: (865), (923) imply:
% 206.31/31.87 | | | | | (927) a_select3(r_ds1_filter, all_74_6, n0) = all_74_4
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | | REDUCE: (864), (923) imply:
% 206.31/31.87 | | | | | (928) a_select3(r_ds1_filter, n0, all_74_6) = all_74_5
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | | REDUCE: (867), (923) imply:
% 206.31/31.87 | | | | | (929) leq(n0, n2)
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | | REDUCE: (860), (923) imply:
% 206.31/31.87 | | | | | (930) leq(n0, n0)
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | | BETA: splitting (869) gives:
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | | Case 1:
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | | (931) gt(all_74_6, n0)
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | | BETA: splitting (873) gives:
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | | Case 1:
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | (932) gt(n2, all_74_6)
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | GROUND_INST: instantiating (1) with all_74_6, n2, n1, simplifying
% 206.31/31.87 | | | | | | | with (57), (104), (126), (932) gives:
% 206.31/31.87 | | | | | | | (933) leq(all_74_6, n1)
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | GROUND_INST: instantiating (5) with all_74_6, simplifying with
% 206.31/31.87 | | | | | | | (57), (861), (933) gives:
% 206.31/31.87 | | | | | | | (934) all_74_6 = n1 | all_74_6 = n0
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | BETA: splitting (872) gives:
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | Case 1:
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | (935) all_74_6 = n0
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | REDUCE: (931), (935) imply:
% 206.31/31.87 | | | | | | | | (936) gt(n0, n0)
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | PRED_UNIFY: (925), (936) imply:
% 206.31/31.87 | | | | | | | | (937) $false
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | CLOSE: (937) is inconsistent.
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | Case 2:
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | (938) ~ (all_74_6 = n0)
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | BETA: splitting (934) gives:
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | Case 1:
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | (939) all_74_6 = n0
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | REDUCE: (938), (939) imply:
% 206.31/31.87 | | | | | | | | | (940) $false
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | CLOSE: (940) is inconsistent.
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | Case 2:
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | (941) all_74_6 = n1
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | REDUCE: (927), (941) imply:
% 206.31/31.87 | | | | | | | | | (942) a_select3(r_ds1_filter, n1, n0) = all_74_4
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | REDUCE: (928), (941) imply:
% 206.31/31.87 | | | | | | | | | (943) a_select3(r_ds1_filter, n0, n1) = all_74_5
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | REDUCE: (866), (941) imply:
% 206.31/31.87 | | | | | | | | | (944) leq(n1, n2)
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | REDUCE: (861), (941) imply:
% 206.31/31.87 | | | | | | | | | (945) leq(n0, n1)
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | GROUND_INST: instantiating (66) with n0, n1, all_74_5,
% 206.31/31.87 | | | | | | | | | simplifying with (13), (88), (930), (943), (945)
% 206.31/31.87 | | | | | | | | | gives:
% 206.31/31.87 | | | | | | | | | (946) ~ leq(n1, all_74_18) | ~ leq(n0, all_74_18) |
% 206.31/31.87 | | | | | | | | | (a_select3(r_ds1_filter, n1, n0) = all_74_5 &
% 206.31/31.87 | | | | | | | | | $i(all_74_5))
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | BETA: splitting (946) gives:
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | Case 1:
% 206.31/31.87 | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | (947) ~ leq(n0, all_74_18)
% 206.31/31.87 | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | REDUCE: (141), (947) imply:
% 206.31/31.87 | | | | | | | | | | (948) ~ leq(n0, n2)
% 206.31/31.87 | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | PRED_UNIFY: (929), (948) imply:
% 206.31/31.87 | | | | | | | | | | (949) $false
% 206.31/31.87 | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | CLOSE: (949) is inconsistent.
% 206.31/31.87 | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | Case 2:
% 206.31/31.87 | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | (950) ~ leq(n1, all_74_18) | (a_select3(r_ds1_filter,
% 206.31/31.87 | | | | | | | | | | n1, n0) = all_74_5 & $i(all_74_5))
% 206.31/31.87 | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | BETA: splitting (950) gives:
% 206.31/31.87 | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | Case 1:
% 206.31/31.87 | | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | | (951) ~ leq(n1, all_74_18)
% 206.31/31.87 | | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | | REDUCE: (141), (951) imply:
% 206.31/31.87 | | | | | | | | | | | (952) ~ leq(n1, n2)
% 206.31/31.87 | | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | | PRED_UNIFY: (944), (952) imply:
% 206.31/31.87 | | | | | | | | | | | (953) $false
% 206.31/31.87 | | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | | CLOSE: (953) is inconsistent.
% 206.31/31.87 | | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | Case 2:
% 206.31/31.87 | | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | | (954) a_select3(r_ds1_filter, n1, n0) = all_74_5 &
% 206.31/31.87 | | | | | | | | | | | $i(all_74_5)
% 206.31/31.87 | | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | | ALPHA: (954) implies:
% 206.31/31.87 | | | | | | | | | | | (955) a_select3(r_ds1_filter, n1, n0) = all_74_5
% 206.31/31.87 | | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | | REF_CLOSE: (19), (859), (942), (955) are inconsistent by
% 206.31/31.87 | | | | | | | | | | | sub-proof #30.
% 206.31/31.87 | | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | | End of split
% 206.31/31.87 | | | | | | | | | |
% 206.31/31.87 | | | | | | | | | End of split
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | End of split
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | End of split
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | Case 2:
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | (956) all_74_6 = n2
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | REDUCE: (927), (956) imply:
% 206.31/31.87 | | | | | | | (957) a_select3(r_ds1_filter, n2, n0) = all_74_4
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | REDUCE: (928), (956) imply:
% 206.31/31.87 | | | | | | | (958) a_select3(r_ds1_filter, n0, n2) = all_74_5
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | REDUCE: (866), (956) imply:
% 206.31/31.87 | | | | | | | (959) leq(n2, n2)
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | GROUND_INST: instantiating (66) with n0, n2, all_74_5, simplifying
% 206.31/31.87 | | | | | | | with (13), (104), (929), (930), (958) gives:
% 206.31/31.87 | | | | | | | (960) ~ leq(n2, all_74_18) | ~ leq(n0, all_74_18) |
% 206.31/31.87 | | | | | | | (a_select3(r_ds1_filter, n2, n0) = all_74_5 &
% 206.31/31.87 | | | | | | | $i(all_74_5))
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | BETA: splitting (960) gives:
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | Case 1:
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | (961) ~ leq(n0, all_74_18)
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | REDUCE: (141), (961) imply:
% 206.31/31.87 | | | | | | | | (962) ~ leq(n0, n2)
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | PRED_UNIFY: (929), (962) imply:
% 206.31/31.87 | | | | | | | | (963) $false
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | CLOSE: (963) is inconsistent.
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | Case 2:
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | (964) ~ leq(n2, all_74_18) | (a_select3(r_ds1_filter, n2,
% 206.31/31.87 | | | | | | | | n0) = all_74_5 & $i(all_74_5))
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | BETA: splitting (964) gives:
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | | Case 1:
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | (965) ~ leq(n2, all_74_18)
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | REDUCE: (141), (965) imply:
% 206.31/31.87 | | | | | | | | | (966) ~ leq(n2, n2)
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | PRED_UNIFY: (959), (966) imply:
% 206.31/31.87 | | | | | | | | | (967) $false
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | CLOSE: (967) is inconsistent.
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | Case 2:
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | (968) a_select3(r_ds1_filter, n2, n0) = all_74_5 &
% 206.31/31.87 | | | | | | | | | $i(all_74_5)
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | ALPHA: (968) implies:
% 206.31/31.87 | | | | | | | | | (969) a_select3(r_ds1_filter, n2, n0) = all_74_5
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | GROUND_INST: instantiating (19) with all_74_4, all_74_5, n0,
% 206.31/31.87 | | | | | | | | | n2, r_ds1_filter, simplifying with (957), (969)
% 206.31/31.87 | | | | | | | | | gives:
% 206.31/31.87 | | | | | | | | | (970) all_74_4 = all_74_5
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | REDUCE: (859), (970) imply:
% 206.31/31.87 | | | | | | | | | (971) $false
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | | CLOSE: (971) is inconsistent.
% 206.31/31.87 | | | | | | | | |
% 206.31/31.87 | | | | | | | | End of split
% 206.31/31.87 | | | | | | | |
% 206.31/31.87 | | | | | | | End of split
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | End of split
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | Case 2:
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | | (972) all_74_6 = n0
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | | REDUCE: (927), (972) imply:
% 206.31/31.87 | | | | | | (973) a_select3(r_ds1_filter, n0, n0) = all_74_4
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | | REDUCE: (928), (972) imply:
% 206.31/31.87 | | | | | | (974) a_select3(r_ds1_filter, n0, n0) = all_74_5
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | | GROUND_INST: instantiating (19) with all_74_5, all_74_4, n0, n0,
% 206.31/31.87 | | | | | | r_ds1_filter, simplifying with (973), (974) gives:
% 206.31/31.87 | | | | | | (975) all_74_4 = all_74_5
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | | REDUCE: (859), (975) imply:
% 206.31/31.87 | | | | | | (976) $false
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | | CLOSE: (976) is inconsistent.
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | End of split
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | End of split
% 206.31/31.87 | | | |
% 206.31/31.87 | | | End of split
% 206.31/31.87 | | |
% 206.31/31.87 | | End of split
% 206.31/31.87 | |
% 206.31/31.87 | Case 2:
% 206.31/31.87 | |
% 206.31/31.87 | | (977) ( ~ (all_74_8 = all_74_9) & a_select3(pminus_ds1_filter, all_74_10,
% 206.31/31.87 | | all_74_11) = all_74_8 & a_select3(pminus_ds1_filter, all_74_11,
% 206.31/31.87 | | all_74_10) = all_74_9 & $i(all_74_8) & $i(all_74_9) &
% 206.31/31.87 | | leq(all_74_10, all_74_19) & leq(all_74_11, all_74_19) & leq(n0,
% 206.31/31.87 | | all_74_10) & leq(n0, all_74_11)) | ( ~ (all_74_12 = all_74_13)
% 206.31/31.87 | | & a_select3(id_ds1_filter, all_74_14, all_74_15) = all_74_12 &
% 206.31/31.87 | | a_select3(id_ds1_filter, all_74_15, all_74_14) = all_74_13 &
% 206.31/31.87 | | $i(all_74_12) & $i(all_74_13) & leq(all_74_14, all_74_19) &
% 206.31/31.87 | | leq(all_74_15, all_74_19) & leq(n0, all_74_14) & leq(n0,
% 206.31/31.87 | | all_74_15))
% 206.31/31.87 | |
% 206.31/31.87 | | BETA: splitting (977) gives:
% 206.31/31.87 | |
% 206.31/31.87 | | Case 1:
% 206.31/31.87 | | |
% 206.31/31.87 | | | (978) ~ (all_74_8 = all_74_9) & a_select3(pminus_ds1_filter,
% 206.31/31.87 | | | all_74_10, all_74_11) = all_74_8 & a_select3(pminus_ds1_filter,
% 206.31/31.87 | | | all_74_11, all_74_10) = all_74_9 & $i(all_74_8) & $i(all_74_9)
% 206.31/31.87 | | | & leq(all_74_10, all_74_19) & leq(all_74_11, all_74_19) & leq(n0,
% 206.31/31.87 | | | all_74_10) & leq(n0, all_74_11)
% 206.31/31.87 | | |
% 206.31/31.87 | | | ALPHA: (978) implies:
% 206.31/31.87 | | | (979) ~ (all_74_8 = all_74_9)
% 206.31/31.87 | | | (980) leq(n0, all_74_11)
% 206.31/31.87 | | | (981) leq(n0, all_74_10)
% 206.31/31.87 | | | (982) leq(all_74_11, all_74_19)
% 206.31/31.87 | | | (983) leq(all_74_10, all_74_19)
% 206.31/31.87 | | | (984) a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9
% 206.31/31.87 | | | (985) a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8
% 206.31/31.87 | | |
% 206.31/31.87 | | | REDUCE: (142), (983) imply:
% 206.31/31.87 | | | (986) leq(all_74_10, n5)
% 206.31/31.87 | | |
% 206.31/31.87 | | | REDUCE: (142), (982) imply:
% 206.31/31.87 | | | (987) leq(all_74_11, n5)
% 206.31/31.87 | | |
% 206.31/31.87 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_11, simplifying with
% 206.31/31.87 | | | (13), (54), (980) gives:
% 206.31/31.87 | | | (988) all_74_11 = n0 | gt(all_74_11, n0)
% 206.31/31.87 | | |
% 206.31/31.87 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_10, simplifying with
% 206.31/31.87 | | | (13), (55), (981) gives:
% 206.31/31.87 | | | (989) all_74_10 = n0 | gt(all_74_10, n0)
% 206.31/31.87 | | |
% 206.31/31.87 | | | GROUND_INST: instantiating (4) with all_74_11, simplifying with (54),
% 206.31/31.87 | | | (980), (987) gives:
% 206.31/31.87 | | | (990) all_74_11 = n5 | all_74_11 = n4 | all_74_11 = n3 | all_74_11 = n2
% 206.31/31.87 | | | | all_74_11 = n1 | all_74_11 = n0
% 206.31/31.87 | | |
% 206.31/31.87 | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n5, simplifying with
% 206.31/31.87 | | | (54), (125), (987) gives:
% 206.31/31.87 | | | (991) all_74_11 = n5 | gt(n5, all_74_11)
% 206.31/31.87 | | |
% 206.31/31.87 | | | GROUND_INST: instantiating (4) with all_74_10, simplifying with (55),
% 206.31/31.87 | | | (981), (986) gives:
% 206.31/31.87 | | | (992) all_74_10 = n5 | all_74_10 = n4 | all_74_10 = n3 | all_74_10 = n2
% 206.31/31.87 | | | | all_74_10 = n1 | all_74_10 = n0
% 206.31/31.87 | | |
% 206.31/31.87 | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n5, simplifying with
% 206.31/31.87 | | | (55), (125), (986) gives:
% 206.31/31.87 | | | (993) all_74_10 = n5 | gt(n5, all_74_10)
% 206.31/31.87 | | |
% 206.31/31.87 | | | BETA: splitting (989) gives:
% 206.31/31.87 | | |
% 206.31/31.87 | | | Case 1:
% 206.31/31.87 | | | |
% 206.31/31.87 | | | | (994) gt(all_74_10, n0)
% 206.31/31.87 | | | |
% 206.31/31.87 | | | | BETA: splitting (988) gives:
% 206.31/31.87 | | | |
% 206.31/31.87 | | | | Case 1:
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | | (995) gt(all_74_11, n0)
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | | BETA: splitting (991) gives:
% 206.31/31.87 | | | | |
% 206.31/31.87 | | | | | Case 1:
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | | (996) gt(n5, all_74_11)
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | | GROUND_INST: instantiating (1) with all_74_11, n5, n4, simplifying
% 206.31/31.87 | | | | | | with (54), (125), (129), (996) gives:
% 206.31/31.87 | | | | | | (997) leq(all_74_11, n4)
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n4, simplifying
% 206.31/31.87 | | | | | | with (54), (122), (997) gives:
% 206.31/31.87 | | | | | | (998) all_74_11 = n4 | gt(n4, all_74_11)
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | | BETA: splitting (993) gives:
% 206.31/31.87 | | | | | |
% 206.31/31.87 | | | | | | Case 1:
% 206.31/31.87 | | | | | | |
% 206.31/31.87 | | | | | | | (999) gt(n5, all_74_10)
% 206.31/31.87 | | | | | | |
% 206.31/31.88 | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n5, n4, simplifying
% 206.31/31.88 | | | | | | | with (55), (125), (129), (999) gives:
% 206.31/31.88 | | | | | | | (1000) leq(all_74_10, n4)
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n4,
% 206.31/31.88 | | | | | | | simplifying with (55), (122), (1000) gives:
% 206.31/31.88 | | | | | | | (1001) all_74_10 = n4 | gt(n4, all_74_10)
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | BETA: splitting (990) gives:
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | Case 1:
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | (1002) all_74_11 = n0
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | REF_CLOSE: (54), (995), (1002), (irreflexivity_gt) are
% 206.31/31.88 | | | | | | | | inconsistent by sub-proof #28.
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | Case 2:
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | (1003) ~ (all_74_11 = n0)
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | BETA: splitting (992) gives:
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | Case 1:
% 206.31/31.88 | | | | | | | | |
% 206.31/31.88 | | | | | | | | | (1004) all_74_10 = n0
% 206.31/31.88 | | | | | | | | |
% 206.31/31.88 | | | | | | | | | REF_CLOSE: (55), (994), (1004), (irreflexivity_gt) are
% 206.31/31.88 | | | | | | | | | inconsistent by sub-proof #27.
% 206.31/31.88 | | | | | | | | |
% 206.31/31.88 | | | | | | | | Case 2:
% 206.31/31.88 | | | | | | | | |
% 206.31/31.88 | | | | | | | | | (1005) ~ (all_74_10 = n0)
% 206.31/31.88 | | | | | | | | |
% 206.31/31.88 | | | | | | | | | REF_CLOSE: (1), (5), (19), (54), (55), (67), (104), (115),
% 206.31/31.88 | | | | | | | | | (122), (126), (127), (128), (142), (979), (980),
% 206.31/31.88 | | | | | | | | | (981), (984), (985), (986), (987), (998), (1001),
% 206.31/31.88 | | | | | | | | | (1003), (1005), (leq_gt2) are inconsistent by
% 206.31/31.88 | | | | | | | | | sub-proof #20.
% 206.31/31.88 | | | | | | | | |
% 206.31/31.88 | | | | | | | | End of split
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | End of split
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | Case 2:
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | (1006) all_74_10 = n5
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | REDUCE: (985), (1006) imply:
% 206.31/31.88 | | | | | | | (1007) a_select3(pminus_ds1_filter, n5, all_74_11) = all_74_8
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | REDUCE: (984), (1006) imply:
% 206.31/31.88 | | | | | | | (1008) a_select3(pminus_ds1_filter, all_74_11, n5) = all_74_9
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | REDUCE: (986), (1006) imply:
% 206.31/31.88 | | | | | | | (1009) leq(n5, n5)
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | REDUCE: (981), (1006) imply:
% 206.31/31.88 | | | | | | | (1010) leq(n0, n5)
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | BETA: splitting (990) gives:
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | Case 1:
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | (1011) all_74_11 = n0
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | REF_CLOSE: (54), (995), (1011), (irreflexivity_gt) are
% 206.31/31.88 | | | | | | | | inconsistent by sub-proof #28.
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | Case 2:
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | (1012) ~ (all_74_11 = n0)
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | REF_CLOSE: (1), (5), (19), (54), (67), (104), (115), (122),
% 206.31/31.88 | | | | | | | | (125), (126), (127), (128), (142), (979), (980),
% 206.31/31.88 | | | | | | | | (987), (998), (1007), (1008), (1009), (1010), (1012),
% 206.31/31.88 | | | | | | | | (leq_gt2) are inconsistent by sub-proof #18.
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | End of split
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | End of split
% 206.31/31.88 | | | | | |
% 206.31/31.88 | | | | | Case 2:
% 206.31/31.88 | | | | | |
% 206.31/31.88 | | | | | | (1013) all_74_11 = n5
% 206.31/31.88 | | | | | |
% 206.31/31.88 | | | | | | REDUCE: (985), (1013) imply:
% 206.31/31.88 | | | | | | (1014) a_select3(pminus_ds1_filter, all_74_10, n5) = all_74_8
% 206.31/31.88 | | | | | |
% 206.31/31.88 | | | | | | REDUCE: (984), (1013) imply:
% 206.31/31.88 | | | | | | (1015) a_select3(pminus_ds1_filter, n5, all_74_10) = all_74_9
% 206.31/31.88 | | | | | |
% 206.31/31.88 | | | | | | REDUCE: (987), (1013) imply:
% 206.31/31.88 | | | | | | (1016) leq(n5, n5)
% 206.31/31.88 | | | | | |
% 206.31/31.88 | | | | | | REDUCE: (980), (1013) imply:
% 206.31/31.88 | | | | | | (1017) leq(n0, n5)
% 206.31/31.88 | | | | | |
% 206.31/31.88 | | | | | | BETA: splitting (993) gives:
% 206.31/31.88 | | | | | |
% 206.31/31.88 | | | | | | Case 1:
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | (1018) gt(n5, all_74_10)
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n5, n4, simplifying
% 206.31/31.88 | | | | | | | with (55), (125), (129), (1018) gives:
% 206.31/31.88 | | | | | | | (1019) leq(all_74_10, n4)
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n4,
% 206.31/31.88 | | | | | | | simplifying with (55), (122), (1019) gives:
% 206.31/31.88 | | | | | | | (1020) all_74_10 = n4 | gt(n4, all_74_10)
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | BETA: splitting (992) gives:
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | Case 1:
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | (1021) all_74_10 = n0
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | REF_CLOSE: (55), (994), (1021), (irreflexivity_gt) are
% 206.31/31.88 | | | | | | | | inconsistent by sub-proof #27.
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | Case 2:
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | (1022) ~ (all_74_10 = n0)
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | REF_CLOSE: (1), (5), (19), (55), (67), (104), (115), (122),
% 206.31/31.88 | | | | | | | | (125), (126), (127), (128), (142), (979), (981),
% 206.31/31.88 | | | | | | | | (986), (1014), (1015), (1016), (1017), (1020),
% 206.31/31.88 | | | | | | | | (1022), (leq_gt2) are inconsistent by sub-proof #17.
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | End of split
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | Case 2:
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | (1023) all_74_10 = n5
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | REDUCE: (1014), (1023) imply:
% 206.31/31.88 | | | | | | | (1024) a_select3(pminus_ds1_filter, n5, n5) = all_74_8
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | REDUCE: (1015), (1023) imply:
% 206.31/31.88 | | | | | | | (1025) a_select3(pminus_ds1_filter, n5, n5) = all_74_9
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | GROUND_INST: instantiating (19) with all_74_9, all_74_8, n5, n5,
% 206.31/31.88 | | | | | | | pminus_ds1_filter, simplifying with (1024), (1025)
% 206.31/31.88 | | | | | | | gives:
% 206.31/31.88 | | | | | | | (1026) all_74_8 = all_74_9
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | REDUCE: (979), (1026) imply:
% 206.31/31.88 | | | | | | | (1027) $false
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | CLOSE: (1027) is inconsistent.
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | End of split
% 206.31/31.88 | | | | | |
% 206.31/31.88 | | | | | End of split
% 206.31/31.88 | | | | |
% 206.31/31.88 | | | | Case 2:
% 206.31/31.88 | | | | |
% 206.31/31.88 | | | | | (1028) all_74_11 = n0
% 206.31/31.88 | | | | | (1029) ~ gt(all_74_11, n0)
% 206.31/31.88 | | | | |
% 206.31/31.88 | | | | | REDUCE: (1028), (1029) imply:
% 206.31/31.88 | | | | | (1030) ~ gt(n0, n0)
% 206.31/31.88 | | | | |
% 206.31/31.88 | | | | | REF_CLOSE: (1), (5), (19), (54), (55), (67), (104), (115), (122),
% 206.31/31.88 | | | | | (125), (126), (127), (128), (129), (142), (979), (980),
% 206.31/31.88 | | | | | (981), (984), (985), (986), (987), (988), (990), (991),
% 206.31/31.88 | | | | | (992), (993), (994), (1030), (leq_gt2) are inconsistent by
% 206.31/31.88 | | | | | sub-proof #13.
% 206.31/31.88 | | | | |
% 206.31/31.88 | | | | End of split
% 206.31/31.88 | | | |
% 206.31/31.88 | | | Case 2:
% 206.31/31.88 | | | |
% 206.31/31.88 | | | | (1031) all_74_10 = n0
% 206.31/31.88 | | | | (1032) ~ gt(all_74_10, n0)
% 206.31/31.88 | | | |
% 206.31/31.88 | | | | REDUCE: (1031), (1032) imply:
% 206.31/31.88 | | | | (1033) ~ gt(n0, n0)
% 206.31/31.88 | | | |
% 206.31/31.88 | | | | BETA: splitting (989) gives:
% 206.31/31.88 | | | |
% 206.31/31.88 | | | | Case 1:
% 206.31/31.88 | | | | |
% 206.31/31.88 | | | | | (1034) gt(all_74_10, n0)
% 206.31/31.88 | | | | |
% 206.31/31.88 | | | | | REF_CLOSE: (1), (5), (19), (54), (55), (67), (104), (115), (122),
% 206.31/31.88 | | | | | (125), (126), (127), (128), (129), (142), (979), (980),
% 206.31/31.88 | | | | | (981), (984), (985), (986), (987), (988), (990), (991),
% 206.31/31.88 | | | | | (992), (993), (1033), (1034), (leq_gt2) are inconsistent by
% 206.31/31.88 | | | | | sub-proof #13.
% 206.31/31.88 | | | | |
% 206.31/31.88 | | | | Case 2:
% 206.31/31.88 | | | | |
% 206.31/31.88 | | | | |
% 206.31/31.88 | | | | | REDUCE: (985), (1031) imply:
% 206.31/31.88 | | | | | (1035) a_select3(pminus_ds1_filter, n0, all_74_11) = all_74_8
% 206.31/31.88 | | | | |
% 206.31/31.88 | | | | | REDUCE: (984), (1031) imply:
% 206.31/31.88 | | | | | (1036) a_select3(pminus_ds1_filter, all_74_11, n0) = all_74_9
% 206.31/31.88 | | | | |
% 206.31/31.88 | | | | | REDUCE: (986), (1031) imply:
% 206.31/31.88 | | | | | (1037) leq(n0, n5)
% 206.31/31.88 | | | | |
% 206.31/31.88 | | | | | REDUCE: (981), (1031) imply:
% 206.31/31.88 | | | | | (1038) leq(n0, n0)
% 206.31/31.88 | | | | |
% 206.31/31.88 | | | | | BETA: splitting (988) gives:
% 206.31/31.88 | | | | |
% 206.31/31.88 | | | | | Case 1:
% 206.31/31.88 | | | | | |
% 206.31/31.88 | | | | | | (1039) gt(all_74_11, n0)
% 206.31/31.88 | | | | | |
% 206.31/31.88 | | | | | | BETA: splitting (991) gives:
% 206.31/31.88 | | | | | |
% 206.31/31.88 | | | | | | Case 1:
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | (1040) gt(n5, all_74_11)
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n5, n4, simplifying
% 206.31/31.88 | | | | | | | with (54), (125), (129), (1040) gives:
% 206.31/31.88 | | | | | | | (1041) leq(all_74_11, n4)
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n4,
% 206.31/31.88 | | | | | | | simplifying with (54), (122), (1041) gives:
% 206.31/31.88 | | | | | | | (1042) all_74_11 = n4 | gt(n4, all_74_11)
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | BETA: splitting (990) gives:
% 206.31/31.88 | | | | | | |
% 206.31/31.88 | | | | | | | Case 1:
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | (1043) all_74_11 = n0
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | REDUCE: (1039), (1043) imply:
% 206.31/31.88 | | | | | | | | (1044) gt(n0, n0)
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | PRED_UNIFY: (1033), (1044) imply:
% 206.31/31.88 | | | | | | | | (1045) $false
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | CLOSE: (1045) is inconsistent.
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | Case 2:
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | (1046) ~ (all_74_11 = n0)
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | BETA: splitting (1042) gives:
% 206.31/31.88 | | | | | | | |
% 206.31/31.88 | | | | | | | | Case 1:
% 206.31/31.88 | | | | | | | | |
% 206.31/31.88 | | | | | | | | | (1047) gt(n4, all_74_11)
% 206.31/31.88 | | | | | | | | |
% 206.31/31.88 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n4, n3,
% 206.31/31.88 | | | | | | | | | simplifying with (54), (122), (128), (1047) gives:
% 206.31/31.88 | | | | | | | | | (1048) leq(all_74_11, n3)
% 206.31/31.88 | | | | | | | | |
% 206.31/31.88 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n3,
% 206.31/31.88 | | | | | | | | | simplifying with (54), (115), (1048) gives:
% 206.31/31.88 | | | | | | | | | (1049) all_74_11 = n3 | gt(n3, all_74_11)
% 206.31/31.88 | | | | | | | | |
% 206.31/31.88 | | | | | | | | | BETA: splitting (1049) gives:
% 206.31/31.88 | | | | | | | | |
% 206.31/31.88 | | | | | | | | | Case 1:
% 206.31/31.88 | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | (1050) gt(n3, all_74_11)
% 206.31/31.88 | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n3, n2,
% 206.31/31.88 | | | | | | | | | | simplifying with (54), (115), (127), (1050) gives:
% 206.31/31.88 | | | | | | | | | | (1051) leq(all_74_11, n2)
% 206.31/31.88 | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n2,
% 206.31/31.88 | | | | | | | | | | simplifying with (54), (104), (1051) gives:
% 206.31/31.88 | | | | | | | | | | (1052) all_74_11 = n2 | gt(n2, all_74_11)
% 206.31/31.88 | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | BETA: splitting (1052) gives:
% 206.31/31.88 | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | Case 1:
% 206.31/31.88 | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | (1053) gt(n2, all_74_11)
% 206.31/31.88 | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n2, n1,
% 206.31/31.88 | | | | | | | | | | | simplifying with (54), (104), (126), (1053) gives:
% 206.31/31.88 | | | | | | | | | | | (1054) leq(all_74_11, n1)
% 206.31/31.88 | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | GROUND_INST: instantiating (5) with all_74_11, simplifying with
% 206.31/31.88 | | | | | | | | | | | (54), (980), (1054) gives:
% 206.31/31.88 | | | | | | | | | | | (1055) all_74_11 = n1 | all_74_11 = n0
% 206.31/31.88 | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | BETA: splitting (1055) gives:
% 206.31/31.88 | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | Case 1:
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | (1056) all_74_11 = n0
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | REDUCE: (1046), (1056) imply:
% 206.31/31.88 | | | | | | | | | | | | (1057) $false
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | CLOSE: (1057) is inconsistent.
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | Case 2:
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | (1058) all_74_11 = n1
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | REDUCE: (1036), (1058) imply:
% 206.31/31.88 | | | | | | | | | | | | (1059) a_select3(pminus_ds1_filter, n1, n0) = all_74_9
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | REDUCE: (1035), (1058) imply:
% 206.31/31.88 | | | | | | | | | | | | (1060) a_select3(pminus_ds1_filter, n0, n1) = all_74_8
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | REDUCE: (987), (1058) imply:
% 206.31/31.88 | | | | | | | | | | | | (1061) leq(n1, n5)
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | REDUCE: (980), (1058) imply:
% 206.31/31.88 | | | | | | | | | | | | (1062) leq(n0, n1)
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | GROUND_INST: instantiating (67) with n0, n1, all_74_8,
% 206.31/31.88 | | | | | | | | | | | | simplifying with (13), (88), (1038), (1060),
% 206.31/31.88 | | | | | | | | | | | | (1062) gives:
% 206.31/31.88 | | | | | | | | | | | | (1063) ~ leq(n1, all_74_19) | ~ leq(n0, all_74_19) |
% 206.31/31.88 | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n1, n0) = all_74_8 &
% 206.31/31.88 | | | | | | | | | | | | $i(all_74_8))
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | BETA: splitting (1063) gives:
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | Case 1:
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | (1064) ~ leq(n0, all_74_19)
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | REDUCE: (142), (1064) imply:
% 206.31/31.88 | | | | | | | | | | | | | (1065) ~ leq(n0, n5)
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | PRED_UNIFY: (1037), (1065) imply:
% 206.31/31.88 | | | | | | | | | | | | | (1066) $false
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | CLOSE: (1066) is inconsistent.
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | Case 2:
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | (1067) ~ leq(n1, all_74_19) |
% 206.31/31.88 | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n1, n0) = all_74_8 &
% 206.31/31.88 | | | | | | | | | | | | | $i(all_74_8))
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | BETA: splitting (1067) gives:
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | Case 1:
% 206.31/31.88 | | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | | (1068) ~ leq(n1, all_74_19)
% 206.31/31.88 | | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | | REDUCE: (142), (1068) imply:
% 206.31/31.88 | | | | | | | | | | | | | | (1069) ~ leq(n1, n5)
% 206.31/31.88 | | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | | PRED_UNIFY: (1061), (1069) imply:
% 206.31/31.88 | | | | | | | | | | | | | | (1070) $false
% 206.31/31.88 | | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | | CLOSE: (1070) is inconsistent.
% 206.31/31.88 | | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | Case 2:
% 206.31/31.88 | | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | | (1071) a_select3(pminus_ds1_filter, n1, n0) = all_74_8 &
% 206.31/31.88 | | | | | | | | | | | | | | $i(all_74_8)
% 206.31/31.88 | | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | | ALPHA: (1071) implies:
% 206.31/31.88 | | | | | | | | | | | | | | (1072) a_select3(pminus_ds1_filter, n1, n0) = all_74_8
% 206.31/31.88 | | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | | REF_CLOSE: (19), (979), (1059), (1072) are inconsistent by
% 206.31/31.88 | | | | | | | | | | | | | | sub-proof #16.
% 206.31/31.88 | | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | End of split
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | End of split
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | End of split
% 206.31/31.88 | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | Case 2:
% 206.31/31.88 | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | (1073) all_74_11 = n2
% 206.31/31.88 | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | REDUCE: (1036), (1073) imply:
% 206.31/31.88 | | | | | | | | | | | (1074) a_select3(pminus_ds1_filter, n2, n0) = all_74_9
% 206.31/31.88 | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | REDUCE: (1035), (1073) imply:
% 206.31/31.88 | | | | | | | | | | | (1075) a_select3(pminus_ds1_filter, n0, n2) = all_74_8
% 206.31/31.88 | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | REDUCE: (987), (1073) imply:
% 206.31/31.88 | | | | | | | | | | | (1076) leq(n2, n5)
% 206.31/31.88 | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | REDUCE: (980), (1073) imply:
% 206.31/31.88 | | | | | | | | | | | (1077) leq(n0, n2)
% 206.31/31.88 | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | GROUND_INST: instantiating (67) with n0, n2, all_74_8,
% 206.31/31.88 | | | | | | | | | | | simplifying with (13), (104), (1038), (1075),
% 206.31/31.88 | | | | | | | | | | | (1077) gives:
% 206.31/31.88 | | | | | | | | | | | (1078) ~ leq(n2, all_74_19) | ~ leq(n0, all_74_19) |
% 206.31/31.88 | | | | | | | | | | | (a_select3(pminus_ds1_filter, n2, n0) = all_74_8 &
% 206.31/31.88 | | | | | | | | | | | $i(all_74_8))
% 206.31/31.88 | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | BETA: splitting (1078) gives:
% 206.31/31.88 | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | Case 1:
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | (1079) ~ leq(n0, all_74_19)
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | REDUCE: (142), (1079) imply:
% 206.31/31.88 | | | | | | | | | | | | (1080) ~ leq(n0, n5)
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | PRED_UNIFY: (1037), (1080) imply:
% 206.31/31.88 | | | | | | | | | | | | (1081) $false
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | CLOSE: (1081) is inconsistent.
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | Case 2:
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | (1082) ~ leq(n2, all_74_19) |
% 206.31/31.88 | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n2, n0) = all_74_8 &
% 206.31/31.88 | | | | | | | | | | | | $i(all_74_8))
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | BETA: splitting (1082) gives:
% 206.31/31.88 | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | Case 1:
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | (1083) ~ leq(n2, all_74_19)
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | REDUCE: (142), (1083) imply:
% 206.31/31.88 | | | | | | | | | | | | | (1084) ~ leq(n2, n5)
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | PRED_UNIFY: (1076), (1084) imply:
% 206.31/31.88 | | | | | | | | | | | | | (1085) $false
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | CLOSE: (1085) is inconsistent.
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | Case 2:
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | (1086) a_select3(pminus_ds1_filter, n2, n0) = all_74_8 &
% 206.31/31.88 | | | | | | | | | | | | | $i(all_74_8)
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | ALPHA: (1086) implies:
% 206.31/31.88 | | | | | | | | | | | | | (1087) a_select3(pminus_ds1_filter, n2, n0) = all_74_8
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.88 | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_74_8, all_74_9, n0,
% 206.31/31.88 | | | | | | | | | | | | | n2, pminus_ds1_filter, simplifying with (1074),
% 206.31/31.88 | | | | | | | | | | | | | (1087) gives:
% 206.31/31.88 | | | | | | | | | | | | | (1088) all_74_8 = all_74_9
% 206.31/31.88 | | | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | | | REDUCE: (979), (1088) imply:
% 206.31/31.89 | | | | | | | | | | | | | (1089) $false
% 206.31/31.89 | | | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | | | CLOSE: (1089) is inconsistent.
% 206.31/31.89 | | | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | | End of split
% 206.31/31.89 | | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | End of split
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | End of split
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | Case 2:
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | (1090) all_74_11 = n3
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | REDUCE: (1036), (1090) imply:
% 206.31/31.89 | | | | | | | | | | (1091) a_select3(pminus_ds1_filter, n3, n0) = all_74_9
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | REDUCE: (1035), (1090) imply:
% 206.31/31.89 | | | | | | | | | | (1092) a_select3(pminus_ds1_filter, n0, n3) = all_74_8
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | REDUCE: (987), (1090) imply:
% 206.31/31.89 | | | | | | | | | | (1093) leq(n3, n5)
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | REDUCE: (980), (1090) imply:
% 206.31/31.89 | | | | | | | | | | (1094) leq(n0, n3)
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | GROUND_INST: instantiating (67) with n0, n3, all_74_8,
% 206.31/31.89 | | | | | | | | | | simplifying with (13), (115), (1038), (1092),
% 206.31/31.89 | | | | | | | | | | (1094) gives:
% 206.31/31.89 | | | | | | | | | | (1095) ~ leq(n3, all_74_19) | ~ leq(n0, all_74_19) |
% 206.31/31.89 | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n0) = all_74_8 &
% 206.31/31.89 | | | | | | | | | | $i(all_74_8))
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | BETA: splitting (1095) gives:
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | Case 1:
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | (1096) ~ leq(n0, all_74_19)
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | REDUCE: (142), (1096) imply:
% 206.31/31.89 | | | | | | | | | | | (1097) ~ leq(n0, n5)
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | PRED_UNIFY: (1037), (1097) imply:
% 206.31/31.89 | | | | | | | | | | | (1098) $false
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | CLOSE: (1098) is inconsistent.
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | Case 2:
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | (1099) ~ leq(n3, all_74_19) |
% 206.31/31.89 | | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n0) = all_74_8 &
% 206.31/31.89 | | | | | | | | | | | $i(all_74_8))
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | BETA: splitting (1099) gives:
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | Case 1:
% 206.31/31.89 | | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | | (1100) ~ leq(n3, all_74_19)
% 206.31/31.89 | | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | | REDUCE: (142), (1100) imply:
% 206.31/31.89 | | | | | | | | | | | | (1101) ~ leq(n3, n5)
% 206.31/31.89 | | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | | PRED_UNIFY: (1093), (1101) imply:
% 206.31/31.89 | | | | | | | | | | | | (1102) $false
% 206.31/31.89 | | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | | CLOSE: (1102) is inconsistent.
% 206.31/31.89 | | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | Case 2:
% 206.31/31.89 | | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | | (1103) a_select3(pminus_ds1_filter, n3, n0) = all_74_8 &
% 206.31/31.89 | | | | | | | | | | | | $i(all_74_8)
% 206.31/31.89 | | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | | ALPHA: (1103) implies:
% 206.31/31.89 | | | | | | | | | | | | (1104) a_select3(pminus_ds1_filter, n3, n0) = all_74_8
% 206.31/31.89 | | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | | REF_CLOSE: (19), (979), (1091), (1104) are inconsistent by
% 206.31/31.89 | | | | | | | | | | | | sub-proof #15.
% 206.31/31.89 | | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | End of split
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | End of split
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | End of split
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | Case 2:
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | (1105) all_74_11 = n4
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | REDUCE: (1036), (1105) imply:
% 206.31/31.89 | | | | | | | | | (1106) a_select3(pminus_ds1_filter, n4, n0) = all_74_9
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | REDUCE: (1035), (1105) imply:
% 206.31/31.89 | | | | | | | | | (1107) a_select3(pminus_ds1_filter, n0, n4) = all_74_8
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | REDUCE: (987), (1105) imply:
% 206.31/31.89 | | | | | | | | | (1108) leq(n4, n5)
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | REDUCE: (980), (1105) imply:
% 206.31/31.89 | | | | | | | | | (1109) leq(n0, n4)
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | GROUND_INST: instantiating (67) with n0, n4, all_74_8,
% 206.31/31.89 | | | | | | | | | simplifying with (13), (122), (1038), (1107),
% 206.31/31.89 | | | | | | | | | (1109) gives:
% 206.31/31.89 | | | | | | | | | (1110) ~ leq(n4, all_74_19) | ~ leq(n0, all_74_19) |
% 206.31/31.89 | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n0) = all_74_8 &
% 206.31/31.89 | | | | | | | | | $i(all_74_8))
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | BETA: splitting (1110) gives:
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | Case 1:
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | (1111) ~ leq(n0, all_74_19)
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | REDUCE: (142), (1111) imply:
% 206.31/31.89 | | | | | | | | | | (1112) ~ leq(n0, n5)
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | PRED_UNIFY: (1037), (1112) imply:
% 206.31/31.89 | | | | | | | | | | (1113) $false
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | CLOSE: (1113) is inconsistent.
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | Case 2:
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | (1114) ~ leq(n4, all_74_19) |
% 206.31/31.89 | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n0) = all_74_8 &
% 206.31/31.89 | | | | | | | | | | $i(all_74_8))
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | BETA: splitting (1114) gives:
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | Case 1:
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | (1115) ~ leq(n4, all_74_19)
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | REDUCE: (142), (1115) imply:
% 206.31/31.89 | | | | | | | | | | | (1116) ~ leq(n4, n5)
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | PRED_UNIFY: (1108), (1116) imply:
% 206.31/31.89 | | | | | | | | | | | (1117) $false
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | CLOSE: (1117) is inconsistent.
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | Case 2:
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | (1118) a_select3(pminus_ds1_filter, n4, n0) = all_74_8 &
% 206.31/31.89 | | | | | | | | | | | $i(all_74_8)
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | ALPHA: (1118) implies:
% 206.31/31.89 | | | | | | | | | | | (1119) a_select3(pminus_ds1_filter, n4, n0) = all_74_8
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | | REF_CLOSE: (19), (979), (1106), (1119) are inconsistent by
% 206.31/31.89 | | | | | | | | | | | sub-proof #14.
% 206.31/31.89 | | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | | End of split
% 206.31/31.89 | | | | | | | | | |
% 206.31/31.89 | | | | | | | | | End of split
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | End of split
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | End of split
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | Case 2:
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | (1120) all_74_11 = n5
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | REDUCE: (1036), (1120) imply:
% 206.31/31.89 | | | | | | | (1121) a_select3(pminus_ds1_filter, n5, n0) = all_74_9
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | REDUCE: (1035), (1120) imply:
% 206.31/31.89 | | | | | | | (1122) a_select3(pminus_ds1_filter, n0, n5) = all_74_8
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | REDUCE: (987), (1120) imply:
% 206.31/31.89 | | | | | | | (1123) leq(n5, n5)
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | GROUND_INST: instantiating (67) with n0, n5, all_74_8, simplifying
% 206.31/31.89 | | | | | | | with (13), (125), (1037), (1038), (1122) gives:
% 206.31/31.89 | | | | | | | (1124) ~ leq(n5, all_74_19) | ~ leq(n0, all_74_19) |
% 206.31/31.89 | | | | | | | (a_select3(pminus_ds1_filter, n5, n0) = all_74_8 &
% 206.31/31.89 | | | | | | | $i(all_74_8))
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | BETA: splitting (1124) gives:
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | Case 1:
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | (1125) ~ leq(n0, all_74_19)
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | REDUCE: (142), (1125) imply:
% 206.31/31.89 | | | | | | | | (1126) ~ leq(n0, n5)
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | PRED_UNIFY: (1037), (1126) imply:
% 206.31/31.89 | | | | | | | | (1127) $false
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | CLOSE: (1127) is inconsistent.
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | Case 2:
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | (1128) ~ leq(n5, all_74_19) | (a_select3(pminus_ds1_filter,
% 206.31/31.89 | | | | | | | | n5, n0) = all_74_8 & $i(all_74_8))
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | BETA: splitting (1128) gives:
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | Case 1:
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | (1129) ~ leq(n5, all_74_19)
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | REDUCE: (142), (1129) imply:
% 206.31/31.89 | | | | | | | | | (1130) ~ leq(n5, n5)
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | PRED_UNIFY: (1123), (1130) imply:
% 206.31/31.89 | | | | | | | | | (1131) $false
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | CLOSE: (1131) is inconsistent.
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | Case 2:
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | (1132) a_select3(pminus_ds1_filter, n5, n0) = all_74_8 &
% 206.31/31.89 | | | | | | | | | $i(all_74_8)
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | ALPHA: (1132) implies:
% 206.31/31.89 | | | | | | | | | (1133) a_select3(pminus_ds1_filter, n5, n0) = all_74_8
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | GROUND_INST: instantiating (19) with all_74_8, all_74_9, n0,
% 206.31/31.89 | | | | | | | | | n5, pminus_ds1_filter, simplifying with (1121),
% 206.31/31.89 | | | | | | | | | (1133) gives:
% 206.31/31.89 | | | | | | | | | (1134) all_74_8 = all_74_9
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | REDUCE: (979), (1134) imply:
% 206.31/31.89 | | | | | | | | | (1135) $false
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | CLOSE: (1135) is inconsistent.
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | End of split
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | End of split
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | End of split
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | Case 2:
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | (1136) all_74_11 = n0
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | REDUCE: (1036), (1136) imply:
% 206.31/31.89 | | | | | | (1137) a_select3(pminus_ds1_filter, n0, n0) = all_74_9
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | REDUCE: (1035), (1136) imply:
% 206.31/31.89 | | | | | | (1138) a_select3(pminus_ds1_filter, n0, n0) = all_74_8
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | GROUND_INST: instantiating (19) with all_74_9, all_74_8, n0, n0,
% 206.31/31.89 | | | | | | pminus_ds1_filter, simplifying with (1137), (1138)
% 206.31/31.89 | | | | | | gives:
% 206.31/31.89 | | | | | | (1139) all_74_8 = all_74_9
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | REDUCE: (979), (1139) imply:
% 206.31/31.89 | | | | | | (1140) $false
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | CLOSE: (1140) is inconsistent.
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | End of split
% 206.31/31.89 | | | | |
% 206.31/31.89 | | | | End of split
% 206.31/31.89 | | | |
% 206.31/31.89 | | | End of split
% 206.31/31.89 | | |
% 206.31/31.89 | | Case 2:
% 206.31/31.89 | | |
% 206.31/31.89 | | | (1141) ~ (all_74_12 = all_74_13) & a_select3(id_ds1_filter, all_74_14,
% 206.31/31.89 | | | all_74_15) = all_74_12 & a_select3(id_ds1_filter, all_74_15,
% 206.31/31.89 | | | all_74_14) = all_74_13 & $i(all_74_12) & $i(all_74_13) &
% 206.31/31.89 | | | leq(all_74_14, all_74_19) & leq(all_74_15, all_74_19) & leq(n0,
% 206.31/31.89 | | | all_74_14) & leq(n0, all_74_15)
% 206.31/31.89 | | |
% 206.31/31.89 | | | ALPHA: (1141) implies:
% 206.31/31.89 | | | (1142) ~ (all_74_12 = all_74_13)
% 206.31/31.89 | | | (1143) leq(n0, all_74_15)
% 206.31/31.89 | | | (1144) leq(n0, all_74_14)
% 206.31/31.89 | | | (1145) leq(all_74_15, all_74_19)
% 206.31/31.89 | | | (1146) leq(all_74_14, all_74_19)
% 206.31/31.89 | | | (1147) a_select3(id_ds1_filter, all_74_15, all_74_14) = all_74_13
% 206.31/31.89 | | | (1148) a_select3(id_ds1_filter, all_74_14, all_74_15) = all_74_12
% 206.31/31.89 | | |
% 206.31/31.89 | | | REDUCE: (142), (1146) imply:
% 206.31/31.89 | | | (1149) leq(all_74_14, n5)
% 206.31/31.89 | | |
% 206.31/31.89 | | | REDUCE: (142), (1145) imply:
% 206.31/31.89 | | | (1150) leq(all_74_15, n5)
% 206.31/31.89 | | |
% 206.31/31.89 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_15, simplifying with
% 206.31/31.89 | | | (13), (52), (1143) gives:
% 206.31/31.89 | | | (1151) all_74_15 = n0 | gt(all_74_15, n0)
% 206.31/31.89 | | |
% 206.31/31.89 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_14, simplifying with
% 206.31/31.89 | | | (13), (53), (1144) gives:
% 206.31/31.89 | | | (1152) all_74_14 = n0 | gt(all_74_14, n0)
% 206.31/31.89 | | |
% 206.31/31.89 | | | GROUND_INST: instantiating (4) with all_74_15, simplifying with (52),
% 206.31/31.89 | | | (1143), (1150) gives:
% 206.31/31.89 | | | (1153) all_74_15 = n5 | all_74_15 = n4 | all_74_15 = n3 | all_74_15 =
% 206.31/31.89 | | | n2 | all_74_15 = n1 | all_74_15 = n0
% 206.31/31.89 | | |
% 206.31/31.89 | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n5, simplifying with
% 206.31/31.89 | | | (52), (125), (1150) gives:
% 206.31/31.89 | | | (1154) all_74_15 = n5 | gt(n5, all_74_15)
% 206.31/31.89 | | |
% 206.31/31.89 | | | GROUND_INST: instantiating (4) with all_74_14, simplifying with (53),
% 206.31/31.89 | | | (1144), (1149) gives:
% 206.31/31.89 | | | (1155) all_74_14 = n5 | all_74_14 = n4 | all_74_14 = n3 | all_74_14 =
% 206.31/31.89 | | | n2 | all_74_14 = n1 | all_74_14 = n0
% 206.31/31.89 | | |
% 206.31/31.89 | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n5, simplifying with
% 206.31/31.89 | | | (53), (125), (1149) gives:
% 206.31/31.89 | | | (1156) all_74_14 = n5 | gt(n5, all_74_14)
% 206.31/31.89 | | |
% 206.31/31.89 | | | BETA: splitting (1152) gives:
% 206.31/31.89 | | |
% 206.31/31.89 | | | Case 1:
% 206.31/31.89 | | | |
% 206.31/31.89 | | | | (1157) gt(all_74_14, n0)
% 206.31/31.89 | | | |
% 206.31/31.89 | | | | BETA: splitting (1151) gives:
% 206.31/31.89 | | | |
% 206.31/31.89 | | | | Case 1:
% 206.31/31.89 | | | | |
% 206.31/31.89 | | | | | (1158) gt(all_74_15, n0)
% 206.31/31.89 | | | | |
% 206.31/31.89 | | | | | BETA: splitting (1154) gives:
% 206.31/31.89 | | | | |
% 206.31/31.89 | | | | | Case 1:
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | (1159) gt(n5, all_74_15)
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | GROUND_INST: instantiating (1) with all_74_15, n5, n4, simplifying
% 206.31/31.89 | | | | | | with (52), (125), (129), (1159) gives:
% 206.31/31.89 | | | | | | (1160) leq(all_74_15, n4)
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n4, simplifying
% 206.31/31.89 | | | | | | with (52), (122), (1160) gives:
% 206.31/31.89 | | | | | | (1161) all_74_15 = n4 | gt(n4, all_74_15)
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | BETA: splitting (1156) gives:
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | Case 1:
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | (1162) gt(n5, all_74_14)
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n5, n4, simplifying
% 206.31/31.89 | | | | | | | with (53), (125), (129), (1162) gives:
% 206.31/31.89 | | | | | | | (1163) leq(all_74_14, n4)
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n4,
% 206.31/31.89 | | | | | | | simplifying with (53), (122), (1163) gives:
% 206.31/31.89 | | | | | | | (1164) all_74_14 = n4 | gt(n4, all_74_14)
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | BETA: splitting (1153) gives:
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | Case 1:
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | (1165) all_74_15 = n0
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | REF_CLOSE: (52), (1158), (1165), (irreflexivity_gt) are
% 206.31/31.89 | | | | | | | | inconsistent by sub-proof #12.
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | Case 2:
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | (1166) ~ (all_74_15 = n0)
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | BETA: splitting (1155) gives:
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | Case 1:
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | (1167) all_74_14 = n0
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | REF_CLOSE: (53), (1157), (1167), (irreflexivity_gt) are
% 206.31/31.89 | | | | | | | | | inconsistent by sub-proof #11.
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | Case 2:
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | (1168) ~ (all_74_14 = n0)
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | | REF_CLOSE: (1), (5), (19), (52), (53), (68), (104), (115),
% 206.31/31.89 | | | | | | | | | (122), (126), (127), (128), (142), (147), (1142),
% 206.31/31.89 | | | | | | | | | (1143), (1144), (1147), (1148), (1149), (1150),
% 206.31/31.89 | | | | | | | | | (1161), (1164), (1166), (1168), (leq_gt2) are
% 206.31/31.89 | | | | | | | | | inconsistent by sub-proof #8.
% 206.31/31.89 | | | | | | | | |
% 206.31/31.89 | | | | | | | | End of split
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | End of split
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | Case 2:
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | (1169) all_74_14 = n5
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | REDUCE: (1148), (1169) imply:
% 206.31/31.89 | | | | | | | (1170) a_select3(id_ds1_filter, n5, all_74_15) = all_74_12
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | REDUCE: (1147), (1169) imply:
% 206.31/31.89 | | | | | | | (1171) a_select3(id_ds1_filter, all_74_15, n5) = all_74_13
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | REDUCE: (1149), (1169) imply:
% 206.31/31.89 | | | | | | | (1172) leq(n5, n5)
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | REDUCE: (1144), (1169) imply:
% 206.31/31.89 | | | | | | | (1173) leq(n0, n5)
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | BETA: splitting (1153) gives:
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | Case 1:
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | (1174) all_74_15 = n0
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | REF_CLOSE: (52), (1158), (1174), (irreflexivity_gt) are
% 206.31/31.89 | | | | | | | | inconsistent by sub-proof #12.
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | Case 2:
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | (1175) ~ (all_74_15 = n0)
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | REF_CLOSE: (1), (5), (19), (52), (68), (104), (115), (122),
% 206.31/31.89 | | | | | | | | (125), (126), (127), (128), (142), (147), (1142),
% 206.31/31.89 | | | | | | | | (1143), (1150), (1161), (1170), (1171), (1172),
% 206.31/31.89 | | | | | | | | (1173), (1175), (leq_gt2) are inconsistent by
% 206.31/31.89 | | | | | | | | sub-proof #6.
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | End of split
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | End of split
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | Case 2:
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | (1176) all_74_15 = n5
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | REDUCE: (1148), (1176) imply:
% 206.31/31.89 | | | | | | (1177) a_select3(id_ds1_filter, all_74_14, n5) = all_74_12
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | REDUCE: (1147), (1176) imply:
% 206.31/31.89 | | | | | | (1178) a_select3(id_ds1_filter, n5, all_74_14) = all_74_13
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | REDUCE: (1150), (1176) imply:
% 206.31/31.89 | | | | | | (1179) leq(n5, n5)
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | REDUCE: (1143), (1176) imply:
% 206.31/31.89 | | | | | | (1180) leq(n0, n5)
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | BETA: splitting (1156) gives:
% 206.31/31.89 | | | | | |
% 206.31/31.89 | | | | | | Case 1:
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | (1181) gt(n5, all_74_14)
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n5, n4, simplifying
% 206.31/31.89 | | | | | | | with (53), (125), (129), (1181) gives:
% 206.31/31.89 | | | | | | | (1182) leq(all_74_14, n4)
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n4,
% 206.31/31.89 | | | | | | | simplifying with (53), (122), (1182) gives:
% 206.31/31.89 | | | | | | | (1183) all_74_14 = n4 | gt(n4, all_74_14)
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | BETA: splitting (1155) gives:
% 206.31/31.89 | | | | | | |
% 206.31/31.89 | | | | | | | Case 1:
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | (1184) all_74_14 = n0
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | REF_CLOSE: (53), (1157), (1184), (irreflexivity_gt) are
% 206.31/31.89 | | | | | | | | inconsistent by sub-proof #11.
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | Case 2:
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | (1185) ~ (all_74_14 = n0)
% 206.31/31.89 | | | | | | | |
% 206.31/31.89 | | | | | | | | REF_CLOSE: (1), (5), (19), (53), (68), (104), (115), (122),
% 206.31/31.90 | | | | | | | | (125), (126), (127), (128), (142), (147), (1142),
% 206.31/31.90 | | | | | | | | (1144), (1149), (1177), (1178), (1179), (1180),
% 206.31/31.90 | | | | | | | | (1183), (1185), (leq_gt2) are inconsistent by
% 206.31/31.90 | | | | | | | | sub-proof #5.
% 206.31/31.90 | | | | | | | |
% 206.31/31.90 | | | | | | | End of split
% 206.31/31.90 | | | | | | |
% 206.31/31.90 | | | | | | Case 2:
% 206.31/31.90 | | | | | | |
% 206.31/31.90 | | | | | | | (1186) all_74_14 = n5
% 206.31/31.90 | | | | | | |
% 206.31/31.90 | | | | | | | REDUCE: (1177), (1186) imply:
% 206.31/31.90 | | | | | | | (1187) a_select3(id_ds1_filter, n5, n5) = all_74_12
% 206.31/31.90 | | | | | | |
% 206.31/31.90 | | | | | | | REDUCE: (1178), (1186) imply:
% 206.31/31.90 | | | | | | | (1188) a_select3(id_ds1_filter, n5, n5) = all_74_13
% 206.31/31.90 | | | | | | |
% 206.31/31.90 | | | | | | | GROUND_INST: instantiating (19) with all_74_13, all_74_12, n5, n5,
% 206.31/31.90 | | | | | | | id_ds1_filter, simplifying with (1187), (1188) gives:
% 206.31/31.90 | | | | | | | (1189) all_74_12 = all_74_13
% 206.31/31.90 | | | | | | |
% 206.31/31.90 | | | | | | | REDUCE: (1142), (1189) imply:
% 206.31/31.90 | | | | | | | (1190) $false
% 206.31/31.90 | | | | | | |
% 206.31/31.90 | | | | | | | CLOSE: (1190) is inconsistent.
% 206.31/31.90 | | | | | | |
% 206.31/31.90 | | | | | | End of split
% 206.31/31.90 | | | | | |
% 206.31/31.90 | | | | | End of split
% 206.31/31.90 | | | | |
% 206.31/31.90 | | | | Case 2:
% 206.31/31.90 | | | | |
% 206.31/31.90 | | | | | (1191) all_74_15 = n0
% 206.31/31.90 | | | | | (1192) ~ gt(all_74_15, n0)
% 206.31/31.90 | | | | |
% 206.31/31.90 | | | | | REDUCE: (1191), (1192) imply:
% 206.31/31.90 | | | | | (1193) ~ gt(n0, n0)
% 206.31/31.90 | | | | |
% 206.31/31.90 | | | | | REF_CLOSE: (1), (5), (19), (52), (53), (68), (104), (115), (122),
% 206.31/31.90 | | | | | (125), (126), (127), (128), (129), (142), (147), (1142),
% 206.31/31.90 | | | | | (1143), (1144), (1147), (1148), (1149), (1150), (1151),
% 206.31/31.90 | | | | | (1153), (1154), (1155), (1156), (1157), (1193), (leq_gt2)
% 206.31/31.90 | | | | | are inconsistent by sub-proof #1.
% 206.31/31.90 | | | | |
% 206.31/31.90 | | | | End of split
% 206.31/31.90 | | | |
% 206.31/31.90 | | | Case 2:
% 206.31/31.90 | | | |
% 206.31/31.90 | | | | (1194) all_74_14 = n0
% 206.31/31.90 | | | | (1195) ~ gt(all_74_14, n0)
% 206.31/31.90 | | | |
% 206.31/31.90 | | | | REDUCE: (1194), (1195) imply:
% 206.31/31.90 | | | | (1196) ~ gt(n0, n0)
% 206.31/31.90 | | | |
% 206.31/31.90 | | | | BETA: splitting (1152) gives:
% 206.31/31.90 | | | |
% 206.31/31.90 | | | | Case 1:
% 206.31/31.90 | | | | |
% 206.31/31.90 | | | | | (1197) gt(all_74_14, n0)
% 206.31/31.90 | | | | |
% 206.31/31.90 | | | | | REF_CLOSE: (1), (5), (19), (52), (53), (68), (104), (115), (122),
% 206.31/31.90 | | | | | (125), (126), (127), (128), (129), (142), (147), (1142),
% 206.31/31.90 | | | | | (1143), (1144), (1147), (1148), (1149), (1150), (1151),
% 206.31/31.90 | | | | | (1153), (1154), (1155), (1156), (1196), (1197), (leq_gt2)
% 206.31/31.90 | | | | | are inconsistent by sub-proof #1.
% 206.31/31.90 | | | | |
% 206.31/31.90 | | | | Case 2:
% 206.31/31.90 | | | | |
% 206.31/31.90 | | | | |
% 206.31/31.90 | | | | | REDUCE: (1148), (1194) imply:
% 206.31/31.90 | | | | | (1198) a_select3(id_ds1_filter, n0, all_74_15) = all_74_12
% 206.31/31.90 | | | | |
% 206.31/31.90 | | | | | REDUCE: (1147), (1194) imply:
% 206.31/31.90 | | | | | (1199) a_select3(id_ds1_filter, all_74_15, n0) = all_74_13
% 206.31/31.90 | | | | |
% 206.31/31.90 | | | | | REDUCE: (1149), (1194) imply:
% 206.31/31.90 | | | | | (1200) leq(n0, n5)
% 206.31/31.90 | | | | |
% 206.31/31.90 | | | | | REDUCE: (1144), (1194) imply:
% 206.31/31.90 | | | | | (1201) leq(n0, n0)
% 206.31/31.90 | | | | |
% 206.31/31.90 | | | | | BETA: splitting (1151) gives:
% 206.31/31.90 | | | | |
% 206.31/31.90 | | | | | Case 1:
% 206.31/31.90 | | | | | |
% 206.31/31.90 | | | | | | (1202) gt(all_74_15, n0)
% 206.31/31.90 | | | | | |
% 206.31/31.90 | | | | | | BETA: splitting (1154) gives:
% 206.31/31.90 | | | | | |
% 206.31/31.90 | | | | | | Case 1:
% 206.31/31.90 | | | | | | |
% 206.31/31.90 | | | | | | | (1203) gt(n5, all_74_15)
% 206.31/31.90 | | | | | | |
% 206.31/31.90 | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n5, n4, simplifying
% 206.31/31.90 | | | | | | | with (52), (125), (129), (1203) gives:
% 206.31/31.90 | | | | | | | (1204) leq(all_74_15, n4)
% 206.31/31.90 | | | | | | |
% 206.31/31.90 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n4,
% 206.31/31.90 | | | | | | | simplifying with (52), (122), (1204) gives:
% 206.31/31.90 | | | | | | | (1205) all_74_15 = n4 | gt(n4, all_74_15)
% 206.31/31.90 | | | | | | |
% 206.31/31.90 | | | | | | | BETA: splitting (1153) gives:
% 206.31/31.90 | | | | | | |
% 206.31/31.90 | | | | | | | Case 1:
% 206.31/31.90 | | | | | | | |
% 206.31/31.90 | | | | | | | | (1206) all_74_15 = n0
% 206.31/31.90 | | | | | | | |
% 206.31/31.90 | | | | | | | | REDUCE: (1202), (1206) imply:
% 206.31/31.90 | | | | | | | | (1207) gt(n0, n0)
% 206.31/31.90 | | | | | | | |
% 206.31/31.90 | | | | | | | | PRED_UNIFY: (1196), (1207) imply:
% 206.31/31.90 | | | | | | | | (1208) $false
% 206.31/31.90 | | | | | | | |
% 206.31/31.90 | | | | | | | | CLOSE: (1208) is inconsistent.
% 206.31/31.90 | | | | | | | |
% 206.31/31.90 | | | | | | | Case 2:
% 206.31/31.90 | | | | | | | |
% 206.31/31.90 | | | | | | | | (1209) ~ (all_74_15 = n0)
% 206.31/31.90 | | | | | | | |
% 206.31/31.90 | | | | | | | | BETA: splitting (1205) gives:
% 206.31/31.90 | | | | | | | |
% 206.31/31.90 | | | | | | | | Case 1:
% 206.31/31.90 | | | | | | | | |
% 206.31/31.90 | | | | | | | | | (1210) gt(n4, all_74_15)
% 206.31/31.90 | | | | | | | | |
% 206.31/31.90 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n4, n3,
% 206.31/31.90 | | | | | | | | | simplifying with (52), (122), (128), (1210) gives:
% 206.31/31.90 | | | | | | | | | (1211) leq(all_74_15, n3)
% 206.31/31.90 | | | | | | | | |
% 206.31/31.90 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n3,
% 206.31/31.90 | | | | | | | | | simplifying with (52), (115), (1211) gives:
% 206.31/31.90 | | | | | | | | | (1212) all_74_15 = n3 | gt(n3, all_74_15)
% 206.31/31.90 | | | | | | | | |
% 206.31/31.90 | | | | | | | | | BETA: splitting (1212) gives:
% 206.31/31.90 | | | | | | | | |
% 206.31/31.90 | | | | | | | | | Case 1:
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | (1213) gt(n3, all_74_15)
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n3, n2,
% 206.31/31.90 | | | | | | | | | | simplifying with (52), (115), (127), (1213) gives:
% 206.31/31.90 | | | | | | | | | | (1214) leq(all_74_15, n2)
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n2,
% 206.31/31.90 | | | | | | | | | | simplifying with (52), (104), (1214) gives:
% 206.31/31.90 | | | | | | | | | | (1215) all_74_15 = n2 | gt(n2, all_74_15)
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | BETA: splitting (1215) gives:
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | Case 1:
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | (1216) gt(n2, all_74_15)
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1,
% 206.31/31.90 | | | | | | | | | | | simplifying with (52), (104), (126), (1216) gives:
% 206.31/31.90 | | | | | | | | | | | (1217) leq(all_74_15, n1)
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | GROUND_INST: instantiating (5) with all_74_15, simplifying with
% 206.31/31.90 | | | | | | | | | | | (52), (1143), (1217) gives:
% 206.31/31.90 | | | | | | | | | | | (1218) all_74_15 = n1 | all_74_15 = n0
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | BETA: splitting (1218) gives:
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | Case 1:
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | (1219) all_74_15 = n0
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | REDUCE: (1209), (1219) imply:
% 206.31/31.90 | | | | | | | | | | | | (1220) $false
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | CLOSE: (1220) is inconsistent.
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | Case 2:
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | (1221) all_74_15 = n1
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | REDUCE: (1199), (1221) imply:
% 206.31/31.90 | | | | | | | | | | | | (1222) a_select3(id_ds1_filter, n1, n0) = all_74_13
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | REDUCE: (1198), (1221) imply:
% 206.31/31.90 | | | | | | | | | | | | (1223) a_select3(id_ds1_filter, n0, n1) = all_74_12
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | REDUCE: (1150), (1221) imply:
% 206.31/31.90 | | | | | | | | | | | | (1224) leq(n1, n5)
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | REDUCE: (1143), (1221) imply:
% 206.31/31.90 | | | | | | | | | | | | (1225) leq(n0, n1)
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | GROUND_INST: instantiating (68) with n0, n1, all_74_12,
% 206.31/31.90 | | | | | | | | | | | | simplifying with (13), (88), (1201), (1223),
% 206.31/31.90 | | | | | | | | | | | | (1225) gives:
% 206.31/31.90 | | | | | | | | | | | | (1226) ~ leq(n1, all_74_19) | ~ leq(n0, all_74_16) |
% 206.31/31.90 | | | | | | | | | | | | (a_select3(id_ds1_filter, n1, n0) = all_74_12 &
% 206.31/31.90 | | | | | | | | | | | | $i(all_74_12))
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | BETA: splitting (1226) gives:
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | Case 1:
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | (1227) ~ leq(n0, all_74_16)
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | REDUCE: (147), (1227) imply:
% 206.31/31.90 | | | | | | | | | | | | | (1228) ~ leq(n0, n5)
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | PRED_UNIFY: (1200), (1228) imply:
% 206.31/31.90 | | | | | | | | | | | | | (1229) $false
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | CLOSE: (1229) is inconsistent.
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | Case 2:
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | (1230) ~ leq(n1, all_74_19) | (a_select3(id_ds1_filter,
% 206.31/31.90 | | | | | | | | | | | | | n1, n0) = all_74_12 & $i(all_74_12))
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | BETA: splitting (1230) gives:
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | Case 1:
% 206.31/31.90 | | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | | (1231) ~ leq(n1, all_74_19)
% 206.31/31.90 | | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | | REDUCE: (142), (1231) imply:
% 206.31/31.90 | | | | | | | | | | | | | | (1232) ~ leq(n1, n5)
% 206.31/31.90 | | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | | PRED_UNIFY: (1224), (1232) imply:
% 206.31/31.90 | | | | | | | | | | | | | | (1233) $false
% 206.31/31.90 | | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | | CLOSE: (1233) is inconsistent.
% 206.31/31.90 | | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | Case 2:
% 206.31/31.90 | | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | | (1234) a_select3(id_ds1_filter, n1, n0) = all_74_12 &
% 206.31/31.90 | | | | | | | | | | | | | | $i(all_74_12)
% 206.31/31.90 | | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | | ALPHA: (1234) implies:
% 206.31/31.90 | | | | | | | | | | | | | | (1235) a_select3(id_ds1_filter, n1, n0) = all_74_12
% 206.31/31.90 | | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_74_13, all_74_12, n0,
% 206.31/31.90 | | | | | | | | | | | | | | n1, id_ds1_filter, simplifying with (1222), (1235)
% 206.31/31.90 | | | | | | | | | | | | | | gives:
% 206.31/31.90 | | | | | | | | | | | | | | (1236) all_74_12 = all_74_13
% 206.31/31.90 | | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | | REDUCE: (1142), (1236) imply:
% 206.31/31.90 | | | | | | | | | | | | | | (1237) $false
% 206.31/31.90 | | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | | CLOSE: (1237) is inconsistent.
% 206.31/31.90 | | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | End of split
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | End of split
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | End of split
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | Case 2:
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | (1238) all_74_15 = n2
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | REDUCE: (1199), (1238) imply:
% 206.31/31.90 | | | | | | | | | | | (1239) a_select3(id_ds1_filter, n2, n0) = all_74_13
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | REDUCE: (1198), (1238) imply:
% 206.31/31.90 | | | | | | | | | | | (1240) a_select3(id_ds1_filter, n0, n2) = all_74_12
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | REDUCE: (1150), (1238) imply:
% 206.31/31.90 | | | | | | | | | | | (1241) leq(n2, n5)
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | REDUCE: (1143), (1238) imply:
% 206.31/31.90 | | | | | | | | | | | (1242) leq(n0, n2)
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | GROUND_INST: instantiating (68) with n0, n2, all_74_12,
% 206.31/31.90 | | | | | | | | | | | simplifying with (13), (104), (1201), (1240),
% 206.31/31.90 | | | | | | | | | | | (1242) gives:
% 206.31/31.90 | | | | | | | | | | | (1243) ~ leq(n2, all_74_19) | ~ leq(n0, all_74_16) |
% 206.31/31.90 | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n0) = all_74_12 &
% 206.31/31.90 | | | | | | | | | | | $i(all_74_12))
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | BETA: splitting (1243) gives:
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | Case 1:
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | (1244) ~ leq(n0, all_74_16)
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | REDUCE: (147), (1244) imply:
% 206.31/31.90 | | | | | | | | | | | | (1245) ~ leq(n0, n5)
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | PRED_UNIFY: (1200), (1245) imply:
% 206.31/31.90 | | | | | | | | | | | | (1246) $false
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | CLOSE: (1246) is inconsistent.
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | Case 2:
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | (1247) ~ leq(n2, all_74_19) | (a_select3(id_ds1_filter,
% 206.31/31.90 | | | | | | | | | | | | n2, n0) = all_74_12 & $i(all_74_12))
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | BETA: splitting (1247) gives:
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | Case 1:
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | (1248) ~ leq(n2, all_74_19)
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | REDUCE: (142), (1248) imply:
% 206.31/31.90 | | | | | | | | | | | | | (1249) ~ leq(n2, n5)
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | PRED_UNIFY: (1241), (1249) imply:
% 206.31/31.90 | | | | | | | | | | | | | (1250) $false
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | CLOSE: (1250) is inconsistent.
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | Case 2:
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | (1251) a_select3(id_ds1_filter, n2, n0) = all_74_12 &
% 206.31/31.90 | | | | | | | | | | | | | $i(all_74_12)
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | ALPHA: (1251) implies:
% 206.31/31.90 | | | | | | | | | | | | | (1252) a_select3(id_ds1_filter, n2, n0) = all_74_12
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | | REF_CLOSE: (19), (1142), (1239), (1252) are inconsistent by
% 206.31/31.90 | | | | | | | | | | | | | sub-proof #4.
% 206.31/31.90 | | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | End of split
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | End of split
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | End of split
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | Case 2:
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | (1253) all_74_15 = n3
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | REDUCE: (1199), (1253) imply:
% 206.31/31.90 | | | | | | | | | | (1254) a_select3(id_ds1_filter, n3, n0) = all_74_13
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | REDUCE: (1198), (1253) imply:
% 206.31/31.90 | | | | | | | | | | (1255) a_select3(id_ds1_filter, n0, n3) = all_74_12
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | REDUCE: (1150), (1253) imply:
% 206.31/31.90 | | | | | | | | | | (1256) leq(n3, n5)
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | REDUCE: (1143), (1253) imply:
% 206.31/31.90 | | | | | | | | | | (1257) leq(n0, n3)
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | GROUND_INST: instantiating (68) with n0, n3, all_74_12,
% 206.31/31.90 | | | | | | | | | | simplifying with (13), (115), (1201), (1255),
% 206.31/31.90 | | | | | | | | | | (1257) gives:
% 206.31/31.90 | | | | | | | | | | (1258) ~ leq(n3, all_74_19) | ~ leq(n0, all_74_16) |
% 206.31/31.90 | | | | | | | | | | (a_select3(id_ds1_filter, n3, n0) = all_74_12 &
% 206.31/31.90 | | | | | | | | | | $i(all_74_12))
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | BETA: splitting (1258) gives:
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | Case 1:
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | (1259) ~ leq(n0, all_74_16)
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | REDUCE: (147), (1259) imply:
% 206.31/31.90 | | | | | | | | | | | (1260) ~ leq(n0, n5)
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | PRED_UNIFY: (1200), (1260) imply:
% 206.31/31.90 | | | | | | | | | | | (1261) $false
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | CLOSE: (1261) is inconsistent.
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | Case 2:
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | (1262) ~ leq(n3, all_74_19) | (a_select3(id_ds1_filter,
% 206.31/31.90 | | | | | | | | | | | n3, n0) = all_74_12 & $i(all_74_12))
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | BETA: splitting (1262) gives:
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | Case 1:
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | (1263) ~ leq(n3, all_74_19)
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | REDUCE: (142), (1263) imply:
% 206.31/31.90 | | | | | | | | | | | | (1264) ~ leq(n3, n5)
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | PRED_UNIFY: (1256), (1264) imply:
% 206.31/31.90 | | | | | | | | | | | | (1265) $false
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | CLOSE: (1265) is inconsistent.
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | Case 2:
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | (1266) a_select3(id_ds1_filter, n3, n0) = all_74_12 &
% 206.31/31.90 | | | | | | | | | | | | $i(all_74_12)
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | ALPHA: (1266) implies:
% 206.31/31.90 | | | | | | | | | | | | (1267) a_select3(id_ds1_filter, n3, n0) = all_74_12
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | | REF_CLOSE: (19), (1142), (1254), (1267) are inconsistent by
% 206.31/31.90 | | | | | | | | | | | | sub-proof #3.
% 206.31/31.90 | | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | End of split
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | End of split
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | End of split
% 206.31/31.90 | | | | | | | | |
% 206.31/31.90 | | | | | | | | Case 2:
% 206.31/31.90 | | | | | | | | |
% 206.31/31.90 | | | | | | | | | (1268) all_74_15 = n4
% 206.31/31.90 | | | | | | | | |
% 206.31/31.90 | | | | | | | | | REDUCE: (1199), (1268) imply:
% 206.31/31.90 | | | | | | | | | (1269) a_select3(id_ds1_filter, n4, n0) = all_74_13
% 206.31/31.90 | | | | | | | | |
% 206.31/31.90 | | | | | | | | | REDUCE: (1198), (1268) imply:
% 206.31/31.90 | | | | | | | | | (1270) a_select3(id_ds1_filter, n0, n4) = all_74_12
% 206.31/31.90 | | | | | | | | |
% 206.31/31.90 | | | | | | | | | REDUCE: (1150), (1268) imply:
% 206.31/31.90 | | | | | | | | | (1271) leq(n4, n5)
% 206.31/31.90 | | | | | | | | |
% 206.31/31.90 | | | | | | | | | REDUCE: (1143), (1268) imply:
% 206.31/31.90 | | | | | | | | | (1272) leq(n0, n4)
% 206.31/31.90 | | | | | | | | |
% 206.31/31.90 | | | | | | | | | GROUND_INST: instantiating (68) with n0, n4, all_74_12,
% 206.31/31.90 | | | | | | | | | simplifying with (13), (122), (1201), (1270),
% 206.31/31.90 | | | | | | | | | (1272) gives:
% 206.31/31.90 | | | | | | | | | (1273) ~ leq(n4, all_74_19) | ~ leq(n0, all_74_16) |
% 206.31/31.90 | | | | | | | | | (a_select3(id_ds1_filter, n4, n0) = all_74_12 &
% 206.31/31.90 | | | | | | | | | $i(all_74_12))
% 206.31/31.90 | | | | | | | | |
% 206.31/31.90 | | | | | | | | | BETA: splitting (1273) gives:
% 206.31/31.90 | | | | | | | | |
% 206.31/31.90 | | | | | | | | | Case 1:
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | (1274) ~ leq(n0, all_74_16)
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | REDUCE: (147), (1274) imply:
% 206.31/31.90 | | | | | | | | | | (1275) ~ leq(n0, n5)
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | PRED_UNIFY: (1200), (1275) imply:
% 206.31/31.90 | | | | | | | | | | (1276) $false
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | CLOSE: (1276) is inconsistent.
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | Case 2:
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | (1277) ~ leq(n4, all_74_19) | (a_select3(id_ds1_filter,
% 206.31/31.90 | | | | | | | | | | n4, n0) = all_74_12 & $i(all_74_12))
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | BETA: splitting (1277) gives:
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | Case 1:
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | (1278) ~ leq(n4, all_74_19)
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | REDUCE: (142), (1278) imply:
% 206.31/31.90 | | | | | | | | | | | (1279) ~ leq(n4, n5)
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | PRED_UNIFY: (1271), (1279) imply:
% 206.31/31.90 | | | | | | | | | | | (1280) $false
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | CLOSE: (1280) is inconsistent.
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | Case 2:
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | (1281) a_select3(id_ds1_filter, n4, n0) = all_74_12 &
% 206.31/31.90 | | | | | | | | | | | $i(all_74_12)
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | ALPHA: (1281) implies:
% 206.31/31.90 | | | | | | | | | | | (1282) a_select3(id_ds1_filter, n4, n0) = all_74_12
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | | REF_CLOSE: (19), (1142), (1269), (1282) are inconsistent by
% 206.31/31.90 | | | | | | | | | | | sub-proof #2.
% 206.31/31.90 | | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | | End of split
% 206.31/31.90 | | | | | | | | | |
% 206.31/31.90 | | | | | | | | | End of split
% 206.31/31.90 | | | | | | | | |
% 206.31/31.91 | | | | | | | | End of split
% 206.31/31.91 | | | | | | | |
% 206.31/31.91 | | | | | | | End of split
% 206.31/31.91 | | | | | | |
% 206.31/31.91 | | | | | | Case 2:
% 206.31/31.91 | | | | | | |
% 206.31/31.91 | | | | | | | (1283) all_74_15 = n5
% 206.31/31.91 | | | | | | |
% 206.31/31.91 | | | | | | | REDUCE: (1199), (1283) imply:
% 206.31/31.91 | | | | | | | (1284) a_select3(id_ds1_filter, n5, n0) = all_74_13
% 206.31/31.91 | | | | | | |
% 206.31/31.91 | | | | | | | REDUCE: (1198), (1283) imply:
% 206.31/31.91 | | | | | | | (1285) a_select3(id_ds1_filter, n0, n5) = all_74_12
% 206.31/31.91 | | | | | | |
% 206.31/31.91 | | | | | | | REDUCE: (1150), (1283) imply:
% 206.31/31.91 | | | | | | | (1286) leq(n5, n5)
% 206.31/31.91 | | | | | | |
% 206.31/31.91 | | | | | | | GROUND_INST: instantiating (68) with n0, n5, all_74_12,
% 206.31/31.91 | | | | | | | simplifying with (13), (125), (1200), (1201), (1285)
% 206.31/31.91 | | | | | | | gives:
% 206.31/31.91 | | | | | | | (1287) ~ leq(n5, all_74_19) | ~ leq(n0, all_74_16) |
% 206.31/31.91 | | | | | | | (a_select3(id_ds1_filter, n5, n0) = all_74_12 &
% 206.31/31.91 | | | | | | | $i(all_74_12))
% 206.31/31.91 | | | | | | |
% 206.31/31.91 | | | | | | | BETA: splitting (1287) gives:
% 206.31/31.91 | | | | | | |
% 206.31/31.91 | | | | | | | Case 1:
% 206.31/31.91 | | | | | | | |
% 206.31/31.91 | | | | | | | | (1288) ~ leq(n0, all_74_16)
% 206.31/31.91 | | | | | | | |
% 206.31/31.91 | | | | | | | | REDUCE: (147), (1288) imply:
% 206.31/31.91 | | | | | | | | (1289) ~ leq(n0, n5)
% 206.31/31.91 | | | | | | | |
% 206.31/31.91 | | | | | | | | PRED_UNIFY: (1200), (1289) imply:
% 206.31/31.91 | | | | | | | | (1290) $false
% 206.31/31.91 | | | | | | | |
% 206.31/31.91 | | | | | | | | CLOSE: (1290) is inconsistent.
% 206.31/31.91 | | | | | | | |
% 206.31/31.91 | | | | | | | Case 2:
% 206.31/31.91 | | | | | | | |
% 206.31/31.91 | | | | | | | | (1291) ~ leq(n5, all_74_19) | (a_select3(id_ds1_filter, n5,
% 206.31/31.91 | | | | | | | | n0) = all_74_12 & $i(all_74_12))
% 206.31/31.91 | | | | | | | |
% 206.31/31.91 | | | | | | | | BETA: splitting (1291) gives:
% 206.31/31.91 | | | | | | | |
% 206.31/31.91 | | | | | | | | Case 1:
% 206.31/31.91 | | | | | | | | |
% 206.31/31.91 | | | | | | | | | (1292) ~ leq(n5, all_74_19)
% 206.31/31.91 | | | | | | | | |
% 206.31/31.91 | | | | | | | | | REDUCE: (142), (1292) imply:
% 206.31/31.91 | | | | | | | | | (1293) ~ leq(n5, n5)
% 206.31/31.91 | | | | | | | | |
% 206.31/31.91 | | | | | | | | | PRED_UNIFY: (1286), (1293) imply:
% 206.31/31.91 | | | | | | | | | (1294) $false
% 206.31/31.91 | | | | | | | | |
% 206.31/31.91 | | | | | | | | | CLOSE: (1294) is inconsistent.
% 206.31/31.91 | | | | | | | | |
% 206.31/31.91 | | | | | | | | Case 2:
% 206.31/31.91 | | | | | | | | |
% 206.31/31.91 | | | | | | | | | (1295) a_select3(id_ds1_filter, n5, n0) = all_74_12 &
% 206.31/31.91 | | | | | | | | | $i(all_74_12)
% 206.31/31.91 | | | | | | | | |
% 206.31/31.91 | | | | | | | | | ALPHA: (1295) implies:
% 206.31/31.91 | | | | | | | | | (1296) a_select3(id_ds1_filter, n5, n0) = all_74_12
% 206.31/31.91 | | | | | | | | |
% 206.31/31.91 | | | | | | | | | GROUND_INST: instantiating (19) with all_74_13, all_74_12, n0,
% 206.31/31.91 | | | | | | | | | n5, id_ds1_filter, simplifying with (1284), (1296)
% 206.31/31.91 | | | | | | | | | gives:
% 206.31/31.91 | | | | | | | | | (1297) all_74_12 = all_74_13
% 206.31/31.91 | | | | | | | | |
% 206.31/31.91 | | | | | | | | | REDUCE: (1142), (1297) imply:
% 206.31/31.91 | | | | | | | | | (1298) $false
% 206.31/31.91 | | | | | | | | |
% 206.31/31.91 | | | | | | | | | CLOSE: (1298) is inconsistent.
% 206.31/31.91 | | | | | | | | |
% 206.31/31.91 | | | | | | | | End of split
% 206.31/31.91 | | | | | | | |
% 206.31/31.91 | | | | | | | End of split
% 206.31/31.91 | | | | | | |
% 206.31/31.91 | | | | | | End of split
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | Case 2:
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | | (1299) all_74_15 = n0
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | | REDUCE: (1199), (1299) imply:
% 206.31/31.91 | | | | | | (1300) a_select3(id_ds1_filter, n0, n0) = all_74_13
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | | REDUCE: (1198), (1299) imply:
% 206.31/31.91 | | | | | | (1301) a_select3(id_ds1_filter, n0, n0) = all_74_12
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | | GROUND_INST: instantiating (19) with all_74_13, all_74_12, n0, n0,
% 206.31/31.91 | | | | | | id_ds1_filter, simplifying with (1300), (1301) gives:
% 206.31/31.91 | | | | | | (1302) all_74_12 = all_74_13
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | | REDUCE: (1142), (1302) imply:
% 206.31/31.91 | | | | | | (1303) $false
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | | CLOSE: (1303) is inconsistent.
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | End of split
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | End of split
% 206.31/31.91 | | | |
% 206.31/31.91 | | | End of split
% 206.31/31.91 | | |
% 206.31/31.91 | | End of split
% 206.31/31.91 | |
% 206.31/31.91 | End of split
% 206.31/31.91 |
% 206.31/31.91 End of proof
% 206.31/31.91
% 206.31/31.91 Sub-proof #1 shows that the following formulas are inconsistent:
% 206.31/31.91 ----------------------------------------------------------------
% 206.31/31.91 (1) leq(all_74_14, n5)
% 206.31/31.91 (2) all_74_15 = n5 | gt(n5, all_74_15)
% 206.31/31.91 (3) gt(all_74_14, n0)
% 206.31/31.91 (4) all_74_15 = n5 | all_74_15 = n4 | all_74_15 = n3 | all_74_15 = n2 |
% 206.31/31.91 all_74_15 = n1 | all_74_15 = n0
% 206.31/31.91 (5) pred(n4) = n3
% 206.31/31.91 (6) $i(n2)
% 206.31/31.91 (7) leq(all_74_15, n5)
% 206.31/31.91 (8) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0,
% 206.31/31.91 v1) | gt(v1, v0))
% 206.31/31.91 (9) $i(all_74_15)
% 206.31/31.91 (10) pred(n3) = n2
% 206.31/31.91 (11) all_74_14 = n5 | gt(n5, all_74_14)
% 206.31/31.91 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 206.31/31.91 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.31/31.91 v0))
% 206.31/31.91 (13) $i(all_74_14)
% 206.31/31.91 (14) pred(n2) = n1
% 206.31/31.91 (15) pred(n5) = n4
% 206.31/31.91 (16) all_74_14 = n5 | all_74_14 = n4 | all_74_14 = n3 | all_74_14 = n2 |
% 206.31/31.91 all_74_14 = n1 | all_74_14 = n0
% 206.31/31.91 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 206.31/31.91 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 206.31/31.91 (18) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 206.31/31.91 leq(n0, v0))
% 206.31/31.91 (19) ~ gt(n0, n0)
% 206.31/31.91 (20) leq(n0, all_74_14)
% 206.31/31.91 (21) all_74_19 = n5
% 206.31/31.91 (22) $i(n4)
% 206.31/31.91 (23) $i(n3)
% 206.31/31.91 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter,
% 206.31/31.91 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_19) | ~
% 206.31/31.91 leq(v0, all_74_16) | ~ leq(n0, v1) | ~ leq(n0, v0) |
% 206.31/31.91 (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2)))
% 206.31/31.91 (25) ~ (all_74_12 = all_74_13)
% 206.31/31.91 (26) a_select3(id_ds1_filter, all_74_15, all_74_14) = all_74_13
% 206.31/31.91 (27) all_74_15 = n0 | gt(all_74_15, n0)
% 206.31/31.91 (28) a_select3(id_ds1_filter, all_74_14, all_74_15) = all_74_12
% 206.31/31.91 (29) $i(n5)
% 206.31/31.91 (30) all_74_16 = n5
% 206.31/31.91 (31) leq(n0, all_74_15)
% 206.31/31.91
% 206.31/31.91 Begin of proof
% 206.31/31.91 |
% 206.31/31.91 | BETA: splitting (27) gives:
% 206.31/31.91 |
% 206.31/31.91 | Case 1:
% 206.31/31.91 | |
% 206.31/31.91 | | (32) gt(all_74_15, n0)
% 206.31/31.91 | |
% 206.31/31.91 | | BETA: splitting (2) gives:
% 206.31/31.91 | |
% 206.31/31.91 | | Case 1:
% 206.31/31.91 | | |
% 206.31/31.91 | | | (33) gt(n5, all_74_15)
% 206.31/31.91 | | |
% 206.31/31.91 | | | GROUND_INST: instantiating (17) with all_74_15, n5, n4, simplifying with
% 206.31/31.91 | | | (9), (15), (29), (33) gives:
% 206.31/31.91 | | | (34) leq(all_74_15, n4)
% 206.31/31.91 | | |
% 206.31/31.91 | | | GROUND_INST: instantiating (8) with all_74_15, n4, simplifying with (9),
% 206.31/31.91 | | | (22), (34) gives:
% 206.31/31.91 | | | (35) all_74_15 = n4 | gt(n4, all_74_15)
% 206.31/31.91 | | |
% 206.31/31.91 | | | BETA: splitting (11) gives:
% 206.31/31.91 | | |
% 206.31/31.91 | | | Case 1:
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | (36) gt(n5, all_74_14)
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | GROUND_INST: instantiating (17) with all_74_14, n5, n4, simplifying with
% 206.31/31.91 | | | | (13), (15), (29), (36) gives:
% 206.31/31.91 | | | | (37) leq(all_74_14, n4)
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | GROUND_INST: instantiating (8) with all_74_14, n4, simplifying with
% 206.31/31.91 | | | | (13), (22), (37) gives:
% 206.31/31.91 | | | | (38) all_74_14 = n4 | gt(n4, all_74_14)
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | BETA: splitting (16) gives:
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | Case 1:
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | (39) all_74_14 = n0
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | REDUCE: (3), (39) imply:
% 206.31/31.91 | | | | | (40) gt(n0, n0)
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | PRED_UNIFY: (19), (40) imply:
% 206.31/31.91 | | | | | (41) $false
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | CLOSE: (41) is inconsistent.
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | Case 2:
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | (42) ~ (all_74_14 = n0)
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | BETA: splitting (4) gives:
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | Case 1:
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | | (43) all_74_15 = n0
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | | REDUCE: (32), (43) imply:
% 206.31/31.91 | | | | | | (44) gt(n0, n0)
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | | PRED_UNIFY: (19), (44) imply:
% 206.31/31.91 | | | | | | (45) $false
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | | CLOSE: (45) is inconsistent.
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | Case 2:
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | | (46) ~ (all_74_15 = n0)
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 206.31/31.91 | | | | | | (17), (18), (20), (21), (22), (23), (24), (25), (26),
% 206.31/31.91 | | | | | | (28), (30), (31), (35), (38), (42), (46) are inconsistent
% 206.31/31.91 | | | | | | by sub-proof #8.
% 206.31/31.91 | | | | | |
% 206.31/31.91 | | | | | End of split
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | End of split
% 206.31/31.91 | | | |
% 206.31/31.91 | | | Case 2:
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | (47) all_74_14 = n5
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | REDUCE: (28), (47) imply:
% 206.31/31.91 | | | | (48) a_select3(id_ds1_filter, n5, all_74_15) = all_74_12
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | REDUCE: (26), (47) imply:
% 206.31/31.91 | | | | (49) a_select3(id_ds1_filter, all_74_15, n5) = all_74_13
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | REDUCE: (1), (47) imply:
% 206.31/31.91 | | | | (50) leq(n5, n5)
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | REDUCE: (20), (47) imply:
% 206.31/31.91 | | | | (51) leq(n0, n5)
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | BETA: splitting (4) gives:
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | Case 1:
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | (52) all_74_15 = n0
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | REDUCE: (32), (52) imply:
% 206.31/31.91 | | | | | (53) gt(n0, n0)
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | PRED_UNIFY: (19), (53) imply:
% 206.31/31.91 | | | | | (54) $false
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | CLOSE: (54) is inconsistent.
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | Case 2:
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | (55) ~ (all_74_15 = n0)
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (12), (14), (17), (18),
% 206.31/31.91 | | | | | (21), (22), (23), (24), (25), (29), (30), (31), (35), (48),
% 206.31/31.91 | | | | | (49), (50), (51), (55) are inconsistent by sub-proof #6.
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | End of split
% 206.31/31.91 | | | |
% 206.31/31.91 | | | End of split
% 206.31/31.91 | | |
% 206.31/31.91 | | Case 2:
% 206.31/31.91 | | |
% 206.31/31.91 | | | (56) all_74_15 = n5
% 206.31/31.91 | | |
% 206.31/31.91 | | | REDUCE: (28), (56) imply:
% 206.31/31.91 | | | (57) a_select3(id_ds1_filter, all_74_14, n5) = all_74_12
% 206.31/31.91 | | |
% 206.31/31.91 | | | REDUCE: (26), (56) imply:
% 206.31/31.91 | | | (58) a_select3(id_ds1_filter, n5, all_74_14) = all_74_13
% 206.31/31.91 | | |
% 206.31/31.91 | | | REDUCE: (7), (56) imply:
% 206.31/31.91 | | | (59) leq(n5, n5)
% 206.31/31.91 | | |
% 206.31/31.91 | | | REDUCE: (31), (56) imply:
% 206.31/31.91 | | | (60) leq(n0, n5)
% 206.31/31.91 | | |
% 206.31/31.91 | | | BETA: splitting (11) gives:
% 206.31/31.91 | | |
% 206.31/31.91 | | | Case 1:
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | (61) gt(n5, all_74_14)
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | GROUND_INST: instantiating (17) with all_74_14, n5, n4, simplifying with
% 206.31/31.91 | | | | (13), (15), (29), (61) gives:
% 206.31/31.91 | | | | (62) leq(all_74_14, n4)
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | GROUND_INST: instantiating (8) with all_74_14, n4, simplifying with
% 206.31/31.91 | | | | (13), (22), (62) gives:
% 206.31/31.91 | | | | (63) all_74_14 = n4 | gt(n4, all_74_14)
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | BETA: splitting (16) gives:
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | Case 1:
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | (64) all_74_14 = n0
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | REDUCE: (3), (64) imply:
% 206.31/31.91 | | | | | (65) gt(n0, n0)
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | PRED_UNIFY: (19), (65) imply:
% 206.31/31.91 | | | | | (66) $false
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | CLOSE: (66) is inconsistent.
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | Case 2:
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | (67) ~ (all_74_14 = n0)
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | | REF_CLOSE: (1), (5), (6), (8), (10), (12), (13), (14), (17), (18),
% 206.31/31.91 | | | | | (20), (21), (22), (23), (24), (25), (29), (30), (57), (58),
% 206.31/31.91 | | | | | (59), (60), (63), (67) are inconsistent by sub-proof #5.
% 206.31/31.91 | | | | |
% 206.31/31.91 | | | | End of split
% 206.31/31.91 | | | |
% 206.31/31.91 | | | Case 2:
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | (68) all_74_14 = n5
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | REDUCE: (57), (68) imply:
% 206.31/31.91 | | | | (69) a_select3(id_ds1_filter, n5, n5) = all_74_12
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | REDUCE: (58), (68) imply:
% 206.31/31.91 | | | | (70) a_select3(id_ds1_filter, n5, n5) = all_74_13
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | GROUND_INST: instantiating (12) with all_74_13, all_74_12, n5, n5,
% 206.31/31.91 | | | | id_ds1_filter, simplifying with (69), (70) gives:
% 206.31/31.91 | | | | (71) all_74_12 = all_74_13
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | REDUCE: (25), (71) imply:
% 206.31/31.91 | | | | (72) $false
% 206.31/31.91 | | | |
% 206.31/31.91 | | | | CLOSE: (72) is inconsistent.
% 206.31/31.91 | | | |
% 206.31/31.91 | | | End of split
% 206.31/31.91 | | |
% 206.31/31.91 | | End of split
% 206.31/31.91 | |
% 206.31/31.91 | Case 2:
% 206.31/31.91 | |
% 206.31/31.91 | | (73) all_74_15 = n0
% 206.31/31.91 | | (74) ~ gt(all_74_15, n0)
% 206.31/31.91 | |
% 206.31/31.91 | | REDUCE: (28), (73) imply:
% 206.31/31.91 | | (75) a_select3(id_ds1_filter, all_74_14, n0) = all_74_12
% 206.31/31.91 | |
% 206.31/31.91 | | REDUCE: (26), (73) imply:
% 206.31/31.91 | | (76) a_select3(id_ds1_filter, n0, all_74_14) = all_74_13
% 206.31/31.91 | |
% 206.31/31.91 | | REDUCE: (9), (73) imply:
% 206.31/31.91 | | (77) $i(n0)
% 206.31/31.91 | |
% 206.31/31.91 | | REDUCE: (7), (73) imply:
% 206.31/31.91 | | (78) leq(n0, n5)
% 206.31/31.91 | |
% 206.31/31.91 | | REDUCE: (31), (73) imply:
% 206.31/31.91 | | (79) leq(n0, n0)
% 206.31/31.91 | |
% 206.31/31.91 | | BETA: splitting (11) gives:
% 206.31/31.91 | |
% 206.31/31.91 | | Case 1:
% 206.31/31.91 | | |
% 206.31/31.91 | | | (80) gt(n5, all_74_14)
% 206.31/31.91 | | |
% 206.31/31.91 | | | GROUND_INST: instantiating (17) with all_74_14, n5, n4, simplifying with
% 206.31/31.91 | | | (13), (15), (29), (80) gives:
% 206.31/31.91 | | | (81) leq(all_74_14, n4)
% 206.31/31.91 | | |
% 206.31/31.91 | | | GROUND_INST: instantiating (8) with all_74_14, n4, simplifying with (13),
% 206.31/31.91 | | | (22), (81) gives:
% 206.31/31.91 | | | (82) all_74_14 = n4 | gt(n4, all_74_14)
% 206.31/31.92 | | |
% 206.31/31.92 | | | BETA: splitting (16) gives:
% 206.31/31.92 | | |
% 206.31/31.92 | | | Case 1:
% 206.31/31.92 | | | |
% 206.31/31.92 | | | | (83) all_74_14 = n0
% 206.31/31.92 | | | |
% 206.31/31.92 | | | | REDUCE: (3), (83) imply:
% 206.31/31.92 | | | | (84) gt(n0, n0)
% 206.31/31.92 | | | |
% 206.31/31.92 | | | | PRED_UNIFY: (19), (84) imply:
% 206.31/31.92 | | | | (85) $false
% 206.31/31.92 | | | |
% 206.31/31.92 | | | | CLOSE: (85) is inconsistent.
% 206.31/31.92 | | | |
% 206.31/31.92 | | | Case 2:
% 206.31/31.92 | | | |
% 206.31/31.92 | | | | (86) ~ (all_74_14 = n0)
% 206.31/31.92 | | | |
% 206.31/31.92 | | | | BETA: splitting (82) gives:
% 206.31/31.92 | | | |
% 206.31/31.92 | | | | Case 1:
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | (87) gt(n4, all_74_14)
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | GROUND_INST: instantiating (17) with all_74_14, n4, n3, simplifying
% 206.31/31.92 | | | | | with (5), (13), (22), (87) gives:
% 206.31/31.92 | | | | | (88) leq(all_74_14, n3)
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | GROUND_INST: instantiating (8) with all_74_14, n3, simplifying with
% 206.31/31.92 | | | | | (13), (23), (88) gives:
% 206.31/31.92 | | | | | (89) all_74_14 = n3 | gt(n3, all_74_14)
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | BETA: splitting (89) gives:
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | Case 1:
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | (90) gt(n3, all_74_14)
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | GROUND_INST: instantiating (17) with all_74_14, n3, n2, simplifying
% 206.31/31.92 | | | | | | with (10), (13), (23), (90) gives:
% 206.31/31.92 | | | | | | (91) leq(all_74_14, n2)
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | GROUND_INST: instantiating (8) with all_74_14, n2, simplifying with
% 206.31/31.92 | | | | | | (6), (13), (91) gives:
% 206.31/31.92 | | | | | | (92) all_74_14 = n2 | gt(n2, all_74_14)
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | BETA: splitting (92) gives:
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | Case 1:
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | (93) gt(n2, all_74_14)
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | GROUND_INST: instantiating (17) with all_74_14, n2, n1,
% 206.31/31.92 | | | | | | | simplifying with (6), (13), (14), (93) gives:
% 206.31/31.92 | | | | | | | (94) leq(all_74_14, n1)
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | GROUND_INST: instantiating (18) with all_74_14, simplifying with
% 206.31/31.92 | | | | | | | (13), (20), (94) gives:
% 206.31/31.92 | | | | | | | (95) all_74_14 = n1 | all_74_14 = n0
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | BETA: splitting (95) gives:
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | Case 1:
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | (96) all_74_14 = n0
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | REDUCE: (86), (96) imply:
% 206.31/31.92 | | | | | | | | (97) $false
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | CLOSE: (97) is inconsistent.
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | Case 2:
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | (98) all_74_14 = n1
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | REDUCE: (75), (98) imply:
% 206.31/31.92 | | | | | | | | (99) a_select3(id_ds1_filter, n1, n0) = all_74_12
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | REDUCE: (76), (98) imply:
% 206.31/31.92 | | | | | | | | (100) a_select3(id_ds1_filter, n0, n1) = all_74_13
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | REDUCE: (13), (98) imply:
% 206.31/31.92 | | | | | | | | (101) $i(n1)
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | REDUCE: (1), (98) imply:
% 206.31/31.92 | | | | | | | | (102) leq(n1, n5)
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | REDUCE: (20), (98) imply:
% 206.31/31.92 | | | | | | | | (103) leq(n0, n1)
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | GROUND_INST: instantiating (24) with n0, n1, all_74_13,
% 206.31/31.92 | | | | | | | | simplifying with (77), (79), (100), (101), (103)
% 206.31/31.92 | | | | | | | | gives:
% 206.31/31.92 | | | | | | | | (104) ~ leq(n1, all_74_19) | ~ leq(n0, all_74_16) |
% 206.31/31.92 | | | | | | | | (a_select3(id_ds1_filter, n1, n0) = all_74_13 &
% 206.31/31.92 | | | | | | | | $i(all_74_13))
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | BETA: splitting (104) gives:
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | Case 1:
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | | (105) ~ leq(n0, all_74_16)
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | | REDUCE: (30), (105) imply:
% 206.31/31.92 | | | | | | | | | (106) ~ leq(n0, n5)
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | | PRED_UNIFY: (78), (106) imply:
% 206.31/31.92 | | | | | | | | | (107) $false
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | | CLOSE: (107) is inconsistent.
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | Case 2:
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | | (108) ~ leq(n1, all_74_19) | (a_select3(id_ds1_filter, n1,
% 206.31/31.92 | | | | | | | | | n0) = all_74_13 & $i(all_74_13))
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | | BETA: splitting (108) gives:
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | | Case 1:
% 206.31/31.92 | | | | | | | | | |
% 206.31/31.92 | | | | | | | | | | (109) ~ leq(n1, all_74_19)
% 206.31/31.92 | | | | | | | | | |
% 206.31/31.92 | | | | | | | | | | REDUCE: (21), (109) imply:
% 206.31/31.92 | | | | | | | | | | (110) ~ leq(n1, n5)
% 206.31/31.92 | | | | | | | | | |
% 206.31/31.92 | | | | | | | | | | PRED_UNIFY: (102), (110) imply:
% 206.31/31.92 | | | | | | | | | | (111) $false
% 206.31/31.92 | | | | | | | | | |
% 206.31/31.92 | | | | | | | | | | CLOSE: (111) is inconsistent.
% 206.31/31.92 | | | | | | | | | |
% 206.31/31.92 | | | | | | | | | Case 2:
% 206.31/31.92 | | | | | | | | | |
% 206.31/31.92 | | | | | | | | | | (112) a_select3(id_ds1_filter, n1, n0) = all_74_13 &
% 206.31/31.92 | | | | | | | | | | $i(all_74_13)
% 206.31/31.92 | | | | | | | | | |
% 206.31/31.92 | | | | | | | | | | ALPHA: (112) implies:
% 206.31/31.92 | | | | | | | | | | (113) a_select3(id_ds1_filter, n1, n0) = all_74_13
% 206.31/31.92 | | | | | | | | | |
% 206.31/31.92 | | | | | | | | | | GROUND_INST: instantiating (12) with all_74_13, all_74_12, n0,
% 206.31/31.92 | | | | | | | | | | n1, id_ds1_filter, simplifying with (99), (113)
% 206.31/31.92 | | | | | | | | | | gives:
% 206.31/31.92 | | | | | | | | | | (114) all_74_12 = all_74_13
% 206.31/31.92 | | | | | | | | | |
% 206.31/31.92 | | | | | | | | | | REDUCE: (25), (114) imply:
% 206.31/31.92 | | | | | | | | | | (115) $false
% 206.31/31.92 | | | | | | | | | |
% 206.31/31.92 | | | | | | | | | | CLOSE: (115) is inconsistent.
% 206.31/31.92 | | | | | | | | | |
% 206.31/31.92 | | | | | | | | | End of split
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | End of split
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | End of split
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | Case 2:
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | (116) all_74_14 = n2
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | REDUCE: (75), (116) imply:
% 206.31/31.92 | | | | | | | (117) a_select3(id_ds1_filter, n2, n0) = all_74_12
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | REDUCE: (76), (116) imply:
% 206.31/31.92 | | | | | | | (118) a_select3(id_ds1_filter, n0, n2) = all_74_13
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | REDUCE: (1), (116) imply:
% 206.31/31.92 | | | | | | | (119) leq(n2, n5)
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | REDUCE: (20), (116) imply:
% 206.31/31.92 | | | | | | | (120) leq(n0, n2)
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | GROUND_INST: instantiating (24) with n0, n2, all_74_13,
% 206.31/31.92 | | | | | | | simplifying with (6), (77), (79), (118), (120) gives:
% 206.31/31.92 | | | | | | | (121) ~ leq(n2, all_74_19) | ~ leq(n0, all_74_16) |
% 206.31/31.92 | | | | | | | (a_select3(id_ds1_filter, n2, n0) = all_74_13 &
% 206.31/31.92 | | | | | | | $i(all_74_13))
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | BETA: splitting (121) gives:
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | Case 1:
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | (122) ~ leq(n0, all_74_16)
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | REDUCE: (30), (122) imply:
% 206.31/31.92 | | | | | | | | (123) ~ leq(n0, n5)
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | PRED_UNIFY: (78), (123) imply:
% 206.31/31.92 | | | | | | | | (124) $false
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | CLOSE: (124) is inconsistent.
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | Case 2:
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | (125) ~ leq(n2, all_74_19) | (a_select3(id_ds1_filter, n2,
% 206.31/31.92 | | | | | | | | n0) = all_74_13 & $i(all_74_13))
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | BETA: splitting (125) gives:
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | Case 1:
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | | (126) ~ leq(n2, all_74_19)
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | | REDUCE: (21), (126) imply:
% 206.31/31.92 | | | | | | | | | (127) ~ leq(n2, n5)
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | | PRED_UNIFY: (119), (127) imply:
% 206.31/31.92 | | | | | | | | | (128) $false
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | | CLOSE: (128) is inconsistent.
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | Case 2:
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | | (129) a_select3(id_ds1_filter, n2, n0) = all_74_13 &
% 206.31/31.92 | | | | | | | | | $i(all_74_13)
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | | ALPHA: (129) implies:
% 206.31/31.92 | | | | | | | | | (130) a_select3(id_ds1_filter, n2, n0) = all_74_13
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | | REF_CLOSE: (12), (25), (117), (130) are inconsistent by
% 206.31/31.92 | | | | | | | | | sub-proof #4.
% 206.31/31.92 | | | | | | | | |
% 206.31/31.92 | | | | | | | | End of split
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | End of split
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | End of split
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | Case 2:
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | (131) all_74_14 = n3
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | REDUCE: (75), (131) imply:
% 206.31/31.92 | | | | | | (132) a_select3(id_ds1_filter, n3, n0) = all_74_12
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | REDUCE: (76), (131) imply:
% 206.31/31.92 | | | | | | (133) a_select3(id_ds1_filter, n0, n3) = all_74_13
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | REDUCE: (1), (131) imply:
% 206.31/31.92 | | | | | | (134) leq(n3, n5)
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | REDUCE: (20), (131) imply:
% 206.31/31.92 | | | | | | (135) leq(n0, n3)
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | GROUND_INST: instantiating (24) with n0, n3, all_74_13, simplifying
% 206.31/31.92 | | | | | | with (23), (77), (79), (133), (135) gives:
% 206.31/31.92 | | | | | | (136) ~ leq(n3, all_74_19) | ~ leq(n0, all_74_16) |
% 206.31/31.92 | | | | | | (a_select3(id_ds1_filter, n3, n0) = all_74_13 &
% 206.31/31.92 | | | | | | $i(all_74_13))
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | BETA: splitting (136) gives:
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | Case 1:
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | (137) ~ leq(n0, all_74_16)
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | REDUCE: (30), (137) imply:
% 206.31/31.92 | | | | | | | (138) ~ leq(n0, n5)
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | PRED_UNIFY: (78), (138) imply:
% 206.31/31.92 | | | | | | | (139) $false
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | CLOSE: (139) is inconsistent.
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | Case 2:
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | (140) ~ leq(n3, all_74_19) | (a_select3(id_ds1_filter, n3, n0)
% 206.31/31.92 | | | | | | | = all_74_13 & $i(all_74_13))
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | BETA: splitting (140) gives:
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | Case 1:
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | (141) ~ leq(n3, all_74_19)
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | REDUCE: (21), (141) imply:
% 206.31/31.92 | | | | | | | | (142) ~ leq(n3, n5)
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | PRED_UNIFY: (134), (142) imply:
% 206.31/31.92 | | | | | | | | (143) $false
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | CLOSE: (143) is inconsistent.
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | Case 2:
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | (144) a_select3(id_ds1_filter, n3, n0) = all_74_13 &
% 206.31/31.92 | | | | | | | | $i(all_74_13)
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | ALPHA: (144) implies:
% 206.31/31.92 | | | | | | | | (145) a_select3(id_ds1_filter, n3, n0) = all_74_13
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | | REF_CLOSE: (12), (25), (132), (145) are inconsistent by
% 206.31/31.92 | | | | | | | | sub-proof #3.
% 206.31/31.92 | | | | | | | |
% 206.31/31.92 | | | | | | | End of split
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | End of split
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | End of split
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | Case 2:
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | (146) all_74_14 = n4
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | REDUCE: (75), (146) imply:
% 206.31/31.92 | | | | | (147) a_select3(id_ds1_filter, n4, n0) = all_74_12
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | REDUCE: (76), (146) imply:
% 206.31/31.92 | | | | | (148) a_select3(id_ds1_filter, n0, n4) = all_74_13
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | REDUCE: (1), (146) imply:
% 206.31/31.92 | | | | | (149) leq(n4, n5)
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | REDUCE: (20), (146) imply:
% 206.31/31.92 | | | | | (150) leq(n0, n4)
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | GROUND_INST: instantiating (24) with n0, n4, all_74_13, simplifying
% 206.31/31.92 | | | | | with (22), (77), (79), (148), (150) gives:
% 206.31/31.92 | | | | | (151) ~ leq(n4, all_74_19) | ~ leq(n0, all_74_16) |
% 206.31/31.92 | | | | | (a_select3(id_ds1_filter, n4, n0) = all_74_13 &
% 206.31/31.92 | | | | | $i(all_74_13))
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | BETA: splitting (151) gives:
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | Case 1:
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | (152) ~ leq(n0, all_74_16)
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | REDUCE: (30), (152) imply:
% 206.31/31.92 | | | | | | (153) ~ leq(n0, n5)
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | PRED_UNIFY: (78), (153) imply:
% 206.31/31.92 | | | | | | (154) $false
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | CLOSE: (154) is inconsistent.
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | Case 2:
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | (155) ~ leq(n4, all_74_19) | (a_select3(id_ds1_filter, n4, n0) =
% 206.31/31.92 | | | | | | all_74_13 & $i(all_74_13))
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | BETA: splitting (155) gives:
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | | Case 1:
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | (156) ~ leq(n4, all_74_19)
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | REDUCE: (21), (156) imply:
% 206.31/31.92 | | | | | | | (157) ~ leq(n4, n5)
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | PRED_UNIFY: (149), (157) imply:
% 206.31/31.92 | | | | | | | (158) $false
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | CLOSE: (158) is inconsistent.
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | Case 2:
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | (159) a_select3(id_ds1_filter, n4, n0) = all_74_13 &
% 206.31/31.92 | | | | | | | $i(all_74_13)
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | ALPHA: (159) implies:
% 206.31/31.92 | | | | | | | (160) a_select3(id_ds1_filter, n4, n0) = all_74_13
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | | REF_CLOSE: (12), (25), (147), (160) are inconsistent by sub-proof
% 206.31/31.92 | | | | | | | #2.
% 206.31/31.92 | | | | | | |
% 206.31/31.92 | | | | | | End of split
% 206.31/31.92 | | | | | |
% 206.31/31.92 | | | | | End of split
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | End of split
% 206.31/31.92 | | | |
% 206.31/31.92 | | | End of split
% 206.31/31.92 | | |
% 206.31/31.92 | | Case 2:
% 206.31/31.92 | | |
% 206.31/31.92 | | | (161) all_74_14 = n5
% 206.31/31.92 | | |
% 206.31/31.92 | | | REDUCE: (75), (161) imply:
% 206.31/31.92 | | | (162) a_select3(id_ds1_filter, n5, n0) = all_74_12
% 206.31/31.92 | | |
% 206.31/31.92 | | | REDUCE: (76), (161) imply:
% 206.31/31.92 | | | (163) a_select3(id_ds1_filter, n0, n5) = all_74_13
% 206.31/31.92 | | |
% 206.31/31.92 | | | REDUCE: (1), (161) imply:
% 206.31/31.92 | | | (164) leq(n5, n5)
% 206.31/31.92 | | |
% 206.31/31.92 | | | GROUND_INST: instantiating (24) with n0, n5, all_74_13, simplifying with
% 206.31/31.92 | | | (29), (77), (78), (79), (163) gives:
% 206.31/31.92 | | | (165) ~ leq(n5, all_74_19) | ~ leq(n0, all_74_16) |
% 206.31/31.92 | | | (a_select3(id_ds1_filter, n5, n0) = all_74_13 & $i(all_74_13))
% 206.31/31.92 | | |
% 206.31/31.92 | | | BETA: splitting (165) gives:
% 206.31/31.92 | | |
% 206.31/31.92 | | | Case 1:
% 206.31/31.92 | | | |
% 206.31/31.92 | | | | (166) ~ leq(n0, all_74_16)
% 206.31/31.92 | | | |
% 206.31/31.92 | | | | REDUCE: (30), (166) imply:
% 206.31/31.92 | | | | (167) ~ leq(n0, n5)
% 206.31/31.92 | | | |
% 206.31/31.92 | | | | PRED_UNIFY: (78), (167) imply:
% 206.31/31.92 | | | | (168) $false
% 206.31/31.92 | | | |
% 206.31/31.92 | | | | CLOSE: (168) is inconsistent.
% 206.31/31.92 | | | |
% 206.31/31.92 | | | Case 2:
% 206.31/31.92 | | | |
% 206.31/31.92 | | | | (169) ~ leq(n5, all_74_19) | (a_select3(id_ds1_filter, n5, n0) =
% 206.31/31.92 | | | | all_74_13 & $i(all_74_13))
% 206.31/31.92 | | | |
% 206.31/31.92 | | | | BETA: splitting (169) gives:
% 206.31/31.92 | | | |
% 206.31/31.92 | | | | Case 1:
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | (170) ~ leq(n5, all_74_19)
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | REDUCE: (21), (170) imply:
% 206.31/31.92 | | | | | (171) ~ leq(n5, n5)
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | PRED_UNIFY: (164), (171) imply:
% 206.31/31.92 | | | | | (172) $false
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | CLOSE: (172) is inconsistent.
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | Case 2:
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | (173) a_select3(id_ds1_filter, n5, n0) = all_74_13 & $i(all_74_13)
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | ALPHA: (173) implies:
% 206.31/31.92 | | | | | (174) a_select3(id_ds1_filter, n5, n0) = all_74_13
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | GROUND_INST: instantiating (12) with all_74_13, all_74_12, n0, n5,
% 206.31/31.92 | | | | | id_ds1_filter, simplifying with (162), (174) gives:
% 206.31/31.92 | | | | | (175) all_74_12 = all_74_13
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | REDUCE: (25), (175) imply:
% 206.31/31.92 | | | | | (176) $false
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | | CLOSE: (176) is inconsistent.
% 206.31/31.92 | | | | |
% 206.31/31.92 | | | | End of split
% 206.31/31.92 | | | |
% 206.31/31.92 | | | End of split
% 206.31/31.92 | | |
% 206.31/31.92 | | End of split
% 206.31/31.92 | |
% 206.31/31.92 | End of split
% 206.31/31.92 |
% 206.31/31.92 End of proof
% 206.31/31.92
% 206.31/31.92 Sub-proof #2 shows that the following formulas are inconsistent:
% 206.31/31.92 ----------------------------------------------------------------
% 206.31/31.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.31/31.92 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.31/31.92 v0))
% 206.31/31.92 (2) a_select3(id_ds1_filter, n4, n0) = all_74_12
% 206.31/31.92 (3) a_select3(id_ds1_filter, n4, n0) = all_74_13
% 206.31/31.92 (4) ~ (all_74_12 = all_74_13)
% 206.31/31.92
% 206.31/31.92 Begin of proof
% 206.31/31.92 |
% 206.31/31.92 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n0, n4,
% 206.31/31.92 | id_ds1_filter, simplifying with (2), (3) gives:
% 206.31/31.92 | (5) all_74_12 = all_74_13
% 206.31/31.92 |
% 206.31/31.92 | REDUCE: (4), (5) imply:
% 206.31/31.92 | (6) $false
% 206.31/31.92 |
% 206.31/31.92 | CLOSE: (6) is inconsistent.
% 206.31/31.92 |
% 206.31/31.92 End of proof
% 206.31/31.92
% 206.31/31.92 Sub-proof #3 shows that the following formulas are inconsistent:
% 206.31/31.92 ----------------------------------------------------------------
% 206.31/31.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.31/31.92 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.31/31.92 v0))
% 206.31/31.92 (2) a_select3(id_ds1_filter, n3, n0) = all_74_12
% 206.31/31.92 (3) a_select3(id_ds1_filter, n3, n0) = all_74_13
% 206.31/31.92 (4) ~ (all_74_12 = all_74_13)
% 206.31/31.92
% 206.31/31.92 Begin of proof
% 206.31/31.92 |
% 206.31/31.92 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n0, n3,
% 206.31/31.92 | id_ds1_filter, simplifying with (2), (3) gives:
% 206.31/31.92 | (5) all_74_12 = all_74_13
% 206.31/31.92 |
% 206.31/31.92 | REDUCE: (4), (5) imply:
% 206.31/31.92 | (6) $false
% 206.31/31.92 |
% 206.31/31.92 | CLOSE: (6) is inconsistent.
% 206.31/31.92 |
% 206.31/31.92 End of proof
% 206.31/31.92
% 206.31/31.92 Sub-proof #4 shows that the following formulas are inconsistent:
% 206.31/31.92 ----------------------------------------------------------------
% 206.31/31.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.31/31.92 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.31/31.92 v0))
% 206.31/31.92 (2) a_select3(id_ds1_filter, n2, n0) = all_74_12
% 206.31/31.92 (3) a_select3(id_ds1_filter, n2, n0) = all_74_13
% 206.31/31.92 (4) ~ (all_74_12 = all_74_13)
% 206.31/31.92
% 206.31/31.92 Begin of proof
% 206.31/31.92 |
% 206.31/31.93 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n0, n2,
% 206.31/31.93 | id_ds1_filter, simplifying with (2), (3) gives:
% 206.31/31.93 | (5) all_74_12 = all_74_13
% 206.31/31.93 |
% 206.31/31.93 | REDUCE: (4), (5) imply:
% 206.31/31.93 | (6) $false
% 206.31/31.93 |
% 206.31/31.93 | CLOSE: (6) is inconsistent.
% 206.31/31.93 |
% 206.31/31.93 End of proof
% 206.31/31.93
% 206.31/31.93 Sub-proof #5 shows that the following formulas are inconsistent:
% 206.31/31.93 ----------------------------------------------------------------
% 206.31/31.93 (1) leq(all_74_14, n5)
% 206.31/31.93 (2) pred(n4) = n3
% 206.31/31.93 (3) $i(n2)
% 206.31/31.93 (4) ~ (all_74_14 = n0)
% 206.31/31.93 (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0,
% 206.31/31.93 v1) | gt(v1, v0))
% 206.31/31.93 (6) pred(n3) = n2
% 206.31/31.93 (7) all_74_14 = n4 | gt(n4, all_74_14)
% 206.31/31.93 (8) leq(n0, n5)
% 206.31/31.93 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.31/31.93 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.31/31.93 v0))
% 206.31/31.93 (10) $i(all_74_14)
% 206.31/31.93 (11) pred(n2) = n1
% 206.31/31.93 (12) a_select3(id_ds1_filter, n5, all_74_14) = all_74_13
% 206.31/31.93 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 206.31/31.93 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 206.31/31.93 (14) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 206.31/31.93 leq(n0, v0))
% 206.31/31.93 (15) leq(n5, n5)
% 206.31/31.93 (16) leq(n0, all_74_14)
% 206.31/31.93 (17) all_74_19 = n5
% 206.31/31.93 (18) $i(n4)
% 206.31/31.93 (19) $i(n3)
% 206.31/31.93 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter,
% 206.31/31.93 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_19) | ~
% 206.31/31.93 leq(v0, all_74_16) | ~ leq(n0, v1) | ~ leq(n0, v0) |
% 206.31/31.93 (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2)))
% 206.31/31.93 (21) ~ (all_74_12 = all_74_13)
% 206.31/31.93 (22) a_select3(id_ds1_filter, all_74_14, n5) = all_74_12
% 206.31/31.93 (23) $i(n5)
% 206.31/31.93 (24) all_74_16 = n5
% 206.31/31.93
% 206.31/31.93 Begin of proof
% 206.31/31.93 |
% 206.31/31.93 | BETA: splitting (7) gives:
% 206.31/31.93 |
% 206.31/31.93 | Case 1:
% 206.31/31.93 | |
% 206.31/31.93 | | (25) gt(n4, all_74_14)
% 206.31/31.93 | |
% 206.31/31.93 | | GROUND_INST: instantiating (13) with all_74_14, n4, n3, simplifying with
% 206.31/31.93 | | (2), (10), (18), (25) gives:
% 206.31/31.93 | | (26) leq(all_74_14, n3)
% 206.31/31.93 | |
% 206.31/31.93 | | GROUND_INST: instantiating (5) with all_74_14, n3, simplifying with (10),
% 206.31/31.93 | | (19), (26) gives:
% 206.31/31.93 | | (27) all_74_14 = n3 | gt(n3, all_74_14)
% 206.31/31.93 | |
% 206.31/31.93 | | BETA: splitting (27) gives:
% 206.31/31.93 | |
% 206.31/31.93 | | Case 1:
% 206.31/31.93 | | |
% 206.31/31.93 | | | (28) gt(n3, all_74_14)
% 206.31/31.93 | | |
% 206.31/31.93 | | | GROUND_INST: instantiating (13) with all_74_14, n3, n2, simplifying with
% 206.31/31.93 | | | (6), (10), (19), (28) gives:
% 206.31/31.93 | | | (29) leq(all_74_14, n2)
% 206.31/31.93 | | |
% 206.31/31.93 | | | GROUND_INST: instantiating (5) with all_74_14, n2, simplifying with (3),
% 206.31/31.93 | | | (10), (29) gives:
% 206.31/31.93 | | | (30) all_74_14 = n2 | gt(n2, all_74_14)
% 206.31/31.93 | | |
% 206.31/31.93 | | | BETA: splitting (30) gives:
% 206.31/31.93 | | |
% 206.31/31.93 | | | Case 1:
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | (31) gt(n2, all_74_14)
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | GROUND_INST: instantiating (13) with all_74_14, n2, n1, simplifying with
% 206.31/31.93 | | | | (3), (10), (11), (31) gives:
% 206.31/31.93 | | | | (32) leq(all_74_14, n1)
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | GROUND_INST: instantiating (14) with all_74_14, simplifying with (10),
% 206.31/31.93 | | | | (16), (32) gives:
% 206.31/31.93 | | | | (33) all_74_14 = n1 | all_74_14 = n0
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | BETA: splitting (33) gives:
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | Case 1:
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | (34) all_74_14 = n0
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | REDUCE: (4), (34) imply:
% 206.31/31.93 | | | | | (35) $false
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | CLOSE: (35) is inconsistent.
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | Case 2:
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | (36) all_74_14 = n1
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | REDUCE: (22), (36) imply:
% 206.31/31.93 | | | | | (37) a_select3(id_ds1_filter, n1, n5) = all_74_12
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | REDUCE: (12), (36) imply:
% 206.31/31.93 | | | | | (38) a_select3(id_ds1_filter, n5, n1) = all_74_13
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | REDUCE: (10), (36) imply:
% 206.31/31.93 | | | | | (39) $i(n1)
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | REDUCE: (1), (36) imply:
% 206.31/31.93 | | | | | (40) leq(n1, n5)
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | REDUCE: (16), (36) imply:
% 206.31/31.93 | | | | | (41) leq(n0, n1)
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | GROUND_INST: instantiating (20) with n1, n5, all_74_12, simplifying
% 206.31/31.93 | | | | | with (8), (23), (37), (39), (41) gives:
% 206.31/31.93 | | | | | (42) ~ leq(n5, all_74_19) | ~ leq(n1, all_74_16) |
% 206.31/31.93 | | | | | (a_select3(id_ds1_filter, n5, n1) = all_74_12 & $i(all_74_12))
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | BETA: splitting (42) gives:
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | Case 1:
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | (43) ~ leq(n5, all_74_19)
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | REDUCE: (17), (43) imply:
% 206.31/31.93 | | | | | | (44) ~ leq(n5, n5)
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | PRED_UNIFY: (15), (44) imply:
% 206.31/31.93 | | | | | | (45) $false
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | CLOSE: (45) is inconsistent.
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | Case 2:
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | (46) ~ leq(n1, all_74_16) | (a_select3(id_ds1_filter, n5, n1) =
% 206.31/31.93 | | | | | | all_74_12 & $i(all_74_12))
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | BETA: splitting (46) gives:
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | Case 1:
% 206.31/31.93 | | | | | | |
% 206.31/31.93 | | | | | | | (47) ~ leq(n1, all_74_16)
% 206.31/31.93 | | | | | | |
% 206.31/31.93 | | | | | | | REDUCE: (24), (47) imply:
% 206.31/31.93 | | | | | | | (48) ~ leq(n1, n5)
% 206.31/31.93 | | | | | | |
% 206.31/31.93 | | | | | | | PRED_UNIFY: (40), (48) imply:
% 206.31/31.93 | | | | | | | (49) $false
% 206.31/31.93 | | | | | | |
% 206.31/31.93 | | | | | | | CLOSE: (49) is inconsistent.
% 206.31/31.93 | | | | | | |
% 206.31/31.93 | | | | | | Case 2:
% 206.31/31.93 | | | | | | |
% 206.31/31.93 | | | | | | | (50) a_select3(id_ds1_filter, n5, n1) = all_74_12 &
% 206.31/31.93 | | | | | | | $i(all_74_12)
% 206.31/31.93 | | | | | | |
% 206.31/31.93 | | | | | | | ALPHA: (50) implies:
% 206.31/31.93 | | | | | | | (51) a_select3(id_ds1_filter, n5, n1) = all_74_12
% 206.31/31.93 | | | | | | |
% 206.31/31.93 | | | | | | | GROUND_INST: instantiating (9) with all_74_13, all_74_12, n1, n5,
% 206.31/31.93 | | | | | | | id_ds1_filter, simplifying with (38), (51) gives:
% 206.31/31.93 | | | | | | | (52) all_74_12 = all_74_13
% 206.31/31.93 | | | | | | |
% 206.31/31.93 | | | | | | | REDUCE: (21), (52) imply:
% 206.31/31.93 | | | | | | | (53) $false
% 206.31/31.93 | | | | | | |
% 206.31/31.93 | | | | | | | CLOSE: (53) is inconsistent.
% 206.31/31.93 | | | | | | |
% 206.31/31.93 | | | | | | End of split
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | End of split
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | End of split
% 206.31/31.93 | | | |
% 206.31/31.93 | | | Case 2:
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | (54) all_74_14 = n2
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | REDUCE: (22), (54) imply:
% 206.31/31.93 | | | | (55) a_select3(id_ds1_filter, n2, n5) = all_74_12
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | REDUCE: (12), (54) imply:
% 206.31/31.93 | | | | (56) a_select3(id_ds1_filter, n5, n2) = all_74_13
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | REDUCE: (1), (54) imply:
% 206.31/31.93 | | | | (57) leq(n2, n5)
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | REDUCE: (16), (54) imply:
% 206.31/31.93 | | | | (58) leq(n0, n2)
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | GROUND_INST: instantiating (20) with n2, n5, all_74_12, simplifying with
% 206.31/31.93 | | | | (3), (8), (23), (55), (58) gives:
% 206.31/31.93 | | | | (59) ~ leq(n5, all_74_19) | ~ leq(n2, all_74_16) |
% 206.31/31.93 | | | | (a_select3(id_ds1_filter, n5, n2) = all_74_12 & $i(all_74_12))
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | BETA: splitting (59) gives:
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | Case 1:
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | (60) ~ leq(n5, all_74_19)
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | REDUCE: (17), (60) imply:
% 206.31/31.93 | | | | | (61) ~ leq(n5, n5)
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | PRED_UNIFY: (15), (61) imply:
% 206.31/31.93 | | | | | (62) $false
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | CLOSE: (62) is inconsistent.
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | Case 2:
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | (63) ~ leq(n2, all_74_16) | (a_select3(id_ds1_filter, n5, n2) =
% 206.31/31.93 | | | | | all_74_12 & $i(all_74_12))
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | BETA: splitting (63) gives:
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | Case 1:
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | (64) ~ leq(n2, all_74_16)
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | REDUCE: (24), (64) imply:
% 206.31/31.93 | | | | | | (65) ~ leq(n2, n5)
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | PRED_UNIFY: (57), (65) imply:
% 206.31/31.93 | | | | | | (66) $false
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | CLOSE: (66) is inconsistent.
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | Case 2:
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | (67) a_select3(id_ds1_filter, n5, n2) = all_74_12 & $i(all_74_12)
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | ALPHA: (67) implies:
% 206.31/31.93 | | | | | | (68) a_select3(id_ds1_filter, n5, n2) = all_74_12
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | GROUND_INST: instantiating (9) with all_74_13, all_74_12, n2, n5,
% 206.31/31.93 | | | | | | id_ds1_filter, simplifying with (56), (68) gives:
% 206.31/31.93 | | | | | | (69) all_74_12 = all_74_13
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | REDUCE: (21), (69) imply:
% 206.31/31.93 | | | | | | (70) $false
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | | CLOSE: (70) is inconsistent.
% 206.31/31.93 | | | | | |
% 206.31/31.93 | | | | | End of split
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | End of split
% 206.31/31.93 | | | |
% 206.31/31.93 | | | End of split
% 206.31/31.93 | | |
% 206.31/31.93 | | Case 2:
% 206.31/31.93 | | |
% 206.31/31.93 | | | (71) all_74_14 = n3
% 206.31/31.93 | | |
% 206.31/31.93 | | | REDUCE: (22), (71) imply:
% 206.31/31.93 | | | (72) a_select3(id_ds1_filter, n3, n5) = all_74_12
% 206.31/31.93 | | |
% 206.31/31.93 | | | REDUCE: (12), (71) imply:
% 206.31/31.93 | | | (73) a_select3(id_ds1_filter, n5, n3) = all_74_13
% 206.31/31.93 | | |
% 206.31/31.93 | | | REDUCE: (1), (71) imply:
% 206.31/31.93 | | | (74) leq(n3, n5)
% 206.31/31.93 | | |
% 206.31/31.93 | | | REDUCE: (16), (71) imply:
% 206.31/31.93 | | | (75) leq(n0, n3)
% 206.31/31.93 | | |
% 206.31/31.93 | | | GROUND_INST: instantiating (20) with n3, n5, all_74_12, simplifying with
% 206.31/31.93 | | | (8), (19), (23), (72), (75) gives:
% 206.31/31.93 | | | (76) ~ leq(n5, all_74_19) | ~ leq(n3, all_74_16) |
% 206.31/31.93 | | | (a_select3(id_ds1_filter, n5, n3) = all_74_12 & $i(all_74_12))
% 206.31/31.93 | | |
% 206.31/31.93 | | | BETA: splitting (76) gives:
% 206.31/31.93 | | |
% 206.31/31.93 | | | Case 1:
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | (77) ~ leq(n5, all_74_19)
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | REDUCE: (17), (77) imply:
% 206.31/31.93 | | | | (78) ~ leq(n5, n5)
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | PRED_UNIFY: (15), (78) imply:
% 206.31/31.93 | | | | (79) $false
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | CLOSE: (79) is inconsistent.
% 206.31/31.93 | | | |
% 206.31/31.93 | | | Case 2:
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | (80) ~ leq(n3, all_74_16) | (a_select3(id_ds1_filter, n5, n3) =
% 206.31/31.93 | | | | all_74_12 & $i(all_74_12))
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | BETA: splitting (80) gives:
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | Case 1:
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | (81) ~ leq(n3, all_74_16)
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | REDUCE: (24), (81) imply:
% 206.31/31.93 | | | | | (82) ~ leq(n3, n5)
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | PRED_UNIFY: (74), (82) imply:
% 206.31/31.93 | | | | | (83) $false
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | CLOSE: (83) is inconsistent.
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | Case 2:
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | (84) a_select3(id_ds1_filter, n5, n3) = all_74_12 & $i(all_74_12)
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | ALPHA: (84) implies:
% 206.31/31.93 | | | | | (85) a_select3(id_ds1_filter, n5, n3) = all_74_12
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | GROUND_INST: instantiating (9) with all_74_13, all_74_12, n3, n5,
% 206.31/31.93 | | | | | id_ds1_filter, simplifying with (73), (85) gives:
% 206.31/31.93 | | | | | (86) all_74_12 = all_74_13
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | REDUCE: (21), (86) imply:
% 206.31/31.93 | | | | | (87) $false
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | | CLOSE: (87) is inconsistent.
% 206.31/31.93 | | | | |
% 206.31/31.93 | | | | End of split
% 206.31/31.93 | | | |
% 206.31/31.93 | | | End of split
% 206.31/31.93 | | |
% 206.31/31.93 | | End of split
% 206.31/31.93 | |
% 206.31/31.93 | Case 2:
% 206.31/31.93 | |
% 206.31/31.93 | | (88) all_74_14 = n4
% 206.31/31.93 | |
% 206.31/31.93 | | REDUCE: (22), (88) imply:
% 206.31/31.93 | | (89) a_select3(id_ds1_filter, n4, n5) = all_74_12
% 206.31/31.93 | |
% 206.31/31.93 | | REDUCE: (12), (88) imply:
% 206.31/31.93 | | (90) a_select3(id_ds1_filter, n5, n4) = all_74_13
% 206.31/31.93 | |
% 206.31/31.93 | | REDUCE: (1), (88) imply:
% 206.31/31.93 | | (91) leq(n4, n5)
% 206.31/31.93 | |
% 206.31/31.93 | | REDUCE: (16), (88) imply:
% 206.31/31.93 | | (92) leq(n0, n4)
% 206.31/31.93 | |
% 206.31/31.93 | | GROUND_INST: instantiating (20) with n4, n5, all_74_12, simplifying with
% 206.31/31.93 | | (8), (18), (23), (89), (92) gives:
% 206.31/31.93 | | (93) ~ leq(n5, all_74_19) | ~ leq(n4, all_74_16) |
% 206.31/31.93 | | (a_select3(id_ds1_filter, n5, n4) = all_74_12 & $i(all_74_12))
% 206.31/31.93 | |
% 206.31/31.93 | | BETA: splitting (93) gives:
% 206.31/31.93 | |
% 206.31/31.93 | | Case 1:
% 206.31/31.93 | | |
% 206.31/31.93 | | | (94) ~ leq(n5, all_74_19)
% 206.31/31.93 | | |
% 206.31/31.93 | | | REDUCE: (17), (94) imply:
% 206.31/31.93 | | | (95) ~ leq(n5, n5)
% 206.31/31.93 | | |
% 206.31/31.93 | | | PRED_UNIFY: (15), (95) imply:
% 206.31/31.93 | | | (96) $false
% 206.31/31.93 | | |
% 206.31/31.93 | | | CLOSE: (96) is inconsistent.
% 206.31/31.93 | | |
% 206.31/31.93 | | Case 2:
% 206.31/31.93 | | |
% 206.31/31.93 | | | (97) ~ leq(n4, all_74_16) | (a_select3(id_ds1_filter, n5, n4) =
% 206.31/31.93 | | | all_74_12 & $i(all_74_12))
% 206.31/31.93 | | |
% 206.31/31.93 | | | BETA: splitting (97) gives:
% 206.31/31.93 | | |
% 206.31/31.93 | | | Case 1:
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | (98) ~ leq(n4, all_74_16)
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | REDUCE: (24), (98) imply:
% 206.31/31.93 | | | | (99) ~ leq(n4, n5)
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | PRED_UNIFY: (91), (99) imply:
% 206.31/31.93 | | | | (100) $false
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | CLOSE: (100) is inconsistent.
% 206.31/31.93 | | | |
% 206.31/31.93 | | | Case 2:
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | (101) a_select3(id_ds1_filter, n5, n4) = all_74_12 & $i(all_74_12)
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | ALPHA: (101) implies:
% 206.31/31.93 | | | | (102) a_select3(id_ds1_filter, n5, n4) = all_74_12
% 206.31/31.93 | | | |
% 206.31/31.93 | | | | REF_CLOSE: (9), (21), (90), (102) are inconsistent by sub-proof #7.
% 206.31/31.93 | | | |
% 206.31/31.93 | | | End of split
% 206.31/31.93 | | |
% 206.31/31.93 | | End of split
% 206.31/31.93 | |
% 206.31/31.93 | End of split
% 206.31/31.93 |
% 206.31/31.93 End of proof
% 206.31/31.93
% 206.31/31.93 Sub-proof #6 shows that the following formulas are inconsistent:
% 206.31/31.93 ----------------------------------------------------------------
% 206.31/31.93 (1) pred(n4) = n3
% 206.31/31.93 (2) $i(n2)
% 206.31/31.93 (3) leq(all_74_15, n5)
% 206.31/31.93 (4) a_select3(id_ds1_filter, n5, all_74_15) = all_74_12
% 206.31/31.93 (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0,
% 206.31/31.93 v1) | gt(v1, v0))
% 206.31/31.93 (6) $i(all_74_15)
% 206.31/31.93 (7) pred(n3) = n2
% 206.31/31.93 (8) leq(n0, n5)
% 206.31/31.93 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.31/31.93 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.31/31.93 v0))
% 206.31/31.93 (10) pred(n2) = n1
% 206.31/31.93 (11) a_select3(id_ds1_filter, all_74_15, n5) = all_74_13
% 206.31/31.93 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 206.31/31.93 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 206.31/31.93 (13) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 206.31/31.93 leq(n0, v0))
% 206.31/31.93 (14) leq(n5, n5)
% 206.31/31.93 (15) all_74_19 = n5
% 206.31/31.93 (16) $i(n4)
% 206.31/31.93 (17) $i(n3)
% 206.31/31.93 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter,
% 206.31/31.93 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_19) | ~
% 206.31/31.93 leq(v0, all_74_16) | ~ leq(n0, v1) | ~ leq(n0, v0) |
% 206.31/31.93 (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2)))
% 206.31/31.93 (19) ~ (all_74_12 = all_74_13)
% 206.31/31.93 (20) $i(n5)
% 206.31/31.93 (21) all_74_16 = n5
% 206.31/31.94 (22) ~ (all_74_15 = n0)
% 206.31/31.94 (23) leq(n0, all_74_15)
% 206.31/31.94 (24) all_74_15 = n4 | gt(n4, all_74_15)
% 206.31/31.94
% 206.31/31.94 Begin of proof
% 206.31/31.94 |
% 206.31/31.94 | BETA: splitting (24) gives:
% 206.31/31.94 |
% 206.31/31.94 | Case 1:
% 206.31/31.94 | |
% 206.31/31.94 | | (25) gt(n4, all_74_15)
% 206.31/31.94 | |
% 206.31/31.94 | | GROUND_INST: instantiating (12) with all_74_15, n4, n3, simplifying with
% 206.31/31.94 | | (1), (6), (16), (25) gives:
% 206.31/31.94 | | (26) leq(all_74_15, n3)
% 206.31/31.94 | |
% 206.31/31.94 | | GROUND_INST: instantiating (5) with all_74_15, n3, simplifying with (6),
% 206.31/31.94 | | (17), (26) gives:
% 206.31/31.94 | | (27) all_74_15 = n3 | gt(n3, all_74_15)
% 206.31/31.94 | |
% 206.31/31.94 | | BETA: splitting (27) gives:
% 206.31/31.94 | |
% 206.31/31.94 | | Case 1:
% 206.31/31.94 | | |
% 206.31/31.94 | | | (28) gt(n3, all_74_15)
% 206.31/31.94 | | |
% 206.31/31.94 | | | GROUND_INST: instantiating (12) with all_74_15, n3, n2, simplifying with
% 206.31/31.94 | | | (6), (7), (17), (28) gives:
% 206.31/31.94 | | | (29) leq(all_74_15, n2)
% 206.31/31.94 | | |
% 206.31/31.94 | | | GROUND_INST: instantiating (5) with all_74_15, n2, simplifying with (2),
% 206.31/31.94 | | | (6), (29) gives:
% 206.31/31.94 | | | (30) all_74_15 = n2 | gt(n2, all_74_15)
% 206.31/31.94 | | |
% 206.31/31.94 | | | BETA: splitting (30) gives:
% 206.31/31.94 | | |
% 206.31/31.94 | | | Case 1:
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | (31) gt(n2, all_74_15)
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | GROUND_INST: instantiating (12) with all_74_15, n2, n1, simplifying with
% 206.31/31.94 | | | | (2), (6), (10), (31) gives:
% 206.31/31.94 | | | | (32) leq(all_74_15, n1)
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying with (6),
% 206.31/31.94 | | | | (23), (32) gives:
% 206.31/31.94 | | | | (33) all_74_15 = n1 | all_74_15 = n0
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | BETA: splitting (33) gives:
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | Case 1:
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | (34) all_74_15 = n0
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | REDUCE: (22), (34) imply:
% 206.31/31.94 | | | | | (35) $false
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | CLOSE: (35) is inconsistent.
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | Case 2:
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | (36) all_74_15 = n1
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | REDUCE: (11), (36) imply:
% 206.31/31.94 | | | | | (37) a_select3(id_ds1_filter, n1, n5) = all_74_13
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | REDUCE: (4), (36) imply:
% 206.31/31.94 | | | | | (38) a_select3(id_ds1_filter, n5, n1) = all_74_12
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | REDUCE: (6), (36) imply:
% 206.31/31.94 | | | | | (39) $i(n1)
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | REDUCE: (3), (36) imply:
% 206.31/31.94 | | | | | (40) leq(n1, n5)
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | REDUCE: (23), (36) imply:
% 206.31/31.94 | | | | | (41) leq(n0, n1)
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | GROUND_INST: instantiating (18) with n1, n5, all_74_13, simplifying
% 206.31/31.94 | | | | | with (8), (20), (37), (39), (41) gives:
% 206.31/31.94 | | | | | (42) ~ leq(n5, all_74_19) | ~ leq(n1, all_74_16) |
% 206.31/31.94 | | | | | (a_select3(id_ds1_filter, n5, n1) = all_74_13 & $i(all_74_13))
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | BETA: splitting (42) gives:
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | Case 1:
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | (43) ~ leq(n5, all_74_19)
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | REDUCE: (15), (43) imply:
% 206.31/31.94 | | | | | | (44) ~ leq(n5, n5)
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | PRED_UNIFY: (14), (44) imply:
% 206.31/31.94 | | | | | | (45) $false
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | CLOSE: (45) is inconsistent.
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | Case 2:
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | (46) ~ leq(n1, all_74_16) | (a_select3(id_ds1_filter, n5, n1) =
% 206.31/31.94 | | | | | | all_74_13 & $i(all_74_13))
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | BETA: splitting (46) gives:
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | Case 1:
% 206.31/31.94 | | | | | | |
% 206.31/31.94 | | | | | | | (47) ~ leq(n1, all_74_16)
% 206.31/31.94 | | | | | | |
% 206.31/31.94 | | | | | | | REDUCE: (21), (47) imply:
% 206.31/31.94 | | | | | | | (48) ~ leq(n1, n5)
% 206.31/31.94 | | | | | | |
% 206.31/31.94 | | | | | | | PRED_UNIFY: (40), (48) imply:
% 206.31/31.94 | | | | | | | (49) $false
% 206.31/31.94 | | | | | | |
% 206.31/31.94 | | | | | | | CLOSE: (49) is inconsistent.
% 206.31/31.94 | | | | | | |
% 206.31/31.94 | | | | | | Case 2:
% 206.31/31.94 | | | | | | |
% 206.31/31.94 | | | | | | | (50) a_select3(id_ds1_filter, n5, n1) = all_74_13 &
% 206.31/31.94 | | | | | | | $i(all_74_13)
% 206.31/31.94 | | | | | | |
% 206.31/31.94 | | | | | | | ALPHA: (50) implies:
% 206.31/31.94 | | | | | | | (51) a_select3(id_ds1_filter, n5, n1) = all_74_13
% 206.31/31.94 | | | | | | |
% 206.31/31.94 | | | | | | | GROUND_INST: instantiating (9) with all_74_13, all_74_12, n1, n5,
% 206.31/31.94 | | | | | | | id_ds1_filter, simplifying with (38), (51) gives:
% 206.31/31.94 | | | | | | | (52) all_74_12 = all_74_13
% 206.31/31.94 | | | | | | |
% 206.31/31.94 | | | | | | | REDUCE: (19), (52) imply:
% 206.31/31.94 | | | | | | | (53) $false
% 206.31/31.94 | | | | | | |
% 206.31/31.94 | | | | | | | CLOSE: (53) is inconsistent.
% 206.31/31.94 | | | | | | |
% 206.31/31.94 | | | | | | End of split
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | End of split
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | End of split
% 206.31/31.94 | | | |
% 206.31/31.94 | | | Case 2:
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | (54) all_74_15 = n2
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | REDUCE: (11), (54) imply:
% 206.31/31.94 | | | | (55) a_select3(id_ds1_filter, n2, n5) = all_74_13
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | REDUCE: (4), (54) imply:
% 206.31/31.94 | | | | (56) a_select3(id_ds1_filter, n5, n2) = all_74_12
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | REDUCE: (3), (54) imply:
% 206.31/31.94 | | | | (57) leq(n2, n5)
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | REDUCE: (23), (54) imply:
% 206.31/31.94 | | | | (58) leq(n0, n2)
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | GROUND_INST: instantiating (18) with n2, n5, all_74_13, simplifying with
% 206.31/31.94 | | | | (2), (8), (20), (55), (58) gives:
% 206.31/31.94 | | | | (59) ~ leq(n5, all_74_19) | ~ leq(n2, all_74_16) |
% 206.31/31.94 | | | | (a_select3(id_ds1_filter, n5, n2) = all_74_13 & $i(all_74_13))
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | BETA: splitting (59) gives:
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | Case 1:
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | (60) ~ leq(n5, all_74_19)
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | REDUCE: (15), (60) imply:
% 206.31/31.94 | | | | | (61) ~ leq(n5, n5)
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | PRED_UNIFY: (14), (61) imply:
% 206.31/31.94 | | | | | (62) $false
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | CLOSE: (62) is inconsistent.
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | Case 2:
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | (63) ~ leq(n2, all_74_16) | (a_select3(id_ds1_filter, n5, n2) =
% 206.31/31.94 | | | | | all_74_13 & $i(all_74_13))
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | BETA: splitting (63) gives:
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | Case 1:
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | (64) ~ leq(n2, all_74_16)
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | REDUCE: (21), (64) imply:
% 206.31/31.94 | | | | | | (65) ~ leq(n2, n5)
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | PRED_UNIFY: (57), (65) imply:
% 206.31/31.94 | | | | | | (66) $false
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | CLOSE: (66) is inconsistent.
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | Case 2:
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | (67) a_select3(id_ds1_filter, n5, n2) = all_74_13 & $i(all_74_13)
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | ALPHA: (67) implies:
% 206.31/31.94 | | | | | | (68) a_select3(id_ds1_filter, n5, n2) = all_74_13
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | GROUND_INST: instantiating (9) with all_74_13, all_74_12, n2, n5,
% 206.31/31.94 | | | | | | id_ds1_filter, simplifying with (56), (68) gives:
% 206.31/31.94 | | | | | | (69) all_74_12 = all_74_13
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | REDUCE: (19), (69) imply:
% 206.31/31.94 | | | | | | (70) $false
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | | CLOSE: (70) is inconsistent.
% 206.31/31.94 | | | | | |
% 206.31/31.94 | | | | | End of split
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | End of split
% 206.31/31.94 | | | |
% 206.31/31.94 | | | End of split
% 206.31/31.94 | | |
% 206.31/31.94 | | Case 2:
% 206.31/31.94 | | |
% 206.31/31.94 | | | (71) all_74_15 = n3
% 206.31/31.94 | | |
% 206.31/31.94 | | | REDUCE: (11), (71) imply:
% 206.31/31.94 | | | (72) a_select3(id_ds1_filter, n3, n5) = all_74_13
% 206.31/31.94 | | |
% 206.31/31.94 | | | REDUCE: (4), (71) imply:
% 206.31/31.94 | | | (73) a_select3(id_ds1_filter, n5, n3) = all_74_12
% 206.31/31.94 | | |
% 206.31/31.94 | | | REDUCE: (3), (71) imply:
% 206.31/31.94 | | | (74) leq(n3, n5)
% 206.31/31.94 | | |
% 206.31/31.94 | | | REDUCE: (23), (71) imply:
% 206.31/31.94 | | | (75) leq(n0, n3)
% 206.31/31.94 | | |
% 206.31/31.94 | | | GROUND_INST: instantiating (18) with n3, n5, all_74_13, simplifying with
% 206.31/31.94 | | | (8), (17), (20), (72), (75) gives:
% 206.31/31.94 | | | (76) ~ leq(n5, all_74_19) | ~ leq(n3, all_74_16) |
% 206.31/31.94 | | | (a_select3(id_ds1_filter, n5, n3) = all_74_13 & $i(all_74_13))
% 206.31/31.94 | | |
% 206.31/31.94 | | | BETA: splitting (76) gives:
% 206.31/31.94 | | |
% 206.31/31.94 | | | Case 1:
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | (77) ~ leq(n5, all_74_19)
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | REDUCE: (15), (77) imply:
% 206.31/31.94 | | | | (78) ~ leq(n5, n5)
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | PRED_UNIFY: (14), (78) imply:
% 206.31/31.94 | | | | (79) $false
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | CLOSE: (79) is inconsistent.
% 206.31/31.94 | | | |
% 206.31/31.94 | | | Case 2:
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | (80) ~ leq(n3, all_74_16) | (a_select3(id_ds1_filter, n5, n3) =
% 206.31/31.94 | | | | all_74_13 & $i(all_74_13))
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | BETA: splitting (80) gives:
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | Case 1:
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | (81) ~ leq(n3, all_74_16)
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | REDUCE: (21), (81) imply:
% 206.31/31.94 | | | | | (82) ~ leq(n3, n5)
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | PRED_UNIFY: (74), (82) imply:
% 206.31/31.94 | | | | | (83) $false
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | CLOSE: (83) is inconsistent.
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | Case 2:
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | (84) a_select3(id_ds1_filter, n5, n3) = all_74_13 & $i(all_74_13)
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | ALPHA: (84) implies:
% 206.31/31.94 | | | | | (85) a_select3(id_ds1_filter, n5, n3) = all_74_13
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | GROUND_INST: instantiating (9) with all_74_13, all_74_12, n3, n5,
% 206.31/31.94 | | | | | id_ds1_filter, simplifying with (73), (85) gives:
% 206.31/31.94 | | | | | (86) all_74_12 = all_74_13
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | REDUCE: (19), (86) imply:
% 206.31/31.94 | | | | | (87) $false
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | CLOSE: (87) is inconsistent.
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | End of split
% 206.31/31.94 | | | |
% 206.31/31.94 | | | End of split
% 206.31/31.94 | | |
% 206.31/31.94 | | End of split
% 206.31/31.94 | |
% 206.31/31.94 | Case 2:
% 206.31/31.94 | |
% 206.31/31.94 | | (88) all_74_15 = n4
% 206.31/31.94 | |
% 206.31/31.94 | | REDUCE: (11), (88) imply:
% 206.31/31.94 | | (89) a_select3(id_ds1_filter, n4, n5) = all_74_13
% 206.31/31.94 | |
% 206.31/31.94 | | REDUCE: (4), (88) imply:
% 206.31/31.94 | | (90) a_select3(id_ds1_filter, n5, n4) = all_74_12
% 206.31/31.94 | |
% 206.31/31.94 | | REDUCE: (3), (88) imply:
% 206.31/31.94 | | (91) leq(n4, n5)
% 206.31/31.94 | |
% 206.31/31.94 | | REDUCE: (23), (88) imply:
% 206.31/31.94 | | (92) leq(n0, n4)
% 206.31/31.94 | |
% 206.31/31.94 | | GROUND_INST: instantiating (18) with n4, n5, all_74_13, simplifying with
% 206.31/31.94 | | (8), (16), (20), (89), (92) gives:
% 206.31/31.94 | | (93) ~ leq(n5, all_74_19) | ~ leq(n4, all_74_16) |
% 206.31/31.94 | | (a_select3(id_ds1_filter, n5, n4) = all_74_13 & $i(all_74_13))
% 206.31/31.94 | |
% 206.31/31.94 | | BETA: splitting (93) gives:
% 206.31/31.94 | |
% 206.31/31.94 | | Case 1:
% 206.31/31.94 | | |
% 206.31/31.94 | | | (94) ~ leq(n5, all_74_19)
% 206.31/31.94 | | |
% 206.31/31.94 | | | REDUCE: (15), (94) imply:
% 206.31/31.94 | | | (95) ~ leq(n5, n5)
% 206.31/31.94 | | |
% 206.31/31.94 | | | PRED_UNIFY: (14), (95) imply:
% 206.31/31.94 | | | (96) $false
% 206.31/31.94 | | |
% 206.31/31.94 | | | CLOSE: (96) is inconsistent.
% 206.31/31.94 | | |
% 206.31/31.94 | | Case 2:
% 206.31/31.94 | | |
% 206.31/31.94 | | | (97) ~ leq(n4, all_74_16) | (a_select3(id_ds1_filter, n5, n4) =
% 206.31/31.94 | | | all_74_13 & $i(all_74_13))
% 206.31/31.94 | | |
% 206.31/31.94 | | | BETA: splitting (97) gives:
% 206.31/31.94 | | |
% 206.31/31.94 | | | Case 1:
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | (98) ~ leq(n4, all_74_16)
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | REDUCE: (21), (98) imply:
% 206.31/31.94 | | | | (99) ~ leq(n4, n5)
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | PRED_UNIFY: (91), (99) imply:
% 206.31/31.94 | | | | (100) $false
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | CLOSE: (100) is inconsistent.
% 206.31/31.94 | | | |
% 206.31/31.94 | | | Case 2:
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | (101) a_select3(id_ds1_filter, n5, n4) = all_74_13 & $i(all_74_13)
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | ALPHA: (101) implies:
% 206.31/31.94 | | | | (102) a_select3(id_ds1_filter, n5, n4) = all_74_13
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | REF_CLOSE: (9), (19), (90), (102) are inconsistent by sub-proof #7.
% 206.31/31.94 | | | |
% 206.31/31.94 | | | End of split
% 206.31/31.94 | | |
% 206.31/31.94 | | End of split
% 206.31/31.94 | |
% 206.31/31.94 | End of split
% 206.31/31.94 |
% 206.31/31.94 End of proof
% 206.31/31.94
% 206.31/31.94 Sub-proof #7 shows that the following formulas are inconsistent:
% 206.31/31.94 ----------------------------------------------------------------
% 206.31/31.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.31/31.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.31/31.94 v0))
% 206.31/31.94 (2) a_select3(id_ds1_filter, n5, n4) = all_74_12
% 206.31/31.94 (3) a_select3(id_ds1_filter, n5, n4) = all_74_13
% 206.31/31.94 (4) ~ (all_74_12 = all_74_13)
% 206.31/31.94
% 206.31/31.94 Begin of proof
% 206.31/31.94 |
% 206.31/31.94 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n4, n5,
% 206.31/31.94 | id_ds1_filter, simplifying with (2), (3) gives:
% 206.31/31.94 | (5) all_74_12 = all_74_13
% 206.31/31.94 |
% 206.31/31.94 | REDUCE: (4), (5) imply:
% 206.31/31.94 | (6) $false
% 206.31/31.94 |
% 206.31/31.94 | CLOSE: (6) is inconsistent.
% 206.31/31.94 |
% 206.31/31.94 End of proof
% 206.31/31.94
% 206.31/31.94 Sub-proof #8 shows that the following formulas are inconsistent:
% 206.31/31.94 ----------------------------------------------------------------
% 206.31/31.94 (1) leq(all_74_14, n5)
% 206.31/31.94 (2) pred(n4) = n3
% 206.31/31.94 (3) $i(n2)
% 206.31/31.94 (4) leq(all_74_15, n5)
% 206.31/31.94 (5) ~ (all_74_14 = n0)
% 206.31/31.94 (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0,
% 206.31/31.94 v1) | gt(v1, v0))
% 206.31/31.94 (7) $i(all_74_15)
% 206.31/31.94 (8) pred(n3) = n2
% 206.31/31.94 (9) all_74_14 = n4 | gt(n4, all_74_14)
% 206.31/31.94 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 206.31/31.94 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.31/31.94 v0))
% 206.31/31.94 (11) $i(all_74_14)
% 206.31/31.94 (12) pred(n2) = n1
% 206.31/31.94 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 206.31/31.94 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 206.31/31.94 (14) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 206.31/31.94 leq(n0, v0))
% 206.31/31.94 (15) leq(n0, all_74_14)
% 206.31/31.94 (16) all_74_19 = n5
% 206.31/31.94 (17) $i(n4)
% 206.31/31.94 (18) $i(n3)
% 206.31/31.94 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter,
% 206.31/31.94 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_19) | ~
% 206.31/31.94 leq(v0, all_74_16) | ~ leq(n0, v1) | ~ leq(n0, v0) |
% 206.31/31.94 (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2)))
% 206.31/31.94 (20) ~ (all_74_12 = all_74_13)
% 206.31/31.94 (21) a_select3(id_ds1_filter, all_74_15, all_74_14) = all_74_13
% 206.31/31.94 (22) a_select3(id_ds1_filter, all_74_14, all_74_15) = all_74_12
% 206.31/31.94 (23) all_74_16 = n5
% 206.31/31.94 (24) ~ (all_74_15 = n0)
% 206.31/31.94 (25) leq(n0, all_74_15)
% 206.31/31.94 (26) all_74_15 = n4 | gt(n4, all_74_15)
% 206.31/31.94
% 206.31/31.94 Begin of proof
% 206.31/31.94 |
% 206.31/31.94 | BETA: splitting (26) gives:
% 206.31/31.94 |
% 206.31/31.94 | Case 1:
% 206.31/31.94 | |
% 206.31/31.94 | | (27) gt(n4, all_74_15)
% 206.31/31.94 | |
% 206.31/31.94 | | GROUND_INST: instantiating (13) with all_74_15, n4, n3, simplifying with
% 206.31/31.94 | | (2), (7), (17), (27) gives:
% 206.31/31.94 | | (28) leq(all_74_15, n3)
% 206.31/31.94 | |
% 206.31/31.94 | | GROUND_INST: instantiating (6) with all_74_15, n3, simplifying with (7),
% 206.31/31.94 | | (18), (28) gives:
% 206.31/31.94 | | (29) all_74_15 = n3 | gt(n3, all_74_15)
% 206.31/31.94 | |
% 206.31/31.94 | | BETA: splitting (9) gives:
% 206.31/31.94 | |
% 206.31/31.94 | | Case 1:
% 206.31/31.94 | | |
% 206.31/31.94 | | | (30) gt(n4, all_74_14)
% 206.31/31.94 | | |
% 206.31/31.94 | | | GROUND_INST: instantiating (13) with all_74_14, n4, n3, simplifying with
% 206.31/31.94 | | | (2), (11), (17), (30) gives:
% 206.31/31.94 | | | (31) leq(all_74_14, n3)
% 206.31/31.94 | | |
% 206.31/31.94 | | | GROUND_INST: instantiating (6) with all_74_14, n3, simplifying with (11),
% 206.31/31.94 | | | (18), (31) gives:
% 206.31/31.94 | | | (32) all_74_14 = n3 | gt(n3, all_74_14)
% 206.31/31.94 | | |
% 206.31/31.94 | | | BETA: splitting (29) gives:
% 206.31/31.94 | | |
% 206.31/31.94 | | | Case 1:
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | (33) gt(n3, all_74_15)
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | GROUND_INST: instantiating (13) with all_74_15, n3, n2, simplifying with
% 206.31/31.94 | | | | (7), (8), (18), (33) gives:
% 206.31/31.94 | | | | (34) leq(all_74_15, n2)
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | GROUND_INST: instantiating (6) with all_74_15, n2, simplifying with (3),
% 206.31/31.94 | | | | (7), (34) gives:
% 206.31/31.94 | | | | (35) all_74_15 = n2 | gt(n2, all_74_15)
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | BETA: splitting (32) gives:
% 206.31/31.94 | | | |
% 206.31/31.94 | | | | Case 1:
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | (36) gt(n3, all_74_14)
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | GROUND_INST: instantiating (13) with all_74_14, n3, n2, simplifying
% 206.31/31.94 | | | | | with (8), (11), (18), (36) gives:
% 206.31/31.94 | | | | | (37) leq(all_74_14, n2)
% 206.31/31.94 | | | | |
% 206.31/31.94 | | | | | GROUND_INST: instantiating (6) with all_74_14, n2, simplifying with
% 206.31/31.94 | | | | | (3), (11), (37) gives:
% 206.31/31.95 | | | | | (38) all_74_14 = n2 | gt(n2, all_74_14)
% 206.31/31.95 | | | | |
% 206.31/31.95 | | | | | BETA: splitting (35) gives:
% 206.31/31.95 | | | | |
% 206.31/31.95 | | | | | Case 1:
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | (39) gt(n2, all_74_15)
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | GROUND_INST: instantiating (13) with all_74_15, n2, n1, simplifying
% 206.31/31.95 | | | | | | with (3), (7), (12), (39) gives:
% 206.31/31.95 | | | | | | (40) leq(all_74_15, n1)
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | GROUND_INST: instantiating (14) with all_74_15, simplifying with
% 206.31/31.95 | | | | | | (7), (25), (40) gives:
% 206.31/31.95 | | | | | | (41) all_74_15 = n1 | all_74_15 = n0
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | BETA: splitting (41) gives:
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | Case 1:
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | (42) all_74_15 = n0
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | REDUCE: (24), (42) imply:
% 206.31/31.95 | | | | | | | (43) $false
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | CLOSE: (43) is inconsistent.
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | Case 2:
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | (44) all_74_15 = n1
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | REDUCE: (22), (44) imply:
% 206.31/31.95 | | | | | | | (45) a_select3(id_ds1_filter, all_74_14, n1) = all_74_12
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | REDUCE: (21), (44) imply:
% 206.31/31.95 | | | | | | | (46) a_select3(id_ds1_filter, n1, all_74_14) = all_74_13
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | REDUCE: (7), (44) imply:
% 206.31/31.95 | | | | | | | (47) $i(n1)
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | REDUCE: (4), (44) imply:
% 206.31/31.95 | | | | | | | (48) leq(n1, n5)
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | REDUCE: (25), (44) imply:
% 206.31/31.95 | | | | | | | (49) leq(n0, n1)
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | BETA: splitting (38) gives:
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | Case 1:
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | (50) gt(n2, all_74_14)
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, n2, n1,
% 206.31/31.95 | | | | | | | | simplifying with (3), (11), (12), (50) gives:
% 206.31/31.95 | | | | | | | | (51) leq(all_74_14, n1)
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | GROUND_INST: instantiating (14) with all_74_14, simplifying with
% 206.31/31.95 | | | | | | | | (11), (15), (51) gives:
% 206.31/31.95 | | | | | | | | (52) all_74_14 = n1 | all_74_14 = n0
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | BETA: splitting (52) gives:
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | Case 1:
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | (53) all_74_14 = n0
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | REDUCE: (5), (53) imply:
% 206.31/31.95 | | | | | | | | | (54) $false
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | CLOSE: (54) is inconsistent.
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | Case 2:
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | (55) all_74_14 = n1
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | REDUCE: (45), (55) imply:
% 206.31/31.95 | | | | | | | | | (56) a_select3(id_ds1_filter, n1, n1) = all_74_12
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | REDUCE: (46), (55) imply:
% 206.31/31.95 | | | | | | | | | (57) a_select3(id_ds1_filter, n1, n1) = all_74_13
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | GROUND_INST: instantiating (10) with all_74_13, all_74_12, n1,
% 206.31/31.95 | | | | | | | | | n1, id_ds1_filter, simplifying with (56), (57)
% 206.31/31.95 | | | | | | | | | gives:
% 206.31/31.95 | | | | | | | | | (58) all_74_12 = all_74_13
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | REDUCE: (20), (58) imply:
% 206.31/31.95 | | | | | | | | | (59) $false
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | CLOSE: (59) is inconsistent.
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | End of split
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | Case 2:
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | (60) all_74_14 = n2
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | REDUCE: (45), (60) imply:
% 206.31/31.95 | | | | | | | | (61) a_select3(id_ds1_filter, n2, n1) = all_74_12
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | REDUCE: (46), (60) imply:
% 206.31/31.95 | | | | | | | | (62) a_select3(id_ds1_filter, n1, n2) = all_74_13
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | REDUCE: (1), (60) imply:
% 206.31/31.95 | | | | | | | | (63) leq(n2, n5)
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | REDUCE: (15), (60) imply:
% 206.31/31.95 | | | | | | | | (64) leq(n0, n2)
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | GROUND_INST: instantiating (19) with n1, n2, all_74_13,
% 206.31/31.95 | | | | | | | | simplifying with (3), (47), (49), (62), (64) gives:
% 206.31/31.95 | | | | | | | | (65) ~ leq(n2, all_74_19) | ~ leq(n1, all_74_16) |
% 206.31/31.95 | | | | | | | | (a_select3(id_ds1_filter, n2, n1) = all_74_13 &
% 206.31/31.95 | | | | | | | | $i(all_74_13))
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | BETA: splitting (65) gives:
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | Case 1:
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | (66) ~ leq(n2, all_74_19)
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | REDUCE: (16), (66) imply:
% 206.31/31.95 | | | | | | | | | (67) ~ leq(n2, n5)
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | PRED_UNIFY: (63), (67) imply:
% 206.31/31.95 | | | | | | | | | (68) $false
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | CLOSE: (68) is inconsistent.
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | Case 2:
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | (69) ~ leq(n1, all_74_16) | (a_select3(id_ds1_filter, n2,
% 206.31/31.95 | | | | | | | | | n1) = all_74_13 & $i(all_74_13))
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | BETA: splitting (69) gives:
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | Case 1:
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | (70) ~ leq(n1, all_74_16)
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | REDUCE: (23), (70) imply:
% 206.31/31.95 | | | | | | | | | | (71) ~ leq(n1, n5)
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | PRED_UNIFY: (48), (71) imply:
% 206.31/31.95 | | | | | | | | | | (72) $false
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | CLOSE: (72) is inconsistent.
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | Case 2:
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | (73) a_select3(id_ds1_filter, n2, n1) = all_74_13 &
% 206.31/31.95 | | | | | | | | | | $i(all_74_13)
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | ALPHA: (73) implies:
% 206.31/31.95 | | | | | | | | | | (74) a_select3(id_ds1_filter, n2, n1) = all_74_13
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | GROUND_INST: instantiating (10) with all_74_13, all_74_12, n1,
% 206.31/31.95 | | | | | | | | | | n2, id_ds1_filter, simplifying with (61), (74)
% 206.31/31.95 | | | | | | | | | | gives:
% 206.31/31.95 | | | | | | | | | | (75) all_74_12 = all_74_13
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | REDUCE: (20), (75) imply:
% 206.31/31.95 | | | | | | | | | | (76) $false
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | CLOSE: (76) is inconsistent.
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | End of split
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | End of split
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | End of split
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | End of split
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | Case 2:
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | (77) all_74_15 = n2
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | REDUCE: (22), (77) imply:
% 206.31/31.95 | | | | | | (78) a_select3(id_ds1_filter, all_74_14, n2) = all_74_12
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | REDUCE: (21), (77) imply:
% 206.31/31.95 | | | | | | (79) a_select3(id_ds1_filter, n2, all_74_14) = all_74_13
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | REDUCE: (4), (77) imply:
% 206.31/31.95 | | | | | | (80) leq(n2, n5)
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | REDUCE: (25), (77) imply:
% 206.31/31.95 | | | | | | (81) leq(n0, n2)
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | BETA: splitting (38) gives:
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | Case 1:
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | (82) gt(n2, all_74_14)
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | GROUND_INST: instantiating (13) with all_74_14, n2, n1,
% 206.31/31.95 | | | | | | | simplifying with (3), (11), (12), (82) gives:
% 206.31/31.95 | | | | | | | (83) leq(all_74_14, n1)
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | GROUND_INST: instantiating (14) with all_74_14, simplifying with
% 206.31/31.95 | | | | | | | (11), (15), (83) gives:
% 206.31/31.95 | | | | | | | (84) all_74_14 = n1 | all_74_14 = n0
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | BETA: splitting (84) gives:
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | Case 1:
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | (85) all_74_14 = n0
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | REDUCE: (5), (85) imply:
% 206.31/31.95 | | | | | | | | (86) $false
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | CLOSE: (86) is inconsistent.
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | Case 2:
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | (87) all_74_14 = n1
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | REDUCE: (78), (87) imply:
% 206.31/31.95 | | | | | | | | (88) a_select3(id_ds1_filter, n1, n2) = all_74_12
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | REDUCE: (79), (87) imply:
% 206.31/31.95 | | | | | | | | (89) a_select3(id_ds1_filter, n2, n1) = all_74_13
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | REDUCE: (11), (87) imply:
% 206.31/31.95 | | | | | | | | (90) $i(n1)
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | REDUCE: (1), (87) imply:
% 206.31/31.95 | | | | | | | | (91) leq(n1, n5)
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | REDUCE: (15), (87) imply:
% 206.31/31.95 | | | | | | | | (92) leq(n0, n1)
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | GROUND_INST: instantiating (19) with n1, n2, all_74_12,
% 206.31/31.95 | | | | | | | | simplifying with (3), (81), (88), (90), (92) gives:
% 206.31/31.95 | | | | | | | | (93) ~ leq(n2, all_74_19) | ~ leq(n1, all_74_16) |
% 206.31/31.95 | | | | | | | | (a_select3(id_ds1_filter, n2, n1) = all_74_12 &
% 206.31/31.95 | | | | | | | | $i(all_74_12))
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | BETA: splitting (93) gives:
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | Case 1:
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | (94) ~ leq(n2, all_74_19)
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | REDUCE: (16), (94) imply:
% 206.31/31.95 | | | | | | | | | (95) ~ leq(n2, n5)
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | PRED_UNIFY: (80), (95) imply:
% 206.31/31.95 | | | | | | | | | (96) $false
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | CLOSE: (96) is inconsistent.
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | Case 2:
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | (97) ~ leq(n1, all_74_16) | (a_select3(id_ds1_filter, n2,
% 206.31/31.95 | | | | | | | | | n1) = all_74_12 & $i(all_74_12))
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | BETA: splitting (97) gives:
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | Case 1:
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | (98) ~ leq(n1, all_74_16)
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | REDUCE: (23), (98) imply:
% 206.31/31.95 | | | | | | | | | | (99) ~ leq(n1, n5)
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | PRED_UNIFY: (91), (99) imply:
% 206.31/31.95 | | | | | | | | | | (100) $false
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | CLOSE: (100) is inconsistent.
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | Case 2:
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | (101) a_select3(id_ds1_filter, n2, n1) = all_74_12 &
% 206.31/31.95 | | | | | | | | | | $i(all_74_12)
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | ALPHA: (101) implies:
% 206.31/31.95 | | | | | | | | | | (102) a_select3(id_ds1_filter, n2, n1) = all_74_12
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | GROUND_INST: instantiating (10) with all_74_13, all_74_12, n1,
% 206.31/31.95 | | | | | | | | | | n2, id_ds1_filter, simplifying with (89), (102)
% 206.31/31.95 | | | | | | | | | | gives:
% 206.31/31.95 | | | | | | | | | | (103) all_74_12 = all_74_13
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | REDUCE: (20), (103) imply:
% 206.31/31.95 | | | | | | | | | | (104) $false
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | | CLOSE: (104) is inconsistent.
% 206.31/31.95 | | | | | | | | | |
% 206.31/31.95 | | | | | | | | | End of split
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | End of split
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | End of split
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | Case 2:
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | (105) all_74_14 = n2
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | REDUCE: (78), (105) imply:
% 206.31/31.95 | | | | | | | (106) a_select3(id_ds1_filter, n2, n2) = all_74_12
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | REDUCE: (79), (105) imply:
% 206.31/31.95 | | | | | | | (107) a_select3(id_ds1_filter, n2, n2) = all_74_13
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | GROUND_INST: instantiating (10) with all_74_13, all_74_12, n2, n2,
% 206.31/31.95 | | | | | | | id_ds1_filter, simplifying with (106), (107) gives:
% 206.31/31.95 | | | | | | | (108) all_74_12 = all_74_13
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | REDUCE: (20), (108) imply:
% 206.31/31.95 | | | | | | | (109) $false
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | CLOSE: (109) is inconsistent.
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | End of split
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | End of split
% 206.31/31.95 | | | | |
% 206.31/31.95 | | | | Case 2:
% 206.31/31.95 | | | | |
% 206.31/31.95 | | | | | (110) all_74_14 = n3
% 206.31/31.95 | | | | |
% 206.31/31.95 | | | | | REDUCE: (22), (110) imply:
% 206.31/31.95 | | | | | (111) a_select3(id_ds1_filter, n3, all_74_15) = all_74_12
% 206.31/31.95 | | | | |
% 206.31/31.95 | | | | | REDUCE: (21), (110) imply:
% 206.31/31.95 | | | | | (112) a_select3(id_ds1_filter, all_74_15, n3) = all_74_13
% 206.31/31.95 | | | | |
% 206.31/31.95 | | | | | REDUCE: (1), (110) imply:
% 206.31/31.95 | | | | | (113) leq(n3, n5)
% 206.31/31.95 | | | | |
% 206.31/31.95 | | | | | REDUCE: (15), (110) imply:
% 206.31/31.95 | | | | | (114) leq(n0, n3)
% 206.31/31.95 | | | | |
% 206.31/31.95 | | | | | BETA: splitting (35) gives:
% 206.31/31.95 | | | | |
% 206.31/31.95 | | | | | Case 1:
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | (115) gt(n2, all_74_15)
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | GROUND_INST: instantiating (13) with all_74_15, n2, n1, simplifying
% 206.31/31.95 | | | | | | with (3), (7), (12), (115) gives:
% 206.31/31.95 | | | | | | (116) leq(all_74_15, n1)
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | GROUND_INST: instantiating (14) with all_74_15, simplifying with
% 206.31/31.95 | | | | | | (7), (25), (116) gives:
% 206.31/31.95 | | | | | | (117) all_74_15 = n1 | all_74_15 = n0
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | BETA: splitting (117) gives:
% 206.31/31.95 | | | | | |
% 206.31/31.95 | | | | | | Case 1:
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | (118) all_74_15 = n0
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | REDUCE: (24), (118) imply:
% 206.31/31.95 | | | | | | | (119) $false
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | CLOSE: (119) is inconsistent.
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | Case 2:
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | (120) all_74_15 = n1
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | REDUCE: (112), (120) imply:
% 206.31/31.95 | | | | | | | (121) a_select3(id_ds1_filter, n1, n3) = all_74_13
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | REDUCE: (111), (120) imply:
% 206.31/31.95 | | | | | | | (122) a_select3(id_ds1_filter, n3, n1) = all_74_12
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | REDUCE: (7), (120) imply:
% 206.31/31.95 | | | | | | | (123) $i(n1)
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | REDUCE: (4), (120) imply:
% 206.31/31.95 | | | | | | | (124) leq(n1, n5)
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | REDUCE: (25), (120) imply:
% 206.31/31.95 | | | | | | | (125) leq(n0, n1)
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | GROUND_INST: instantiating (19) with n1, n3, all_74_13,
% 206.31/31.95 | | | | | | | simplifying with (18), (114), (121), (123), (125)
% 206.31/31.95 | | | | | | | gives:
% 206.31/31.95 | | | | | | | (126) ~ leq(n3, all_74_19) | ~ leq(n1, all_74_16) |
% 206.31/31.95 | | | | | | | (a_select3(id_ds1_filter, n3, n1) = all_74_13 &
% 206.31/31.95 | | | | | | | $i(all_74_13))
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | BETA: splitting (126) gives:
% 206.31/31.95 | | | | | | |
% 206.31/31.95 | | | | | | | Case 1:
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | (127) ~ leq(n3, all_74_19)
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | REDUCE: (16), (127) imply:
% 206.31/31.95 | | | | | | | | (128) ~ leq(n3, n5)
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | PRED_UNIFY: (113), (128) imply:
% 206.31/31.95 | | | | | | | | (129) $false
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | CLOSE: (129) is inconsistent.
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | Case 2:
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | (130) ~ leq(n1, all_74_16) | (a_select3(id_ds1_filter, n3,
% 206.31/31.95 | | | | | | | | n1) = all_74_13 & $i(all_74_13))
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | BETA: splitting (130) gives:
% 206.31/31.95 | | | | | | | |
% 206.31/31.95 | | | | | | | | Case 1:
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | (131) ~ leq(n1, all_74_16)
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | REDUCE: (23), (131) imply:
% 206.31/31.95 | | | | | | | | | (132) ~ leq(n1, n5)
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | PRED_UNIFY: (124), (132) imply:
% 206.31/31.95 | | | | | | | | | (133) $false
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | CLOSE: (133) is inconsistent.
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | Case 2:
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | (134) a_select3(id_ds1_filter, n3, n1) = all_74_13 &
% 206.31/31.95 | | | | | | | | | $i(all_74_13)
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | ALPHA: (134) implies:
% 206.31/31.95 | | | | | | | | | (135) a_select3(id_ds1_filter, n3, n1) = all_74_13
% 206.31/31.95 | | | | | | | | |
% 206.31/31.95 | | | | | | | | | REF_CLOSE: (10), (20), (122), (135) are inconsistent by
% 206.73/31.95 | | | | | | | | | sub-proof #10.
% 206.73/31.95 | | | | | | | | |
% 206.73/31.95 | | | | | | | | End of split
% 206.73/31.95 | | | | | | | |
% 206.73/31.95 | | | | | | | End of split
% 206.73/31.95 | | | | | | |
% 206.73/31.95 | | | | | | End of split
% 206.73/31.95 | | | | | |
% 206.73/31.95 | | | | | Case 2:
% 206.73/31.95 | | | | | |
% 206.73/31.95 | | | | | | (136) all_74_15 = n2
% 206.73/31.95 | | | | | |
% 206.73/31.95 | | | | | | REDUCE: (112), (136) imply:
% 206.73/31.95 | | | | | | (137) a_select3(id_ds1_filter, n2, n3) = all_74_13
% 206.73/31.95 | | | | | |
% 206.73/31.95 | | | | | | REDUCE: (111), (136) imply:
% 206.73/31.95 | | | | | | (138) a_select3(id_ds1_filter, n3, n2) = all_74_12
% 206.73/31.95 | | | | | |
% 206.73/31.95 | | | | | | REDUCE: (4), (136) imply:
% 206.73/31.95 | | | | | | (139) leq(n2, n5)
% 206.73/31.95 | | | | | |
% 206.73/31.95 | | | | | | REDUCE: (25), (136) imply:
% 206.73/31.95 | | | | | | (140) leq(n0, n2)
% 206.73/31.95 | | | | | |
% 206.73/31.95 | | | | | | GROUND_INST: instantiating (19) with n2, n3, all_74_13, simplifying
% 206.73/31.95 | | | | | | with (3), (18), (114), (137), (140) gives:
% 206.73/31.95 | | | | | | (141) ~ leq(n3, all_74_19) | ~ leq(n2, all_74_16) |
% 206.73/31.95 | | | | | | (a_select3(id_ds1_filter, n3, n2) = all_74_13 &
% 206.73/31.95 | | | | | | $i(all_74_13))
% 206.73/31.95 | | | | | |
% 206.73/31.95 | | | | | | BETA: splitting (141) gives:
% 206.73/31.95 | | | | | |
% 206.73/31.95 | | | | | | Case 1:
% 206.73/31.95 | | | | | | |
% 206.73/31.95 | | | | | | | (142) ~ leq(n3, all_74_19)
% 206.73/31.95 | | | | | | |
% 206.73/31.95 | | | | | | | REDUCE: (16), (142) imply:
% 206.73/31.95 | | | | | | | (143) ~ leq(n3, n5)
% 206.73/31.95 | | | | | | |
% 206.73/31.95 | | | | | | | PRED_UNIFY: (113), (143) imply:
% 206.73/31.95 | | | | | | | (144) $false
% 206.73/31.95 | | | | | | |
% 206.73/31.95 | | | | | | | CLOSE: (144) is inconsistent.
% 206.73/31.95 | | | | | | |
% 206.73/31.95 | | | | | | Case 2:
% 206.73/31.95 | | | | | | |
% 206.73/31.95 | | | | | | | (145) ~ leq(n2, all_74_16) | (a_select3(id_ds1_filter, n3, n2)
% 206.73/31.95 | | | | | | | = all_74_13 & $i(all_74_13))
% 206.73/31.95 | | | | | | |
% 206.73/31.95 | | | | | | | BETA: splitting (145) gives:
% 206.73/31.95 | | | | | | |
% 206.73/31.95 | | | | | | | Case 1:
% 206.73/31.95 | | | | | | | |
% 206.73/31.95 | | | | | | | | (146) ~ leq(n2, all_74_16)
% 206.73/31.95 | | | | | | | |
% 206.73/31.95 | | | | | | | | REDUCE: (23), (146) imply:
% 206.73/31.95 | | | | | | | | (147) ~ leq(n2, n5)
% 206.73/31.95 | | | | | | | |
% 206.73/31.95 | | | | | | | | PRED_UNIFY: (139), (147) imply:
% 206.73/31.95 | | | | | | | | (148) $false
% 206.73/31.95 | | | | | | | |
% 206.73/31.95 | | | | | | | | CLOSE: (148) is inconsistent.
% 206.73/31.95 | | | | | | | |
% 206.73/31.95 | | | | | | | Case 2:
% 206.73/31.95 | | | | | | | |
% 206.73/31.95 | | | | | | | | (149) a_select3(id_ds1_filter, n3, n2) = all_74_13 &
% 206.73/31.95 | | | | | | | | $i(all_74_13)
% 206.73/31.95 | | | | | | | |
% 206.73/31.95 | | | | | | | | ALPHA: (149) implies:
% 206.73/31.95 | | | | | | | | (150) a_select3(id_ds1_filter, n3, n2) = all_74_13
% 206.73/31.95 | | | | | | | |
% 206.73/31.95 | | | | | | | | GROUND_INST: instantiating (10) with all_74_13, all_74_12, n2,
% 206.73/31.95 | | | | | | | | n3, id_ds1_filter, simplifying with (138), (150)
% 206.73/31.95 | | | | | | | | gives:
% 206.73/31.95 | | | | | | | | (151) all_74_12 = all_74_13
% 206.73/31.95 | | | | | | | |
% 206.73/31.95 | | | | | | | | REDUCE: (20), (151) imply:
% 206.73/31.95 | | | | | | | | (152) $false
% 206.73/31.95 | | | | | | | |
% 206.73/31.95 | | | | | | | | CLOSE: (152) is inconsistent.
% 206.73/31.95 | | | | | | | |
% 206.73/31.95 | | | | | | | End of split
% 206.73/31.95 | | | | | | |
% 206.73/31.95 | | | | | | End of split
% 206.73/31.95 | | | | | |
% 206.73/31.95 | | | | | End of split
% 206.73/31.95 | | | | |
% 206.73/31.95 | | | | End of split
% 206.73/31.95 | | | |
% 206.73/31.95 | | | Case 2:
% 206.73/31.95 | | | |
% 206.73/31.95 | | | | (153) all_74_15 = n3
% 206.73/31.95 | | | |
% 206.73/31.95 | | | | REDUCE: (22), (153) imply:
% 206.73/31.95 | | | | (154) a_select3(id_ds1_filter, all_74_14, n3) = all_74_12
% 206.73/31.95 | | | |
% 206.73/31.95 | | | | REDUCE: (21), (153) imply:
% 206.73/31.95 | | | | (155) a_select3(id_ds1_filter, n3, all_74_14) = all_74_13
% 206.73/31.95 | | | |
% 206.73/31.95 | | | | REDUCE: (4), (153) imply:
% 206.73/31.95 | | | | (156) leq(n3, n5)
% 206.73/31.95 | | | |
% 206.73/31.95 | | | | REDUCE: (25), (153) imply:
% 206.73/31.95 | | | | (157) leq(n0, n3)
% 206.73/31.95 | | | |
% 206.73/31.95 | | | | BETA: splitting (32) gives:
% 206.73/31.95 | | | |
% 206.73/31.95 | | | | Case 1:
% 206.73/31.95 | | | | |
% 206.73/31.95 | | | | | (158) gt(n3, all_74_14)
% 206.73/31.95 | | | | |
% 206.73/31.95 | | | | | GROUND_INST: instantiating (13) with all_74_14, n3, n2, simplifying
% 206.73/31.95 | | | | | with (8), (11), (18), (158) gives:
% 206.73/31.96 | | | | | (159) leq(all_74_14, n2)
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | GROUND_INST: instantiating (6) with all_74_14, n2, simplifying with
% 206.73/31.96 | | | | | (3), (11), (159) gives:
% 206.73/31.96 | | | | | (160) all_74_14 = n2 | gt(n2, all_74_14)
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | BETA: splitting (160) gives:
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | Case 1:
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | (161) gt(n2, all_74_14)
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | GROUND_INST: instantiating (13) with all_74_14, n2, n1, simplifying
% 206.73/31.96 | | | | | | with (3), (11), (12), (161) gives:
% 206.73/31.96 | | | | | | (162) leq(all_74_14, n1)
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | GROUND_INST: instantiating (14) with all_74_14, simplifying with
% 206.73/31.96 | | | | | | (11), (15), (162) gives:
% 206.73/31.96 | | | | | | (163) all_74_14 = n1 | all_74_14 = n0
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | BETA: splitting (163) gives:
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | Case 1:
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | (164) all_74_14 = n0
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | REDUCE: (5), (164) imply:
% 206.73/31.96 | | | | | | | (165) $false
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | CLOSE: (165) is inconsistent.
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | Case 2:
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | (166) all_74_14 = n1
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | REDUCE: (154), (166) imply:
% 206.73/31.96 | | | | | | | (167) a_select3(id_ds1_filter, n1, n3) = all_74_12
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | REDUCE: (155), (166) imply:
% 206.73/31.96 | | | | | | | (168) a_select3(id_ds1_filter, n3, n1) = all_74_13
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | REDUCE: (11), (166) imply:
% 206.73/31.96 | | | | | | | (169) $i(n1)
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | REDUCE: (1), (166) imply:
% 206.73/31.96 | | | | | | | (170) leq(n1, n5)
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | REDUCE: (15), (166) imply:
% 206.73/31.96 | | | | | | | (171) leq(n0, n1)
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | GROUND_INST: instantiating (19) with n1, n3, all_74_12,
% 206.73/31.96 | | | | | | | simplifying with (18), (157), (167), (169), (171)
% 206.73/31.96 | | | | | | | gives:
% 206.73/31.96 | | | | | | | (172) ~ leq(n3, all_74_19) | ~ leq(n1, all_74_16) |
% 206.73/31.96 | | | | | | | (a_select3(id_ds1_filter, n3, n1) = all_74_12 &
% 206.73/31.96 | | | | | | | $i(all_74_12))
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | BETA: splitting (172) gives:
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | Case 1:
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | (173) ~ leq(n3, all_74_19)
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | REDUCE: (16), (173) imply:
% 206.73/31.96 | | | | | | | | (174) ~ leq(n3, n5)
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | PRED_UNIFY: (156), (174) imply:
% 206.73/31.96 | | | | | | | | (175) $false
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | CLOSE: (175) is inconsistent.
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | Case 2:
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | (176) ~ leq(n1, all_74_16) | (a_select3(id_ds1_filter, n3,
% 206.73/31.96 | | | | | | | | n1) = all_74_12 & $i(all_74_12))
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | BETA: splitting (176) gives:
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | Case 1:
% 206.73/31.96 | | | | | | | | |
% 206.73/31.96 | | | | | | | | | (177) ~ leq(n1, all_74_16)
% 206.73/31.96 | | | | | | | | |
% 206.73/31.96 | | | | | | | | | REDUCE: (23), (177) imply:
% 206.73/31.96 | | | | | | | | | (178) ~ leq(n1, n5)
% 206.73/31.96 | | | | | | | | |
% 206.73/31.96 | | | | | | | | | PRED_UNIFY: (170), (178) imply:
% 206.73/31.96 | | | | | | | | | (179) $false
% 206.73/31.96 | | | | | | | | |
% 206.73/31.96 | | | | | | | | | CLOSE: (179) is inconsistent.
% 206.73/31.96 | | | | | | | | |
% 206.73/31.96 | | | | | | | | Case 2:
% 206.73/31.96 | | | | | | | | |
% 206.73/31.96 | | | | | | | | | (180) a_select3(id_ds1_filter, n3, n1) = all_74_12 &
% 206.73/31.96 | | | | | | | | | $i(all_74_12)
% 206.73/31.96 | | | | | | | | |
% 206.73/31.96 | | | | | | | | | ALPHA: (180) implies:
% 206.73/31.96 | | | | | | | | | (181) a_select3(id_ds1_filter, n3, n1) = all_74_12
% 206.73/31.96 | | | | | | | | |
% 206.73/31.96 | | | | | | | | | REF_CLOSE: (10), (20), (168), (181) are inconsistent by
% 206.73/31.96 | | | | | | | | | sub-proof #10.
% 206.73/31.96 | | | | | | | | |
% 206.73/31.96 | | | | | | | | End of split
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | End of split
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | End of split
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | Case 2:
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | (182) all_74_14 = n2
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | REDUCE: (154), (182) imply:
% 206.73/31.96 | | | | | | (183) a_select3(id_ds1_filter, n2, n3) = all_74_12
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | REDUCE: (155), (182) imply:
% 206.73/31.96 | | | | | | (184) a_select3(id_ds1_filter, n3, n2) = all_74_13
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | REDUCE: (1), (182) imply:
% 206.73/31.96 | | | | | | (185) leq(n2, n5)
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | REDUCE: (15), (182) imply:
% 206.73/31.96 | | | | | | (186) leq(n0, n2)
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | GROUND_INST: instantiating (19) with n2, n3, all_74_12, simplifying
% 206.73/31.96 | | | | | | with (3), (18), (157), (183), (186) gives:
% 206.73/31.96 | | | | | | (187) ~ leq(n3, all_74_19) | ~ leq(n2, all_74_16) |
% 206.73/31.96 | | | | | | (a_select3(id_ds1_filter, n3, n2) = all_74_12 &
% 206.73/31.96 | | | | | | $i(all_74_12))
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | BETA: splitting (187) gives:
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | Case 1:
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | (188) ~ leq(n3, all_74_19)
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | REDUCE: (16), (188) imply:
% 206.73/31.96 | | | | | | | (189) ~ leq(n3, n5)
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | PRED_UNIFY: (156), (189) imply:
% 206.73/31.96 | | | | | | | (190) $false
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | CLOSE: (190) is inconsistent.
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | Case 2:
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | (191) ~ leq(n2, all_74_16) | (a_select3(id_ds1_filter, n3, n2)
% 206.73/31.96 | | | | | | | = all_74_12 & $i(all_74_12))
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | BETA: splitting (191) gives:
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | Case 1:
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | (192) ~ leq(n2, all_74_16)
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | REDUCE: (23), (192) imply:
% 206.73/31.96 | | | | | | | | (193) ~ leq(n2, n5)
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | PRED_UNIFY: (185), (193) imply:
% 206.73/31.96 | | | | | | | | (194) $false
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | CLOSE: (194) is inconsistent.
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | Case 2:
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | (195) a_select3(id_ds1_filter, n3, n2) = all_74_12 &
% 206.73/31.96 | | | | | | | | $i(all_74_12)
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | ALPHA: (195) implies:
% 206.73/31.96 | | | | | | | | (196) a_select3(id_ds1_filter, n3, n2) = all_74_12
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | GROUND_INST: instantiating (10) with all_74_13, all_74_12, n2,
% 206.73/31.96 | | | | | | | | n3, id_ds1_filter, simplifying with (184), (196)
% 206.73/31.96 | | | | | | | | gives:
% 206.73/31.96 | | | | | | | | (197) all_74_12 = all_74_13
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | REDUCE: (20), (197) imply:
% 206.73/31.96 | | | | | | | | (198) $false
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | CLOSE: (198) is inconsistent.
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | End of split
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | End of split
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | End of split
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | Case 2:
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | (199) all_74_14 = n3
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | REDUCE: (154), (199) imply:
% 206.73/31.96 | | | | | (200) a_select3(id_ds1_filter, n3, n3) = all_74_12
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | REDUCE: (155), (199) imply:
% 206.73/31.96 | | | | | (201) a_select3(id_ds1_filter, n3, n3) = all_74_13
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | GROUND_INST: instantiating (10) with all_74_13, all_74_12, n3, n3,
% 206.73/31.96 | | | | | id_ds1_filter, simplifying with (200), (201) gives:
% 206.73/31.96 | | | | | (202) all_74_12 = all_74_13
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | REDUCE: (20), (202) imply:
% 206.73/31.96 | | | | | (203) $false
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | CLOSE: (203) is inconsistent.
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | End of split
% 206.73/31.96 | | | |
% 206.73/31.96 | | | End of split
% 206.73/31.96 | | |
% 206.73/31.96 | | Case 2:
% 206.73/31.96 | | |
% 206.73/31.96 | | | (204) all_74_14 = n4
% 206.73/31.96 | | |
% 206.73/31.96 | | | REDUCE: (22), (204) imply:
% 206.73/31.96 | | | (205) a_select3(id_ds1_filter, n4, all_74_15) = all_74_12
% 206.73/31.96 | | |
% 206.73/31.96 | | | REDUCE: (21), (204) imply:
% 206.73/31.96 | | | (206) a_select3(id_ds1_filter, all_74_15, n4) = all_74_13
% 206.73/31.96 | | |
% 206.73/31.96 | | | REDUCE: (1), (204) imply:
% 206.73/31.96 | | | (207) leq(n4, n5)
% 206.73/31.96 | | |
% 206.73/31.96 | | | REDUCE: (15), (204) imply:
% 206.73/31.96 | | | (208) leq(n0, n4)
% 206.73/31.96 | | |
% 206.73/31.96 | | | BETA: splitting (29) gives:
% 206.73/31.96 | | |
% 206.73/31.96 | | | Case 1:
% 206.73/31.96 | | | |
% 206.73/31.96 | | | | (209) gt(n3, all_74_15)
% 206.73/31.96 | | | |
% 206.73/31.96 | | | | GROUND_INST: instantiating (13) with all_74_15, n3, n2, simplifying with
% 206.73/31.96 | | | | (7), (8), (18), (209) gives:
% 206.73/31.96 | | | | (210) leq(all_74_15, n2)
% 206.73/31.96 | | | |
% 206.73/31.96 | | | | GROUND_INST: instantiating (6) with all_74_15, n2, simplifying with (3),
% 206.73/31.96 | | | | (7), (210) gives:
% 206.73/31.96 | | | | (211) all_74_15 = n2 | gt(n2, all_74_15)
% 206.73/31.96 | | | |
% 206.73/31.96 | | | | BETA: splitting (211) gives:
% 206.73/31.96 | | | |
% 206.73/31.96 | | | | Case 1:
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | (212) gt(n2, all_74_15)
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | GROUND_INST: instantiating (13) with all_74_15, n2, n1, simplifying
% 206.73/31.96 | | | | | with (3), (7), (12), (212) gives:
% 206.73/31.96 | | | | | (213) leq(all_74_15, n1)
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | GROUND_INST: instantiating (14) with all_74_15, simplifying with (7),
% 206.73/31.96 | | | | | (25), (213) gives:
% 206.73/31.96 | | | | | (214) all_74_15 = n1 | all_74_15 = n0
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | BETA: splitting (214) gives:
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | Case 1:
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | (215) all_74_15 = n0
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | REDUCE: (24), (215) imply:
% 206.73/31.96 | | | | | | (216) $false
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | CLOSE: (216) is inconsistent.
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | Case 2:
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | (217) all_74_15 = n1
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | REDUCE: (206), (217) imply:
% 206.73/31.96 | | | | | | (218) a_select3(id_ds1_filter, n1, n4) = all_74_13
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | REDUCE: (205), (217) imply:
% 206.73/31.96 | | | | | | (219) a_select3(id_ds1_filter, n4, n1) = all_74_12
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | REDUCE: (7), (217) imply:
% 206.73/31.96 | | | | | | (220) $i(n1)
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | REDUCE: (4), (217) imply:
% 206.73/31.96 | | | | | | (221) leq(n1, n5)
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | REDUCE: (25), (217) imply:
% 206.73/31.96 | | | | | | (222) leq(n0, n1)
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | GROUND_INST: instantiating (19) with n1, n4, all_74_13, simplifying
% 206.73/31.96 | | | | | | with (17), (208), (218), (220), (222) gives:
% 206.73/31.96 | | | | | | (223) ~ leq(n4, all_74_19) | ~ leq(n1, all_74_16) |
% 206.73/31.96 | | | | | | (a_select3(id_ds1_filter, n4, n1) = all_74_13 &
% 206.73/31.96 | | | | | | $i(all_74_13))
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | BETA: splitting (223) gives:
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | Case 1:
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | (224) ~ leq(n4, all_74_19)
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | REDUCE: (16), (224) imply:
% 206.73/31.96 | | | | | | | (225) ~ leq(n4, n5)
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | PRED_UNIFY: (207), (225) imply:
% 206.73/31.96 | | | | | | | (226) $false
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | CLOSE: (226) is inconsistent.
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | Case 2:
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | (227) ~ leq(n1, all_74_16) | (a_select3(id_ds1_filter, n4, n1)
% 206.73/31.96 | | | | | | | = all_74_13 & $i(all_74_13))
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | BETA: splitting (227) gives:
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | Case 1:
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | (228) ~ leq(n1, all_74_16)
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | REDUCE: (23), (228) imply:
% 206.73/31.96 | | | | | | | | (229) ~ leq(n1, n5)
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | PRED_UNIFY: (221), (229) imply:
% 206.73/31.96 | | | | | | | | (230) $false
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | CLOSE: (230) is inconsistent.
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | Case 2:
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | (231) a_select3(id_ds1_filter, n4, n1) = all_74_13 &
% 206.73/31.96 | | | | | | | | $i(all_74_13)
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | ALPHA: (231) implies:
% 206.73/31.96 | | | | | | | | (232) a_select3(id_ds1_filter, n4, n1) = all_74_13
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | | REF_CLOSE: (10), (20), (219), (232) are inconsistent by
% 206.73/31.96 | | | | | | | | sub-proof #9.
% 206.73/31.96 | | | | | | | |
% 206.73/31.96 | | | | | | | End of split
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | End of split
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | End of split
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | Case 2:
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | (233) all_74_15 = n2
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | REDUCE: (206), (233) imply:
% 206.73/31.96 | | | | | (234) a_select3(id_ds1_filter, n2, n4) = all_74_13
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | REDUCE: (205), (233) imply:
% 206.73/31.96 | | | | | (235) a_select3(id_ds1_filter, n4, n2) = all_74_12
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | REDUCE: (4), (233) imply:
% 206.73/31.96 | | | | | (236) leq(n2, n5)
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | REDUCE: (25), (233) imply:
% 206.73/31.96 | | | | | (237) leq(n0, n2)
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | GROUND_INST: instantiating (19) with n2, n4, all_74_13, simplifying
% 206.73/31.96 | | | | | with (3), (17), (208), (234), (237) gives:
% 206.73/31.96 | | | | | (238) ~ leq(n4, all_74_19) | ~ leq(n2, all_74_16) |
% 206.73/31.96 | | | | | (a_select3(id_ds1_filter, n4, n2) = all_74_13 &
% 206.73/31.96 | | | | | $i(all_74_13))
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | BETA: splitting (238) gives:
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | Case 1:
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | (239) ~ leq(n4, all_74_19)
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | REDUCE: (16), (239) imply:
% 206.73/31.96 | | | | | | (240) ~ leq(n4, n5)
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | PRED_UNIFY: (207), (240) imply:
% 206.73/31.96 | | | | | | (241) $false
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | CLOSE: (241) is inconsistent.
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | Case 2:
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | (242) ~ leq(n2, all_74_16) | (a_select3(id_ds1_filter, n4, n2) =
% 206.73/31.96 | | | | | | all_74_13 & $i(all_74_13))
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | BETA: splitting (242) gives:
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | Case 1:
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | (243) ~ leq(n2, all_74_16)
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | REDUCE: (23), (243) imply:
% 206.73/31.96 | | | | | | | (244) ~ leq(n2, n5)
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | PRED_UNIFY: (236), (244) imply:
% 206.73/31.96 | | | | | | | (245) $false
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | CLOSE: (245) is inconsistent.
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | Case 2:
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | (246) a_select3(id_ds1_filter, n4, n2) = all_74_13 &
% 206.73/31.96 | | | | | | | $i(all_74_13)
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | ALPHA: (246) implies:
% 206.73/31.96 | | | | | | | (247) a_select3(id_ds1_filter, n4, n2) = all_74_13
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | GROUND_INST: instantiating (10) with all_74_13, all_74_12, n2, n4,
% 206.73/31.96 | | | | | | | id_ds1_filter, simplifying with (235), (247) gives:
% 206.73/31.96 | | | | | | | (248) all_74_12 = all_74_13
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | REDUCE: (20), (248) imply:
% 206.73/31.96 | | | | | | | (249) $false
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | | CLOSE: (249) is inconsistent.
% 206.73/31.96 | | | | | | |
% 206.73/31.96 | | | | | | End of split
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | End of split
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | End of split
% 206.73/31.96 | | | |
% 206.73/31.96 | | | Case 2:
% 206.73/31.96 | | | |
% 206.73/31.96 | | | | (250) all_74_15 = n3
% 206.73/31.96 | | | |
% 206.73/31.96 | | | | REDUCE: (206), (250) imply:
% 206.73/31.96 | | | | (251) a_select3(id_ds1_filter, n3, n4) = all_74_13
% 206.73/31.96 | | | |
% 206.73/31.96 | | | | REDUCE: (205), (250) imply:
% 206.73/31.96 | | | | (252) a_select3(id_ds1_filter, n4, n3) = all_74_12
% 206.73/31.96 | | | |
% 206.73/31.96 | | | | REDUCE: (4), (250) imply:
% 206.73/31.96 | | | | (253) leq(n3, n5)
% 206.73/31.96 | | | |
% 206.73/31.96 | | | | REDUCE: (25), (250) imply:
% 206.73/31.96 | | | | (254) leq(n0, n3)
% 206.73/31.96 | | | |
% 206.73/31.96 | | | | GROUND_INST: instantiating (19) with n3, n4, all_74_13, simplifying with
% 206.73/31.96 | | | | (17), (18), (208), (251), (254) gives:
% 206.73/31.96 | | | | (255) ~ leq(n4, all_74_19) | ~ leq(n3, all_74_16) |
% 206.73/31.96 | | | | (a_select3(id_ds1_filter, n4, n3) = all_74_13 & $i(all_74_13))
% 206.73/31.96 | | | |
% 206.73/31.96 | | | | BETA: splitting (255) gives:
% 206.73/31.96 | | | |
% 206.73/31.96 | | | | Case 1:
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | (256) ~ leq(n4, all_74_19)
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | REDUCE: (16), (256) imply:
% 206.73/31.96 | | | | | (257) ~ leq(n4, n5)
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | PRED_UNIFY: (207), (257) imply:
% 206.73/31.96 | | | | | (258) $false
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | CLOSE: (258) is inconsistent.
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | Case 2:
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | (259) ~ leq(n3, all_74_16) | (a_select3(id_ds1_filter, n4, n3) =
% 206.73/31.96 | | | | | all_74_13 & $i(all_74_13))
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | BETA: splitting (259) gives:
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | | Case 1:
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | (260) ~ leq(n3, all_74_16)
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | REDUCE: (23), (260) imply:
% 206.73/31.96 | | | | | | (261) ~ leq(n3, n5)
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | PRED_UNIFY: (253), (261) imply:
% 206.73/31.96 | | | | | | (262) $false
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | CLOSE: (262) is inconsistent.
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | Case 2:
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | (263) a_select3(id_ds1_filter, n4, n3) = all_74_13 &
% 206.73/31.96 | | | | | | $i(all_74_13)
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | ALPHA: (263) implies:
% 206.73/31.96 | | | | | | (264) a_select3(id_ds1_filter, n4, n3) = all_74_13
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | GROUND_INST: instantiating (10) with all_74_13, all_74_12, n3, n4,
% 206.73/31.96 | | | | | | id_ds1_filter, simplifying with (252), (264) gives:
% 206.73/31.96 | | | | | | (265) all_74_12 = all_74_13
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | REDUCE: (20), (265) imply:
% 206.73/31.96 | | | | | | (266) $false
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | | CLOSE: (266) is inconsistent.
% 206.73/31.96 | | | | | |
% 206.73/31.96 | | | | | End of split
% 206.73/31.96 | | | | |
% 206.73/31.96 | | | | End of split
% 206.73/31.96 | | | |
% 206.73/31.96 | | | End of split
% 206.73/31.96 | | |
% 206.73/31.96 | | End of split
% 206.73/31.96 | |
% 206.73/31.96 | Case 2:
% 206.73/31.96 | |
% 206.73/31.96 | | (267) all_74_15 = n4
% 206.73/31.96 | |
% 206.73/31.96 | | REDUCE: (22), (267) imply:
% 206.73/31.96 | | (268) a_select3(id_ds1_filter, all_74_14, n4) = all_74_12
% 206.73/31.96 | |
% 206.73/31.96 | | REDUCE: (21), (267) imply:
% 206.73/31.96 | | (269) a_select3(id_ds1_filter, n4, all_74_14) = all_74_13
% 206.73/31.96 | |
% 206.73/31.96 | | REDUCE: (4), (267) imply:
% 206.73/31.96 | | (270) leq(n4, n5)
% 206.73/31.96 | |
% 206.73/31.96 | | REDUCE: (25), (267) imply:
% 206.73/31.96 | | (271) leq(n0, n4)
% 206.73/31.96 | |
% 206.73/31.96 | | BETA: splitting (9) gives:
% 206.73/31.96 | |
% 206.73/31.96 | | Case 1:
% 206.73/31.96 | | |
% 206.73/31.96 | | | (272) gt(n4, all_74_14)
% 206.73/31.96 | | |
% 206.73/31.96 | | | GROUND_INST: instantiating (13) with all_74_14, n4, n3, simplifying with
% 206.73/31.96 | | | (2), (11), (17), (272) gives:
% 206.73/31.96 | | | (273) leq(all_74_14, n3)
% 206.73/31.96 | | |
% 206.73/31.96 | | | GROUND_INST: instantiating (6) with all_74_14, n3, simplifying with (11),
% 206.73/31.96 | | | (18), (273) gives:
% 206.73/31.97 | | | (274) all_74_14 = n3 | gt(n3, all_74_14)
% 206.73/31.97 | | |
% 206.73/31.97 | | | BETA: splitting (274) gives:
% 206.73/31.97 | | |
% 206.73/31.97 | | | Case 1:
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | (275) gt(n3, all_74_14)
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | GROUND_INST: instantiating (13) with all_74_14, n3, n2, simplifying with
% 206.73/31.97 | | | | (8), (11), (18), (275) gives:
% 206.73/31.97 | | | | (276) leq(all_74_14, n2)
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | GROUND_INST: instantiating (6) with all_74_14, n2, simplifying with (3),
% 206.73/31.97 | | | | (11), (276) gives:
% 206.73/31.97 | | | | (277) all_74_14 = n2 | gt(n2, all_74_14)
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | BETA: splitting (277) gives:
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | Case 1:
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | (278) gt(n2, all_74_14)
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | GROUND_INST: instantiating (13) with all_74_14, n2, n1, simplifying
% 206.73/31.97 | | | | | with (3), (11), (12), (278) gives:
% 206.73/31.97 | | | | | (279) leq(all_74_14, n1)
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | GROUND_INST: instantiating (14) with all_74_14, simplifying with (11),
% 206.73/31.97 | | | | | (15), (279) gives:
% 206.73/31.97 | | | | | (280) all_74_14 = n1 | all_74_14 = n0
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | BETA: splitting (280) gives:
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | Case 1:
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | (281) all_74_14 = n0
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | REDUCE: (5), (281) imply:
% 206.73/31.97 | | | | | | (282) $false
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | CLOSE: (282) is inconsistent.
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | Case 2:
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | (283) all_74_14 = n1
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | REDUCE: (268), (283) imply:
% 206.73/31.97 | | | | | | (284) a_select3(id_ds1_filter, n1, n4) = all_74_12
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | REDUCE: (269), (283) imply:
% 206.73/31.97 | | | | | | (285) a_select3(id_ds1_filter, n4, n1) = all_74_13
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | REDUCE: (11), (283) imply:
% 206.73/31.97 | | | | | | (286) $i(n1)
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | REDUCE: (1), (283) imply:
% 206.73/31.97 | | | | | | (287) leq(n1, n5)
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | REDUCE: (15), (283) imply:
% 206.73/31.97 | | | | | | (288) leq(n0, n1)
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | GROUND_INST: instantiating (19) with n1, n4, all_74_12, simplifying
% 206.73/31.97 | | | | | | with (17), (271), (284), (286), (288) gives:
% 206.73/31.97 | | | | | | (289) ~ leq(n4, all_74_19) | ~ leq(n1, all_74_16) |
% 206.73/31.97 | | | | | | (a_select3(id_ds1_filter, n4, n1) = all_74_12 &
% 206.73/31.97 | | | | | | $i(all_74_12))
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | BETA: splitting (289) gives:
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | Case 1:
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | (290) ~ leq(n4, all_74_19)
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | REDUCE: (16), (290) imply:
% 206.73/31.97 | | | | | | | (291) ~ leq(n4, n5)
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | PRED_UNIFY: (270), (291) imply:
% 206.73/31.97 | | | | | | | (292) $false
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | CLOSE: (292) is inconsistent.
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | Case 2:
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | (293) ~ leq(n1, all_74_16) | (a_select3(id_ds1_filter, n4, n1)
% 206.73/31.97 | | | | | | | = all_74_12 & $i(all_74_12))
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | BETA: splitting (293) gives:
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | Case 1:
% 206.73/31.97 | | | | | | | |
% 206.73/31.97 | | | | | | | | (294) ~ leq(n1, all_74_16)
% 206.73/31.97 | | | | | | | |
% 206.73/31.97 | | | | | | | | REDUCE: (23), (294) imply:
% 206.73/31.97 | | | | | | | | (295) ~ leq(n1, n5)
% 206.73/31.97 | | | | | | | |
% 206.73/31.97 | | | | | | | | PRED_UNIFY: (287), (295) imply:
% 206.73/31.97 | | | | | | | | (296) $false
% 206.73/31.97 | | | | | | | |
% 206.73/31.97 | | | | | | | | CLOSE: (296) is inconsistent.
% 206.73/31.97 | | | | | | | |
% 206.73/31.97 | | | | | | | Case 2:
% 206.73/31.97 | | | | | | | |
% 206.73/31.97 | | | | | | | | (297) a_select3(id_ds1_filter, n4, n1) = all_74_12 &
% 206.73/31.97 | | | | | | | | $i(all_74_12)
% 206.73/31.97 | | | | | | | |
% 206.73/31.97 | | | | | | | | ALPHA: (297) implies:
% 206.73/31.97 | | | | | | | | (298) a_select3(id_ds1_filter, n4, n1) = all_74_12
% 206.73/31.97 | | | | | | | |
% 206.73/31.97 | | | | | | | | REF_CLOSE: (10), (20), (285), (298) are inconsistent by
% 206.73/31.97 | | | | | | | | sub-proof #9.
% 206.73/31.97 | | | | | | | |
% 206.73/31.97 | | | | | | | End of split
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | End of split
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | End of split
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | Case 2:
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | (299) all_74_14 = n2
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | REDUCE: (268), (299) imply:
% 206.73/31.97 | | | | | (300) a_select3(id_ds1_filter, n2, n4) = all_74_12
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | REDUCE: (269), (299) imply:
% 206.73/31.97 | | | | | (301) a_select3(id_ds1_filter, n4, n2) = all_74_13
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | REDUCE: (1), (299) imply:
% 206.73/31.97 | | | | | (302) leq(n2, n5)
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | REDUCE: (15), (299) imply:
% 206.73/31.97 | | | | | (303) leq(n0, n2)
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | GROUND_INST: instantiating (19) with n2, n4, all_74_12, simplifying
% 206.73/31.97 | | | | | with (3), (17), (271), (300), (303) gives:
% 206.73/31.97 | | | | | (304) ~ leq(n4, all_74_19) | ~ leq(n2, all_74_16) |
% 206.73/31.97 | | | | | (a_select3(id_ds1_filter, n4, n2) = all_74_12 &
% 206.73/31.97 | | | | | $i(all_74_12))
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | BETA: splitting (304) gives:
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | Case 1:
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | (305) ~ leq(n4, all_74_19)
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | REDUCE: (16), (305) imply:
% 206.73/31.97 | | | | | | (306) ~ leq(n4, n5)
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | PRED_UNIFY: (270), (306) imply:
% 206.73/31.97 | | | | | | (307) $false
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | CLOSE: (307) is inconsistent.
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | Case 2:
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | (308) ~ leq(n2, all_74_16) | (a_select3(id_ds1_filter, n4, n2) =
% 206.73/31.97 | | | | | | all_74_12 & $i(all_74_12))
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | BETA: splitting (308) gives:
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | Case 1:
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | (309) ~ leq(n2, all_74_16)
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | REDUCE: (23), (309) imply:
% 206.73/31.97 | | | | | | | (310) ~ leq(n2, n5)
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | PRED_UNIFY: (302), (310) imply:
% 206.73/31.97 | | | | | | | (311) $false
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | CLOSE: (311) is inconsistent.
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | Case 2:
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | (312) a_select3(id_ds1_filter, n4, n2) = all_74_12 &
% 206.73/31.97 | | | | | | | $i(all_74_12)
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | ALPHA: (312) implies:
% 206.73/31.97 | | | | | | | (313) a_select3(id_ds1_filter, n4, n2) = all_74_12
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | GROUND_INST: instantiating (10) with all_74_13, all_74_12, n2, n4,
% 206.73/31.97 | | | | | | | id_ds1_filter, simplifying with (301), (313) gives:
% 206.73/31.97 | | | | | | | (314) all_74_12 = all_74_13
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | REDUCE: (20), (314) imply:
% 206.73/31.97 | | | | | | | (315) $false
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | | CLOSE: (315) is inconsistent.
% 206.73/31.97 | | | | | | |
% 206.73/31.97 | | | | | | End of split
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | End of split
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | End of split
% 206.73/31.97 | | | |
% 206.73/31.97 | | | Case 2:
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | (316) all_74_14 = n3
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | REDUCE: (268), (316) imply:
% 206.73/31.97 | | | | (317) a_select3(id_ds1_filter, n3, n4) = all_74_12
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | REDUCE: (269), (316) imply:
% 206.73/31.97 | | | | (318) a_select3(id_ds1_filter, n4, n3) = all_74_13
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | REDUCE: (1), (316) imply:
% 206.73/31.97 | | | | (319) leq(n3, n5)
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | REDUCE: (15), (316) imply:
% 206.73/31.97 | | | | (320) leq(n0, n3)
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | GROUND_INST: instantiating (19) with n3, n4, all_74_12, simplifying with
% 206.73/31.97 | | | | (17), (18), (271), (317), (320) gives:
% 206.73/31.97 | | | | (321) ~ leq(n4, all_74_19) | ~ leq(n3, all_74_16) |
% 206.73/31.97 | | | | (a_select3(id_ds1_filter, n4, n3) = all_74_12 & $i(all_74_12))
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | BETA: splitting (321) gives:
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | Case 1:
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | (322) ~ leq(n4, all_74_19)
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | REDUCE: (16), (322) imply:
% 206.73/31.97 | | | | | (323) ~ leq(n4, n5)
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | PRED_UNIFY: (270), (323) imply:
% 206.73/31.97 | | | | | (324) $false
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | CLOSE: (324) is inconsistent.
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | Case 2:
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | (325) ~ leq(n3, all_74_16) | (a_select3(id_ds1_filter, n4, n3) =
% 206.73/31.97 | | | | | all_74_12 & $i(all_74_12))
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | BETA: splitting (325) gives:
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | Case 1:
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | (326) ~ leq(n3, all_74_16)
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | REDUCE: (23), (326) imply:
% 206.73/31.97 | | | | | | (327) ~ leq(n3, n5)
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | PRED_UNIFY: (319), (327) imply:
% 206.73/31.97 | | | | | | (328) $false
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | CLOSE: (328) is inconsistent.
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | Case 2:
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | (329) a_select3(id_ds1_filter, n4, n3) = all_74_12 &
% 206.73/31.97 | | | | | | $i(all_74_12)
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | ALPHA: (329) implies:
% 206.73/31.97 | | | | | | (330) a_select3(id_ds1_filter, n4, n3) = all_74_12
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | GROUND_INST: instantiating (10) with all_74_13, all_74_12, n3, n4,
% 206.73/31.97 | | | | | | id_ds1_filter, simplifying with (318), (330) gives:
% 206.73/31.97 | | | | | | (331) all_74_12 = all_74_13
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | REDUCE: (20), (331) imply:
% 206.73/31.97 | | | | | | (332) $false
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | CLOSE: (332) is inconsistent.
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | End of split
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | End of split
% 206.73/31.97 | | | |
% 206.73/31.97 | | | End of split
% 206.73/31.97 | | |
% 206.73/31.97 | | Case 2:
% 206.73/31.97 | | |
% 206.73/31.97 | | | (333) all_74_14 = n4
% 206.73/31.97 | | |
% 206.73/31.97 | | | REDUCE: (268), (333) imply:
% 206.73/31.97 | | | (334) a_select3(id_ds1_filter, n4, n4) = all_74_12
% 206.73/31.97 | | |
% 206.73/31.97 | | | REDUCE: (269), (333) imply:
% 206.73/31.97 | | | (335) a_select3(id_ds1_filter, n4, n4) = all_74_13
% 206.73/31.97 | | |
% 206.73/31.97 | | | GROUND_INST: instantiating (10) with all_74_13, all_74_12, n4, n4,
% 206.73/31.97 | | | id_ds1_filter, simplifying with (334), (335) gives:
% 206.73/31.97 | | | (336) all_74_12 = all_74_13
% 206.73/31.97 | | |
% 206.73/31.97 | | | REDUCE: (20), (336) imply:
% 206.73/31.97 | | | (337) $false
% 206.73/31.97 | | |
% 206.73/31.97 | | | CLOSE: (337) is inconsistent.
% 206.73/31.97 | | |
% 206.73/31.97 | | End of split
% 206.73/31.97 | |
% 206.73/31.97 | End of split
% 206.73/31.97 |
% 206.73/31.97 End of proof
% 206.73/31.97
% 206.73/31.97 Sub-proof #9 shows that the following formulas are inconsistent:
% 206.73/31.97 ----------------------------------------------------------------
% 206.73/31.97 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.73/31.97 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.73/31.97 v0))
% 206.73/31.97 (2) a_select3(id_ds1_filter, n4, n1) = all_74_12
% 206.73/31.97 (3) a_select3(id_ds1_filter, n4, n1) = all_74_13
% 206.73/31.97 (4) ~ (all_74_12 = all_74_13)
% 206.73/31.97
% 206.73/31.97 Begin of proof
% 206.73/31.97 |
% 206.73/31.97 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n1, n4,
% 206.73/31.97 | id_ds1_filter, simplifying with (2), (3) gives:
% 206.73/31.97 | (5) all_74_12 = all_74_13
% 206.73/31.97 |
% 206.73/31.97 | REDUCE: (4), (5) imply:
% 206.73/31.97 | (6) $false
% 206.73/31.97 |
% 206.73/31.97 | CLOSE: (6) is inconsistent.
% 206.73/31.97 |
% 206.73/31.97 End of proof
% 206.73/31.97
% 206.73/31.97 Sub-proof #10 shows that the following formulas are inconsistent:
% 206.73/31.97 ----------------------------------------------------------------
% 206.73/31.97 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.73/31.97 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.73/31.97 v0))
% 206.73/31.97 (2) a_select3(id_ds1_filter, n3, n1) = all_74_12
% 206.73/31.97 (3) a_select3(id_ds1_filter, n3, n1) = all_74_13
% 206.73/31.97 (4) ~ (all_74_12 = all_74_13)
% 206.73/31.97
% 206.73/31.97 Begin of proof
% 206.73/31.97 |
% 206.73/31.97 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n1, n3,
% 206.73/31.97 | id_ds1_filter, simplifying with (2), (3) gives:
% 206.73/31.97 | (5) all_74_12 = all_74_13
% 206.73/31.97 |
% 206.73/31.97 | REDUCE: (4), (5) imply:
% 206.73/31.97 | (6) $false
% 206.73/31.97 |
% 206.73/31.97 | CLOSE: (6) is inconsistent.
% 206.73/31.97 |
% 206.73/31.97 End of proof
% 206.73/31.97
% 206.73/31.97 Sub-proof #11 shows that the following formulas are inconsistent:
% 206.73/31.97 ----------------------------------------------------------------
% 206.73/31.97 (1) $i(all_74_14)
% 206.73/31.97 (2) all_74_14 = n0
% 206.73/31.97 (3) gt(all_74_14, n0)
% 206.73/31.97 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0))
% 206.73/31.97
% 206.73/31.97 Begin of proof
% 206.73/31.97 |
% 206.73/31.97 | REDUCE: (1), (2) imply:
% 206.73/31.97 | (5) $i(n0)
% 206.73/31.97 |
% 206.73/31.97 | REDUCE: (2), (3) imply:
% 206.73/31.97 | (6) gt(n0, n0)
% 206.73/31.97 |
% 206.73/31.97 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives:
% 206.73/31.97 | (7) $false
% 206.73/31.97 |
% 206.73/31.97 | CLOSE: (7) is inconsistent.
% 206.73/31.97 |
% 206.73/31.97 End of proof
% 206.73/31.97
% 206.73/31.97 Sub-proof #12 shows that the following formulas are inconsistent:
% 206.73/31.97 ----------------------------------------------------------------
% 206.73/31.97 (1) $i(all_74_15)
% 206.73/31.97 (2) all_74_15 = n0
% 206.73/31.97 (3) gt(all_74_15, n0)
% 206.73/31.97 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0))
% 206.73/31.97
% 206.73/31.97 Begin of proof
% 206.73/31.97 |
% 206.73/31.97 | REDUCE: (1), (2) imply:
% 206.73/31.97 | (5) $i(n0)
% 206.73/31.97 |
% 206.73/31.97 | REDUCE: (2), (3) imply:
% 206.73/31.97 | (6) gt(n0, n0)
% 206.73/31.97 |
% 206.73/31.97 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives:
% 206.73/31.97 | (7) $false
% 206.73/31.97 |
% 206.73/31.97 | CLOSE: (7) is inconsistent.
% 206.73/31.97 |
% 206.73/31.97 End of proof
% 206.73/31.97
% 206.73/31.97 Sub-proof #13 shows that the following formulas are inconsistent:
% 206.73/31.97 ----------------------------------------------------------------
% 206.73/31.97 (1) a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8
% 206.73/31.97 (2) gt(all_74_10, n0)
% 206.73/31.97 (3) all_74_11 = n5 | gt(n5, all_74_11)
% 206.73/31.97 (4) pred(n4) = n3
% 206.73/31.97 (5) leq(all_74_10, n5)
% 206.73/31.97 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 206.73/31.97 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 206.73/31.97 ~ leq(v1, all_74_19) | ~ leq(v0, all_74_19) | ~ leq(n0, v1) | ~
% 206.73/31.97 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2)))
% 206.73/31.97 (7) $i(n2)
% 206.73/31.97 (8) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0,
% 206.73/31.97 v1) | gt(v1, v0))
% 206.73/31.97 (9) pred(n3) = n2
% 206.73/31.97 (10) leq(n0, all_74_10)
% 206.73/31.97 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 206.73/31.97 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.73/31.97 v0))
% 206.73/31.97 (12) all_74_11 = n5 | all_74_11 = n4 | all_74_11 = n3 | all_74_11 = n2 |
% 206.73/31.97 all_74_11 = n1 | all_74_11 = n0
% 206.73/31.97 (13) $i(all_74_10)
% 206.73/31.97 (14) pred(n2) = n1
% 206.73/31.97 (15) pred(n5) = n4
% 206.73/31.97 (16) leq(all_74_11, n5)
% 206.73/31.97 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 206.73/31.97 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 206.73/31.97 (18) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 206.73/31.97 leq(n0, v0))
% 206.73/31.97 (19) ~ gt(n0, n0)
% 206.73/31.97 (20) all_74_10 = n5 | gt(n5, all_74_10)
% 206.73/31.97 (21) all_74_19 = n5
% 206.73/31.97 (22) $i(n4)
% 206.73/31.97 (23) $i(n3)
% 206.73/31.97 (24) all_74_11 = n0 | gt(all_74_11, n0)
% 206.73/31.97 (25) leq(n0, all_74_11)
% 206.73/31.97 (26) $i(n5)
% 206.73/31.97 (27) all_74_10 = n5 | all_74_10 = n4 | all_74_10 = n3 | all_74_10 = n2 |
% 206.73/31.97 all_74_10 = n1 | all_74_10 = n0
% 206.73/31.97 (28) ~ (all_74_8 = all_74_9)
% 206.73/31.97 (29) a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9
% 206.73/31.97 (30) $i(all_74_11)
% 206.73/31.97
% 206.73/31.97 Begin of proof
% 206.73/31.97 |
% 206.73/31.97 | BETA: splitting (24) gives:
% 206.73/31.97 |
% 206.73/31.97 | Case 1:
% 206.73/31.97 | |
% 206.73/31.97 | | (31) gt(all_74_11, n0)
% 206.73/31.97 | |
% 206.73/31.97 | | BETA: splitting (3) gives:
% 206.73/31.97 | |
% 206.73/31.97 | | Case 1:
% 206.73/31.97 | | |
% 206.73/31.97 | | | (32) gt(n5, all_74_11)
% 206.73/31.97 | | |
% 206.73/31.97 | | | GROUND_INST: instantiating (17) with all_74_11, n5, n4, simplifying with
% 206.73/31.97 | | | (15), (26), (30), (32) gives:
% 206.73/31.97 | | | (33) leq(all_74_11, n4)
% 206.73/31.97 | | |
% 206.73/31.97 | | | GROUND_INST: instantiating (8) with all_74_11, n4, simplifying with (22),
% 206.73/31.97 | | | (30), (33) gives:
% 206.73/31.97 | | | (34) all_74_11 = n4 | gt(n4, all_74_11)
% 206.73/31.97 | | |
% 206.73/31.97 | | | BETA: splitting (20) gives:
% 206.73/31.97 | | |
% 206.73/31.97 | | | Case 1:
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | (35) gt(n5, all_74_10)
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | GROUND_INST: instantiating (17) with all_74_10, n5, n4, simplifying with
% 206.73/31.97 | | | | (13), (15), (26), (35) gives:
% 206.73/31.97 | | | | (36) leq(all_74_10, n4)
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | GROUND_INST: instantiating (8) with all_74_10, n4, simplifying with
% 206.73/31.97 | | | | (13), (22), (36) gives:
% 206.73/31.97 | | | | (37) all_74_10 = n4 | gt(n4, all_74_10)
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | BETA: splitting (27) gives:
% 206.73/31.97 | | | |
% 206.73/31.97 | | | | Case 1:
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | (38) all_74_10 = n0
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | REDUCE: (2), (38) imply:
% 206.73/31.97 | | | | | (39) gt(n0, n0)
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | PRED_UNIFY: (19), (39) imply:
% 206.73/31.97 | | | | | (40) $false
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | CLOSE: (40) is inconsistent.
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | Case 2:
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | (41) ~ (all_74_10 = n0)
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | BETA: splitting (12) gives:
% 206.73/31.97 | | | | |
% 206.73/31.97 | | | | | Case 1:
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | (42) all_74_11 = n0
% 206.73/31.97 | | | | | |
% 206.73/31.97 | | | | | | REDUCE: (31), (42) imply:
% 206.73/31.98 | | | | | | (43) gt(n0, n0)
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | PRED_UNIFY: (19), (43) imply:
% 206.73/31.98 | | | | | | (44) $false
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | CLOSE: (44) is inconsistent.
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | Case 2:
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | (45) ~ (all_74_11 = n0)
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 206.73/31.98 | | | | | | (14), (16), (17), (18), (21), (22), (23), (25), (28),
% 206.73/31.98 | | | | | | (29), (30), (34), (37), (41), (45) are inconsistent by
% 206.73/31.98 | | | | | | sub-proof #20.
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | End of split
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | End of split
% 206.73/31.98 | | | |
% 206.73/31.98 | | | Case 2:
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | (46) all_74_10 = n5
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | REDUCE: (1), (46) imply:
% 206.73/31.98 | | | | (47) a_select3(pminus_ds1_filter, n5, all_74_11) = all_74_8
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | REDUCE: (29), (46) imply:
% 206.73/31.98 | | | | (48) a_select3(pminus_ds1_filter, all_74_11, n5) = all_74_9
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | REDUCE: (5), (46) imply:
% 206.73/31.98 | | | | (49) leq(n5, n5)
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | REDUCE: (10), (46) imply:
% 206.73/31.98 | | | | (50) leq(n0, n5)
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | BETA: splitting (12) gives:
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | Case 1:
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | (51) all_74_11 = n0
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | REDUCE: (31), (51) imply:
% 206.73/31.98 | | | | | (52) gt(n0, n0)
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | PRED_UNIFY: (19), (52) imply:
% 206.73/31.98 | | | | | (53) $false
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | CLOSE: (53) is inconsistent.
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | Case 2:
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | (54) ~ (all_74_11 = n0)
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (11), (14), (16), (17), (18),
% 206.73/31.98 | | | | | (21), (22), (23), (25), (26), (28), (30), (34), (47), (48),
% 206.73/31.98 | | | | | (49), (50), (54) are inconsistent by sub-proof #18.
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | End of split
% 206.73/31.98 | | | |
% 206.73/31.98 | | | End of split
% 206.73/31.98 | | |
% 206.73/31.98 | | Case 2:
% 206.73/31.98 | | |
% 206.73/31.98 | | | (55) all_74_11 = n5
% 206.73/31.98 | | |
% 206.73/31.98 | | | REDUCE: (1), (55) imply:
% 206.73/31.98 | | | (56) a_select3(pminus_ds1_filter, all_74_10, n5) = all_74_8
% 206.73/31.98 | | |
% 206.73/31.98 | | | REDUCE: (29), (55) imply:
% 206.73/31.98 | | | (57) a_select3(pminus_ds1_filter, n5, all_74_10) = all_74_9
% 206.73/31.98 | | |
% 206.73/31.98 | | | REDUCE: (16), (55) imply:
% 206.73/31.98 | | | (58) leq(n5, n5)
% 206.73/31.98 | | |
% 206.73/31.98 | | | REDUCE: (25), (55) imply:
% 206.73/31.98 | | | (59) leq(n0, n5)
% 206.73/31.98 | | |
% 206.73/31.98 | | | BETA: splitting (20) gives:
% 206.73/31.98 | | |
% 206.73/31.98 | | | Case 1:
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | (60) gt(n5, all_74_10)
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | GROUND_INST: instantiating (17) with all_74_10, n5, n4, simplifying with
% 206.73/31.98 | | | | (13), (15), (26), (60) gives:
% 206.73/31.98 | | | | (61) leq(all_74_10, n4)
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | GROUND_INST: instantiating (8) with all_74_10, n4, simplifying with
% 206.73/31.98 | | | | (13), (22), (61) gives:
% 206.73/31.98 | | | | (62) all_74_10 = n4 | gt(n4, all_74_10)
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | BETA: splitting (27) gives:
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | Case 1:
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | (63) all_74_10 = n0
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | REDUCE: (2), (63) imply:
% 206.73/31.98 | | | | | (64) gt(n0, n0)
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | PRED_UNIFY: (19), (64) imply:
% 206.73/31.98 | | | | | (65) $false
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | CLOSE: (65) is inconsistent.
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | Case 2:
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | (66) ~ (all_74_10 = n0)
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (13), (14), (17),
% 206.73/31.98 | | | | | (18), (21), (22), (23), (26), (28), (56), (57), (58), (59),
% 206.73/31.98 | | | | | (62), (66) are inconsistent by sub-proof #17.
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | End of split
% 206.73/31.98 | | | |
% 206.73/31.98 | | | Case 2:
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | (67) all_74_10 = n5
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | REDUCE: (56), (67) imply:
% 206.73/31.98 | | | | (68) a_select3(pminus_ds1_filter, n5, n5) = all_74_8
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | REDUCE: (57), (67) imply:
% 206.73/31.98 | | | | (69) a_select3(pminus_ds1_filter, n5, n5) = all_74_9
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | GROUND_INST: instantiating (11) with all_74_9, all_74_8, n5, n5,
% 206.73/31.98 | | | | pminus_ds1_filter, simplifying with (68), (69) gives:
% 206.73/31.98 | | | | (70) all_74_8 = all_74_9
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | REDUCE: (28), (70) imply:
% 206.73/31.98 | | | | (71) $false
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | CLOSE: (71) is inconsistent.
% 206.73/31.98 | | | |
% 206.73/31.98 | | | End of split
% 206.73/31.98 | | |
% 206.73/31.98 | | End of split
% 206.73/31.98 | |
% 206.73/31.98 | Case 2:
% 206.73/31.98 | |
% 206.73/31.98 | | (72) all_74_11 = n0
% 206.73/31.98 | | (73) ~ gt(all_74_11, n0)
% 206.73/31.98 | |
% 206.73/31.98 | | REDUCE: (1), (72) imply:
% 206.73/31.98 | | (74) a_select3(pminus_ds1_filter, all_74_10, n0) = all_74_8
% 206.73/31.98 | |
% 206.73/31.98 | | REDUCE: (29), (72) imply:
% 206.73/31.98 | | (75) a_select3(pminus_ds1_filter, n0, all_74_10) = all_74_9
% 206.73/31.98 | |
% 206.73/31.98 | | REDUCE: (30), (72) imply:
% 206.73/31.98 | | (76) $i(n0)
% 206.73/31.98 | |
% 206.73/31.98 | | REDUCE: (16), (72) imply:
% 206.73/31.98 | | (77) leq(n0, n5)
% 206.73/31.98 | |
% 206.73/31.98 | | REDUCE: (25), (72) imply:
% 206.73/31.98 | | (78) leq(n0, n0)
% 206.73/31.98 | |
% 206.73/31.98 | | BETA: splitting (20) gives:
% 206.73/31.98 | |
% 206.73/31.98 | | Case 1:
% 206.73/31.98 | | |
% 206.73/31.98 | | | (79) gt(n5, all_74_10)
% 206.73/31.98 | | |
% 206.73/31.98 | | | GROUND_INST: instantiating (17) with all_74_10, n5, n4, simplifying with
% 206.73/31.98 | | | (13), (15), (26), (79) gives:
% 206.73/31.98 | | | (80) leq(all_74_10, n4)
% 206.73/31.98 | | |
% 206.73/31.98 | | | GROUND_INST: instantiating (8) with all_74_10, n4, simplifying with (13),
% 206.73/31.98 | | | (22), (80) gives:
% 206.73/31.98 | | | (81) all_74_10 = n4 | gt(n4, all_74_10)
% 206.73/31.98 | | |
% 206.73/31.98 | | | BETA: splitting (27) gives:
% 206.73/31.98 | | |
% 206.73/31.98 | | | Case 1:
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | (82) all_74_10 = n0
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | REDUCE: (2), (82) imply:
% 206.73/31.98 | | | | (83) gt(n0, n0)
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | PRED_UNIFY: (19), (83) imply:
% 206.73/31.98 | | | | (84) $false
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | CLOSE: (84) is inconsistent.
% 206.73/31.98 | | | |
% 206.73/31.98 | | | Case 2:
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | (85) ~ (all_74_10 = n0)
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | BETA: splitting (81) gives:
% 206.73/31.98 | | | |
% 206.73/31.98 | | | | Case 1:
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | (86) gt(n4, all_74_10)
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | GROUND_INST: instantiating (17) with all_74_10, n4, n3, simplifying
% 206.73/31.98 | | | | | with (4), (13), (22), (86) gives:
% 206.73/31.98 | | | | | (87) leq(all_74_10, n3)
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | GROUND_INST: instantiating (8) with all_74_10, n3, simplifying with
% 206.73/31.98 | | | | | (13), (23), (87) gives:
% 206.73/31.98 | | | | | (88) all_74_10 = n3 | gt(n3, all_74_10)
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | BETA: splitting (88) gives:
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | Case 1:
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | (89) gt(n3, all_74_10)
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | GROUND_INST: instantiating (17) with all_74_10, n3, n2, simplifying
% 206.73/31.98 | | | | | | with (9), (13), (23), (89) gives:
% 206.73/31.98 | | | | | | (90) leq(all_74_10, n2)
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | GROUND_INST: instantiating (8) with all_74_10, n2, simplifying with
% 206.73/31.98 | | | | | | (7), (13), (90) gives:
% 206.73/31.98 | | | | | | (91) all_74_10 = n2 | gt(n2, all_74_10)
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | BETA: splitting (91) gives:
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | Case 1:
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | (92) gt(n2, all_74_10)
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | GROUND_INST: instantiating (17) with all_74_10, n2, n1,
% 206.73/31.98 | | | | | | | simplifying with (7), (13), (14), (92) gives:
% 206.73/31.98 | | | | | | | (93) leq(all_74_10, n1)
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | GROUND_INST: instantiating (18) with all_74_10, simplifying with
% 206.73/31.98 | | | | | | | (10), (13), (93) gives:
% 206.73/31.98 | | | | | | | (94) all_74_10 = n1 | all_74_10 = n0
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | BETA: splitting (94) gives:
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | Case 1:
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | (95) all_74_10 = n0
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | REDUCE: (85), (95) imply:
% 206.73/31.98 | | | | | | | | (96) $false
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | CLOSE: (96) is inconsistent.
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | Case 2:
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | (97) all_74_10 = n1
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | REDUCE: (74), (97) imply:
% 206.73/31.98 | | | | | | | | (98) a_select3(pminus_ds1_filter, n1, n0) = all_74_8
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | REDUCE: (75), (97) imply:
% 206.73/31.98 | | | | | | | | (99) a_select3(pminus_ds1_filter, n0, n1) = all_74_9
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | REDUCE: (13), (97) imply:
% 206.73/31.98 | | | | | | | | (100) $i(n1)
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | REDUCE: (5), (97) imply:
% 206.73/31.98 | | | | | | | | (101) leq(n1, n5)
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | REDUCE: (10), (97) imply:
% 206.73/31.98 | | | | | | | | (102) leq(n0, n1)
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | GROUND_INST: instantiating (6) with n0, n1, all_74_9,
% 206.73/31.98 | | | | | | | | simplifying with (76), (78), (99), (100), (102)
% 206.73/31.98 | | | | | | | | gives:
% 206.73/31.98 | | | | | | | | (103) ~ leq(n1, all_74_19) | ~ leq(n0, all_74_19) |
% 206.73/31.98 | | | | | | | | (a_select3(pminus_ds1_filter, n1, n0) = all_74_9 &
% 206.73/31.98 | | | | | | | | $i(all_74_9))
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | BETA: splitting (103) gives:
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | Case 1:
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | (104) ~ leq(n0, all_74_19)
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | REDUCE: (21), (104) imply:
% 206.73/31.98 | | | | | | | | | (105) ~ leq(n0, n5)
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | PRED_UNIFY: (77), (105) imply:
% 206.73/31.98 | | | | | | | | | (106) $false
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | CLOSE: (106) is inconsistent.
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | Case 2:
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | (107) ~ leq(n1, all_74_19) | (a_select3(pminus_ds1_filter,
% 206.73/31.98 | | | | | | | | | n1, n0) = all_74_9 & $i(all_74_9))
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | BETA: splitting (107) gives:
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | Case 1:
% 206.73/31.98 | | | | | | | | | |
% 206.73/31.98 | | | | | | | | | | (108) ~ leq(n1, all_74_19)
% 206.73/31.98 | | | | | | | | | |
% 206.73/31.98 | | | | | | | | | | REDUCE: (21), (108) imply:
% 206.73/31.98 | | | | | | | | | | (109) ~ leq(n1, n5)
% 206.73/31.98 | | | | | | | | | |
% 206.73/31.98 | | | | | | | | | | PRED_UNIFY: (101), (109) imply:
% 206.73/31.98 | | | | | | | | | | (110) $false
% 206.73/31.98 | | | | | | | | | |
% 206.73/31.98 | | | | | | | | | | CLOSE: (110) is inconsistent.
% 206.73/31.98 | | | | | | | | | |
% 206.73/31.98 | | | | | | | | | Case 2:
% 206.73/31.98 | | | | | | | | | |
% 206.73/31.98 | | | | | | | | | | (111) a_select3(pminus_ds1_filter, n1, n0) = all_74_9 &
% 206.73/31.98 | | | | | | | | | | $i(all_74_9)
% 206.73/31.98 | | | | | | | | | |
% 206.73/31.98 | | | | | | | | | | ALPHA: (111) implies:
% 206.73/31.98 | | | | | | | | | | (112) a_select3(pminus_ds1_filter, n1, n0) = all_74_9
% 206.73/31.98 | | | | | | | | | |
% 206.73/31.98 | | | | | | | | | | REF_CLOSE: (11), (28), (98), (112) are inconsistent by
% 206.73/31.98 | | | | | | | | | | sub-proof #16.
% 206.73/31.98 | | | | | | | | | |
% 206.73/31.98 | | | | | | | | | End of split
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | End of split
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | End of split
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | Case 2:
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | (113) all_74_10 = n2
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | REDUCE: (74), (113) imply:
% 206.73/31.98 | | | | | | | (114) a_select3(pminus_ds1_filter, n2, n0) = all_74_8
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | REDUCE: (75), (113) imply:
% 206.73/31.98 | | | | | | | (115) a_select3(pminus_ds1_filter, n0, n2) = all_74_9
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | REDUCE: (5), (113) imply:
% 206.73/31.98 | | | | | | | (116) leq(n2, n5)
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | REDUCE: (10), (113) imply:
% 206.73/31.98 | | | | | | | (117) leq(n0, n2)
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | GROUND_INST: instantiating (6) with n0, n2, all_74_9, simplifying
% 206.73/31.98 | | | | | | | with (7), (76), (78), (115), (117) gives:
% 206.73/31.98 | | | | | | | (118) ~ leq(n2, all_74_19) | ~ leq(n0, all_74_19) |
% 206.73/31.98 | | | | | | | (a_select3(pminus_ds1_filter, n2, n0) = all_74_9 &
% 206.73/31.98 | | | | | | | $i(all_74_9))
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | BETA: splitting (118) gives:
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | Case 1:
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | (119) ~ leq(n0, all_74_19)
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | REDUCE: (21), (119) imply:
% 206.73/31.98 | | | | | | | | (120) ~ leq(n0, n5)
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | PRED_UNIFY: (77), (120) imply:
% 206.73/31.98 | | | | | | | | (121) $false
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | CLOSE: (121) is inconsistent.
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | Case 2:
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | (122) ~ leq(n2, all_74_19) | (a_select3(pminus_ds1_filter,
% 206.73/31.98 | | | | | | | | n2, n0) = all_74_9 & $i(all_74_9))
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | BETA: splitting (122) gives:
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | Case 1:
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | (123) ~ leq(n2, all_74_19)
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | REDUCE: (21), (123) imply:
% 206.73/31.98 | | | | | | | | | (124) ~ leq(n2, n5)
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | PRED_UNIFY: (116), (124) imply:
% 206.73/31.98 | | | | | | | | | (125) $false
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | CLOSE: (125) is inconsistent.
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | Case 2:
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | (126) a_select3(pminus_ds1_filter, n2, n0) = all_74_9 &
% 206.73/31.98 | | | | | | | | | $i(all_74_9)
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | ALPHA: (126) implies:
% 206.73/31.98 | | | | | | | | | (127) a_select3(pminus_ds1_filter, n2, n0) = all_74_9
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | GROUND_INST: instantiating (11) with all_74_8, all_74_9, n0,
% 206.73/31.98 | | | | | | | | | n2, pminus_ds1_filter, simplifying with (114),
% 206.73/31.98 | | | | | | | | | (127) gives:
% 206.73/31.98 | | | | | | | | | (128) all_74_8 = all_74_9
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | REDUCE: (28), (128) imply:
% 206.73/31.98 | | | | | | | | | (129) $false
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | | CLOSE: (129) is inconsistent.
% 206.73/31.98 | | | | | | | | |
% 206.73/31.98 | | | | | | | | End of split
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | End of split
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | End of split
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | Case 2:
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | (130) all_74_10 = n3
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | REDUCE: (74), (130) imply:
% 206.73/31.98 | | | | | | (131) a_select3(pminus_ds1_filter, n3, n0) = all_74_8
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | REDUCE: (75), (130) imply:
% 206.73/31.98 | | | | | | (132) a_select3(pminus_ds1_filter, n0, n3) = all_74_9
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | REDUCE: (5), (130) imply:
% 206.73/31.98 | | | | | | (133) leq(n3, n5)
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | REDUCE: (10), (130) imply:
% 206.73/31.98 | | | | | | (134) leq(n0, n3)
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | GROUND_INST: instantiating (6) with n0, n3, all_74_9, simplifying
% 206.73/31.98 | | | | | | with (23), (76), (78), (132), (134) gives:
% 206.73/31.98 | | | | | | (135) ~ leq(n3, all_74_19) | ~ leq(n0, all_74_19) |
% 206.73/31.98 | | | | | | (a_select3(pminus_ds1_filter, n3, n0) = all_74_9 &
% 206.73/31.98 | | | | | | $i(all_74_9))
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | BETA: splitting (135) gives:
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | Case 1:
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | (136) ~ leq(n0, all_74_19)
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | REDUCE: (21), (136) imply:
% 206.73/31.98 | | | | | | | (137) ~ leq(n0, n5)
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | PRED_UNIFY: (77), (137) imply:
% 206.73/31.98 | | | | | | | (138) $false
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | CLOSE: (138) is inconsistent.
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | Case 2:
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | (139) ~ leq(n3, all_74_19) | (a_select3(pminus_ds1_filter, n3,
% 206.73/31.98 | | | | | | | n0) = all_74_9 & $i(all_74_9))
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | BETA: splitting (139) gives:
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | Case 1:
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | (140) ~ leq(n3, all_74_19)
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | REDUCE: (21), (140) imply:
% 206.73/31.98 | | | | | | | | (141) ~ leq(n3, n5)
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | PRED_UNIFY: (133), (141) imply:
% 206.73/31.98 | | | | | | | | (142) $false
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | CLOSE: (142) is inconsistent.
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | Case 2:
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | (143) a_select3(pminus_ds1_filter, n3, n0) = all_74_9 &
% 206.73/31.98 | | | | | | | | $i(all_74_9)
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | ALPHA: (143) implies:
% 206.73/31.98 | | | | | | | | (144) a_select3(pminus_ds1_filter, n3, n0) = all_74_9
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | | REF_CLOSE: (11), (28), (131), (144) are inconsistent by
% 206.73/31.98 | | | | | | | | sub-proof #15.
% 206.73/31.98 | | | | | | | |
% 206.73/31.98 | | | | | | | End of split
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | End of split
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | End of split
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | Case 2:
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | (145) all_74_10 = n4
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | REDUCE: (74), (145) imply:
% 206.73/31.98 | | | | | (146) a_select3(pminus_ds1_filter, n4, n0) = all_74_8
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | REDUCE: (75), (145) imply:
% 206.73/31.98 | | | | | (147) a_select3(pminus_ds1_filter, n0, n4) = all_74_9
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | REDUCE: (5), (145) imply:
% 206.73/31.98 | | | | | (148) leq(n4, n5)
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | REDUCE: (10), (145) imply:
% 206.73/31.98 | | | | | (149) leq(n0, n4)
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | GROUND_INST: instantiating (6) with n0, n4, all_74_9, simplifying with
% 206.73/31.98 | | | | | (22), (76), (78), (147), (149) gives:
% 206.73/31.98 | | | | | (150) ~ leq(n4, all_74_19) | ~ leq(n0, all_74_19) |
% 206.73/31.98 | | | | | (a_select3(pminus_ds1_filter, n4, n0) = all_74_9 &
% 206.73/31.98 | | | | | $i(all_74_9))
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | BETA: splitting (150) gives:
% 206.73/31.98 | | | | |
% 206.73/31.98 | | | | | Case 1:
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | (151) ~ leq(n0, all_74_19)
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | REDUCE: (21), (151) imply:
% 206.73/31.98 | | | | | | (152) ~ leq(n0, n5)
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | PRED_UNIFY: (77), (152) imply:
% 206.73/31.98 | | | | | | (153) $false
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | CLOSE: (153) is inconsistent.
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | Case 2:
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | (154) ~ leq(n4, all_74_19) | (a_select3(pminus_ds1_filter, n4,
% 206.73/31.98 | | | | | | n0) = all_74_9 & $i(all_74_9))
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | BETA: splitting (154) gives:
% 206.73/31.98 | | | | | |
% 206.73/31.98 | | | | | | Case 1:
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | (155) ~ leq(n4, all_74_19)
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | REDUCE: (21), (155) imply:
% 206.73/31.98 | | | | | | | (156) ~ leq(n4, n5)
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | PRED_UNIFY: (148), (156) imply:
% 206.73/31.98 | | | | | | | (157) $false
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | CLOSE: (157) is inconsistent.
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | Case 2:
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | (158) a_select3(pminus_ds1_filter, n4, n0) = all_74_9 &
% 206.73/31.98 | | | | | | | $i(all_74_9)
% 206.73/31.98 | | | | | | |
% 206.73/31.98 | | | | | | | ALPHA: (158) implies:
% 206.73/31.99 | | | | | | | (159) a_select3(pminus_ds1_filter, n4, n0) = all_74_9
% 206.73/31.99 | | | | | | |
% 206.73/31.99 | | | | | | | REF_CLOSE: (11), (28), (146), (159) are inconsistent by sub-proof
% 206.73/31.99 | | | | | | | #14.
% 206.73/31.99 | | | | | | |
% 206.73/31.99 | | | | | | End of split
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | End of split
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | End of split
% 206.73/31.99 | | | |
% 206.73/31.99 | | | End of split
% 206.73/31.99 | | |
% 206.73/31.99 | | Case 2:
% 206.73/31.99 | | |
% 206.73/31.99 | | | (160) all_74_10 = n5
% 206.73/31.99 | | |
% 206.73/31.99 | | | REDUCE: (74), (160) imply:
% 206.73/31.99 | | | (161) a_select3(pminus_ds1_filter, n5, n0) = all_74_8
% 206.73/31.99 | | |
% 206.73/31.99 | | | REDUCE: (75), (160) imply:
% 206.73/31.99 | | | (162) a_select3(pminus_ds1_filter, n0, n5) = all_74_9
% 206.73/31.99 | | |
% 206.73/31.99 | | | REDUCE: (5), (160) imply:
% 206.73/31.99 | | | (163) leq(n5, n5)
% 206.73/31.99 | | |
% 206.73/31.99 | | | GROUND_INST: instantiating (6) with n0, n5, all_74_9, simplifying with
% 206.73/31.99 | | | (26), (76), (77), (78), (162) gives:
% 206.73/31.99 | | | (164) ~ leq(n5, all_74_19) | ~ leq(n0, all_74_19) |
% 206.73/31.99 | | | (a_select3(pminus_ds1_filter, n5, n0) = all_74_9 & $i(all_74_9))
% 206.73/31.99 | | |
% 206.73/31.99 | | | BETA: splitting (164) gives:
% 206.73/31.99 | | |
% 206.73/31.99 | | | Case 1:
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | (165) ~ leq(n0, all_74_19)
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | REDUCE: (21), (165) imply:
% 206.73/31.99 | | | | (166) ~ leq(n0, n5)
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | PRED_UNIFY: (77), (166) imply:
% 206.73/31.99 | | | | (167) $false
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | CLOSE: (167) is inconsistent.
% 206.73/31.99 | | | |
% 206.73/31.99 | | | Case 2:
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | (168) ~ leq(n5, all_74_19) | (a_select3(pminus_ds1_filter, n5, n0) =
% 206.73/31.99 | | | | all_74_9 & $i(all_74_9))
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | BETA: splitting (168) gives:
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | Case 1:
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | (169) ~ leq(n5, all_74_19)
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | REDUCE: (21), (169) imply:
% 206.73/31.99 | | | | | (170) ~ leq(n5, n5)
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | PRED_UNIFY: (163), (170) imply:
% 206.73/31.99 | | | | | (171) $false
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | CLOSE: (171) is inconsistent.
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | Case 2:
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | (172) a_select3(pminus_ds1_filter, n5, n0) = all_74_9 &
% 206.73/31.99 | | | | | $i(all_74_9)
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | ALPHA: (172) implies:
% 206.73/31.99 | | | | | (173) a_select3(pminus_ds1_filter, n5, n0) = all_74_9
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | GROUND_INST: instantiating (11) with all_74_8, all_74_9, n0, n5,
% 206.73/31.99 | | | | | pminus_ds1_filter, simplifying with (161), (173) gives:
% 206.73/31.99 | | | | | (174) all_74_8 = all_74_9
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | REDUCE: (28), (174) imply:
% 206.73/31.99 | | | | | (175) $false
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | CLOSE: (175) is inconsistent.
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | End of split
% 206.73/31.99 | | | |
% 206.73/31.99 | | | End of split
% 206.73/31.99 | | |
% 206.73/31.99 | | End of split
% 206.73/31.99 | |
% 206.73/31.99 | End of split
% 206.73/31.99 |
% 206.73/31.99 End of proof
% 206.73/31.99
% 206.73/31.99 Sub-proof #14 shows that the following formulas are inconsistent:
% 206.73/31.99 ----------------------------------------------------------------
% 206.73/31.99 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.73/31.99 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.73/31.99 v0))
% 206.73/31.99 (2) a_select3(pminus_ds1_filter, n4, n0) = all_74_8
% 206.73/31.99 (3) a_select3(pminus_ds1_filter, n4, n0) = all_74_9
% 206.73/31.99 (4) ~ (all_74_8 = all_74_9)
% 206.73/31.99
% 206.73/31.99 Begin of proof
% 206.73/31.99 |
% 206.73/31.99 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n0, n4,
% 206.73/31.99 | pminus_ds1_filter, simplifying with (2), (3) gives:
% 206.73/31.99 | (5) all_74_8 = all_74_9
% 206.73/31.99 |
% 206.73/31.99 | REDUCE: (4), (5) imply:
% 206.73/31.99 | (6) $false
% 206.73/31.99 |
% 206.73/31.99 | CLOSE: (6) is inconsistent.
% 206.73/31.99 |
% 206.73/31.99 End of proof
% 206.73/31.99
% 206.73/31.99 Sub-proof #15 shows that the following formulas are inconsistent:
% 206.73/31.99 ----------------------------------------------------------------
% 206.73/31.99 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.73/31.99 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.73/31.99 v0))
% 206.73/31.99 (2) a_select3(pminus_ds1_filter, n3, n0) = all_74_8
% 206.73/31.99 (3) a_select3(pminus_ds1_filter, n3, n0) = all_74_9
% 206.73/31.99 (4) ~ (all_74_8 = all_74_9)
% 206.73/31.99
% 206.73/31.99 Begin of proof
% 206.73/31.99 |
% 206.73/31.99 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n0, n3,
% 206.73/31.99 | pminus_ds1_filter, simplifying with (2), (3) gives:
% 206.73/31.99 | (5) all_74_8 = all_74_9
% 206.73/31.99 |
% 206.73/31.99 | REDUCE: (4), (5) imply:
% 206.73/31.99 | (6) $false
% 206.73/31.99 |
% 206.73/31.99 | CLOSE: (6) is inconsistent.
% 206.73/31.99 |
% 206.73/31.99 End of proof
% 206.73/31.99
% 206.73/31.99 Sub-proof #16 shows that the following formulas are inconsistent:
% 206.73/31.99 ----------------------------------------------------------------
% 206.73/31.99 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.73/31.99 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.73/31.99 v0))
% 206.73/31.99 (2) a_select3(pminus_ds1_filter, n1, n0) = all_74_8
% 206.73/31.99 (3) a_select3(pminus_ds1_filter, n1, n0) = all_74_9
% 206.73/31.99 (4) ~ (all_74_8 = all_74_9)
% 206.73/31.99
% 206.73/31.99 Begin of proof
% 206.73/31.99 |
% 206.73/31.99 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n0, n1,
% 206.73/31.99 | pminus_ds1_filter, simplifying with (2), (3) gives:
% 206.73/31.99 | (5) all_74_8 = all_74_9
% 206.73/31.99 |
% 206.73/31.99 | REDUCE: (4), (5) imply:
% 206.73/31.99 | (6) $false
% 206.73/31.99 |
% 206.73/31.99 | CLOSE: (6) is inconsistent.
% 206.73/31.99 |
% 206.73/31.99 End of proof
% 206.73/31.99
% 206.73/31.99 Sub-proof #17 shows that the following formulas are inconsistent:
% 206.73/31.99 ----------------------------------------------------------------
% 206.73/31.99 (1) all_74_10 = n4 | gt(n4, all_74_10)
% 206.73/31.99 (2) pred(n4) = n3
% 206.73/31.99 (3) leq(all_74_10, n5)
% 206.73/31.99 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 206.73/31.99 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 206.73/31.99 ~ leq(v1, all_74_19) | ~ leq(v0, all_74_19) | ~ leq(n0, v1) | ~
% 206.73/31.99 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2)))
% 206.73/31.99 (5) $i(n2)
% 206.73/31.99 (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0,
% 206.73/31.99 v1) | gt(v1, v0))
% 206.73/31.99 (7) pred(n3) = n2
% 206.73/31.99 (8) leq(n0, all_74_10)
% 206.73/31.99 (9) leq(n0, n5)
% 206.73/31.99 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 206.73/31.99 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.73/31.99 v0))
% 206.73/31.99 (11) $i(all_74_10)
% 206.73/31.99 (12) a_select3(pminus_ds1_filter, n5, all_74_10) = all_74_9
% 206.73/31.99 (13) pred(n2) = n1
% 206.73/31.99 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 206.73/31.99 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 206.73/31.99 (15) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 206.73/31.99 leq(n0, v0))
% 206.73/31.99 (16) leq(n5, n5)
% 206.73/31.99 (17) all_74_19 = n5
% 206.73/31.99 (18) ~ (all_74_10 = n0)
% 206.73/31.99 (19) $i(n4)
% 206.73/31.99 (20) a_select3(pminus_ds1_filter, all_74_10, n5) = all_74_8
% 206.73/31.99 (21) $i(n3)
% 206.73/31.99 (22) $i(n5)
% 206.73/31.99 (23) ~ (all_74_8 = all_74_9)
% 206.73/31.99
% 206.73/31.99 Begin of proof
% 206.73/31.99 |
% 206.73/31.99 | BETA: splitting (1) gives:
% 206.73/31.99 |
% 206.73/31.99 | Case 1:
% 206.73/31.99 | |
% 206.73/31.99 | | (24) gt(n4, all_74_10)
% 206.73/31.99 | |
% 206.73/31.99 | | GROUND_INST: instantiating (14) with all_74_10, n4, n3, simplifying with
% 206.73/31.99 | | (2), (11), (19), (24) gives:
% 206.73/31.99 | | (25) leq(all_74_10, n3)
% 206.73/31.99 | |
% 206.73/31.99 | | GROUND_INST: instantiating (6) with all_74_10, n3, simplifying with (11),
% 206.73/31.99 | | (21), (25) gives:
% 206.73/31.99 | | (26) all_74_10 = n3 | gt(n3, all_74_10)
% 206.73/31.99 | |
% 206.73/31.99 | | BETA: splitting (26) gives:
% 206.73/31.99 | |
% 206.73/31.99 | | Case 1:
% 206.73/31.99 | | |
% 206.73/31.99 | | | (27) gt(n3, all_74_10)
% 206.73/31.99 | | |
% 206.73/31.99 | | | GROUND_INST: instantiating (14) with all_74_10, n3, n2, simplifying with
% 206.73/31.99 | | | (7), (11), (21), (27) gives:
% 206.73/31.99 | | | (28) leq(all_74_10, n2)
% 206.73/31.99 | | |
% 206.73/31.99 | | | GROUND_INST: instantiating (6) with all_74_10, n2, simplifying with (5),
% 206.73/31.99 | | | (11), (28) gives:
% 206.73/31.99 | | | (29) all_74_10 = n2 | gt(n2, all_74_10)
% 206.73/31.99 | | |
% 206.73/31.99 | | | BETA: splitting (29) gives:
% 206.73/31.99 | | |
% 206.73/31.99 | | | Case 1:
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | (30) gt(n2, all_74_10)
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | GROUND_INST: instantiating (14) with all_74_10, n2, n1, simplifying with
% 206.73/31.99 | | | | (5), (11), (13), (30) gives:
% 206.73/31.99 | | | | (31) leq(all_74_10, n1)
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | GROUND_INST: instantiating (15) with all_74_10, simplifying with (8),
% 206.73/31.99 | | | | (11), (31) gives:
% 206.73/31.99 | | | | (32) all_74_10 = n1 | all_74_10 = n0
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | BETA: splitting (32) gives:
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | Case 1:
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | (33) all_74_10 = n0
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | REDUCE: (18), (33) imply:
% 206.73/31.99 | | | | | (34) $false
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | CLOSE: (34) is inconsistent.
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | Case 2:
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | (35) all_74_10 = n1
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | REDUCE: (20), (35) imply:
% 206.73/31.99 | | | | | (36) a_select3(pminus_ds1_filter, n1, n5) = all_74_8
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | REDUCE: (12), (35) imply:
% 206.73/31.99 | | | | | (37) a_select3(pminus_ds1_filter, n5, n1) = all_74_9
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | REDUCE: (11), (35) imply:
% 206.73/31.99 | | | | | (38) $i(n1)
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | REDUCE: (3), (35) imply:
% 206.73/31.99 | | | | | (39) leq(n1, n5)
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | REDUCE: (8), (35) imply:
% 206.73/31.99 | | | | | (40) leq(n0, n1)
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | GROUND_INST: instantiating (4) with n1, n5, all_74_8, simplifying with
% 206.73/31.99 | | | | | (9), (22), (36), (38), (40) gives:
% 206.73/31.99 | | | | | (41) ~ leq(n5, all_74_19) | ~ leq(n1, all_74_19) |
% 206.73/31.99 | | | | | (a_select3(pminus_ds1_filter, n5, n1) = all_74_8 &
% 206.73/31.99 | | | | | $i(all_74_8))
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | BETA: splitting (41) gives:
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | Case 1:
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | (42) ~ leq(n5, all_74_19)
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | REDUCE: (17), (42) imply:
% 206.73/31.99 | | | | | | (43) ~ leq(n5, n5)
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | PRED_UNIFY: (16), (43) imply:
% 206.73/31.99 | | | | | | (44) $false
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | CLOSE: (44) is inconsistent.
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | Case 2:
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | (45) ~ leq(n1, all_74_19) | (a_select3(pminus_ds1_filter, n5,
% 206.73/31.99 | | | | | | n1) = all_74_8 & $i(all_74_8))
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | BETA: splitting (45) gives:
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | Case 1:
% 206.73/31.99 | | | | | | |
% 206.73/31.99 | | | | | | | (46) ~ leq(n1, all_74_19)
% 206.73/31.99 | | | | | | |
% 206.73/31.99 | | | | | | | REDUCE: (17), (46) imply:
% 206.73/31.99 | | | | | | | (47) ~ leq(n1, n5)
% 206.73/31.99 | | | | | | |
% 206.73/31.99 | | | | | | | PRED_UNIFY: (39), (47) imply:
% 206.73/31.99 | | | | | | | (48) $false
% 206.73/31.99 | | | | | | |
% 206.73/31.99 | | | | | | | CLOSE: (48) is inconsistent.
% 206.73/31.99 | | | | | | |
% 206.73/31.99 | | | | | | Case 2:
% 206.73/31.99 | | | | | | |
% 206.73/31.99 | | | | | | | (49) a_select3(pminus_ds1_filter, n5, n1) = all_74_8 &
% 206.73/31.99 | | | | | | | $i(all_74_8)
% 206.73/31.99 | | | | | | |
% 206.73/31.99 | | | | | | | ALPHA: (49) implies:
% 206.73/31.99 | | | | | | | (50) a_select3(pminus_ds1_filter, n5, n1) = all_74_8
% 206.73/31.99 | | | | | | |
% 206.73/31.99 | | | | | | | GROUND_INST: instantiating (10) with all_74_9, all_74_8, n1, n5,
% 206.73/31.99 | | | | | | | pminus_ds1_filter, simplifying with (37), (50) gives:
% 206.73/31.99 | | | | | | | (51) all_74_8 = all_74_9
% 206.73/31.99 | | | | | | |
% 206.73/31.99 | | | | | | | REDUCE: (23), (51) imply:
% 206.73/31.99 | | | | | | | (52) $false
% 206.73/31.99 | | | | | | |
% 206.73/31.99 | | | | | | | CLOSE: (52) is inconsistent.
% 206.73/31.99 | | | | | | |
% 206.73/31.99 | | | | | | End of split
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | End of split
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | End of split
% 206.73/31.99 | | | |
% 206.73/31.99 | | | Case 2:
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | (53) all_74_10 = n2
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | REDUCE: (20), (53) imply:
% 206.73/31.99 | | | | (54) a_select3(pminus_ds1_filter, n2, n5) = all_74_8
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | REDUCE: (12), (53) imply:
% 206.73/31.99 | | | | (55) a_select3(pminus_ds1_filter, n5, n2) = all_74_9
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | REDUCE: (3), (53) imply:
% 206.73/31.99 | | | | (56) leq(n2, n5)
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | REDUCE: (8), (53) imply:
% 206.73/31.99 | | | | (57) leq(n0, n2)
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | GROUND_INST: instantiating (4) with n2, n5, all_74_8, simplifying with
% 206.73/31.99 | | | | (5), (9), (22), (54), (57) gives:
% 206.73/31.99 | | | | (58) ~ leq(n5, all_74_19) | ~ leq(n2, all_74_19) |
% 206.73/31.99 | | | | (a_select3(pminus_ds1_filter, n5, n2) = all_74_8 & $i(all_74_8))
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | BETA: splitting (58) gives:
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | Case 1:
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | (59) ~ leq(n5, all_74_19)
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | REDUCE: (17), (59) imply:
% 206.73/31.99 | | | | | (60) ~ leq(n5, n5)
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | PRED_UNIFY: (16), (60) imply:
% 206.73/31.99 | | | | | (61) $false
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | CLOSE: (61) is inconsistent.
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | Case 2:
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | (62) ~ leq(n2, all_74_19) | (a_select3(pminus_ds1_filter, n5, n2)
% 206.73/31.99 | | | | | = all_74_8 & $i(all_74_8))
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | BETA: splitting (62) gives:
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | Case 1:
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | (63) ~ leq(n2, all_74_19)
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | REDUCE: (17), (63) imply:
% 206.73/31.99 | | | | | | (64) ~ leq(n2, n5)
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | PRED_UNIFY: (56), (64) imply:
% 206.73/31.99 | | | | | | (65) $false
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | CLOSE: (65) is inconsistent.
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | Case 2:
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | (66) a_select3(pminus_ds1_filter, n5, n2) = all_74_8 &
% 206.73/31.99 | | | | | | $i(all_74_8)
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | ALPHA: (66) implies:
% 206.73/31.99 | | | | | | (67) a_select3(pminus_ds1_filter, n5, n2) = all_74_8
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | GROUND_INST: instantiating (10) with all_74_9, all_74_8, n2, n5,
% 206.73/31.99 | | | | | | pminus_ds1_filter, simplifying with (55), (67) gives:
% 206.73/31.99 | | | | | | (68) all_74_8 = all_74_9
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | REDUCE: (23), (68) imply:
% 206.73/31.99 | | | | | | (69) $false
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | | CLOSE: (69) is inconsistent.
% 206.73/31.99 | | | | | |
% 206.73/31.99 | | | | | End of split
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | End of split
% 206.73/31.99 | | | |
% 206.73/31.99 | | | End of split
% 206.73/31.99 | | |
% 206.73/31.99 | | Case 2:
% 206.73/31.99 | | |
% 206.73/31.99 | | | (70) all_74_10 = n3
% 206.73/31.99 | | |
% 206.73/31.99 | | | REDUCE: (20), (70) imply:
% 206.73/31.99 | | | (71) a_select3(pminus_ds1_filter, n3, n5) = all_74_8
% 206.73/31.99 | | |
% 206.73/31.99 | | | REDUCE: (12), (70) imply:
% 206.73/31.99 | | | (72) a_select3(pminus_ds1_filter, n5, n3) = all_74_9
% 206.73/31.99 | | |
% 206.73/31.99 | | | REDUCE: (3), (70) imply:
% 206.73/31.99 | | | (73) leq(n3, n5)
% 206.73/31.99 | | |
% 206.73/31.99 | | | REDUCE: (8), (70) imply:
% 206.73/31.99 | | | (74) leq(n0, n3)
% 206.73/31.99 | | |
% 206.73/31.99 | | | GROUND_INST: instantiating (4) with n3, n5, all_74_8, simplifying with
% 206.73/31.99 | | | (9), (21), (22), (71), (74) gives:
% 206.73/31.99 | | | (75) ~ leq(n5, all_74_19) | ~ leq(n3, all_74_19) |
% 206.73/31.99 | | | (a_select3(pminus_ds1_filter, n5, n3) = all_74_8 & $i(all_74_8))
% 206.73/31.99 | | |
% 206.73/31.99 | | | BETA: splitting (75) gives:
% 206.73/31.99 | | |
% 206.73/31.99 | | | Case 1:
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | (76) ~ leq(n5, all_74_19)
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | REDUCE: (17), (76) imply:
% 206.73/31.99 | | | | (77) ~ leq(n5, n5)
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | PRED_UNIFY: (16), (77) imply:
% 206.73/31.99 | | | | (78) $false
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | CLOSE: (78) is inconsistent.
% 206.73/31.99 | | | |
% 206.73/31.99 | | | Case 2:
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | (79) ~ leq(n3, all_74_19) | (a_select3(pminus_ds1_filter, n5, n3) =
% 206.73/31.99 | | | | all_74_8 & $i(all_74_8))
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | BETA: splitting (79) gives:
% 206.73/31.99 | | | |
% 206.73/31.99 | | | | Case 1:
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | (80) ~ leq(n3, all_74_19)
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | REDUCE: (17), (80) imply:
% 206.73/31.99 | | | | | (81) ~ leq(n3, n5)
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | PRED_UNIFY: (73), (81) imply:
% 206.73/31.99 | | | | | (82) $false
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | CLOSE: (82) is inconsistent.
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | Case 2:
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | (83) a_select3(pminus_ds1_filter, n5, n3) = all_74_8 & $i(all_74_8)
% 206.73/31.99 | | | | |
% 206.73/31.99 | | | | | ALPHA: (83) implies:
% 206.73/31.99 | | | | | (84) a_select3(pminus_ds1_filter, n5, n3) = all_74_8
% 206.73/31.99 | | | | |
% 206.90/31.99 | | | | | GROUND_INST: instantiating (10) with all_74_9, all_74_8, n3, n5,
% 206.90/31.99 | | | | | pminus_ds1_filter, simplifying with (72), (84) gives:
% 206.90/31.99 | | | | | (85) all_74_8 = all_74_9
% 206.90/31.99 | | | | |
% 206.90/31.99 | | | | | REDUCE: (23), (85) imply:
% 206.90/31.99 | | | | | (86) $false
% 206.90/31.99 | | | | |
% 206.90/31.99 | | | | | CLOSE: (86) is inconsistent.
% 206.90/31.99 | | | | |
% 206.90/31.99 | | | | End of split
% 206.90/31.99 | | | |
% 206.90/31.99 | | | End of split
% 206.90/31.99 | | |
% 206.90/31.99 | | End of split
% 206.90/31.99 | |
% 206.90/31.99 | Case 2:
% 206.90/31.99 | |
% 206.90/31.99 | | (87) all_74_10 = n4
% 206.90/31.99 | |
% 206.90/31.99 | | REDUCE: (20), (87) imply:
% 206.90/31.99 | | (88) a_select3(pminus_ds1_filter, n4, n5) = all_74_8
% 206.90/31.99 | |
% 206.90/31.99 | | REDUCE: (12), (87) imply:
% 206.90/31.99 | | (89) a_select3(pminus_ds1_filter, n5, n4) = all_74_9
% 206.90/31.99 | |
% 206.90/31.99 | | REDUCE: (3), (87) imply:
% 206.90/31.99 | | (90) leq(n4, n5)
% 206.90/31.99 | |
% 206.90/31.99 | | REDUCE: (8), (87) imply:
% 206.90/31.99 | | (91) leq(n0, n4)
% 206.90/31.99 | |
% 206.90/32.00 | | GROUND_INST: instantiating (4) with n4, n5, all_74_8, simplifying with (9),
% 206.90/32.00 | | (19), (22), (88), (91) gives:
% 206.90/32.00 | | (92) ~ leq(n5, all_74_19) | ~ leq(n4, all_74_19) |
% 206.90/32.00 | | (a_select3(pminus_ds1_filter, n5, n4) = all_74_8 & $i(all_74_8))
% 206.90/32.00 | |
% 206.90/32.00 | | BETA: splitting (92) gives:
% 206.90/32.00 | |
% 206.90/32.00 | | Case 1:
% 206.90/32.00 | | |
% 206.90/32.00 | | | (93) ~ leq(n5, all_74_19)
% 206.90/32.00 | | |
% 206.90/32.00 | | | REDUCE: (17), (93) imply:
% 206.90/32.00 | | | (94) ~ leq(n5, n5)
% 206.90/32.00 | | |
% 206.90/32.00 | | | PRED_UNIFY: (16), (94) imply:
% 206.90/32.00 | | | (95) $false
% 206.90/32.00 | | |
% 206.90/32.00 | | | CLOSE: (95) is inconsistent.
% 206.90/32.00 | | |
% 206.90/32.00 | | Case 2:
% 206.90/32.00 | | |
% 206.90/32.00 | | | (96) ~ leq(n4, all_74_19) | (a_select3(pminus_ds1_filter, n5, n4) =
% 206.90/32.00 | | | all_74_8 & $i(all_74_8))
% 206.90/32.00 | | |
% 206.90/32.00 | | | BETA: splitting (96) gives:
% 206.90/32.00 | | |
% 206.90/32.00 | | | Case 1:
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | (97) ~ leq(n4, all_74_19)
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | REDUCE: (17), (97) imply:
% 206.90/32.00 | | | | (98) ~ leq(n4, n5)
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | PRED_UNIFY: (90), (98) imply:
% 206.90/32.00 | | | | (99) $false
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | CLOSE: (99) is inconsistent.
% 206.90/32.00 | | | |
% 206.90/32.00 | | | Case 2:
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | (100) a_select3(pminus_ds1_filter, n5, n4) = all_74_8 & $i(all_74_8)
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | ALPHA: (100) implies:
% 206.90/32.00 | | | | (101) a_select3(pminus_ds1_filter, n5, n4) = all_74_8
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | REF_CLOSE: (10), (23), (89), (101) are inconsistent by sub-proof #19.
% 206.90/32.00 | | | |
% 206.90/32.00 | | | End of split
% 206.90/32.00 | | |
% 206.90/32.00 | | End of split
% 206.90/32.00 | |
% 206.90/32.00 | End of split
% 206.90/32.00 |
% 206.90/32.00 End of proof
% 206.90/32.00
% 206.90/32.00 Sub-proof #18 shows that the following formulas are inconsistent:
% 206.90/32.00 ----------------------------------------------------------------
% 206.90/32.00 (1) all_74_11 = n4 | gt(n4, all_74_11)
% 206.90/32.00 (2) pred(n4) = n3
% 206.90/32.00 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 206.90/32.00 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 206.90/32.00 ~ leq(v1, all_74_19) | ~ leq(v0, all_74_19) | ~ leq(n0, v1) | ~
% 206.90/32.00 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2)))
% 206.90/32.00 (4) $i(n2)
% 206.90/32.00 (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0,
% 206.90/32.00 v1) | gt(v1, v0))
% 206.90/32.00 (6) pred(n3) = n2
% 206.90/32.00 (7) leq(n0, n5)
% 206.90/32.00 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.90/32.00 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.90/32.00 v0))
% 206.90/32.00 (9) pred(n2) = n1
% 206.90/32.00 (10) a_select3(pminus_ds1_filter, all_74_11, n5) = all_74_9
% 206.90/32.00 (11) leq(all_74_11, n5)
% 206.90/32.00 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 206.90/32.00 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 206.90/32.00 (13) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 206.90/32.00 leq(n0, v0))
% 206.90/32.00 (14) leq(n5, n5)
% 206.90/32.00 (15) all_74_19 = n5
% 206.90/32.00 (16) ~ (all_74_11 = n0)
% 206.90/32.00 (17) $i(n4)
% 206.90/32.00 (18) $i(n3)
% 206.90/32.00 (19) a_select3(pminus_ds1_filter, n5, all_74_11) = all_74_8
% 206.90/32.00 (20) leq(n0, all_74_11)
% 206.90/32.00 (21) $i(n5)
% 206.90/32.00 (22) ~ (all_74_8 = all_74_9)
% 206.90/32.00 (23) $i(all_74_11)
% 206.90/32.00
% 206.90/32.00 Begin of proof
% 206.90/32.00 |
% 206.90/32.00 | BETA: splitting (1) gives:
% 206.90/32.00 |
% 206.90/32.00 | Case 1:
% 206.90/32.00 | |
% 206.90/32.00 | | (24) gt(n4, all_74_11)
% 206.90/32.00 | |
% 206.90/32.00 | | GROUND_INST: instantiating (12) with all_74_11, n4, n3, simplifying with
% 206.90/32.00 | | (2), (17), (23), (24) gives:
% 206.90/32.00 | | (25) leq(all_74_11, n3)
% 206.90/32.00 | |
% 206.90/32.00 | | GROUND_INST: instantiating (5) with all_74_11, n3, simplifying with (18),
% 206.90/32.00 | | (23), (25) gives:
% 206.90/32.00 | | (26) all_74_11 = n3 | gt(n3, all_74_11)
% 206.90/32.00 | |
% 206.90/32.00 | | BETA: splitting (26) gives:
% 206.90/32.00 | |
% 206.90/32.00 | | Case 1:
% 206.90/32.00 | | |
% 206.90/32.00 | | | (27) gt(n3, all_74_11)
% 206.90/32.00 | | |
% 206.90/32.00 | | | GROUND_INST: instantiating (12) with all_74_11, n3, n2, simplifying with
% 206.90/32.00 | | | (6), (18), (23), (27) gives:
% 206.90/32.00 | | | (28) leq(all_74_11, n2)
% 206.90/32.00 | | |
% 206.90/32.00 | | | GROUND_INST: instantiating (5) with all_74_11, n2, simplifying with (4),
% 206.90/32.00 | | | (23), (28) gives:
% 206.90/32.00 | | | (29) all_74_11 = n2 | gt(n2, all_74_11)
% 206.90/32.00 | | |
% 206.90/32.00 | | | BETA: splitting (29) gives:
% 206.90/32.00 | | |
% 206.90/32.00 | | | Case 1:
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | (30) gt(n2, all_74_11)
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | GROUND_INST: instantiating (12) with all_74_11, n2, n1, simplifying with
% 206.90/32.00 | | | | (4), (9), (23), (30) gives:
% 206.90/32.00 | | | | (31) leq(all_74_11, n1)
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | GROUND_INST: instantiating (13) with all_74_11, simplifying with (20),
% 206.90/32.00 | | | | (23), (31) gives:
% 206.90/32.00 | | | | (32) all_74_11 = n1 | all_74_11 = n0
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | BETA: splitting (32) gives:
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | Case 1:
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | (33) all_74_11 = n0
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | REDUCE: (16), (33) imply:
% 206.90/32.00 | | | | | (34) $false
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | CLOSE: (34) is inconsistent.
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | Case 2:
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | (35) all_74_11 = n1
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | REDUCE: (10), (35) imply:
% 206.90/32.00 | | | | | (36) a_select3(pminus_ds1_filter, n1, n5) = all_74_9
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | REDUCE: (19), (35) imply:
% 206.90/32.00 | | | | | (37) a_select3(pminus_ds1_filter, n5, n1) = all_74_8
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | REDUCE: (23), (35) imply:
% 206.90/32.00 | | | | | (38) $i(n1)
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | REDUCE: (11), (35) imply:
% 206.90/32.00 | | | | | (39) leq(n1, n5)
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | REDUCE: (20), (35) imply:
% 206.90/32.00 | | | | | (40) leq(n0, n1)
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | GROUND_INST: instantiating (3) with n1, n5, all_74_9, simplifying with
% 206.90/32.00 | | | | | (7), (21), (36), (38), (40) gives:
% 206.90/32.00 | | | | | (41) ~ leq(n5, all_74_19) | ~ leq(n1, all_74_19) |
% 206.90/32.00 | | | | | (a_select3(pminus_ds1_filter, n5, n1) = all_74_9 &
% 206.90/32.00 | | | | | $i(all_74_9))
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | BETA: splitting (41) gives:
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | Case 1:
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | (42) ~ leq(n5, all_74_19)
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | REDUCE: (15), (42) imply:
% 206.90/32.00 | | | | | | (43) ~ leq(n5, n5)
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | PRED_UNIFY: (14), (43) imply:
% 206.90/32.00 | | | | | | (44) $false
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | CLOSE: (44) is inconsistent.
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | Case 2:
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | (45) ~ leq(n1, all_74_19) | (a_select3(pminus_ds1_filter, n5,
% 206.90/32.00 | | | | | | n1) = all_74_9 & $i(all_74_9))
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | BETA: splitting (45) gives:
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | Case 1:
% 206.90/32.00 | | | | | | |
% 206.90/32.00 | | | | | | | (46) ~ leq(n1, all_74_19)
% 206.90/32.00 | | | | | | |
% 206.90/32.00 | | | | | | | REDUCE: (15), (46) imply:
% 206.90/32.00 | | | | | | | (47) ~ leq(n1, n5)
% 206.90/32.00 | | | | | | |
% 206.90/32.00 | | | | | | | PRED_UNIFY: (39), (47) imply:
% 206.90/32.00 | | | | | | | (48) $false
% 206.90/32.00 | | | | | | |
% 206.90/32.00 | | | | | | | CLOSE: (48) is inconsistent.
% 206.90/32.00 | | | | | | |
% 206.90/32.00 | | | | | | Case 2:
% 206.90/32.00 | | | | | | |
% 206.90/32.00 | | | | | | | (49) a_select3(pminus_ds1_filter, n5, n1) = all_74_9 &
% 206.90/32.00 | | | | | | | $i(all_74_9)
% 206.90/32.00 | | | | | | |
% 206.90/32.00 | | | | | | | ALPHA: (49) implies:
% 206.90/32.00 | | | | | | | (50) a_select3(pminus_ds1_filter, n5, n1) = all_74_9
% 206.90/32.00 | | | | | | |
% 206.90/32.00 | | | | | | | GROUND_INST: instantiating (8) with all_74_9, all_74_8, n1, n5,
% 206.90/32.00 | | | | | | | pminus_ds1_filter, simplifying with (37), (50) gives:
% 206.90/32.00 | | | | | | | (51) all_74_8 = all_74_9
% 206.90/32.00 | | | | | | |
% 206.90/32.00 | | | | | | | REDUCE: (22), (51) imply:
% 206.90/32.00 | | | | | | | (52) $false
% 206.90/32.00 | | | | | | |
% 206.90/32.00 | | | | | | | CLOSE: (52) is inconsistent.
% 206.90/32.00 | | | | | | |
% 206.90/32.00 | | | | | | End of split
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | End of split
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | End of split
% 206.90/32.00 | | | |
% 206.90/32.00 | | | Case 2:
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | (53) all_74_11 = n2
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | REDUCE: (10), (53) imply:
% 206.90/32.00 | | | | (54) a_select3(pminus_ds1_filter, n2, n5) = all_74_9
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | REDUCE: (19), (53) imply:
% 206.90/32.00 | | | | (55) a_select3(pminus_ds1_filter, n5, n2) = all_74_8
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | REDUCE: (11), (53) imply:
% 206.90/32.00 | | | | (56) leq(n2, n5)
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | REDUCE: (20), (53) imply:
% 206.90/32.00 | | | | (57) leq(n0, n2)
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | GROUND_INST: instantiating (3) with n2, n5, all_74_9, simplifying with
% 206.90/32.00 | | | | (4), (7), (21), (54), (57) gives:
% 206.90/32.00 | | | | (58) ~ leq(n5, all_74_19) | ~ leq(n2, all_74_19) |
% 206.90/32.00 | | | | (a_select3(pminus_ds1_filter, n5, n2) = all_74_9 & $i(all_74_9))
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | BETA: splitting (58) gives:
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | Case 1:
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | (59) ~ leq(n5, all_74_19)
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | REDUCE: (15), (59) imply:
% 206.90/32.00 | | | | | (60) ~ leq(n5, n5)
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | PRED_UNIFY: (14), (60) imply:
% 206.90/32.00 | | | | | (61) $false
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | CLOSE: (61) is inconsistent.
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | Case 2:
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | (62) ~ leq(n2, all_74_19) | (a_select3(pminus_ds1_filter, n5, n2)
% 206.90/32.00 | | | | | = all_74_9 & $i(all_74_9))
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | BETA: splitting (62) gives:
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | Case 1:
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | (63) ~ leq(n2, all_74_19)
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | REDUCE: (15), (63) imply:
% 206.90/32.00 | | | | | | (64) ~ leq(n2, n5)
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | PRED_UNIFY: (56), (64) imply:
% 206.90/32.00 | | | | | | (65) $false
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | CLOSE: (65) is inconsistent.
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | Case 2:
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | (66) a_select3(pminus_ds1_filter, n5, n2) = all_74_9 &
% 206.90/32.00 | | | | | | $i(all_74_9)
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | ALPHA: (66) implies:
% 206.90/32.00 | | | | | | (67) a_select3(pminus_ds1_filter, n5, n2) = all_74_9
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | GROUND_INST: instantiating (8) with all_74_9, all_74_8, n2, n5,
% 206.90/32.00 | | | | | | pminus_ds1_filter, simplifying with (55), (67) gives:
% 206.90/32.00 | | | | | | (68) all_74_8 = all_74_9
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | REDUCE: (22), (68) imply:
% 206.90/32.00 | | | | | | (69) $false
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | | CLOSE: (69) is inconsistent.
% 206.90/32.00 | | | | | |
% 206.90/32.00 | | | | | End of split
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | End of split
% 206.90/32.00 | | | |
% 206.90/32.00 | | | End of split
% 206.90/32.00 | | |
% 206.90/32.00 | | Case 2:
% 206.90/32.00 | | |
% 206.90/32.00 | | | (70) all_74_11 = n3
% 206.90/32.00 | | |
% 206.90/32.00 | | | REDUCE: (10), (70) imply:
% 206.90/32.00 | | | (71) a_select3(pminus_ds1_filter, n3, n5) = all_74_9
% 206.90/32.00 | | |
% 206.90/32.00 | | | REDUCE: (19), (70) imply:
% 206.90/32.00 | | | (72) a_select3(pminus_ds1_filter, n5, n3) = all_74_8
% 206.90/32.00 | | |
% 206.90/32.00 | | | REDUCE: (11), (70) imply:
% 206.90/32.00 | | | (73) leq(n3, n5)
% 206.90/32.00 | | |
% 206.90/32.00 | | | REDUCE: (20), (70) imply:
% 206.90/32.00 | | | (74) leq(n0, n3)
% 206.90/32.00 | | |
% 206.90/32.00 | | | GROUND_INST: instantiating (3) with n3, n5, all_74_9, simplifying with
% 206.90/32.00 | | | (7), (18), (21), (71), (74) gives:
% 206.90/32.00 | | | (75) ~ leq(n5, all_74_19) | ~ leq(n3, all_74_19) |
% 206.90/32.00 | | | (a_select3(pminus_ds1_filter, n5, n3) = all_74_9 & $i(all_74_9))
% 206.90/32.00 | | |
% 206.90/32.00 | | | BETA: splitting (75) gives:
% 206.90/32.00 | | |
% 206.90/32.00 | | | Case 1:
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | (76) ~ leq(n5, all_74_19)
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | REDUCE: (15), (76) imply:
% 206.90/32.00 | | | | (77) ~ leq(n5, n5)
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | PRED_UNIFY: (14), (77) imply:
% 206.90/32.00 | | | | (78) $false
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | CLOSE: (78) is inconsistent.
% 206.90/32.00 | | | |
% 206.90/32.00 | | | Case 2:
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | (79) ~ leq(n3, all_74_19) | (a_select3(pminus_ds1_filter, n5, n3) =
% 206.90/32.00 | | | | all_74_9 & $i(all_74_9))
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | BETA: splitting (79) gives:
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | Case 1:
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | (80) ~ leq(n3, all_74_19)
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | REDUCE: (15), (80) imply:
% 206.90/32.00 | | | | | (81) ~ leq(n3, n5)
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | PRED_UNIFY: (73), (81) imply:
% 206.90/32.00 | | | | | (82) $false
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | CLOSE: (82) is inconsistent.
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | Case 2:
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | (83) a_select3(pminus_ds1_filter, n5, n3) = all_74_9 & $i(all_74_9)
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | ALPHA: (83) implies:
% 206.90/32.00 | | | | | (84) a_select3(pminus_ds1_filter, n5, n3) = all_74_9
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | GROUND_INST: instantiating (8) with all_74_9, all_74_8, n3, n5,
% 206.90/32.00 | | | | | pminus_ds1_filter, simplifying with (72), (84) gives:
% 206.90/32.00 | | | | | (85) all_74_8 = all_74_9
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | REDUCE: (22), (85) imply:
% 206.90/32.00 | | | | | (86) $false
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | | CLOSE: (86) is inconsistent.
% 206.90/32.00 | | | | |
% 206.90/32.00 | | | | End of split
% 206.90/32.00 | | | |
% 206.90/32.00 | | | End of split
% 206.90/32.00 | | |
% 206.90/32.00 | | End of split
% 206.90/32.00 | |
% 206.90/32.00 | Case 2:
% 206.90/32.00 | |
% 206.90/32.00 | | (87) all_74_11 = n4
% 206.90/32.00 | |
% 206.90/32.00 | | REDUCE: (10), (87) imply:
% 206.90/32.00 | | (88) a_select3(pminus_ds1_filter, n4, n5) = all_74_9
% 206.90/32.00 | |
% 206.90/32.00 | | REDUCE: (19), (87) imply:
% 206.90/32.00 | | (89) a_select3(pminus_ds1_filter, n5, n4) = all_74_8
% 206.90/32.00 | |
% 206.90/32.00 | | REDUCE: (11), (87) imply:
% 206.90/32.00 | | (90) leq(n4, n5)
% 206.90/32.00 | |
% 206.90/32.00 | | REDUCE: (20), (87) imply:
% 206.90/32.00 | | (91) leq(n0, n4)
% 206.90/32.00 | |
% 206.90/32.00 | | GROUND_INST: instantiating (3) with n4, n5, all_74_9, simplifying with (7),
% 206.90/32.00 | | (17), (21), (88), (91) gives:
% 206.90/32.00 | | (92) ~ leq(n5, all_74_19) | ~ leq(n4, all_74_19) |
% 206.90/32.00 | | (a_select3(pminus_ds1_filter, n5, n4) = all_74_9 & $i(all_74_9))
% 206.90/32.00 | |
% 206.90/32.00 | | BETA: splitting (92) gives:
% 206.90/32.00 | |
% 206.90/32.00 | | Case 1:
% 206.90/32.00 | | |
% 206.90/32.00 | | | (93) ~ leq(n5, all_74_19)
% 206.90/32.00 | | |
% 206.90/32.00 | | | REDUCE: (15), (93) imply:
% 206.90/32.00 | | | (94) ~ leq(n5, n5)
% 206.90/32.00 | | |
% 206.90/32.00 | | | PRED_UNIFY: (14), (94) imply:
% 206.90/32.00 | | | (95) $false
% 206.90/32.00 | | |
% 206.90/32.00 | | | CLOSE: (95) is inconsistent.
% 206.90/32.00 | | |
% 206.90/32.00 | | Case 2:
% 206.90/32.00 | | |
% 206.90/32.00 | | | (96) ~ leq(n4, all_74_19) | (a_select3(pminus_ds1_filter, n5, n4) =
% 206.90/32.00 | | | all_74_9 & $i(all_74_9))
% 206.90/32.00 | | |
% 206.90/32.00 | | | BETA: splitting (96) gives:
% 206.90/32.00 | | |
% 206.90/32.00 | | | Case 1:
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | (97) ~ leq(n4, all_74_19)
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | REDUCE: (15), (97) imply:
% 206.90/32.00 | | | | (98) ~ leq(n4, n5)
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | PRED_UNIFY: (90), (98) imply:
% 206.90/32.00 | | | | (99) $false
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | CLOSE: (99) is inconsistent.
% 206.90/32.00 | | | |
% 206.90/32.00 | | | Case 2:
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | (100) a_select3(pminus_ds1_filter, n5, n4) = all_74_9 & $i(all_74_9)
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | ALPHA: (100) implies:
% 206.90/32.00 | | | | (101) a_select3(pminus_ds1_filter, n5, n4) = all_74_9
% 206.90/32.00 | | | |
% 206.90/32.00 | | | | REF_CLOSE: (8), (22), (89), (101) are inconsistent by sub-proof #19.
% 206.90/32.00 | | | |
% 206.90/32.00 | | | End of split
% 206.90/32.00 | | |
% 206.90/32.00 | | End of split
% 206.90/32.00 | |
% 206.90/32.00 | End of split
% 206.90/32.00 |
% 206.90/32.00 End of proof
% 206.90/32.00
% 206.90/32.00 Sub-proof #19 shows that the following formulas are inconsistent:
% 206.90/32.00 ----------------------------------------------------------------
% 206.90/32.00 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.90/32.00 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.90/32.00 v0))
% 206.90/32.00 (2) a_select3(pminus_ds1_filter, n5, n4) = all_74_8
% 206.90/32.00 (3) a_select3(pminus_ds1_filter, n5, n4) = all_74_9
% 206.90/32.00 (4) ~ (all_74_8 = all_74_9)
% 206.90/32.00
% 206.90/32.00 Begin of proof
% 206.90/32.00 |
% 206.90/32.00 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n4, n5,
% 206.90/32.00 | pminus_ds1_filter, simplifying with (2), (3) gives:
% 206.90/32.00 | (5) all_74_8 = all_74_9
% 206.90/32.00 |
% 206.90/32.00 | REDUCE: (4), (5) imply:
% 206.90/32.00 | (6) $false
% 206.90/32.00 |
% 206.90/32.00 | CLOSE: (6) is inconsistent.
% 206.90/32.00 |
% 206.90/32.00 End of proof
% 206.90/32.00
% 206.90/32.00 Sub-proof #20 shows that the following formulas are inconsistent:
% 206.90/32.00 ----------------------------------------------------------------
% 206.90/32.00 (1) a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8
% 206.90/32.00 (2) all_74_11 = n4 | gt(n4, all_74_11)
% 206.90/32.00 (3) all_74_10 = n4 | gt(n4, all_74_10)
% 206.90/32.00 (4) pred(n4) = n3
% 206.90/32.00 (5) leq(all_74_10, n5)
% 206.90/32.00 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 206.90/32.00 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 206.90/32.00 ~ leq(v1, all_74_19) | ~ leq(v0, all_74_19) | ~ leq(n0, v1) | ~
% 206.90/32.00 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2)))
% 206.90/32.00 (7) $i(n2)
% 206.90/32.01 (8) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0,
% 206.90/32.01 v1) | gt(v1, v0))
% 206.90/32.01 (9) pred(n3) = n2
% 206.90/32.01 (10) leq(n0, all_74_10)
% 206.90/32.01 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 206.90/32.01 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.90/32.01 v0))
% 206.90/32.01 (12) $i(all_74_10)
% 206.90/32.01 (13) pred(n2) = n1
% 206.90/32.01 (14) leq(all_74_11, n5)
% 206.90/32.01 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 206.90/32.01 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 206.90/32.01 (16) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 206.90/32.01 leq(n0, v0))
% 206.90/32.01 (17) all_74_19 = n5
% 206.90/32.01 (18) ~ (all_74_11 = n0)
% 206.90/32.01 (19) ~ (all_74_10 = n0)
% 206.90/32.01 (20) $i(n4)
% 206.90/32.01 (21) $i(n3)
% 206.90/32.01 (22) leq(n0, all_74_11)
% 206.90/32.01 (23) ~ (all_74_8 = all_74_9)
% 206.90/32.01 (24) a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9
% 206.90/32.01 (25) $i(all_74_11)
% 206.90/32.01
% 206.90/32.01 Begin of proof
% 206.90/32.01 |
% 206.90/32.01 | BETA: splitting (2) gives:
% 206.90/32.01 |
% 206.90/32.01 | Case 1:
% 206.90/32.01 | |
% 206.90/32.01 | | (26) gt(n4, all_74_11)
% 206.90/32.01 | |
% 206.90/32.01 | | GROUND_INST: instantiating (15) with all_74_11, n4, n3, simplifying with
% 206.90/32.01 | | (4), (20), (25), (26) gives:
% 206.90/32.01 | | (27) leq(all_74_11, n3)
% 206.90/32.01 | |
% 206.90/32.01 | | GROUND_INST: instantiating (8) with all_74_11, n3, simplifying with (21),
% 206.90/32.01 | | (25), (27) gives:
% 206.90/32.01 | | (28) all_74_11 = n3 | gt(n3, all_74_11)
% 206.90/32.01 | |
% 206.90/32.01 | | BETA: splitting (3) gives:
% 206.90/32.01 | |
% 206.90/32.01 | | Case 1:
% 206.90/32.01 | | |
% 206.90/32.01 | | | (29) gt(n4, all_74_10)
% 206.90/32.01 | | |
% 206.90/32.01 | | | GROUND_INST: instantiating (15) with all_74_10, n4, n3, simplifying with
% 206.90/32.01 | | | (4), (12), (20), (29) gives:
% 206.90/32.01 | | | (30) leq(all_74_10, n3)
% 206.90/32.01 | | |
% 206.90/32.01 | | | GROUND_INST: instantiating (8) with all_74_10, n3, simplifying with (12),
% 206.90/32.01 | | | (21), (30) gives:
% 206.90/32.01 | | | (31) all_74_10 = n3 | gt(n3, all_74_10)
% 206.90/32.01 | | |
% 206.90/32.01 | | | BETA: splitting (28) gives:
% 206.90/32.01 | | |
% 206.90/32.01 | | | Case 1:
% 206.90/32.01 | | | |
% 206.90/32.01 | | | | (32) gt(n3, all_74_11)
% 206.90/32.01 | | | |
% 206.90/32.01 | | | | GROUND_INST: instantiating (15) with all_74_11, n3, n2, simplifying with
% 206.90/32.01 | | | | (9), (21), (25), (32) gives:
% 206.90/32.01 | | | | (33) leq(all_74_11, n2)
% 206.90/32.01 | | | |
% 206.90/32.01 | | | | GROUND_INST: instantiating (8) with all_74_11, n2, simplifying with (7),
% 206.90/32.01 | | | | (25), (33) gives:
% 206.90/32.01 | | | | (34) all_74_11 = n2 | gt(n2, all_74_11)
% 206.90/32.01 | | | |
% 206.90/32.01 | | | | BETA: splitting (31) gives:
% 206.90/32.01 | | | |
% 206.90/32.01 | | | | Case 1:
% 206.90/32.01 | | | | |
% 206.90/32.01 | | | | | (35) gt(n3, all_74_10)
% 206.90/32.01 | | | | |
% 206.90/32.01 | | | | | GROUND_INST: instantiating (15) with all_74_10, n3, n2, simplifying
% 206.90/32.01 | | | | | with (9), (12), (21), (35) gives:
% 206.90/32.01 | | | | | (36) leq(all_74_10, n2)
% 206.90/32.01 | | | | |
% 206.90/32.01 | | | | | GROUND_INST: instantiating (8) with all_74_10, n2, simplifying with
% 206.90/32.01 | | | | | (7), (12), (36) gives:
% 206.90/32.01 | | | | | (37) all_74_10 = n2 | gt(n2, all_74_10)
% 206.90/32.01 | | | | |
% 206.90/32.01 | | | | | BETA: splitting (34) gives:
% 206.90/32.01 | | | | |
% 206.90/32.01 | | | | | Case 1:
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | (38) gt(n2, all_74_11)
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | GROUND_INST: instantiating (15) with all_74_11, n2, n1, simplifying
% 206.90/32.01 | | | | | | with (7), (13), (25), (38) gives:
% 206.90/32.01 | | | | | | (39) leq(all_74_11, n1)
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | GROUND_INST: instantiating (16) with all_74_11, simplifying with
% 206.90/32.01 | | | | | | (22), (25), (39) gives:
% 206.90/32.01 | | | | | | (40) all_74_11 = n1 | all_74_11 = n0
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | BETA: splitting (40) gives:
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | Case 1:
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | (41) all_74_11 = n0
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | REDUCE: (18), (41) imply:
% 206.90/32.01 | | | | | | | (42) $false
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | CLOSE: (42) is inconsistent.
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | Case 2:
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | (43) all_74_11 = n1
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | REDUCE: (1), (43) imply:
% 206.90/32.01 | | | | | | | (44) a_select3(pminus_ds1_filter, all_74_10, n1) = all_74_8
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | REDUCE: (24), (43) imply:
% 206.90/32.01 | | | | | | | (45) a_select3(pminus_ds1_filter, n1, all_74_10) = all_74_9
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | REDUCE: (25), (43) imply:
% 206.90/32.01 | | | | | | | (46) $i(n1)
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | REDUCE: (14), (43) imply:
% 206.90/32.01 | | | | | | | (47) leq(n1, n5)
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | REDUCE: (22), (43) imply:
% 206.90/32.01 | | | | | | | (48) leq(n0, n1)
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | BETA: splitting (37) gives:
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | Case 1:
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | (49) gt(n2, all_74_10)
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | GROUND_INST: instantiating (15) with all_74_10, n2, n1,
% 206.90/32.01 | | | | | | | | simplifying with (7), (12), (13), (49) gives:
% 206.90/32.01 | | | | | | | | (50) leq(all_74_10, n1)
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | GROUND_INST: instantiating (16) with all_74_10, simplifying with
% 206.90/32.01 | | | | | | | | (10), (12), (50) gives:
% 206.90/32.01 | | | | | | | | (51) all_74_10 = n1 | all_74_10 = n0
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | BETA: splitting (51) gives:
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | Case 1:
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | (52) all_74_10 = n0
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | REDUCE: (19), (52) imply:
% 206.90/32.01 | | | | | | | | | (53) $false
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | CLOSE: (53) is inconsistent.
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | Case 2:
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | (54) all_74_10 = n1
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | REDUCE: (44), (54) imply:
% 206.90/32.01 | | | | | | | | | (55) a_select3(pminus_ds1_filter, n1, n1) = all_74_8
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | REDUCE: (45), (54) imply:
% 206.90/32.01 | | | | | | | | | (56) a_select3(pminus_ds1_filter, n1, n1) = all_74_9
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | GROUND_INST: instantiating (11) with all_74_9, all_74_8, n1,
% 206.90/32.01 | | | | | | | | | n1, pminus_ds1_filter, simplifying with (55), (56)
% 206.90/32.01 | | | | | | | | | gives:
% 206.90/32.01 | | | | | | | | | (57) all_74_8 = all_74_9
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | REDUCE: (23), (57) imply:
% 206.90/32.01 | | | | | | | | | (58) $false
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | CLOSE: (58) is inconsistent.
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | End of split
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | Case 2:
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | (59) all_74_10 = n2
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | REDUCE: (44), (59) imply:
% 206.90/32.01 | | | | | | | | (60) a_select3(pminus_ds1_filter, n2, n1) = all_74_8
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | REDUCE: (45), (59) imply:
% 206.90/32.01 | | | | | | | | (61) a_select3(pminus_ds1_filter, n1, n2) = all_74_9
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | REDUCE: (5), (59) imply:
% 206.90/32.01 | | | | | | | | (62) leq(n2, n5)
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | REDUCE: (10), (59) imply:
% 206.90/32.01 | | | | | | | | (63) leq(n0, n2)
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | GROUND_INST: instantiating (6) with n1, n2, all_74_9,
% 206.90/32.01 | | | | | | | | simplifying with (7), (46), (48), (61), (63) gives:
% 206.90/32.01 | | | | | | | | (64) ~ leq(n2, all_74_19) | ~ leq(n1, all_74_19) |
% 206.90/32.01 | | | | | | | | (a_select3(pminus_ds1_filter, n2, n1) = all_74_9 &
% 206.90/32.01 | | | | | | | | $i(all_74_9))
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | BETA: splitting (64) gives:
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | Case 1:
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | (65) ~ leq(n2, all_74_19)
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | REDUCE: (17), (65) imply:
% 206.90/32.01 | | | | | | | | | (66) ~ leq(n2, n5)
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | PRED_UNIFY: (62), (66) imply:
% 206.90/32.01 | | | | | | | | | (67) $false
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | CLOSE: (67) is inconsistent.
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | Case 2:
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | (68) ~ leq(n1, all_74_19) | (a_select3(pminus_ds1_filter,
% 206.90/32.01 | | | | | | | | | n2, n1) = all_74_9 & $i(all_74_9))
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | BETA: splitting (68) gives:
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | Case 1:
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | | (69) ~ leq(n1, all_74_19)
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | | REDUCE: (17), (69) imply:
% 206.90/32.01 | | | | | | | | | | (70) ~ leq(n1, n5)
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | | PRED_UNIFY: (47), (70) imply:
% 206.90/32.01 | | | | | | | | | | (71) $false
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | | CLOSE: (71) is inconsistent.
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | Case 2:
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | | (72) a_select3(pminus_ds1_filter, n2, n1) = all_74_9 &
% 206.90/32.01 | | | | | | | | | | $i(all_74_9)
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | | ALPHA: (72) implies:
% 206.90/32.01 | | | | | | | | | | (73) a_select3(pminus_ds1_filter, n2, n1) = all_74_9
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | | REF_CLOSE: (11), (23), (60), (73) are inconsistent by
% 206.90/32.01 | | | | | | | | | | sub-proof #26.
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | End of split
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | End of split
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | End of split
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | End of split
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | Case 2:
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | (74) all_74_11 = n2
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | REDUCE: (1), (74) imply:
% 206.90/32.01 | | | | | | (75) a_select3(pminus_ds1_filter, all_74_10, n2) = all_74_8
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | REDUCE: (24), (74) imply:
% 206.90/32.01 | | | | | | (76) a_select3(pminus_ds1_filter, n2, all_74_10) = all_74_9
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | REDUCE: (14), (74) imply:
% 206.90/32.01 | | | | | | (77) leq(n2, n5)
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | REDUCE: (22), (74) imply:
% 206.90/32.01 | | | | | | (78) leq(n0, n2)
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | BETA: splitting (37) gives:
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | Case 1:
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | (79) gt(n2, all_74_10)
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | GROUND_INST: instantiating (15) with all_74_10, n2, n1,
% 206.90/32.01 | | | | | | | simplifying with (7), (12), (13), (79) gives:
% 206.90/32.01 | | | | | | | (80) leq(all_74_10, n1)
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | GROUND_INST: instantiating (16) with all_74_10, simplifying with
% 206.90/32.01 | | | | | | | (10), (12), (80) gives:
% 206.90/32.01 | | | | | | | (81) all_74_10 = n1 | all_74_10 = n0
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | BETA: splitting (81) gives:
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | Case 1:
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | (82) all_74_10 = n0
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | REDUCE: (19), (82) imply:
% 206.90/32.01 | | | | | | | | (83) $false
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | CLOSE: (83) is inconsistent.
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | Case 2:
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | (84) all_74_10 = n1
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | REDUCE: (75), (84) imply:
% 206.90/32.01 | | | | | | | | (85) a_select3(pminus_ds1_filter, n1, n2) = all_74_8
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | REDUCE: (76), (84) imply:
% 206.90/32.01 | | | | | | | | (86) a_select3(pminus_ds1_filter, n2, n1) = all_74_9
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | REDUCE: (12), (84) imply:
% 206.90/32.01 | | | | | | | | (87) $i(n1)
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | REDUCE: (5), (84) imply:
% 206.90/32.01 | | | | | | | | (88) leq(n1, n5)
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | REDUCE: (10), (84) imply:
% 206.90/32.01 | | | | | | | | (89) leq(n0, n1)
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | GROUND_INST: instantiating (6) with n1, n2, all_74_8,
% 206.90/32.01 | | | | | | | | simplifying with (7), (78), (85), (87), (89) gives:
% 206.90/32.01 | | | | | | | | (90) ~ leq(n2, all_74_19) | ~ leq(n1, all_74_19) |
% 206.90/32.01 | | | | | | | | (a_select3(pminus_ds1_filter, n2, n1) = all_74_8 &
% 206.90/32.01 | | | | | | | | $i(all_74_8))
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | BETA: splitting (90) gives:
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | Case 1:
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | (91) ~ leq(n2, all_74_19)
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | REDUCE: (17), (91) imply:
% 206.90/32.01 | | | | | | | | | (92) ~ leq(n2, n5)
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | PRED_UNIFY: (77), (92) imply:
% 206.90/32.01 | | | | | | | | | (93) $false
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | CLOSE: (93) is inconsistent.
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | Case 2:
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | (94) ~ leq(n1, all_74_19) | (a_select3(pminus_ds1_filter,
% 206.90/32.01 | | | | | | | | | n2, n1) = all_74_8 & $i(all_74_8))
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | BETA: splitting (94) gives:
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | Case 1:
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | | (95) ~ leq(n1, all_74_19)
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | | REDUCE: (17), (95) imply:
% 206.90/32.01 | | | | | | | | | | (96) ~ leq(n1, n5)
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | | PRED_UNIFY: (88), (96) imply:
% 206.90/32.01 | | | | | | | | | | (97) $false
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | | CLOSE: (97) is inconsistent.
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | Case 2:
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | | (98) a_select3(pminus_ds1_filter, n2, n1) = all_74_8 &
% 206.90/32.01 | | | | | | | | | | $i(all_74_8)
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | | ALPHA: (98) implies:
% 206.90/32.01 | | | | | | | | | | (99) a_select3(pminus_ds1_filter, n2, n1) = all_74_8
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | | REF_CLOSE: (11), (23), (86), (99) are inconsistent by
% 206.90/32.01 | | | | | | | | | | sub-proof #26.
% 206.90/32.01 | | | | | | | | | |
% 206.90/32.01 | | | | | | | | | End of split
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | End of split
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | End of split
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | Case 2:
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | (100) all_74_10 = n2
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | REDUCE: (75), (100) imply:
% 206.90/32.01 | | | | | | | (101) a_select3(pminus_ds1_filter, n2, n2) = all_74_8
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | REDUCE: (76), (100) imply:
% 206.90/32.01 | | | | | | | (102) a_select3(pminus_ds1_filter, n2, n2) = all_74_9
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | GROUND_INST: instantiating (11) with all_74_9, all_74_8, n2, n2,
% 206.90/32.01 | | | | | | | pminus_ds1_filter, simplifying with (101), (102)
% 206.90/32.01 | | | | | | | gives:
% 206.90/32.01 | | | | | | | (103) all_74_8 = all_74_9
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | REDUCE: (23), (103) imply:
% 206.90/32.01 | | | | | | | (104) $false
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | CLOSE: (104) is inconsistent.
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | End of split
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | End of split
% 206.90/32.01 | | | | |
% 206.90/32.01 | | | | Case 2:
% 206.90/32.01 | | | | |
% 206.90/32.01 | | | | | (105) all_74_10 = n3
% 206.90/32.01 | | | | |
% 206.90/32.01 | | | | | REDUCE: (1), (105) imply:
% 206.90/32.01 | | | | | (106) a_select3(pminus_ds1_filter, n3, all_74_11) = all_74_8
% 206.90/32.01 | | | | |
% 206.90/32.01 | | | | | REDUCE: (24), (105) imply:
% 206.90/32.01 | | | | | (107) a_select3(pminus_ds1_filter, all_74_11, n3) = all_74_9
% 206.90/32.01 | | | | |
% 206.90/32.01 | | | | | REDUCE: (5), (105) imply:
% 206.90/32.01 | | | | | (108) leq(n3, n5)
% 206.90/32.01 | | | | |
% 206.90/32.01 | | | | | REDUCE: (10), (105) imply:
% 206.90/32.01 | | | | | (109) leq(n0, n3)
% 206.90/32.01 | | | | |
% 206.90/32.01 | | | | | BETA: splitting (34) gives:
% 206.90/32.01 | | | | |
% 206.90/32.01 | | | | | Case 1:
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | (110) gt(n2, all_74_11)
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | GROUND_INST: instantiating (15) with all_74_11, n2, n1, simplifying
% 206.90/32.01 | | | | | | with (7), (13), (25), (110) gives:
% 206.90/32.01 | | | | | | (111) leq(all_74_11, n1)
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | GROUND_INST: instantiating (16) with all_74_11, simplifying with
% 206.90/32.01 | | | | | | (22), (25), (111) gives:
% 206.90/32.01 | | | | | | (112) all_74_11 = n1 | all_74_11 = n0
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | BETA: splitting (112) gives:
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | Case 1:
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | (113) all_74_11 = n0
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | REDUCE: (18), (113) imply:
% 206.90/32.01 | | | | | | | (114) $false
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | CLOSE: (114) is inconsistent.
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | Case 2:
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | (115) all_74_11 = n1
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | REDUCE: (107), (115) imply:
% 206.90/32.01 | | | | | | | (116) a_select3(pminus_ds1_filter, n1, n3) = all_74_9
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | REDUCE: (106), (115) imply:
% 206.90/32.01 | | | | | | | (117) a_select3(pminus_ds1_filter, n3, n1) = all_74_8
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | REDUCE: (25), (115) imply:
% 206.90/32.01 | | | | | | | (118) $i(n1)
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | REDUCE: (14), (115) imply:
% 206.90/32.01 | | | | | | | (119) leq(n1, n5)
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | REDUCE: (22), (115) imply:
% 206.90/32.01 | | | | | | | (120) leq(n0, n1)
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | GROUND_INST: instantiating (6) with n1, n3, all_74_9, simplifying
% 206.90/32.01 | | | | | | | with (21), (109), (116), (118), (120) gives:
% 206.90/32.01 | | | | | | | (121) ~ leq(n3, all_74_19) | ~ leq(n1, all_74_19) |
% 206.90/32.01 | | | | | | | (a_select3(pminus_ds1_filter, n3, n1) = all_74_9 &
% 206.90/32.01 | | | | | | | $i(all_74_9))
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | BETA: splitting (121) gives:
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | | Case 1:
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | (122) ~ leq(n3, all_74_19)
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | REDUCE: (17), (122) imply:
% 206.90/32.01 | | | | | | | | (123) ~ leq(n3, n5)
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | PRED_UNIFY: (108), (123) imply:
% 206.90/32.01 | | | | | | | | (124) $false
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | CLOSE: (124) is inconsistent.
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | Case 2:
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | (125) ~ leq(n1, all_74_19) | (a_select3(pminus_ds1_filter,
% 206.90/32.01 | | | | | | | | n3, n1) = all_74_9 & $i(all_74_9))
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | BETA: splitting (125) gives:
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | | Case 1:
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | (126) ~ leq(n1, all_74_19)
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | REDUCE: (17), (126) imply:
% 206.90/32.01 | | | | | | | | | (127) ~ leq(n1, n5)
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | PRED_UNIFY: (119), (127) imply:
% 206.90/32.01 | | | | | | | | | (128) $false
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | CLOSE: (128) is inconsistent.
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | Case 2:
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | (129) a_select3(pminus_ds1_filter, n3, n1) = all_74_9 &
% 206.90/32.01 | | | | | | | | | $i(all_74_9)
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | ALPHA: (129) implies:
% 206.90/32.01 | | | | | | | | | (130) a_select3(pminus_ds1_filter, n3, n1) = all_74_9
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | | REF_CLOSE: (11), (23), (117), (130) are inconsistent by
% 206.90/32.01 | | | | | | | | | sub-proof #25.
% 206.90/32.01 | | | | | | | | |
% 206.90/32.01 | | | | | | | | End of split
% 206.90/32.01 | | | | | | | |
% 206.90/32.01 | | | | | | | End of split
% 206.90/32.01 | | | | | | |
% 206.90/32.01 | | | | | | End of split
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | Case 2:
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | (131) all_74_11 = n2
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | REDUCE: (107), (131) imply:
% 206.90/32.01 | | | | | | (132) a_select3(pminus_ds1_filter, n2, n3) = all_74_9
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | REDUCE: (106), (131) imply:
% 206.90/32.01 | | | | | | (133) a_select3(pminus_ds1_filter, n3, n2) = all_74_8
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | REDUCE: (14), (131) imply:
% 206.90/32.01 | | | | | | (134) leq(n2, n5)
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | REDUCE: (22), (131) imply:
% 206.90/32.01 | | | | | | (135) leq(n0, n2)
% 206.90/32.01 | | | | | |
% 206.90/32.01 | | | | | | GROUND_INST: instantiating (6) with n2, n3, all_74_9, simplifying
% 206.90/32.01 | | | | | | with (7), (21), (109), (132), (135) gives:
% 206.90/32.01 | | | | | | (136) ~ leq(n3, all_74_19) | ~ leq(n2, all_74_19) |
% 206.90/32.01 | | | | | | (a_select3(pminus_ds1_filter, n3, n2) = all_74_9 &
% 206.90/32.01 | | | | | | $i(all_74_9))
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | BETA: splitting (136) gives:
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | Case 1:
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | (137) ~ leq(n3, all_74_19)
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | REDUCE: (17), (137) imply:
% 206.90/32.02 | | | | | | | (138) ~ leq(n3, n5)
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | PRED_UNIFY: (108), (138) imply:
% 206.90/32.02 | | | | | | | (139) $false
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | CLOSE: (139) is inconsistent.
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | Case 2:
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | (140) ~ leq(n2, all_74_19) | (a_select3(pminus_ds1_filter, n3,
% 206.90/32.02 | | | | | | | n2) = all_74_9 & $i(all_74_9))
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | BETA: splitting (140) gives:
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | Case 1:
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | (141) ~ leq(n2, all_74_19)
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | REDUCE: (17), (141) imply:
% 206.90/32.02 | | | | | | | | (142) ~ leq(n2, n5)
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | PRED_UNIFY: (134), (142) imply:
% 206.90/32.02 | | | | | | | | (143) $false
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | CLOSE: (143) is inconsistent.
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | Case 2:
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | (144) a_select3(pminus_ds1_filter, n3, n2) = all_74_9 &
% 206.90/32.02 | | | | | | | | $i(all_74_9)
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | ALPHA: (144) implies:
% 206.90/32.02 | | | | | | | | (145) a_select3(pminus_ds1_filter, n3, n2) = all_74_9
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | REF_CLOSE: (11), (23), (133), (145) are inconsistent by
% 206.90/32.02 | | | | | | | | sub-proof #24.
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | End of split
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | End of split
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | End of split
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | End of split
% 206.90/32.02 | | | |
% 206.90/32.02 | | | Case 2:
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | (146) all_74_11 = n3
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | REDUCE: (1), (146) imply:
% 206.90/32.02 | | | | (147) a_select3(pminus_ds1_filter, all_74_10, n3) = all_74_8
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | REDUCE: (24), (146) imply:
% 206.90/32.02 | | | | (148) a_select3(pminus_ds1_filter, n3, all_74_10) = all_74_9
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | REDUCE: (14), (146) imply:
% 206.90/32.02 | | | | (149) leq(n3, n5)
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | REDUCE: (22), (146) imply:
% 206.90/32.02 | | | | (150) leq(n0, n3)
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | BETA: splitting (31) gives:
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | Case 1:
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | (151) gt(n3, all_74_10)
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | GROUND_INST: instantiating (15) with all_74_10, n3, n2, simplifying
% 206.90/32.02 | | | | | with (9), (12), (21), (151) gives:
% 206.90/32.02 | | | | | (152) leq(all_74_10, n2)
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | GROUND_INST: instantiating (8) with all_74_10, n2, simplifying with
% 206.90/32.02 | | | | | (7), (12), (152) gives:
% 206.90/32.02 | | | | | (153) all_74_10 = n2 | gt(n2, all_74_10)
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | BETA: splitting (153) gives:
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | Case 1:
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | (154) gt(n2, all_74_10)
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | GROUND_INST: instantiating (15) with all_74_10, n2, n1, simplifying
% 206.90/32.02 | | | | | | with (7), (12), (13), (154) gives:
% 206.90/32.02 | | | | | | (155) leq(all_74_10, n1)
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | GROUND_INST: instantiating (16) with all_74_10, simplifying with
% 206.90/32.02 | | | | | | (10), (12), (155) gives:
% 206.90/32.02 | | | | | | (156) all_74_10 = n1 | all_74_10 = n0
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | BETA: splitting (156) gives:
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | Case 1:
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | (157) all_74_10 = n0
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | REDUCE: (19), (157) imply:
% 206.90/32.02 | | | | | | | (158) $false
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | CLOSE: (158) is inconsistent.
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | Case 2:
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | (159) all_74_10 = n1
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | REDUCE: (147), (159) imply:
% 206.90/32.02 | | | | | | | (160) a_select3(pminus_ds1_filter, n1, n3) = all_74_8
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | REDUCE: (148), (159) imply:
% 206.90/32.02 | | | | | | | (161) a_select3(pminus_ds1_filter, n3, n1) = all_74_9
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | REDUCE: (12), (159) imply:
% 206.90/32.02 | | | | | | | (162) $i(n1)
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | REDUCE: (5), (159) imply:
% 206.90/32.02 | | | | | | | (163) leq(n1, n5)
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | REDUCE: (10), (159) imply:
% 206.90/32.02 | | | | | | | (164) leq(n0, n1)
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | GROUND_INST: instantiating (6) with n1, n3, all_74_8, simplifying
% 206.90/32.02 | | | | | | | with (21), (150), (160), (162), (164) gives:
% 206.90/32.02 | | | | | | | (165) ~ leq(n3, all_74_19) | ~ leq(n1, all_74_19) |
% 206.90/32.02 | | | | | | | (a_select3(pminus_ds1_filter, n3, n1) = all_74_8 &
% 206.90/32.02 | | | | | | | $i(all_74_8))
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | BETA: splitting (165) gives:
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | Case 1:
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | (166) ~ leq(n3, all_74_19)
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | REDUCE: (17), (166) imply:
% 206.90/32.02 | | | | | | | | (167) ~ leq(n3, n5)
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | PRED_UNIFY: (149), (167) imply:
% 206.90/32.02 | | | | | | | | (168) $false
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | CLOSE: (168) is inconsistent.
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | Case 2:
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | (169) ~ leq(n1, all_74_19) | (a_select3(pminus_ds1_filter,
% 206.90/32.02 | | | | | | | | n3, n1) = all_74_8 & $i(all_74_8))
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | BETA: splitting (169) gives:
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | Case 1:
% 206.90/32.02 | | | | | | | | |
% 206.90/32.02 | | | | | | | | | (170) ~ leq(n1, all_74_19)
% 206.90/32.02 | | | | | | | | |
% 206.90/32.02 | | | | | | | | | REDUCE: (17), (170) imply:
% 206.90/32.02 | | | | | | | | | (171) ~ leq(n1, n5)
% 206.90/32.02 | | | | | | | | |
% 206.90/32.02 | | | | | | | | | PRED_UNIFY: (163), (171) imply:
% 206.90/32.02 | | | | | | | | | (172) $false
% 206.90/32.02 | | | | | | | | |
% 206.90/32.02 | | | | | | | | | CLOSE: (172) is inconsistent.
% 206.90/32.02 | | | | | | | | |
% 206.90/32.02 | | | | | | | | Case 2:
% 206.90/32.02 | | | | | | | | |
% 206.90/32.02 | | | | | | | | | (173) a_select3(pminus_ds1_filter, n3, n1) = all_74_8 &
% 206.90/32.02 | | | | | | | | | $i(all_74_8)
% 206.90/32.02 | | | | | | | | |
% 206.90/32.02 | | | | | | | | | ALPHA: (173) implies:
% 206.90/32.02 | | | | | | | | | (174) a_select3(pminus_ds1_filter, n3, n1) = all_74_8
% 206.90/32.02 | | | | | | | | |
% 206.90/32.02 | | | | | | | | | REF_CLOSE: (11), (23), (161), (174) are inconsistent by
% 206.90/32.02 | | | | | | | | | sub-proof #25.
% 206.90/32.02 | | | | | | | | |
% 206.90/32.02 | | | | | | | | End of split
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | End of split
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | End of split
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | Case 2:
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | (175) all_74_10 = n2
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | REDUCE: (147), (175) imply:
% 206.90/32.02 | | | | | | (176) a_select3(pminus_ds1_filter, n2, n3) = all_74_8
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | REDUCE: (148), (175) imply:
% 206.90/32.02 | | | | | | (177) a_select3(pminus_ds1_filter, n3, n2) = all_74_9
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | REDUCE: (5), (175) imply:
% 206.90/32.02 | | | | | | (178) leq(n2, n5)
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | REDUCE: (10), (175) imply:
% 206.90/32.02 | | | | | | (179) leq(n0, n2)
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | GROUND_INST: instantiating (6) with n2, n3, all_74_8, simplifying
% 206.90/32.02 | | | | | | with (7), (21), (150), (176), (179) gives:
% 206.90/32.02 | | | | | | (180) ~ leq(n3, all_74_19) | ~ leq(n2, all_74_19) |
% 206.90/32.02 | | | | | | (a_select3(pminus_ds1_filter, n3, n2) = all_74_8 &
% 206.90/32.02 | | | | | | $i(all_74_8))
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | BETA: splitting (180) gives:
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | Case 1:
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | (181) ~ leq(n3, all_74_19)
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | REDUCE: (17), (181) imply:
% 206.90/32.02 | | | | | | | (182) ~ leq(n3, n5)
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | PRED_UNIFY: (149), (182) imply:
% 206.90/32.02 | | | | | | | (183) $false
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | CLOSE: (183) is inconsistent.
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | Case 2:
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | (184) ~ leq(n2, all_74_19) | (a_select3(pminus_ds1_filter, n3,
% 206.90/32.02 | | | | | | | n2) = all_74_8 & $i(all_74_8))
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | BETA: splitting (184) gives:
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | Case 1:
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | (185) ~ leq(n2, all_74_19)
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | REDUCE: (17), (185) imply:
% 206.90/32.02 | | | | | | | | (186) ~ leq(n2, n5)
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | PRED_UNIFY: (178), (186) imply:
% 206.90/32.02 | | | | | | | | (187) $false
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | CLOSE: (187) is inconsistent.
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | Case 2:
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | (188) a_select3(pminus_ds1_filter, n3, n2) = all_74_8 &
% 206.90/32.02 | | | | | | | | $i(all_74_8)
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | ALPHA: (188) implies:
% 206.90/32.02 | | | | | | | | (189) a_select3(pminus_ds1_filter, n3, n2) = all_74_8
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | REF_CLOSE: (11), (23), (177), (189) are inconsistent by
% 206.90/32.02 | | | | | | | | sub-proof #24.
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | End of split
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | End of split
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | End of split
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | Case 2:
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | (190) all_74_10 = n3
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | REDUCE: (147), (190) imply:
% 206.90/32.02 | | | | | (191) a_select3(pminus_ds1_filter, n3, n3) = all_74_8
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | REDUCE: (148), (190) imply:
% 206.90/32.02 | | | | | (192) a_select3(pminus_ds1_filter, n3, n3) = all_74_9
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | GROUND_INST: instantiating (11) with all_74_9, all_74_8, n3, n3,
% 206.90/32.02 | | | | | pminus_ds1_filter, simplifying with (191), (192) gives:
% 206.90/32.02 | | | | | (193) all_74_8 = all_74_9
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | REDUCE: (23), (193) imply:
% 206.90/32.02 | | | | | (194) $false
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | CLOSE: (194) is inconsistent.
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | End of split
% 206.90/32.02 | | | |
% 206.90/32.02 | | | End of split
% 206.90/32.02 | | |
% 206.90/32.02 | | Case 2:
% 206.90/32.02 | | |
% 206.90/32.02 | | | (195) all_74_10 = n4
% 206.90/32.02 | | |
% 206.90/32.02 | | | REDUCE: (1), (195) imply:
% 206.90/32.02 | | | (196) a_select3(pminus_ds1_filter, n4, all_74_11) = all_74_8
% 206.90/32.02 | | |
% 206.90/32.02 | | | REDUCE: (24), (195) imply:
% 206.90/32.02 | | | (197) a_select3(pminus_ds1_filter, all_74_11, n4) = all_74_9
% 206.90/32.02 | | |
% 206.90/32.02 | | | REDUCE: (5), (195) imply:
% 206.90/32.02 | | | (198) leq(n4, n5)
% 206.90/32.02 | | |
% 206.90/32.02 | | | REDUCE: (10), (195) imply:
% 206.90/32.02 | | | (199) leq(n0, n4)
% 206.90/32.02 | | |
% 206.90/32.02 | | | BETA: splitting (28) gives:
% 206.90/32.02 | | |
% 206.90/32.02 | | | Case 1:
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | (200) gt(n3, all_74_11)
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | GROUND_INST: instantiating (15) with all_74_11, n3, n2, simplifying with
% 206.90/32.02 | | | | (9), (21), (25), (200) gives:
% 206.90/32.02 | | | | (201) leq(all_74_11, n2)
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | GROUND_INST: instantiating (8) with all_74_11, n2, simplifying with (7),
% 206.90/32.02 | | | | (25), (201) gives:
% 206.90/32.02 | | | | (202) all_74_11 = n2 | gt(n2, all_74_11)
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | BETA: splitting (202) gives:
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | Case 1:
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | (203) gt(n2, all_74_11)
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | GROUND_INST: instantiating (15) with all_74_11, n2, n1, simplifying
% 206.90/32.02 | | | | | with (7), (13), (25), (203) gives:
% 206.90/32.02 | | | | | (204) leq(all_74_11, n1)
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | GROUND_INST: instantiating (16) with all_74_11, simplifying with (22),
% 206.90/32.02 | | | | | (25), (204) gives:
% 206.90/32.02 | | | | | (205) all_74_11 = n1 | all_74_11 = n0
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | BETA: splitting (205) gives:
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | Case 1:
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | (206) all_74_11 = n0
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | REDUCE: (18), (206) imply:
% 206.90/32.02 | | | | | | (207) $false
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | CLOSE: (207) is inconsistent.
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | Case 2:
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | (208) all_74_11 = n1
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | REDUCE: (197), (208) imply:
% 206.90/32.02 | | | | | | (209) a_select3(pminus_ds1_filter, n1, n4) = all_74_9
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | REDUCE: (196), (208) imply:
% 206.90/32.02 | | | | | | (210) a_select3(pminus_ds1_filter, n4, n1) = all_74_8
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | REDUCE: (25), (208) imply:
% 206.90/32.02 | | | | | | (211) $i(n1)
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | REDUCE: (14), (208) imply:
% 206.90/32.02 | | | | | | (212) leq(n1, n5)
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | REDUCE: (22), (208) imply:
% 206.90/32.02 | | | | | | (213) leq(n0, n1)
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | GROUND_INST: instantiating (6) with n1, n4, all_74_9, simplifying
% 206.90/32.02 | | | | | | with (20), (199), (209), (211), (213) gives:
% 206.90/32.02 | | | | | | (214) ~ leq(n4, all_74_19) | ~ leq(n1, all_74_19) |
% 206.90/32.02 | | | | | | (a_select3(pminus_ds1_filter, n4, n1) = all_74_9 &
% 206.90/32.02 | | | | | | $i(all_74_9))
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | BETA: splitting (214) gives:
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | Case 1:
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | (215) ~ leq(n4, all_74_19)
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | REDUCE: (17), (215) imply:
% 206.90/32.02 | | | | | | | (216) ~ leq(n4, n5)
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | PRED_UNIFY: (198), (216) imply:
% 206.90/32.02 | | | | | | | (217) $false
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | CLOSE: (217) is inconsistent.
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | Case 2:
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | (218) ~ leq(n1, all_74_19) | (a_select3(pminus_ds1_filter, n4,
% 206.90/32.02 | | | | | | | n1) = all_74_9 & $i(all_74_9))
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | BETA: splitting (218) gives:
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | Case 1:
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | (219) ~ leq(n1, all_74_19)
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | REDUCE: (17), (219) imply:
% 206.90/32.02 | | | | | | | | (220) ~ leq(n1, n5)
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | PRED_UNIFY: (212), (220) imply:
% 206.90/32.02 | | | | | | | | (221) $false
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | CLOSE: (221) is inconsistent.
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | Case 2:
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | (222) a_select3(pminus_ds1_filter, n4, n1) = all_74_9 &
% 206.90/32.02 | | | | | | | | $i(all_74_9)
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | ALPHA: (222) implies:
% 206.90/32.02 | | | | | | | | (223) a_select3(pminus_ds1_filter, n4, n1) = all_74_9
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | | REF_CLOSE: (11), (23), (210), (223) are inconsistent by
% 206.90/32.02 | | | | | | | | sub-proof #23.
% 206.90/32.02 | | | | | | | |
% 206.90/32.02 | | | | | | | End of split
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | End of split
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | End of split
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | Case 2:
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | (224) all_74_11 = n2
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | REDUCE: (197), (224) imply:
% 206.90/32.02 | | | | | (225) a_select3(pminus_ds1_filter, n2, n4) = all_74_9
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | REDUCE: (196), (224) imply:
% 206.90/32.02 | | | | | (226) a_select3(pminus_ds1_filter, n4, n2) = all_74_8
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | REDUCE: (14), (224) imply:
% 206.90/32.02 | | | | | (227) leq(n2, n5)
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | REDUCE: (22), (224) imply:
% 206.90/32.02 | | | | | (228) leq(n0, n2)
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | GROUND_INST: instantiating (6) with n2, n4, all_74_9, simplifying with
% 206.90/32.02 | | | | | (7), (20), (199), (225), (228) gives:
% 206.90/32.02 | | | | | (229) ~ leq(n4, all_74_19) | ~ leq(n2, all_74_19) |
% 206.90/32.02 | | | | | (a_select3(pminus_ds1_filter, n4, n2) = all_74_9 &
% 206.90/32.02 | | | | | $i(all_74_9))
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | BETA: splitting (229) gives:
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | Case 1:
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | (230) ~ leq(n4, all_74_19)
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | REDUCE: (17), (230) imply:
% 206.90/32.02 | | | | | | (231) ~ leq(n4, n5)
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | PRED_UNIFY: (198), (231) imply:
% 206.90/32.02 | | | | | | (232) $false
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | CLOSE: (232) is inconsistent.
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | Case 2:
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | (233) ~ leq(n2, all_74_19) | (a_select3(pminus_ds1_filter, n4,
% 206.90/32.02 | | | | | | n2) = all_74_9 & $i(all_74_9))
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | BETA: splitting (233) gives:
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | Case 1:
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | (234) ~ leq(n2, all_74_19)
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | REDUCE: (17), (234) imply:
% 206.90/32.02 | | | | | | | (235) ~ leq(n2, n5)
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | PRED_UNIFY: (227), (235) imply:
% 206.90/32.02 | | | | | | | (236) $false
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | CLOSE: (236) is inconsistent.
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | Case 2:
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | (237) a_select3(pminus_ds1_filter, n4, n2) = all_74_9 &
% 206.90/32.02 | | | | | | | $i(all_74_9)
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | ALPHA: (237) implies:
% 206.90/32.02 | | | | | | | (238) a_select3(pminus_ds1_filter, n4, n2) = all_74_9
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | | REF_CLOSE: (11), (23), (226), (238) are inconsistent by sub-proof
% 206.90/32.02 | | | | | | | #22.
% 206.90/32.02 | | | | | | |
% 206.90/32.02 | | | | | | End of split
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | End of split
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | End of split
% 206.90/32.02 | | | |
% 206.90/32.02 | | | Case 2:
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | (239) all_74_11 = n3
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | REDUCE: (197), (239) imply:
% 206.90/32.02 | | | | (240) a_select3(pminus_ds1_filter, n3, n4) = all_74_9
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | REDUCE: (196), (239) imply:
% 206.90/32.02 | | | | (241) a_select3(pminus_ds1_filter, n4, n3) = all_74_8
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | REDUCE: (14), (239) imply:
% 206.90/32.02 | | | | (242) leq(n3, n5)
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | REDUCE: (22), (239) imply:
% 206.90/32.02 | | | | (243) leq(n0, n3)
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | GROUND_INST: instantiating (6) with n3, n4, all_74_9, simplifying with
% 206.90/32.02 | | | | (20), (21), (199), (240), (243) gives:
% 206.90/32.02 | | | | (244) ~ leq(n4, all_74_19) | ~ leq(n3, all_74_19) |
% 206.90/32.02 | | | | (a_select3(pminus_ds1_filter, n4, n3) = all_74_9 &
% 206.90/32.02 | | | | $i(all_74_9))
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | BETA: splitting (244) gives:
% 206.90/32.02 | | | |
% 206.90/32.02 | | | | Case 1:
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | (245) ~ leq(n4, all_74_19)
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | REDUCE: (17), (245) imply:
% 206.90/32.02 | | | | | (246) ~ leq(n4, n5)
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | PRED_UNIFY: (198), (246) imply:
% 206.90/32.02 | | | | | (247) $false
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | CLOSE: (247) is inconsistent.
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | Case 2:
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | (248) ~ leq(n3, all_74_19) | (a_select3(pminus_ds1_filter, n4, n3)
% 206.90/32.02 | | | | | = all_74_9 & $i(all_74_9))
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | BETA: splitting (248) gives:
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | | Case 1:
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | (249) ~ leq(n3, all_74_19)
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | REDUCE: (17), (249) imply:
% 206.90/32.02 | | | | | | (250) ~ leq(n3, n5)
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | PRED_UNIFY: (242), (250) imply:
% 206.90/32.02 | | | | | | (251) $false
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | CLOSE: (251) is inconsistent.
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | Case 2:
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | (252) a_select3(pminus_ds1_filter, n4, n3) = all_74_9 &
% 206.90/32.02 | | | | | | $i(all_74_9)
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | ALPHA: (252) implies:
% 206.90/32.02 | | | | | | (253) a_select3(pminus_ds1_filter, n4, n3) = all_74_9
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | | REF_CLOSE: (11), (23), (241), (253) are inconsistent by sub-proof
% 206.90/32.02 | | | | | | #21.
% 206.90/32.02 | | | | | |
% 206.90/32.02 | | | | | End of split
% 206.90/32.02 | | | | |
% 206.90/32.02 | | | | End of split
% 206.90/32.02 | | | |
% 206.90/32.02 | | | End of split
% 206.90/32.02 | | |
% 206.90/32.02 | | End of split
% 206.90/32.02 | |
% 206.90/32.02 | Case 2:
% 206.90/32.02 | |
% 206.90/32.02 | | (254) all_74_11 = n4
% 206.90/32.02 | |
% 206.90/32.02 | | REDUCE: (1), (254) imply:
% 206.90/32.02 | | (255) a_select3(pminus_ds1_filter, all_74_10, n4) = all_74_8
% 206.90/32.02 | |
% 206.90/32.02 | | REDUCE: (24), (254) imply:
% 206.90/32.02 | | (256) a_select3(pminus_ds1_filter, n4, all_74_10) = all_74_9
% 206.90/32.02 | |
% 206.90/32.02 | | REDUCE: (14), (254) imply:
% 206.90/32.02 | | (257) leq(n4, n5)
% 206.90/32.02 | |
% 206.90/32.02 | | REDUCE: (22), (254) imply:
% 206.90/32.02 | | (258) leq(n0, n4)
% 206.90/32.02 | |
% 206.90/32.02 | | BETA: splitting (3) gives:
% 206.90/32.02 | |
% 206.90/32.02 | | Case 1:
% 206.90/32.02 | | |
% 206.90/32.02 | | | (259) gt(n4, all_74_10)
% 206.90/32.02 | | |
% 206.90/32.02 | | | GROUND_INST: instantiating (15) with all_74_10, n4, n3, simplifying with
% 206.90/32.03 | | | (4), (12), (20), (259) gives:
% 206.90/32.03 | | | (260) leq(all_74_10, n3)
% 206.90/32.03 | | |
% 206.90/32.03 | | | GROUND_INST: instantiating (8) with all_74_10, n3, simplifying with (12),
% 206.90/32.03 | | | (21), (260) gives:
% 206.90/32.03 | | | (261) all_74_10 = n3 | gt(n3, all_74_10)
% 206.90/32.03 | | |
% 206.90/32.03 | | | BETA: splitting (261) gives:
% 206.90/32.03 | | |
% 206.90/32.03 | | | Case 1:
% 206.90/32.03 | | | |
% 206.90/32.03 | | | | (262) gt(n3, all_74_10)
% 206.90/32.03 | | | |
% 206.90/32.03 | | | | GROUND_INST: instantiating (15) with all_74_10, n3, n2, simplifying with
% 206.90/32.03 | | | | (9), (12), (21), (262) gives:
% 206.90/32.03 | | | | (263) leq(all_74_10, n2)
% 206.90/32.03 | | | |
% 206.90/32.03 | | | | GROUND_INST: instantiating (8) with all_74_10, n2, simplifying with (7),
% 206.90/32.03 | | | | (12), (263) gives:
% 206.90/32.03 | | | | (264) all_74_10 = n2 | gt(n2, all_74_10)
% 206.90/32.03 | | | |
% 206.90/32.03 | | | | BETA: splitting (264) gives:
% 206.90/32.03 | | | |
% 206.90/32.03 | | | | Case 1:
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | (265) gt(n2, all_74_10)
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | GROUND_INST: instantiating (15) with all_74_10, n2, n1, simplifying
% 206.90/32.03 | | | | | with (7), (12), (13), (265) gives:
% 206.90/32.03 | | | | | (266) leq(all_74_10, n1)
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | GROUND_INST: instantiating (16) with all_74_10, simplifying with (10),
% 206.90/32.03 | | | | | (12), (266) gives:
% 206.90/32.03 | | | | | (267) all_74_10 = n1 | all_74_10 = n0
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | BETA: splitting (267) gives:
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | Case 1:
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | (268) all_74_10 = n0
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | REDUCE: (19), (268) imply:
% 206.90/32.03 | | | | | | (269) $false
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | CLOSE: (269) is inconsistent.
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | Case 2:
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | (270) all_74_10 = n1
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | REDUCE: (255), (270) imply:
% 206.90/32.03 | | | | | | (271) a_select3(pminus_ds1_filter, n1, n4) = all_74_8
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | REDUCE: (256), (270) imply:
% 206.90/32.03 | | | | | | (272) a_select3(pminus_ds1_filter, n4, n1) = all_74_9
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | REDUCE: (12), (270) imply:
% 206.90/32.03 | | | | | | (273) $i(n1)
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | REDUCE: (5), (270) imply:
% 206.90/32.03 | | | | | | (274) leq(n1, n5)
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | REDUCE: (10), (270) imply:
% 206.90/32.03 | | | | | | (275) leq(n0, n1)
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | GROUND_INST: instantiating (6) with n1, n4, all_74_8, simplifying
% 206.90/32.03 | | | | | | with (20), (258), (271), (273), (275) gives:
% 206.90/32.03 | | | | | | (276) ~ leq(n4, all_74_19) | ~ leq(n1, all_74_19) |
% 206.90/32.03 | | | | | | (a_select3(pminus_ds1_filter, n4, n1) = all_74_8 &
% 206.90/32.03 | | | | | | $i(all_74_8))
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | BETA: splitting (276) gives:
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | Case 1:
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | | (277) ~ leq(n4, all_74_19)
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | | REDUCE: (17), (277) imply:
% 206.90/32.03 | | | | | | | (278) ~ leq(n4, n5)
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | | PRED_UNIFY: (257), (278) imply:
% 206.90/32.03 | | | | | | | (279) $false
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | | CLOSE: (279) is inconsistent.
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | Case 2:
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | | (280) ~ leq(n1, all_74_19) | (a_select3(pminus_ds1_filter, n4,
% 206.90/32.03 | | | | | | | n1) = all_74_8 & $i(all_74_8))
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | | BETA: splitting (280) gives:
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | | Case 1:
% 206.90/32.03 | | | | | | | |
% 206.90/32.03 | | | | | | | | (281) ~ leq(n1, all_74_19)
% 206.90/32.03 | | | | | | | |
% 206.90/32.03 | | | | | | | | REDUCE: (17), (281) imply:
% 206.90/32.03 | | | | | | | | (282) ~ leq(n1, n5)
% 206.90/32.03 | | | | | | | |
% 206.90/32.03 | | | | | | | | PRED_UNIFY: (274), (282) imply:
% 206.90/32.03 | | | | | | | | (283) $false
% 206.90/32.03 | | | | | | | |
% 206.90/32.03 | | | | | | | | CLOSE: (283) is inconsistent.
% 206.90/32.03 | | | | | | | |
% 206.90/32.03 | | | | | | | Case 2:
% 206.90/32.03 | | | | | | | |
% 206.90/32.03 | | | | | | | | (284) a_select3(pminus_ds1_filter, n4, n1) = all_74_8 &
% 206.90/32.03 | | | | | | | | $i(all_74_8)
% 206.90/32.03 | | | | | | | |
% 206.90/32.03 | | | | | | | | ALPHA: (284) implies:
% 206.90/32.03 | | | | | | | | (285) a_select3(pminus_ds1_filter, n4, n1) = all_74_8
% 206.90/32.03 | | | | | | | |
% 206.90/32.03 | | | | | | | | REF_CLOSE: (11), (23), (272), (285) are inconsistent by
% 206.90/32.03 | | | | | | | | sub-proof #23.
% 206.90/32.03 | | | | | | | |
% 206.90/32.03 | | | | | | | End of split
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | End of split
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | End of split
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | Case 2:
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | (286) all_74_10 = n2
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | REDUCE: (255), (286) imply:
% 206.90/32.03 | | | | | (287) a_select3(pminus_ds1_filter, n2, n4) = all_74_8
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | REDUCE: (256), (286) imply:
% 206.90/32.03 | | | | | (288) a_select3(pminus_ds1_filter, n4, n2) = all_74_9
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | REDUCE: (5), (286) imply:
% 206.90/32.03 | | | | | (289) leq(n2, n5)
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | REDUCE: (10), (286) imply:
% 206.90/32.03 | | | | | (290) leq(n0, n2)
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | GROUND_INST: instantiating (6) with n2, n4, all_74_8, simplifying with
% 206.90/32.03 | | | | | (7), (20), (258), (287), (290) gives:
% 206.90/32.03 | | | | | (291) ~ leq(n4, all_74_19) | ~ leq(n2, all_74_19) |
% 206.90/32.03 | | | | | (a_select3(pminus_ds1_filter, n4, n2) = all_74_8 &
% 206.90/32.03 | | | | | $i(all_74_8))
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | BETA: splitting (291) gives:
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | Case 1:
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | (292) ~ leq(n4, all_74_19)
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | REDUCE: (17), (292) imply:
% 206.90/32.03 | | | | | | (293) ~ leq(n4, n5)
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | PRED_UNIFY: (257), (293) imply:
% 206.90/32.03 | | | | | | (294) $false
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | CLOSE: (294) is inconsistent.
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | Case 2:
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | (295) ~ leq(n2, all_74_19) | (a_select3(pminus_ds1_filter, n4,
% 206.90/32.03 | | | | | | n2) = all_74_8 & $i(all_74_8))
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | BETA: splitting (295) gives:
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | Case 1:
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | | (296) ~ leq(n2, all_74_19)
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | | REDUCE: (17), (296) imply:
% 206.90/32.03 | | | | | | | (297) ~ leq(n2, n5)
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | | PRED_UNIFY: (289), (297) imply:
% 206.90/32.03 | | | | | | | (298) $false
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | | CLOSE: (298) is inconsistent.
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | Case 2:
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | | (299) a_select3(pminus_ds1_filter, n4, n2) = all_74_8 &
% 206.90/32.03 | | | | | | | $i(all_74_8)
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | | ALPHA: (299) implies:
% 206.90/32.03 | | | | | | | (300) a_select3(pminus_ds1_filter, n4, n2) = all_74_8
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | | REF_CLOSE: (11), (23), (288), (300) are inconsistent by sub-proof
% 206.90/32.03 | | | | | | | #22.
% 206.90/32.03 | | | | | | |
% 206.90/32.03 | | | | | | End of split
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | End of split
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | End of split
% 206.90/32.03 | | | |
% 206.90/32.03 | | | Case 2:
% 206.90/32.03 | | | |
% 206.90/32.03 | | | | (301) all_74_10 = n3
% 206.90/32.03 | | | |
% 206.90/32.03 | | | | REDUCE: (255), (301) imply:
% 206.90/32.03 | | | | (302) a_select3(pminus_ds1_filter, n3, n4) = all_74_8
% 206.90/32.03 | | | |
% 206.90/32.03 | | | | REDUCE: (256), (301) imply:
% 206.90/32.03 | | | | (303) a_select3(pminus_ds1_filter, n4, n3) = all_74_9
% 206.90/32.03 | | | |
% 206.90/32.03 | | | | REDUCE: (5), (301) imply:
% 206.90/32.03 | | | | (304) leq(n3, n5)
% 206.90/32.03 | | | |
% 206.90/32.03 | | | | REDUCE: (10), (301) imply:
% 206.90/32.03 | | | | (305) leq(n0, n3)
% 206.90/32.03 | | | |
% 206.90/32.03 | | | | GROUND_INST: instantiating (6) with n3, n4, all_74_8, simplifying with
% 206.90/32.03 | | | | (20), (21), (258), (302), (305) gives:
% 206.90/32.03 | | | | (306) ~ leq(n4, all_74_19) | ~ leq(n3, all_74_19) |
% 206.90/32.03 | | | | (a_select3(pminus_ds1_filter, n4, n3) = all_74_8 &
% 206.90/32.03 | | | | $i(all_74_8))
% 206.90/32.03 | | | |
% 206.90/32.03 | | | | BETA: splitting (306) gives:
% 206.90/32.03 | | | |
% 206.90/32.03 | | | | Case 1:
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | (307) ~ leq(n4, all_74_19)
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | REDUCE: (17), (307) imply:
% 206.90/32.03 | | | | | (308) ~ leq(n4, n5)
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | PRED_UNIFY: (257), (308) imply:
% 206.90/32.03 | | | | | (309) $false
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | CLOSE: (309) is inconsistent.
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | Case 2:
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | (310) ~ leq(n3, all_74_19) | (a_select3(pminus_ds1_filter, n4, n3)
% 206.90/32.03 | | | | | = all_74_8 & $i(all_74_8))
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | BETA: splitting (310) gives:
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | | Case 1:
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | (311) ~ leq(n3, all_74_19)
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | REDUCE: (17), (311) imply:
% 206.90/32.03 | | | | | | (312) ~ leq(n3, n5)
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | PRED_UNIFY: (304), (312) imply:
% 206.90/32.03 | | | | | | (313) $false
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | CLOSE: (313) is inconsistent.
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | Case 2:
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | (314) a_select3(pminus_ds1_filter, n4, n3) = all_74_8 &
% 206.90/32.03 | | | | | | $i(all_74_8)
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | ALPHA: (314) implies:
% 206.90/32.03 | | | | | | (315) a_select3(pminus_ds1_filter, n4, n3) = all_74_8
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | | REF_CLOSE: (11), (23), (303), (315) are inconsistent by sub-proof
% 206.90/32.03 | | | | | | #21.
% 206.90/32.03 | | | | | |
% 206.90/32.03 | | | | | End of split
% 206.90/32.03 | | | | |
% 206.90/32.03 | | | | End of split
% 206.90/32.03 | | | |
% 206.90/32.03 | | | End of split
% 206.90/32.03 | | |
% 206.90/32.03 | | Case 2:
% 206.90/32.03 | | |
% 206.90/32.03 | | | (316) all_74_10 = n4
% 206.90/32.03 | | |
% 206.90/32.03 | | | REDUCE: (255), (316) imply:
% 206.90/32.03 | | | (317) a_select3(pminus_ds1_filter, n4, n4) = all_74_8
% 206.90/32.03 | | |
% 206.90/32.03 | | | REDUCE: (256), (316) imply:
% 206.90/32.03 | | | (318) a_select3(pminus_ds1_filter, n4, n4) = all_74_9
% 206.90/32.03 | | |
% 206.90/32.03 | | | GROUND_INST: instantiating (11) with all_74_9, all_74_8, n4, n4,
% 206.90/32.03 | | | pminus_ds1_filter, simplifying with (317), (318) gives:
% 206.90/32.03 | | | (319) all_74_8 = all_74_9
% 206.90/32.03 | | |
% 206.90/32.03 | | | REDUCE: (23), (319) imply:
% 206.90/32.03 | | | (320) $false
% 206.90/32.03 | | |
% 206.90/32.03 | | | CLOSE: (320) is inconsistent.
% 206.90/32.03 | | |
% 206.90/32.03 | | End of split
% 206.90/32.03 | |
% 206.90/32.03 | End of split
% 206.90/32.03 |
% 206.90/32.03 End of proof
% 206.90/32.03
% 206.90/32.03 Sub-proof #21 shows that the following formulas are inconsistent:
% 206.90/32.03 ----------------------------------------------------------------
% 206.90/32.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.90/32.03 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.90/32.03 v0))
% 206.90/32.03 (2) a_select3(pminus_ds1_filter, n4, n3) = all_74_8
% 206.90/32.03 (3) a_select3(pminus_ds1_filter, n4, n3) = all_74_9
% 206.90/32.03 (4) ~ (all_74_8 = all_74_9)
% 206.90/32.03
% 206.90/32.03 Begin of proof
% 206.90/32.03 |
% 206.90/32.03 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n3, n4,
% 206.90/32.03 | pminus_ds1_filter, simplifying with (2), (3) gives:
% 206.90/32.03 | (5) all_74_8 = all_74_9
% 206.90/32.03 |
% 206.90/32.03 | REDUCE: (4), (5) imply:
% 206.90/32.03 | (6) $false
% 206.90/32.03 |
% 206.90/32.03 | CLOSE: (6) is inconsistent.
% 206.90/32.03 |
% 206.90/32.03 End of proof
% 206.90/32.03
% 206.90/32.03 Sub-proof #22 shows that the following formulas are inconsistent:
% 206.90/32.03 ----------------------------------------------------------------
% 206.90/32.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.90/32.03 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.90/32.03 v0))
% 206.90/32.03 (2) a_select3(pminus_ds1_filter, n4, n2) = all_74_8
% 206.90/32.03 (3) a_select3(pminus_ds1_filter, n4, n2) = all_74_9
% 206.90/32.03 (4) ~ (all_74_8 = all_74_9)
% 206.90/32.03
% 206.90/32.03 Begin of proof
% 206.90/32.03 |
% 206.90/32.03 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n2, n4,
% 206.90/32.03 | pminus_ds1_filter, simplifying with (2), (3) gives:
% 206.90/32.03 | (5) all_74_8 = all_74_9
% 206.90/32.03 |
% 206.90/32.03 | REDUCE: (4), (5) imply:
% 206.90/32.03 | (6) $false
% 206.90/32.03 |
% 206.90/32.03 | CLOSE: (6) is inconsistent.
% 206.90/32.03 |
% 206.90/32.03 End of proof
% 206.90/32.03
% 206.90/32.03 Sub-proof #23 shows that the following formulas are inconsistent:
% 206.90/32.03 ----------------------------------------------------------------
% 206.90/32.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.90/32.03 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.90/32.03 v0))
% 206.90/32.03 (2) a_select3(pminus_ds1_filter, n4, n1) = all_74_8
% 206.90/32.03 (3) a_select3(pminus_ds1_filter, n4, n1) = all_74_9
% 206.90/32.03 (4) ~ (all_74_8 = all_74_9)
% 206.90/32.03
% 206.90/32.03 Begin of proof
% 206.90/32.03 |
% 206.90/32.03 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n1, n4,
% 206.90/32.03 | pminus_ds1_filter, simplifying with (2), (3) gives:
% 206.90/32.03 | (5) all_74_8 = all_74_9
% 206.90/32.03 |
% 206.90/32.03 | REDUCE: (4), (5) imply:
% 206.90/32.03 | (6) $false
% 206.90/32.03 |
% 206.90/32.03 | CLOSE: (6) is inconsistent.
% 206.90/32.03 |
% 206.90/32.03 End of proof
% 206.90/32.03
% 206.90/32.03 Sub-proof #24 shows that the following formulas are inconsistent:
% 206.90/32.03 ----------------------------------------------------------------
% 206.90/32.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.90/32.03 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.90/32.03 v0))
% 206.90/32.03 (2) a_select3(pminus_ds1_filter, n3, n2) = all_74_8
% 206.90/32.03 (3) a_select3(pminus_ds1_filter, n3, n2) = all_74_9
% 206.90/32.03 (4) ~ (all_74_8 = all_74_9)
% 206.90/32.03
% 206.90/32.03 Begin of proof
% 206.90/32.03 |
% 206.90/32.03 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n2, n3,
% 206.90/32.03 | pminus_ds1_filter, simplifying with (2), (3) gives:
% 206.90/32.03 | (5) all_74_8 = all_74_9
% 206.90/32.03 |
% 206.90/32.03 | REDUCE: (4), (5) imply:
% 206.90/32.03 | (6) $false
% 206.90/32.03 |
% 206.90/32.03 | CLOSE: (6) is inconsistent.
% 206.90/32.03 |
% 206.90/32.03 End of proof
% 206.90/32.03
% 206.90/32.03 Sub-proof #25 shows that the following formulas are inconsistent:
% 206.90/32.03 ----------------------------------------------------------------
% 206.90/32.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.90/32.03 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.90/32.03 v0))
% 206.90/32.03 (2) a_select3(pminus_ds1_filter, n3, n1) = all_74_8
% 206.90/32.03 (3) a_select3(pminus_ds1_filter, n3, n1) = all_74_9
% 206.90/32.03 (4) ~ (all_74_8 = all_74_9)
% 206.90/32.03
% 206.90/32.03 Begin of proof
% 206.90/32.03 |
% 206.90/32.03 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n1, n3,
% 206.90/32.03 | pminus_ds1_filter, simplifying with (2), (3) gives:
% 206.90/32.03 | (5) all_74_8 = all_74_9
% 206.90/32.03 |
% 206.90/32.03 | REDUCE: (4), (5) imply:
% 206.90/32.03 | (6) $false
% 206.90/32.03 |
% 206.90/32.03 | CLOSE: (6) is inconsistent.
% 206.90/32.03 |
% 206.90/32.03 End of proof
% 206.90/32.03
% 206.90/32.03 Sub-proof #26 shows that the following formulas are inconsistent:
% 206.90/32.03 ----------------------------------------------------------------
% 206.90/32.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 206.90/32.03 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.90/32.03 v0))
% 206.90/32.03 (2) a_select3(pminus_ds1_filter, n2, n1) = all_74_8
% 206.90/32.03 (3) a_select3(pminus_ds1_filter, n2, n1) = all_74_9
% 206.90/32.03 (4) ~ (all_74_8 = all_74_9)
% 206.90/32.03
% 206.90/32.03 Begin of proof
% 206.90/32.03 |
% 206.90/32.03 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n1, n2,
% 206.90/32.03 | pminus_ds1_filter, simplifying with (2), (3) gives:
% 206.90/32.03 | (5) all_74_8 = all_74_9
% 206.90/32.03 |
% 206.90/32.03 | REDUCE: (4), (5) imply:
% 206.90/32.03 | (6) $false
% 206.90/32.03 |
% 206.90/32.03 | CLOSE: (6) is inconsistent.
% 206.90/32.03 |
% 206.90/32.03 End of proof
% 206.90/32.03
% 206.90/32.03 Sub-proof #27 shows that the following formulas are inconsistent:
% 206.90/32.03 ----------------------------------------------------------------
% 206.90/32.03 (1) $i(all_74_10)
% 206.90/32.03 (2) all_74_10 = n0
% 206.90/32.03 (3) gt(all_74_10, n0)
% 206.90/32.03 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0))
% 206.90/32.03
% 206.90/32.03 Begin of proof
% 206.90/32.03 |
% 206.90/32.03 | REDUCE: (1), (2) imply:
% 206.90/32.03 | (5) $i(n0)
% 206.90/32.03 |
% 206.90/32.03 | REDUCE: (2), (3) imply:
% 206.90/32.03 | (6) gt(n0, n0)
% 206.90/32.03 |
% 206.90/32.03 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives:
% 206.90/32.03 | (7) $false
% 206.90/32.03 |
% 206.90/32.03 | CLOSE: (7) is inconsistent.
% 206.90/32.03 |
% 206.90/32.03 End of proof
% 206.90/32.03
% 206.90/32.03 Sub-proof #28 shows that the following formulas are inconsistent:
% 206.90/32.03 ----------------------------------------------------------------
% 206.90/32.03 (1) $i(all_74_11)
% 206.90/32.03 (2) all_74_11 = n0
% 206.90/32.03 (3) gt(all_74_11, n0)
% 206.90/32.03 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0))
% 206.90/32.03
% 206.90/32.03 Begin of proof
% 206.90/32.03 |
% 206.90/32.03 | REDUCE: (1), (2) imply:
% 206.90/32.03 | (5) $i(n0)
% 206.90/32.03 |
% 206.90/32.03 | REDUCE: (2), (3) imply:
% 206.90/32.03 | (6) gt(n0, n0)
% 206.90/32.03 |
% 206.90/32.03 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives:
% 206.90/32.03 | (7) $false
% 206.90/32.03 |
% 206.90/32.03 | CLOSE: (7) is inconsistent.
% 206.90/32.03 |
% 206.90/32.03 End of proof
% 206.90/32.03
% 206.90/32.03 Sub-proof #29 shows that the following formulas are inconsistent:
% 206.90/32.03 ----------------------------------------------------------------
% 206.90/32.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(r_ds1_filter,
% 206.90/32.03 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_18) | ~
% 206.90/32.03 leq(v0, all_74_18) | ~ leq(n0, v1) | ~ leq(n0, v0) |
% 206.90/32.03 (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2)))
% 206.90/32.03 (2) gt(all_74_7, n0)
% 206.90/32.03 (3) leq(all_74_6, n2)
% 206.90/32.03 (4) leq(n0, all_74_7)
% 206.90/32.03 (5) $i(n2)
% 206.90/32.03 (6) all_74_18 = n2
% 206.90/32.03 (7) all_74_6 = n2 | all_74_6 = n1 | all_74_6 = n0
% 206.90/32.03 (8) ~ (all_74_4 = all_74_5)
% 206.90/32.03 (9) leq(all_74_7, n2)
% 206.90/32.03 (10) a_select3(r_ds1_filter, all_74_6, all_74_7) = all_74_4
% 206.90/32.03 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 206.90/32.03 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 206.90/32.03 v0))
% 206.90/32.03 (12) $i(all_74_6)
% 206.90/32.03 (13) pred(n2) = n1
% 206.90/32.03 (14) leq(n0, all_74_6)
% 206.90/32.03 (15) all_74_6 = n0 | gt(all_74_6, n0)
% 206.90/32.03 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 206.90/32.03 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 206.90/32.03 (17) a_select3(r_ds1_filter, all_74_7, all_74_6) = all_74_5
% 206.90/32.03 (18) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~
% 206.90/32.03 leq(n0, v0))
% 206.90/32.03 (19) ~ gt(n0, n0)
% 206.90/32.03 (20) all_74_6 = n2 | gt(n2, all_74_6)
% 206.90/32.03 (21) all_74_7 = n2 | all_74_7 = n1 | all_74_7 = n0
% 206.90/32.03 (22) all_74_7 = n2 | gt(n2, all_74_7)
% 206.90/32.03 (23) $i(all_74_7)
% 206.90/32.03
% 206.90/32.03 Begin of proof
% 206.90/32.03 |
% 206.90/32.03 | BETA: splitting (15) gives:
% 206.90/32.03 |
% 206.90/32.03 | Case 1:
% 206.90/32.03 | |
% 206.90/32.03 | | (24) gt(all_74_6, n0)
% 206.90/32.04 | |
% 206.90/32.04 | | BETA: splitting (20) gives:
% 206.90/32.04 | |
% 206.90/32.04 | | Case 1:
% 206.90/32.04 | | |
% 206.90/32.04 | | | (25) gt(n2, all_74_6)
% 206.90/32.04 | | |
% 206.90/32.04 | | | GROUND_INST: instantiating (16) with all_74_6, n2, n1, simplifying with
% 206.90/32.04 | | | (5), (12), (13), (25) gives:
% 206.90/32.04 | | | (26) leq(all_74_6, n1)
% 206.90/32.04 | | |
% 206.90/32.04 | | | GROUND_INST: instantiating (18) with all_74_6, simplifying with (12),
% 206.90/32.04 | | | (14), (26) gives:
% 206.90/32.04 | | | (27) all_74_6 = n1 | all_74_6 = n0
% 206.90/32.04 | | |
% 206.90/32.04 | | | BETA: splitting (22) gives:
% 206.90/32.04 | | |
% 206.90/32.04 | | | Case 1:
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | (28) gt(n2, all_74_7)
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | GROUND_INST: instantiating (16) with all_74_7, n2, n1, simplifying with
% 206.90/32.04 | | | | (5), (13), (23), (28) gives:
% 206.90/32.04 | | | | (29) leq(all_74_7, n1)
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | GROUND_INST: instantiating (18) with all_74_7, simplifying with (4),
% 206.90/32.04 | | | | (23), (29) gives:
% 206.90/32.04 | | | | (30) all_74_7 = n1 | all_74_7 = n0
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | BETA: splitting (21) gives:
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | Case 1:
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | (31) all_74_7 = n0
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | REDUCE: (2), (31) imply:
% 206.90/32.04 | | | | | (32) gt(n0, n0)
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | PRED_UNIFY: (19), (32) imply:
% 206.90/32.04 | | | | | (33) $false
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | CLOSE: (33) is inconsistent.
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | Case 2:
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | (34) ~ (all_74_7 = n0)
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | BETA: splitting (30) gives:
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | Case 1:
% 206.90/32.04 | | | | | |
% 206.90/32.04 | | | | | | (35) all_74_7 = n0
% 206.90/32.04 | | | | | |
% 206.90/32.04 | | | | | | REDUCE: (34), (35) imply:
% 206.90/32.04 | | | | | | (36) $false
% 206.90/32.04 | | | | | |
% 206.90/32.04 | | | | | | CLOSE: (36) is inconsistent.
% 206.90/32.04 | | | | | |
% 206.90/32.04 | | | | | Case 2:
% 206.90/32.04 | | | | | |
% 206.90/32.04 | | | | | | (37) all_74_7 = n1
% 206.90/32.04 | | | | | |
% 206.90/32.04 | | | | | | REDUCE: (10), (37) imply:
% 206.90/32.04 | | | | | | (38) a_select3(r_ds1_filter, all_74_6, n1) = all_74_4
% 206.90/32.04 | | | | | |
% 206.90/32.04 | | | | | | REDUCE: (17), (37) imply:
% 206.90/32.04 | | | | | | (39) a_select3(r_ds1_filter, n1, all_74_6) = all_74_5
% 206.90/32.04 | | | | | |
% 206.90/32.04 | | | | | | BETA: splitting (7) gives:
% 206.90/32.04 | | | | | |
% 206.90/32.04 | | | | | | Case 1:
% 206.90/32.04 | | | | | | |
% 206.90/32.04 | | | | | | | (40) all_74_6 = n0
% 206.90/32.04 | | | | | | |
% 206.90/32.04 | | | | | | | REDUCE: (24), (40) imply:
% 206.90/32.04 | | | | | | | (41) gt(n0, n0)
% 206.90/32.04 | | | | | | |
% 206.90/32.04 | | | | | | | PRED_UNIFY: (19), (41) imply:
% 206.90/32.04 | | | | | | | (42) $false
% 206.90/32.04 | | | | | | |
% 206.90/32.04 | | | | | | | CLOSE: (42) is inconsistent.
% 206.90/32.04 | | | | | | |
% 206.90/32.04 | | | | | | Case 2:
% 206.90/32.04 | | | | | | |
% 206.90/32.04 | | | | | | | (43) ~ (all_74_6 = n0)
% 206.90/32.04 | | | | | | |
% 206.90/32.04 | | | | | | | BETA: splitting (27) gives:
% 206.90/32.04 | | | | | | |
% 206.90/32.04 | | | | | | | Case 1:
% 206.90/32.04 | | | | | | | |
% 206.90/32.04 | | | | | | | | (44) all_74_6 = n0
% 206.90/32.04 | | | | | | | |
% 206.90/32.04 | | | | | | | | REDUCE: (43), (44) imply:
% 206.90/32.04 | | | | | | | | (45) $false
% 206.90/32.04 | | | | | | | |
% 206.90/32.04 | | | | | | | | CLOSE: (45) is inconsistent.
% 206.90/32.04 | | | | | | | |
% 206.90/32.04 | | | | | | | Case 2:
% 206.90/32.04 | | | | | | | |
% 206.90/32.04 | | | | | | | | (46) all_74_6 = n1
% 206.90/32.04 | | | | | | | |
% 206.90/32.04 | | | | | | | | REDUCE: (38), (46) imply:
% 206.90/32.04 | | | | | | | | (47) a_select3(r_ds1_filter, n1, n1) = all_74_4
% 206.90/32.04 | | | | | | | |
% 206.90/32.04 | | | | | | | | REDUCE: (39), (46) imply:
% 206.90/32.04 | | | | | | | | (48) a_select3(r_ds1_filter, n1, n1) = all_74_5
% 206.90/32.04 | | | | | | | |
% 206.90/32.04 | | | | | | | | GROUND_INST: instantiating (11) with all_74_5, all_74_4, n1, n1,
% 206.90/32.04 | | | | | | | | r_ds1_filter, simplifying with (47), (48) gives:
% 206.90/32.04 | | | | | | | | (49) all_74_4 = all_74_5
% 206.90/32.04 | | | | | | | |
% 206.90/32.04 | | | | | | | | REDUCE: (8), (49) imply:
% 206.90/32.04 | | | | | | | | (50) $false
% 206.90/32.04 | | | | | | | |
% 206.90/32.04 | | | | | | | | CLOSE: (50) is inconsistent.
% 206.90/32.04 | | | | | | | |
% 206.90/32.04 | | | | | | | End of split
% 206.90/32.04 | | | | | | |
% 206.90/32.04 | | | | | | End of split
% 206.90/32.04 | | | | | |
% 206.90/32.04 | | | | | End of split
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | End of split
% 206.90/32.04 | | | |
% 206.90/32.04 | | | Case 2:
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | (51) all_74_7 = n2
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | REDUCE: (10), (51) imply:
% 206.90/32.04 | | | | (52) a_select3(r_ds1_filter, all_74_6, n2) = all_74_4
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | REDUCE: (17), (51) imply:
% 206.90/32.04 | | | | (53) a_select3(r_ds1_filter, n2, all_74_6) = all_74_5
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | REDUCE: (9), (51) imply:
% 206.90/32.04 | | | | (54) leq(n2, n2)
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | REDUCE: (4), (51) imply:
% 206.90/32.04 | | | | (55) leq(n0, n2)
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | BETA: splitting (7) gives:
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | Case 1:
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | (56) all_74_6 = n0
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | REDUCE: (24), (56) imply:
% 206.90/32.04 | | | | | (57) gt(n0, n0)
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | PRED_UNIFY: (19), (57) imply:
% 206.90/32.04 | | | | | (58) $false
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | CLOSE: (58) is inconsistent.
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | Case 2:
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | (59) ~ (all_74_6 = n0)
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (11), (12), (14), (27), (52),
% 206.90/32.04 | | | | | (53), (54), (55), (59) are inconsistent by sub-proof #32.
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | End of split
% 206.90/32.04 | | | |
% 206.90/32.04 | | | End of split
% 206.90/32.04 | | |
% 206.90/32.04 | | Case 2:
% 206.90/32.04 | | |
% 206.90/32.04 | | | (60) all_74_6 = n2
% 206.90/32.04 | | |
% 206.90/32.04 | | | REDUCE: (10), (60) imply:
% 206.90/32.04 | | | (61) a_select3(r_ds1_filter, n2, all_74_7) = all_74_4
% 206.90/32.04 | | |
% 206.90/32.04 | | | REDUCE: (17), (60) imply:
% 206.90/32.04 | | | (62) a_select3(r_ds1_filter, all_74_7, n2) = all_74_5
% 206.90/32.04 | | |
% 206.90/32.04 | | | REDUCE: (3), (60) imply:
% 206.90/32.04 | | | (63) leq(n2, n2)
% 206.90/32.04 | | |
% 206.90/32.04 | | | REDUCE: (14), (60) imply:
% 206.90/32.04 | | | (64) leq(n0, n2)
% 206.90/32.04 | | |
% 206.90/32.04 | | | BETA: splitting (22) gives:
% 206.90/32.04 | | |
% 206.90/32.04 | | | Case 1:
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | (65) gt(n2, all_74_7)
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | GROUND_INST: instantiating (16) with all_74_7, n2, n1, simplifying with
% 206.90/32.04 | | | | (5), (13), (23), (65) gives:
% 206.90/32.04 | | | | (66) leq(all_74_7, n1)
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | GROUND_INST: instantiating (18) with all_74_7, simplifying with (4),
% 206.90/32.04 | | | | (23), (66) gives:
% 206.90/32.04 | | | | (67) all_74_7 = n1 | all_74_7 = n0
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | BETA: splitting (21) gives:
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | Case 1:
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | (68) all_74_7 = n0
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | REDUCE: (2), (68) imply:
% 206.90/32.04 | | | | | (69) gt(n0, n0)
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | PRED_UNIFY: (19), (69) imply:
% 206.90/32.04 | | | | | (70) $false
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | CLOSE: (70) is inconsistent.
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | Case 2:
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | (71) ~ (all_74_7 = n0)
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (11), (23), (61), (62), (63),
% 206.90/32.04 | | | | | (64), (67), (71) are inconsistent by sub-proof #31.
% 206.90/32.04 | | | | |
% 206.90/32.04 | | | | End of split
% 206.90/32.04 | | | |
% 206.90/32.04 | | | Case 2:
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | (72) all_74_7 = n2
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | REDUCE: (62), (72) imply:
% 206.90/32.04 | | | | (73) a_select3(r_ds1_filter, n2, n2) = all_74_5
% 206.90/32.04 | | | |
% 206.90/32.04 | | | | REDUCE: (61), (72) imply:
% 206.90/32.04 | | | | (74) a_select3(r_ds1_filter, n2, n2) = all_74_4
% 206.90/32.04 | | | |
% 207.07/32.04 | | | | GROUND_INST: instantiating (11) with all_74_5, all_74_4, n2, n2,
% 207.07/32.04 | | | | r_ds1_filter, simplifying with (73), (74) gives:
% 207.07/32.04 | | | | (75) all_74_4 = all_74_5
% 207.07/32.04 | | | |
% 207.07/32.04 | | | | REDUCE: (8), (75) imply:
% 207.07/32.04 | | | | (76) $false
% 207.07/32.04 | | | |
% 207.07/32.04 | | | | CLOSE: (76) is inconsistent.
% 207.07/32.04 | | | |
% 207.07/32.04 | | | End of split
% 207.07/32.04 | | |
% 207.07/32.04 | | End of split
% 207.07/32.04 | |
% 207.07/32.04 | Case 2:
% 207.07/32.04 | |
% 207.07/32.04 | | (77) all_74_6 = n0
% 207.07/32.04 | | (78) ~ gt(all_74_6, n0)
% 207.07/32.04 | |
% 207.07/32.04 | | REDUCE: (10), (77) imply:
% 207.07/32.04 | | (79) a_select3(r_ds1_filter, n0, all_74_7) = all_74_4
% 207.07/32.04 | |
% 207.07/32.04 | | REDUCE: (17), (77) imply:
% 207.07/32.04 | | (80) a_select3(r_ds1_filter, all_74_7, n0) = all_74_5
% 207.07/32.04 | |
% 207.07/32.04 | | REDUCE: (12), (77) imply:
% 207.07/32.04 | | (81) $i(n0)
% 207.07/32.04 | |
% 207.07/32.04 | | REDUCE: (3), (77) imply:
% 207.07/32.04 | | (82) leq(n0, n2)
% 207.07/32.04 | |
% 207.07/32.04 | | REDUCE: (14), (77) imply:
% 207.07/32.04 | | (83) leq(n0, n0)
% 207.07/32.04 | |
% 207.07/32.04 | | BETA: splitting (22) gives:
% 207.07/32.04 | |
% 207.07/32.04 | | Case 1:
% 207.07/32.04 | | |
% 207.07/32.04 | | | (84) gt(n2, all_74_7)
% 207.07/32.04 | | |
% 207.07/32.04 | | | GROUND_INST: instantiating (16) with all_74_7, n2, n1, simplifying with
% 207.07/32.04 | | | (5), (13), (23), (84) gives:
% 207.07/32.04 | | | (85) leq(all_74_7, n1)
% 207.07/32.04 | | |
% 207.07/32.04 | | | GROUND_INST: instantiating (18) with all_74_7, simplifying with (4), (23),
% 207.07/32.04 | | | (85) gives:
% 207.07/32.04 | | | (86) all_74_7 = n1 | all_74_7 = n0
% 207.07/32.04 | | |
% 207.07/32.04 | | | BETA: splitting (21) gives:
% 207.07/32.04 | | |
% 207.07/32.04 | | | Case 1:
% 207.07/32.04 | | | |
% 207.07/32.04 | | | | (87) all_74_7 = n0
% 207.07/32.04 | | | |
% 207.07/32.04 | | | | REDUCE: (2), (87) imply:
% 207.07/32.04 | | | | (88) gt(n0, n0)
% 207.07/32.04 | | | |
% 207.07/32.04 | | | | PRED_UNIFY: (19), (88) imply:
% 207.07/32.04 | | | | (89) $false
% 207.07/32.04 | | | |
% 207.07/32.04 | | | | CLOSE: (89) is inconsistent.
% 207.07/32.04 | | | |
% 207.07/32.04 | | | Case 2:
% 207.07/32.04 | | | |
% 207.07/32.04 | | | | (90) ~ (all_74_7 = n0)
% 207.07/32.04 | | | |
% 207.07/32.04 | | | | BETA: splitting (86) gives:
% 207.07/32.04 | | | |
% 207.07/32.04 | | | | Case 1:
% 207.07/32.04 | | | | |
% 207.07/32.04 | | | | | (91) all_74_7 = n0
% 207.07/32.04 | | | | |
% 207.07/32.04 | | | | | REDUCE: (90), (91) imply:
% 207.07/32.04 | | | | | (92) $false
% 207.07/32.04 | | | | |
% 207.07/32.04 | | | | | CLOSE: (92) is inconsistent.
% 207.07/32.04 | | | | |
% 207.07/32.04 | | | | Case 2:
% 207.07/32.04 | | | | |
% 207.07/32.04 | | | | | (93) all_74_7 = n1
% 207.07/32.04 | | | | |
% 207.07/32.04 | | | | | REDUCE: (80), (93) imply:
% 207.07/32.04 | | | | | (94) a_select3(r_ds1_filter, n1, n0) = all_74_5
% 207.07/32.04 | | | | |
% 207.07/32.04 | | | | | REDUCE: (79), (93) imply:
% 207.07/32.04 | | | | | (95) a_select3(r_ds1_filter, n0, n1) = all_74_4
% 207.07/32.04 | | | | |
% 207.07/32.04 | | | | | REDUCE: (23), (93) imply:
% 207.07/32.04 | | | | | (96) $i(n1)
% 207.07/32.04 | | | | |
% 207.07/32.04 | | | | | REDUCE: (9), (93) imply:
% 207.07/32.04 | | | | | (97) leq(n1, n2)
% 207.07/32.04 | | | | |
% 207.07/32.04 | | | | | REDUCE: (4), (93) imply:
% 207.07/32.04 | | | | | (98) leq(n0, n1)
% 207.07/32.04 | | | | |
% 207.07/32.04 | | | | | GROUND_INST: instantiating (1) with n0, n1, all_74_4, simplifying with
% 207.07/32.04 | | | | | (81), (83), (95), (96), (98) gives:
% 207.07/32.04 | | | | | (99) ~ leq(n1, all_74_18) | ~ leq(n0, all_74_18) |
% 207.07/32.04 | | | | | (a_select3(r_ds1_filter, n1, n0) = all_74_4 & $i(all_74_4))
% 207.07/32.04 | | | | |
% 207.07/32.04 | | | | | BETA: splitting (99) gives:
% 207.07/32.04 | | | | |
% 207.07/32.04 | | | | | Case 1:
% 207.07/32.04 | | | | | |
% 207.07/32.04 | | | | | | (100) ~ leq(n0, all_74_18)
% 207.07/32.04 | | | | | |
% 207.07/32.04 | | | | | | REDUCE: (6), (100) imply:
% 207.07/32.04 | | | | | | (101) ~ leq(n0, n2)
% 207.07/32.04 | | | | | |
% 207.07/32.04 | | | | | | PRED_UNIFY: (82), (101) imply:
% 207.07/32.04 | | | | | | (102) $false
% 207.07/32.04 | | | | | |
% 207.07/32.04 | | | | | | CLOSE: (102) is inconsistent.
% 207.07/32.04 | | | | | |
% 207.07/32.04 | | | | | Case 2:
% 207.07/32.04 | | | | | |
% 207.07/32.04 | | | | | | (103) ~ leq(n1, all_74_18) | (a_select3(r_ds1_filter, n1, n0) =
% 207.07/32.04 | | | | | | all_74_4 & $i(all_74_4))
% 207.07/32.04 | | | | | |
% 207.07/32.04 | | | | | | BETA: splitting (103) gives:
% 207.07/32.04 | | | | | |
% 207.07/32.04 | | | | | | Case 1:
% 207.07/32.04 | | | | | | |
% 207.07/32.04 | | | | | | | (104) ~ leq(n1, all_74_18)
% 207.07/32.04 | | | | | | |
% 207.07/32.04 | | | | | | | REDUCE: (6), (104) imply:
% 207.07/32.04 | | | | | | | (105) ~ leq(n1, n2)
% 207.07/32.04 | | | | | | |
% 207.07/32.04 | | | | | | | PRED_UNIFY: (97), (105) imply:
% 207.07/32.04 | | | | | | | (106) $false
% 207.07/32.04 | | | | | | |
% 207.07/32.04 | | | | | | | CLOSE: (106) is inconsistent.
% 207.07/32.04 | | | | | | |
% 207.07/32.04 | | | | | | Case 2:
% 207.07/32.04 | | | | | | |
% 207.08/32.04 | | | | | | | (107) a_select3(r_ds1_filter, n1, n0) = all_74_4 & $i(all_74_4)
% 207.08/32.04 | | | | | | |
% 207.08/32.04 | | | | | | | ALPHA: (107) implies:
% 207.08/32.04 | | | | | | | (108) a_select3(r_ds1_filter, n1, n0) = all_74_4
% 207.08/32.04 | | | | | | |
% 207.08/32.04 | | | | | | | REF_CLOSE: (8), (11), (94), (108) are inconsistent by sub-proof
% 207.08/32.04 | | | | | | | #30.
% 207.08/32.04 | | | | | | |
% 207.08/32.04 | | | | | | End of split
% 207.08/32.04 | | | | | |
% 207.08/32.04 | | | | | End of split
% 207.08/32.04 | | | | |
% 207.08/32.04 | | | | End of split
% 207.08/32.04 | | | |
% 207.08/32.04 | | | End of split
% 207.08/32.04 | | |
% 207.08/32.04 | | Case 2:
% 207.08/32.04 | | |
% 207.08/32.04 | | | (109) all_74_7 = n2
% 207.08/32.04 | | |
% 207.08/32.04 | | | REDUCE: (80), (109) imply:
% 207.08/32.04 | | | (110) a_select3(r_ds1_filter, n2, n0) = all_74_5
% 207.08/32.04 | | |
% 207.08/32.04 | | | REDUCE: (79), (109) imply:
% 207.08/32.04 | | | (111) a_select3(r_ds1_filter, n0, n2) = all_74_4
% 207.08/32.04 | | |
% 207.08/32.04 | | | REDUCE: (9), (109) imply:
% 207.08/32.04 | | | (112) leq(n2, n2)
% 207.08/32.04 | | |
% 207.08/32.04 | | | GROUND_INST: instantiating (1) with n0, n2, all_74_4, simplifying with
% 207.08/32.04 | | | (5), (81), (82), (83), (111) gives:
% 207.08/32.04 | | | (113) ~ leq(n2, all_74_18) | ~ leq(n0, all_74_18) |
% 207.08/32.04 | | | (a_select3(r_ds1_filter, n2, n0) = all_74_4 & $i(all_74_4))
% 207.08/32.04 | | |
% 207.08/32.04 | | | BETA: splitting (113) gives:
% 207.08/32.04 | | |
% 207.08/32.04 | | | Case 1:
% 207.08/32.04 | | | |
% 207.08/32.04 | | | | (114) ~ leq(n0, all_74_18)
% 207.08/32.04 | | | |
% 207.08/32.04 | | | | REDUCE: (6), (114) imply:
% 207.08/32.04 | | | | (115) ~ leq(n0, n2)
% 207.08/32.04 | | | |
% 207.08/32.04 | | | | PRED_UNIFY: (82), (115) imply:
% 207.08/32.04 | | | | (116) $false
% 207.08/32.04 | | | |
% 207.08/32.04 | | | | CLOSE: (116) is inconsistent.
% 207.08/32.04 | | | |
% 207.08/32.04 | | | Case 2:
% 207.08/32.04 | | | |
% 207.08/32.04 | | | | (117) ~ leq(n2, all_74_18) | (a_select3(r_ds1_filter, n2, n0) =
% 207.08/32.04 | | | | all_74_4 & $i(all_74_4))
% 207.08/32.04 | | | |
% 207.08/32.04 | | | | BETA: splitting (117) gives:
% 207.08/32.04 | | | |
% 207.08/32.04 | | | | Case 1:
% 207.08/32.04 | | | | |
% 207.08/32.04 | | | | | (118) ~ leq(n2, all_74_18)
% 207.08/32.04 | | | | |
% 207.08/32.04 | | | | | REDUCE: (6), (118) imply:
% 207.08/32.04 | | | | | (119) ~ leq(n2, n2)
% 207.08/32.04 | | | | |
% 207.08/32.04 | | | | | PRED_UNIFY: (112), (119) imply:
% 207.08/32.04 | | | | | (120) $false
% 207.08/32.04 | | | | |
% 207.08/32.04 | | | | | CLOSE: (120) is inconsistent.
% 207.08/32.04 | | | | |
% 207.08/32.04 | | | | Case 2:
% 207.08/32.04 | | | | |
% 207.08/32.04 | | | | | (121) a_select3(r_ds1_filter, n2, n0) = all_74_4 & $i(all_74_4)
% 207.08/32.04 | | | | |
% 207.08/32.04 | | | | | ALPHA: (121) implies:
% 207.08/32.04 | | | | | (122) a_select3(r_ds1_filter, n2, n0) = all_74_4
% 207.08/32.04 | | | | |
% 207.08/32.04 | | | | | GROUND_INST: instantiating (11) with all_74_4, all_74_5, n0, n2,
% 207.08/32.04 | | | | | r_ds1_filter, simplifying with (110), (122) gives:
% 207.08/32.04 | | | | | (123) all_74_4 = all_74_5
% 207.08/32.04 | | | | |
% 207.08/32.04 | | | | | REDUCE: (8), (123) imply:
% 207.08/32.04 | | | | | (124) $false
% 207.08/32.04 | | | | |
% 207.08/32.04 | | | | | CLOSE: (124) is inconsistent.
% 207.08/32.04 | | | | |
% 207.08/32.04 | | | | End of split
% 207.08/32.04 | | | |
% 207.08/32.04 | | | End of split
% 207.08/32.04 | | |
% 207.08/32.04 | | End of split
% 207.08/32.04 | |
% 207.08/32.04 | End of split
% 207.08/32.04 |
% 207.08/32.04 End of proof
% 207.08/32.04
% 207.08/32.04 Sub-proof #30 shows that the following formulas are inconsistent:
% 207.08/32.04 ----------------------------------------------------------------
% 207.08/32.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 207.08/32.04 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 207.08/32.04 v0))
% 207.08/32.04 (2) a_select3(r_ds1_filter, n1, n0) = all_74_4
% 207.08/32.04 (3) a_select3(r_ds1_filter, n1, n0) = all_74_5
% 207.08/32.04 (4) ~ (all_74_4 = all_74_5)
% 207.08/32.04
% 207.08/32.04 Begin of proof
% 207.08/32.04 |
% 207.08/32.04 | GROUND_INST: instantiating (1) with all_74_4, all_74_5, n0, n1, r_ds1_filter,
% 207.08/32.04 | simplifying with (2), (3) gives:
% 207.08/32.04 | (5) all_74_4 = all_74_5
% 207.08/32.04 |
% 207.08/32.04 | REDUCE: (4), (5) imply:
% 207.08/32.04 | (6) $false
% 207.08/32.04 |
% 207.08/32.04 | CLOSE: (6) is inconsistent.
% 207.08/32.04 |
% 207.08/32.04 End of proof
% 207.08/32.04
% 207.08/32.04 Sub-proof #31 shows that the following formulas are inconsistent:
% 207.08/32.04 ----------------------------------------------------------------
% 207.08/32.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(r_ds1_filter,
% 207.08/32.04 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_18) | ~
% 207.08/32.04 leq(v0, all_74_18) | ~ leq(n0, v1) | ~ leq(n0, v0) |
% 207.08/32.04 (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2)))
% 207.08/32.04 (2) a_select3(r_ds1_filter, all_74_7, n2) = all_74_5
% 207.08/32.04 (3) leq(n0, all_74_7)
% 207.08/32.04 (4) $i(n2)
% 207.08/32.04 (5) all_74_18 = n2
% 207.08/32.04 (6) ~ (all_74_4 = all_74_5)
% 207.08/32.04 (7) leq(all_74_7, n2)
% 207.08/32.04 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 207.08/32.04 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 207.08/32.04 v0))
% 207.08/32.04 (9) leq(n0, n2)
% 207.08/32.04 (10) all_74_7 = n1 | all_74_7 = n0
% 207.08/32.04 (11) a_select3(r_ds1_filter, n2, all_74_7) = all_74_4
% 207.08/32.04 (12) ~ (all_74_7 = n0)
% 207.08/32.04 (13) leq(n2, n2)
% 207.08/32.04 (14) $i(all_74_7)
% 207.08/32.04
% 207.08/32.04 Begin of proof
% 207.08/32.04 |
% 207.08/32.04 | BETA: splitting (10) gives:
% 207.08/32.04 |
% 207.08/32.04 | Case 1:
% 207.08/32.04 | |
% 207.08/32.04 | | (15) all_74_7 = n0
% 207.08/32.04 | |
% 207.08/32.04 | | REDUCE: (12), (15) imply:
% 207.08/32.04 | | (16) $false
% 207.08/32.04 | |
% 207.08/32.04 | | CLOSE: (16) is inconsistent.
% 207.08/32.04 | |
% 207.08/32.04 | Case 2:
% 207.08/32.04 | |
% 207.08/32.04 | | (17) all_74_7 = n1
% 207.08/32.04 | |
% 207.08/32.04 | | REDUCE: (2), (17) imply:
% 207.08/32.04 | | (18) a_select3(r_ds1_filter, n1, n2) = all_74_5
% 207.08/32.04 | |
% 207.08/32.04 | | REDUCE: (11), (17) imply:
% 207.08/32.04 | | (19) a_select3(r_ds1_filter, n2, n1) = all_74_4
% 207.08/32.04 | |
% 207.08/32.04 | | REDUCE: (14), (17) imply:
% 207.08/32.04 | | (20) $i(n1)
% 207.08/32.04 | |
% 207.08/32.04 | | REDUCE: (7), (17) imply:
% 207.08/32.04 | | (21) leq(n1, n2)
% 207.08/32.04 | |
% 207.08/32.04 | | REDUCE: (3), (17) imply:
% 207.08/32.04 | | (22) leq(n0, n1)
% 207.08/32.04 | |
% 207.08/32.04 | | GROUND_INST: instantiating (1) with n1, n2, all_74_5, simplifying with (4),
% 207.08/32.04 | | (9), (18), (20), (22) gives:
% 207.08/32.04 | | (23) ~ leq(n2, all_74_18) | ~ leq(n1, all_74_18) |
% 207.08/32.04 | | (a_select3(r_ds1_filter, n2, n1) = all_74_5 & $i(all_74_5))
% 207.08/32.04 | |
% 207.08/32.04 | | BETA: splitting (23) gives:
% 207.08/32.04 | |
% 207.08/32.04 | | Case 1:
% 207.08/32.04 | | |
% 207.08/32.04 | | | (24) ~ leq(n2, all_74_18)
% 207.08/32.04 | | |
% 207.08/32.04 | | | REDUCE: (5), (24) imply:
% 207.08/32.04 | | | (25) ~ leq(n2, n2)
% 207.08/32.04 | | |
% 207.08/32.04 | | | PRED_UNIFY: (13), (25) imply:
% 207.08/32.04 | | | (26) $false
% 207.08/32.04 | | |
% 207.08/32.04 | | | CLOSE: (26) is inconsistent.
% 207.08/32.04 | | |
% 207.08/32.04 | | Case 2:
% 207.08/32.04 | | |
% 207.08/32.04 | | | (27) ~ leq(n1, all_74_18) | (a_select3(r_ds1_filter, n2, n1) =
% 207.08/32.04 | | | all_74_5 & $i(all_74_5))
% 207.08/32.04 | | |
% 207.08/32.04 | | | BETA: splitting (27) gives:
% 207.08/32.04 | | |
% 207.08/32.04 | | | Case 1:
% 207.08/32.04 | | | |
% 207.08/32.05 | | | | (28) ~ leq(n1, all_74_18)
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | REDUCE: (5), (28) imply:
% 207.08/32.05 | | | | (29) ~ leq(n1, n2)
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | PRED_UNIFY: (21), (29) imply:
% 207.08/32.05 | | | | (30) $false
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | CLOSE: (30) is inconsistent.
% 207.08/32.05 | | | |
% 207.08/32.05 | | | Case 2:
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | (31) a_select3(r_ds1_filter, n2, n1) = all_74_5 & $i(all_74_5)
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | ALPHA: (31) implies:
% 207.08/32.05 | | | | (32) a_select3(r_ds1_filter, n2, n1) = all_74_5
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | GROUND_INST: instantiating (8) with all_74_5, all_74_4, n1, n2,
% 207.08/32.05 | | | | r_ds1_filter, simplifying with (19), (32) gives:
% 207.08/32.05 | | | | (33) all_74_4 = all_74_5
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | REDUCE: (6), (33) imply:
% 207.08/32.05 | | | | (34) $false
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | CLOSE: (34) is inconsistent.
% 207.08/32.05 | | | |
% 207.08/32.05 | | | End of split
% 207.08/32.05 | | |
% 207.08/32.05 | | End of split
% 207.08/32.05 | |
% 207.08/32.05 | End of split
% 207.08/32.05 |
% 207.08/32.05 End of proof
% 207.08/32.05
% 207.08/32.05 Sub-proof #32 shows that the following formulas are inconsistent:
% 207.08/32.05 ----------------------------------------------------------------
% 207.08/32.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(r_ds1_filter,
% 207.08/32.05 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_18) | ~
% 207.08/32.05 leq(v0, all_74_18) | ~ leq(n0, v1) | ~ leq(n0, v0) |
% 207.08/32.05 (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2)))
% 207.08/32.05 (2) all_74_6 = n1 | all_74_6 = n0
% 207.08/32.05 (3) leq(all_74_6, n2)
% 207.08/32.05 (4) $i(n2)
% 207.08/32.05 (5) all_74_18 = n2
% 207.08/32.05 (6) ~ (all_74_4 = all_74_5)
% 207.08/32.05 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 207.08/32.05 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 207.08/32.05 v0))
% 207.08/32.05 (8) ~ (all_74_6 = n0)
% 207.08/32.05 (9) $i(all_74_6)
% 207.08/32.05 (10) leq(n0, n2)
% 207.08/32.05 (11) leq(n0, all_74_6)
% 207.08/32.05 (12) leq(n2, n2)
% 207.08/32.05 (13) a_select3(r_ds1_filter, n2, all_74_6) = all_74_5
% 207.08/32.05 (14) a_select3(r_ds1_filter, all_74_6, n2) = all_74_4
% 207.08/32.05
% 207.08/32.05 Begin of proof
% 207.08/32.05 |
% 207.08/32.05 | BETA: splitting (2) gives:
% 207.08/32.05 |
% 207.08/32.05 | Case 1:
% 207.08/32.05 | |
% 207.08/32.05 | | (15) all_74_6 = n0
% 207.08/32.05 | |
% 207.08/32.05 | | REDUCE: (8), (15) imply:
% 207.08/32.05 | | (16) $false
% 207.08/32.05 | |
% 207.08/32.05 | | CLOSE: (16) is inconsistent.
% 207.08/32.05 | |
% 207.08/32.05 | Case 2:
% 207.08/32.05 | |
% 207.08/32.05 | | (17) all_74_6 = n1
% 207.08/32.05 | |
% 207.08/32.05 | | REDUCE: (14), (17) imply:
% 207.08/32.05 | | (18) a_select3(r_ds1_filter, n1, n2) = all_74_4
% 207.08/32.05 | |
% 207.08/32.05 | | REDUCE: (13), (17) imply:
% 207.08/32.05 | | (19) a_select3(r_ds1_filter, n2, n1) = all_74_5
% 207.08/32.05 | |
% 207.08/32.05 | | REDUCE: (9), (17) imply:
% 207.08/32.05 | | (20) $i(n1)
% 207.08/32.05 | |
% 207.08/32.05 | | REDUCE: (3), (17) imply:
% 207.08/32.05 | | (21) leq(n1, n2)
% 207.08/32.05 | |
% 207.08/32.05 | | REDUCE: (11), (17) imply:
% 207.08/32.05 | | (22) leq(n0, n1)
% 207.08/32.05 | |
% 207.08/32.05 | | GROUND_INST: instantiating (1) with n1, n2, all_74_4, simplifying with (4),
% 207.08/32.05 | | (10), (18), (20), (22) gives:
% 207.08/32.05 | | (23) ~ leq(n2, all_74_18) | ~ leq(n1, all_74_18) |
% 207.08/32.05 | | (a_select3(r_ds1_filter, n2, n1) = all_74_4 & $i(all_74_4))
% 207.08/32.05 | |
% 207.08/32.05 | | BETA: splitting (23) gives:
% 207.08/32.05 | |
% 207.08/32.05 | | Case 1:
% 207.08/32.05 | | |
% 207.08/32.05 | | | (24) ~ leq(n2, all_74_18)
% 207.08/32.05 | | |
% 207.08/32.05 | | | REDUCE: (5), (24) imply:
% 207.08/32.05 | | | (25) ~ leq(n2, n2)
% 207.08/32.05 | | |
% 207.08/32.05 | | | PRED_UNIFY: (12), (25) imply:
% 207.08/32.05 | | | (26) $false
% 207.08/32.05 | | |
% 207.08/32.05 | | | CLOSE: (26) is inconsistent.
% 207.08/32.05 | | |
% 207.08/32.05 | | Case 2:
% 207.08/32.05 | | |
% 207.08/32.05 | | | (27) ~ leq(n1, all_74_18) | (a_select3(r_ds1_filter, n2, n1) =
% 207.08/32.05 | | | all_74_4 & $i(all_74_4))
% 207.08/32.05 | | |
% 207.08/32.05 | | | BETA: splitting (27) gives:
% 207.08/32.05 | | |
% 207.08/32.05 | | | Case 1:
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | (28) ~ leq(n1, all_74_18)
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | REDUCE: (5), (28) imply:
% 207.08/32.05 | | | | (29) ~ leq(n1, n2)
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | PRED_UNIFY: (21), (29) imply:
% 207.08/32.05 | | | | (30) $false
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | CLOSE: (30) is inconsistent.
% 207.08/32.05 | | | |
% 207.08/32.05 | | | Case 2:
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | (31) a_select3(r_ds1_filter, n2, n1) = all_74_4 & $i(all_74_4)
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | ALPHA: (31) implies:
% 207.08/32.05 | | | | (32) a_select3(r_ds1_filter, n2, n1) = all_74_4
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | GROUND_INST: instantiating (7) with all_74_5, all_74_4, n1, n2,
% 207.08/32.05 | | | | r_ds1_filter, simplifying with (19), (32) gives:
% 207.08/32.05 | | | | (33) all_74_4 = all_74_5
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | REDUCE: (6), (33) imply:
% 207.08/32.05 | | | | (34) $false
% 207.08/32.05 | | | |
% 207.08/32.05 | | | | CLOSE: (34) is inconsistent.
% 207.08/32.05 | | | |
% 207.08/32.05 | | | End of split
% 207.08/32.05 | | |
% 207.08/32.05 | | End of split
% 207.08/32.05 | |
% 207.08/32.05 | End of split
% 207.08/32.05 |
% 207.08/32.05 End of proof
% 207.08/32.05
% 207.08/32.05 Sub-proof #33 shows that the following formulas are inconsistent:
% 207.08/32.05 ----------------------------------------------------------------
% 207.08/32.05 (1) $i(all_74_6)
% 207.08/32.05 (2) all_74_6 = n0
% 207.08/32.05 (3) gt(all_74_6, n0)
% 207.08/32.05 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0))
% 207.08/32.05
% 207.08/32.05 Begin of proof
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (1), (2) imply:
% 207.08/32.05 | (5) $i(n0)
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (2), (3) imply:
% 207.08/32.05 | (6) gt(n0, n0)
% 207.08/32.05 |
% 207.08/32.05 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives:
% 207.08/32.05 | (7) $false
% 207.08/32.05 |
% 207.08/32.05 | CLOSE: (7) is inconsistent.
% 207.08/32.05 |
% 207.08/32.05 End of proof
% 207.08/32.05
% 207.08/32.05 Sub-proof #34 shows that the following formulas are inconsistent:
% 207.08/32.05 ----------------------------------------------------------------
% 207.08/32.05 (1) $i(all_74_7)
% 207.08/32.05 (2) all_74_7 = n0
% 207.08/32.05 (3) gt(all_74_7, n0)
% 207.08/32.05 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0))
% 207.08/32.05
% 207.08/32.05 Begin of proof
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (1), (2) imply:
% 207.08/32.05 | (5) $i(n0)
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (2), (3) imply:
% 207.08/32.05 | (6) gt(n0, n0)
% 207.08/32.05 |
% 207.08/32.05 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives:
% 207.08/32.05 | (7) $false
% 207.08/32.05 |
% 207.08/32.05 | CLOSE: (7) is inconsistent.
% 207.08/32.05 |
% 207.08/32.05 End of proof
% 207.08/32.05
% 207.08/32.05 Sub-proof #35 shows that the following formulas are inconsistent:
% 207.08/32.05 ----------------------------------------------------------------
% 207.08/32.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 207.08/32.05 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 207.08/32.05 v0))
% 207.08/32.05 (2) a_select3(q_ds1_filter, n4, n0) = all_74_0
% 207.08/32.05 (3) a_select3(q_ds1_filter, n4, n0) = all_74_1
% 207.08/32.05 (4) ~ (all_74_0 = all_74_1)
% 207.08/32.05
% 207.08/32.05 Begin of proof
% 207.08/32.05 |
% 207.08/32.05 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n0, n4, q_ds1_filter,
% 207.08/32.05 | simplifying with (2), (3) gives:
% 207.08/32.05 | (5) all_74_0 = all_74_1
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (4), (5) imply:
% 207.08/32.05 | (6) $false
% 207.08/32.05 |
% 207.08/32.05 | CLOSE: (6) is inconsistent.
% 207.08/32.05 |
% 207.08/32.05 End of proof
% 207.08/32.05
% 207.08/32.05 Sub-proof #36 shows that the following formulas are inconsistent:
% 207.08/32.05 ----------------------------------------------------------------
% 207.08/32.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 207.08/32.05 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 207.08/32.05 v0))
% 207.08/32.05 (2) a_select3(q_ds1_filter, n3, n0) = all_74_0
% 207.08/32.05 (3) a_select3(q_ds1_filter, n3, n0) = all_74_1
% 207.08/32.05 (4) ~ (all_74_0 = all_74_1)
% 207.08/32.05
% 207.08/32.05 Begin of proof
% 207.08/32.05 |
% 207.08/32.05 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n0, n3, q_ds1_filter,
% 207.08/32.05 | simplifying with (2), (3) gives:
% 207.08/32.05 | (5) all_74_0 = all_74_1
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (4), (5) imply:
% 207.08/32.05 | (6) $false
% 207.08/32.05 |
% 207.08/32.05 | CLOSE: (6) is inconsistent.
% 207.08/32.05 |
% 207.08/32.05 End of proof
% 207.08/32.05
% 207.08/32.05 Sub-proof #37 shows that the following formulas are inconsistent:
% 207.08/32.05 ----------------------------------------------------------------
% 207.08/32.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 207.08/32.05 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 207.08/32.05 v0))
% 207.08/32.05 (2) a_select3(q_ds1_filter, n1, n0) = all_74_0
% 207.08/32.05 (3) a_select3(q_ds1_filter, n1, n0) = all_74_1
% 207.08/32.05 (4) ~ (all_74_0 = all_74_1)
% 207.08/32.05
% 207.08/32.05 Begin of proof
% 207.08/32.05 |
% 207.08/32.05 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n0, n1, q_ds1_filter,
% 207.08/32.05 | simplifying with (2), (3) gives:
% 207.08/32.05 | (5) all_74_0 = all_74_1
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (4), (5) imply:
% 207.08/32.05 | (6) $false
% 207.08/32.05 |
% 207.08/32.05 | CLOSE: (6) is inconsistent.
% 207.08/32.05 |
% 207.08/32.05 End of proof
% 207.08/32.05
% 207.08/32.05 Sub-proof #38 shows that the following formulas are inconsistent:
% 207.08/32.05 ----------------------------------------------------------------
% 207.08/32.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 207.08/32.05 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 207.08/32.05 v0))
% 207.08/32.05 (2) a_select3(q_ds1_filter, n5, n4) = all_74_0
% 207.08/32.05 (3) a_select3(q_ds1_filter, n5, n4) = all_74_1
% 207.08/32.05 (4) ~ (all_74_0 = all_74_1)
% 207.08/32.05
% 207.08/32.05 Begin of proof
% 207.08/32.05 |
% 207.08/32.05 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n4, n5, q_ds1_filter,
% 207.08/32.05 | simplifying with (2), (3) gives:
% 207.08/32.05 | (5) all_74_0 = all_74_1
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (4), (5) imply:
% 207.08/32.05 | (6) $false
% 207.08/32.05 |
% 207.08/32.05 | CLOSE: (6) is inconsistent.
% 207.08/32.05 |
% 207.08/32.05 End of proof
% 207.08/32.05
% 207.08/32.05 Sub-proof #39 shows that the following formulas are inconsistent:
% 207.08/32.05 ----------------------------------------------------------------
% 207.08/32.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 207.08/32.05 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 207.08/32.05 v0))
% 207.08/32.05 (2) a_select3(q_ds1_filter, n5, n3) = all_74_0
% 207.08/32.05 (3) a_select3(q_ds1_filter, n5, n3) = all_74_1
% 207.08/32.05 (4) ~ (all_74_0 = all_74_1)
% 207.08/32.05
% 207.08/32.05 Begin of proof
% 207.08/32.05 |
% 207.08/32.05 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n3, n5, q_ds1_filter,
% 207.08/32.05 | simplifying with (2), (3) gives:
% 207.08/32.05 | (5) all_74_0 = all_74_1
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (4), (5) imply:
% 207.08/32.05 | (6) $false
% 207.08/32.05 |
% 207.08/32.05 | CLOSE: (6) is inconsistent.
% 207.08/32.05 |
% 207.08/32.05 End of proof
% 207.08/32.05
% 207.08/32.05 Sub-proof #40 shows that the following formulas are inconsistent:
% 207.08/32.05 ----------------------------------------------------------------
% 207.08/32.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 207.08/32.05 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 207.08/32.05 v0))
% 207.08/32.05 (2) a_select3(q_ds1_filter, n5, n1) = all_74_0
% 207.08/32.05 (3) a_select3(q_ds1_filter, n5, n1) = all_74_1
% 207.08/32.05 (4) ~ (all_74_0 = all_74_1)
% 207.08/32.05
% 207.08/32.05 Begin of proof
% 207.08/32.05 |
% 207.08/32.05 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n1, n5, q_ds1_filter,
% 207.08/32.05 | simplifying with (2), (3) gives:
% 207.08/32.05 | (5) all_74_0 = all_74_1
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (4), (5) imply:
% 207.08/32.05 | (6) $false
% 207.08/32.05 |
% 207.08/32.05 | CLOSE: (6) is inconsistent.
% 207.08/32.05 |
% 207.08/32.05 End of proof
% 207.08/32.05
% 207.08/32.05 Sub-proof #41 shows that the following formulas are inconsistent:
% 207.08/32.05 ----------------------------------------------------------------
% 207.08/32.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 207.08/32.05 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 207.08/32.05 v0))
% 207.08/32.05 (2) a_select3(q_ds1_filter, n4, n3) = all_74_0
% 207.08/32.05 (3) a_select3(q_ds1_filter, n4, n3) = all_74_1
% 207.08/32.05 (4) ~ (all_74_0 = all_74_1)
% 207.08/32.05
% 207.08/32.05 Begin of proof
% 207.08/32.05 |
% 207.08/32.05 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n3, n4, q_ds1_filter,
% 207.08/32.05 | simplifying with (2), (3) gives:
% 207.08/32.05 | (5) all_74_0 = all_74_1
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (4), (5) imply:
% 207.08/32.05 | (6) $false
% 207.08/32.05 |
% 207.08/32.05 | CLOSE: (6) is inconsistent.
% 207.08/32.05 |
% 207.08/32.05 End of proof
% 207.08/32.05
% 207.08/32.05 Sub-proof #42 shows that the following formulas are inconsistent:
% 207.08/32.05 ----------------------------------------------------------------
% 207.08/32.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 207.08/32.05 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 207.08/32.05 v0))
% 207.08/32.05 (2) a_select3(q_ds1_filter, n3, n2) = all_74_0
% 207.08/32.05 (3) a_select3(q_ds1_filter, n3, n2) = all_74_1
% 207.08/32.05 (4) ~ (all_74_0 = all_74_1)
% 207.08/32.05
% 207.08/32.05 Begin of proof
% 207.08/32.05 |
% 207.08/32.05 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n2, n3, q_ds1_filter,
% 207.08/32.05 | simplifying with (2), (3) gives:
% 207.08/32.05 | (5) all_74_0 = all_74_1
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (4), (5) imply:
% 207.08/32.05 | (6) $false
% 207.08/32.05 |
% 207.08/32.05 | CLOSE: (6) is inconsistent.
% 207.08/32.05 |
% 207.08/32.05 End of proof
% 207.08/32.05
% 207.08/32.05 Sub-proof #43 shows that the following formulas are inconsistent:
% 207.08/32.05 ----------------------------------------------------------------
% 207.08/32.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 207.08/32.05 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 207.08/32.05 v0))
% 207.08/32.05 (2) a_select3(q_ds1_filter, n3, n1) = all_74_0
% 207.08/32.05 (3) a_select3(q_ds1_filter, n3, n1) = all_74_1
% 207.08/32.05 (4) ~ (all_74_0 = all_74_1)
% 207.08/32.05
% 207.08/32.05 Begin of proof
% 207.08/32.05 |
% 207.08/32.05 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n1, n3, q_ds1_filter,
% 207.08/32.05 | simplifying with (2), (3) gives:
% 207.08/32.05 | (5) all_74_0 = all_74_1
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (4), (5) imply:
% 207.08/32.05 | (6) $false
% 207.08/32.05 |
% 207.08/32.05 | CLOSE: (6) is inconsistent.
% 207.08/32.05 |
% 207.08/32.05 End of proof
% 207.08/32.05
% 207.08/32.05 Sub-proof #44 shows that the following formulas are inconsistent:
% 207.08/32.05 ----------------------------------------------------------------
% 207.08/32.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 207.08/32.05 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) =
% 207.08/32.05 v0))
% 207.08/32.05 (2) a_select3(q_ds1_filter, n2, n1) = all_74_0
% 207.08/32.05 (3) a_select3(q_ds1_filter, n2, n1) = all_74_1
% 207.08/32.05 (4) ~ (all_74_0 = all_74_1)
% 207.08/32.05
% 207.08/32.05 Begin of proof
% 207.08/32.05 |
% 207.08/32.05 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n1, n2, q_ds1_filter,
% 207.08/32.05 | simplifying with (2), (3) gives:
% 207.08/32.05 | (5) all_74_0 = all_74_1
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (4), (5) imply:
% 207.08/32.05 | (6) $false
% 207.08/32.05 |
% 207.08/32.05 | CLOSE: (6) is inconsistent.
% 207.08/32.05 |
% 207.08/32.05 End of proof
% 207.08/32.05
% 207.08/32.05 Sub-proof #45 shows that the following formulas are inconsistent:
% 207.08/32.05 ----------------------------------------------------------------
% 207.08/32.05 (1) $i(all_74_3)
% 207.08/32.05 (2) all_74_3 = n0
% 207.08/32.05 (3) gt(all_74_3, n0)
% 207.08/32.05 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0))
% 207.08/32.05
% 207.08/32.05 Begin of proof
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (1), (2) imply:
% 207.08/32.05 | (5) $i(n0)
% 207.08/32.05 |
% 207.08/32.05 | REDUCE: (2), (3) imply:
% 207.08/32.05 | (6) gt(n0, n0)
% 207.08/32.05 |
% 207.08/32.05 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives:
% 207.08/32.05 | (7) $false
% 207.08/32.05 |
% 207.08/32.05 | CLOSE: (7) is inconsistent.
% 207.08/32.05 |
% 207.08/32.05 End of proof
% 207.08/32.05 % SZS output end Proof for theBenchmark
% 207.08/32.05
% 207.08/32.05 31464ms
%------------------------------------------------------------------------------